Hosting Capacity for Smart Power Grids 303040028X, 9783030400286

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Ahmed F. Zobaa Shady H.E. Abdel Aleem Sherif M. Ismael Paulo F. Ribeiro  Editors

Hosting Capacity for Smart Power Grids

Hosting Capacity for Smart Power Grids

Ahmed F. Zobaa • Shady H. E. Abdel Aleem Sherif M. Ismael • Paulo F. Ribeiro Editors

Hosting Capacity for Smart Power Grids

Editors Ahmed F. Zobaa College of Engineering Design and Physical Sciences Brunel University London Uxbridge, UK Sherif M. Ismael Electrical Engineering Division Engineering for the Petroleum and Process Industries (Enppi) Cairo, Egypt

Shady H. E. Abdel Aleem Mathematical, Physical and Engineering Sciences Department 15th of May Higher Institute of Engineering Cairo, Egypt Paulo F. Ribeiro Advanced Power Technologies and Innovations in Systems and Smart Grids Group Federal University of Itajuba Itajuba, MG, Brazil

ISBN 978-3-030-40028-6 ISBN 978-3-030-40029-3 https://doi.org/10.1007/978-3-030-40029-3

(eBook)

© Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

Today’s power systems are becoming much more complex, expandable, dynamic, and non-predictable; therefore, accurate and up-to-date hosting capacity (HC) analysis studies are necessary to face the significant challenges associated with the massive integration of renewable energy resources into modern electrical power systems. This book is designed to be essentially an introduction to the concepts and historical developments of the hosting capacity assessment. It will be beneficial to distribution system operators, network planners, distribution generation investors, and researchers in this field as it presents past, present, and future possibilities regarding HC research. It is expected that the HC will play a significant role in future power systems and smart grids. Using the HC approach to drive network requirements could steer distributed generation (DG) toward areas of the network where it could have the greatest positive impact on network reliability and win-win benefits with DG owners. Finally, smarter DG integration into future electrical systems can be met if utilities have a clear forecast of their potential network HC. As can be seen, the chapters in each section maintain their own thematic continuity and at the same time have significant overlaps with chapters in other sections. Therefore, one may read the book in its entirety or focus on individual chapters. Due to its broad scope, this book will be an ideal resource for students in advanced graduate-level courses and special topics in the field of smart grids, hosting capacity assessment, and enhancement in modern electrical power systems. HC research is a key enabler for affordable, reliable, and renewable energy sources, so it is possible to transition away from traditional high-carbon energy sources. Therefore, it is imperative that novel solutions be sought to enable networks to cope with future developments to realize resilient distribution networks that can host the pushy DG penetration while enhancing the system reliability of power supplies and controlling the over-hosted areas. Based on the editors’ experiences, we believe that this book is an important guide to the researchers, distribution system operators, and network planners who are interested in the integration of renewable energy resources in the electrical power systems. Comprehensive presentation of the hosting

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capacity concepts, calculation methods, performance limits, enhancement techniques, and case studies will be introduced in this book. The book is mainly focused on the concept of hosting capacity applied to modern power grids, but each of the book’s chapters begins with the fundamental structure of the problem required for a basic understanding of the methods described. It is sorted out and organized in 10 chapters. Chapter 1: This chapter presents an overview of the hosting capacity concept and its developments and defines the main HC performance limits and its up-to-date enhancement techniques. It also presents the concept of dynamic hosting capacity as well as its application to energy storage systems. Chapter 2: This chapter presents a new methodology in quantifying the system risk encountered by distribution networks during high PV penetration. The establishment of a number of operational risk indices is achieved. The network’s hosting capacity is calculated using sparse grid technique which showed superior performance compared with the Monte Carlo technique from both computational time and calculation accuracy perspectives. Chapter 3: In this chapter, the concept of local hosting capacity is applied through the evaluation of allowed voltage rises due to harmonic distortion. Moreover, a brief discussion on the definition of background harmonic distortion of electrical systems resulting from additional connections, such as consumers, distributed degeneration, and nonlinear loads, are presented. It is clearly concluded that the high levels of background harmonic distortion can result in equipment malfunction, decreasing the likelihood of meeting international standards, for example, IEEE 519 or IEEE 1547, as well as the impact on the hosting capacity value of electrical systems. Chapter 4: In this chapter, the effect of harmonics caused by different distributed energy resources on the hosting capacity is examined. The analysis also considers voltage violation and ampacity constraints. The entire modelling and simulation is performed in MATLAB and validated through Typhoon HIL to prove its efficacy for real-time implementation. Various distribution test systems are simulated with different loading and uncertainty in source conditions to validate the effect of different distributed energy resources in the hosting capacity assessment. Chapter 5: This chapter presents a comprehensive method to identify the minimum required battery energy storage systems (BESS) for increasing the hosting capacity of a system, considering the uncertainties associated with the distributed energy resources and loads. Then, an economic model has been developed to assess the minimum required BESS from an economic perspective. Finally, the performance of the developed models is assessed on a real agricultural feeder in Australia. Chapter 6: In this chapter, two categories of market power indices were presented to assess the capacity withholding of generation companies (GenCos) in the presence of DERs. These indices are effective and can be used by independent system operators (ISO) besides the technical assessment of hosting capacity. In addition, the mitigation of capacity withholding of GenCos and the impacts of distributed generation units on capacity withholding are described.

Preface

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Chapter 7: This chapter elaborates a generalized deterministic approach to evaluate the PV hosting capacity for LV distribution networks under different operating conditions. The proposed approach establishes safe limits for solar PV hosting capacities (cumulative values) for a given distribution feeder based on the locational and operational aspects of the solar PV units employed. Safe limit of hosting capacity has been developed employing a number of sensitivity analyses considering the influencing factors. From a distribution system planning perspective, the use of such a deterministic approach is convenient and more practical compared to the use of extensive simulations. Furthermore, the proposed method can be used as an approximate guide or a rule of thumb to evaluate solar PV hosting capacity at a given location of an LV distribution feeder without using complex stochastic techniques. Chapter 8: In this chapter, a strategy is proposed to maximize DG integration in the distribution network without violating system operational limits. The strategy is based on the available active and reactive powers provided by a substation. The proposed strategy aims to prepare the distribution network using distribution network reconfiguration (DNR) and soft open points (SOPs) installations to accommodate more distributed generation (DG) installations in the distribution system. In order to solve the MINLP problem under investigation, a new metaheuristic optimization technique, called expanded Invasive Weed Optimization (exIWO), is used. A case study was conducted to maximize the HC of the 83-bus distribution system. The proposed strategy has proven its ability to increase the hosting capacity of the distribution network at three loading levels. Chapter 9: In this chapter, the mathematical model for incorporating hosting capacity using power flow equations in large signal and transfer function model in the small signal analysis is examined. This chapter presents the Internet of Things (IoT) applications in the study. Moreover, it discusses the communication-based control strategy implemented in Gasa Island, South Korea, and the Taiwanese microgrid under normal and disturbance conditions that have been implemented with a MAS platform in Taiwan using agent-oriented programming. Chapter 10: This chapter introduces the concept of market hosting capacity, expressing the maximum amount of renewables that can be connected to a given power network while preserving their profitability in a deregulated environment. It has also developed a suitable mathematical model to quantify this market hosting capacity, founded on bi-level optimization principles. This is a new measure for hosting capacity from a market point of view, which is useful to understand how various factors, such as network investments, subsidies, and generation flexibility, can effectively support higher investments in renewable generation. In conclusion, this book aims to introduce good practice with new research outcomes, programs, and ideas that connect the past, current, and future roles of hosting capacity for modern power grids. It introduces innovative research outcomes, programs, algorithms, and approaches that consolidate the present and future and opportunities and challenges of the hosting capacity approach from various

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perspectives. It is a useful tool for the network planners, designers, operators, and practicing engineers of modern power systems who are concerned with renewable energy resources and their challenges, reliability, and security. Likewise, it is a key resource for advanced students, postgraduates, academics, and researchers who had some background in electrical power systems. In an experiment in criticism [1], the author suggests that books allow us to see the world through other people’s eyes and view it as someone else sees it—and experience their view “from the inside.” This is what gives books a profound and mysterious power. At the same time, each of us sees the world through our own perspective. Thus, the editors wish you may find this book useful to stimulate your imagination and go even further by applying the concept of HC, but doing it with your own sensitive and critical eyes.

Reference 1. Lewis, C. S. (1961). An experiment in criticism. Cambridge: Cambridge University Press.

Contents

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An Overview of Hosting Capacity for Modern Power Grids . . . . . . Tiago E. Castelo de Oliveira, Paulo F. Ribeiro, Ahmed F. Zobaa, Shady H. E. Abdel Aleem, and Sherif M. Ismael

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Hosting Capacity Determination via Risk Analysis Approach Involving Likelihood and Severity of Operational Constraint Violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hassan Al-Saadi

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4

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A Methodology Proposal for Calculation of Hosting Capacity Including Different Power Quality Phenomena . . . . . . . . . . . . . . . . Tiago E. Castelo de Oliveira and Paulo F. Ribeiro

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Effect of Harmonics due to Distributed Energy Resources on Hosting Capacity of Microgrid: A Hardware in Loop-Based Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sourav Kumar Sahu, Debomita Ghosh, and Dusmanta Kumar Mohanta

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A Scenario-Based Approach for Storage Capacity Determination to Improve the Hosting Capacity of Distribution Systems . . . . . . . . Mohammad Seydali Seyf Abad, Jin Ma, and Jing Qiu

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Impact of Capacity Withholding on Hosting Capacity Analyzing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Saeed Salarkheili and Mehrdad SetayeshNazar

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A Generalised Deterministic Approach to Evaluate PV Hosting Capacity of LV Distribution Networks Under Different Operating Conditions . . . . . . . . . . . . . . . . . . . . . . 149 D. Chathurangi, U. Jayatunga, S. Perera, and A. Agalgaonkar

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Contents

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Hosting Capacity Maximization Based on Optimal Reconfiguration of Distribution Networks with Optimized Soft Open Point Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Ibrahim Mohamed Diaaeldin, Shady H. E. Abdel Aleem, Ahmed El-Rafei, Almoataz Y. Abdelaziz, and Ahmed F. Zobaa

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Generation Regulation Control Systems . . . . . . . . . . . . . . . . . . . . . 195 Krishnan Manickavasagam, Ilango Karuppasamy, and Vineetha Puttaraj

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Exploring the Concept of Hosting Capacity from an Electricity Market Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Elias Valenzuela, Rodrigo Moreno, Dimitrios Papadaskalopoulos, Francisco D. Muñoz, and Yujian Ye

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

Chapter 1

An Overview of Hosting Capacity for Modern Power Grids Tiago E. Castelo de Oliveira, Paulo F. Ribeiro, Ahmed F. Zobaa, Shady H. E. Abdel Aleem, and Sherif M. Ismael

1.1

Introduction

Conventional fossil fuel-based resources are affected by several problems, such as diminishing fuel resources, global fuel price instabilities, and greenhouse gas emissions, particularly gases such as carbon dioxide and carbon monoxide which adversely affect the environment. Currently, renewable energy-based power generation is rapidly emerging across the world in response to technical, economic, and environmental developments, as well as political and social initiatives. Now, renewable energy-based power generation is being rapidly developed, worldwide, thanks

T. E. Castelo de Oliveira (*) Eindhoven University of Technology, Eindhoven, the Netherlands e-mail: [email protected] P. F. Ribeiro Advanced Power Technologies and Innovations in Systems and Smart Grids Group, Federal University of Itajuba, Itajuba, MG, Brazil e-mail: [email protected] A. F. Zobaa College of Engineering, Design and Physical Sciences, Brunel University London, Uxbridge, UK e-mail: [email protected] S. H. E. Abdel Aleem Mathematical, Physical and Engineering Sciences Department, 15th of May Higher Institute of Engineering, Cairo, Egypt e-mail: [email protected] S. M. Ismael Electrical Engineering Division, Engineering for the Petroleum and Process Industries (Enppi), Cairo, Egypt e-mail: [email protected] © Springer Nature Switzerland AG 2020 A. F. Zobaa et al. (eds.), Hosting Capacity for Smart Power Grids, https://doi.org/10.1007/978-3-030-40029-3_1

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to various technical, economic, and environmental factors and political and social initiatives [1–3]. However, the booming integration of distributed generation (DG) units, if not properly assessed, may lead to various problems such as over- and under-voltages, excessive line losses, overloading of transformers and feeders, protection failure, and high harmonic distortion levels exceeding the limits of international standards. These problems occur when the number of DG units exceeds the maximum permissible penetration level, in short when the system exceeds its hosting capacity (HC) limit. The HC concept is essential to evaluate the system capacity to host these DG newcomers without exceeding the allowable operational performance. Practically speaking, a conflict of interest has been found among the DG owners/ investors and distribution system operators (DSOs) in deregulated energy markets. It is because the DG investors are looking forward to more and more DG integration into electrical networks, while DSOs are concerned about excessive DG penetration problems. Therefore, the HC concept was proposed to resolve this conflict, as it provides a fair and transparent solution that clearly indicates when to accept or to reject new DG integration requests [4–6]. Today’s power systems are becoming much more complex, expandable, dynamic, and non-predictable; therefore, accurate to-date HC analysis studies are necessary to face the significant challenges associated with the high penetration of renewable energy resources into modern electrical power systems. HC is a key enabler for affordable and reliable renewable energy sources; hence, it is possible to transition away from traditional high-carbon energy sources. It is expected that the HC will play a significant role in future power systems and smart grids. Using an HC approach to drive network requirements could steer DG toward areas of the network where it could have the greatest positive impact on network reliability and win-win benefits with DG owners. Thus, it is imperative that novel solutions be sought to enable networks to cope with future developments to realize resilient distribution networks that can host the pushy DG penetration while enhancing the system reliability of power supplies and controlling the over-hosted areas, that is, the areas that have problems because of violation of technical performance metrics. Not long ago, quick but conservative methods were used to limit integrated DG capacities. Nowadays, the HC concept has been developed to define the maximum amount of DG that can be integrated into the electrical network accurately, without exceeding any operational performance limits. In addition, the HC is a specific, measurable, practical, and fair concept that facilitates the ease of use of clear performance limits as evaluation criteria for DG penetration. Currently, enhancing the system HC is considered one of the important goals for DSOs, worldwide [1]. In the literature, common HC enhancement techniques were investigated, namely, reactive power control, automatic voltage control techniques such as on-load tap changer (OLTC) transformers, active power curtailment, network reconfiguration and reinforcement, and harmonic mitigation techniques. The authors believe that along with these HC enhancement techniques, energy storage (ES) technologies will play a significant role in the near future as a promising

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HC enhancement tool. ES systems help in overcoming the overvoltage resulting from high DG penetration, thus allowing the increase of the system’s HC. ES systems allow the demand and generation of electricity to be mutually decoupled. Even though ES is still expensive, it offers unique benefits that cannot be achieved using other means. Proper sizing and allocation of the ES technologies may postpone DSO’s plans for network reinforcements. Accordingly, customer-owned and DSO-owned ES systems should be carefully investigated to help increase the allowed DG penetration. In the next sections, the concept of dynamic hosting capacity (DHC) will be presented. Further, an application of ES in a system is addressed as a powerful tool to improve a distribution system performance.

1.2

Dynamic Hosting Capacity Approach

In [7–14], HC issues related to voltage regulation and reverse power flow are presented. However, it is necessary to consider also the time-varying impact of harmonics on the voltage regulation in the presence of renewables. This poses a problem as HC conditions vary in time. The main limitation of determining the HC is its reliability, particularly when the system is under constant harmonic injection due to the aggregated electronic devices connected to the electrical system, thus making it a dynamic harmonic injection issue. One question that needs to be raised is how a dynamic harmonic injection could affect the global HC value due to its impact on the voltage profile. A related hypothesis maintains that a dynamic harmonic injection, originating from external conditions, such as the background harmonic injection, as well as distortion from the inverters (e.g., in photovoltaic (PV) systems), leads to a DHC profile which follows the tendency of their harmonic injection. This suggests that it presents a constructive curve in time, showing that harmonic distortion problems should be considered when planning improvement strategies to be applied in electrical distribution systems. The fundamental characteristic of DHC can be described as the allowance to increase and expand the usual approach of HC by applying a time variance, which can designate its behavior against both external and internal variations regarding the system, such as load conditions, background harmonic distortion, and irradiation index, among others [15, 16]. Furthermore, in accordance with [15], the HC at the point of common coupling (PCC) can be defined as the sum of maximum power possible to be injected for each frequency. Furthermore, time variation is set as a vital factor in (1.1) within this analysis.

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T. E. Castelo de Oliveira et al. Unacceptable region

Dynamic HC

Fig. 1.1 Dynamic hosting capacity (DHC) approach [9]

Maximum HC

Acceptable region

Minimum HC

Time

  h V max ,h V max ,h  V h ðt Þ X g g o 1 max ,h   ðt Þ ¼ Pmax PPV g ðt Þ ¼ R hX f f 1 þ tan ðφÞ h¼1 h¼1 h X

ð1:1Þ

Rf

is the system’s HC; Pmax where Pmax g PV is the maximum active power generated by the DG unit; Rf and Xf are the Thevenin’s resistance and reactance at the PCC, respectively; and V hg and V ho are the hth voltage magnitude at the load and the source, respectively. It is important to highlight the maximum quantity and the minimum quantity of power that will be assumed regarding the harmonic voltage values which will be defined for each instant of time [15]. A descriptive graph of the DHC approach is shown in Fig. 1.1. According to Fig. 1.1, it is shown that the maximum and the minimum HC values have analytical consequences to the electrical grid. Firstly, the minimum value is deterministic to describe the efficiency of the grid, and it is usually determined according to the regulations and technical performance metrics of a grid. In other words, the harmonic backgrounds at the PCC, as well as the voltage values, are close to cross their respective limits imposed by local standards [15, 16]. Therefore, the maximum value will regulate the region where the best power quality indices can be found. Clearly, to achieve these values, it is necessary to perform conditioning improvements. The determination of these ranges suggests an acceptable region that can be defined between the minimum and maximum HC values [15]. Conclusively, the larger the acceptable region is, the better the system performance will be. This concept can determine that the DHC analysis is an important tool to determine a further analysis regarding better conditions on the grid, considering the insertion of the distributed energy resources (DER).

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Fig. 1.2 Conventional power flow

P Voltage

Load Distance 'V

Fig. 1.3 Bidirectional power flow due to high DER penetration

Pg DERs

P P = Pg – Pc

Pc

Voltage

Load 'V Distance

1.3

Dynamic Hosting Capacity Considering Storage Systems

Conventional electrical networks consider the total load flow directly from the substation to the load. In regard to this fact, there is a voltage drop throughout the transmission line, as shown in Fig. 1.2. This unidirectional load flow allows for easy planning of the distribution transformers and the conductor section of the feeders [17]. When there is a high penetration of DER in the electrical network, there may be a reversal and/or bidirectionality of the power flow. As an example, the DER absorbs the consumption of the load to which it is connected, and the additional power will be injected into the distribution network, feeding other loads nearby. The phenomenon is shown in Fig. 1.3. Due to the bidirectional power flow, some negative aspects can be registered, for example, a voltage rise at the connection point where the DERs are installed, which can exceed standard indices, leading to possible losses [17]. Alternatively, storage systems could help the system at the connection point by absorbing excessive energy generation of renewables. Several researchers have called this into question, claiming that storage systems can lead to improvements into the distribution system, such as avoiding the voltage rises due to the bidirectional power flow, as well as improving the HC of the system. Figure 1.4 shows the storage system’s impact at the connection point. It is possible to understand that the voltage would not rise in the system because there is no bidirectional load flow into the system.

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Fig. 1.4 The storage system and its operational impacts

Pg

P’

DERs

Ps

Pc

Storage

Load

Voltage

'V |0

Pg –(Pc + Ps) = 0

Distance

HC

Fig. 1.5 The DHC with and without the ES system

Maximum HC without storage

Maximum HC with storage

Time

This problem can be outlined in terms of the power of the system. In this case, the power’s sum will be zero due to the relation Pg  (Ps + Ps), where Pg is the power generated by DERs, Pc is the power consumed by loads, and Ps is the power which will be stored by the storage system. It is important to highlight that the sum will be zero, as long as there is a generation from the DERs, for example, in regard to PVs, only at the moment when there is solar irradiation. This allows for a formal solution to be found, where ΔV  0. In theory, the lesser the voltage rise, the better the HC will be. It is easily verifiable that there are two possible options in order to bring improvement at the connection point: either regulate the voltage through regulators such as OLTC or connect some storage systems into the connection point. It is necessary to analyze which option is better economically speaking. In this analysis, the storage systems will be under investigation with the intention of bringing improvement regarding the DHC profile for the system, as shown in Fig. 1.5. This proposed hypothesis examines how to solve the voltage rise problem in electrical grids using energy storage systems in order to improve the DHC approach. The ES system is examined with the intention of finding the best contribution to decrease the voltage rises, as well as keeping at zero the reverse power flow, thus improving the hosting capacity. This is a feasible but expensive solution for distribution systems in relation to voltage rise indices due to DERs connected at the electrical grid.

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1.4

7

Formulation of the DHC with Energy Storage Systems (ESS)

In the following sections, the importance of considering the maximum amount of energy and its dependence on the harmonic voltage values are highlighted, which are defined for each instant of time. The DHC can be used to calculate the hosting capacity considering time-varying energy storage systems, which can be defined as the dynamic-storage-hosting capacity (DSTHC). Consequently, we need to formulate a hypothesis for it. The DSTHC concept is applied to the allowed voltage magnitude for the system, in this case, determined by local standards. In theory, the concept of hosting capacity, either static or dynamic, makes it clear that the maximum voltage magnitude allowed is the determining factor to find its global value. The DSTHC was prepared using the same procedure as for dynamic HC, but taking into account one specific consideration, which has already been mentioned before. In this way, this assessment considers the voltage rise caused by the bidirectional load flow into the system, thus determining the outline conditions. Instead of basing the maximum voltage magnitude allowed for the system on local standards, the allowed voltage magnitude can be assumed to be equal to the voltage rise for systems without an ES system. Moreover, the voltage reference will be nominal, which means equal to 1.0 (p.u). Those considerations are shown below. (

V gmax ,1 ¼ V o ðt Þ V 1o ðt Þ ¼ 1:0 ðp:uÞ

This method represents an alternative to analyze the storage system behavior because, in this case, the maximum voltage rises already existent at the system, considering the DERs, are the determinant factor to find a hosting capacity value. In addition, the maximum storage power is calculated only for the fundamental frequency, where the voltage rise is an important impact factor. Thus, Eq. (1.1) can be given in (1.2). ΔPmax storage ðt Þ ¼

1 V o ðt ÞðV o ðt Þ  1, 0Þ   Rf 1 þ tan ðφÞ XRff

ð1:2Þ

Taking advantage of DSTHC, we can hypothetically propose that the maximum power stored found in (1.2) is a complement of the maximum power generated given in (1.1). Combining (1.1) and (1.2), we have a total maximum power generation for the system considering an energy storage system, given in (1.3).

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T. E. Castelo de Oliveira et al. max Pgmax 0 ðt Þ ¼ Pmax g ðt Þ þ ΔPstorage ðt Þ

ð1:3Þ

It is easily verifiable that the maximum dynamic HC can be extended by (1.3) in (1.4), where it can be defined by linear regression. max 0 max DSTHCtotal ðt Þ ¼ HCmax total ðt Þ þ ΔHCstorage ðt Þ

ð1:4Þ

The new voltage profile for the system after the energy storage system can be verified. There will not be a voltage rise. The voltage drop can be determined by (1.2). Thus, the new voltage value is given in (1.5). V 0o ðt Þ ¼ V o ðt Þ  ΔV storage ðt Þ

ð1:5Þ

It is important to highlight that the local DER system, considering an ES system, will be dimensioned by (1.4) and (1.5), in order to ensure future improvement in the current installation.

1.5

Further Remarks

HC research is a key enabler for affordable, reliable, and renewable energy sources, so it is possible to transition away from traditional high-carbon energy sources. Therefore, it is imperative that novel solutions be sought to enable networks to cope with future developments to realize resilient distribution networks that can host the pushy DG penetration while enhancing the system reliability of power supplies and controlling the over-hosted areas. This chapter presents an overview of the HC concept and its developments, defines the main HC performance limits, and its up-to-date enhancement techniques. Then, the chapter presents the concept of dynamic HC as well as its application to energy storage systems. The authors presented a new concept for calculating the local HC as a contribution to the context of planning and improving DER installations into distribution systems. The definition of DHC has been discussed, as well as its application to energy storage systems.

References 1. Ismael, S. M., Aleem, S. H. E., Abdelaziz, A. Y., & Zobaa, A. F. (2019). State-of-the-art of hosting capacity in modern power systems with distributed generation. Renewable Energy, 130, 1002–1020. https://doi.org/10.1016/j.renene.2018.07.008. 2. Ismael, S. M., Aleem, S. H. E., Abdelaziz, A. Y., & Zobaa, A. F. (2018). Practical considerations for optimal conductor reinforcement and hosting capacity enhancement in radial

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distribution systems. IEEE Access, 6, 27268–27277. https://doi.org/10.1109/ACCESS.2018. 2835165. 3. Ismael, S. M., Aleem, S. H. E., Abdelaziz, A. Y., & Zobaa, A. F. (2019). Probabilistic hosting capacity enhancement in non-sinusoidal power distribution systems using a hybrid PSOGSA optimization algorithm. Energies, 12(6), 1018. https://doi.org/10.3390/en12061018. 4. Sakar, S., Balci, M. E., Aleem, S. H. E. A., & Zobaa, A. F. (2016). Hosting capacity assessment and improvement for photovoltaic-based distributed generation in distorted distribution networks. In 2016 IEEE 16th International Conference on Environment and Electrical Engineering (EEEIC) (pp. 1–6). Florence. https://doi.org/10.1109/EEEIC.2016.7555515. 5. Sakar, S., Balci, M. E., Aleem, S. H. E. A., & Zobaa, A. F. (2017). Increasing PV hosting capacity in distorted distribution systems using passive harmonic filtering. Electric Power Systems Research, 148, 74–86. https://doi.org/10.1016/j.epsr.2017.03.020. 6. Sakar, S., Balci, M. E., Abdel Aleem, S. H. E., & Zobaa, A. F. (2018). Integration of large-scale PV plants in non-sinusoidal environments: Considerations on hosting capacity and harmonic distortion limits. Renewable and Sustainable Energy Reviews, 82(part 1), 1–1684. https://doi. org/10.1016/j.rser.2017.09.028. 7. Pesaran H.A, M., Huy, P. D., & Ramachandaramurthy, V. K. (2017). A review of the optimal allocation of distributed generation: Objectives, constraints, methods, and algorithms. Renewable and Sustainable Energy Reviews, 75(2015), 293–312. 8. Tan, W. S., Hassan, M. Y., Majid, M. S., & Abdul Rahman, H. (2013). Optimal distributed renewable generation planning: A review of different approaches. Renewable and Sustainable Energy Reviews, 18, 626–645. 9. Bollen, M., & Hassan, F. (2011). Voltage magnitude variations. In Integration of distributed generation in the power system (pp. 141–222). Hoboken: Wiley. 10. Carvalho, P. M. S., Correia, P. F., & Ferreira, L. a. F. (2008). Distributed reactive power generation control for voltage rise mitigation in distribution networks. IEEE Transactions on Power Apparatus and Systems, 23(2), 766–772. 11. De Oliveira, T. E. C., Bonatto, B. D., Filho, J. M. C., Ribeiro, P. F., & Santos, I. N. (2015). Análise Econômica da Hospedagem de Fontes de Geração Distribuída no Sistema Elétrico de um Campus Universitário. In An. do CBQEE 2015 – XI Conferência Bras. sobre Qual. da Energ. Elétrica. 12. Bollen, M. H. J., & Rönnberg, S. K. (2017). Hosting capacity of the power grid for renewable electricity production and new large consumption equipment. Energies, 10(9), 1325. 13. De Oliveira, T. E. C., Ribeiro, P. F., & Santos, I. N. (2016). Determining the harmonic hosting capacity of PV sources for a university campus. In Proceedings International Conference on Harmonics and Quality of Power (ICHQP) (Vol. 2016–Decem, pp. 836–841). 14. Baccino, F., De Nigris, M., Gianinoni, I., Grillo, S., Massucco, S., & Tironi, E. (2012). A methodology for evaluating PEVs hosting capacity margins in distribution grids. In IEEE Power Energy Society General Meeting (pp. 1–6). 15. de Oliveira, T. E. C., Bollen, M., Ribeiro, P. F., de Carvalho, P. M. S., Zambroni, A. C., & Bonatto, B. D. (2019). The concept of dynamic hosting capacity for distributed energy resources: Analytics and practical considerations. Energies, 12(13), 1–18. 16. De Oliveira, T. E. C., Carvalho, P. M. S., Ribeiro, P. F., & Bonatto, B. D. (2018). PV hosting capacity dependence on harmonic voltage distortion in low-voltage grids: Model validation with experimental data. Energies, 11(2), 465. 17. Paludo, J. A. (2014). Avaliação dos Impactos de Elevados Níveis de Penetração da Geração Fotovoltaica no Desempenho de Sistemas de Distribuição de Energia Elétrica em Regime Permanente.

Chapter 2

Hosting Capacity Determination via Risk Analysis Approach Involving Likelihood and Severity of Operational Constraint Violation Hassan Al-Saadi

2.1

Introduction

The high-power penetration into a distribution network exported from photovoltaics (PVs) during noon times has been cited to have negative impacts on normal operational condition. While a low penetration could be associated with positive impacts like voltage improvement or transformer relief, high penetration can have adverse impacts on voltage regulators, LV feeder congestion, direction of the power flow, frequency, etc. [1]. One problem is that the power injected into the network from PVs can intermittently influence the voltage profile of the distribution lines, causing them to be either over or under specified limits. For another example, Automatic Q Control (AQC) that compensates reactive power will be significantly overloaded especially when most distributed generators (DGs) such as PVs export only active power. When the power penetration is high, the active power directed from a substation toward the low-stream buses will be low, unbalancing activereactive power adversely. The power factor (PF) correction will be triggered intermittently in which the capacitor banks and tap-changing transformers might be exposed into a situation that is not designed to operate. On-line voltage regulator (OLVR) may disfunction its working principle conditions as well. During normal operation (without high power penetration from PVs), OLVR reacts in accordance with measurement units located usually at the end of the feeder to maintain the voltage within utility standards. During high power penetration, PVs connected at the end of the distribution feeder may allow the measurements to send deceptive voltage readings. As a result, voltage dip may dominate feeder voltage profile, which H. Al-Saadi (*) School of Electrical and Electronic Engineering, University of Adelaide, Adelaide, SA, Australia e-mail: [email protected] © Springer Nature Switzerland AG 2020 A. F. Zobaa et al. (eds.), Hosting Capacity for Smart Power Grids, https://doi.org/10.1007/978-3-030-40029-3_2

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H. Al-Saadi

specifically could occur in the mid of the feeder [2]. The problems mentioned above, and others not mentioned here, give rise to a new expression in the taxonomy of power system called “hosting capacity” (HC). While the general definition may simply be referred to a maximum limit of a power network in hosting PVs without jeopardizing connected appliances, the determination of HC is still an attractive topic that has not reached the consensus yet. It has been found that the definitions of HC seem to converge in their implication in the published literature. Examples of these definitions are as follows: The hosting capacity of the LV grid for dispersed generation is restricted by the maximum permissible voltage rise within the grid and the maximum short-term loading of the transformer and the cables, due to the diurnal cycle of the PV [3] The maximum amount of new production or consumption that can be connected without endangering the reliability or quality for other customers” and “the acceptable degree of DER1 penetration under given circumstances [4] The upper limit of DG before network congestion occurs [5] The largest PV generation that can be accommodated without violating the feeder’s operational limits [6]

In this chapter, the adopted definition of hosting capacity (HC) is the maximum capacity of DGs connected in a distribution network without disrupting the normal operational conditions of that network.

2.2

Recent Methods on Hosting Capacity Determination

This section provides a quick summary of different techniques used to determine HC in the recent web available sources. In the existing literature for HC determination, DGs’ types, sizes, locations, and network’s specifications factorize the value of HC. The HC is network oriented and based on DGs’ types and number with other details explained in Table 2.1 for existing methods for assessing high DG impacts and HC. In addition, a summary for a number of studies conducted with different approaches tackling HC is provided. In the table, the studies are classified into steady-state planning [7] or dynamic planning [8–12]. The attempt for steady-state planning is to determine the HC of network regardless of the daily time variation, whereas the dynamic related studies are meant to determine the HC according to a specific date and daytime. Thus, the HC has been evaluated with different criteria, methods, and power flow directions. The direction of power flow is assessed to be either unidirectional, from distribution transformer to the consumers, or bidirectional, from local distribution transformers to consumers or from consumers to nearby transformers. The bidirectional power flow occurs when the total amount of generation from DGs suppresses the local demands in which the network starts

1

DER is the abbreviation of distributed energy resource.

[9]

[8]

[7]

302 low-voltage rural and suburban grids

Case study Two buses with PV connected into one bus and the another is substation bus with constant voltage in addition to the assumption of loads summed up and connected into the PV bus Use an actual and large distribution feeder in California with commercial and residential urban and rural feeders, modelled using OpenDSS

3% voltage variation, no overloading electrical components

For HC purposes, ANSI C84.1 standards as overvoltage criteria were taken. Other criteria taken for other analyses such as frequency distortion

Criteria Voltage and line current limits

Table 2.1 The summary on the existing different methods for HC studies

Create different scenarios wherein the PV penetration, at each scenario, is increased by the insertion of the additional PVs on the randomly selected locations The PVs inserted are selected from a set of PV sizes (43,502 residential preferred PVs, 2625 commercial preferred PVs which are based on SCADA and AMI, provided from California Solar Initiative Survey) in which that set is probabilistically distributed according to customer services of PV sellers Classification approach is about classifying the HC capability of the grids into five categories (very weak up to very strong) using Weibull fitting model HC capability of a grid is probabilistically treated using Weibull distribution as well after evaluating the single grid with a number of DG random sizes with different configurations DG penetration is performed in piecewise increase with discrete interval 0.1 kW

HC and penetration method Analyze the steady-state bus voltage and line current behavior when PV penetration increases with different scenarios such as different PFs, percentages of load penetration, and substation voltages

(continued)

Unidirectional

Unidirectional

Grid type Bidirectional

2 Hosting Capacity Determination via Risk Analysis Approach Involving Likelihood. . . 13

Case study 232 residential feeders in the North West of England

400 kV national grid in Sweden.

Medium- and low-voltage network (16 buses, 61 buses)

[10]

[11]

[12]

Table 2.1 (continued)

Coincident hours with voltage and line thermal current constraints

Bus voltages and transformer and cable ampacity

Criteria Line to neutral voltage limit with line ampacity

HC and penetration method Then at each penetration, 1-day analysis (5 min) is performed using real PV and load profiles from Elexon PV penetration is done by the increase of the percentages of customers with PV panels (e.g., 10% of customers with PVs or 20% of customers with PV), 3 kW for each PV. HC is calculated once one of the criteria is met The actual feeders are classified according to their parameters from HC perspective in an extrapolated way The 100 stepwise increases of two virtual pre-allocated wind turbines are performed with the use of weather-recorded data of 2 years (2009 and 2010) resulting in 2 million LF calculations At each increase, the criteria are checked to draw a system performance line in relation with wind power penetration Piecewise ranges of load and WT percentages are created to find the joint probability of occurrence among these ranges to create different scenarios (e.g., 10% demand with 20% WT generation or 80% demand with 50% WT generation). The annual profiles are used for finding the periodic joint probabilities The summarized steps are as follows: 1. Specify a range of load and DG (e.g., 10–20% load and 70–80% DG connected) that needs to be evaluated Perform hourly LF for 1 year using 2003 recorded profiles of one or two pre-allocated WT outputs and one profile for all loads. When the range in step 1 occurs, record the duration of the number of hours that coincide at this range which is called “coincidence hours” Go to step 1 and specify different range and then perform steps 2 and 3 till all ranges are reached Bidirectional

Bidirectional

Grid type Unidirectional

14 H. Al-Saadi

2 Hosting Capacity Determination via Risk Analysis Approach Involving Likelihood. . .

15

exporting power back to the bulk grid through grid supply point. Each referenced method is intensively reviewed and analyzed within this table. The method that grabbed attention most and is adopted in the current work is introduced by Bollen and Hassan [4]. They explain their concept for HC determination and introduced the general fundamentals to seize the impacts of DGs. It is stated that “The impact of distributed generation can be quantified only by using a set of performance indicators.” The further explanation of this concept is provided in [13]. The summarized steps are as follows: First stage Second stage

Third stage Fourth stage

Establish a number of performance indices. Specify a number of standardized permissible limits for the established indices in the 1st stage such as a limit can be defined by EN50160 [14] or any other standards defined by the local utility. Find the mathematical relationship between the indices and the increases in the number of DG connections. Identify network HC by streamlining the different states (acceptable deterioration, unacceptable deterioration or critical deterioration) according to the exceedance of the limits in second stage.

The last mentioned method is depicted in Fig. 2.1. The x-axis displays DG penetration increases starting from a prespecified amount of power penetration. The y-axis displays the degree of deterioration accompanied with these increases. The region shaded in light green indicates that the system is under tolerable deterioration. The region shaded in red is where the system is considered under intolerable deterioration. The network HC limit is identified once the deterioration index crosses from one region into another. There is a possibility of having critical region that could deliver two different values of HC limits. This region is shown in the figure with partially yellowish color. In this chapter, this method is promoted, thereby establishing new risk indices for operational performance which is introduced in the next section.

Fig. 2.1 HC determination method. Adapted from [4]

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2.3

H. Al-Saadi

System Formulation and Evaluation

2.3.1

System Evaluation

One of the deterring obstacles in the topics of risk assessment in power system is the analytical expression of relative frequency of occurrence. The number and different sources of uncertainties in the network make the task of finding analytical representation non-trivial, especially in linking the input variables to the response variable. Instead of the analytical solution, the power of numerical computing techniques is proven to provide feasible answers for many engineering problems. Therefore, in this chapter, the nonintrusive method is employed for a set of scenarios. For each scenario, the numerical simulation is adopted for the evaluation of the system through probabilistic distributions and statistical analysis. To formulate the problem mathematically, two quantities are considered: uncertain quantities and fixed ones, noted by x and d, respectively. While the uncertain quantities, x, stand for the intermittent output power of the connected PV or loads, the fixed quantities, d, represent the level of PV increase connection and the time of the day. In Fig. 2.2, two stages are essential in using nonintrusive method: formulating the uncertainty, x, and propagating in the form of quantity of interest. The procedures of system evaluation can be explained in three steps.

2.3.1.1

Step A: Uncertainty Characterization

This step characterizes the involved uncertainties by scenario-based method or probability density distribution or fuzzy numbers. This characterization is usually achieved through intensive work in a multidisciplinary environment. The common practice in power system is to consider the grid-connected PV as a power injector with linear relation to the solar radiation incident on the surface. However, if the uncertain quantity known as clearness index, kt, is considered instead of solar radiation, then the output power of PV is treated with nonlinear relation to this index. The clearness index represents the degree of the transparency in the atmosphere during a specified time in the day, t. It is bounded with minimum

Fig. 2.2 System evaluation using nonintrusive method

2 Hosting Capacity Determination via Risk Analysis Approach Involving Likelihood. . .

17

and maximum values, noted kt min and kt max, respectively. The more tendency of this quantity to the maximum values means having more cloudless atmosphere. With the assumption that each PV is equipped with maximum power point tracker, the output power of PV as a function of clearness index, PPV(kt), is provided as follows: PPV ðkt Þ ¼ A ∙ η ∙ I βt ðkt Þ

ð2:1Þ

where η is the efficiency of the entire PV unit including the aging degradation; A is the surface area; and I βt ðkt Þ is the radiation incident on the surface with the incline angle, β. The latest is a function of clearness index which can be expressed as follows [15]: 8 kt > > D ∙ k t þ D0 > 0 > 1 þ eBðB kt < β kt I t ðk t Þ ¼ D ∙ k t  D0 > 0 > B > 1 þ e ðB kt > : 0

Þ

D > 0&D0  0

Þ

D > 0&D0 < 0

ð2:2Þ

D0

where D and D0 are composed of different fixed parameters, which can be tracked back following the same reference. B and B0 are the fixed parameters of the logistic function that shapes the relational curve between the diffuse fraction and kt. The probabilistic representations of this quantity have been addressed with different probability density functions (PDFs) such as Weibull, Gaussian, double beta, Boltzmann, single gamma, beta, bi-exponential, double Gaussian, triple Gaussian, Weibull-logistic, etc. Single gamma [16] is adopted for this work. The performance of the presented model is depicted in Fig. 2.3. In this figure, the solar radiation received on the surface of the connected PV is represented in z-axis (black striped area edged with red line) and varies according to y-axis that represents different times during a single day. For demonstration purposes, three different times (8:00 AM, 12:00 PM, and 1:00 PM) are considered to represent the probability densities, which are aligned according to the axis of day hour. The x-axis, named “power flow net,” represents the actual power import/export from or to the utility grid. In each single hour, the probability density of solar irradiation is depicted against the power flow net, showing the most likely occurrence of export/import power from a PV during single hour in a day. In this step, only single hour is considered for the uncertainty characterization.

2.3.1.2

Step B: System Evaluation via Nonintrusive Method

The large number of factors considered in the evaluation of the system increases the complexity of the evaluation task. The nonintrusive method is applicable for numerical based evaluation taking into the account the recent advances in computing power. It has been utilized in the recent studies that concern the problems of

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H. Al-Saadi

Fig. 2.3 The probabilistic representation of output power produced by grid-connected PV in relation to the probability density of solar irradiation. Three PDFs across different daytimes (8:00 AM, 12:00 PM, and 1:00 PM) are shown

power system such as the computation of the probabilistic power flows [17, 18]. The nonintrusive methods govern the response variable to the uncertain input quantities without the need to deal with the internal mathematical relation. It views the system as a black box and allows us to analyze the stochastic performance cheaply through the statistics such expectations, medians, quantiles, etc. Let us consider the system to have uncertain functions represented by n dimensional random vector, X, and parametrized by the fixed quantities represented by d; then the function of the black box can be considered as g(X, d ), and the response vector of variables of interest, represented by Y, can be expressed as follows: Y ¼ gðX, dÞ

ð2:3Þ

Herein, the number of variables, n, in each vector is shared equally likely for PVs and loads; the function g(X, d ) comprises internal computational relation that is not

2 Hosting Capacity Determination via Risk Analysis Approach Involving Likelihood. . .

19

checked by the author of this chapter. The internal relations are based on the used software for computing power load flows. The nonintrusive method simplifies the use of statistics such as sampling, quadrature treating, and regressions, by employing m stochastic runs of deterministic evaluations.

2.3.1.3

Step C: Hypothesis Testing

Hypothesis testing is when the variables of interest are analyzed, and statistics-based decisions are made. It should be noted that it is not possible to 100% accept or reject the decision made out of a hypothesis. Instead, these decisions should be assessed carefully in accordance with common traditional practices such as confidence intervals, standard deviations, and variances. In the case of this work, the statistical results of the sparse grid technique to the Monte Carlo technique is tested by relative error and used for driving the statistical analysis such as the use of expectation in the histogram and bar-stem diagram.

2.3.2

Sparse Grid Technique

In multidimensional environment, the univariate quadrature rule can be employed to solve the numerical integration if the random variables are mutually independent. Commonly, tensorization is used when applying such rule. With the high number of dimensions, however, the classical tensorization would become arduous to be solved due to the curse of dimensionality. The solution is to use sparse grid technique that requires a smaller number of points within the dimensions. Let us consider Λlr denotes one-dimensional integration involving a sequence of univariate quadrature rules for a function, g, given its weight function, f, at i-th dimension, as follows: Λli ¼

XM l

i

ki ¼1

gðxli ,ki Þf ðxli ,ki Þwli ,ki ,

ð2:4Þ

where the index li denotes the accuracy’s level for a dimension i, i ¼ 1, 2, . . ., n, which depends on the nodes’ number mli ; wli ,ki represents precomputed quadrature weights; and xli ,ki 2 ½0, 1 represents nodes (abscissas). The exactness of Λli improves with higher li, where li 2 ℕ . In the classical tensor, the curse of dimensionality emerges as a big problem when high level of accuracy is required with large dimensional problem. The classical tensor leads to computation degree to be O(mn) which requires the increase of computing power exponentially if the number of dimensions increases. The sparse grid technique, in the meanwhile, which is introduced first by Smolyak [19], deals

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H. Al-Saadi

with the finest number of nodes, letting the degree of computation to be O (m ∙ (Log m)n  1) maintaining similar accuracy. Therefore, employing the sparse grid technique on tensor product results in a weighted sum of product rules, indexed by the level of accuracy, as follows [20]: Ξn ðℓ Þ ¼

Xℓ

Uℓ z¼ℓnþ1 z

X l2Θnz

ðΛl1 ⨂  ⨂Λln Þ,

ð2:5Þ

where Θnz denotes the index set of multi-index vectors, fℓi gni¼1 , such that Θnz ¼ o   n  P ℓ 2 fℕgn : jℓ j ¼ di¼1 ℓ i ¼ z þ n &f∅ : z < 0g , and U ℓz ¼ ð1Þℓz n1 ℓz . The extended formula of the tensor product is as follows: Λl1 ⨂  ⨂Λln ¼

 XM n  1 n    w ⨂  ⨂w i1 in i1 ¼1 i2 ¼1 rn ¼1      g x1i1 ,   , xnin ∙ f x1i1 ,   , xnin : Xm1 Xm2

ð2:6Þ

Due to the nesting feature, the selection of Kronrod-Patterson rule is adopted for univariate quadrature. This rule adds more nodes to the preceding level of accuracy, li  1, thereby improving the exactness in the dimension evaluation.

2.4 2.4.1

Proposed Risk Analysis Approach for Hosting Capacity Determination Risk Definition

The involvement of the risk assessment require clarification and definition for the sake of approaching clear and directive framework. In this regard, the term “risk” has been introduced by ISO/IEC [21] to be “The combination of probability of an event and its consequence.” ISO/IEC also introduces “risk analysis” to be “systematic use of information to identify and to estimate the risk.” Later, ISO replaced the risk’s definition into “Effect of uncertainty on objectives” [22]. In Australia/New Zealand, AS/NZS ISO 31000:2009 adopted the last definition [23]. In addition, the definition of the term “risk” has been addressed, by Kaplan and Garrick [24], using triplet questions: what are the possible events, what are the consequences of these events, and what are the associated probabilities of an event? Afterward, these triplet questions become the main contributor for defining the so-called quantitative risk assessment (QRA), especially in engineering applications, such as in [25]. After identification and description of possible hazardous phenomena, the relative frequency of occurrence (occurrence probability) can be used to quantify the identified risk [26].

2 Hosting Capacity Determination via Risk Analysis Approach Involving Likelihood. . .

2.4.2

Deterioration Indices and Hosting Capacity

2.4.2.1

Risk Indices

21

The violations of the prespecified rated current in the line and standardized voltage ranges are two problems identified previously in [27] and discussed in [28, 29] to have a negative impact on the operational performance of distribution network when large number of PVs is connected. These steady-state operational constraints can be used to assess the degree of risk exposure to the network. The degree might be eased or hardened depending on the technical standards adopted by the distribution power utility. During an hourly assessment of the operational performance (as discussed in Fig. 2.3), the violations concerning bus voltages and ampacity of lines are considered for formulating the deterioration indices, signified as D.Index 1 and D.Index 2, respectively. Each risk can be quantified based on the number of violation and on the extent of consequence according to [26]. Both can characterize the likelihood and severity of risk components. Therefore, in each risk index, the number of violation (s) occurring in the entire network, denoted by N , and the extended consequence of the violation(s), denoted by D , are considered. The extended consequence, D, is formulated here as an accumulative sum of the percentage of the overvoltage subtracted from the maximum acceptable voltage bound, symbolized by Vmax. The following steps counted for overvoltage violation, D.Index 1, are used to determine the values of N and D during each stochastic pocess run: First step Second step Third step

Set N 0 ¼ 0 and D 0 ¼ 0. If |Vbus(i)| > Vmax, then N i ¼ N i1 þ 1 and jV max ðiÞ D i ¼ D i1 þ jV bus ðViÞmax , where i refers to the node number. ðiÞ

Fourth step Fifth step

Repeat step 2 until all buses are covered. Store the data so that N ) D:Index 1N and D ) D:Index 1D .

After performing m-times of evaluations, each risk index can be quantified by computing the expectation of its likelihood of violation’s occurrence and severity of its consequence. Following the black box in Fig. 2.2, functional relation between joint PDFs denoted by fjoint(X, d ) and internal functions of the system denoted by g (X, d) can be used to estimate the expectation of likelihood as follows: Z ½D:Index 1N  ¼

D:Index 1N ðgðX, dÞÞ ∙ f joint ðX, d Þ dX, X

and the expectation of the severity is estimated as follows:

ð2:7Þ

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H. Al-Saadi

Z ½D:Index 1D  ¼

D:Index 1D ðgðX, dÞÞ ∙ f joint ðX, dÞ dX,

ð2:8Þ

X

Similarly, the expectations of the likelihood and severity of D. Index 2 are estimated in the same way.

2.4.2.2

Hosting Capacity Determination

The probability-consequence diagrams are common for risk visualization. Others are risk bubble representations, curve approaches, uncertainty boxes, and strength-ofevidence assessment [30]. However, a precise diagram has not been recommended yet for the era of the current power grids. This leaves the debate open as the informative graphical diagram for risk display may rely on the nature of the problem, which can be ultimately decided by the risk analysts/reporters. The expectations of the system performance when increasing multiple PV connections are displayed in terms of two directions of risk index, i.e., likelihood and severity. The likelihood takes the vertical axis, whereas the severity takes the horizontal axis. The stepwise increases of PV connections are depicted as a third axis using scatter points and distinguished by the size/color according to jet-colored bar. Using expected values, streamlining different regions, to extinguish the state of risk from being negligible into unacceptable, is edged by a stripped red line. To clarify further, the striped red line partitions diagram into two areas: not shaded area where the PV connections expose no thread to system’s performance. The red shaded area indicates that PV connection is expected to expose the system into a thread of technical violation. In Fig. 2.4, three risk indices are drawn, and the values of these indices when crossing among the specified areas are shown in the jet-colored bar. Depending on the significance of each index, the limit of HC is decided considering these three indications. Mathematically speaking, the limit of HC can be formulated if the maximum bound of risk index is preassigned such as maximum bound of likelihood, Lmax, and maximum bound of severity, Smax, for D.Index 1, as follows:  HCðD:Index 1Þ ¼

ðD:Index 1N , D:Index 1D Þ : D:Index 1N  Lmax  ε _ D:Index 1D  Smax  ε, ε 2 ℕ

 ,

ð2:9Þ

where ε means the degree of allowance error that depends on the resolution of the stepwise PV increase. Similarly, other HC limits for other D.Index can be driven and concluded for final HC determination.

2 Hosting Capacity Determination via Risk Analysis Approach Involving Likelihood. . .

23

Fig. 2.4 Risk-based analysis method

2.5

Case Studies

Two case studies are presented in this chapter to show the effectiveness of this approach. The work is implemented using MATLAB R2018b on a desktop computer (Intel® i7-2600 4-core with 3.4GHz processor). In this section, the simulation of superior of spare grid technique is tested against Monte Carlo technique. Then, the approach of HC is implemented on two distribution feeders and networks named 11 bus distribution feeder and large distribution network. The operational voltage at the main substation transformer for both cases is kept constant via On-Load Tap Changer (OLTC) to be 1 pu all the time (the effect of OLTC on HC is out of the scope of this chapter). The PDF of the clearness index, kt, is set to follow the time characteristics of Adelaide city (35oS), Australia. The values of parameters of the PV model introduced in (2.2) for three different times are shown in Table 2.2. The loads are characterized by Gaussian PDFs using the 3-σ principle around the load maximum values. The nominal voltage is expected to be 1 pu, and voltage exceeding 1.1 pu is considered as an overvoltage violation, as specified by voltage standard EN50160 [14]. An overcurrent is counted when the current flow at any line within the targeted zone exceeds 150% of that line’s rated-current capacity.

2.5.1

Simulation Test

In the comparison between Monte Carlo technique and sparse grid technique, two quantities are tested: relative error and computational time. The reference result is computed by the number of 40,000 samples using Monte Carlo technique. The aim

24 Table 2.2 PV data for the uncertainty model at different daytimes in a day in December

H. Al-Saadi PV model parameters Time D D0 12:00 1.327 0.0465 10:00 1.174 0.0246 8:00 1.094 0.0122

PV model specifications β 15o η 0.7 θ 15o ρ 0.3

Fig. 2.5 Relative errors against the number of samples for fair comparison between Monte Carlo technique and sparse grid technique

of using the relative error is to compare the modelling accuracy. The results are shown in Fig. 2.5 displaying the values of up to 1000 samples. The relative errors computed using sparse grid technique shows a steady tendency toward the optimal values, i.e., without deviating arbitrarily. This is because the coverage of Monte Carlo technique is completely random and not expected to be steadily improving, unless a large number of samples are used, which is computationally inefficient. Following the aforementioned analysis, the sample number used for the computation of Eqs. (2.7) and (2.8) is 1000 that induces the relative error equal or less than the value of 0.003. Another feature of sparse grid technique is the time speed performance. In Fig. 2.6, Monte Carlo technique seems to perform faster with the number of samples less than 200. The last result is not beneficial due to the lack of stable relative errors. Instead, sparse grid technique performs in the sample number of 1000 as five times faster as the performance of Monte Carlo technique. Therefore, sparse grid technique is employed only in the following simulation results. It is obvious that sparse grid proves its superiority over Monte Carlo technique, explained by selecting the finest number of samples through a unique quadrature rule mentioned earlier. It should be noted that this feature is considerably important in the purpose of providing accuratefast hourly risk assessment that can be incorporated easily with other time-based automation approaches in the modern power grids.

2 Hosting Capacity Determination via Risk Analysis Approach Involving Likelihood. . .

25

Fig. 2.6 The computational time in seconds consumed for both techniques during the assessment against the number of samples

Fig. 2.7 Radial distribution network with nine points of customer connections feeding 36 PV-installed households Table 2.3 Details of the maximum contractual loads (kW) in each house, point of customer connection, and feeder Level Each house Each point Entire feeder

2.5.2

Middle feeder 3.3 9.9 59.7

Sided feeder 3.3 19.8 29.7

11 Bus Actual Feeder

An actual distribution network with a 11/0.4 kV substation (see Fig. 2.7) is used to implement the proposed risk-based approach. The technical details are shown in Tables 2.3 and 2.4 (refer to [31] as the original source of this feeder). The rated power of the substation transformer is 125 kVA. With an average of maximum contractual load of 3.3 kW in each house and typical load profile shown in Fig. 2.8, the performance of the network is estimated through the aforementioned risk indices. The assessment is conducted through a 10-kW stepwise increase of PV connections at the point of common coupling which is, in this case, the same as the point of customer connection. At each step, stochastic run is performed with the use of

26 Table 2.4 Technical details of the distribution feeder

H. Al-Saadi Specification Cable type Resistance (ohm/km) Reactance (ohm/km) Total length (m) Max ampacity (A)

Middle feeder 3  50 + 25Cu 0.391 0.391 240 166

Sided feeders 3  50 + 25Cu 0.078 0.078 300 166

Fig. 2.8 Daily load profile for typical residential electric consumptions

two-dimension sparse grid technique of 13 levels. In Fig. 2.9, three different daytimes (8:00 AM, 10:00 AM, and 12:00 PM) are considered. The risk indices, D.Index 1 and D.Index 2, are estimated for each time accordingly; see the subfigures (a–f). The threshold for severity for D.Index 1 is set to be 150% of the specified ampacity. The threshold for D.Index 2 is set to be 0.1 pu over the nominal voltage of the point of customer connection. For D.Index 1, it is obvious that introducing PVs improves the system performance during the PV increase from 0 kW up to 10 kW. This is especially clear when the time changes from 8:00 AM, subfigure (a), to 12:00 PM, subfigure (e). At 12:00 PM, the PVs are expected to contribute the most, thereby relieving the network stress. However, at more than 30 kW of PV connection, the network exacerbates rapidly, suggesting actions/regulations to be taken/drawn. It is important to mention that the household load has been set to follow the percentages out of its maximum contractual values, as indicated in Fig. 2.8. This timely averaged load varies significantly according to statistics of the dweller’s behavior in energy consumption, which is commonly modelled considering the diversity factor. The severity of this index is recorded as a violation when connecting 30 kW at 10:00 AM and 20 kW at 12:00 PM. No severe threat is indicated when increasing PV connections from 0 to 60 kW during the hour around 8:00 AM. In terms of D.Index 2, the network is expected to experience overvoltage issues if 60 kW or more of PV connection is placed during the hour around 8:00 AM; see subfigure (b). At 10:00 AM, “1.5” bus in any feeder is expected to experience an overvoltage problem if 20 kW of PVs is installed in each point of customer connection; see subfigure (d). At 12:00 PM, 20 kW is expected to increase the likelihood of number of buses with an overvoltage issue; see subfigure (f) with likelihood at “2.8.” However, from subfigures (d) and (f), it is clear that the value, 20 kW, of PV connections is not expected to cause a severe overvoltage in the points

2 Hosting Capacity Determination via Risk Analysis Approach Involving Likelihood. . .

Likelihood

Severity

2

Severity’s threshold 4

D.Index 1

Likelihood & Severity

8:00AM

a)

D.Index 2

1.5

3

1

2

0.5

1

0

b)

Likelihood & Severity

5

0 6

6

10:00AM

D.Index 1

5

4

4

3

3

2

2

1

1

c) 0

d) 0

8

8

Likelihood & Severity

12:00AM

e)

27

D.Index 1

D.Index 2

6

6

4

4

2

2

0 0 10 20 30 40 50 60 PV increase (kW)

D.Index 2

f)

0 0 10 20 30 40 50 60 PV increase (kW)

Fig. 2.9 Three risk assessments for D.Index 1 and D.Index 2 at three different daytimes (8:00 AM, 10:00 AM, and 12:00 PM)

of customer. The network is expected to experience a severe overvoltage problem during 10:00 AM and 12:00 PM when 30 kW or more is connected; see the stem (red pointed) lines at subfigure (d) and subfigure (f).

28

H. Al-Saadi

Table 2.5 Hosting capacity limits for 11 bus feeder according to likelihood only Time 8:00 AM 10:00 AM 12:00 PM

Load percent (%) 35 60 80

HC limit1 (kW) HCBF

PG

> HCSPV =HCWECS , with compensation

83

ð4:10Þ

Where, HCCAL ¼ Calculated hosting capcity. HCBF_PG ¼ Hosting capacity due to bio-fuel powered generator. HCSPV ¼ Hosting capacity due to solar powered generator. HCWECS ¼ Hosting capacity due to wind power generation system.

HCTHD

8 > < HCMax , When all the sources are bio‐fuel powered genertors ¼ HCMin , When all the sources are wind powered generators > : HCMax > HC > HCMin , When combination of sources are connected ð4:11Þ

Based on the conclusion drawn in Eqs. (4.10) and (4.11), the HC of the network can be planned to serve quality power without hampering the THD limits as well as over-voltage and ampacity of the conductor so as to inject power optimally.

4.7

Conclusion and Future Work

The sprawl of power system network has led to the injection of DERs in the form of solar, wind, biofuel, etc. The planning of the size and quantity of these DERs in the network is essential to obtain reliable and quality power. The DERs, especially solar and wind, are totally nature dependent and are highly uncertain. Thus, the network HC due to these DERs needs careful assessment. Due to the uncertain nature of these sources, the THD, distorting the fundamental signal and violating the voltage and ampacity limits, plays a significant role in HC assessment. The effect of THD on HC at different irradiation conditions for SPV and different wind speed is analyzed both in MATLAB and in real-time emulator using Typhoon HIL. The analysis is also compared with biofuel-powered generators to monitor the varying effect of THD on HC. As the energy consumption per capita is exponentially growing, meeting the energy demand is the biggest challenge. To optimally handle the emerging power crunch problem, each bus should be injected with the maximum possible power, that is, enhanced hosting capacity (EHC), which will not only solve the power crunch but also encourage the individual to install DERs.

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References 1. Harvey, R., Xu, Y., Qu, Z., & Namerikawa, T. (2017). Dissipativity-based design of local and wide-area DER controls for large-scale power systems with high penetration of renewables. In 2017 IEEE conference on control technology and applications (CCTA), pp. 2180–2187. 2. Tsikalakis, A. G., & Hatziargyriou, N. D. (2007). Environmental benefits of distributed generation with and without emissions trading. Energy Policy, 35(6), 3395–3409. 3. Munkhchuluun, E., & Meegahapola, L. (2017). Impact of the solar photovoltaic (PV) generation on long-term voltage stability of a power network. In 2017 IEEE innovative smart grid technologies – Asia (ISGT-Asia), pp. 1–6. 4. Bollen, M. H. J., & Rönnberg, S. K. (2017). Hosting capacity of the power grid for renewable electricity production and new large consumption equipment. Energies, 10(9), 1325. 5. Zhou, Y., & Li, H. (2014). Analysis and suppression of leakage current in cascaded-multilevelinverter-based PV systems. IEEE Transactions on Power Electronics, 29(10), 5265–5277. 6. Stratford, R. P. (1980). Rectifier harmonics in power systems. IEEE Transactions on Industry Applications, IA-16(2), 271–276. 7. Wang, J., Guo, Q., Yang, Z., Wang, Y., Bai, Z., & Ma, H. (2015). Modeling and research of three-phase inverter powering nonlinear load., IEEE 24th International Symposium on Industrial Electronics (ISIE), Buzios, 2015 pp, 331–336. 8. Sebaay, A. E. L., Ramadan, M., & Adma, M. A. A. (2017). Studying the effect of non-linear loads harmonics on electric generator power rating selection. European Scientific Journal, ESJ, 13(18), 548. 9. Sakar, S., Balci, M. E., Aleem, S. H. E. A., & Zobaa, A. F. (2016). Hosting capacity assessment and improvement for photovoltaic-based distributed generation in distorted distribution networks. In EEEIC 2016 – International conference on environmental and electrical engineering, pp. 2–7. 10. Cundeva, S., Bollen, M., & Schwanz, D. (2017). Hosting capacity of the grid for wind generators set by voltage magnitude and distortion levels. In Mediterranean conference on power generation, transmission, distribution and energy conversion (MedPower 2016), pp. 73–79. 11. Gupta, S. C., Kumar, Y., & Agnihotri, G. (2008). Optimal sizing of solar-wind hybrid system. In ICTES, pp. 282–287. 12. Alturki, M., Khodaei, A., Paaso, A., & Bahramirad, S. (2018). Optimization-based distribution grid hosting capacity calculations. Applied Energy, 219(March), 350–360. 13. Patsalides, M., et al. (2017). The effect of solar irradiance on the power quality behaviour of grid connected photovoltaic systems. Renewable Energy and Power Quality Journal, 1(05), 323–330. 14. Al-Saadi, H., Zivanovic, R., & Al-Sarawi, S. F. (2017). Probabilistic hosting capacity for active distribution networks. IEEE Transactions on Industrial Informatics, 13(5), 2519–2532. 15. Selvakumar, S., Madhusmita, M., Koodalsamy, C., Simon, S. P., & Sood, Y. R. (2019). Highspeed maximum power point tracking module for PV systems. IEEE Transactions on Industrial Electronics, 66(2), 1119–1129. 16. Fathabadi, H. (2017). Novel maximum electrical and mechanical power tracking controllers for wind energy conversion systems. IEEE Journal of Emerging and Selected Topics in Power Electronics, 5(4), 1739–1745. 17. Sun, W., Harrison, G. P., & Djokic, S. Z. (2012). Distribution network capacity assessment: Incorporating harmonic distortion limits. In IEEE power and energy society general meeting, pp. 1–7. 18. Cantero, A. S. (2018). Modeling and characterization of a wind turbine emulator. In Advances in renewable energies and power technologies (pp. 491–508). Elsevier https://www.elsevier. com/books/advances-in-renewable-energies-and-power-technologies/yahyaoui/978-0-12812959-3.

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19. Neill, S. P., Hashemi, M. R., Neill, S. P., & Hashemi, M. R. (2018). Offshore wind. In Fundamentals of ocean renewable energy (pp. 83–106). Academic Press https://www. elsevier.com/books/fundamentals-of-ocean-renewable-energy/neill/978-0-12-810448-4. 20. Huleihil, M., & Mazor, G. (2012). Wind turbine power: The Betz limit and beyond. In Advances in wind power. IntechOpen. 21. Singh, G. K. (2013). Solar power generation by PV (photovoltaic) technology: A review. Energy, 53, 1–13. 22. Poulios, V., Vrettos, E., Kienzle, F., Kaffe, E., Luternauer, H., & Andersson, G. (2014). Optimal placement and sizing of battery storage to increase the PV hosting capacity of low voltage grids. Master thesis. In International ETG Congress 2015; Die Energiewende – Blueprints for the new energy age, pp. 85–92. 23. Etherden, N., & Bollen, M. (2014). The use of battery storage for increasing the hosting capacity of the grid for renewable electricity production. In Conference Innovations Security. 24. Kapusta, Ł. J., Sundell, J. P., & Teodorczyk, A. (2011). Liquid biofuels-promising energy source for a small scale power plants. Silniki Spalinowe/Combustion Engines, 3(146), 1–6. 25. Shayani, R. A., Member, S., Aurélio, M., De Oliveira, G., & Member, S. (2011). Photovoltaic Generation Penetration Limits in Radial Distribution Systems," in IEEE Transactions on Power Systems, 3(26), 1625–1631. 26. Sharma, S. K., Chandra, A., Saad, M., Lefebvre, S., Asber, D., & Lenoir, L. (2017). Voltage flicker mitigation employing smart loads with high penetration of renewable energy in distribution systems. IEEE Transactions on Sustainable Energy, 8(1), 414–424. 27. Carnovale, D. J. (2014). Application of IEEE Std 519-2014 harmonic limits. In IEEE IAS Atlanta Section, pp. 1–19. 28. C. Studies. (2014). IEEE_STD_519_1992vs2014. 29. Alalamat, F. (2015). Increasing the hosting capacity of radial distribution grids in Jordan. 30. Akram, U., Khalid, M., & Shafiq, S. (2018). Optimal sizing of a wind/solar/battery hybrid gridconnected microgrid system. IET Renewable Power Generation, 12(1), 72–80. 31. Xu, L., Ruan, X., Mao, C., Zhang, B., & Luo, Y. (2013). An improved optimal sizing method for wind-solar-battery hybrid power system. IEEE Transactions on Sustainable Energy, 4(3), 774–785. 32. Laksmi Kumari, R. V. S., Nagesh Kumar, G. V., Siva Nagaraju, S., & Babita Jain, M. (2018, January). Optimal sizing of distributed generation using particle swarm optimization. In 2017 international conference on intelligent computing, instrumentation and control technologies ICICICT 2017, pp. 499–505. 33. Alizadeh, S. M., Ozansoy, C., & Alpcan, T. (2016). The impact of X/R ratio on voltage stability in a distribution network penetrated by wind farms. In Proceedings 2016 Australasian Universities Power Engineering Conference AUPEC 2016, pp. 1–6. 34. JRC photovoltaic geographical information system (PVGIS) – European Commission. [Online]. Available: https://re.jrc.ec.europa.eu/pvg_tools/en/tools.html. Accessed 23 September 2019. 35. Rajaram, R., Sathish Kumar, K., & Rajasekar, N. (2015). Power system reconfiguration in a radial distribution network for reducing losses and to improve voltage profile using modified plant growth simulation algorithm with distributed generation (DG). Energy Reports, 1, 116–122.

Chapter 5

A Scenario-Based Approach for Storage Capacity Determination to Improve the Hosting Capacity of Distribution Systems Mohammad Seydali Seyf Abad, Jin Ma, and Jing Qiu

5.1

Introduction

The penetration of distributed energy resources (DERs) in distribution systems has been increasing in recent years. However, the capacity of distribution systems to host DERs is bounded by different technical constraints. Different methods such as network augmentation [1], reactive power control [2, 3], and active power curtailment [3–5] have been proposed to increase the hosting capacity (HC) by addressing the technical challenges incurred due to high penetration of DERs. However, these methods have some technical and/or economic drawbacks. For instance, reactive power control of DERs can effectively increase the HC only when the X/R ratio is high. But X/R ratio is usually low in distribution systems. Further, although network augmentation methods can effectively increase the HC, they are usually costly for the utility [1]. Similarly, active power curtailment methods can effectively increase the HC. However, power curtailment-based methods are usually not popular among the DER owners as the curtailed energy is not totally compensated. Using battery energy storage systems (BESSs) to address the issues associated with DERs is another popular method. The application of BESSs includes preventing over-voltage [6], smoothing the output of renewable resources [7], peak shaving [8], and energy arbitrage [9]. Generally, studies that focused on the application of BESSs in resolving the technical issues associated with high penetration of DERs can be divided into two categories: (i) those that resolved the technical issues by controlling the BESSs [10, 11] and (ii) and those that resolved the technical issues by optimally allocating the BESSs [12–14]. In the first category, the size and M. S. S. Abad (*) · J. Ma · J. Qiu University of Sydney, Sydney, NSW, Australia e-mail: [email protected]; [email protected]; jeremy. [email protected] © Springer Nature Switzerland AG 2020 A. F. Zobaa et al. (eds.), Hosting Capacity for Smart Power Grids, https://doi.org/10.1007/978-3-030-40029-3_5

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location of DERs and BESSs are given, and the unknown variables are the active and reactive power of the BESSs. However, if BESSs are to be utilized for increasing the HC of a system, their sizes and locations are unknown. Therefore, the methods in the first category cannot be used directly for increasing the HC of a system. Nevertheless, the second category, which is based on the optimal allocation of BESSs could have a better performance as the optimal size, location, and control action can be identified to increase the HC. Studies related to the allocation of BESSs have mainly focused on the following aspects: authors in [15] allocated distributed energy storage systems to increase the efficiency of distribution and transmission systems by using bilevel optimization. A robust model to minimize the procurement cost by optimally allocating energy storage systems and renewable energy sources was presented in [16]. Authors in [17] allocated energy storage systems to maximize the benefit of the system operator. The study exploited an accelerated Benders decomposition to solve the problem. Energy storage systems were optimally allocated in [18] for maintaining the power balance in active distribution networks considering the efficiency and life cycle of the storage units. In [12], a methodology for allocating BESSs in a distribution network is developed to minimize the wind energy curtailment as well as the annual supply cost of the electricity. Authors in [19] defined a multi-objective optimization to allocate the BESS by identifying a trade-off between the technical and economic goals by minimizing the voltage deviation, network losses, feeder congestions, and costs of supplying loads. In [13], a method for optimal placement, sizing, and control of a community BESS to increase the HC of rooftop PVs in low-voltage (LV) networks is proposed. Authors in [20] developed a stochastic optimizationbased method for BESS allocation and operation to ensure a desired voltage stability margin in wind-intensive distribution systems. In [21], a convex optimization approach has been used for BESS planning and operation in systems with high PV penetration level. In that study, the minimum BESS required for mitigating the technical impacts of high uptake of PVs has been estimated by using OpenDSS simulation tool. Then, an optimization model has been used to identify the location of BESSs. Authors in [22] proposed a heuristic strategy based on voltage sensitivity in combination with an optimal power flow (OPF) framework to identify the optimal number, size, and location of BESSs that prevent over-voltage and under-voltage in an LV distribution network. To properly model the uncertainties associated with the output of DERs and loads, authors in [6] proposed a scenario-based method to identify the minimum required BESSs that prevents over-voltage in distribution system with high PV penetration level. The proposed method in that study is based on the voltage sensitivity of the scenarios associated with the customers’ injected power. Nevertheless, to the best of the authors’ knowledge, the common drawback of the aforementioned methods that utilize BESSs for HC improvement is that they did not consider the uncertainty associated with the location and size of DERs. Hence, they have only identified the required BESS capacity for a given scenario. Therefore, in this chapter, a comprehensive method has been proposed to identify the minimum required BESSs for increasing the HC of a system considering the uncertainties

5 A Scenario-Based Approach for Storage Capacity Determination to Improve. . .

89

associated with the DERs and loads. Then, an economic model has been developed to assess the minimum required BESS from an economic perspective. Finally, the performance of the developed models is assessed on an agricultural feeder in Australia.

5.2

Energy Storage System Classification and Application

As shown in Fig. 5.1, energy storage technologies can be divided into five categories, as follows: 1. Electrochemical: These energy storage devices have been becoming more popular due to the decreasing trend of their costs as well as their high performances. The main idea in these storages is storing electrical energy in the form of chemical energy in batteries. The most popular electrochemical storages include lithiumion, lead-acid, nickel-cadmium, sodium-sulfur (NaS), and vanadium redox (VRB) batteries. 2. Mechanical: These storages can store energy in different mechanical forms. Mechanical storages include flywheel, pumped hydro, and compressed air energy storages. Flywheels are electromechanical systems that can store mechanical energy in the angular momentum of a rotating mass. Pumped hydro storages are based on storing and releasing the potential energy of water. The charging process consists of converting the electrical energy to potential energy by pumping water from a lower to an upper reservoir. The discharging process

Energy storage technologies

Electrochemical

Thermal

Mechanical

Chemical

Lithium-ion battery

Thermochemical

Compressed air

Hydrogen

NaS battery

Sensible heat

Pumped hydro

Methane

Lead-acid battery

Latent heat

Flywheels

Redox flow battery Nickelcadmium

Fig. 5.1 Classification of energy storage technologies

Electrical

Supercapacitor

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consists of rotating a turbine by releasing water from the upper to lower reservoir to generate electricity. Compressed air energy storage’s working principle is accumulating energy by compressing and storing air in sealed tanks or underground vessels. However, during the discharge process, the compressed air is heated and released through a turbine to generate electricity. 3. Chemical: The basic idea in these storages is storing hydrogen as a compressed gas or in the liquid form and synthesizing it to methane and finally generating electricity by using fuel cells, combustion engines, or gas turbines. 4. Thermal: The working principle of these storages is storing energy in the form of heat in different types of materials and generating electricity using steam turbines. Generally, there are three types of thermal storages, namely, sensible heat, latent heat, and thermo-mechanical storages. Please refer to [23] for more details. 5. Electrical: These storages can store electricity in the form of an electric field. Electrical storages include supercapacitors, which have high efficiency and long lifetime. The electrochemical storages have been significantly progressing in recent years [24]. The leading countries on electrochemical storages in terms of accumulated rating power and number of installations are presented in Fig. 5.2, which is based on all storage statuses, including operational, under construction, under repair, announced, off-line, contracted, and decommissioned. Figure 5.3 shows the accumulated rating power and the number of installed electrochemical BESSs that are operational in 2015 [24]. As shown, the USA with a total capacity of 354 MW

400 350

1000

300 800

250 200

600

150

400

100 200

50

NUMBER OF STORAGE PROJECTS

TOTAL CAPACITY (MW)

1200

0

0

Estimated capacity (MW)

Number of storage projects

Fig. 5.2 Estimated battery storage capacity including operational, under repair, off-line, under construction, contracted, and decommissioned by country in 2015

5 A Scenario-Based Approach for Storage Capacity Determination to Improve. . .

91

400

TOTAL CAPACITY (MW)

350 200

300 250

150

200 100

150 100

50

50

NUMBER OF STORAGE PROJECTS

250

0

0

Estimated capacity (MW)

Number of storage projects

Fig. 5.3 Estimated operational battery storage by country in 2015 Fig. 5.4 Percentage of different electrochemical battery project in the world

612 projects 100

2444 MWh

1350 MW

10.8 30.6

11.8

80

43

Share in (%)

12.6 5.7

60

12.3 11.1 6

40 62.6

48.7 20

39.2

0 Projects Lithium ion

Lead acid

MWh Capacity Flow battery

Sodium salt

MW Capacity Nickel based

Others

(192 installations) is in the first place, Japan with a total capacity of 97 MW (35 installations) is in the second place, and China with 48 MW (53 installations) is in the third place. Analysis of the existing electrochemical storages shows that lithium-ion storages make up for more than 50% of the total projects. Figure 5.4 shows the share of different electrochemical battery technologies. This figure is based on analyzing 612 battery projects across 42 countries with a total installed capacity of 1350 MW/

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2444 MWh. As can be seen, 99.1% of all the considered projects belongs to lithiumion, lead-acid, flow battery, sodium-salt, and nickel-based categories.

5.3

Hosting Capacity Estimation

In this section, a framework that estimates the HC of a radial distribution system is presented, which is based on a comprehensive probabilistic approach, proposed in [25]. This modular framework is based on an optimization model that aims to maximize the injected power to the system at each time step. Figure 5.5 summarizes the main components of the framework. The first module is a scenario generator, which is designed to address the uncertainties associated with the type and location of DERs. The second module comprises a time series analysis to address the uncertainties associated with loads and the output power of DERs using an HC optimization model. The third module is the probabilistic analysis of the results obtained from the second module. The core of the framework is the HC optimization model, as follows: maximize |fflfflfflfflfflffl{zfflfflfflfflfflffl} N gi,t

X

pgi,t ,

ð5:1Þ

i2DG

subjected to Pij,t ¼

X

Pjk,t þ pdj,t  pgj,t

8j 2 DG,

ð5:2Þ

8j 2 fN ∖DG g,

ð5:3Þ

k:j!k

Pij,t ¼

X

Pjk,t þ pdj,t

k:j!k

Qij,t ¼

X

Qjk,t þ qdj,t  qgj,t

8j 2 DG,

ð5:4Þ

k:j!k

Module 1

Module 2

Module 3

Scenario Generator

Time series analysis based on the optimization model

Probabilistic analysis

Fig. 5.5 General framework for HC estimation

5 A Scenario-Based Approach for Storage Capacity Determination to Improve. . .

Qij,t ¼

X

Qjk,t þ qdj,t

93

8j 2 fN ∖DG g,

ð5:5Þ

k:j!k

υ j,t

pgj,t ¼ ηgj,t  Capgj  N gj,t 8j 2 DG,   qgj,t ¼ pgj,t  tan ϕgj 8j 2 DG,   ¼ υi,t  2 r ij Pij,t þ xij Qij,t 8ði, jÞ 2 B,

ð5:6Þ ð5:7Þ ð5:8Þ

υi,t  υ 8i 2 N , N gj,t

ð5:9Þ

 1 8j 2 DG,

ð5:10Þ

where Pij, t and Qij, t are the active and reactive power flow from bus (i) to bus ( j) at the time step (t); pdi,t and qdi,t are the active and reactive load at bus (i) and time step (t); pgi,t and qgi,t are the active and reactive generation at bus (i) and time step (t); ϕgi is the power factor angle at bus (i) and time step (t); υi, t ¼ |Vi, t|2, where |Vi, t| is the voltage magnitude at bus (i) and time step (t); Capgi and ηgi,t are the capacity and capacity factor of the DER at the time (t) and bus (i); N gi,t represents the number of DER at the time (t) and bus (i); N and DG are the set of all buses and the set of DG locations, respectively; B is the set of all lines and υ represents the maximum allowable voltage; rij + jxij is the impedance from bus (i) to ( j); (i, j) and j ! k represents the line from bus (i) to bus ( j). According to the third module, the HC of a distribution system could be divided into three regions, as shown in Fig. 5.6. Region (A) shows the DER penetration levels that do not cause any violation in technical constraints, regardless of DER locations. Region (B) represents the DER penetration levels that do not cause any technical violation when DERs are located at certain locations. It was demonstrated Fig. 5.6 Possible regions as well as the distribution curve of HC

Cumulative probability curve Probability distribution curve

A

B

Increasing DER penetration

C

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in [25] that the probability distribution curve of the HC in the region (B) could be approximated by a Gaussian-shape distribution. The start point of the probability distribution curve is the border between regions (A) and (B). This start point is defined as the minimum HC of the system. Region (C) represents all DER penetration levels that would cause a violation of technical constraints, regardless of the location of DERs. The border between regions (B) and (C) is defined as the maximum HC. BESS is one of the options that can be used to increase both the minimum and the maximum HC. Section 5.4 presents a methodology to identify the minimum required BESS to increase the minimum and maximum HC up to a certain level.

5.4

Storage Sizing Framework

In this section, a comprehensive method and an approximated method for identifying the minimum BESS capacity required to increase the minimum HC are proposed. The proposed methods are based on the estimation of the required active power curtailment.

5.4.1

Comprehensive Method

As shown in Fig. 5.6, the HC depends on the location of DERs in the region (B). Therefore, any HC in the region (B) would cause a technical constraint violation for some DER location scenarios. However, it is possible to resolve the constraint violations by curtailing DERs. The optimization model for calculating the minimum active power curtailment required to avoid technical constraint violation is as follows: maximize |fflfflfflfflfflffl{zfflfflfflfflfflffl} APCgi,t

X

pgi,t  APCgi,t ,

ð5:11Þ

i2DG

subjected to Pij,t ¼

X k:j!k

Pij,t ¼

Pjk,t þ pdj,t  pgj,t þ APCgj,t X

Pjk,t þ pdj,t

8j 2 DG,

8j 2 fN ∖DG g,

ð5:12Þ ð5:13Þ

k:j!k

Qij,t ¼

X

k:j!k

Qjk,t þ qdj,t  qgj,t

8j 2 DG,

ð5:14Þ

5 A Scenario-Based Approach for Storage Capacity Determination to Improve. . .

Qij,t ¼

X

Qjk,t þ qdj,t

8j 2 fN ∖DG g,

95

ð5:15Þ

k:j!k

  υ j,t ¼ υi,t  2 r ij Pij,t þ xij Qij,t

8ði, jÞ 2 B,

υi,t  υ 8i 2 N , APCgj,t

qgj,t



pgj,t

8j 2 DG,

pgj,t ¼ ηgj,t  Capgj 8j 2 DG,     ¼ pgj,t  APCgj,t  tan ϕgj 8j 2 DG:

ð5:16Þ ð5:17Þ ð5:18Þ ð5:19Þ ð5:20Þ

Solving the optimization models (5.11), (5.12), (5.13), (5.14), (5.15), (5.16), (5.17), (5.18), (5.19), and (5.20) results in the active power curtailment required at each time step. To identify the minimum required BESS for a scenario, the models (5.11), (5.12), (5.13), (5.14), (5.15), (5.16), (5.17), (5.18), (5.19), and (5.20) should be solved over the studied period. The maximum curtailed power during an hour over the studied period is the minimum rating power required for the BESS for that scenario. Similarly, the maximum curtailed energy during a day over the studied period is the minimum energy rating of the required BESS. The rating power and energy capacity of the required BESS should be identified for different scenarios that would result in the same HC. Figure 5.7 represents the framework for identifying the minimum BESS required to increase the minimum HC to a certain level (HCref) in the region (B). The main idea of the framework is generating expansion scenarios that would result in the total DER capacity of HCref. Then, the required rating power and energy capacity of BESS should be identified. Finally, the required BESS is estimated based on the designed BESS for the generated scenarios. In the following, the steps of the framework are explained in detail. • Step A: The focus of this step is addressing the uncertainty associated with the size of DERs. Depending on the DER technology, there is a distribution curve for the size of the units based on the historical statistics. For instance, Fig. 5.8 represents the distribution curve of PV systems in California. Generate a scenario by sampling from the distribution curve of DERs. The sum of the samples should be equal to the minimum HC level (HCref). • Step B: This step is designed to address the uncertainty associated with the location of DERs. To do so, the location of generated DER sample in Step B is selected randomly, using a uniform distribution from the pool of potential locations. • Step C: After carrying out steps A and B, the optimization models (5.11), (5.12), (5.13), (5.14), (5.15), (5.16), (5.17), (5.18), (5.19), and (5.20) should be used to identify the required active power curtailment over the study period. Then, based on the obtained curtailed power, determine the required BESS for the scenario. If the curtailed power over the studied period is zero, the scenario is not a valid scenario as it does not cause any technical constraint violation over the study period. Thus, the following indicator for each scenario is defined to identify the validity of each scenario.

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• Step A: Generate a scenario by sampling from the distribution curve of DERs. The sum of the samples should be equal to the minimum HC level (HCref).

• Step B: The location of generated DER samples in Step B is selected randomly using a uniform distribution from the pool of potential locations.

• Step C: Solve the optimization model (11)-(20) to identify the required active power curtailment over the study period for the defined scenarion in steps A and B.

• Step D: Repeat steps A, B and C until repetition condition is not violated.

Frequency

Fig. 5.7 The proposed framework for minimum BESS estimation

Capacity (kW)

Fig. 5.8 The distribution curve of PV systems based on California solar statistics [26]

 ΘBESS ð jÞ ¼

1

Total APC > 0

0

Otherwise

ð5:21Þ

• Step D: Repeat steps A, B, and C until repetition condition is not violated. As it was mentioned, the HC in region (B) has a distribution function. Therefore, it is possible to calculate the probability of constraint violations for the new minimum HC (HCref) as follows:

5 A Scenario-Based Approach for Storage Capacity Determination to Improve. . .

Z ProbCV ¼

HCref

pdf HC ,

97

ð5:22Þ

0

where pdfHC is the probability distribution function of the HC. It was also mentioned that the active power curtailment over the study period is zero for some of the generated scenarios in steps A and B. The probability of valid generated scenarios is as follows: PN BESS PrAPC ¼

ΘBESS ð jÞ , N BESS

j¼1

ð5:23Þ

where NBESS is the total generated scenarios. Repeat steps A, B, and C while the following condition is held: N BESS  100

5.4.2

&&,

ð5:24Þ

0 < PrAPC  ProbCV ,

ð5:25Þ

Approximated Method

Estimating the required BESS using the proposed comprehensive method is based on solving an optimization model over the study period for different expansion scenarios, which means that the comprehensive method could have a considerable computational burden. However, an important question is how to estimate the required BESS without extensive computational burden? An approximated method to estimate the BESS size is presented in this section. The proposed method only uses the probability distribution function of the HC as well as the load and generation profiles in the system. The approximation method is based on the maximum backfeed in the system. To have a better understanding of the method, consider a simplified distribution system as shown in Fig. 5.9. The back-feed can be calculated as follows: pbf ¼ pgen  pLd ,

ð5:26Þ

pgen ¼ sgen  PFgen ,

ð5:27Þ

where sgen and PFgen are the capacity and power factor of DER and pbf represents the active power that is injected to the upstream grid via distribution system transformer. In this system, back-feed is the main limiting factor of the HC as it would result in an over-voltage issue in bus (2). Thus, the HC of the system could be used to calculate the maximum allowable back-feed as follows:

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1

2 pbf, qbf

Grid

pgen, qgen

pLd, qLd

Transformer

V1

V2

Fig. 5.9 A simple representation of a distribution system

max psafe bf ¼ sgen  PFgen  pLd ,

ð5:28Þ

where smax gen is the maximum DER capacity that could be accommodated in the system, i.e., HC of the system. The maximum allowable back-feed can be used as an index to estimate the minimum BESS required to increase the HC. Please refer to [27] for more details on limitations of back-feed in real distribution systems. Any safe DER with a higher capacity than smax gen would result in a higher back-feed than pbf , hence the over-voltage problem. The excess back-feed power that would cause the constraint violation can be calculated as follows: pexcess ¼ sgen  PFgen  psafe bf ,

ð5:29Þ

where sgen  smax gen . To resolve the constraint violation, a BESS can be designed to store the excess back-feed power. The minimum rating power required for the BESS is the maximum excess back-feed power during an hour over the studied period. Similarly, the minimum energy rating of the required BESS is the maximum excess back-feed power during a day over the studied period. The same concept can be applied to an actual distribution system. Therefore, maximum back-feed power can be defined for any distribution system based on the minimum HC of the system. The steps for estimating the minimum required BESS based on the safe back-feed concept are as follows: • Step 1: Identify the maximum back-feed for the system by simplifying the distribution system to the model presented in Fig. 5.9. To do so, the loads should be aggregated at the secondary side of the transformer, and the network configuration should be neglected. Then, the minimum HC should be allocated next to the aggregated load. Next, the back-feed power should be calculated using the aggregated load, minimum HC, as well as the load and DER profiles. Finally, the maximum of the back-feed power should be identified over the studied period. • Step 2: Identify the excess back-feed power. To do so, the new minimum HC should be connected next to the location of the aggregated load. Then, the backfeed power should be calculated using the aggregated load, new minimum HC, as well as the load and DER profiles. As shown in Fig. 5.10, the excess back-feed power can be identified by comparing the back-feed with the maximum back-feed over the study period.

5 A Scenario-Based Approach for Storage Capacity Determination to Improve. . . Back-feed power

99

Excess back-feed

Substation power

Maximum back-feed power

time

Maximum excess back-feed power

Fig. 5.10 Determination of excess back-feed power (red area) by comparison of maximum backfeed power (dashed blue line) and back-feed power (solid green line)

• Step 3: Estimate the minimum required BESS based on the excess back-feed over the study period. The maximum excess back-feed power during an hour over the studied period is the minimum rating power required for the BESS. Similarly, the maximum excess back-feed power during a day over the studied period is the minimum energy rating of the required BESS.

5.5

Economic Assessment

This section explains the proposed method for performing the economic assessment of the designed BESSs. It should be mentioned that the economic assessment in this section is based on the annual costs and benefits of the BESSs.

5.5.1

The Annual Costs of the Estimated BESSs

The annual cost of BESS comprises three main terms as follows: • Total annual capital cost: The total capital cost of an energy storage system includes the capital costs required for different parts of a BESS. Figure 5.11 shows the structure of a BESS. Three terms should be considered as the capital costs of the BESS: (1) energy cost for BESS, which is the cost of the devices that store the energy; (2) cost of power, which is the cost of power electronic devices (inverter) in the BESS; and (3) the total cost for the balance of plant, which is

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Battery

Inverter

Grid

Supporting structure

Fig. 5.11 The structure of a BESS

defined as the cost of all the auxiliary systems of a BESS including the transformer and supporting structures that are required to exchange the energy. • Operation and maintenance cost: This term is defined to identify the annual cost of maintenance and operation of the BESSs. • Replacement cost: This term is designed to cover the cost of battery replacement at the end of the life cycle of the battery. If the planning horizon is longer than the life cycle of batteries, then this term should be considered. The calculation of the total annual capital cost is as follows [28]: BEC ¼ UCSC 

EESS Total , Eff

ð5:30Þ

where BEC and UCSC represent the total cost ($) and the unit cost ($/kWh) of storage device, respectively; E ESS Total is the designed energy capacity of the storage device (kWh); and Eff represents the BESS efficiency. PEC ¼ UCPE  SESS Total ,

ð5:31Þ

where PEC and UCPE represent the total cost ($) and the unit cost ($/kW) of power electronic device, respectively, and SESS Total is the rated power of the BESS (kW). BOP ¼ UBOP 

E ESS Total , Eff

ð5:32Þ

where BOP and UBOP represent the total cost ($) and the unit cost ($/kWh) of the balance of plant, respectively. Thus, the total capital cost can be calculated as follows: TCC ¼ BEC þ PEC þ BOP,

ð5:33Þ

5 A Scenario-Based Approach for Storage Capacity Determination to Improve. . .

101

where TCC denotes the total capital cost. Then, the total annual capital cost is as follows: ACC ¼ TCC  CAF,

ð5:34Þ

where CAF ¼

IRð1 þ IRÞhzn , ð1 þ IRÞhzn  1

ð5:35Þ

where IR is the annual interest rate and hzn is the planning horizon. Further, the operation and maintenance cost can be calculated as follows: AOMC ¼ FOM  SESS Total ,

ð5:36Þ

where AOMC and FOM denote the total annual cost ($/year) and the fixed unit cost ($/(kW.year)) of the maintenance and operation of BESS, respectively. Finally, the replacement cost can be calculated as follows: ARC ¼ AFactor 

EESS Total , Eff

ð5:37Þ

where h i AFactor ¼ F factor  ð1 þ IRÞr þ ð1 þ IRÞ2r þ     CAF, r¼

CycleTotal , CycleDay  N year

ð5:38Þ ð5:39Þ

where Ffactor represents the future value of the battery replacement cost ($/kWh); CycleTotal and CycleDay denote the number of charge/discharge cycles of the storage during its life cycle and during a day, respectively; and Nyear is the number of operating days in a year for the storage system. Therefore, the total annual cost (TAC) can be calculated as follows: TAC ¼ ACC þ AOMC þ ARC:

5.5.2

ð5:40Þ

The Annual Costs of the Active Power Curtailment

Compensation of the curtailed energy highly depends on the contract between the off-taker and the generator owner. Usually, the compensation of active power

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curtailment of renewable generators is based on the type of curtailment, the technology of renewable generation, and the amount of curtailed energy. Most commonly, generators are compensated based on the market value for the curtailed energy. However, usually, this compensation does not include revenue lost from support mechanisms such as green energy credits. Some countries such as Ireland and Romania have such a compensation policy. In some countries, the curtailment compensation only covers a fraction of the curtailed energy. This fraction could vary from 15% to 50% or more. For instance, Greece only compensates 30% of the curtailed energy of the wind facilities. However, there is no curtailment compensation for other technologies in Greece. Moreover, the classification and reason behind the curtailment are important in the compensation policies. For example, the congestion curtailments are usually compensated, while the curtailments related to the security of the system are not. This policy has been used in Belgium and Germany. Other countries might use a different dichotomy. For instance, real-time curtailments are compensated, while the scheduled ones are not [29]. If it is supposed that there is no compensation for the curtailed energy, then the curtailed energy is an opportunity cost for the DER owner. In such a case, the annual cost of the active power curtailment for all DER owners can be calculated as follows: CostAPC ¼

8760 XX

T grid  APCgi,t , t

ð5:41Þ

i2DG t¼1

where T grid is the network electricity price at time (t). t

5.5.3

The Annual Benefit of BESSs for the Utility

The focus of this section is identifying the benefits of the integration of BESSs in the system for the utility. Two obvious options could benefit the utility, which are the reduction in the network losses as well as the energy arbitrage between peak and off-peak periods. Both of these objectives can be achieved by minimizing the costs of supplying energy from a utility perspective. Therefore, the objective function can be defined as follows: Minimize costs ¼

8760 X X ði, jÞ2B t¼1

T grid  r ij  ℓij,t  t

8760 XX i

grid pESS i,t  T t :

ð5:42Þ

t¼1

The decision variables are the optimal size and location of BESSs. The constraints of the optimization problem include the BESS installation and operation constraints, network constraints, and DER constraints, which are given as follows:

5 A Scenario-Based Approach for Storage Capacity Determination to Improve. . .

103

1. BESS installation constraints X

BESS  BESS i total ,

ð5:43Þ

i min max  SESS,  SESS  BESS  SESS, , BESS i i i i i

ð5:44Þ

min max  E ESS,  EESS  BESS  E ESS, , BESS i i i i i X SESS  SESS i Total ,

ð5:45Þ ð5:46Þ

i

X

E ESS  E ESS i Total ,

ð5:47Þ

i

BESS 2 f01g, i

ð5:48Þ

where BESS total is the total number of locations in which BESSs could be installed; ESS and EESS Bi represents the binary variable to allocate BESS at bus (i); SESS i i denote the power rating and energy capacity of a given BESS at bus (i), max max and EESS, represent the maximum power rating and respectively; SESS, i i min min energy capacity of a given BESS at bus (i); and SESS, and EESS, denote the i i minimum power rating and energy capacity of a given BESS at bus (i). Constraints (5.46) and (5.47) limit the total power rating and energy capacity of the BESS to the minimum required BESS, which was identified in Sect. 5.4. 2. BESS operation constraints [19] t  X t 0 ¼0 t  X t 0 ¼0

 ESS  E ESS pESS i,t 0  Δt þ Lossi,t 0 i,t 0 ¼0

8t 2 H ,

 ESS pESS  E ESS  EESS i,t 0  Δt  Lossi,t 0 i i,t 0 ¼0

8t 2 H ,

ESS ESS ESS EESS i,t ¼ E i,t1  pi,t  Δt  Lossi,t  Δt, ESS  pESS SESS i i,t  Si

8t 2 H ,

max  E ESS  E ESS  E ESS 8t 2 H , εmin i i i,t  εi i     ESS  8t 2 H , LossESS  pESS i,t ¼ 1  ηi i,t

ð5:49Þ ð5:50Þ ð5:51Þ ð5:52Þ ð5:53Þ ð5:54Þ

ESS RURD pESS i,t  pi,t1 þ pi

8t 2 H ,

ð5:55Þ

ESS RURD pESS i,t  pi,t1  pi

8t 2 H ,

ð5:56Þ

where H and Δt are the set of time steps and the length of each time step, min respectively; EESS i,t 0 ¼0 represents the initial stored energy in BESS at bus (i); εi ,

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ESS εmax denote the minimum and maximum allowable stored energy level i , and ηi as well as the efficiency of the BESS at bus (i), respectively; and pRURD is the i charging/discharging rate of BESS at bus (i). Constraint (5.49) is defined to make sure that the sum of all stored and taken energy over all the steps of the study period is less than the initial stored energy. Similarly, constraint (5.50) is defined to keep the sum of all stored and taken energy over all the steps of the study period below the initial available capacity of BESS. Constraint (5.51) models the relationship between the state of charge and the output power of BESS at the time (t) and bus (i). Constraint (5.52) keeps BESS power below their rating power; constraint (5.53) is defined to set the minimum and maximum state of charge of BESS at bus (i); constraint (5.54) is defined to model the energy losses in each BESS at each time step; constraints (5.55) and (5.56) define the maximum charging and discharging rate of BESSs. Finally, constraint (5.54) can be written in a linear form by defining new variables as follows:

pESS i,t ¼ XX i,t  YY i,t ,

ð5:57Þ

max 0  XX i,t  SESS, , i

ð5:58Þ

max 0  YY i,t  SESS, , i   max ESS 0  LossESS ðXX i,t  YY i,t Þ  2  SESS,  DD2,i,t , i i,t  1  ηi   max ESS ðYY i,t  XX i,t Þ  2  SESS,  DD1,i,t , 0  LossESS i i,t  1  ηi

ð5:59Þ ð5:60Þ ð5:61Þ

DD1,i,t þ DD2,i,t ¼ 1,

ð5:62Þ

DD1,i,t , DD2,i,t 2 f0, 1g,

ð5:63Þ

where DD1,i,t and DD2,i,t are binary variables that identify the charging/ discharging status of the BESS. DD1,i,t ¼ 1 when the BESS is discharging, and DD2,i,t ¼ 1 when the BESS is charging. 3. Network constraints These constraints include the power flow as well as over-voltage constraints. Any other technical constraints such as thermal capacity could be also defined as a network constraint. The network constraints considered in this study are as follows: Pij,t ¼

X

Pjk,t þ pdj,t  pgj,t  pESS j,t þ r ij ℓ ij,t

8j 2 DG,

ð5:64Þ

8j 2 fN ∖DG g,

ð5:65Þ

k:j!k

Pij,t ¼

X

k:j!k

Pjk,t þ pdj,t  pESS j,t þ r ij ℓ ij,t

5 A Scenario-Based Approach for Storage Capacity Determination to Improve. . .

Qij,t ¼

X

Qjk,t þ qdj,t  qgj,t þ xij ℓij,t

105

8j 2 DG,

ð5:66Þ

8j 2 fN ∖DG g,

ð5:67Þ

k:j!k

Qij,t ¼

X

Qjk,t þ qdj,t þ xij ℓ ij,t

k:j!k

    υ j,t ¼ υi,t  2 r ij Pij,t þ xij Qij,t þ r 2ij þ x2ij ℓ ij,t ℓ ij,t ¼

P2ij,t þ Q2ij,t υi,t

8ði, jÞ 2 B,

8ði, jÞ 2 B,

υ  υi,t  υ 8i 2 N ,

ð5:68Þ ð5:69Þ ð5:70Þ

where υ represents the minimum allowable voltage in the system. Further, constraints (5.64), (5.65), (5.66), and (5.67) represent the active and reactive power balance in the network; constraints (5.68) and (5.69) represent the power flow equations in the line (i, j); constraint (5.70) would make sure that the voltage of the buses would stay in the operation range. Considering the objective function and the constraints, the defined optimization is an optimal power flow (OPF) problem. The relaxed OPF problem, which is formed by eliminating voltage and current angles from power flow equations, is still non-convex due to the quadratic constraint (5.69). This quadratic term can be approximated using a piecewise linear function. Generally, a nonlinear function f(t) can be approximated over an interval [a, b] by a piecewise linear function bf ðt Þ by using the break points a ¼ t0 < t1 < t2 < . . . < tk ¼ b as follows:

t¼

k X v¼0

λv t v ,

k X

λv ¼ 1,

λv  0

8v 2 f0, 1, 2, . . . , k g,

ð5:71Þ

v¼0

bf ðt Þ ¼

k X

λvbf ðt v Þ,

ð5:72Þ

v¼0

where t0 < t1 < t2 < . . . < tk represent the ending points of the pieces. Further, λv 8 v 2 {0, 1, . . ., k} are special order set of type 2 variables. This means that only two adjacent λv are non-zero. This restriction can be removed by using binary variables as follows: 0  λ0  w 0 , 0  λv  wv1 þ wv ,

8v 2 f1, 2, . . . , k  1g,

0  λk  wk1 ,

ð5:73Þ ð5:74Þ ð5:75Þ

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M. S. S. Abad et al. k1 X

wv ¼ 1,

ð5:76Þ

wv 2 f0, 1g:

ð5:77Þ

v¼0

This linearization technique is only valid for single variable functions. However, ℓ ij, t in constraint (5.69) is a function of (P, Q, v). Nevertheless, if it is supposed that v is fixed, then constraint (5.69) turns into a separable function. A function such as f(Var1, Var2, . . ., Varn) is called separable if it could be expressed as a summation of n single variable function such as f1(Var1), f2(Var2), . . ., fn(Varn). Thus, each single variable function can be approximated with a piecewise linear function. Please refer to [27] for more information regarding approximating the nonlinear term (5.69) with a piecewise linear function. 4. DER constraints pgi,t ¼ ηgi,t  Capgi qgi,t ¼ pgi,t  tan ðϕgi Þ

8i 2 DG, 8i 2 DG,

ð5:78Þ ð5:79Þ

where ηgi,t is the capacity factor of DER at time (t) and Capgi and ϕgi are the capacity and power factor angle of DER at bus (i).The optimization model for allocating the BESSs to minimize the costs of supplying loads is a mixed-integer linear programming (MILP).

5.5.4

Cost/Benefit Assessment

The total benefits for DER owner as well as the utility are compared to the annual cost of installing the required BESS. If the annual benefit is higher than the annual costs, using BESSs to improve the HC is justifiable.

5.6

Different Energy Storage Technologies

There are different electrical energy storages, including lead-acid (LA), sodiumsulfur (NaS), vanadium redox (VRB), and zinc/bromine (ZnBr). The comparison of different BESSs is presented in Table 5.1 based on the development status, energy, and power capital costs [30]. As can be seen, there is a considerable difference between the capital cost of these BESS technologies, which can affect the feasibility of the required BESS capacity from an economic perspective.

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Table 5.1 Comparison of the BESS technologies based on cost and development status indexes Technology Lead-acid (LA) Sodium-sulfur (NaS) Vanadium redox (VRB)

Energy storage installation cost ($/kWh)

Zinc/bromine (ZnBr)

Development status Mature Commercialized Early commercialization stage Developed

Energy capital cost (US $/kWh) 200–400 275–500 600–1500 200–400

Power capital cost (US $/kW) 200–600 1000–3000 150–1000 150–1000

1000 900 800 700 600 500 400 300 200 100 0 2016

2030

Lead acid (Flooded)

Lead acid (VRLA)

Sodium-sulfur

Sodium-Nickel chloride

Flow (VRFB)

Flow (ZBFB)

Lithium-ion (NMC/LMC) Lithium-ion (LFP) Fig. 5.12 Installation cost estimation of battery storages in 2016 and 2030

It should be mentioned that the capital cost of BESSs has been decreasing, which means that although a BESS technology might not be economically feasible now, it may become feasible in the future. Figure 5.12 shows the energy capital cost estimation for different battery technologies in 2016 and 2030 [31]. As can be seen, it is expected to have up to 66% decrease in capital costs by 2030. Similarly, it is expected to experience an increase in the efficiency of battery storages. Figure 5.13 presents the expected change in the energy capital cost as well as the efficiency of battery storage technologies in 2016 and 2030 [31].

Energy storage installation cost ($/kWh)

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M. S. S. Abad et al.

1000

2016

900 800 700 600

2016

500 400

2016 2030 2016

2016

300 200

2030

100 0 68

2016

2016 2030 2030 2030

2016 2030

2030

2030 73

78

Lead acid (Flooded) Sodium-sulfur Flow (VRFB)

83 88 93 98 Efficiency (%) Lead acid (VRLA) Sodium-Nickel chloride Flow (ZBFB)

Fig. 5.13 Estimated changes in the installation costs as well as the efficiency of battery storages from 2016 to 2030

5.7

Numerical Results

In this section, simulations are carried out to assess the performance of the proposed methodology. Initially, the effectiveness of the proposed method for identifying the minimum BESS capacity is evaluated. Then, the economic feasibility of the minimum required BESS for different technologies is discussed. Finally, the effect of DER technologies on the minimum required BESS is assessed.

5.7.1

Test System

The proposed methodology is examined on a balanced distribution system. The system is a 33-kV feeder in Australia, as shown in Fig. 5.14 [32]. This feeder is the representative of agricultural feeders in Australia, which supplies loads such as irrigation pumps and dairies. The green circles are the load points, and the total load is 4.48 MW in the test system. The maximum allowable voltage rise is 5%.

5.7.2

Input Data

Figure 5.15 represents the normalized load profile, which is used to model the load variation in the test network. The load profile is derived from the data made available

5 A Scenario-Based Approach for Storage Capacity Determination to Improve. . .

Substation

1 166 163 162

160

157 146

113

134

161

14

159 158

165

15 12

10 8

155

13 154

147

148

16

17

142

143

33

167

44

11

55

22

77

153

152

149

81

150

151

63

71

70

69

62

61 82

144

83 65

64

60

59

141

84 18

19

73

20

72

140 138

139

21

23

137

57

85

58

86

136

87 25

24 135 133 128

80 91

102 164

109

90

92 130

37

132

129

93

40 95

131

26

27 2

123

122

29

36

39

28

35

38

127 114

94 96

109

108

111

124

99 100

112

101 110

107

47

49

115

51

103

48

50

116

52

104

117

53

Fig. 5.14 Topology of an agricultural feeder in Australia

by the Australian Energy Market Operator (AEMO) [33]. The normalized PV and wind profiles are presented in Figs. 5.16 and 5.17, which are derived from [34, 35], respectively. The distribution of PV and wind sizes are derived from [25].

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1 0.9

Load profile

0.8 0.7 0.6 0.5 0.4 0.3 300 20

200

15 10

100 5

Day

Hour

Fig. 5.15 Normalized hourly load profile for New South Wales from 1/1/2014 to 30/12/2014

1

PV profile

0.8 0.6 0.4 0.2 0 300 20

200

15 10

100 Day

5 Hour

Fig. 5.16 Normalized hourly PV profiles for New South Wales from 1/1/2014 to 30/12/2014

5 A Scenario-Based Approach for Storage Capacity Determination to Improve. . .

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Fig. 5.17 Wind production profile for New South Wales from 1/1/2014 to 30/12/2014

Table 5.2 Parameters for BESS economical assessment Parameter Efficiency Unit cost for power electronic inverter (US $/kW)

LA 0.75 175

VRLA 0.75 175

NaS 0.77 1000

ZnBr 0.7 175

Unit cost for battery storage (US $/kWh) Unit cost for balance of plant (US $/kWh) Fixed operation and maintenance cost (US $/kW) Future replacement cost (US $/kWh) Number of charge/discharge life cycle

305

360

500

225

VRB 0.7 Included in the unit cost for battery storage 740

50

50

0

0

30

15

5

20

20

20

305 3200

360 1000

500 2500

225 10,000

222 10,000

Table 5.3 Electricity price data Electricity price scheme Flat Time of use (ToU)

Anytime energy (c/kWh) 29.8 –

Off-peak energy (c/kWh) – 19.6

Shoulder energy (c/kWh) – 36.8

Peak energy (c/kWh) – 45

Table 5.2 represents all the parameters required for calculating the annual installation cost of BESS for different technologies [28]. Table 5.3 shows the electricity price rate for two different schemes from Origin Energy [36]. Peak period mentioned in Table 5.3 is from 1 to 8 pm; shoulder period is from 7 am to 1 pm and from 8 to 10 pm; and off-peak period is from 10 to 7 am.

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CDF

Fig. 5.18 PV HC probability curve for the agricultural feeder

5.7.3

Hosting Capacity Discussion

PV and wind HC of the test system are estimated based on the HC calculation method presented in Sect. 5.3. Figure 5.18 presents PV HC curve for the test system, which can be approximated using the Gaussian-shape distribution as (5.80) with α ¼ 0.56, μ ¼ 19.97 MW, and σ ¼ 6.42 MW. The minimum PV HC for the test system is 3.198 MW. ðxμÞ2   α HC  α  N μ, σ 2 ¼ pffiffiffiffiffiffiffiffiffiffi e 2σ2 : 2πσ 2

ð5:80Þ

Figure 5.19 presents wind HC curve for the test system, which can be approximated using the Gaussian-shape distribution as (5.80) with α ¼ 0.956, μ ¼ 37.21 MW, and σ ¼ 0.7092 MW. The minimum wind HC for the test system is 2.92 MW. As it can be seen, the HC distribution for wind is significantly different from PV HC. This is mainly due to the difference between the wind and PV generation profiles as well as the distribution of wind and PV sizes.

5.7.4

Minimum Required BESS

The performance of the proposed methods for estimating the minimum required BESS is examined in this section. The minimum HC for PV and wind generation is 3.198 MW and 2.92 MW, respectively. Table 5.4 presents the estimated required BESS to increase the minimum HC to 4 MW.

5 A Scenario-Based Approach for Storage Capacity Determination to Improve. . . 0.6

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Histogram Gaussian PDF

0.5

Probability

0.4

0.3

0.2

0.1

0 5

10

15 20 25 Hosting Capacity (MW)

30

35

Fig. 5.19 Wind HC probability curve for the agricultural feeder

Table 5.4 Minimum required BESS to increase the HC to 4 MW for PV and wind technologies using the comprehensive and approximated methods

DER technology PV Wind

Comprehensive method Energy capacity Rating power (MWh) (MW) 5.275 0.6697 9.879 0.5212

Approximated method Energy capacity Rating power (MWh) (MW) 5.515 0.75 10.279 1.07

As can be seen, the minimum required BESS obtained by the approximated method is higher than that of the comprehensive method. However, the advantage of the approximated method over the comprehensive method is that it does not require the network model. Therefore, it can be calculated without any computational burden. The drawback of the approximated method is that it would overestimate the required BESS capacity, which could affect the feasibility of the required BESS from an economic perspective. Moreover, the minimum required BESS energy capacity for increasing the wind HC to 4 MW is 87.28% higher than that of PV HC. Further, the minimum power rating of the required BESS for wind technology is 22.17% lower than of that for PV technology. This shows that the minimum required BESS capacity in a system depends on the type of distributed energy resources that would be accommodated in that system.

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Economic Feasibility Assessment of the Required BESS

This section discusses the economic feasibility of the estimated BESS that is required for different technologies. To do so, the total annual cost of the required BESS for different technologies is compared with the annual benefits of the corresponding BESS. Table 5.5 shows the total annual cost for the required BESS estimated using the proposed comprehensive method for PV and wind technologies, respectively. As can be seen, using the ZnBr battery would result in the lowest total annual costs for both PV and wind technologies, while the valve-regulated lead-acid (VRLA) battery has the highest total annual costs. If the total annual profit of the designed battery is higher than the minimum annual costs, the designed BESS is economically feasible. Tables 5.6 and 5.7 present the optimal allocation of the required BESS in the system for both PV and wind technologies when the electricity price follows a flat rate. As can be seen, the required BESS capacity is not distributed equally. Further, the optimal BESS location for PV technology is different from that of wind technology. Tables 5.8 and 5.9 present the optimal allocation of the required BESS in the system for both PV and wind technologies when the electricity price follows a ToU rate. Observe that the required BESS capacity is not distributed equally. Further, the optimal BESS location for PV technology is different from that of wind technology. Another important factor that has a considerable impact on the allocation of the Table 5.5 Total annual costs of the required BESS for different technologies in US $ (2014) DER technology PV Wind

BESS technology LA VRLA 902,323 2,124,994 1,656,803 3,953,947

NaS 1,696,292 3,036,043

ZnBr 370,760 657,629

VRB 1,056,548 1,964,038

Table 5.6 Optimal allocation of the required BESS in the test system for PV generation when the electricity price follows the flat rate Location Energy capacity (MWh) Rating power (MW)

BESS1 149 3.6 0.3

BESS2 159 1.675 0.3697

Table 5.7 Optimal allocation of the required BESS in the test system for wind generation when the electricity price follows the flat rate Location Energy capacity (MWh) Rating power (MW)

BESS1 151 5.4 0.2643

BESS2 162 4.479 0.2569

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Table 5.8 Optimal allocation of the required BESS in the test system for PV generation when the electricity price follows the ToU rate BESS1 149 1.675 0.297

Location Energy capacity (MWh) Rating power (MW)

BESS2 159 3.6 0.3727

Table 5.9 Optimal allocation of the required BESS in the test system for wind generation when the electricity price follows the ToU rate BESS1 151 5.4 0.2468

Profit in US $ (Thousands)

Location Energy capacity (MWh) Rating power (MW)

BESS2 162 4.479 0.2744

200 180 160 140 120 100 80 60 40 20 0 PV

Wind Flat rate

ToU rate

Fig. 5.20 Utility annual profit from installing the required BESS for PV and wind generation for both flat and ToU electricity price rates

required BESS for both PV and wind technologies is the electricity price. Considering Tables 5.6 and 5.8, it can be noted that the optimal location of BESSs for both flat and ToU electricity prices is the same. However, the energy capacity and the rating power of the optimal BESSs are different. Figure 5.20 demonstrates the annual benefit that utility would gain from installing the BESSs for both PV and wind technologies. As can be seen, the annual profit of the utility with ToU tariff is higher than that of the flat tariff. Further, the BESS benefit for PV generation is much higher than that of wind generation in the test system. Moreover, the total annual profit of the utility is below the total annual costs of the minimum required BESS for different storage technologies, which might convey that BESS is not an economically feasible solution for increasing the

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US $ (Thousands)

3000 2500 2000 1500 1000 500 0 Utility DERs Utility DERs total Total LA cost VRLA NaS cost ZnBr profit profit profit profit profit Profit cost cost with flat with flat with with with flat with rate rate ToU rateToU rate rate ToU rate PV Total annual profit of BESS for PV

VRB cost

Wind Total annual profit of BESS for wind

Fig. 5.21 Total annual profit compared with the total annual cost for different BESS technologies

HC. Nevertheless, the utility benefit is only a part of the BESS benefit. DER owners also gain some benefit from avoiding active power curtailment. Figure 5.21 shows the total annual profit of both utility and DER owners compared with the total annual costs of different BESS technologies. As it can be seen, the total annual profit of the BESS with both flat and ToU electricity price rates is still lower than the total annual costs of all BESS technologies, which means that although BESSs can increase the HC of the system, they are not a feasible option from an economic perspective. However, it was also noted that the total annual profit of BESS for PV technology, when the electricity price followed ToU rate, was 325,353.00$, which is considerably close to the total annual cost of ZnBr battery technology, i.e., 370,760.00$. Another considerable point in Fig. 5.21 is that the total annual profit of BESS for wind generation is considerably lower than the total annual cost of all BESS technologies. This implies that there are a few days that the spilled wind energy is very high, but the spilled wind energy for the rest of the days is at a low level. Finally, it should be mentioned that although some of BESS technologies are economically infeasible now, it does not mean that they will continue to be infeasible in the future. As it was mentioned in Sect. 5.6, it is predicted that the price of BESSs would decrease and their efficiency would increase. Figure 5.22 presents the total annual profit of both utility and DER owners compared with the expected annual costs of different BESS technologies in 2030. As can be seen, ZnBr battery

5 A Scenario-Based Approach for Storage Capacity Determination to Improve. . .

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3500 3000

US $ (Thousands)

2500 2000 1500 1000 500 0 Utility DERs Utility DERs total Total LA cost VRLA NaS cost ZnBr profit profit profit profit profit Profit cost cost with flat with flat with with with flat with rate rate ToU rateToU rate rate ToU rate

VRB cost

PV Wind Total annual profit of BESS for PV with ToU rate Total annual profit of BESS for wind with ToU rate Total annual profit of BESS for PV with flat rate

Fig. 5.22 Expected total annual profit in 2030 compared with the total annual cost for different BESS technologies

technology is expected to be economically feasible in 2030 with both flat and ToU electricity rates for PV technology. However, even the future decrease in the price of energy storages would not make BESSs a feasible option for increasing the HC for wind technology.

5.8

Summary

Technical issues such as over-voltage and overloading of lines and transformers bound DERs that could be accommodated in distribution systems. Therefore, it is of great importance to know how distribution systems can accommodate a higher level of DERs. This chapter proposed a comprehensive method and an approximated approach to identify the minimum required battery energy storage to increase the HC of a system to a certain level. The comprehensive method aims to maximize the injected power in the system while minimizing the curtailed energy. The outcomes of this methodology are the minimum required power and energy capacity rating of BESSs to increase the HC of the system. The second step of the methodology is the economic assessment of the determined BESSs. The performance of the

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comprehensive and approximated methods is assessed on an agricultural distribution system in Australia. It was shown that the approximated method result is the solution of the comprehensive method with an error of 5%. Then, the cost/benefit analysis is carried out to assess the feasibility of the obtained BESSs. It was shown that the BESS technology highly affects the feasibility of BESSs for HC improvement. Further, it was demonstrated that none of the considered BESS technologies is economically feasible for increasing the HC of the test system. Next, the impact of DER technology (i.e., photovoltaics and wind) on the size as well as the economic feasibility of the required BESS was assessed. It was shown that the required BESS for increasing the HC of the test system for PV technology is 46.6% less than what is required for wind technology. Moreover, it was demonstrated that the use of BESS for increasing the HC of the system for PV technology would be economically feasible in 2030. However, the use of BESSs for increasing the HC would not be a feasible option for wind technology in the test system in 2030. Another factor that has been assessed in this chapter was the effect of electricity price on the allocation of the required BESS. It was shown that the ToU electricity price rate would yield in a higher profit level for the utility than the flat electricity price rate, i.e., 12.78% for PV and 126.8% for wind technology. Further, it was noted that the electricity price rate did not affect the optimal location of the required BESSs. It, however, would affect the energy capacity and rating power of the allocated BESSs in the system.

5.9

Future Works

As it was shown, community BESS could be an economically feasible solution to increase the HC. However, there are other viable options such as using the on-load tap changer (OLTC) of transformers, reactive power control of DERs, and reactive power resources such as reactors. Although the aforementioned options could increase the power losses in the system, they would decrease the APC by increasing the HC. Therefore, these options could also be feasible from an economic point of view. Thus, to choose the best option to increase the HC, a techno-economical assessment should be performed to compare the profits of community BESS, transformer’s OLTC, DER-based reactive power control, and reactive power sources such as reactors. The second research question that could be addressed in the future is whether residential BESSs could substitute community BESSs. The penetration level of residential BESSs has been increasing in the recent years. Although residential BESSs could be used to store the excess energy, they are usually controlled in a way to maximize the profit of the prosumers. However, the best control scheme from the prosumers’ point of view could be different from the best control scheme from the network viewpoint. Thus, there is no guarantee that the aggregated residential BESSs would increase the HC in the same way as community BESSs. Therefore, if it is supposed that the required community storage to increase the HC to a certain level (HCref) is (BESSCOM), we would like to estimate the required residential BESSs that would increase the HC to the same HC level (HCref).

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20. Jalali, A., & Aldeen, M. (2019). Risk-based stochastic allocation of ESS to ensure voltage stability margin for distribution systems. IEEE Transactions on Power Systems, 34(2), 1264–1277. 21. Li, Q., Ayyanar, R., & Vittal, V. (2016). Convex optimization for DES planning and operation in radial distribution systems with high penetration of photovoltaic resources. IEEE Transactions on Sustainable Energy, 7(3), 985–995. 22. Giannitrapani, A., et al. (2017). Optimal allocation of energy storage systems for voltage control in LV distribution networks. IEEE Transactions on Smart Grid, 8(6), 2859–2870. 23. Dusonchet, L., et al. (2019). Technological and legislative status point of stationary energy storages in the EU. Renewable & Sustainable Energy Reviews, 101, 158–167. 24. Telaretti, E., & Dusonchet, L. (2017). Stationary battery technologies in the US: Development trends and prospects. Renewable & Sustainable Energy Reviews, 75, 380–392. 25. Seydali Seyf Abad, M., et al. (2018). Probabilistic assessment of hosting capacity in radial distribution systems. IEEE Transactions on Sustainable Energy, 9(4), 1935–1947. 26. Dubey, A., Santoso, S., & Maitra, A. (2015). Understanding photovoltaic hosting capacity of distribution circuits. In 2015 IEEE Power & Energy Society General Meeting, Denver, CO, pp 1–5. 27. Seydali Seyf Abad, M., Ma, J., & Han, X. (2019). Distribution systems hosting capacity assessment: Relaxation and linearization. In Smart power distribution systems (pp 555–586). Cambridge, Massachusetts, USA: Elsevier. 28. Poonpun, P., & Jewell, W. T. (2008). Analysis of the cost per kilowatt hour to store electricity. IEEE Transactions on Energy Conversion, 23(2), 529–534. 29. Lori Bird, J. C., & Wang, X. (2014). Wind and solar energy curtailment: Experience and practices in the United States. Golden: National Renewable Energy Laboratory. 30. Akinyele, D., Belikov, J., & Levron, Y. (2017). Battery storage technologies for electrical applications: Impact in stand-alone photovoltaic systems. Energies, 10(11), 1760–1799. 31. Pablo Ralon, M. T., Ilas, A., Diaz-Bone, H., & Kairies, K.-P. (2017). Electricity storage and renewables: Costs and markets to 2030. Australia: IRENA. 32. Berry, A., et al. (2013). National feeder taxonomy; describing a representative feeder set for Australian networks. Newcastle: CSIRO. 33. AEMO, National transmission network development plan 2015. 2015. 34. Pfenninger, S., & Staffell, I. (2016). Long-term patterns of European PV output using 30 years of validated hourly reanalysis and satellite data. Energy, 114, 1251–1265. 35. Staffell, I., & Pfenninger, S. (2016). Using bias-corrected reanalysis to simulate current and future wind power output. Energy, 114, 1224–1239. 36. Energy, O. (2018). NSW residential energy price fact sheet. NSW, Australia: Origin Energy.

Chapter 6

Impact of Capacity Withholding on Hosting Capacity Analyzing Saeed Salarkheili and Mehrdad SetayeshNazar

6.1

Introduction

Many vertically integrated power companies have been restructured worldwide during the last three decades for improving the competitiveness and efficiency of energy industry [1]. However, a perfectly competitive power market does not exist in real world, and most of the present electricity markets can be considered as oligopoly electricity markets [2]. Some generation companies (GenCos), in these imperfect competition situations, possess market power to obtain more profits at the cost of other market players. Strategies of market power can be categorized as capacity withholding and financial withholding. When either strategy is successful, higher profits of GenCos and lower market performance are expected [3–7]. Various indices and models should be used by market monitoring to analyze GenCos’ market power in electricity markets [3–7]. In addition, regulators should use market power mitigation problem. A proper program for the mitigation of market power can force the extra producer surpluses acquired by the GenCos’ market power back to the customer side. The 2000–2001 California electricity crisis demonstrated that the programs for market power mitigation play a key role for electricity markets. In fact, the capacity withholding of GenCos which was aggravated by the tight conditions of market during the summer of 2000 combined with the absence of proper programs for market power mitigation to create energy market crisis. It means that the GenCos’ capacity withholding can lead to high market prices and scarcity of generation capacity. Implementing capacity withholding analyzing in the process of S. Salarkheili (*) Faculty of Electrical Engineering, Shahid Beheshti University, A.C, Tehran, Iran Tehran Regional Electric Company (TREC), Tehran, Iran e-mail: [email protected] M. SetayeshNazar Faculty of Electrical Engineering, Shahid Beheshti University, A.C, Tehran, Iran © Springer Nature Switzerland AG 2020 A. F. Zobaa et al. (eds.), Hosting Capacity for Smart Power Grids, https://doi.org/10.1007/978-3-030-40029-3_6

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hosting capacity (HC) analyzing can cause to select proper capacities and locations of DGs to mitigate capacity withholding in power markets. In this chapter, capacity withholding analyzing of GenCos is described and different indices are proposed. In Sect. 6.2, the effect of generation limits on the capacity withholding of GenCos is analyzed. In the next section, the capacity withholding of GenCos is evaluated in transmission-constrained power markets. In Sect. 6.4, the mitigation of capacity of withholding of GenCos and the impact of DGs on capacity withholding are described.

6.2

Capacity Withholding Analyzing by Considering Capacity Constraints

In an oligopoly market GenCos is able to exercise market power through different bidding strategies. As mentioned above, capacity withholding and financial (economic) withholding are the two parts of market power. Financial withholding means that GenCos bid their full capacity but increase their bidding prices extremely above their marginal cost to acquire higher profits. Since the market operator almost knows GenCos’ marginal costs, financial withholding is usually easily detected and, then, hard to implement in electricity markets with working market monitoring mechanisms in place. On the other hand, GenCos’ capacity withholding can be justified by pointing to operational requirements, which are not easy to verify and challenge by authorities. In addition, capacity withholding can cause high-cost power units to operate and increase the electricity market price. The ability of a GenCo to exercise capacity withholding depends on its capacity limits, parameters of cost function, transmission network limits, and the elasticity of electricity demand. In this section, the effects of capacity constraints and demand elasticity are assessed.

6.2.1

Power Market Modeling

Noncollusive game models such as Cournot and supply function equilibrium (SFE) models are broadly used for analyzing of market power [3–30]. The Cournot model is used in this chapter to represent the strategic GenCos’ behavior in the presence of elastic demands. Therefore, the theory of Cournot-NE (CNE) is used to find the market equilibrium considering the GenCos’ capacity withholding. Suppose in the market there are N GenCos and each GenCo has the following cost function: ci ¼ 0:5ai q2i þ bi qi

i ¼ 1, . . . , N

ð6:1Þ

6 Impact of Capacity Withholding on Hosting Capacity Analyzing

123

where qi is the quantity generated by GenCo i and ai and bi are the coefficients of the GenCo’s cost function with ai  0 and bi  0. The aggregate demand function is λ ¼ αY þ β α>0 where Y ¼

N P

ð6:2Þ

yi and the transmission loss is ignorable. α and β are parameters of the

i¼1

aggregate demand function and λ is the electricity market price. Each GenCo seeks in the market to maximize its profit (Ωi), and the optimization problem faced by GenCo i is determined as follows: max

Ωi ¼ qi λ  c i

s:t:

qmin  qi  qmax i i

ð6:3Þ

where qmax and qmin are upper and lower production constraints of GenCo i, i i respectively. The Lagrange function of the problem (6.3) is     Li ¼ qi λ  ci þ θmax qi  qmax qi  qmin  θmin i i i i

ð6:4Þ

where θmax and θmin are Lagrange multipliers associated with lower and upper i i production limits of GenCo i, respectively. Differentiating the (6.4) with respect to qi and setting it as zero obtains ∂Li ∂λ ¼ qi þ λ  ai qi  bi þ θmax  θmin ¼0 i i ∂qi ∂qi

ð6:5Þ

In a perfectly competitive market, all GenCos are not price maker and the term ∂π/∂yi in (6.5) is equal to zero. But in an oligopoly market, GenCos are not price taker and they are price taker and ∂π/∂yi 6¼ 0 in (6.5) can be yields. So qi of GenCo i under perfect competition can be obtained by qi ¼

λ  bi  θmax þ θmin i i ai

ð6:6Þ

According to (6.5) and by using (6.2), qi each GenCo under Cournot model can be obtained by qi ¼

λ  bi  θmax þ θmin i i ð α þ ai Þ

ð6:7Þ

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Capacity Withholding Indices

Many indices have been proposed for market power assessment. There are different categorizations for indices of market power. One of them categorizes indices of market power into comparison and concentration indices. In comparison indices, the oligopoly market’s results are compared with those of perfectly competitive market, and concentration indices are based on the GenCos’ market shares. As another categorization, the indices of market power can be classified into ex ante indices, based on the simulation tools and market models, and ex post indices, in which the results of real market are used. As a third categorization, there are global and nodal indices. The nodal indices are used for analyzing of market power in each bus of power system, and global indices assess the market power in the whole system. Nodal indices are appropriate for transmission-constrained power markets [26–29]. A set of comparison indices is used in this chapter to analyze the capacity withholding of GenCos. In the proposed indices, the results of oligopoly market are compared with those of two types of markets: perfectly competitive market with the nodal prices of oligopoly market and perfectly competitive market. The superscripts e, p, and p(e) are used for the values associated with the equilibriums of oligopoly market, perfectly competitive market, and perfectly competitive market with the nodal prices of oligopoly market, respectively. It should be noted that in this section, the transmission constraints are ignored and nodal prices are equal. Based on (6.6) and (6.7), the generation of GenCo i under perfectly competitive market (qpi ) can be determined by qpi ¼

λp  bi  θpi max þ θpi min ai

ð6:8Þ

where θpi max and θpi min are Lagrange multipliers associated with upper and lower production constrains of GenCo i under perfectly completive market, respectively. The generation of GenCo under oligopoly market (qei ) can be written as qei ¼

λe  bi  θei max þ θei min ð ai þ α Þ

ð6:9Þ

where θei min and θei max are Lagrange multipliers associated with lower and upper production limits of GenCo i under oligopoly market, respectively. The generation of GenCo under perfectly competitive market with the nodal prices of oligopoly market can be also written as pðeÞ

qi

¼

pðeÞ max

λ e  bi  θ i

ai

pðeÞ min

þ θi

ð6:10Þ

6 Impact of Capacity Withholding on Hosting Capacity Analyzing

125

p

Fig. 6.1 Capacity withholding indices

Strategic offer

Marginal cost curve

le lp

Dldistortion

Demand curve Dqidistortion qei

pðeÞ max

q

e

p i

qp(p )i

q

pðeÞ min

where θi and θi are Lagrange multipliers associated with upper and lower production constraints of GenCo i under perfectly competitive market with the nodal prices of oligopoly market, respectively. Aforementioned results were used to formulate the capacity withholding index (Δqwithheld ), capacity distortion index (Δqdistortion ), and price distortion index i i distortion (Δλ ). These indices were defined as the following: pðeÞ

Δqwithheld ¼ qi i

 qei

ð6:11Þ

Δqdistortion ¼ qpi  qei i

ð6:12Þ

Δλdistortion ¼ λe  λp

ð6:13Þ

DWI ¼

ΔQdistortion ΔQwithheld

ð6:14Þ

As shown in Fig. 6.1, λ p is the competitive market clearing price and qpi is the GenCo i’s competitive generation. The output of GenCo i decreases to qei , and the pðeÞ market clearing price increases to λe due to the capacity withholding. qi is the e competitive output which would be generated at λ by GenCo i. In (6.14), N N P P ΔQwithheld ¼ Δqwithheld and ΔQdistortion ¼ Δqdistortion . The capacity withholding i i i¼1

i¼1

indices are reported in Fig. 6.1. DWI ranges from 0 to 1 as it analyzes the market power of GenCos from the perspective of their potential ability for capacity withholding. DWI indicates a decrement in the ability of GenCos for capacity withholding when it approaches 1. In contrast, when this index is lower, it is more likely that producers have a high potential ability for capacity withholding. It can be seen that when market power is low, the GenCos will have less incentive to raise the market pðeÞ price. It means that λe, qi , and Δqwithheld approach λ p, qpi, and Δqdistortion , i i respectively. It means that DWI approaches 1, as a result of the changes in both Δqwithheld and Δqdistortion . i i

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Substituting (6.10) and (6.9) into (6.11) yields ¼ Δqwithheld i pðeÞ max

Δθwithheld ¼ θi i

α e Δθwithheld q þ i αi i ai pðeÞ min

þ θei min  θi

ð6:15aÞ  θei max

ð6:15bÞ

is influenced by the slope of aggregate demand It can be seen that Δqwithheld i function and slope of marginal cost functions of GenCos (α/ai ratio). Therefore, a GenCo with small slope of marginal cost function has a high potential ability to withhold the capacity. Substituting (6.8) and (6.9) into (6.12) produces Δqdistortion ¼ i N X

 Δθdistortion α e qi  ΔQdistortion þ i ai ai

ð6:16aÞ

Δqdistortion ¼ ΔQdistortion i

ð6:16bÞ

i¼1

Δθdistortion ¼ θpi max þ θei min  θpi min  θei max i

ð6:16cÞ

It can be seen that the value of capacity distortion index may be negative or positive. It depends on slope of the marginal cost functions of GenCos and the slope of aggregate demand function. It is to be mentioned that α/ai ratio is significant for analyzing the ability of GenCos for capacity withholding. For GenCos with large ratio of α/ai, capacity distortion index may be positive. This shows that the generation of these GenCos has been decreased with respect to the perfectly competitive market. It means that these GenCos indirectly can control the market price and make the GenCos with small α/ai ratio become the marginal producers by capacity withholding. It may cause the producers with small α/ai to produce more than their perfectly competitive generations (qpi), and for them qei > qpi (Δqdistortion < 0) can be i achieved. Δθwithheld Δθdistortion The terms i ai and i ai represent the effect of the capacity limits of GenCos on capacity withholding. Then, we would have 8 pðeÞ >  qi  qmax when qmin > i i

> : pðeÞ > 0 when qi ¼ qmin i 8 min when qi  qpi  qmax > i

: > 0 when qpi ¼ qmin i

ð6:17Þ

ð6:18Þ

6 Impact of Capacity Withholding on Hosting Capacity Analyzing

127 pðeÞ

It should be noted that according to (6.8), (6.9), and (6.10), qei  qpi  qi can be pðeÞ obtained. It means that if qi is between qmin and qmax , qei and qpi are also between i i and qmax . qmin i i By using (6.2), Δπ distortion can be obtained by Δλdistortion ¼ αY e þ β  ðαY p þ βÞ ¼ αΔQdistortion Ye ¼

N X

ð6:19aÞ

qei ¼ Qe

ð6:19bÞ

qpi ¼ Qp

ð6:19cÞ

i¼1

Yp ¼

N X i¼1

Ideally, with the increase of the total capacity distortion (ΔQdistortion), the expected outcome would be the increment in Δqdistortion . (6.19) represents that i Δqdistortion is affected by the aggregate demand function’s slope. It indicates that in i a market with a large slope of demand function, producers will have more potential ability to increase the market price. By summing capacity distortions of all GenCos in (6.16), ΔQdistortion can be obtained by N  P α

ΔQdistortion ¼

i¼1

ai

qei þ

1þ

Δθdistortion i ai

N P i¼1

 ð6:20Þ

α ai

Based on (6.20), DWI can be determined by 0  1 N 1 P Δθdistortion α e i 1 B C a qi þ ai C B CBi¼1 i N ¼@ P C AB N   α @P withheld A 1þ Δθi α e ai q þ i¼1 ai i ai 0

DWI ¼

ΔQdistortion ΔQwithheld

ð6:21Þ

i¼1

DWI can be obtained by DWI ¼ DWIuc  CF DWIuc ¼ 1þ

1 N P i¼1

ð6:22aÞ ð6:22bÞ

α ai

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S. Salarkheili and M. SetayeshNazar N  P α

CF ¼

e a i qi þ

Δθdistortion i ai

α ai

Δθwithheld i ai

i¼1 N  P i¼1

qei

þ

 ð6:22cÞ



The superscript uc shows the unconstrained production. It can be seen that in the case of limited production, this index is composed of two parts. The first part is unconstrained DWI (DWIuc) which is independent of the market model. The second part is constraint factor of DWI (CF) which indicates the decrease of the potential ability of GenCos for capacity withholding due to the capacity limits. If no GenCo is pðπ e Þ binding at its generation constraints (i.e., qmin < qi < qmax ), that means i i withheld distortion ¼ Δθi ¼ 0 and CF ¼ 1, and then DWI ¼ DWIuc can be obtained. Δθi

6.2.3

Case Study

We present the case study of GenCos’ capacity withholding by using a three GenCo power system. The GenCos’ cost parameters are shown in Table 6.1. The aggregate demand parameters are α ¼ 2 $/(MW2) and β ¼ 90 $/MW. We have used GAMS software and CONOPT solver to solve the optimization problems of the case study. The following simulation cases are carried out: Case A Case B Case C Case D

Perfect competition Cournot-type competition Cournot-type competition with decrease in demand elasticity Cournot-type competition with decrease in demand elasticity and capacity of GenCos

The simulation results of cases A and B are listed in Table 6.2. It is assumed that pðeÞ the generation upper limits of GenCos are greater than qi . Therefore, the production constraints can be disregarded in the analyzing of capacity withholding indices. These indices are listed in Table 6.3. It can be observed that the capacity withholding of GenCo 1 is higher than the others due to its small slope of the marginal cost. To analyze the impacts of capacity limits of GenCos and demand elasticity on capacity withholding, two cases C and D are performed. In these cases, GenCos use Cournot-type competition and the demand function’s slope is decreased from α ¼ 2 Table 6.1 Cost parameters GenCo no. 1 2 3

Cost parameter ai ($/MW2) 1 1.5 2

Cost parameter bi ($/MW) 12 10 8

qmin (GW) i 0.3 0.8 1

qmax (GW) i 30 25 20

6 Impact of Capacity Withholding on Hosting Capacity Analyzing

129

Table 6.2 Simulation results for cases A, B, C1, C2, C3, and C4 Case A

B

qei (GW) – – – 9.11 8.38 7.83

GenCo no. 1 2 3 1 2 3

pðeÞ

qpi (GW) 13.375 10.250 8.687 – – –

λ ($/MW) 25.375

qi (GW) – – – 27.330 19.553 15.660

39.34

Table 6.3 Capacity withholding indices for case B case B

GenCo no. 1 2 3

Δqwithheld (GW) i 18.220 11.173 7.830

Δqdistortion (GW) i 4.262 1.868 0.851

Δλdistortion ($/MW) 13.96

DWI 0.187

5

DWI

4 3 2 1 0

α=1. α=1. α=1. α=0. α=0. α=0. α=0. α=1 7 5 3 8 5 4 3 DWI(Case C) 0.187 0.214 0.235 0.262 0.315 0.365 0.488 0.532 0.606 DWI(Case D) 1 0.816 0.672 0.536 0.339 0.365 0.488 0.532 0.606 α=2

CF(Case D)

5.34 3.82 2.85 2.04 1.07

1

1

1

1

Fig. 6.2 Illustration of the simulation results for cases C and D

$/(MW2) to α ¼ 0.3 $/(MW2) while keeping the demand function’s intercept constant. It is also assumed that the generation upper constraints of GenCos 1, 2, and 3 in case D are decreased to 13 GW, 10 GW, and 9 GW, respectively. It can be observed in Fig. 6.2 that in case C and in the considered range of incremental demand elasticity, DWI is increased from 0.187 to 0.606. In case D, DWI first decreases from 1 to 0.339 with the decrease of the slope of demand function from α ¼ 2 $/(MW2) to α ¼ 1 $/(MW2). Then, with further increase of demand elasticity, it increases from 0.339 to 0.606. The coefficient accounts for the marginal impacts of capacity limits on DWI. It can be seen that DWI will be decreased if CF is greater than 1. The opposite changing trends of DWI in cases C and D indicate that the potential ability of GenCos for capacity withholding is increased up to the point where α is equal to 0.8 $/(MW2). It means that, with the increase of demand

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elasticity, the expected result in terms of DWI would be a decreasing pattern along with the releasing capacities of generation until the minimum value of CF (CF ¼ 1) is reached. The value 1 of CF indicates that the values of DWI in cases C and D are pðeÞ equal and for all GenCos (qi < qmax ). i

6.3

Capacity Withholding Analyzing in Transmission-Constrained Market

In the electricity markets, the potential ability of GenCos for capacity withholding increases during the transmission congestion [3, 4, 15, 18, 25, 28, 29]. In Sect. 6.2, a method for the capacity withholding analyzing of GenCos in electricity markets based on some comparison indices has been presented. These indices can be used for the capacity withholding assessment of GenCos. However, the impacts of transmission network congestion have been not considered in them, and they cannot be used for nodal capacity withholding analyzing during the transmission congestion. This section presents the development of the aforementioned method and offers some contributions in comparison with the previous section. 1. Market model is extended to evaluate the transmission limits and other parameters that affect GenCos’ capacity withholding. 2. Nodal capacity distortion index, nodal price distortion index, and nodal capacity withholding index are formulated to assess the effect of transmission network congestion on GenCos’ capacity withholding. In addition, DWI is reformulated to include the transmission network limits. 3. In order to evaluate the potential ability of GenCos for exerting capacity withholding by considering the transmission congestion, a new index, called nodal withholding-supply ratio (NWSR), is defined in this section.

6.3.1

Power Market Modeling

The main goal of this subsection is to model the capacity withholding of GenCos during transmission congestion. This will be done by modeling a game theory-based formulation. The Cournot model is consider to model the strategic behavior of generators in the presence of demand elasticity. Then, the model of Cournot-Nash equilibrium (CNE) is applied to calculate the market equilibrium considering the GenCos’ capacity withholding. For the sake of simplicity, the market equilibrium model is first formulated with any constraints; then it is extended for the market with transmission congestion.

6 Impact of Capacity Withholding on Hosting Capacity Analyzing

131

Suppose that there are I GenCos in the power market, and each of them has a generation unit. The cost function of GenCo at bus i is determined as follows: ci ¼ 1=2ai q2i þ bi qi :

ð6:23Þ

The consumption at bus j is supposed as an inverse demand function: λ j ¼ α j y j þ β j :

ð6:24Þ

If there is no transmission congestion, the nodal price at bus n, λn and the price at the reference bus λ are equal. By ignoring the transmission losses, the generation of all GenCos and the aggregate demand are the same as described in (6.25) X X X X qi ¼ y j ¼ λ 1=α j þ β j =α j ¼ λ=αequal þ βequal =αequal i2I

j2J

j2J

ð6:25Þ

j2J

where αequal and βequal are equivalent parameters of the aggregate demand. Based on (6.25), the aggregate demand function can be expressed as an inverse demand function as follows: λ ¼ αequal

X

y j þ βequal :

ð6:26Þ

j2J

6.3.1.1

Market Equilibrium Without Considering Generation and Transmission Limits

Each GenCo in the market competes with the others to maximize its own profit by choosing its generation. The maximization problem of a GenCo at bus i can be written as max Ωi ¼ λi qi  ci :

ð6:27Þ

ISO also seeks to maximize social welfare. GenCos in a perfectly competitive market cannot affect the market price, and there is no strategic behaviors. However, the market price can be influenced by the capacity withholding of GenCos in an oligopoly market. Then, social welfare can be decreased compared with that of perfectly competitive market. In an oligopoly market with Cournot model, the of market equilibrium problem can be described as a nonlinear programming (NLP) problem as follows:

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max

Xh j2J

1=2α j y2j

þ β jy j

i

! X  X  2 equal 2 1=2ai qi þ bi qi  1=2α qi  i2I

i2I

X X y j ¼ 0: s:t: qi  i2I

ð6:28Þ ð6:29Þ

j2J

Equation (6.28) shows the decreased social welfare in Cournot model due to the GenCos’ capacity withholding and includes three terms: • Demands’ cost • GenCos’ cost • Reduction in social welfare due to the capacity withholding of GenCos The first two terms explain the social welfare in a perfectly competitive market. By involving the third term, the market is cleared at the CNE point; otherwise, the market is cleared at the perfect competition point. In fact, the third term explains the effect of oligopolistic competition on the social welfare of perfectly competitive market. It is to be considered that in the problem (6.28 and 6.29), the optimization problems of each GenCo is implicit. By solving this single optimization problem, the generations of all GenCos are determined [28, 29].

6.3.1.2

Market Equilibrium Model by Considering Generation and Transmission Limits

Given the strategic decisions of GenCos, the ISO would determine the corresponding generation of GenCos, the consumption of loads, and each node’s price by solving the market clearing problem based on DC power flow. The ISO’s optimization problem in Cournot model can be written in the vector form as j max

in which

k j k j k 1=2yT αy þ yT β  1=2qT aq þ qT b  1=2qT αequal q

ð6:30Þ

s:t: eTI q  eTJ y ¼ 0   F  T q  y  F

ð6:31Þ

qmin  q  qmax

ð6:33Þ

ymin  y  ymax :

ð6:34Þ

ð6:32Þ

6 Impact of Capacity Withholding on Hosting Capacity Analyzing

q=y

Vector

of

generation/load,

133

q ¼ ½q1 , q2 , . . . , qi , . . . , qI T ðMWÞ,

 T y ¼ y1 , y2 , . . . , y j , . . . , yJ ðMWÞ qe =qp qpðeÞ a=b α=β

a/α pmax =pmin ymax =ymin F T T TI =T TJ Tmn eI =eJ

Vector of generation in oligopoly/perfectly competitive market (MW) Vector of generation in perfectly competitive market with the nodal prices of oligopoly market (MW) Vector of slope/intercept of GenCos’ marginal cost function, a ¼ ½a1 , a2 , . . . , ai , . . . , aI T ($/MW2), b ¼ ½b1 , b2 , . . . , bi , . . . , bI T ($/MW) Vector of slope/intercept of inverse demand functions, α ¼  T  T ($/MW2), β ¼ β1 , β2 , . . . , β j , . . . , βJ α1 , α2 , . . . , α j , . . . , αJ ($/MW) Diagonal matrix of the vector a=α Vector of maximum/minimum generation capacity constraints of GenCos (MW) Vector of maximum/minimum demand capacity constraints of consumers (MW) Vector of power transmission line flow constraints, F ¼ ½F 1 , F 2 , . . . , F m , . . . , F M T (MW) Power transfer distribution factors (PTDFs) matrix Rows of transposed T matrix for generation/consumption buses Element of T matrix Identity vector with I/J dimension

The key point of Cournot model is to solve the optimization problem of the social welfare subject to generation and consumption balance, transmission network limits, and capacity limits of GenCos. The Lagrangian function of the problem (6.30, 6.31, 6.32, 6.33, and 6.34) can be expressed as i h i   h L q, y, λ, μþ , μ , θmax , θmin , ωmax , ωmin ¼ 1=2yT αy þ yT β  1=2qT aq þ qT b h i   h   i h   i  1=2qT αequal q þ λ eTI q  eTJ y  μTþ T q  y  F þ μT T q  y þ F         θT max q  qmax þ θT min q  qmin  ωT max y  ymax þ ωT min y  ymin : ð6:35Þ The Karush-Kuhn-Tucker (KKT) constraints that are significant for optimality of (6.35) can be obtained by

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    ∂L=∂q ¼ aq  b  αequal q þ λIq  T TI μþ  μ  θmax  θmin ¼ 0     ∂L=∂y ¼ αy þ β  λIy þ T TJ μþ  μ  ωmax  ωmin ¼ 0 eTI q  eTJ y ¼ 0   FT qy F qmin  q  qmax ymin  y  ymax h   i μþ T q  y  F ¼ 0 h   i μ T q  y þ F ¼ 0   θmax q  qmax ¼ 0   θmin qmin  q ¼ 0   ωmax y  ymax ¼ 0   ωmin ymin  y ¼ 0 μþ , μ , θmax , θmax , ωmax , ωmin  0: ð6:36Þ where μþ =μ μeþ =μe μpþ =μp θmax =θmin θe max =θe min θp max =θp min θpðeÞ max =θpðeÞ min

Vector of Lagrangian multiplier associated with positive/ negative direction of transmission line flow constraints ($/MW) Vector of Lagrangian multiplier in oligopoly market associated with positive/negative direction of transmission line flow constraints ($/MW) Vector of Lagrangian multiplier in perfectly competitive market associated with positive/negative direction of transmission line flow constraints ($/MW) Vector of Lagrangian multiplier associated with maximum/ minimum generation capacity constraints of GenCos ($/MW) Vector of Lagrangian multiplier in oligopoly market associated with maximum/minimum generation capacity constraints of GenCos ($/MW) Vector of Lagrangian multiplier in perfectly competitive market associated with maximum/minimum generation capacity constraints of GenCos ($/MW) Vector of Lagrangian multiplier in perfectly competitive market with the nodal prices of oligopoly market associated with

6 Impact of Capacity Withholding on Hosting Capacity Analyzing

135

maximum/minimum generation capacity constraints of GenCos ($/MW) Vector of Lagrangian multiplier associated with maximum/ minimum demand capacity constraints of consumers ($/MW) Properly dimensioned zero vector

ωmax =ωmin 0

The first two terms of (6.36) show the derivatives of (6.35) with respect to generation and consumption, respectively. Then, the generation of GenCo at bus i and the consumption of load at bus j can be written as the following equations, respectively: λ  bi  qi ¼

P m2M

μþ m T mi þ

P m2M

max μ þ θmin m T mi  θ i i

ð6:37Þ

ðai þ αequal Þ P þ P  λ þ β j þ μm T mj þ μm T mj  ωmax þ ωmin j j yj ¼

m2M

m2M

:

αj

ð6:38Þ

The nodal price at bus n can be obtained by λn ¼ λ 

X m2M

μþ m T mn þ

X m2M

μ m T mn :

ð6:39Þ

If there is no transmission congestion, the Lagrangian multipliers associated with the transmission line flow constraints are zero. Then, according to (6.39), λn ¼ λ can be achieved. However, when there is transmission congestion, the Lagrangian multiplier at each node shows the nodal price λn.

6.3.2

Capacity Withholding Indices

Nodal capacity withholding index and NWSR can be used for analyzing GenCos’ market power. They compare the generations at oligopoly market and perfectly competitive market with the nodal prices of oligopoly market. Nodal price distortion indices and nodal capacity distortion can be used to analyze the distortions of the oligopoly market from perfectly competitive market. pðeÞ

Δqwithheld ¼ qi i Δqdistortion ¼ i

qpi

 qei :

ð6:40Þ

 qei :

ð6:41Þ

Δλdistortion ¼ λen  λpn : n

ð6:42Þ

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NWSRi ¼ Δqwithheld =qei : i

ð6:43Þ

According to (6.37) and (6.39), qei can be written as qei ¼

λei  bi  θei max þ θei min ðai þ αequal Þ

ð6:44Þ

where λei can be expressed as λei ¼ λe 

X m2M

μeþ m T mi þ

X m2M

μe m T mi :

ð6:45Þ

The generation of each GenCo in perfectly competitive market can be determined by neglecting the third term in (6.30). Therefore, qpi could be written as qpi ¼

λpi  bi  θpi max þ θpi min ai

ð6:46Þ

where λpi can be obtained by λpi ¼ λp 

X m2M

pðeÞ

Based on (6.46), qi

X m2M

μp m T mi :

ð6:47Þ

can be determined by

pðeÞ

qi

μpþ m T mi þ

pðeÞ max

¼

λei  bi  θi

ai

pðeÞ min

þ θi

:

ð6:48Þ

Because of GenCos’ capacity withholding, the nodal prices and the generations of GenCos deviate from their perfectly competitive levels to oligopoly. Then, the nodal capacity distortion and the nodal price distortion can be formulated as Δqdistortion ¼ i qpi  qei and Δλdistortion ¼ λen  λpn , respectively. It is to be noted that the withheld n capacity for each GenCo is not equal to qpi  qei ; rather, it is formulated as pðeÞ Δqwithheld ¼ qi  qei , indicating that the generation of GenCo at bus i with nodal i pðeÞ price λei would be qi but, in fact, it was reduced to qei because of the capacity pðeÞ withholding of GenCo in the oligopoly market. It should be noted that qi is the e competitive generation, which could be generated at λi by GenCo at bus i. According to (6.46) and (6.47), if GenCo at bus i does not hit its generation capacity constraints, pðeÞ > Δqdistortion can be obtained. qi gets larger than qpi ; then, Δqwithheld i i By substituting (6.44) and (6.48) into (6.40), Δqwithheld can be determined by i

6 Impact of Capacity Withholding on Hosting Capacity Analyzing

137

  Δqwithheld ¼ 1=ai αequal qei  Δθwithheld i i pðeÞ max

ð6:49Þ

pðeÞ min

where Δθwithheld ¼ θi þ θei min  θi  θei max . i According to (6.49), NWSRi of GenCo at bus i can be obtained by   NWSRi ¼ 1=ai αequal  Δθwithheld =qei : i

ð6:50Þ

Based on (6.50), it is possible to analyze the different parameters that influence the capacity withholding of GenCos. If the GenCo at bus i does not exceed its pðeÞ pðeÞ max generation capacity limits (qmin < qei , qi < qmax ), that means θi ¼ θei min ¼ i i pðeÞ min equal e max θi ¼ θi ¼ 0, and then NWSRi would be equal to α /ai ratio. Then, in this case, the NWSRi of GenCo depends on the slope of its marginal cost function and the slope of the aggregate inverse demand function. If the GenCo exceeds its pðeÞ ), then Δθwithheld is positive. maximum generation capacity limit (qi ¼ qmax i i According to (6.50), NWSRi decreases in a way depending on the values of Δθwithheld and qei . The effect of network limits on the ability of GenCo for capacity i withholding is considered implicitly by qei. Also, NWSRi can be rewritten by (6.44) and (6.50) with the below equation: NWSRi ¼ 0 B equal Bα B B ai  @

  ! Δθwithheld ai þ αequal αequal i  ¼   e ai ai λi  bi  θei max þ θei min   Δθwithheld ai þ αequal i ai λ e 

P m2M

μeþ m T mi þ

P m2M

1 C ð6:51Þ C !C C: e min A

e max μe þ θi m T mi  bi  θ i

It can be seen that in addition to αequal/ai ratio, NWSRi could be influenced by μeþ m , Tmi, Δθwithheld , θei max , θei min , and bi in a transmission-constrained market. i In the same way, Δqdistortion can be obtained by using (6.41, 6.42, 6.44, 6.45, 6.46, i and 6.47) as follows: μe m ,

  Δqdistortion ¼ 1=ai αequal qei  Δλdistortion  Δθdistortion i i i

ð6:52Þ

where Δθdistortion ¼ θpi max þ θei min  θpi min  θei max . i , which is positive, Δqdistortion can be negative or positive. A Unlike Δqwithheld i i positive (negative) value of Δqdistortion implies that the generation of GenCo has been i decreased (increased) with respect to the perfect competition model. The sign of capacity distortion index depends on the slope of the marginal cost function of GenCo i. For high-cost GenCos, capacity distortion index can be negative. It means that these GenCos don’t have high market shares; however, because of the capacity withholding of low-cost GenCos, which have high ability for the capacity

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withholding, their market shares may be increased. Then, the high-cost GenCos in oligopoly market may generate more than in perfectly competitive market, and negative Δqdistortion may be achieved. i Based on (6.42), (6.45), and (6.47), Δλdistortion at the generator connected buses i can be obtained by ¼ Δλdistortion  Δλdistortion i

X m2M

Δμdistortion T mi m

ð6:53Þ

eþ pþ e where Δλdistortion ¼ λe  λ p and Δμdistrotion ¼ μp m m þ μm  μm  μm . distortion of GenCo at bus i can be According to (6.52), (6.53), and (6.26), Δqi obtained by

Δqdistortion i

¼ 1=ai

αequal qei

α

equal

! X X distortion distortion distortion Δqi  Δθi  Δμm T mi : i2I

m2M

ð6:54Þ Another index to assess the capacity withholding may be defined by DWI, which can be obtained by DWI ¼

X X Δqdistortion = Δqwithheld : i i i2I

ð6:55Þ

i2I

As mentioned before, DWI gives the information about the potential ability of GenCos in power markets for capacity withholding. Equation (6.56) provides reformulation of this index by considering network and GenCos limits: 0

1 1 DWI ¼ @1 þ P αequal =a A i 0P

i2I

1 P P αequal qei =ai  Δθdistortion =ai  Δμdistortion T mi =ai m i i2I m 2 M, i 2 I Bi 2 I C P P equal e @ A ¼ DWIUC  CF α qi =ai  Δθwithheld =a i i i2I

i2I

ð6:56Þ 0

1 1 where DWIUC ¼ @1 þ P αequal =a A and i i2I 0 P equal e 1 P distortion P α qi =ai  Δθi =ai  Δμdistortion T mi =ai m i2I m 2 M, i 2 I Bi 2 I C CF ¼ @ P P equal e A. α qi =ai  Δθwithheld =a i i i2I

i2I

6 Impact of Capacity Withholding on Hosting Capacity Analyzing

139

The constraint factor (CF) shows the effect of the GenCos and transmission network constraints on the potential ability in the market for capacity withholding. If the GenCos and the transmission lines do not hit their constraints, therefore Δθdistortion , Δθwithheld , and Δμdistortion are equal to zero. Then, CF is equal to 1 and i i m DWI is equal to the unconstrained DWI (DWIUC). According to (6.56), DWIUC depends on αequal/ai ratio. CF becomes greater than 1, when the GenCos hit their constraints. Then, DWI becomes greater than DWIUC. It means that the potential ability in the market for capacity withholding is decreased because of the capacity limits of GenCos. It can be seen that when the transmission line flow constraints are exceeded, CF becomes lower than 1. The expected outcome with the increase of transmission congestion, in terms of the capacity withholding of GenCos, could be an increasing pattern along with the decreasing DWI.

6.3.3

Case Study

A modified IEEE 30-bus power system is studied to conceptually evaluate the approach used for analyzing the transmission limits impacts via the defined indices. The load parameters and transmission network data, power transfer distribution factors (PTDFs), and topology are based on MatPower 5.1 Toolbox. There are six generators in the power system, and it is supposed that each GenCo has only one generator. The reference bus is bus 1. The GenCos’ parameters are shown in Table 6.4. The inverse demand function of each load is λj ¼  αjyj + 45. The slope of each inverse demand function is selected in a way that λj ¼ 35 $/MW for the value of yj in MatPower 5.1 Toolbox. The aggregate demand’s parameters in (3) are αequal ¼ 0.03528 $/MW2 and βequal ¼ 45 $/MW. To analyze the capacity withholding indices, six simulation cases from A to F are considered. To use the capacity withholding indices, it is necessary to calculate λpi, λei pðeÞ , qi , qpi, and qei for simulation cases, as listed in Table 6.5. The indices are listed in Table 6.6. In case A, the line flow constraints of transmission network are the same as the data determined in MatPower 5.1 Toolbox. For transmission congestion modeling, the flow constraints of transmission lines 2, 3, 6, 8, and 9 are decreased to 60 MW, 13 MW, 13 MW, 14 MW, and 15 MW in case B, respectively. For all buses in Table 6.4 GenCos parameters for IEEE 30-bus test system Bus number of GenCo 1 2 5 8 11 13

ai ($/MW2) 0.075 0.35 1.25 0.1668 0.5 0.5

bi($/MW) 20 17.5 10 32.5 30 30

pmin(MW) 50 20 15 10 10 12

pmax(MW) 200 80 50 35 30 40

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Table 6.5 Simulation results of modified IEEE 30-bus test system for cases A to F Case A

B

C

D

E

F

Bus number of GenCo 1 2 5 8 11 13 1 2 5 8 11 13 1 2 5 8 11 13 1 2 5 8 11 13 1 2 5 8 11 13 1 2 5 8 11 13

λpi ($/MW) 34.559 34.559 34.559 34.559 34.559 34.559 27.299 25.189 38.355 39.210 38.590 36.990 26.106 24.128 35.921 37.271 36.690 35.190 29.742 27.545 41.540 42.141 41.496 39.831 30.724 29.242 38.553 39.088 38.653 37.529 23.422 20.575 38.355 39.490 38.654 36.496

λei ($/MW) 36.028 36.028 36.028 36.028 36.028 36.028 29.403 27.648 38.416 39.311 38.795 37.464 28.842 27.255 36.404 37.795 37.330 36.127 30.996 29.026 41.558 42.117 41.538 40.044 32.067 30.795 38.799 39.243 38.869 37.905 26.340 24.020 38.416 39.431 38.750 36.992

pðeÞ

qi (MW) 200 52.937 20.822 21.151 12.056 12.056 125.38 28.994 22.733 35 17.591 14.930 117.886 27.871 21.123 31.749 14.66 12.254 146.620 32.931 25.246 35 23.078 20.090 80.444 37.986 23.039 35 17.740 15.812 151.196 20 22.733 35 17.502 13.984

qpi (MW) 193.549 48.740 19.644 12.291 10 12 97.323 21.968 22.684 35 17.181 13.981 81.415 20 20.737 28.604 13.381 12 129.896 28.700 25.232 35 22.993 19.662 71.492 33.548 22.842 35 17.306 15.059 112.289 20 22.684 35 17.308 12.992

qei (MW) 145.328 48.088 20.250 17.456 11.261 12 85.263 26.338 22.108 33.702 16.432 13.945 69.116 24.211 20.265 24.1 13.256 12 118.694 31.350 24.895 35 22.291 19.405 65.125 34.508 22.406 33.365 16.570 14.769 102.823 20 22.108 34.300 16.348 13.063

case A, λpi , λei , and Δλdistortion are 34.559 $/MW, 36.028 $/MW, and 1.469 $/MW, i respectively. The nodal prices in case B are not the same because of the transmission network congestion. In this case, the flow constraints of transmission lines 6 and 9 are limited in positive directions. It is to be noted that the positive directions of transmission lines 6 and 9 are from bus 2 to bus 6 and from bus 6 to

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Table 6.6 Capacity withholding indices of modified IEEE 30-bus test system for cases A to F

Case A

B

C

D

E

F

Bus number of GenCo 1 2 5 8 11 13 1 2 5 8 11 13 1 2 5 8 11 13 1 2 5 8 11 13 1 2 5 8 11 13 1 2 5 8 11 13

Δλdistortion i ($/MW) 1.469 1.469 1.469 1.469 1.469 1.469 2.104 2.459 0.061 0.101 0.205 0.474 2.736 3.128 0.483 0.524 0.639 0.936 1.254 1.481 0.018 0.025 0.041 0.213 1.343 1.554 0.246 0.155 0.216 0.376 2.918 3.446 0.061 0.058 0.096 0.496

Δqwithheld i

Δqdistortion i

(MW) 54.672 4.849 0.572 3.695 0.795 0.056 40.117 2.656 0.625 1.298 1.159 0.985 48.77 3.66 0.858 7.649 1.404 0.254 27.927 1.581 0.352 0 0.788 0.686 15.319 3.479 0.633 1.635 1.170 1.043 48.373 0 0.625 0.700 1.154 0.922

(MW) 48.221 0.652 0.606 5.165 1.261 0 12.060 4.370 0.576 1.298 0.749 0.036 12.299 4.211 0.472 4.504 0.125 0 11.202 2.650 0.337 0 0.703 0.257 6.366 0.960 0.436 1.635 0.736 0.290 9.466 0 0.575 0.700 0.961 0.071

NWSRi 0.3761 0.1008 0.0282 0.2116 0.0705 0.0046 0.4705 0.1008 0.0282 0.0385 0.0705 0.0705 0.7056 0.1511 0.0423 0.3173 0.1059 0.0211 0.2353 0.0504 0.0141 0 0.0353 0.0353 0.2352 0.1008 0.0282 0.0490 0.0705 0.0705 0.4705 0 0.0282 0.0204 0.0705 0.0705

DWI 0.6472

0.2209

0.2106

0.3143

0.3653

0.2246

bus 7, respectively. The flow constraints of transmission line 8 is limited in the negative direction from bus 7 to bus 5. Because of the different locations in the network, Δλdistortion decreases for some buses and increases for some others. i

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When evaluating cases A and B, it can be observed that because of the transmission network congestion, NWSRi for the GenCos at buses 1 and 13 increases to 0.4705 and to 0.0705, respectively. Moreover, the NWSRi of GenCo at bus 8 reduces to 0.0385. In addition, the values of αequal/ai ratios for GenCos at buses 1, 8, and 13 are 0.4705, 0.0705, and 0.2116, respectively. Therefore, on the one hand,NWSRi values of GenCos at buses 1 and 13 will become lower than their αequal/ai ratios pðeÞ ¼ 200 MW and qe13 ¼ when their constraints are bounded in case A (q1 ¼ qmax 1 min q13 ¼ 12 MW). On the other hand, in case B, the generation capacity constraints of pðeÞ GenCos at buses 1 and 13 are not limited (q1 ¼ 125:38 MW and qe13 ¼ 13:945 MW), and based on (6.50) and (6.51), NWSRi of GenCos grow up to the points where NWSR1 ¼ αequal/a1 ¼ 0.4705 and NWSR13 ¼ αequal/a13 ¼ 0.0705. The opposite outcomes are seen for the GenCo at bus 8. In case A, the generation pðeÞ < qe8 , q8 < qmax ) and capacity constraints of the GenCo are not limited (qmin 8 8 equal NWSR8 ¼ α /a8 ¼ 0.2116. Due to the congestion of transmission network in case B, the GenCo hits its upper generation capacity constraint pðeÞ ¼ 35 MW ), and NWSR8 reduces to 0.0385. The constant NWSRi (q8 ¼ qmax 8 values of GenCos at buses 2, 5, and 11 in cases A and B show that the constraints pðeÞ of qi and qei for these GenCos are not limited. Then, their NWSRi for them are not affected by the transmission network constraints. Based on (6.56), unconstrained DWI of the system is 0.5122. In case A, DWI and CF are 0.6472 and 1.2635, respectively. It means that the potential ability of GenCos for capacity withholding is decreased because of the generation limits of GenCos 1, 11, and 13. Therefore, in case B, due to the congested lines 6, 8, and 9, CF reduces to 0.4327 causing DWI to reduce to 0.2209. It implies that the GenCos’ ability for market power is increased. Note that the reduced CF should be ascribed to the transmission congestion. The effect of demand elasticity on the GenCos’ capacity withholding is also analyzed. Cases C and D are the same as case B except for αequal ¼ 0.05292 and αequal ¼ 0.01764, respectively. These slopes are achieved from 50% increase to 50% decrease in the inverse demand functions’ slopes of case B, respectively. As listed in Table III, the indices show an improvement with the decrease of αequal. In addition, in case D, DWI increases to 0.3143 and the NWSRi decreases. Other conditions are studied for analyzing the effect of cost parameters on the GenCos’ capacity withholding. Cases E and F are the same as case B except for a1 ¼ 0.15 and b1 ¼ 15, respectively. By reducing of a1 in case E, NWSR1 reduces to 0.2352, showing that the GenCos’ potential ability reduces. However, NWSR8 increases to 0.0490; the growth of DWI to 0.3653 indicates that the GenCos’ ability for market power decreases. Therefore, GenCo at bus 1 is more effective than GenCo at bus 8, and a decrement in its capacity withholding can affect the market considerably. The values of NWSR1 for GenCos at buses 1, 5, 8, 11, and 13 in case F are the same as those in case B. Although, NWSR2 reduces to 0, leading DWI to increase to 0.2246.

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143

Capacity Withholding Mitigation and the Impact of DGs on It

Market power and capacity withholding may be controlled by various programs, which can be categorized in two classifications: the demand (consumer) side and the supply (generator) side programs. Demand side programs are used to reduce the consumption and increase the elasticity of demand. A significant subject in demand side programs is interruptible load contracts. In fact, by increasing of the generations of GenCos, specifically GenCos with low generation cost, the outcome in terms of the capacity withholding of GenCos should be a decreasing trend along with the decreasing market price. ISO by using the supply side programs motivates GenCos to increase their generations up to the point where the market price is equal to their marginal costs. Distributed energy resources (DERs) can play an important role in capacity withholding mitigation as supply side programs. For instance, by locating DGs in congested areas of systems, capacity withholding of GenCos decreases. In fact, ISO in hosting capacity analyzing can use the defined indices to select appropriate programs for mitigation of capacity withholding as illustrated in Fig. 6.3. The left and right panels in Fig. 6.3 are the market before and after capacity withholding mitigation programs, respectively. Figure 6.3a, b is related to supply side programs and Fig. 6.3c, d is based on demand side programs, and it is supposed that there is one GenCo in the market. Based on Fig. 6.3a, the generation capacity constraint for pðeÞ GenCo i is greater than qi and DWI < 1 can be obtained. Therefore, this GenCo can produce more than its oligopoly generation (qei ). As illustrated in Fig. 6.3b, because of the eased decreased market power and increased generation, ΔQwithheld, ΔQdistortion, and Δλdistortion are reduced. When evaluating Fig. 6.3a, b, it can be observed that DWI is higher when a supply side program is used. Therefore, the increased DWI should be ascribed to the mitigation of the capacity withholding. The impacts of generation capacity limits on the GenCo i’s capacity withholding are illustrated in Fig. 6.3c. In this figure, a deeper evaluation should be made to avoid misunderstanding. Figure 6.3a, c is the same, except for considering the decreased pðeÞ maximum capacity constraint of GenCo i and setting qmax ¼ qpi ¼ qi . Because of i withheld distortion distortion the reduced maximum capacity constraint, ΔQ , ΔQ are , and Δλ withheld distortion decreased. Therefore, ΔQ and ΔQ are the same and then DWI equals to 1. Then, the value 1 of DWI shows that the GenCo could not increase its generation up to the perfect market output. Therefore, supply side programs cannot provide a way to decrease capacity withholding, and demand side programs are essential to improve the demand elasticity. An increase in demand elasticity is coherent with lower level of capacity withholding and power consumption. The demand curve with higher elasticity will be located in lower position with respect to the original one, as illustrated in Fig. 6.3d. Because of the effect of price modifications on the optimal behavior of the generators, GenCo i will find it better to bid a lower price to improve its market share. This is illustrated by the shift from the strategic offer in Fig. 6.3c to the strategic offer in Fig. 6.3d, which is closer to the marginal cost curve [30, 31].

144 Fig. 6.3 Assessment of capacity withholding mitigation programs. (a) Unconstrained market. (b) Effects of a supply side program. (c) Constrained market. (d) Effects of a demand side program

S. Salarkheili and M. SetayeshNazar

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In hosting capacity analysis, the maximum amount DERs that can be installed in the power system is determined. In this study, the major concerns are technical constraints such as adequacy and security limits of system. After this analysis, the market operator or the ISO can evaluate the outcomes of the technical analysis from market power and capacity withholding assessment. In other words, the ISO can use the proposed global and nodal indices to measure the effects of DERs on capacity withholding. In fact, ISO can use global index to analyze the effect of DERs on capacity withholding in the whole system. In addition, by nodal indices the impacts of DERs on capacity withholding at each bus of system can be analyzed. Then, the ISO can use the optimum strategies to control the market power of GenCos. In addition, ISO can propose new locations of DERs to decrease capacity withholding in different buses of system by using nodal indices such as nodal price distortion index and nodal capacity withholding index. The new locations should be analyzed from technical constraints of system such as substations and feeder capacities. In Fig. 6.4, the flowchart of this procedure is shown. Fig. 6.4 Hosting capacity analysis from capacity withholding point of view

Start

Finding the maximum amount of DERs in power system.

Calculating global and nodal indices in the presence of DERs.

NO Is DWI acceptable?

The market is fundamentally inefficient and the ISO should use market mitigation programs.

Yes NO

Change the capacity or location of DERs.

Are nodal indices acceptable?

NO Are nodal indices acceptable?

Yes Yes

Are Technical constraints exceeded?

End

NO

Yes

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Future Works

In this chapter, two categories of market power indices were presented to assess the capacity withholding of GenCos in the presence of DERs. This indices are effective and they can be used by the ISO besides the technical assessment of hosting capacity. Future works are needed to evaluate the defined indices when maintenance scheduling of generators and strategic transmission system operators (TransCo) are considered.

References 1. Gan, D., & Bourcier, D. V. (2002). Locational market power screening and congestion management: Experience and suggestion. IEEE Transactions on Power Systems, 17(1), 180–185. 2. Wang, P., Xiao, Y., & Ding, Y. (2004). Nodal market power assessment in electricity markets. IEEE Transactions on Power Apparatus and Systems, 19(3), 1373–1379. 3. Bompard, E., Ma, Y. C., Napoli, R., & Jiang, C. W. (2006). Assessing the market power due to the network constraints in competitive electricity markets. Electric Power Systems Research, 76, 953–961. 4. Bompard, E., Lu, W., & Napoli, R. (2006). Network constraint impacts on the competitive electricity markets under supply-side strategic bidding. IEEE Transactions on Power Apparatus and Systems, 21(1), 160–170. 5. Bompard, E., Ma, Y. C., Napoli, R., & Abrate, G. (2007). The demand elasticity impacts on the strategic bidding behavior of the electricity producers. IEEE Transactions on Power Apparatus and Systems, 22(1), 188–197. 6. Hesamzadeh, M. R., Biggar, D. R., & Hosseinzadeh, N. (2011). The TC-PSI indicator for forecasting the potential ability for market power in wholesale electricity markets. Energy Policy, 39, 5988–5998. 7. Lee, Y. Y., Hur, J., Baldick, R., & Pineda, S. (2011). New indices of market power in transmission-constrained electricity markets. IEEE Transactions on Power Apparatus and Systems, 26(2), 681–689. 8. Gabriel, S. A., Conejo, A. J., Fuller, J. D., Hobbs, B. F., & Ruiz, C. (2013). Complementarity modeling in energy markets. New York: Springer Press. 9. Latorre, M. D. L., & Graville, S. (2003). The Stackelberg equilibrium applied to AC power systems-a non-interior point algorithm. IEEE Transactions on Power Apparatus and Systems, 18(2), 611–618. 10. Chen, H., Wong, K. P., Chung, C. Y., & Nguyen, D. H. M. (2006). A coevolutionary approach to analyzing supply function equilibrium model. IEEE Transactions on Power Apparatus and Systems, 21(3), 1019–1028. 11. Hasan, E., & Galiana, F. D. (2008). Electricity markets cleared by merit order – Part II: Strategic offer and market power. IEEE Transactions on Power Apparatus and Systems, 23(2), 372–379. 12. Ruiz, C., Conejo, A. J., & Bertand, R. G. (2008). Some analytical results pertaining to Cournot models for short-term electricity markets. Electric Power Systems Research, 78, 1672–1678. 13. Bushnell, J. B. (2003). Looking for trouble competition policy in the US electricity industry. Center for the Study of Energy Markets: Univ. California Energy Institute, California. 14. Baldick, R., Grant, R., & Kahn, E. (2004). Theory and application of linear supply function equilibrium in electricity markets. Journal of Regulatory Economics, 25, 143–167.

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15. Cunningham, L. B., Baldick, R., & Baughman, M. L. (2002). An empirical study of applied game theory: Transmission constrained Cournot behavior. IEEE Transactions on Power Apparatus and Systems, 17(1), 166–172. 16. Yang, Y., Zhang, Y., Li, F., & Chen, H. (2012). Computing all Nash equilibria of multiplayer games in electricity markets by solving polynomial equations’. IEEE Transactions on Power Apparatus and Systems, 27(1), 81–91. 17. Helman, U., & Hobbs, B. F. (2010). Large-scale market power modeling: Analyzing of the U.S. eastern interconnection and regulatory applications. IEEE Transactions on Power Apparatus and Systems, 25(3), 1434–1448. 18. Yu, C. W., Zhang, S. H., Wang, X., & Chung, T. S. (2010). Modeling and analysis of strategic forward contracting in transmission constrained power markets. Electric Power Systems Research, 354–361. 19. Xiaohong, G., Ho, Y. C., & Peypyne, D. L. (2001). Gaming and price spikes in electric power markets. IEEE Transactions on Power Apparatus and Systems, 16(3), 402–408. 20. Tellidou, A. C., & Bakirtzis, A. G. (2007). Agent-based analysis of capacity withholding and tacit collusion in electricity markets. IEEE Transactions on Power Apparatus and Systems, 22 (4), 1735–1742. 21. Hongyan, L. I., & Tesfatsion, L. (2009). Capacity withholding in restructured wholesale power markets: An agent-based test bed study, Power Systems Conference and Exposition. 22. Mohtavipour, S. S., Haghifam, M. R., & Sheik-El-Eslami, M. K. (2011). Emergence of capacity withholding: An agent based simulation of a double price cap electricity market. IET Generation Transmission and Distribution, 6(1), 69–78. 23. Chattopadhay, D. (2004). A game theoretic model for strategic maintenance and dispatch decision. IEEE Transactions on Power Apparatus and Systems, 19(4), 2014–2021. 24. Wang, J., Shahidehpour, M., Li, Z., & Botterud, A. (2009). Strategic generation capacity expansion planning with incomplete information. IEEE Transactions on Power Apparatus and Systems, 24(2), 1002–1010. 25. Hesamzadeh, M. R., Hosseinzadeh, N., & Wolfs, P. J. (2010). Transmission system augmentation based on the concepts of quantity withholding and monopoly rent for reducing market power. IEEE Transactions on Power Apparatus and Systems, 25(1), 167–180. 26. Salarkheili, S., & Akbariforoud, A. (2012). Market power assessment in electricity markets: Supply function equilibrium-based model. International Transactions on Electrical Energy Systems, 23(4), 553–569. 27. Salarkheili, S., & SetayeshNazar. M. (2015). New indices of capacity withholding in power markets. International Transaction on Electrical Energ Systems, 25(1), 180–196. 28. Salarkheili, S., & SetayeshNazar, M. (2016). Capacity withholding analysis in transmissionconstrained electricity markets. IET Generation Transmission and Distribution, 10(2), 487–495. 29. Salarkheili, S., & SetayeshNazar, M. (2017). Capacity withholding assessment in the presence of integrated generation and transmission maintenance scheduling. IET Generation Transmission and Distribution, 11(16), 3903–3911. 30. Ameri, M., Rahimian, M., & Latifi, M. A. (2018). Capacity withholding constrained by operational limits of generation under financial virtual divestiture in a day-ahead market. IEEE Transactions on Power Apparatus and Systems, 33(1), 771–780. 31. Guo, H., Chen, Q., Xia, Q., & Kang, C. (2019). Market power mitigation clearing mechanism based on constrained bidding capacities. IEEE Transactions on Power Systems, 34(6), 4817–4827.

Chapter 7

A Generalised Deterministic Approach to Evaluate PV Hosting Capacity of LV Distribution Networks Under Different Operating Conditions D. Chathurangi, U. Jayatunga, S. Perera, and A. Agalgaonkar

7.1

Introduction

Distributed generation (DG) in the form of renewable energy sources is gradually becoming an integral part of many power systems around the world. Concurrently, they are progressively replacing greenhouse gas-emitting technologies, accelerating the transition towards an eco-friendly low-carbon environment. Recent rapid growth of solar photovoltaics (PV) compared to other electricity generation technologies is clearly evident. The total worldwide installed capacity of solar PV generation has exceeded 505 GW in 2018 [1]. The year 2018 was a landmark year for solar PV where 100 GW was installed worldwide for electricity generation which is more than the cumulative sum of the capacities of other generating technologies installed [1]. Challenges associated with solar PV are its intermittency and non-dispatchability, rendering it hard to match supply and demand. Thus, there is a necessity for active management of distribution networks which have not been previously designed to D. Chathurangi (*) Department of Electrical Engineering, University of Moratuwa, Moratuwa, Sri Lanka Collaborated Research, School of Electrical, Computer & Telecommunications Engineering, Faculty of Engineering and Information Science, University of Wollongong, Wollongong, Australia e-mail: [email protected] U. Jayatunga Department of Electrical Engineering, University of Moratuwa, Moratuwa, Sri Lanka e-mail: [email protected] S. Perera · A. Agalgaonkar School of Electrical, Computer & Telecommunications Engineering, Faculty of Engineering and Information Science, University of Wollongong, Wollongong, Australia e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2020 A. F. Zobaa et al. (eds.), Hosting Capacity for Smart Power Grids, https://doi.org/10.1007/978-3-030-40029-3_7

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accommodate DG. Bidirectional power flows are in reality with increased solar PV penetration levels and can degrade the performance of LV distribution networks resulting in a number of power quality and other related issues (such as overvoltage limit violations, voltage unbalance, overloading of transformers and feeders, excessive line losses, high harmonic distortion levels exceeding the stipulated limits and protection mal-operation [2]). Degree of the occurrence of these problems increases with the maximum permissible penetration level, especially when the hosting capacity exceeds acceptable limits [3, 4]. Key negative impacts associated with high solar PV penetration levels may be overcome by network reinforcements such as asset upgrades (conductors and transformers) and advanced monitoring and protection schemes. However, such reinforcements are not economically feasible in general. Given the potential obstacles, it is desirable to develop systematic approaches for new solar PV deployment from network planning perspectives so as to optimally utilise existing assets instead of the network augmentation. Distribution network service providers (DNSPs) are required to ensure that the connection of new solar PV systems does not violate any associated technical limits. Technical issues that limit solar PV hosting capacity of LV distribution networks include thermal overloading of the network components, overvoltage, voltage regulation, increasing short circuit levels and power quality issues, in addition to islanding considerations and the possibility of reverse of power flows. At present, most DNSPs follow simple practices and rules of thumb in order to assess the solar PV hosting capacity of existing distribution networks. However, there is a necessity for the development of systematic approaches for hosting capacity evaluation considering influential factors such as geographical layout of networks as well as electrical parameters. Solar PV hosting capacity has to be determined using a transparent approach, that is, to define an appropriate index or indices subject to well-defined performance criteria or limits (e.g. feeder voltage, line loading level, voltage unbalance, harmonic levels) [5]. However, such a hosting capacity can take multiple values when different performance indices are utilised as constraints. Moreover, a series of constraining performance indices can be utilised in order to assess the solar PV hosting capacities of a given distribution network by accommodating stochastic solar PV generation at different locations through the use of Monte Carlo methodologies. Accordingly, a single value cannot be specified as the PV hosting capacity for a given network. The work presented in this chapter covers a generalised deterministic approach to evaluate the solar PV hosting capacity of low-voltage (LV) distribution networks considering overvoltage as the constraining criterion and the performance parameter. This drive to develop a deterministic approach is justified by considering the drawbacks of a stochastic approach. Furthermore, the generalised framework of the solar PV hosting capacity estimation aims at capturing all network and PV plant characteristics to maximise the solar PV penetration level in LV distribution networks.

7 A Generalised Deterministic Approach to Evaluate PV Hosting Capacity of LV. . .

7.2

151

High Penetration of Solar PV Generation in LV Networks Resulting in Overvoltage Issues: A Case Study from Sri Lanka

This section discusses the most common impacts of higher solar PV penetration levels in distribution networks, based on a case study of an urban LV distribution network in Sri Lanka which is reported in this section with the aid of feeders with the highest levels of rooftop solar PV generation. This case study investigates overvoltage issues associated with high solar penetration levels in LV distribution networks. The selected test network consists of a 250 kVA, 11 kV/400 V distribution transformer with three radial feeders that supply a total of 336 customers including 253 single-phase customers and 83 three-phase customers. More than 90% of the load on the system is shared by 315 residential customers, and the remaining is classified as commercial consumers. The installed solar PV capacity in the system associated with 24 solar PV systems (single-phase and three-phase) distributed along the three feeders is 104 kW. The geographical layout of the network is shown in Fig. 7.1, while Table 7.1 provides relevant network details. Measured voltage profiles of selected six customers in feeders 2 and 3 at different locations (marked as A, B, C, D, E and F in Fig. 7.1) are analysed in Sect. 7.2.1 in relation to the overvoltage problem.

Fig. 7.1 Geographical layout of the distribution network [6]

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Table 7.1 Details of the test network [6] Transformer rating Present maximum demanda No. of customers served No. of customers with rooftop solar PV generators Solar penetration level (by transformer capacity) Conductor type a

250 kVA, 11 kV/400 V 154 kW (77%) 336 24 40% 3 Phase Aerial Bundle Cable (ABC)

Recorded data for July 2017

Load profiles of more than 30% of the customers are derived based on the actual 15-minute energy data recorded remotely through smart meters. The remaining load profiles are obtained by deriving an average load profile (using the measured data). These average load profiles are used to generate load profiles of the remaining customers (without smart meters) based on the monthly energy consumption data acquired for individual customers. Further, the constant power factor of 0.8 lagging is assumed for all the customers.

7.2.1

Impact of Solar PVs on LV Network Performance

Voltage rise in LV distribution networks in the presence of solar PVs is known to be one of the main constraining factors that limit the maximum PV penetration levels [6]. The voltage rise is highly sensitive to the location and capacity of PVs along the feeder. Analysis of customer voltage profiles for the selected test network, obtained from smart energy meter readings (at six different locations on feeders 2 and 3), provides clear evidence of a violation of upper voltage limit during solar peak times (i.e. between 10 am and 2 pm) as shown in Fig. 7.2a, b. Figure 7.2a shows voltage profiles of a solar customer (at location F as shown in Fig. 7.1) and a non-solar customer (at location E as shown in Fig. 7.1), located at the middle of feeder 2, affected by overvoltage condition. Further, Fig. 7.2b shows four selected customer’s voltage profiles for both solar and non-solar along feeder 3, where a solar customer (at location C as shown in Fig. 7.1) and a non-solar customer (at location D as shown in Fig. 7.1) towards the feeder end are affected by overvoltage condition during the solar peak times. However, customers who are close to the transformer end (both solar customer at location A and non-solar customer at location B) are not affected. It is to be noted that the upper voltage limit stipulated by the concerned DNSP in Sri Lanka is in the range of +/
6% of the nominal voltage.

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Fig. 7.2 Voltage profiles of solar/non-solar customers at different locations; (a) feeder 2 and (b) feeder 3 [6]

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Stochastic Approach for Determining Solar PV Hosting Capacity

In this section, a stochastic analysis framework followed using Monte Carlo simulation (MCS) method to assess the solar PV hosting capacity of the test system is presented. The performance indices are selected as overvoltage and overloading criterion with regard to the selection of an appropriate solar PV hosting capacity level. Accurate analysis of solar PV hosting capacity requires the development of solar deployment scenarios for all possible future PV locations and corresponding PV installation size in the network. It is not feasible to simulate all possible PV deployment scenarios for a given network. Thus, to represent the impact of the location of a new solar PV connection, the MCS approach is used with a limited number of PV deployment scenarios at a particular level of penetration. For the test network, solar PV penetration level (N ) is defined as the ratio of the number of customers with PV units and the total number of customers. With increasing penetration levels, a number of stochastic solar PV deployment scenarios (M) can be considered in such a way that in each scenario, the location of the PV customers is randomly selected from the pool of solar customers in the network. Furthermore, each simulated scenario is unique in order that PVs are deployed. The overall framework developed for solar deployment scenarios for each of the penetration level is illustrated in Fig. 7.3. Since this systematic approach is applied to a practical distribution network, solar PV connections are only allocated to customers with energy consumption greater than 120 kWh per month, assuming that the solar PV installations are financially feasible for these customers. Capacity of the solar PV system is determined based on

Fig. 7.3 Stochastic analysis framework for solar PV deployment

7 A Generalised Deterministic Approach to Evaluate PV Hosting Capacity of LV. . . Table 7.2 Operational limits for hosting capacity analysis

Criterion Overvoltage Thermal loading

Definition Feeder bus voltage Line and transformer loading

155 Limit 1.06 pu 100%

the monthly energy consumption and assigned as a net metered1 customer. The total customer demand is assumed to be constant for different solar PV penetration levels. Following this method, several deployment scenarios are systematically developed, until all financially feasible solar deployments are connected to the network. It is assumed that all installed solar PV units are to provide active power at unity power factor which is a common practice. The influential factors governing the impact of solar PVs on the performance of the LV distribution system include an accurate representation of the solar PV systems, in particular the PV unit size and solar irradiance level which inherently drives the solar PV output. Solar irradiance profiles for each PV units were developed using the System Advisor Model (SAM) software considering the irradiance data applicable to Sri Lanka.

7.2.3

Overvoltage and Overloading Criteria

Maximum feeder voltage violation and line overloading are commonly reported as the deciding and critical factors in assessing solar PV hosting capacity in distribution networks. The considered test network is already associated with overvoltage violation issues as discussed in Sect. 7.2.1. With this in mind, solar PV hosting capacity was evaluated for the test network by defining the maximum feeder voltage in addition to considering the line and transformer loading violations. In each PV deployment scenario, network power flows are monitored, and the corresponding network voltages and line and transformer loading levels are calculated in order to verify whether any performance standards are violated. The threshold values for each performance index considered in this analysis are given in Table 7.2. It is important to highlight that threshold value for a given performance index is mutually exclusive of the rest of performance indices. MCS results shown in Fig. 7.4a–c elaborate the resulting maximum feeder voltage, maximum line loading and transformer loading levels, respectively, under different solar penetration levels for a total number of 66,000 solar deployment scenarios. Based on the MCS results, two levels of solar PV hosting capacity can be identified as minimum hosting capacity (HCmin) and maximum hosting capacity (HCmax) compliant with the given performance index, as shown in Fig. 7.4 and summarised in Table 7.3. With the minimum hosting capacity level, none of the solar penetration levels violates the criteria of the performance index, i.e. 48 kW of solar 1 This allows customers to be paid in cash for any surplus power generation from the solar PV systems at the end of monthly billing cycles.

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Fig. 7.4 Hosting capacity limits for performance index: (a) maximum feeder voltage criterion, (b) maximum line loading criterion and (c) transformer loading criterion Table 7.3 Solar deployment limits for the test network

Criterion Overvoltage Thermal loading Line overloading Transformer overloading

HCmin (kW) 48

HCmax (kW) 178

244 250

>400 332

PVs can be integrated to the test network not to violate the steady-state maximum feeder voltage limits without any concern of the PV location. Similarly, considering only the thermal overloading limits of line conductors and transformer, the same network can withstand up to 244 kW solar PV units (note that the voltage violation criterion is excluded in thermal loading analysis and vice versa). Solar penetration levels in excess of the maximum hosting capacity limit, independent of the location of the solar installation, will violate the relevant operational limits. Moreover, the range in between minimum and maximum hosting capacity levels, certain solar penetration levels which arise from random PV locations, may violate the network constraints. Therefore, detailed studies are necessary with precise solar PV locations to verify that a given level of penetration is safe.

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Fig. 7.5 Variation of hosting capacity limit with the number of solar deployment scenarios for overvoltage criterion; minimum hosting capacity and maximum hosting capacity

The dependency of the number of solar PV deployments on the accuracy of the results obtained through the MCS method was tested by changing the number of solar deployment scenarios and repeating the process for overvoltage criteria as shown in Fig. 7.5a, b. All network modelling is carried out using DIgSILENT PowerFactory.

7.2.4

Limitations with Stochastic Evaluation Framework

Evaluation of solar PV hosting capacity as discussed in Sect. 7.2.2 is a complex task that requires accurate network modelling including extensive data. A major drawback of Monte Carlo-based studies is the higher computational time and storage requirements in order to reach superior convergence of the final output. Furthermore, stochastic assessment methodologies for addressing the randomness of the position and rating of solar PVs are not easy to implement due to complexity and high computational times in the evaluation procedures. In addition, solar PV hosting capacity of a network depends on the characteristics of the network (feeder length, type of conductor, level of loading, etc.), so each network will have a distinctive solar PV hosting capacity value. From a network planning perspective, evaluation of the PV hosting capacity of LV distribution networks through stochastic method is unrealistic. Thus, there is a need for systematic approaches to assess the PV hosting capacity with theoretical verifications wherever possible.

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Sensitivity Analyses for Determining Solar PV Hosting Capacities

PV hosting capacity depends on many factors including feeder characteristics and solar PV system. Therefore, sensitivity analysis should be performed on individual influential factors to determine their effects on the hosting capacity. The major factors influencing the hosting capacity as identified are solar PV system rating and its location [7] and feeder characteristics which include their operating voltage, loading level, topology, conductor type, length and existing power/voltage control mechanisms [6]. This section presents two sensitivity studies in detail on the solar PV hosting capacity, location sensitivity and feeder characteristics.

7.3.1

Influence of PV Location on Hosting Capacity

Solar PV location and its aggregated capacity along the feeder are vital factors in assessing hosting capacity for a given distribution network. A simple case study is presented here to show the influence of solar PV system location and aggregated capacity on maximum penetration level. A single feeder network which is 1 km long (conductor type: AAC-Fly type (all aluminium conductor), R ¼ 0.4505 Ω/km, X ¼ 0.292 Ω/km) is considered with the daily peak demand of 40 kW and 30 kVAr. The total load is assumed to be divided equally between three phases and evenly distributed along the feeder. Figure 7.6 shows the voltage profile of the feeder for maximum solar power that can be injected at three different locations; an aggregated capacity is considered at a given location at a time (distance are measured from the transformer end), not to violate overvoltage conditions. The results clearly show how power injection levels tend to reduce when solar PV is connected towards the feeder end.

7.3.1.1

Study Methodology

How solar PV location and aggregated capacity affect the PV hosting capacity levels is assessed by considering a simple LV distribution network which has two feeders. The study network comprises 11 kV/400 V, 100kVA transformer with a loading level of 50%. Two different feeder lengths, 500 m and 1000 m (conductor type: AAC-Fly type), are considered to analyse the effect of feeder length on the PV hosting capacity. To assess the effect of load changes on PV hosting capacity, two loading levels are considered—Case 1: 60% of total load is allocated to feeder 1, and the rest (40%) is assigned to feeder 2, and Case 2: 40% of total load is allocated to feeder 1, and the remaining (60%) is assigned to feeder 2. In addition, constant power factor, 0.8 lagging, is assumed for all load points. For simplicity, balanced and evenly distributed loads are considered. Each feeder length is analysed by dividing

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Fig. 7.6 Feasible solar PV generation levels at different locations

Fig. 7.7 Feeder segments for hosting capacity analysis

into three equal-length segments as shown in Fig. 7.7 where the randomness of the solar PV deployment is applied to each segment. Accordingly, four solar deployment scenarios are considered by changing the locations of the solar PV connections in relation to Cases 1 and 2: Scenario 1: Solar PVs are distributed in the feeder end segment. Scenario 2: Solar PVs are distributed in the feeder middle segment. Scenario 3: Solar PVs are distributed in the feeder front segment. Scenario 4: Solar PVs are distributed over all segments of the feeder.

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As a specific case, solar PV hosting capacity at a predetermined location is also investigated by evaluating the maximum connectable solar capacity in three phases at the boundaries of each segment such that voltage limit is not violated.

7.3.1.2

Study Results

Initial values of maximum feeder voltage drop and line loading levels of the network are given in Table 7.4 for both Case 1 and Case 2 (without any solar PV connections). The test network is analysed to examine the maximum connectable solar PV capacity at different segments ensuring that the voltage upper limits are not violated. Figure 7.8 shows the maximum connectable solar PV capacities at the boundaries (the specific case of fixed locations of PV) of the three segments for both Case 1 and Case 2 (hosting capacity values are given in per unit using a base Sb ¼ 100 kVA which is the step down transformer rating, thus allowing the line loading level to be compared against). Further, solar PV units are to provide only active power operating at unity power factor. The voltage at the secondary of the transformer was maintained to a constant value of 1 pu. The same two-feeder network is analysed using MCS method, and for illustrative purposes, results obtained for Case 1 scenarios are shown in Figs. 7.9 and 7.10 with Table 7.4 States of the feeder without solar PVs [6]

Max. voltage drop Max. line loading

Case 1 (F1–60/F2–40) Feeder 1 Feeder 2 3% 4% 0.3 pu 0.2 pu

Case 2 (F1–40/F2–60) Feeder 1 Feeder 2 2% 6% 0.2 pu 0.3 pu

Fig. 7.8 Maximum connectable solar capacity at different locations of two-feeder network [6]

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Fig. 7.9 Variation of segment-wise hosting capacity levels for overvoltage criteria; Case 1, solar PVs distributed in (a) feeder end segment, (b) feeder middle segment, (c) feeder front segment and (d) over all segments of the feeder [6]

regard to overvoltage and line loading criterion, respectively. The limit for overvoltage exceedance is 1.06 pu, and the acceptable line loading limit is considered to be 100% of the thermal loading of the conductor. In this analysis, transformer loading level was not considered as the aim was to consider the feeder level PV hosting capacity only. However, it is vital that transformer loading levels are considered in the application of the above methodology. Referring to Fig. 7.10, it can be seen that when solar PVs are distributed in the feeder front segment, the connectable maximum solar PV capacity level is essentially limited by the line conductor and transformer overloading. Table 7.5 gives the summary for minimum and maximum hosting capacity (HC) values (considering overvoltage and line overloading criterion) derived using MCS for both Case 1 and Case 2. Referring to simulation outcomes presented with regard to fixed locations, as in Fig. 7.8, it clearly indicates that the maximum connectable PV capacity increases as the solar PVs are distributed towards the feeder front (close to the distribution transformer). As shown in Fig. 7.8, in Case 1, for the end segment, the lowest hosting capacity was obtained at the feeder end as 0.36 pu (at point A2 in feeder 2). Further, for the same case, the summation of the hosting capacities at the nearest end to the transformer of both feeders in the end segment is 1.42 pu (hosting capacities at points B1 and B2). These values are equal to minimum and maximum solar PV

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Fig. 7.10 Variation of segment-wise hosting capacity levels for maximum line loading criteria; Case 1, solar PV distributed in (a) feeder end segment, (b) feeder middle segment, (c) feeder front segment and (d) over all segments of the feeder Table 7.5 Solar PV deployment limits for the two-feeder network [6]

Scenario 1: End segment Scenario 2: Middle segment Scenario 3: Front segment Scenario 4: Over all segments

Case 1 HCmin 0.4 0.5 0.8 0.7

HCmax 1.4 2.3 3.4 2.5

Case 2 HCmin 0.45 0.6 0.9 0.9

HCmax 1.4 2.3 3.4 3.0

hosting capacity values obtained from MCS method. Same argument is valid for all three segments. Hence, for a multi-feeder network, minimum hosting capacity of the entire network is the lowest of the minimum hosting capacities of all feeders. Thus, considering a single feeder network, minimum hosting capacity can be defined as the maximum connectable solar PV capacity at the far end of the given feeder, while maximum hosting capacity is the maximum connectable solar PV capacity at the nearest end to the transformer. The same argument is valid for segment-wise analysis as well. In other words, the minimum and maximum hosting capacities are the connectable maximum solar PV capacity at the boundaries of each segment, far end of the feeder segment and nearest end to the transformer, respectively.

7 A Generalised Deterministic Approach to Evaluate PV Hosting Capacity of LV. . .

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163

Influence of Feeder Characteristics

Multi-feeder LV distribution networks with different feeder characteristics were simulated in DIgSILENT simulation platform in order to analyse the influence of feeder characteristics on PV hosting capacity. In this study, all test networks comprise a 11 kV/400 V, 100 kVA transformer with a transformer loading level of 50% (all multi-feeder scenarios are considered at the same transformer loading level). In addition, a common network classification of urban and rural networks is represented by selecting different length of feeders. Same analysis is repeated for different types of conductors in order to analyse the effect of R/X ratios on hosting capacity. For simplicity, balanced and evenly distributed loads are assumed. Furthermore, it is assumed that the constant power factor of all load points is 0.8 lagging. Voltage at the transformer terminal is maintained at a constant value of 1 pu. This analysis is mainly focused on the maximum connectable solar PV capacity at the feeder end (i.e. the minimum hosting capacity level) where the results are given in the following sections.

7.3.2.1

Number of Parallel Feeders

To estimate the effect of number of parallel feeders on solar PV hosting capacity, the analysis is carried out by increasing the number of parallel feeders. Total loading level of the network (in terms of transformer loading level) is maintained to a constant value (50% of the transformer capacity), and identical feeders are used to observe the impact only of number of parallel feeders.

7.3.2.2

Feeder Length

A common LV network classification of urban and rural networks is represented by selecting different length of feeders. In this work, 600-m-long feeders are used to represent urban network, whereas 1200-m-long feeders are used to represent rural networks. Total network loading levels are maintained at a constant value of 50% by the transformer capacity.

7.3.2.3

Conductor Type

Analysis described in Sect. 7.3.2 is repeated for different conductor types, AAC-Fly and ABC, in order to examine the effect of R/X ratio on solar PV hosting capacity. The relevant conductor specifications are given in column one of Table 7.6.

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Table 7.6 Solar deployment limits for two-feeder network per unit [6]

Type of conductor AAC-Fly R ¼ 0.4505 Ω/km X ¼ 0.292 Ω/km R/X ¼ 1.5 ABC–70 mm2 R ¼ 0.441 Ω/km X ¼ 0.08 Ω/km R/X ¼ 5.5 ABC–50 mm2 R ¼ 0.641 Ω/km X ¼ 0.08 Ω/km R/X ¼ 8

7.3.2.4

Number of parallel feeders 1 2 3 4 1 2 3 4 1 2 3 4

Network 1 (feeder length – 600 m) kW 73 55 50 46 64 51 47 45 51 38 34 32

Network 2 (feeder length – 1200 m) kW 55 36 30 28 45 32 27 25 38 26 21 19

Loading Level

Feeder loading level is one of the vital factors which govern the solar PV hosting capacity. In the analysis of impact of multi-feeders on hosting capacity, each feeder is applied with different loading levels while maintaining the same total transformer loading level of 50% of the transformer rating. The corresponding results are analysed to investigate the impact of loading level on the hosting capacity.

7.3.2.5

Study Results

The estimated PV hosting capacities in relation to influence factors discussed in Sects. 7.3.2.1, 7.3.2.2, 7.3.2.3 and 7.3.2.4 are given in Table 7.6. As per the results, since a number of factors are simultaneously influencing the hosting capacity, it is difficult to derive a direct correlation between solar PV hosting capacity and individual parameters. Nevertheless, it can be seen that for a given radial feeder, the minimum hosting capacity decreases as the feeder length increases, and the R/X ratio and the number of parallel feeders in the network increase. Furthermore, the minimum hosting capacity of a given feeder increases with feeder loading level.

7.3.3

Feeder-Based Hosting Capacity Approach

The detailed analysis of location sensitivity and feeder characteristics on PV hosting capacity shows that the PV hosting capacity essentially depends on the size and location of a solar PV system, feeder loading level, feeder length and conductor type.

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Thusly, for multi-feeder networks, individual feeders will exhibit different PV hosting capacities. In addition, the minimum hosting capacity of a distribution feeder is the maximum connectable solar PV capacity at the feeder end. Thus, for a given LV distribution network, the minimum PV hosting capacity can be formulated as given in (7.1).

HCmin ¼

8 HCF1,end > > > > < HCF2,end > > > > :

⋮

ð7:1Þ

HCFn,end

where HCFn, end is the maximum connectable solar PV capacity at the feeder end of nth feeder (n ¼ 1, 2, 3,. . .. . .). Furthermore, maximum hosting capacity increases with distribution of solar PV systems closer to the transformer. Comparison of hosting capacity values obtained from spot simulations (hosting capacities at boundaries of the feeder segments) and MCS method has led to define segment-wise minimum and maximum solar PV hosting capacities as: • Minimum hosting capacity in a given segment is the connectable maximum PV capacity at the furthest end (from the transformer) of that segment. • Maximum hosting capacity in a given segment is the connectable maximum PV capacity at the nearest end (to the transformer) of that segment. It is evident that extensive analytical efforts are required for accurate hosting capacity evaluation process because of the complexity associated with distribution networks. Thus, there should be generalised approaches that are extendable to address various aspects of concern. Thus, feeder-based hosting capacity approach is the best as individual hosting capacity of each feeder has to be established in multifeeder networks. Such a methodology needs to be extended in order to better capture the complexity of network modelling, constraints and technologies that will enable the greatest potential in generalisation. In essence, the development of a new deterministic approach for the evaluation of solar PV hosting capacity in a feeder level is important from a distribution planning perspective. Further, such an approach will facilitate the connection of solar PVs in a cost-effective way, thus increasing the associated environmental and social benefits. In this regard, Sect. 7.4 presents a generalised deterministic approach that can be used to evaluate the feeder level solar PV hosting capacity levels. By implementing such a methodology, distribution network operators can allow solar PV connections up to the feeder minimum hosting capacity level. Further, detailed network analysis will allow examination of whether new connections are permissible by increasing PV capacities beyond the bounds of minimum PV hosting capacity level.

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Devising Analytical Framework for Evaluating Solar PV Hosting Capacity

This section explores a novel deterministic approach which facilitates the evaluation of maximum solar PV penetration level governed by overvoltage limits which will enable better understanding of the associated benefits.

7.4.1

Theoretical Background

This section first explains the principles underlying power flow and voltage calculations using a simple feeder model with balanced and uniformly distributed loads. The principles are then extended to deal with distribution feeders embedded with solar PV generation using examples. Consider the single-line diagram of a single feeder network shown in Fig. 7.11. The resistance and reactance of the line are R and X in ohm per unit length, respectively, and the shunt capacitance is neglected. Vs is the supply voltage at the secondary of the transformer. The total voltage drop VDl in per unit (pu) of the feeder can be written as [8] VDl ¼

lðRPs þ XQs Þ lðXPs
RQs Þ þj 2V 2b 2V 2b

ð7:2Þ

where Vb is the nominal line-line voltage, Ps and Qs are the total real and reactive power components of the total load that is uniformly distributed in the feeder, and l is the total length of the feeder. Active power and reactive power flow at a distance d from the transformer can be written as (7.3).  Pd ¼ PS

 d 1
, l

  d Qd ¼ QS 1
l

ð7:3Þ

where Pd and Qd are the active and reactive power flow at distance d from the transformer.

Fig. 7.11 Simplified distribution feeder model

7 A Generalised Deterministic Approach to Evaluate PV Hosting Capacity of LV. . . Active power

167

Reactive power

Ps

Qs

Pd

Qd

d

0

l

Distance

0

d

l

Distance

Fig. 7.12 Active and reactive power profiles along the feeder (without solar PV)

nd

II

Quadrant

Distribution Grid Vs

R

X P Q

Solar Photovoltaic

POC

P

Q

st

I Quadrant Distribution Grid Vs

R

X

R

X

P Q

PL, QL

POC P

P

rd

III Quadrant

L,

P

Q

Q

PV , PV

PL, QL Solar Photovoltaic

Distribution Grid Vs

R

X

PV , PV

P Q

POC

PV , PV

Solar Photovoltaic Distribution Grid Vs

Solar Photovoltaic

POC

P

Q

PV , PV

P Q

QL

PL, QL

th

IV Quadrant

Fig. 7.13 Four-quadrant operation at POC of a distribution feeder [9]

Figure 7.12 illustrates PS and QS distribution in (7.3) graphically. As the actual voltage of the feeder is affected by the connection of solar PV in the feeder, (7.2) can be modified suitably. The next section discusses this aspect subjected to different operating conditions of the solar PV inverter.

7.4.2

Modelling Regimes

Modern-day solar PV systems possess reactive power capability allowing inverters to control the voltage at their point of connections (POC). In general, such an operational capability can be referred to as four-quadrant operation as shown in Fig. 7.13, where PPV and QPV are the real and reactive power outputs of the solar PV system and PL and QL are the real and reactive power demands of the connected load

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(this may include the battery). These operating scenarios of the distribution feeder can be listed as follows: • Ist Quadrant – POC operating at a lagging power factor while net P (PL
PPV) and net Q (QL
QPV) are positive • IInd Quadrant – POC operating at a lagging power factor while net P (PL
PPV) is negative and net Q (QL
QPV) is positive • IIIrd Quadrant – POC operating at a leading power factor while net P (PL
PPV) and net Q (QL
QPV) are negative • IVth Quadrant – POC operating at a leading power factor while net P (PL
PPV) is positive and net Q (QL
QPV) is negative In general, deterministic models should be developed in such a way that they can represent the four-quadrant operation of the solar PV system (which may include a battery) where possible. In specific terms, the operation at a unity power factor or at a fixed leading or lagging power factor must be considered.

7.4.2.1

Solar PV Inverters Operating at Unity Power Factor

Suppose that a solar PV generator is installed at a distance d from the distribution transformer and let PPV is the real power output of the PV system while reactive power output, QPV, is zero as unity power factor operation. At the POC, the voltage is VPV. When PPV > Pd, active and reactive power flows along the feeder are illustrated in Fig. 7.16. Zero crossing point denoted by d0 in Fig. 7.14 is where the transition to the direction of active power flow occurs. Just to the right of the zero crossing point, active power flows towards the transformer, and just to the left of the zero crossing point, active power flows from the transformer. The zero crossing point can be established as d

0

 ¼

 PPV 1
l PS

ð7:4Þ

Reverse power flow due to the solar system causes a voltage rise at the POC. Using (7.2), the new magnitude of the drop in the voltage from 0 to d0 can be written as in (7.5): VD0
d0 ¼

d 0 RðPS
PPV Þ þ X ðQS þ Q0 Þ d0 þ j 2 2 V 2b 

X ðPS
PPV Þ
RðQS þ Q0 Þ V 2b

ð7:5Þ

The magnitude of the rise in voltage from d0 to d can be written as in (7.6):

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0 Fig. 7.14 Active and reactive power profiles along the feeder (with unity power factor solar inverter)

VRd0
d ¼

ðd
d 0 Þ RðPPV
Pd Þ
X ð Q0 þ Qd Þ ðd
d 0 Þ þ j 2 2 V 2b 

X ðPPV
Pd Þ þ Rð Q0 þ Qd Þ V 2b

ð7:6Þ

 0 where Q0 ¼ Qs 1
dl The total voltage rise from distribution transformer to the POC can be obtained by subtracting (7.5) from (7.6). VR0
d ¼

   re  im dRPPV  dXPPV  2 2 VD VD
2λ
λ þ j
2λ
λ l l V 2b V 2b

ð7:7Þ

im where λ ¼ dl , VDre l is the real component of voltage drop and VDl is the reactive component of voltage drop. The voltage rise in (7.7) is a linear function of the solar PV system as well as its location on the feeder. Hence, the maximum connectable solar capacity at a fixed location can be derived theoretically that can give rise to the maximum allowable voltage rise in the feeder. For unity power factor operation of solar PV inverter, the maximum connectable solar PV capacity in three phases at a distance d from the distribution transformer can be formulated as given in (7.8). Here, VPV, VS and VDl are in pu, and the phase angle deviations of VPV and VS have been neglected.

PPV ¼

   V 2b  ðV PV
V S Þ þ 2λ
λ2 VDl Rd

ð7:8Þ

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7.4.2.2

Solar PV Inverters Operating at Leading Power Factor

Suppose that a solar PV generator is installed at a distance d from the distribution transformer and let PPV and QPV be the real and reactive power outputs of the PV system. This case is illustrated in Fig. 7.15 where the reversal of both active and reactive power flows exists when solar inverter is operating at a leading power factor. Zero crossing point of reactive power flow profile along the feeder can be formulated similar to (7.4) leading to (7.9). d00 ¼

  Q 1
PV l QS

ð7:9Þ

The total voltage rise from distribution transformer to the POC can be decomposed using active and reactive power flows. VR0
d ¼

   dPPV R þ X tan cos
1 pf pv

þj

V 2b

 
2λ
λ2 VDre l

   dPPV X
R tan cos
1 pf pv V 2b




2λ
λ VDim l

!

ð7:10Þ

2

If the PV inverter operates at a fixed power factor, then the reactive power becomes QPV ¼ PPV tan (cos
1pfpv). Maximum amount of solar power generation that will cause the voltage to reach the overvoltage limit at a distance d from the transformer for a leading power factor operation can be formulated as in (7.11). Here, VPV, VS and VDl are in pu, and the phase angle deviations of VPV and VS have been neglected.     V 2b   ðV PV
V S Þ þ 2λ
λ2 VDl PPV ¼ 
1 d R þ X tan cos pf pv

ð7:11Þ

Fig. 7.15 Active and reactive power profiles along the feeder (with leading power factor solar inverter)

7 A Generalised Deterministic Approach to Evaluate PV Hosting Capacity of LV. . .

7.4.2.3

171

Solar PV Inverters Operating at Lagging Power Factor

Suppose that a solar PV generator is installed at a distance d from the distribution transformer and let PPV and
QPV be the real and reactive power outputs of the PV system. As shown in Fig. 7.16, reactive power supplied by the grid is increased due to solar PV inverter operating as an inductive load. In this case, solar PV inverter will cause an additional voltage drop in the feeder. The total voltage rise from distribution transformer to the POC can be decomposed using active and reactive power flows. VR0
d ¼

   dPPV R
X tan cos
1 pf pv V 2b

þj

 
2λ
λ2 VDre l

!      im dPPV X þ R tan cos
1 pf pv 2
2λ
λ VDl V 2b

ð7:12Þ

Similar to Sect. 7.4.2.2, maximum amount of solar power generation that will cause the voltage to reach the overvoltage limit at a distance d from the transformer for lagging power factor operation can be formulated as in (7.13). Here, VPV, VS and VDl are in pu, and the phase angle deviations of VPV and VS have been neglected.     V 2b   ðV PV
V S Þ þ 2λ
λ2 VDl PPV ¼  d R
X tan cos
1 pf pv

ð7:13Þ

Table 7.7 summarises the mathematical models developed for evaluation of solar PV hosting capacity at a given point in a feeder considering three different operating conditions of a PV inverter. The simplified equation for the feeder end hosting capacity (i.e. when d ¼ l) is also shown in the same table.

Fig. 7.16 Active and reactive power profiles along the feeder (with lagging power factor solar inverter)

Lagging power factor

Leading power factor

PV inverter operation mode Unity power factor

 V 2b ðV PV d ðR
X tan ð cos
1 pf pv ÞÞ

  
V S Þ þ 2λ
λ2 VDl

V 2b fðV PV R
X tan ð cos
1 pf pv Þ

V S Þ þ VDl g
V S Þ þ VDl g



  2λ
λ2 VDl

At the feeder end (d ¼ l) V 2b Rd fðV PV
V S Þ þ VDl g V 2b fðV PV
RþX tan ð cos
1 pf pv Þ

   V 2b  2 Rd ðV PV
V S Þ þ 2λ
λ VDl  V 2b ðV PV
V S Þ þ d ðRþX tan ð cos
1 pf pv ÞÞ

At a distance d from the transformer

Table 7.7 Generalised mathematical models for different operation conditions of PV inverters

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7 A Generalised Deterministic Approach to Evaluate PV Hosting Capacity of LV. . . Table 7.8 Safe limits of solar PV hosting capacity for the urban LV network

7.4.3

Feeder 1 Feeder 2 Feeder 3

Safe limit for HC calculated from model (kW) 32 48 37

173

Safe limit for HC simulated (kW) 30 41 38

Verification of the Proposed Analytical Framework

The proposed deterministic approach in Sect. 7.4.2 is used to evaluate the hosting capacity of the practical distribution network discussed in Sect. 7.2 (named as Case 1) and of the simple distribution feeder (Case 2) with the aid of DIgSILENT PowerFactory simulations for verification purposes. Case 1: Practical LV distribution network The total midday peak demand of the distribution network is (PS and QS) 82 kW and 60 kVAr, respectively (40% by the transformer capacity). Based on the assumption that all three feeders are loaded equally, the total voltage drop along each feeder can be calculated using (7.2). These calculated total voltage drops of feeder 1 (ABC-50 mm2), feeder 2 (ABC-70 mm2) and feeder 3 (ABC-70 mm2) are about 3%, 1.7% and 2.6%, respectively, at the solar peak time. The safe limits of the solar PV hosting capacities of each feeder are calculated using (7.8) where PV inverters are operating at the unity power factor. Table 7.8 gives safe limits of hosting capacity values calculated using the mathematical models and spot simulations constrained by overvoltage for each feeder. As an example, detailed calculations relevant to identifying safe limit of solar PV hosting capacity on feeder 1 are given below: Example The total voltage drop in feeder 1 is approximately 3%. The secondary line-line voltage at the distribution transformer is set at 1.04 pu to ensure that the voltage is within the stipulated limits under maximum demand conditions at the night peak. At this loading level (40%), supply voltage2 of the distribution transformer is about 1.024 pu. From (7.8), the maximum connectable solar PV capacity at feeder end is PPV,Feeder 1 ¼

4002 fð1:06
1:024Þ þ 0:03g  32 kW 0:641  0:51

Case 2: A single feeder test network The network consists of a 100kVA, 11 kV/400 V transformer connected to a 1-km-long feeder as shown in Fig. 7.17. The total midday peak demand on the feeder is (PS and QS) 40 kW and 30 kVAr (50% by the transformer capacity). Total load is assumed to be balanced and uniformly distributed on ten nodes along the feeder. Further, secondary of the transformer is assumed to be at a constant voltage of 1 pu. 2

Secondary voltage of the transformer depends on the transformer loading level.

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Fig. 7.17 Single distribution feeder model Table 7.9 Maximum connectable solar capacity when solar PV system operates at unity power factor [9]

AAC-Fly ABC – 70 mm2 ABC – 50 mm2

HC at feeder end Simulated 0.58 0.49 0.41

Calculated 0.57 0.49 0.41

HC at feeder middle Simulated Calculated 0.96 0.96 0.84 0.84 0.69 0.69

Table 7.10 Maximum connectable solar capacity when solar PV system operates at 0.9 leading power factor [9]

AAC-Fly ABC – 70 mm2 ABC – 50 mm2

HC at feeder end Simulated 0.48 0.50 0.43

Calculated 0.48 0.50 0.43

HC at feeder middle Simulated Calculated 0.79 0.81 0.84 0.85 0.71 0.73

Table 7.11 Maximum connectable solar capacity when solar PV system operates at 0.9 lagging power factor [9]

AAC-Fly ABC – 70 mm2 ABC – 50 mm2

HC at feeder end Simulated 1.41 0.63 0.52

Calculated 0.92 0.59 0.49

HC at feeder middle Simulated Calculated 1.98 1.55 1.06 1.02 0.85 0.82

The test network is analysed for maximum connectable solar PV capacity at two different locations so that the upper voltage limit stipulated by the utility (taken as +6%) is not violated. The analysis has been repeated for different types of conductors considered in Sect. 7.3 in order to investigate the effect of R/X ratio on solar PV hosting capacity. Accordingly, three cases are presented for different operating scenarios of the PV inverters: unity power factor, 0.9 leading power factor and 0.9 lagging power factor. Solar PV hosting capacity values which were obtained from the simulations and mathematical model are given in Tables 7.9, 7.10 and 7.11 for the three scenarios. In

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each case, hosting capacity values relevant to feeder end and middle of the feeder were evaluated and compared against the results from the mathematical models. All solar PV capacity values are given in per unit with transformer ratings as base values. As shown in Tables 7.9, 7.10 and 7.11, solar PV hosting capacities obtained from simulations and proposed deterministic method are in close agreement verifying the accuracy of the deterministic approach. The minimum hosting capacity of a given radial distribution feeder is the maximum connectable solar PV capacity at the feeder end which can be defined as the safe limit of the hosting capacity. Thus, the proposed mathematical model enables the evaluation of a safe limit of the PV hosting capacity of distribution networks without resorting to complex computer simulations. From a distribution system planning perspective, the initial use of a deterministic approach is convenient and more practical than using extensive simulations. Therefore, utilities can make use of the proposed approach as a guide to evaluate the maximum connectable solar capacity of a given distribution feeder using the data which are not overly demanding.

7.4.4

Comparison of the Proposed Deterministic Approach with Stochastic Approach

As stated in Sect. 7.3.3, the minimum PV hosting capacity (safe limit of the hosting capacity) for a given radial distribution feeder is the maximum connectable solar PV capacity at the feeder end (verified using stochastic Monte Carlo simulations). Thus, the analysis presented in Sect. 7.4.3 (Case 2) justified that the PV hosting capacity values obtained from both stochastic and deterministic approaches are in close agreement. The pros and cons of stochastic and deterministic approaches in PV hosting capacity analysis are shown in Table 7.12. Table 7.12 Comparison of stochastic and feeder level deterministic methods in hosting capacity analysis Pros

Cons

Stochastic approach Randomness of solar PV location and capacity of PV system can be addressed easily

Needs detailed network modelling Increased computational burden Cannot be generalised Variability in accuracy depends on the number of simulations and complexity of the network model

Deterministic approach Feeder-based limitations and diversity can be accommodated Can be generalised Improved accuracy Easier and more practical Whole network PV hosting capacity can be maximised Reduces computational effort Can be applied to one location at a time Not able to capture all performance criteria for hosing capacity

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As per Table 7.12, the deterministic approach for feeder level PV hosting capacity offers substantial benefits over a stochastic approach.

7.5

Conclusions and Future Works

In this chapter, a feeder based, deterministic approach was proposed for the evaluation of the solar PV hosting capacity in LV distribution networks. The hosting capacity was essentially constrained by overvoltage limits of many of the LV distribution networks. The deterministic method was developed in order to evaluate the maximum allowable solar PV capacity at a given point of distribution feeder constrained by overvoltage limits. Related to PV hosting capacity evaluation, Monte Carlo-type stochastic simulations are not practical in distribution network planning environments due to extensive network modelling efforts and the complexity. Thus, individual feeder-based analysis approach is recommended and considered to be more effective. Based on the findings, a safe limit of the solar PV hosting capacity (the minimum hosting capacity) is defined as the maximum allowable solar PV capacity at the far end of a feeder that can be evaluated using the proposed deterministic approach. Under this framework, distribution network operators and planners can investigate the capability and limitations of solar PV penetration. The proposed feeder-based hosting capacity evaluation approach can be seen to capture all influencing factors on solar PV hosting capacity. Thus, this can be used as an approximate guide or a rule of thumb to evaluate solar PV hosting capacity at a given point of LV feeders for overvoltage curtailment without using complex stochastic techniques. Further research is needed to confirm the applicability of the developed approach in realistic network environments. Other network performance indices such as voltage unbalance due to PV hosting have not been considered in the present work and require investigation of whether such parameters become dominant or not. Acknowledgments This work was supported by SRC grant SRC/LT/2017/16, University of Moratuwa, Sri Lanka. The authors would like to thank Lanka Electricity Company Ltd., Sri Lanka, and RMA Pvt. Ltd., Sri Lanka, for providing necessary data and field measurements for this study.

References 1. REN 21 (2019). Renewables 2019 global energy report. Technical Report. 2. Smith, J., Rönnberg, S., Blanco, A., Bollen, M., Emin, Z., Ilisiu, D., et al. (2016). Power quality aspects of solar power. Available via https://e-cigre.org/publication/672. Accessed Dec 2016.

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3. Bollen, M., & Rönnberg, S. (2017). Hosting capacity of the power grid for renewable electricity production and new large consumption equipment. Energies. https://doi.org/10.3390/ en10091325. 4. Jothibasu, S., Dubey, A., & Santoso, S. (2016). Integration photovoltaic generation. Research Gate. https://doi.org/10.13140/RG.2.2.33939.37928. 5. Chathurangi, D., Jayatunga, U., Rathnayake, M., Wickramasinghe, A., Agalgaonkar, A., & Perera, S. (2018a). Potential power quality impacts on LV distribution networks with high penetration levels of solar PV. Paper presented at 18th international conference on Harmonics and Quality of Power, Ljubljana, Slovenia. 6. Chathurangi, D., Jayatunga, U., Siyambalapitiya, T., Wickramasinghe, A., Perera, S., & Agalgaonkar, A. (2018b). Connection of solar PV to LV networks: Considerations for maximum penetration level. Paper presented at Australasian Universities Power Engineering conference on transition to a low-carbon energy future, University of Auckland, New Zealand. 7. Ismael, S. M., Aleem, S. H. E. A., Abdelaziz, A. Y., & Zobaa, A. F. (2019). Review: State-of-theart of hosting capacity in modern power system with distributed generation. Renewable Energy. https://doi.org/10.1016/j.renene.2018.07.008. 8. Kersting, W. H. (2012). Distribution system modelling and analysis (3rd ed.). London: Taylor and Francis Group. 9. Chathurangi, D., Jayatunga, U., Perera, S., & Agalgaonkar, A. (2019). Evaluation of maximum solar PV penetration: Deterministic approach for overvoltage curtailments. Paper presented at 9th IEEE international conference on Innovative Smart Grid Technologies, University of Politehnica, Bucharest, Romania.

Chapter 8

Hosting Capacity Maximization Based on Optimal Reconfiguration of Distribution Networks with Optimized Soft Open Point Operation Ibrahim Mohamed Diaaeldin, Shady H. E. Abdel Aleem, Ahmed El-Rafei, Almoataz Y. Abdelaziz, and Ahmed F. Zobaa

8.1

Introduction

Distribution network reconfiguration (DNR) is the change in the status of operating lines in order to provide the resilience of distribution network topologies. DNR is broadly used to minimize power losses, improve the voltage profile, and increase network reliability. The requirements for applying DNR correctly hinges on maintaining the radial topology of the distribution network, serving the connected loads, keeping the branches within their specified thermal limits, and preserving the network’s voltage limits. DNR was previously solved using various optimization techniques. These optimization techniques are divided into three categories: heuristic, metaheuristic, and mathematical techniques. From the mathematical technique

I. M. Diaaeldin (*) · A. El-Rafei Engineering Physics and Mathematics Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt e-mail: [email protected]; [email protected]; [email protected] S. H. E. Abdel Aleem Mathematical, Physical and Engineering Sciences Department, 15th of May Higher Institute of Engineering, Cairo, Egypt e-mail: [email protected] A. Y. Abdelaziz Faculty of Engineering and Technology, Future University in Egypt, Cairo, Egypt e-mail: [email protected] A. F. Zobaa College of Engineering, Design and Physical Sciences, Brunel University London, Uxbridge, UK e-mail: [email protected] © Springer Nature Switzerland AG 2020 A. F. Zobaa et al. (eds.), Hosting Capacity for Smart Power Grids, https://doi.org/10.1007/978-3-030-40029-3_8

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point of view, it provides a near-global solution of the distribution system configuration like mixed-integer nonlinear programming (MINLP) [1] and mixed-integer second-order cone programming (MISOCP) [2]. From the heuristic and metaheuristic viewpoint, it provides an acceptable local optimal solution, like genetic algorithm [3], particle swarm optimization [4], Harris hawks optimization algorithm [5], and others. Meanwhile, DGs are widely integrated into the distribution network along with fossil-fuel-based power stations. The wide integration of renewables has many impacts on the system’s operational and performance indices, including total harmonic distortion, aggregated voltage deviation, voltage profile, overall system’s power factor, and others. As a result of these impacts as well as the emerging concepts of smart grids that have made the power system more complex and unpredictable, the hosting capacity (HC) limit of the distribution network is formulated to act as a simple but reliable index that can help decide where and when to add more DGs into the system as the HC provides an indication for network operators about the available DG powers that can be accommodated by the distribution network. In the literature, many perspectives were investigated to maximize HC [6] such as power quality improvement, network reinforcement, DNR application, and soft open point allocation. From the power quality perspective, studies were conducted in [7, 8] to maximize constrained harmonic distortion HC using a C-type passive filter to mitigate harmonic distortion and in turn maximize the harmonic constrained HC. From the perspective of network reinforcement, a study was conducted in [9] on an existing Egyptian distribution network to maximize its HC using network reinforcement. From the perspective of DNR, a study was conducted in [10] on a distribution network in Japan that contains 235 switches in order to maximize HC by selecting the best configurations of the distribution network. Benefits of static and dynamic reconfiguration were investigated in [11], in which a static reconfiguration was found to be beneficial in the planning stage while a dynamic reconfiguration was found effective for active distribution networks especially when a higher number of remotely controlled switches are available. A minimum number of switching events was done to maximize HC using multi-period reconfiguration in [12]. From the perspective of SOP allocation, a strengthened second-order cone programming was investigated on the IEEE 33-bus system for maximizing its HC using SOPs [13]; a project was analyzed in [14] connecting island of Anglesey network with the mainland in North Wales using an SOP to maximize HC of the network. In this chapter, a strategy is proposed to maximize DG integration in the distribution network without violating system operational limits. The strategy is based on the available active and reactive powers provided by the substation. The proposed strategy aims to prepare the distribution network using DNR and SOP installations to host more DG installations in the distribution system. In order to solve the MINLP problem under investigation, a new metaheuristic optimization technique named expanded invasive weed optimization (exIWO), proposed by Josiński et al. [15], was used. This chapter is organized as follows: Sect. 8.2 presents a detailed problem statement including power flow equations, DG and SOP models, and DNR

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methodology; Sect. 8.3 illustrates the problem formulation and a brief description of the exIWO algorithm; Sect. 8.4 presents the results of the case studies under investigation; and Sect. 8.5 is dedicated to the conclusions of this research.

8.2

Problem Statement

In this section, the power flow equations, DG and SOP modeling, and the proposed DNR methodology are illustrated in detail. The distribution system model is illustrated in Fig. 8.1a in the presence of DGs and SOPs, and SOP-based IGBT connection model is illustrated in Fig. 8.1b.

Fig. 8.1 Distribution system modeling with DG and SOP: (a) power injection model, (b) SOP-based IGBT connection model

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Power Flow Equations

Power flow equations essential to solve the distribution system under study are expressed as follows: Pkþ1 ¼ Pk  Pload kþ1  r k,kþ1  Qkþ1 ¼ Qk  Qload kþ1  xk,kþ1 

P2k þ Q2k jV k j2 P2k þ Q2k jV k j2

ð8:1Þ ð8:2Þ


 P2 þ Q2 jV kþ1 j2 ¼ jV k j2  2ðr k,kþ1  Pk þ xk,kþ1  Qk Þ þ r 2k,kþ1 þ x2k,kþ1 k 2 k ð8:3Þ jV k j where Pk and Qk are the injected active and reactive powers at the kth bus, load respectively; Pload kþ1 and Qkþ1 are the active and reactive powers of loads attached to bus k + 1 loads, respectively; |Vk| is the magnitude of the kth bus voltage; and rk, k + 1 and xk, k + 1 are the branch resistance and reactance, joining between buses k and k + 1, respectively.

8.2.2

DG Modeling

In this study, DG is modeled as a generator with a unity power factor. A constraint regarding the DG installed capacity limit is given in (8.4). It should be mentioned that other DG sets with smart inverters can be used; however, there is no need for them as the SOP can regulate both active and reactive powers in the system. 0  PDG k  DGcap ,

8k 2 N bus

ð8:4Þ

where PDG is the injected DG active power at bus k, DGcap is the maximum DG k capacity limit, and Nbus is the number of buses in the distribution system.

8.2.3

SOP Modeling

Soft open points were first proposed by Bloemink and Green [16]. Three different topologies were employed to integrate SOPs, and they are composed of back-to-back (B2B) voltage source converter (VSC), static synchronous series compensator, and unified power flow controller [17]. The B2BVSC is used in this study because of its capabilities to enhance power quality. An SOP is modeled using its injected powers (active and reactive) at its terminals as shown in Fig. 8.1. In addition, the algebraic

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sum of the SOP active powers injected at its terminals and its internal active losses by its VSCs must equal to zero, as expressed in Eq. (8.5). Thus, PSOP þ PSOP þ PSOPloss þ PSOPloss ¼0 I J I J

ð8:5Þ

The reactive power limits are provided in Eq. (8.6), and the SOP size limit is presented in Eq. (8.7). Thus, min max  QSOP  QSOP , 8I, J 2 N f QSOP I I I q
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2
SOP 2  SSOP PSOP þ QI , 8I 2 N f I I

ð8:6Þ ð8:7Þ

where Nf is the number of feeders, PSOP is the SOP’s active power transferred to the I is the SOP’s active power transferred to the Jth feeder, PSOPloss is Ith feeder, PSOP J I the internal power loss of the VSC coupled to the Ith feeder, PSOPloss is the internal J is the SOP’s reactive power active loss of the VSC coupled to the Jth feeder, QSOP I is the SOP’s reactive power transferred to the Jth transferred to the Ith feeder, QSOP J min SOP max and Q are the lower and upper limits of the SOP’s reactive feeder, QSOP I I is the maximum size of the planned power transferred to the Ith feeder, and SSOP I and PSOPloss ) is expressed in SOP. Further, the active loss of each VSC (PSOPloss I J Eq. (8.8): ¼ ASOP PSOPloss I loss

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
SOP 2
SOP 2ffi PI , 8I 2 N f þ QI

ð8:8Þ

where ASOP loss is the loss coefficient associated to converter internal power loss [18], which signifies the percentage of leakage in the delivered power between feeders.

8.2.4

Network Reconfiguration

In this study, the procedure of DNR is employed as follows [19]: (i) An individual sectionalized line is chosen inside each loop in order to be changed to a tie-line line. (ii) The previous tie line in this loop changes to a sectionalized line, as described in Fig. 8.2. Thus, there is no need to check radiality as the exchange between switches was done on the same loop without violating the network’s radial structure. (iii) The procedure is repeated while keeping the number of tie lines fixed before and after reconfiguration.

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Fig. 8.2 DNR procedure: (a) before DNR, (b) after DNR

8.3 8.3.1

Problem Formulation Objective Function

The overall hosting capacity (HC) is the objective function, needed to be maximized. HC is formulated as follows: PN DG DG Pi Max HC ð%Þ ¼ PN bus i¼1  100 loadnormal P k¼1 k

ð8:9Þ

is the active demanded power at bus k at the normal loading where Ploadnormal k conditions.

8.3.2

Constraints

In addition to the DG capacity limit expressed in (8.4), SOP reactive power constraints given in Eq. (8.6), and SOP size limit given in Eq. (8.7), constraints concerning slack bus power factor (PFslack), voltage magnitudes, and lines thermal capacities are formulated as follows: slack PFslack  PFslack min  PF max

V min  jV k j  V max , jI k,kþ1 j  I rated k,kþ1 ,

8k 2 N bus 8k 2 N bus

ð8:10Þ ð8:11Þ ð8:12Þ

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slack where PFslack min and PFmax are the minimum and maximum slack power factor limits, respectively; Ik, k + 1 is the current flowing in the branch joining buses k and k + 1; and I rated k,kþ1 is the rated current of this branch. Besides, the reverse power due to SOP and DG installations is not permitted in this study as expressed in Eq. (8.13). Moreover, reactive power provided by SOPs is limited as shown in Eq. (8.14) to avoid overcompensation of the network.

PLi  α  PDG  β  PSOP  γ  PSOP  0, i I J X


8i 2 N bus

N bus  X SOP QSOP þ Q Qload  I J p

ð8:13Þ ð8:14Þ

p¼1

where α equals 1 when a DG unit is connected to bus i, β equals 1 when an SOP is connected to feeder I of bus i, and γ equals 1 when an SOP is connected to feeder J of bus i; otherwise, α ¼ β ¼ γ ¼ 0.

8.3.3

Expanded Invasive Weed Optimization

The invasive weed optimization (IWO) algorithm was designed by Mehrabian and Lucas [20] to deal with nonlinear optimization problems (Fig. 8.3). The motivation of the IWO is based on the colonization of weed and was further upgraded in 2014 [15] to deal with MINLP problems including discrete and continuous variables. The effectiveness of the exIWO arises in its fast convergence toward finding the global optimum and also its ability to solve mixed continuous-discrete problems. The exIWO is based on the propagation of weeds and their compliance with ecological conditions. The population is divided into individuals and seeds. First, the population assigned by random values. Further, each individual i produces a bunch of seeds (Si) based on its objective function value (Fi) as follows: 

S  Smin Si ¼ Smin þ ðF i  F min Þ max F max  F min

 ð8:15Þ

where Smax and Smin are the upper and lower number of seeds, respectively. Fmax and Fmin represent the best and worst objective function value of the population. Second, the exploration phase includes three methodologies: spreading, dispersing, and rolling down. The spreading hinges on seed dissemination, in which a set of new individuals is produced by each seed randomly. Besides, the dispersing is known as the divergence among individuals and their offspring. It signifies the distance covered by the seed from the parent plant to its final placement. The distance formulated as a normal distribution function in which its standard deviation is expressed Eq. (8.15).

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Fig. 8.3 Proposed problem formulation using exIWO algorithm

 σ iter ¼

itermax  iter itermax

m ðσ init  σ fin Þ þ σ fin

ð8:16Þ

where iter is the present iteration, itermax is the iterations’ maximum limit, σ init and σ fin are the initial and final values of the standard deviation, and m is a nonlinear modulation factor. Further, the rolling down resembles the placement of a seed to a new location based on its objective function value. Finally, the procedure is then started over again from the exploration phase until the termination criteria are met. Termination is fulfilled if iter is higher than itermax or the difference between individuals’ objective function values was lower than a predefined value.

8.3.4

HC Maximization Strategy

Starting from the aim of this study, i.e., HC maximization resulting from the installation of more DGs, the main obstacle facing maximization of HC is PFslack as a result of injecting active power from DGs; the PFslack will decrease, and it will be limited by PFslack min . Therefore, increasing DG penetration depends on the reactive

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power provided by the slack bus (Qslack), where the initial injected active, reactive, and apparent powers by the slack bus are Pslack , Qslack , and Sslack , respectively. In 0 0 0 order to increase DG penetration, the following strategy is deployed as follows: Step 1: DNR is done first to provide the resilience of the network topology. Step 2: SOPs are installed instead of tie lines after DNR is done to inject reactive powers to the system, and as a result, the reactive power injected by the slack bus Qslack will decrease to Qslack , and also PFslack will increase until it reaches its near 0 1 maximum/maximum limit PFslack max . decreased to Pslack , and PFslack will decrease Step 3: DGs are then installed, Pslack 0 2 again until it reaches its near minimum/minimum limit PFslack min . The proposed strategy will be tested in the following section.

8.4

Simulation Results and Discussions

In this study, the 83-bus distribution system [21] is the system investigated to maximize its HC. The topology of this system consists of 83 nodes and 96 lines, as shown in Fig. 8.4. These lines are composed of 96 lines including sectionalized and tie lines. The voltage limits Vmin and Vmax are set to 0.95 and 1.05 p.u., respectively, and I rated k,kþ1 is set to 310 A. The number of installed SOPs ranges from one to five, and SSOP ¼ SSOP are set to 5 MVA and ASOP I J loss is set to 2% [18]. The results obtained after installing DGs along with DNR with and without SOPs for the 83-bus distribution system are shown in Tables 8.1, 8.2, 8.3, and 8.4. Results showed that applying DNR only did not guarantee a solution due to the violation of PFslack limit at different loading levels. However, installing SOPs min allowed DG installations as it injects reactive power in order to improve PFslack to be greater than PFslack min . Besides, it is notable that HC increases proportionally as the number of SOPs increases. The best HC values resulted from simultaneous DNR along with DG and SOP installations, displayed in bold in Table 8.1, where five SOPs are installed at the three loading levels. Optimal network configuration, capacity, and sites of SOPs and DGs for five installed SOPs at normal loading conditions are given in Table 8.5. Branch current and voltage profiles at normal loading conditions for five installed SOPs at normal loading conditions are given in Figs. 8.5 and 8.6, respectively. An 83-bus compensated system at normal loading condition for five installed SOPs is given in Fig. 8.7.

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Fig. 8.4 83-bus distribution system Table 8.1 HC results at different loading levels Loading level Light (50%) Normal (100%) Heavy (130%) a

DNR only NAa NA NA

Simultaneous DNR with SOP and DG allocation 1 SOP 2 SOPs 3 SOPs 4 SOPs 29.1164 29.4533 29.8589 29.8059 9.1711 53.9682 56.1905 56.7901 NA NA 71.0758 72.0031

5 SOPs 30.7760 59.0829 73.2427

NA means not applicable

Table 8.2 NDG at different loading levels Loading level Light (50%) Normal (100%) Heavy (130%)

DNR only NA NA NA

Simultaneous DNR with SOP and DG allocation 1 SOP 2 SOPs 3 SOPs 4 SOPs 58 14 59 14 2 14 59 14 NA NA 14 59

5 SOPs 60 24 59

Table 8.3 Total active losses in kW at different loading levels Loading level Light (50%) Normal (100%) Heavy (130%)

DNR only NA NA NA

Simultaneous DNR with SOP and DG allocation 1 SOP 2 SOPs 3 SOPs 4 SOPs 290.6481 318.8077 258.2105 256.0974 728.9004 627.7467 725.2993 595.8846 NA NA 914.4549 860.9542

5 SOPs 266.5299 645.9454 904.6237

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Table 8.4 PFslack at different loading levels Loading level Light (50%) Normal (100%) Heavy (130%)

Simultaneous DNR with SOP and DG allocation 1 SOP 2 SOPs 3 SOPs 4 SOPs 0.9017 0.9031 0.9022 0.9009 0.9021 0.9089 0.9080 0.9096 NA NA 0.9116 0.9126

DNR only NA NA NA

5 SOPs 0.9000 0.9009 0.9105

Table 8.5 Optimal network configuration, capacity, and sites of SOPs and DGs for five SOPs at normal loading condition Configuration (tie lines) 16-42-72-84-8586-88-89-91-9293-94-96

SOP sizing

SOP locations (tie lines) 85

PSOP I (MW) 0.4000

PSOP J (MW) 0.540

QSOP I (MVAr) 3.2806

QSOP J (MVAr) 3.6594

72

0.3290

0.2000

3.2128

1.7144

93

0.2000

0.2193

0.5545

0.3055

92

0.3084

0.2000

2.6975

0

0

0

94

0

0

DG location (bus) 28 31 19 6 83 80 79 78 41 40 36 53 52 32 75 12 27 46 45 10 8 44 68 71

DG sizing (MW) 1.8000 1.8000 1.2000 1.1000 0.4000 0.2000 2.0000 0.4000 0.2000 0.0200 0.1000 0.5000 0.5000 0 1.2000 1.2000 0.1000 0.2000 0.8000 0.3000 0.3000 0.0300 0.4000 2.0000

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Fig. 8.5 Branch current profile at normal loading condition

Fig. 8.6 Voltage profile at normal loading condition

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8

A

1

55

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~

22 23

20 18

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D

H

~ ~

65

~

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~

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~

~

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42

77

K

~ DG node

~

F

43

46

~

~

SOP

Fig. 8.7 An 83-bus compensated system at normal loading condition for five installed SOPs

8.5

Conclusion

Feeder reconfiguration is an integral component of smart distribution strategy in modern active distribution networks. Also, much attention has been paid to the concept of the HC approach to determine how much of new renewable energy resources or DG units can be connected to the network at a certain feeder based on the comparison of a set of performance indices with a known index limit for each of them. Once any of those indices exceeds its limit, the HC is determined. If more than a value for each index is determined, the minimum (safer) value is then chosen as the overall HC value of the network [22]. In this regard, this chapter presents an integral component strategy to optimally allocate DGs using DNR and SOP allocation in order to maximize the HC of an 83-distribution network. The exIWO metaheuristic algorithm was employed to solve the MINLP problem under study. A case study was conducted to increase the HC of the 83-bus distribution system. The proposed strategy has proven its ability to maximize the HC of the distribution network at three loading levels.

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References 1. Paterakis, N. G., et al. (2016). Multi-objective reconfiguration of radial distribution systems using reliability indices. IEEE Transactions on Power Apparatus and Systems, 31, 1048. https:// doi.org/10.1109/TPWRS.2015.2425801. 2. Taylor, J. A., & Hover, F. S. (2012). Convex models of distribution system reconfiguration. IEEE Transactions on Power Apparatus and Systems, 27, 1407–1413. 3. Eldurssi, A. M., & O’Connell, R. M. (2015). A fast nondominated sorting guided genetic algorithm for multi-objective power distribution system reconfiguration problem. IEEE Transactions on Power Apparatus and Systems, 30, 593. https://doi.org/10.1109/TPWRS.2014. 2332953. 4. Sulaima, M. F., Shamsudin, N. H., Jaafar, H. I., Dahalan, W. M., & Mokhlis, H. (2014). A DNR and DG sizing simultaneously by using EPSO. In 2014 5th International conference on intelligent systems, modelling and simulation (pp. 405–410). IEEE. https://doi.org/10.1109/ ISMS.2014.75. 5. Abdel Aleem, S. H. E., Zobaa, A. F., Balci, M. E., & Ismael, S. M. (2019). Harmonic overloading minimization of frequency-dependent components in harmonics polluted distribution systems using Harris Hawks optimization algorithm. IEEE Access, 7, 100824–100837. 6. Ismael, S. M., Abdel Aleem, S. H. E., Abdelaziz, A. Y., & Zobaa, A. F. (2019). State-of-the-art of hosting capacity in modern power systems with distributed generation. Renewable Energy, 130, 1002–1020. 7. Sakar, S., Balci, M. E., Aleem, S. H. E. A., & Zobaa, A. F. (2016). Hosting capacity assessment and improvement for photovoltaic-based distributed generation in distorted distribution networks. In 2016 IEEE 16th International conference on environment and electrical engineering (EEEIC) (pp. 1–6). IEEE. https://doi.org/10.1109/EEEIC.2016.7555515. 8. Sakar, S., Balci, M. E., Abdel Aleem, S. H. E., & Zobaa, A. F. (2017). Increasing PV hosting capacity in distorted distribution systems using passive harmonic filtering. Electric Power Systems Research, 148, 74–86. 9. Ismael, S. M., Abdel Aleem, S. H. E., Abdelaziz, A. Y., & Zobaa, A. F. (2018). Practical considerations for optimal conductor reinforcement and hosting capacity enhancement in radial distribution systems. IEEE Access, 6, 27268–27277. 10. Takenobu, Y., Yasuda, N., Minato, S., & Hayashi, Y. (2019). Scalable enumeration approach for maximizing hosting capacity of distributed generation. International Journal of Electrical Power & Energy Systems, 105, 867–876. 11. Capitanescu, F., Ochoa, L. F., Margossian, H., & Hatziargyriou, N. D. (2015). Assessing the potential of network reconfiguration to improve distributed generation hosting capacity in active distribution systems. IEEE Transactions on Power Apparatus and Systems, 30, 346–356. 12. Fu, Y. Y., & Chiang, H. D. (2018). Toward optimal multi-period network reconfiguration for increasing the hosting capacity of distribution networks. In IEEE power and energy society general meeting. https://doi.org/10.1109/PESGM.2017.8274614. 13. Qi, Q., et al. (2017). Using an MVDC link to increase DG hosting capacity of a distribution network. Energy Procedia, 142, 2224–2229. 14. Ji, H., et al. (2017). A strengthened SOCP-based approach for evaluating the distributed generation hosting capacity with soft open points. Energy Procedia, 142, 1947–1952. 15. Josiński, H., Kostrzewa, D., Michalczuk, A., & Świtoński, A. (2014). The expanded invasive weed optimization Metaheuristic for solving continuous and discrete optimization problems. Scientific World Journal, 2014, 1–14. 16. Bloemink, J. M., & Green, T. C. (2011). Increasing photovoltaic penetration with local energy storage and soft normally-open points. In 2011 IEEE power and energy society general meeting (pp. 1–8). IEEE. https://doi.org/10.1109/PES.2011.6039561. 17. Bloemink, J. M., & Green, T. C. (2013). Benefits of distribution-level power electronics for supporting distributed generation growth. IEEE Transactions on Power Delivery, 28, 911–919.

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18. Diaaeldin, I., Abdel Aleem, S., El-Rafei, A., Abdelaziz, A., & Zobaa, A. F. (2019). Optimal network reconfiguration in active distribution networks with soft open points and distributed generation. Energies, 12, 4172. 19. Chiou, J.-P., Chang, C.-F., & Su, C.-T. (2005). Variable scaling hybrid differential evolution for solving network reconfiguration of distribution systems. IEEE Transactions on Power Apparatus and Systems, 20, 668–674. 20. Mehrabian, A. R., & Lucas, C. (2006). A novel numerical optimization algorithm inspired from weed colonization. Ecological Informatics, 1, 355–366. 21. Mohamed Diaaeldin, I., Aleem, S. H. E., El-Rafei, A., Abdelaziz, A. Y., & Zobaa, A. F. (2019). A novel graphically-based network reconfiguration for power loss minimization in large distribution systems. Mathematics, 7, 1182. 22. Bollen, M., et al. (2017). Consequences of smart grids for power quality: Overview of the results from CIGRE joint working group C4.24/CIRED. In 2017 IEEE PES innovative smart grid technologies conference Europe (ISGT-Europe) (pp. 1–6). IEEE. https://doi.org/10.1109/ ISGTEurope.2017.8260116.

Chapter 9

Generation Regulation Control Systems Krishnan Manickavasagam, Ilango Karuppasamy, and Vineetha Puttaraj

9.1

Introduction

Power systems are steadily growing to meet the power demand. Increase in demand is a challenging concern in developing countries. To meet this ever-increasing demand, enhancement of power generation is required in conventional as well as non-conventional form. Conventional power generation has its own limitations such as land requirement and environmental concern for future enhancement. Conventional power generation has its own limitations such as land requirement, environmental associated pollution and exploitation of fossil fuel. At the same time, worldwide, distributed generations (DGs) are contributing more due to sustainability, pollution free environmnet, ease of energy, and load management. It is expected that the renewable energy capacity will reach 30 GW over the next two decades, merely 10% new capacity addition of DG during this period [1]. Integration of DG into grid is in practice for the past few decades in many countries. Conventional power system consists of thermal, hydro, and nuclear power plants interconnected with grid, transmission system, and distribution system. The purpose of controlling generation is to track load change by adjusting the generation automatically to restore the frequency and tie-line power flow within the prescribed limit using automatic generation control (AGC) in a conventional power system. Under normal conditions, generators are operated at a scheduled output, and system frequency is maintained constant [2]. The primary objective of AGC is to minimize

K. Manickavasagam · V. Puttaraj Department of Electrical Engineering, M. S. Ramaiah University of Applied Sciences, Bangalore, Karnataka, India I. Karuppasamy (*) Department of Electrical and Electronics Engineering, Amrita School of Engineering, Chennai Campus, Amrita Vishwa Vidyapeetham, Chennai, Tamil Nadu, India © Springer Nature Switzerland AG 2020 A. F. Zobaa et al. (eds.), Hosting Capacity for Smart Power Grids, https://doi.org/10.1007/978-3-030-40029-3_9

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the frequency deviation and tie-line error to zero such that operating costs of power system are at a minimum [2]. In a power system, change in load is reflected throughout the system as a change in frequency. In response to change in system frequency, load frequency control (LFC) is regulating generator output within a prescribed limit. LFC controls the frequency deviation, as well as tie-line power flow for maintaining system frequency and scheduled interchange of power with inter-areas within prescribed limits [2]. Penetration of distributed generation (DG) into the power system is quantified by hosting capacity approach. This approach aids in better understanding the customer requirement on the system and requirements of the system operator on customer for reliable operation. The maximum value of DG penetration up to which power system operates smoothly without any disturbance is termed hosting capacity. This is determined by performance index of DG penetration limit. Power system operates satisfactorily if the performance index is less than hosting capacity. The European Distributed Energy Partnership (EU-DEEP) project had been started in 2004 for removing technical and non-technical barriers that prevent a massive deployment of distributed energy resources (DER) in Europe. Hosting capacity concept was introduced in a systematic approach starting with the definition of a number of performance indices and performance objectives. Hosting capacity calculation varies differently based on power quality events. Hosting capacity calculation of voltage variations is different from hosting capacity calculation of frequency variations. The hosting capacity varies depending on structure of the network, type of DG unit, load, climate, and type of power quality event. There is no existence of general objectives for power quality events. There are no general accepted limits for interruptions and dips. Some countries use maximum number of interruption and maximum duration of interruption as indices and limits to determine the hosting capacity of their networks [28]. The main purpose of this chapter is to present the mathematical model for incorporating hosting capacity using power flow equations in large signal and transfer function model in small signal analysis.

9.2

Regulation Control Schemes

In general, power system dynamics is classified as large signal (static) and small signal (dynamic) analysis [7]. Large signal analysis is used to study major disturbances, in which the magnitude of voltage and power may suddenly increase up to 100% of normal operating values [6–10]. Static equations are used in steady-state power flow analysis to control existing power system by calculating steady-state powers and voltages at various buses [10–12]. Small signal analysis is used when minor disturbances occur, in which the magnitude of voltage and power may increase few percent of normal operating values. Linear differential equations and Laplace transform analysis are used for finding the solution in small signal analysis. The renewable energy generation is usually analyzed by small signal analysis which is dynamic in nature, since the electrical parameters pertaining to DG such as voltage,

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Fig. 9.1 Control strategies for DG connected to microgrid

current, and frequency are always continuously varying in nature and time dependent. The control strategies for DG connected to microgrid are shown in Fig. 9.1. DG operations in microgrid are classified as (i) grid-connected mode and (ii) island or autonomous mode [3]. In grid-connected mode, main grid is absorbing or delivering power to the microgrid similar to an infinite bus [4]. In island mode, supply and demand have to be managed by DG connected to microgrid without power from the main grid [5]. The control strategies for island mode are classified further into two categories: communication based and droop based.

9.2.1

Large Signal Analysis

In large signal analysis, speed and voltage control of a generator is achieved by automatic generation control (AGC) in a power system which consists of conventional energy sources. AGC controls the governor, based on the frequency deviation for adjusting the generation according to the load to minimize frequency deviation and tie-line error to the prescribed limit when disturbance occurs. The real power and system frequency of power system are strengthened depending on the amount of DG incorporated at the same time increasing hosting capacity issues. In developed countries, deregulation of power system is in practice, and sufficient generating units are always kept under reserve. Load sharing is carried out by economic dispatch controller (EDC), and the selection of utility is decided based on market price. Developing countries follow vertically integrated utility (VIU)

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where the supply-demand gap always exists. The majority share of supply-demand gap balancing is achieved by controlling the output of conventional generation resources. In addition, with conventional energy sources, DG can be integrated using AGC. Hence, modification is required in AGC to integrate DG in addition to conventional energy sources. Research challenges are involved to integrate DG into the conventional power systems [6]. In practice, frequency deviation is measured in the power system network by using frequency meter, and the measured data such as real power, reactive power, system frequency, and voltages at various buses are sent to the energy control center (ECC). AGC will adjust the governor according to the measured frequency deviation and tie-line error to generate required power to match the load in economic way using EDC. Solar power penetration into the grid is achieved by grid tie inverter. Wind power generation is used to inject power into the grid when the induction motor speed is more than synchronous speed. Thus, the DG penetration into the grid is achieved based on the availability of natural resources. At present, the contribution of DG is tremendously increasing worldwide due to their inherent advantages [13]. At the same time, integration of DG into a power system is a challenging task because of the dynamic nature of the resources [13, 14]. Setting limits to the introduction of DG to power system network is only possible when there is agreement on performance indices and objectives. If the power quality requirements on the network operator are too narrow, then lesser DG can only be connected to power system network. It necessitates the need of a wider range of performance indices and objectives [29]. In this section, method of computing frequency deviation, voltage magnitude variation, and tie-line error between areas from load flow equations have been explained by mathematical model.

9.2.1.1

Generator Model

Generator’s prime mover responses according to the load change which has been initiated by governor action of AGC. The generator model can be represented by the mathematical model with the following nomenclature: αi B F0 ΔF Pgi Pgseti ΔPgi Pgmin i Pgmax i PT PT0 ri

Participation factor of ith generation Bias factor setting of AGC regulator constant for area load-frequency characteristics Scheduled system frequency in p.u. Frequency deviation Active power generation Active power generation schedule Active power generation due to primary and secondary control Minimum active power generation Maximum active power generation Actual tie-line power flow Scheduled tie-line power flow Speed-droop setting on turbine governor of ith generating unit

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The nomenclatures are mentioned for ith bus in p.u. Active power generation Pgi is obtained by Pgi ¼ Pgseti þ ΔPgi

ð9:1Þ

ΔPgi ¼ ð1=r i ÞΔF þ αi ðΔPtie þ BΔF Þ

ð9:2Þ

ΔF ¼ F  F 0 &ΔPtie ¼ PT  PTO

ð9:3Þ

where Pgmax i > Pgi > Pgmin i

The generation in each area is to be controlled to maintain the scheduled power interchange [14] when an interconnected power system consists of two or more independent control areas in addition to control of frequency within the area. The effect of DG on tile-line power flow is ignored in this chapter. By ignoring tile-line power flow, Eq. 9.2 becomes ΔPgi ¼ ð1=r i ÞΔF

9.2.2

ð9:4Þ

Mathematical Model for Regulation Characteristics

The mathematical modelling of regulation characteristics is obtained by power flow equations with the following nomenclature: N M (N  1)

Number of buses Voltage controlled buses Number of voltage phase angles except the reference bus

For a N bus system, bus 1 is considered as reference bus for the purpose of voltage and phase angle calculations of other buses. (N  M) number of voltage magnitudes are unknowns at (N  M ) buses. From complex power balance equations at N buses, 2N number of nonlinear equations are obtained by separating real and imaginary parts. This is solved by the application of decoupled Newton-Raphson (NR) method as follows: Si ¼ Pi þ jQi
 Pi ¼ Pgseti þ Pgi  PLi

ð9:5Þ

Pgseti ¼ Pgi þ PLi þ Pi

ð9:7Þ

Qi ¼ Qgi  QLi ;

Qgi ¼ QLi  Qi

ð9:6Þ

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With bus 1 as reference, the equations for computing the voltage and phase angle of other buses using decoupled Newton-Raphson iterative solution method are given: 2

2 6 6 6 6 6 6 4

ΔP1

3

2

3

2

Δx

3

∂P1 =∂x ∂P1 =∂δ2    ∂P1 =∂δN 6 7 7 6 7 6 ΔP 7 6 76 Δδ 7 6 6 2 7 2 ∂P =∂x ∂P =∂δ    ∂P =∂δ 2 2 2 2 N 76 7¼6 7 6 6 7 7 4  6 6 56    7    7 6  7 5 5 4 4 ∂PN =∂x ∂PN =∂δ2    ∂PN =∂δN ΔPN ΔδN 3 ΔQ1 2 3 ∂Q1 =∂V 1 ∂Q1 =∂V 2  ∂Q1 =∂δNM 7 7 ΔQ2 7 6 ∂Q2 =∂V 1 ∂Q2 =∂V 2  ∂Q2 =∂δNM 7 7 7¼6 6 7 7 4 5             7  5 ∂QNM =∂V 1 ∂QNM =∂V 2    ∂QNM =∂δNM ΔQN 3 2 ΔV 1 7 6 6 ΔV 7 6 2 7 7 6 7 6 7 6    5 4 ΔV NM

ð9:8Þ

ð9:9Þ

The above relations can be written as  ½ΔP ¼ ½J 1 

Δx



Δδ

½ΔQ ¼ ½J 2 ½ΔV 

ð9:10Þ ð9:11Þ

where the size of J1 is [N, N] and J2 is [(N  M), (N  M)]. In Eq. (9.10), Δx will be replaced by ΔF to calculate frequency deviation. The same procedure is repeated to find tie-line error by replacing Δx by ΔPtie. The active and reactive powers are calculated using Eqs. (9.10) and (9.11) by assuming that initial bus voltages are 1 ∠ 0. The differences between the specified and calculated values give the changes in power. ΔPK ¼ P specified  P calculated ΔQK ¼ Q specified  Q calculated Elements of the Jacobian matrices J1and J2 are obtained from estimated bus voltages, x, and calculated powers. ΔQ and ΔV are obtained by the triangularization method from the set of linear Eqs. (9.10) and (9.11) that are solved. Frequency

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deviation and tie-line error are treated as Δx is in this work. To observe range of ΔF and ΔV from minimum to maximum, generation and load are varied accordingly, and economic allocation of generations is stored in a lookup table.

9.2.2.1

Algorithm for AGC in Large Signal Analysis

The following steps are used to calculate the steady-state frequency deviation and tie-line exchange deviation using decoupled NR method [8, 16, 17] which is one of the inputs to the fuzzy logic controller (FLC). Flat frequency control (FFC), flat tie-line control (FTC), and bias tie-line control (BTC) are different types of AGC control strategies. This analysis is assumed in an FFC environment to integrate DG. I. Calculation of AGC Components 1. Input power system data related to: (a) Network, scheduled loads, and primary and secondary control characteristics (b) Type of control strategy used (in this case FFC) 2. Form the bus admittance matrix. 3. Evaluate steady-state frequency deviation ΔF. Subroutine: (i) Calculate active power mismatch vector [ΔP]. (ii) Check active power mismatch is within specified tolerance (ε) at all the buses; if [ΔP < ε], then go to step (iv); else, continue. (iii) Calculate the Jacobian matrix [J1], vector of unknowns [Δx], and update voltage [Δx] and phase angles [Δδ]. (iv) Calculate the reactive power mismatch vector [ΔQ]. (v) Check reactive power mismatch is within specified tolerance (ε) at all the buses; if [ΔQ < ε], then go to main routine; else, continue. (vi) Compute the Jacobian matrix [J2] and vector of unknowns [ΔV], update the estimated voltage magnitude [V], and go to step (i). 4. Check whether [ΔF < ε]. If ΔF lies within specified limits, print the results. 5. If ΔF is not less than ε, the corrective action ΔPgi is determined by conventional controller, FLC, and artificial neural network controller (ANNC). ΔPgi is added with existing generation Pgi and repeat the steps from number 3. In large signal analysis, frequency deviation and voltage deviations are considered for performance indices. The allowable limit of frequency deviation is 0.05 Hz and voltage magnitude 0.05 p.u. as shown in Fig. 9.2. If hosting capacity exceeds performance indices, then power system will not perform satisfactorily. Control action of AGC is performing in between negative to positive limit for satisfactory action of power system.

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Fig. 9.2 Holding capacity versus performance indices

9.2.2.2

Assumptions Made for Large Signal Analysis

Performance indices are assumed as [ΔF] and [ΔV]. The values are assumed [ΔF] as 0.05 Hz and [ΔV]  0.05 p.u.

9.2.2.3

Flowchart for AGC

Flowchart is shown in Fig. 9.3.

9.3 9.3.1

Design of Controllers Conventional Controller Model

The design of conventional controller is obtained by considering system frequency and tie-line power flow as feedback signals for the controller. These signals are obtained from regulating characteristics (ri) and participation factors (αi) of the generator units using Eq. (9.2) to evaluate the required change in generation. The designed conventional controller is represented in Fig. 9.4. αi ¼ ΔPdi =ΔPD , ΔPdi¼ unit load change ΔPD¼ sum of individual unit load changes B ¼ (1/ri) + D is constant [8] ri – p.u. change in frequency in load/p.u. change in unit output ¼ 0.05 as in [8] D percentage change in load/percentage change in frequency ¼ ΔPL/Δω

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Fig. 9.4 Conventional controller

9.3.2

Fuzzy Logic Controller

Fuzzy logic controller is used for decision-making based on the availability of wind velocity, solar irradiation, and the calculated steady-state frequency deviation of power system. The design procedure of FLC is discussed in the following section. 9.3.2.1

Selection of Input and Output Variables

Three inputs have been considered to design FLC, i.e., ΔF calculated from power system network data using decoupled NR method, solar irradiation, and wind speed. The output of FLC is the available amount of power generation from solar and wind resources.

9.3.2.2

Ranges of Input and Output Variables

The input ΔF varies from 0.025 to 0 Hz, solar irradiation varies from 0 to 1500 W/m2, and wind velocity varies from 0 to 20 m/s.

9.3.2.3

Knowledge Base

The input and output variables are divided into a suitable number of linguistic variables [17]. Similarly, the output solar and wind power generated is divided into a suitable number of linguistic variables. Based on the number of linguistic variables, the rule base is formed. The input and output conditions have been described by fuzzy sets. For example, “if solar irradiation is very high, wind speed is very high, and ΔF is zero, then SPV is no power and wind power (WP) is excess. When this rule is executed power will not be generated from DG.” These rules can be developed from operator’s practical experience, knowledge, survey results, general principles, etc.

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205

Defuzzification

The process of converting a fuzzified value into actual crisp value is known as defuzzification. A centroid defuzzification method is normally used to represent the center of gravity as in (9.12) of the fuzzy set. PR 0 μr H r u ¼ Pr¼1 R r¼1 H r

ð9:12Þ

The defuzzified values from FLC are the required amount of power generation from DG to minimize the AGC component.

9.3.3

Artificial Neural Network Controller (ANNC)

A multilayer perceptron (MLP) network is typically composed of input layer, hidden layer, and output layer. An input layer is receiving external information, and output layer is presenting the solution. Hidden layers separate the input layer and output layer. Hidden layer has no direct contact with the external environment, and it is internal to network. Every output layer is connected to every node of the next network layer and is said to be fully connected. Figure 9.5 shows a fully connected multilayer feed-forward neural network. ANN must be trained before performing any task. The process of determining and updating the connecting (synaptic) weights is known as training of neural network. Training is the key element of an ANN. The learning of the network is stored in the synapses in the form of synaptic weights and nodes in the form of node biases. An ANN is trained for complex nonlinear mapping through connecting weights from input nodes to output nodes. The desired output (target value) of the network for each input pattern is always available for supervised MLP training. Input variables or training patterns are the training input data in the form of vectors. Input vector of each element is connected to an input node of input layer in Fig. 9.5 A typical feedforward neural network

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the network, and so the input vectors are equal to the number of input nodes. Estimation of connection (synaptic) weights is done by the training set. Measurement of the generalization ability of the network has been performed by the test set. The synaptic weights are considered as free parameters. Hidden layers are using nonlinear activation functions such as logistic sigmoid and hyperbolic tangent.

9.3.4

Incorporation of DG for Large Signal Analysis with Centralized RES

In the proposed method, the hosting capacity of the system [ΔF and ΔV] is calculated from the steps given in flow chart Fig. 9.3 using load flow equations. Performance indices are assumed as 0.05 Hz and  0.05 p.u. After penetration of DG, sudden changes in input parameters such as solar irradiation wind velocity lead to unwanted fluctuations in voltage, frequency, and power. The hosting capacity exceeds performance indices and creates a power system stability problem. Sudden decrease or increase in load also results in achieving higher value of hosting capacity than performance indices and causes problem in power system. The operator guideline has to be fixed by company authories as a policy to choose of their own performance indices.

9.4

Small Signal Analysis

Small signal analysis is performed by modelling state space equations of single-area, two-area, and multi-area power system. Small signal analysis is dealt with variables such as deviations of frequency, angle, and voltage from its normal operating value, ΔF, Δδ, and ΔV, respectively. Laplace transformation has been used for solving small signal model analysis.

9.4.1

Conventional Generator Control Loops

All generators are installed with LFC and automatic voltage regulator (AVR) in an interconnected power system. The controllers are designed to take care of sudden disturbances in load to maintain frequency and voltage magnitude within the specified limits. Changes in rotor angle cause disturbance in frequency as well as real power. Voltage magnitude affects the reactive power in the power system. When time constant of prime mover and excitation system is compared, prime mover time

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constant is larger than excitation system time constant. Hence, comparing the effect of LFC loop with AVR loop, AVR loop is neglected. In practice, AVR loop and LFC loop are analyzed independently.

9.4.2

Single-Area System

Turbine, generator, governor, and load are connected to feedback loop as is shown in Fig. 9.6 to represent in block diagram an isolated power system. In block diagram, K and T represent gain and time constant of main component governor (Kg and Tg), turbine (Kt and Tt), generator ((Kg and Tg), and sudden load change (ΔPD).

9.4.3

Design of Controllers

Conventionally, PID controllers are used for small signal analysis in AGC. PID controllers consist of the following elements: The different combinations of P, I, D, PI, PD, and PID controllers are possible to implement in AGC. The integral controller is an effective controller for AGC as per the literature. FLC and ANNC can be designed for controlling AGC of small signal analysis with the same techniques discussed in Sects. 9.3.2 and 9.3.3.

9.4.4

Incorporation of DG for Small Signal Analysis

The corrective action determined by integral controller, FLC, and ANNC has to be checked with availability of solar and wind power generation. The available DG can be incorporated with various types of droop control and communication control strategy as discussed in Sect. 9.2.

Fig. 9.6 Single-area system without controller

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9.4.5

Droop-Based Control Strategy

9.4.5.1

Conventional Droop Control Strategy

AC and DC microgrids are widely controlled by droop control scheme [5]. In AC microgrid, voltage magnitude V and frequency f are determined from the measurement of real power P and reactive power Q using the following equations: f y ¼ f x þ mx Px

ð9:13Þ

V y ¼ V x þ nx Qx

ð9:14Þ

where Vx is the maximum voltage at no load, fx is the maximum frequency at no load, and mx, nx are negative droop coefficients. In DC microgrid, reactive power and frequency terms are not present, and active power P is only considered. The DC droop equations are written using the following:

9.4.5.2

V dc,y ¼ V dc,x þ kx Pdc,x

ð9:15Þ

k1 Sdc,1 ¼ k 2 Sdc,2 ¼ . . . ¼ k x Sdc,x

ð9:16Þ

Angle Droop Control

Real and reactive power flow control is obtained from an angle of voltage in an angle droop control. Equations (9.19) and (9.20) give the relation of P–δ and Q–V.
 δj ¼ δrat  ma Pj  P j,rat
 V j ¼ V rat  na Qj  Q j,rat

ð9:17Þ ð9:18Þ

where δrat is the rated voltage angle, Vrat is the rated voltage magnitude, and ma, na are angle droop coefficients. Angle droop control is utilized in scenario such that DG coupled converters are used to form an AC microgrid. In angle droop control, output voltage angle of VSC is instantaneously changed to reach steady state. Droop coefficient values are determined by DG ratings for voltage regulation.

9.4.5.3

Droop-Based Voltage and Frequency Control Strategy

An active power-frequency (P  f ) droop is used for frequency stability by balancing active power, and reactive power-voltage (Q  V ) droop is used for

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voltage stability by balancing reactive power. In practice, Battery Energy Management System (BEMS) is built using bidirectional voltage source converter (VSC) that consists of external and internal embedded cascaded control loops. An external loop is controlled (P  f ) droop and (Q  V ) droop. Battery Energy Storage active and reactive power is given by: PB ¼ PL  PðPVþWÞ

ð9:19Þ

QB ¼ QL  QðPVþWÞ

ð9:20Þ

Frequency droop ( fdroop) is derived from active power of battery PBattery using Eq. (9.19). Voltage droop (Vdroop) is derived from reactive power of battery QBattery using Eq. (9.20). Control relationships for fdroop and Vdroop from Eqs. (9.19) and (9.20) can be written as   f droop ¼ f at noload  m PBðat fullloadÞ  PBðat noloadÞ h i V droop ¼ V at noload  n QBðat fullloadÞ  QBðat noloadÞ

ð9:21Þ ð9:22Þ

System stability is controlled within their acceptable limits by choosing droop control coefficients m and n using f droop and V droop from Eqs. (9.21) and (9.22). Droop characteristics for sharing the power under various operating conditions of standalone hybrid renewable energy system (SHRES) are illustrated in Table 9.1. An internal control loop is controlled in three-phase voltage reference frame based on f droop and V droop with the following equations: 8 > < V aref ¼V droop sin
ðωt þ θÞ   V bref ¼V droop sin ωt  120 þ θ >
 :  V cref ¼V droop sin ωt  240 þ θ

ð9:23Þ

By integrating f droop in Eq. (9.23), the phase angle θ is derived. Voltage and current controllers are used to configure the internal control loop. Droop control can be implemented even sources are separated by long distances with low bandwidth data lines. However, for nonlinear loads, droop control scheme does not consider current and voltage harmonics. The presence of circulating currents makes reactive power control difficult. The major disadvantage of using droop control is the need for a secondary control to compensate steady-state error. During operation of the system, droop coefficients are normally constant, and occasionally, re-set will be done according to the system requirement.

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Table 9.1 Droop characteristics of power sharing Operating conditions No DG generation

Voltage and frequency Droops

DG generation PD

Increases

9.4.6

Droop characteristics At steady-state value, the decrease in voltage and frequency is regulated Within acceptable limits, the decrease in voltage and frequency is regulated At the nominal value, the voltage and frequency values are maintained stable Within acceptable limits, the increase in voltage and frequency is regulated

Power sharing The total power demand (PD) is supplied by the battery energy storage Battery discharge power proportional to decrease in bus voltage and frequency up to minimum discharging limit The total PD is supplied by PV and wind sources while battery energy storage is operated at idle state Battery absorbs excess power proportional to increase in bus voltage and frequency up to the maximum charging limit

Incorporation of Hosting Capacity in Small Signal Analysis with Decentralized RES

In small signal analysis, frequency and voltage deviations [ΔF and ΔV] are considered for hosting capacity, and performance indices are assumed with allowable limit of 0.05 Hz and  0.05 p.u. Implementation of FLC by replacing integral controller for area 1 is shown in Fig. 9.7. In the same way, multi-area can be controlled by replacing conventional controller shown in Fig. 9.8 for a multi-area system. Individual FLC and ANNC for each area or single FLC and ANNC for three areas can be developed for a decentralized multi-area system [30]. If hosting capacity exceeds performance indices, then power system will not perform satisfactorily. The important task of various controllers is to maintain performance indices within the hosting capacity.

9.4.6.1

Assumptions Made for Small Signal Analysis

Performance indices are assumed as [ΔF] and [ΔV]. The values are assumed [ΔF] as 0.05 Hz and [ΔV]  0.05 p.u.

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Fig. 9.7 Incorporation of hosting capacity in small signal analysis in area 1

Fig. 9.8 Incorporation of hosting capacity in small signal analysis in three area system [30]

9.5 9.5.1

Case Study Case Study 1

A stand-alone 95-kW capacity microgrid is installed in Gasa Island, South Korea [25]. This microgrid is considered for case study of DG and power demand. Korea Electric Power Corporation (KEPCO) constructed a microgrid in Gasa Island. An automated energy management system (EMS) is developed to forecast demand, track electricity consumption and decision-making of power delivers to load or store energy in Battery Energy Storage System (BESS). Performance analysis of connected loads to the microgrid is an important design parameter in stand-alone

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microgrid. Connected load in Gasa Island consists of a school, a town hall, a lighthouse, and seaweed and fish farms. An average monthly load of Gasa Island is shown in Fig. 9.9. Monthly average global horizontal irradiance (GHI) for a 1-year period is shown in Fig. 9.10. Monthly average wind speed for a 1-year period is shown in Fig. 9.11. DER locations and single line diagram of GASA Island as in [25] are shown in Figs. 9.12 and 9.13, respectively. DG and load demand data are given below as per NASA Surface Meteorology and Solar Energy website: • Annual average solar radiation is 4.01 kW/m2/day. • Annual average wind speed is 6.07 m/s at 50 m above the sea level. • Average load demand is 2164 kWh/day with a load factor of 0.48.

Fig. 9.9 Average daily load profile as in [25]

Fig. 9.10 Month-wise average GHI as in [25]

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Fig. 9.11 Month-wise average wind speed as in [29]

Fig. 9.12 DER locations in GASA Island as in [25]

9.5.2

Case Study 2

Seoul National University (SNU), South Korea [26], is planning to implement DC microgrid in campus. Rooftop 36-kW solar PV panels are connected through converters to form DC grid. EVs, AC utility, AC and DC hybrid distribution system, and building integrated photovoltaic (BIPV) cells are connected to the DC

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Fig. 9.13 Single line diagram of electric circuit model of Gasa Island microgrid

microgrid. DC microgrid is controlled in two ways as shown in Fig. 9.14. Overview of Korea Micro Energy Grid (K-MEG) is shown in Fig. 9.15. The advantages and disadvantages of DC microgrid control strategy are as follows: • Centralized control Advantage: Simple implementation and improved regulation Disadvantage: Communication burden and single point of failure • Decentralized control Advantages: Autonomous operation, high reliability, and high expandability Disadvantages: Low control flexibility and regulation trade-off • A low-voltage DC distribution has the following advantages: • Reduction in converters between DG and loads. • Increase in system efficiency due to reduction in converters. • Less number of converters will reduce harmonics in power supply. • Improvement in power quality. • No need of synchronization. • No need of reactive power compensation. • Simplified converter design. The main motivations of SNU to implement DC distribution are as follows: • Increase the usage of DC loads such as consumer electronics, digital, LED, electric vehicles (EVs), and inverter-based loads • Penetration of DG into mail grid if surplus power is available • Development of power electronics and device technology Theoretically, combining conventional energy sources and renewable energy sources is a difficult task because of their static and dynamic nature. Automatic generation control including renewable energy sources is successfully implemented in this algorithm. Similar type of work is carried out in Canada.

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Central

High band communication link

Distributed Generation

Decentral

Central Controller

Distributed Generation

Distributed Generation

DC bus

Local Controller

Local Controller

Local Controller

Distributed Generation

Distributed Generation

Distributed Generation

Power link

DC bus

DC loads

Power link

DC loads

Fig. 9.14 Representation of centralized and decentralized DC microgrid [25]

Fig. 9.15 Overview of Korea Micro Energy Grid (K-MEG)

9.6

Communication-Based Control

Communication-based control uses communication lines with high bandwidth for sharing information between sources and loads. Communication-based control is exchange of information within the modules using high bandwidth [19–23]. Actual information can be communicated with less delay as compared to autonomous strategies for achieving high accuracy. However, there are chances of loss of communication link which causes system stability, security, and reliability issues.

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These problems can be avoided by combining droop and communication-based methods using the hierarchical control structures proposed in [24–27]. Both control strategies are used to achieve localized device-level control and system-level coordination simultaneously.

9.6.1

Software and IoT Applications

The Internet of Things (IoT) is a platform to connect physical world to digital world. Any objects physically not connected with any type of network can be connected by IoT. Various sensors are used to quantify physical parameters, and actuators are used to change the condition of the Internet. Radio-frequency identification (RFID) is encoded in digital data tags to find, distinguish, compute, and store data using cloud technology in IoT. The term “Things” refers to the everyday physical objects, and the term “Internet” represents the interconnection between networks of heterogeneous objects. There are many potential research areas of interest, and one of them is software architecture and solution. A class is formed for a set of IoT solutions to illustrate the solution space by investigating the similarities and differences of few IoT solutions. At the same time, it is not possible to identify a complete set of classes for achieving such a one-size-fits-all architecture. In literature, most importantly, the following two qualities are discussed by various authors: • • • • • •

IoT is a network which referred to singular form with only one IoT. Characteristic definitions refer to the things in the IoT. These physical objects are installed by innovation for. Associate with the IoT. State measurement and their changes. Communicate with each other for greater value and service.

Since the IoT applications are enormous variety, accomplishing greater value and service is extremely broad. Greater value and service is achieved by: • Formation of new functionality, previously not possible without physical network • Increasing the quality of existing processes with the help of the IoT The requirement of IoT should have the following property: • Self-conjuring, always adaptable for change • Accessible everywhere • Seamless communication infrastructure with the following: (i). One-to-one relationship (ii). One-to-many relationship (iii). Many-to-many relationships

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The present state of the IoT can be categorized into connected home, connected body, associated retail, associated transportation, smart city, industrial application, E-Health, and smart energy. Methodology for analyzing the solutions is performed by identifying the following variables: • • • • • • • •

Physical Entity being measured Attribute(s) of the physical element being measured Type of IoT connector(s) used in the solution Topology of diagram showing the relationship between parts Direction of messages passed between the components in a diagram Area of application with logic and data storage Possibilities of client interaction Estimation of the scalability requirement of each component with the following: (i). Fixed scale (ii). Potential increase

9.6.2

Implementation of IoT for DG

9.6.2.1

Case Study 1

Implementation of IoT-based monitoring system consists of identification of system architecture, program analysis, and implementation method of DG. The open IoT platforms available are Arduino, Raspberry Pi, and low-cost Long Range (LoRa) network [28]. Architecture of energy monitoring system is shown in Fig. 9.16, and its purposes are given below: • Energy IoT node: Power generation data collection status from energy device • IoT gateway: Data capturing and storing from nodes at remote site • Low cost LoRa network: Wide area networking (WAN) for low-cost wireless communication Serial interface is used to connect energy device controller and Arduino-based IoT node. Voltage, current, temperature, and battery current status information are collected and sent to IoT. The LoRa modem and Arduino are connected in serial interface. The application program interface (API) function from the LoRa protocol stack will be called by the embedded application. IoT node utilizes the power level sleep function to support a low-power mode and is configured by periodically wakeup function. Arduino-based IoT sensor platform is shown in Fig. 9.17. Raspberry Pi operates as a server of energy IoT gateway for monitoring the system accessed by web protocol. The transfer is done by LoRa modem for sending and receiving energy data to Raspberry Pi through serial interface as shown in

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Fig. 9.16 Energy monitoring system architecture

Fig. 9.17 Arduino-based IoT sensor platform

Fig. 9.18. Control, radio, and timestamp information are also carried out by Raspberry Pi. Mongo data base (DB) stores data received through the LoRa modem and works with NoSQL method to support the structure suitable for large-capacity big data.

9.6.2.2

IoT Impact on the HC

IoT-based monitoring and control of microgrid required a reliable router. Router performance is based on the number of IoT devices connected and the number of video streams activated at once. The user intends to add high-bandwidth streams; even though the total value router capacity is less than theoretical throughput, a higher quality of router is required. Implementation of IoT in microgrid is creating limitation on hosting capacity.

9.6.2.3

Future Work

In this chapter, mathematical modelling of incorporating hosting capacity using power flow equations in large signal and transfer function model in small signal

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Fig. 9.18 Raspberry Pi monitoring system

analysis are discussed. A mathematical model including hosting capacity with all possible variables can be developed in the future. The requirement of bandwidth of IoT may be increasing in the future. Multi-agent system (MAS) based control scheme is used to monitor, coordinate, control and display data of the system [6]. These tasks are assigned with various agents such as DER agent, control agent, database agent, and visualizer or user agent in energy control center. Implementation of MAS will replace the burden on IoT; in turn, hosting capacity may increase to higher value.

References 1. Basso, T., & Friedman, N. R. (2003). IEEE 1547 national standard for interconnecting distributed generation: How could it help my facility? Preprint (No. NREL/JA-560-34875). National Renewable Energy Lab., Golden, Co.(US). 2. Kanniah, J., Tripathy, S. C., Malik, O. P., & Hope, G. S. (1984). Microprocessor-based adaptive load-frequency control. IEE Proceedings C Generation, Transmission and Distribution, 131(4), 121–128. 3. Radwan, A. A. A., & Mohamed, Y. A. R. I. (2014). Bidirectional power management in hybrid AC-DC islanded microgrid system. In 2014 IEEE PES General Meeting Conference & Exposition (pp. 1–5). IEEE. 4. Nejabatkhah, F., & Li, Y. W. (2014). Overview of power management strategies of hybrid AC/DC microgrid. IEEE Transactions on Power Electronics, 30(12), 7072–7089. 5. Majumder, R., Chaudhuri, B., Ghosh, A., Majumder, R., & Ledwich, G. F. (2010). Improvement of stability and load sharing in an autonomous microgrid using supplementary droop control loop. IEEE Transactions on Power Systems, 25(2), 796–808. 6. Manickavasagam, K. (2014). Intelligent energy control center for distributed generators using multi-agent system. IEEE Transactions on Power Systems, 30(5), 2442–2449. 7. Elgerd, O. I. (1982). Electric energy systems theory: An introduction. McGraw-Hill, New York, US.

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8. Subbaraj, P., & Manickavasagam, K. (2007). Generation control of interconnected power systems using computational intelligence techniques. IET Generation, Transmission & Distribution, 1(4), 557–563. 9. Michael, N. (2005). Artificial intelligence a guide to intelligent systems, Pearson Education Limited, New Delhi, India 10. Dos Santos, M. J., Pereira, J. L. R., De Oliveira, E. J., & da Silva, I. C. (2004). A new approach for area interchange control modeling. IEEE Transactions on Power Systems, 19(3), 1271–1276. 11. Chang, S. K., & Brandwajn, V. (1988). Adjusted solutions in fast decoupled load flow. IEEE Transactions on Power Systems, 3(2), 726–733. 12. Saikia, L. C., Nanda, J., & Mishra, S. (2011). Performance comparison of several classical controllers in AGC for multi-area interconnected thermal system. International Journal of Electrical Power & Energy Systems, 33(3), 394–401. 13. Moreno-Munoz, A., De La Rosa, J. J. G., Lopez, M. A., & De Castro, A. G. (2009). Grid interconnection of distributed generation: The Spanish normative. In 2009 International Conference on Clean Electrical Power (pp. 466–470). IEEE. 14. Dugan, R. C., McDermott, T. E., & Ball, G. J. (2001). Planning for distributed generation. IEEE Industry Applications Magazine, 7(2), 80–88. 15. Logenthiran, T., Naayagi, R. T., Woo, W. L., Phan, V. T., & Abidi, K. (2015). Intelligent control system for microgrids using multiagent system. IEEE Journal of Emerging and Selected Topics in Power Electronics, 3(4), 1036–1045. 16. Thukaram, D., Iyengar, R., Khincha, H. P., & Parthasarathy, K. (1984). Steady state power flow analysis incorporating load and generation regulation characteristics. Journal of the Institution of Engineers (India), 64(5), 274–279. 17. https://www.springer.com/productFlyer_978-3-540-76283-6.pdf?SGWID¼0-0-1297173779129-0 18. Eid, B. M., Rahim, N. A., Selvaraj, J., & El Khateb, A. H. (2014). Control methods and objectives for electronically coupled distributed energy resources in microgrids: A review. IEEE Systems Journal, 10(2), 446–458. 19. Ren, W., & Beard, R. W. (2008). Distributed consensus in multi-vehicle cooperative control (pp. 71–82). London: Springer. 20. Behjati, H., Davoudi, A., & Lewis, F. (2014). Modular DC–DC converters on graphs: Cooperative control. IEEE Transactions on Power Electronics, 29(12), 6725–6741. 21. Nasirian, V., Moayedi, S., Davoudi, A., & Lewis, F. L. (2014). Distributed cooperative control of DC microgrids. IEEE Transactions on Power Electronics, 30(4), 2288–2303. 22. Baghaee, H. R., Mirsalim, M., & Gharehpetian, G. B. (2016). Performance improvement of multi-DER microgrid for small-and large-signal disturbances and nonlinear loads: Novel complementary control loop and fuzzy controller in a hierarchical droop-based control scheme. IEEE Systems Journal, 12(1), 444–451. 23. Zhao, Z., Yang, P., Guerrero, J. M., Xu, Z., & Green, T. C. (2015). Multiple-time-scales hierarchical frequency stability control strategy of medium-voltage isolated microgrid. IEEE Transactions on Power Electronics, 31(8), 5974–5991. 24. Wei, B., Yuehao, Y., Bo, K., Yuanhong, C., & Xin, L. (2015). An novel hierarchical control of microgrid composed of multi-droop controlled distributed power resources. In 2015 5th international conference on Electric Utility Deregulation and Restructuring and Power Technologies (DRPT) (pp. 2173–2178). IEEE. 25. Husein, M., Hau, V. B., Chung, I. Y., Chae, W. K., & Lee, H. J. (2017). Design and dynamic performance analysis of a stand-alone microgrid. Journal of Electrical Engineering & Technology, 12(5), 1777–1788. 26. http://microgrid-symposiums.org/wpcontent/uploads/2014/12/tianjin_bo-hyung-cho.pdf 27. Choi, C. S., Jeong, J. D., Lee, I. W., & Park, W. K. (2018). LoRa based renewable energy monitoring system with open IoT platform. In 2018 international conference on Electronics, Information, and Communication (ICEIC) (pp. 1–2). IEEE.

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28. Nayanatara, C., Divya, S., & Mahalakshmi, E. K. (2018). Micro-Grid management strategy with the integration of renewable energy using IoT. International conference on Computation of Power, Energy, Information and Communication (ICCPEIC) (pp. 160–165), IEEE. 29. Yang, Y., & Bollen, M. H. J. (2008). Power quality and reliability in distribution networks with increased levels of distributed generation’ (Report Elforsk, Stockholm, Sweden, 2008). 30. Saha, A., Saikia, L. C., Tasnin, W., Rajbongshi, R., & Saha, D. (2018). Automatic generation control of multi-area multisource system incorporating distributed generation units and RFB. 2nd international conference on Power, Energy and Environment: Towards Smart Technology (ICEPE) (pp. 1–6). Shillong, India.

Chapter 10

Exploring the Concept of Hosting Capacity from an Electricity Market Perspective Elias Valenzuela, Rodrigo Moreno, Dimitrios Papadaskalopoulos, Francisco D. Muñoz, and Yujian Ye

Nomenclature In this section, the notation of the most important terms used throughout this chapter is presented for a quick reference. A. Index and Sets i2I In n, m 2 M Mn t2T V VLL

Index and set of conventional generation units Subset of conventional generation units connected to node n Indexes and set of nodes Set of nodes connected to node n through a line Index and set of hours Set of decision variables of MPEC model Set of decision variables of lower level problem

E. Valenzuela University of Chile, Santiago, Chile R. Moreno University of Chile, Santiago, Chile Imperial College London, London, UK Instituto Sistemas Complejos de Ingeniería (ISCI), Santiago, Chile D. Papadaskalopoulos (*) · Y. Ye Imperial College London, London, UK e-mail: [email protected] F. D. Muñoz Instituto Sistemas Complejos de Ingeniería (ISCI), Santiago, Chile Universidad Adolfo Ibáñez, Santiago, Chile © Springer Nature Switzerland AG 2020 A. F. Zobaa et al. (eds.), Hosting Capacity for Smart Power Grids, https://doi.org/10.1007/978-3-030-40029-3_10

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B. Parameters ai bi dn, t τt
n,m F g

Quadratic coefficient of operating cost of conventional generation unit i ($/MW2) Linear coefficient of operating cost of conventional generation unit i ($/MW) Demand at node n and time period t (MW) Weighting factor of hour t Capacity of line (n, m) (MW) Minimum output of conventional generation unit i (MW)


gi K xn, m βn, t γ

Maximum output of conventional generation unit i (MW) Annuitized investment cost of renewable generation ($/MW/year) Reactance of line (n, m) (p.u.) Normalized output of renewable generation at node n and hour t Price of renewable energy certificate ($/MWh)

i

C. Decision Variables gi, t rn, t Rn θn, t λn, t

10.1

Output of conventional generation unit i at hour t (MW) Actual output of renewable generation at node n and hour t (MW) Capacity of renewable generation at node n (MW) Voltage angle at node n and period t (rad) Market clearing price at node n and hour t ($/MWh)

Introduction

10.1.1 Background Electricity systems are currently facing fundamental challenges associated with the necessary decarbonization measures to tackle climate change. Such measures need to consider the deregulated setting of the electricity market, where infrastructure’s owners, particularly in the generation sector, need clear economic incentives to deploy future expansions. The continuously increasing levels of greenhouse gas emissions and the associated environmental concerns have driven governments worldwide to take significant initiatives for the large-scale integration of renewable generation. In Europe, the European Commission (EC) has put forward a legally binding target for renewable energy sources to cover 20% and 27% of the total energy consumption in the European Union (EU) by 2020 and 2030, respectively [1, 2]. In the USA, many states have opted for different kinds of policies that promote renewable energy generation. For example, in the state of Oregon, the Renewable Portfolio Standards (RPS) require that large utilities supply 25% of electricity from renewable resources by 2050, whereas smaller utilities must provide between 5% and 10% by 2025 [3]. In Latin America, there are countries such as Chile, Peru, Colombia, Brazil, and Mexico with specific targets for renewable generation and other regulatory policies to foster its integration. In Chile,

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for instance, there is a 20% target (i.e., percentage of the electricity demand supplied by renewables) by 2025 and a 70% target by 2050 [4]. However, this large-scale integration of renewable generation introduces significant techno-economic challenges to the operation and planning of electricity grids. First of all, the inherent variability and limited predictability and controllability of renewable generation imply that conventional generators need to remain in the system and operate in an inefficient fashion (part loaded and with more frequent start-up and shut-down cycles) to provide the required balancing services to the system [5]. Furthermore, integration of inverter-connected renewable generation reduces the system inertia (which is provided by the kinetic energy stored in the rotating mass of the conventional generators), which implies that imbalances between supply and demand change system frequency more rapidly, challenging the stability of the system [6]. Finally, the large-scale connection of renewable generation to transmission and distribution grids creates certain network challenges, such as congestion (due to thermal and stability limits), increased voltage levels, and increased short-circuit current levels, which threaten the security of these grids [7]. In order to capture and quantitatively analyze these challenges, the concept of hosting capacity was firstly introduced to determine the maximum limits of distributed energy resources (DER) that can be connected to a distribution network without harming power quality [8, 9]. In the same vein, references [10, 11] establish maximum quantities of distributed generation (DG) capacity, especially PV, that respect network’s voltage limits. Other relevant papers have investigated the hosting capacity of distribution grids beyond voltage issues, considering thermal, short-circuit current and harmonic distortions [12–15]. Apart from the calculation of the hosting capacity, measures to enhance it have been proposed too in [16–18], including advanced control and operational measures, network reinforcements, and the installation of storage facilities and reactive power equipment. Although the vast majority of the relevant literature is focused on distribution networks [12, 19–24], at a fundamental level, the concept can be applied to transmission networks too as in [25]. Hence, the concept of hosting capacity is useful for governments, regulators, and central policy makers as it expresses the maximum capacity of renewable generation that can be integrated to electricity grids without breaching its technical limits and threatening its secure operation and/or without surpassing certain system cost thresholds. In combination with the abovementioned challenges of decarbonization, we need to consider that the electricity industry has been deregulated in many countries, allowing market forces to guide future investments. This deregulation has led to unbundling of vertically integrated monopoly utilities and the introduction of competition in the generation sector [26]. Chile and the UK are good examples of early deregulation of electricity markets in the beginning of the 1980s and 1990s, respectively. The deregulation of electricity markets, however, has not been implemented everywhere, but more and more countries are adhering to this practice since deregulation has been key to promote cost efficiency and investments [27]. In this context, generation investment planning is not anymore carried out by a central regulated utility aiming to minimize system costs but relies on profit-driven decisions of self-interested generation companies, operating within a competitive electricity market. In this setting, the large-scale integration of renewable generation

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introduces a fundamental market challenge: given that operating costs of renewables are very low, the electricity prices are significantly reduced, threatening the recovery of their investment costs and therefore their profitability [28–30].

10.1.2 Motivation and Contributions The motivation behind this work lies in the fact that previous work has investigated the renewable generation hosting capacity of electricity systems from a technical perspective, but no work has been carried out in exploring and analyzing the same concept from a market perspective, considering the abovementioned challenges of investment cost recovery and overall profitability. This chapter makes the first attempt to fill this knowledge gap by proposing a new modeling approach aiming to quantitatively determine the maximum renewable generation capacity that can be integrated in electricity grids, while respecting long-term profitability constraints, which we define as the market hosting capacity (MHC) of renewable generation. This approach involves a bi-level optimization model. The upper level aims at optimizing renewable generation investments in different locations of the network so as to maximize the total renewable generation capacity integrated, subject to the non-negative long-term profit constraint imposed by generation owners. The lower level represents endogenously the market clearing process and determines the generation dispatch and electricity prices. The proposed model is validated through case studies on a simple 2-node system, the IEEE 24-node system, and a 42-node model of the Chilean electricity system. These case studies quantitatively analyze the dependence of the MHC on a number of factors, including the network capacity, the flexibility of the conventional generation fleet, and renewable generation subsidies. Interestingly enough, our results demonstrate that a stronger network does not always increase the MHC.

10.1.3 Chapter Organization The rest of this chapter is organized as follows. Section 10.2 details the proposed modeling approach. Case studies and quantitative results are presented in Sects. 10.3 and 10.4. Finally, Sect. 10.5 discusses conclusions and future extensions of this work.

10.2

Proposed Modeling Approach

10.2.1 General Description As mentioned earlier, the MHC concept introduced in this work aims to identify the maximum renewable generation capacity that an electricity network can host from a market perspective. This maximum value exists since the more the

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renewable capacity connected to a network, the lower the electricity prices. Evidently, if prices drop too much, there will be no incentives for investors to integrate more renewables. Thus, there is a maximum limit of renewable generation capacity that can be integrated in a profitable fashion. Note that the impact of new generation capacity on prices is not uniform across the network, meaning that zones with higher energy prices may present better opportunities for connecting more renewables than zones with lower prices. Thus, we aim to identify those promising areas for integrating large amounts of renewables. We also determine amounts of renewables to be connected in other less promising areas. Overall, we attempt to maximize the total installed capacity of renewables integrated in a given power grid, without affecting the ability of owners to recover their capital invested in renewable generation. In order to formulate the abovementioned problem, we use a bi-level optimization approach, the structure of which is illustrated in Fig. 10.1. Since we need to represent the market clearing process to obtain prices and generation dispatches, we use a classical dispatch model that minimizes total operational costs for a given network and set of generation capacities, assuming that the entire operation of the network is resolved by a single market operator at the transmission or distribution network level. It should be noted that this model can deliver both dispatches (as primal variables) and energy prices per node (as dual variables). As shown in Fig. 10.1, we use this model as the lower level problem within our bi-level optimization framework. As we aim to maximize integration of new renewable generation so as to determine the MHC, we establish this objective in an upper level, which is subject to the previous lower level, market clearing problem and an additional constraint that avoids negative profits. This bi-level problem is solved after converting it to a Mathematical Program with Equilibrium Constraints (MPEC) and subsequently to a mixed-integer linear problem (MILP). The details of the model assumptions, formulation, and solution strategy are described next.

Fig. 10.1 Structure of proposed bi-level optimization model

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10.2.2 Model Assumptions For clarity reasons, next, we declare the main assumptions behind the proposed model: • The model assumes a static planning approach with a yearly operation horizon, implying that the renewable generation capacity is maximized considering a single, future target year. This yearly operation horizon is discretized and divided into a number of representative hours. Both investment and operating costs and revenues are calculated at the same yearly basis. • The considered electricity market is a pool-based energy-only market which is cleared by the market operator through the solution of a short-term social welfare maximization problem. In order to account for the effect of the network, the market clearing process incorporates a DC power flow model and yields locational marginal prices (LMP) λn, t for each node n and time period t. Note that the LMP system can be applied on both transmission and distribution networks [31], and thus, our results are equally applicable to both as long as energy is priced in every node following the LMP principles. • For simplicity reasons and without loss of generality, a single type of renewable generation technology is considered, but its normalized output profile is generally different in different nodes of the network in order to account for the locational availability of renewable energy sources. Its operating costs are assumed zero, and their output can be curtailed if required. • Each conventional generation technology is characterized by a different operating cost as well as different maximum output and minimum output constraints, with the latter representing the operation of must-run generation technologies. • The demand side is assumed inelastic.

10.2.3 Bi-level Optimization Model The proposed bi-level optimization model (Fig. 10.1) aims at maximizing the total renewable generation capacity subject to long-term profitability constraints and is formulated as follows: (Upper Level) max

X

Rn

ð10:1Þ

n

subject to X n, t

(Lower Level)

τt ðλn,t þ γ Þr n,t 

X KRn  0 n

ð10:2Þ

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min V LL

X

ai gi,t þ bi g2i,t

229

ð10:3Þ

i, t

where   V LL ¼ gi,t , r n,t , θn,t

ð10:4Þ

subject to d n,t 

X X θn,t  θm,t gi,t  r n,t þ ¼ 0 : λn,t , xn,m i2I m2M n

þ gi  gi,t  gi : μ i,t , μi,t ,

8i, 8t

þ 0  r n,t  βn,t Rn : ν n,t , νn,t ,


n,m  F

8n, 8t

ð10:5Þ

n

θn,t  θm,t
þ  F n,m : π  n,m,t , π n,m,t , xn,m

8n, 8m 2 M n , 8t

þ π  θn,t  π : ρ n,t , ρn,t ,

θ1,t ¼ 0 : φt ,

8n, 8t

8t

8n, 8t

ð10:6Þ ð10:7Þ ð10:8Þ ð10:9Þ ð10:10Þ

The upper level (UL) problem determines the optimal renewable generation investments at the different nodes of the network so as to maximize the total renewable generation capacity (10.1). This problem is subject to the renewable generation’s long-term profitability constraint (10.2), which ensures that its revenue from the energy market and potential renewable energy certificates [32] is higher than or equal (i.e., it at least recovers) to its investment cost, as well as the lower level (LL) problems (10.3), (10.4), (10.5), (10.6), (10.7), (10.8), (10.9), and (10.10). The latter represents the market clearing process at each representative hour, minimizing the total cost of the conventional generation units (10.3), subject to nodal demandsupply balance constraints (10.5) (the Lagrangian multipliers of which constitute the LMP), the operating constraints of conventional generators (10.6) and renewable generation (10.7), and network constraints (10.8), (10.9), and (10.10). These two problems are coupled, since the renewable generation capacity determined by the UL problem affects the constraints (10.7) of the LL problem, while the renewable generation dispatch and the LMP determined by the LL problem affect the constraint (10.2) of the UL problem.

10.2.4 MPEC Formulation In order to solve the abovementioned bi-level optimization problem, the LL problem is replaced by its Karush-Kuhn-Tucker (KKT) optimality conditions, a replacement

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enabled by the continuity and convexity of the LL problem. This converts the bi-level problem to a single-level MPEC which is formulated as max V

X

ð10:11Þ

Rn

n

where   þ  þ  þ  þ V ¼ Rn , V LL , λn,t , μ i,t , μi,t , νn,t , νn,t , π n,m,t , π n,m,t , ρn,t , ρn,t , φt

ð10:12Þ

subject to (10.2), (10.5), (10.10), þ ai þ bi gi,t  λðn:i2I n Þ,t  μ i,t þ μi,t ¼ 0, þ λn,t  ν n,t þ νn,t ¼ 0,

8i, 8t

8n, 8t

þ  X λn,t  λm,t X ρþ X ρ n,m,t  ρm,n,t n,m,t  ρm,n,t  þ  þ σþ n,t  σ n,t þ xn,m xn,m xn,m m2M m2M m2M n

n

ð10:13Þ ð10:14Þ ð10:15Þ

n

ðφt Þn¼1 ¼ 0, 8n, 8t

8i, 8t 0  μ i,t ⊥gi,t  0,   8i, 8t 0  μþ i,t ⊥ gi  gi,t  0, 0  ν 8n, n,t ⊥r n,t  0,   0  νþ n,t ⊥ β n,t Rn  r n,t  0,   θn,t  θm,t 
 0, 8n, 0  ρn,m,t ⊥ F n,m þ xn,m   θn,t  θm,t þ
0  ρn,m,t ⊥ F n,m   0, 8n, xn,m

ð10:16Þ ð10:17Þ

8t

ð10:18Þ

8n, 8t

ð10:19Þ

8m 2 M n , 8t

ð10:20Þ

8m 2 M n , 8t

ð10:21Þ

0  σ n,t ⊥ðπ þ θ n,t Þ  0,

8n, 8t

ð10:22Þ

0  σþ n,t ⊥ðπ  θ n,t Þ  0,

8n, 8t

ð10:23Þ

The objective function of the MPEC formulation (10.11) coincides with the objective function of the UL problem. The set of decision variables of the MPEC formulation (10.12) includes the decision variables of the UL problem and the LL problem as well as the Lagrangian multipliers associated with the constraints of the LL problem. The KKT optimality conditions of the LL problem correspond to Eqs. (10.13), (10.14), (10.15), (10.16), (10.17), (10.18), (10.19), (10.20), (10.21), (10.22), and (10.23).

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10.2.5 MILP Formulation The abovementioned MPEC formulation is nonlinear implying that any solution obtained by commercial optimization solvers is not guaranteed to be globally optimal. In order to address this challenge, this MPEC is converted to a regular MILP, which commercial branch-and-cut solvers can efficiently solve to global optimality [33]. Specifically, the abovementioned MPEC formulation includes two types of nonlinearities. The first one involves the bilinear terms ∑n,trn,tλn,t in constraint (10.2). In order to linearize it, we adopt the linearization approach proposed in [34] which uses some of the KKT conditions. First of all, by making use of the nodal demand-supply balance constraints (10.5), and summing for every n and t, we obtain X X X r n,t ¼ dn,t  gði2I n Þ,t þ n, t

n, t

X n, ðm2M n Þ, t

n, t

θn,t  θm,t xn,m

ð10:24Þ

By multiplying both sides of (10.24) by λn,t, the nonlinear term becomes equal to X X X r n,t λn,t ¼ dn,t λn,t  gði2I n Þ,t λn,t þ n, t

n, t

n, t

X n, ðm2M n Þ, t

ðθn,t  θm,t Þλn,t xn,m

ð10:25Þ

By multiplying both sides of (10.13) by gi,t, summing for every i and t, and rearranging some terms, we obtain X X   X  λðn:i2I n Þ,t gi,t ¼ ai þ bi gi,t gi,t þ μþ gði2I n Þ,t λn,t ð10:26Þ i,t gi,t  μi,t gi,t ¼ i, t

n, t

i, t

By making use of (10.16) and (10.17), Eq. (10.26) becomes X

gði2I n Þ,t λn,t ¼

n, t

X

  ai þ bi gi,t gi,t þ μþ i,t gi

ð10:27Þ

i, t

By multiplying both sides of (10.15) by θn, summing for every n and t, making use of (10.10), and rearranging some terms, we obtain X

λn,t

n, ðm2M n Þ, t

ðθn,t  θm,t Þ ¼ xn,m

X



þ ρ n,m,t þ ρn,m,t

n, ðm2M n Þ, t

 ðθn,t  θm,t Þ xn,m

ð10:28Þ

By making use of (10.20) and (10.21), Eq. (10.28) becomes X n, ðm2M n Þ, t

λn,t

ðθn,t  θm,t Þ ¼ xn,m

X

n, ðm2M n Þ, t

  
ρn,m,t þ ρþ n,m,t F n,m

ð10:29Þ

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By substituting (10.27) and (10.29) into (10.25), this bilinear term is replaced by the following quadratic expression: X

r n,t λn,t ¼

n, t

X X   d n,t λn,t  ai þ bi gi,t gi,t þ μþ i,t gi n, t



X



i, t

ρ n,m,t


þ ρþ n,m,t F n,m

ð10:30Þ

n, ðm2M n Þ, t

The second type of nonlinearity involves the bilinear terms in constraints (10.16), (10.17), (10.18), (10.19), (10.20), (10.21), (10.22), and (10.23), which can be written in the generic form 0  μ ⊥ p  0, with μ and p representing generic dual and primal terms, respectively. The linearization approach proposed by Fortuny-Amat and McCarl in [35] replaces each of these conditions with the set of mixed-integer linear conditions μ  0, p  0, μ  ωMD, p  (1  ω)MP, where ω is an auxiliary binary variable, while MD and MP are large positive constants. The set of decision variables of the MILP formulation includes the set (10.12) as well as the auxiliary binary variables introduced for linearizing (10.16), (10.17), (10.18), (10.19), (10.20), (10.21), (10.22), and (10.23).

10.3

Theoretical Case Studies

10.3.1 Small-Scale Study: Illustration, Validation, and Analysis over 2-Bus Network This section studies the impacts of maximizing renewable generation capacity on a given illustrative network, calculating the so-called market hosting capacity. We run several sensitivity analyses for different network capacities, focusing on how the market hosting capacity varies. This small network also serves to illustrate and validate the model proposed in this chapter.

10.3.1.1

Input Data

Figure 10.2 shows the configuration of the 2-bus network with two conventional units, two solar power units, two demands, two buses, and one line. This network is a modified version of the 2-bus Borduria (node 1) and Syldavia (node 2) example described in [26]. The specific data used in this chapter is shown in Table 10.1. Note that while demand is the highest in node 2, the variable cost of thermal generation is the lowest in node 1. Also, node 1 exhibits the highest availability of the solar power resource. With all of the above, we can anticipate that power transfers will go from node 1 to node 2.

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Fig. 10.2 Two busbar example Table 10.1 Input data of illustrative example Parameter Demand (MW) Installed capacity of thermal generation (MW) Variable cost of thermal generation ($/MWh) Normalized availability of solar power resource (p.u.) Investment cost of solar generation ($/MW/h)

Node 1 500 2000

Node 2 1500 2000

2 10  P1 þ 0:01 2  P1 P1 represents the output of thermal generation in node 1 0.28

2 13  P2 þ 0:02 2  P2 P2 represents the output of thermal generation in node 2 0.15

5

5

For illustrative purposes, the following results are obtained assuming a single operating hour; hence, both operating and investment costs are calculated hourly. Overall, we study 2400 cases with different network capacities ranging from 0 to 1200 MW with a step of 0.5 MW, in which we seek to calculate, for each of them, the maximum capacity of solar power generation that can be installed in a profitable fashion in both nodes.

10.3.1.2

Results and Discussion

Figure 10.3 shows the market hosting capacity of the 2-bus network as a function of the line capacity. Interestingly, for smaller line capacity values (i.e., between 0 and 400 MW), the hosting capacity decreases, while the line capacity increases. Note this result is very counterintuitive since, in practice, we usually expand networks to increase HC. This counterintuitive result is justified because demand in node 2 can be supplied by higher volumes of low-cost generation in node 1 (thermal and solar power generation) when network capacity expands, which replaces capacity of solar power generation in node 2. Note that building more line capacity clearly hampers business opportunities for investors in node 2, as node 1 features lower fuel costs and higher availability factors for solar power generation, making these resources more

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Fig. 10.3 MHC versus network capacity

Fig. 10.4 Power generation versus network capacity

preferable. In this context, Fig. 10.4 shows how power generations change with network capacity expansions. Note also that the lower investment levels in solar power generation in node 2 are not replaced by more investments in solar power generation in node 1 but are rather replaced by existing low-cost thermal generation in node 1 that can be exported due to network expansions. This clearly reduces the

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Fig. 10.5 Locational marginal price versus network capacity

overall MHC since the utilization of existing generation capacity is favored over new investments in renewables. However, as existing low-cost thermal generation features a limited capacity, for larger network expansions (above 400 MW), generation in node 2 is replaced by investments in new solar power generation capacity in node 1 (while thermal generation in node 1 is producing at its maximum output). Hence, it is demonstrated that network expansions above 400 MW unlock the significant solar power generation potential in node 1, increasing the overall MHC. This is also shown in Fig. 10.4, where, for power transfers above 400 MW, both thermal and solar power generations in node 2 decrease due to line capacity expansions that facilitate the installation of new solar power generation capacity in node 1. Figure 10.5 shows the increase in the price of node 1 and the decrease in the price of node 2, as the line capacity increases. This is because the output of the low-cost thermal generator located in node 1 can be increased while network capacity expands, exporting power to node 2. This low-cost energy produced in node 1, in turn, displaces costly energy production in node 2, reducing its locational marginal price. Therefore, the increase in line capacity constantly reduces the economic attractiveness of node 2 for investors and increases that in node 1. All of the abovementioned arguments demonstrate that increasing the capacity of the network does not necessarily allow private investors to integrate higher volumes of renewables. On the contrary, increasing network capacity can even reduce the business opportunities for new renewable generation developments, especially in those areas close to the load centers and with higher electricity prices.

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10.3.2 IEEE RTS Study: Analyzing the Effect of Network Capacity, Generation Flexibility, and Subsidies on MHC This section determines and analyzes the market hosting capacity of different network configurations, carrying out sensitivity analyses around the capacity of the network, the flexibility of conventional generation, and the potential subsidies that may exist to foster a larger penetration of renewable generation.

10.3.2.1

Input Data

We have modified the IEEE RTS described in [36] and shown in Fig. 10.6 by carrying out the following changes: (a) Reduction of all lines and transformers’ capacities by 50% (b) Increase of thermal generation capacity in nodes 1 and 2 by 10 (MW) (c) Reduction of thermal generation capacity in node 7 by 50 (MW) These changes (a–c), implemented in our base case, are aimed to enhance congestion in the system and increase prices in the low voltage area. Also, we consider that solar power generators can be installed in every node at an annuitized investment cost of 110 k$/MW.year, and all nodes present the same availability profile of renewable sources across different time periods. To represent the multiple market clearing processes that occur across a year, various combinations of different demand and solar power levels are selected through standard clustering techniques, e.g., K-means (following [37]). For this particular case, we use demand and solar profiles observed in Chile. The relevant operational cost data is shown in Table 10.2.

10.3.2.2

Case Studies

We analyze three case studies which demonstrate how the market hosting capacity changes for: (a) Four different network capacity levels (b) Four different levels of flexibility in conventional generation technologies, which is varied by changing their must-run output (c) Four different levels of subsidies in the form of a renewables certificate 10.3.2.3

Results and Discussion

Table 10.3 shows the market hosting capacity levels of various modified versions of the IEEE RTS system when line capacities are increased by 10%, 20%, and 30% with respect to the base case. Interestingly, the most attractive case to maximize

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Fig. 10.6 IEEE RTS system

Table 10.2 Variable cost per technology in the IEEE RTS Type U12 U20 U76 U100 U155 U197 U350 U400

Technology Oil/steam Oil/CT Coal/steam Oil/steam Coal/steam Oil/steam Coal/steam Nuclear

Variable cost ($/MWh) 56.56 130.00 16.08 43.66 12.39 45.58 11.85 4.42

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Table 10.3 MHC sensitivity to network capacity Case Base case Base case + 10% increase in line capacity Base case + 20% increase in line capacity Base case + 30% increase in line capacity Base case + 1 increase in line capacity

MHC (MW) 617 524 395 299 0

Table 10.4 Hosting capacity sensitivity operational flexibility Case Base case (no must-run generation) Base case + must-run generation of 10%a Base case + must-run generation of 20%a Base case + must-run generation of 30%a Base case + must-run generation of 40%a a

MHC (MW) 617 508 372 270 171

Percentage with respect to maximum capacity

renewables penetration in a profitable fashion is that of minimum network capacity, and this is so because of the higher LMPs present in the base case due to increased network congestion. Furthermore, in the case where the network capacity is increased by 30%, the market hosting capacity of the network is zero. A key point in this example is that the load factors of renewables are the same across the whole network. This makes less attractive the usual business case (absent in this particular example but present in the previous 2-bus example) to expand network capacity in order to access remote renewable resources with higher load factors. In other words, network capacity expansions may impose a barrier for the development of new renewable generation in the presence of equally attractive renewable resources across a power system, and this is a key result to be considered by planners and policy makers. We also analyze how operational flexibility may support higher renewables integration levels. Hence, Table 10.4 shows the market hosting capacity levels of various cases for different levels of must-run generation limits. The results demonstrate that lower levels of operational flexibility (i.e., higher levels of must-run generation) lead to smaller levels of renewables integration in a profitable fashion. This is so since higher must-run generation increases the level of reviewable generation curtailment and thus decreases average energy prices. Finally, we study the effect of subsidies, which in this study involve a certificate type payment for each MWh of renewable energy produced, on top of the energy price. As expected, a higher price of this certificate increases the amount of renewables that can be integrated profitably. For example, Table 10.5 shows that a subsidy of 12 $/MWh can achieve more than 50% increase in MHC with respect to the base case. This is so since potentially negative profits can be cancelled due to the presence of extra revenue streams from subsidies. Furthermore, by running

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Table 10.5 Hosting capacity sensitivity to certificate prices Case Base case (no subsidy/certificate) Base case + subsidy/certificate of 3 $/MWh Base case + subsidy/certificate of 6 $/MWh Base case + subsidy/certificate of 9 $/MWh Base case + subsidy/certificate of 12 $/MWh

MHC (MW) 617 687 771 854 958

several sensitivities, we can demonstrate that the efficacy of these subsidies may depend on network capacity and generation flexibility. This is an important piece of information for policy makers since subsidies may not present a significantly positive impact on promoting renewables due to other inefficiencies in terms of network configuration and level of (in)flexibility of generation plants.

10.4

Practical Case Study: Investigating the Impact of Massive HVDC Line Investment on MHC on the Chilean Power Sector

10.4.1 Background The planning authority in Chile (which is within the regulatory office) has recently approved a $1.3 billion investment in a new high voltage direct current (HVDC) line that will interconnect the north of the country, particularly the Atacama Desert (location with one of the highest solar irradiation levels in the world), with the load center of the electricity network located in Santiago, where about 30% of the national electricity demand is placed. This massive transmission network investment, with a capacity of 2000 MW and a length of 1500 km, has been justified for shipping low-cost solar power that can be produced in the Atacama Desert to the main load center of the country, without originating congestions and without the need for further network investments in the rest of the AC power network corridor. This important transmission project, however, received several objections from a number of market participants, who remained concerned about the benefits of the new asset in question. One of the strongest arguments used against the project was that solar resources (and other renewable resources) in Chile are present all along the country, not only in Atacama, and thus, renewable generation can be perfectly connected closer to the load center without escalating network investment costs. Furthermore, these market participants officially took a stand against this project, bringing their arguments to the Expert Panel. The Expert Panel is a special tribunal created in Chile to resolve disputes either among market participants or between market participants and the regulator or planning authority [38]. The first time this project was proposed by the regulator, the Expert Panel favored the position of those

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market participants who opposed the project. In the second time, nevertheless, the regulator faced no opposition, and hence, the project should go forward. Despite this, there are currently various concerns regarding the effectiveness of this new network investment option, especially in terms of supporting cost-effective integration of renewable generation. In this context, we aim to investigate the effect of the proposed HVDC line on MHC, particularly analyzing whether (or not) more network capacity really drives higher MHC in a realistic setting like the Chilean electricity market. Note that the effect of network investments on the ability of the electricity grid to absorb more renewable generation capacity is unclear due to the changes driven by network investments on LMPs. So, we use the concept of MHC to determine whether, in this case, more network investments may lead to a higher penetration of renewables.

10.4.2 Brief Description of the Chilean Electricity Market and Transmission Network Figure 10.7 illustrates the Chilean transmission system, which is modeled by using a 40-node representative network with 56 transmission corridors. We focus our analysis on the year 2018 with a total demand equal to 76 TWh/year and 13 GW in terms of energy consumption and peak power, respectively. Its generation fleet contains hydropower (28%), coal (22%), gas (19%), and variable wind and solar resources (16%), with a total installed generation capacity of 24 GW. Regarding the market organization, as mentioned in Sect. 10.1, Chile was deregulated in the early 1980s, unbundling generation, transmission, and distribution and establishing generation as a competitive market while networks remain as regulated monopolies. Despite this early deregulation, the market clearing in Chile is not bid based but rather cost based with audited costs. Under this cost-based approach, it is clear that zero variable cost generation, such as wind and solar power, will drive energy prices down if their penetration is too large.

10.4.2.1

Case Studies

We aim to investigate the effects of the HVDC line on MHC in Chile. In Fig. 10.7, the HVDC line (indicated as a dotted line) goes from node 4 to node 29, bypassing all existing electrical infrastructure between the Atacama Desert (node 4) and Santiago (node 29). As the line is of HVDC type, we neglect the effect of the second Kirchhoff’s law in the model for this particular line, considering the ability to fully control the power flows through this asset due to the associated flexible converterbased substations at its both ends. For this model, an additional constraint (to those

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Fig. 10.7 Chilean transmission network in 2018, indicating topology, generation and demand nodes, and number of circuits per corridor. The HVDC link is depicted as a dotted line

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Table 10.6 Investment cost of renewables in Chile Case Base case Sensitivity 1 Sensitivity 2 Sensitivity 3

Investment cost – solar power ($/kW) 1000 950 1000 950

Investment cost – wind power ($/kW) 1300 1300 1250 1250

indicated in Sect. 10.2) has been added to the hydro reservoirs to make water management more efficient, limiting the available energy generated per hydropower plant in addition to the maximum power that each unit can generate, referring to the limited amount of water available to generate energy. Apart from applying the proposed model (in which the summation of the wind and solar power generation capacity invested across the entire system is maximized) with and without the HVDC link, we run three sensitivity scenarios with different investment costs for wind and solar power generation, presented in Table 10.6. These values are annuitized by using a discount rate of 10% and a life span of 25 years. Finally, the cost data used in this study can be found in [39, 40], and the availability profiles of renewable generation are specified in [41, 42]. As mentioned earlier, the richest solar power resources are located in the north of Chile, specifically in the Atacama Desert.

10.4.2.2

Results

Table 10.7 shows the MHC for the four examined cases, demonstrating that MHC increases when the HVDC line is built. Furthermore, the MHC is clearly more sensitive to variations in the investment cost of solar rather than wind power generation, and this is because the new generation capacity built by the model corresponds mostly to solar power generation as shown in Fig. 10.8. Indeed, with the HVDC line, new solar power generation can significantly increase its market position from 4.7% to 12.7% of the total energy produced. This significant increase in the penetration of solar power generation due to the installation of the HVDC line displaces mainly thermal generation from a participation of 40% in the case without the HVDC line to 34% in the case with the HVDC line. There is also 1.5% decrease in the participation of hydropower generation when the HVDC line is built, and this is because the model attempts to maximize new renewable generation capacity, regardless of the effects of doing so on existing generation capacity. As demonstrated above, at least for this real case study, expanding network capacity will increase MHC due to the need to export higher amounts of solar power generation from the Atacama Desert to the rest of the country, where the use of more expensive thermal generation will be reduced. In fact, this result is in line with our previous finding (particularly that on the 2-bus network) that determines the value of large network capacity expansions in terms of increasing MHC

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Table 10.7 MHC in Chile Case Base case Sensitivity 1 Sensitivity 2 Sensitivity 3

MHC without HVDC link (MW) 1075 3217 1075 3217

MHC with HVDC link (MW) 2925 4149 2934 4166

50% 45%

Energy partication [%]

40% 35% 30% 25% 20% 15% 10% 5% 0% (a) (b) (c) (a) (b) (c) (a) (b) (c) (a) (b) (c) Thermal

Hydro

(a) (b) (c) (a) (b) (c)

Existing wind Existing solar New wing

New solar

Fig. 10.8 Energy participation per technology in the base case and (a) without generation expansion, (b) with generation expansion and no HVDC line, and (c) with generation expansion and HVDC line

when there are significantly richer renewable resources in a specific area that need to be exploited. Hence, extra network capacity will favor an increase in MHC in order to facilitate the shipping of valuable renewable resources to other locations, particularly large load centers.

10.5

Conclusions and Future Work

This chapter has introduced for the first time the concept of market hosting capacity, expressing the maximum amount of renewables that can be connected to a given power network while preserving their profitability in a deregulated environment. This chapter has also developed a suitable mathematical model to quantify this market hosting capacity, founded on bi-level optimization principles. This is a new measure for hosting capacity from a market point of view, which is useful to understand how various factors, such as network investments, subsidies, and

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generation flexibility, can effectively support higher investments in renewable generation. This new measure can be applied to both distribution and transmission networks as long as the network in question uses an LMP system to price energy. In this context, we demonstrate (through two theoretical studies and one practical study) that higher network capacity does not necessarily drive higher renewable generation investment since prices may drop in key areas of the network. We also demonstrate how system flexibility and subsidies can significantly support higher levels of MHC. Two key results with important implications from a policy and regulatory perspective are that (i) more network investments may not necessarily drive higher levels of MHC and that (ii) efficacy of subsidies to increase MHC is subject to network configuration and levels of flexibility of the generation fleet. Regarding the former, we demonstrated that, indeed, network expansions may threaten investment opportunities in renewable generation as network congestion can originate high prices in key importing areas, which can be attractive to invest in new renewable generation. Regarding the latter, it is important to understand up to which point subsidies can be an effective manner to increase MHC or whether there are other more effective means to achieve such MHC increase. Future work aims at enhancing the presented model in two directions. First of all, the proposed bi-level optimization model to quantify the MHC, as well as all bi-level optimization models employed in electricity market modeling, neglects the non-convex unit commitment constraints of conventional generators, due to their inherent inability to capture binary decision variables in their representation of the market clearing process. However, these complex operating properties affect the market outcome and subsequently the MHC, as they encapsulate the actual flexibility characteristics of the generation side. In this context, future work will explore mathematical approaches enabling incorporation of these complex constraints in the developed model without deteriorating significantly its computational performance. Furthermore, the inherent variability and limited controllability of renewable generation have lately attracted significant research interest around the value of flexible technologies, in particular energy storage and demand response, in enabling a higher integration of renewables. In this context, future work will investigate the impact of these technologies on the MHC by properly incorporating a representation of their time-coupling operating characteristics in the developed model. Acknowledgement The research presented in this chapter was supported by grants ANID/ FONDECYT/1181928 and FONDECYT/1190228, the Complex Engineering Systems Institute (ANID PIA/BASAL AFB180003), SERC-CHILE (ANID/FONDAP/15110019), ANID-Basal Project FB0008, and ANID/PIA/ACT192094.

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Index

A Active power curtailment, 102 Actual distribution network, 25 Agricultural feeder, 109 Angle droop control, 208 Annual capital cost, 101 Application program interface (API) function, 217 Approximation method, 97 Arduino-based IoT sensor platform, 217, 218 Artificial Neural Network Controller (ANNC), 205 Automatic generation control (AGC), 195, 197 components, 201 flowchart, 202 Automatic Q Control (AQC), 11 Automatic voltage regulator (AVR), 206

B Background harmonic distortion (BHD) electrical networks, 37 knowledge, 35 power system, 36 primary emission, 36 secondary emission, 36 television viewing, 38 voltage distortion, 36 Balanced distribution system, 108 Battery Energy Management System (BEMS), 209 Battery energy storage systems (BESSs), 87, 211 annual costs, 116 charge and output power, 104

economic feasibility, 114 installation constraints, 103 network constraints, 104 operation constraints, 103 optimal allocation, 114 optimal size and location, 102 parameters, 111 PV and wind generation, 112 Betz limit, 52 Bidirectional power flow, 5 Bi-level optimization approach, 227 Bi-level optimization model, 228, 229 Biofuel, 55 Biofuel-powered generators, 74, 82 2-bus network, 232, 233 5-bus distribution system, 64 DG connections, 65 line and load data, 64 MATLAB, 69 solar photovoltaic sources, 70 wind power plant, 73 11 bus feeder, 28 83-bus compensated system, 191 83-bus distribution system, 187, 188, 191

C California electricity crisis, 121 Capacity distortion index, 125, 126 Capacity withholding, 122, 125 electricity markets, 130 transmission congestion, 130 Capacity withholding assessment, 130 Capacity withholding indices, 124, 125, 128, 129, 141

© Springer Nature Switzerland AG 2020 A. F. Zobaa et al. (eds.), Hosting Capacity for Smart Power Grids, https://doi.org/10.1007/978-3-030-40029-3

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250 Capacity withholding mitigation, 143, 145 Chilean transmission system, 240 Clearness index (CI), 16, 17, 56 Communication-based control, 215 Concentrated solar power (CSP), 53 Constraint factor (CF), 139 Conventional controller, 202 Conventional electrical networks, 5 Conventional generation technology, 228 Conventional power generation, 195 Conventional power system, 48, 195 Cost and development status indexes, 107 Cost/benefit assessment, 106 Cournot model, 131–133 Cournot-Nash equilibrium (CNE), 122, 130 Cournot-type competition, 128

D Decarbonization, 224, 225 Defuzzification method, 205 Demand elasticity, 122, 128, 129 Demand side programs, 143 Deregulation, 225 Design of controllers, 202 Deterministic approach, 150 Distributed energy resources (DERs), 4, 48, 56, 87, 143, 196, 225 optimal sizing, 57 penetration, 5 Distributed energy technology, 56 Distributed generation (DG), 2, 40, 149, 195, 196, 225 owners/investors, 2 penetration problems, 2 Distribution feeder, 26 Distribution network reconfiguration (DNR), 179 Distribution network service providers (DNSPs), 150 Distribution system, 97, 98 Distribution system model, 181 Distribution system operators (DSOs), 2 Droop control, 209 Droop control scheme, 208 Dynamic hosting capacity (DHC), 3, 51 analysis, 4 characteristic, 3 descriptive graph, 4 and DSTHC concept, 7 PCC, 4 profile, 3 Dynamic-storage-hosting capacity (DSTHC), 7

Index E Economic assessment annual cost, 99 capital cost, 99 maintenance and operation, 100 Economic dispatch controller (EDC), 197 Electrical grid, 38 Electricity market, 228 Electricity network, 226 Electricity price data, 111 Electricity systems, 224 Electrochemical battery technologies, 91 Electrochemical storages, 90 Energy control center (ECC), 198 Energy management system (EMS), 211 Energy monitoring system architecture, 218 Energy storage (ES), 2, 6 Energy storage technologies classification, 89 electric field, 90 electrochemical, 89 mechanical forms, 89 steam turbines, 90 Enhanced hosting capacity (EHC), 83 European Distributed Energy Partnership (EU-DEEP), 196 exIWO algorithm, 186 Expanded invasive weed optimization (exIWO), 180

F Feeder characteristics conductor types, 163 length, 163 loading level, 164 location sensitivity, 164 parallel feeders, 163 Feeder reconfiguration, 191 Financial withholding, 122 Flat tie-line control (FTC), 201 FPGA-based HIL platform, 58 Frequency droop, 209 Fuzzy logic controller (FLC), 201, 204 ANN, 205 defuzzification method, 205 inputs, 204 output, 204 solar and wind power, 204

G Game theory-based formulation, 130

Index Gaussian-shape distribution, 112 GenCo’s cost function, 123 GenCos’ marginal costs, 122 Generation companies (GenCos), 121 ability, 122 capacity withholding, 121, 122, 126, 128 cost function, 122, 126, 131 cost parameters, 128 Cournot model, 123 generation, 124 market performance, 121 market power, 121 oligopoly market, 123 parameters, 139 Generation investment planning, 225 Geographical information system (GIS) data, 64 Global horizontal irradiance (GHI), 212 Global information system (GIS), 50

H Harmonic sources, 39 Harmonics MATLAB, 57 Typhoon HIL emulator, 58 HC Maximization strategy, 187 High-carbon energy sources, 2 High PV penetration, 32 Hosting capacity estimation, 92 distribution system, 93 framework, 92 Hosting capacity (HC), 12, 49, 87, 121 analytical analysis, 40, 145, 155, 159 approach, 39 calculation, 196 concepts and applications, 39 definition, 12 determination method, 15 and DG impacts, 12 LV grid, 12 science and technology, 50 studies, 13 x-axis, 15 Holding capacity vs. performance indices, 202 Hypothesis testing, 19

I IEEE 30-bus power system, 139 IEEE 30-bus test system, 140 IEEE 33-bus distribution system, 76, 78 biofuel-powered generator, 82

251 line and load data, 75 MATLAB, 76 solar photovoltaic, 78 wind speed, 79 IEEE 519, 57 IEEE RTS study, 236 hosting capacity levels, 236 variable cost, 237 Integrated hosting capacity PCC, 43 RMS, 41 sensitivity analysis, 44 voltage rise, 43 Interconnected power system, 199 Internal control loop, 209 Internet of Things (IoT), 216 cloud technology, 216 implementation, 217 microgrid, 218 requirement, 216 Invasive weed optimization (IWO), 185 Inverse demand function, 139 Investment cost recovery, 226

J Jacobian matrices, 200

K Karush-Kuhn-Tucker (KKT), 133, 229 Kirchhoff’s voltage law (KVL), 51 Korea Micro Energy Grid (K-MEG), 214, 215 Kronrod-Patterson rule, 20

L Lagrangian function, 123, 133 Lagrangian multiplier, 134, 135 Linearization technique, 106 Locational marginal prices (LMP), 228 Low-voltage (LV) distribution networks, 150, 173

M Maiming power system, 36 Market equilibrium, 131 Market equilibrium model, 130 Market hosting capacity (MHC), 226, 232, 238 Market power and capacity withholding, 143 Mathematical program with equilibrium constraints (MPEC), 227, 230

252 Maximum connectable solar capacity, 174 MHC sensitivity, 238 Microgrids biofuel, 55 solar energy, 53 structure, 51 supercapacitors, 55 WECS, 52 wind power plant, 53 Mixed-integer linear problem (MILP), 227, 231, 232 Modern-day solar PV systems, 167 Monte Carlo methodologies, 150 Monte Carlo simulation (MCS) method, 154 Monte Carlo technique, 19, 23, 24 Multi-agent system (MAS), 219 Multi-feeder LV distribution networks, 163 Multilayer perceptron (MLP), 205

N Network reconfiguration, 183 Network reinforcement, 57 Newton-Raphson iterative solution method, 200 Nodal capacity distortion index, 130 Nodal indices, 124 Nodal price distortion indices, 135 Nodal withholding-supply ratio (NWSR), 130 Nonintrusive method, 16, 17 Nonlinear programming (NLP) problem, 131 Numerical simulation, 16

O Oligopoly market, 135 On-line tap changer (OLTC), 23 On-line voltage regulator (OLVR), 11 On-load tap changer (OLTC), 2 Optimal allocation, 114 Optimal network configuration, 187 Optimal power flow (OPF), 88 Optimization model, 97 Over-voltage, 88, 97

P Perfect competition, 128 Performance indices, 206 Photovoltaics (PVs), 11, 54 Point of common coupling (PCC), 35, 57 Point of connections (POC), 167

Index Power flow equations, 182 Power generation vs. network capacity, 234 Power market modeling, 122 transmission congestion, 130 Power quality, 4 Power systems, 195 Power transfer distribution factors (PTDFs), 139 Probability-consequence diagrams, 22 Probability density functions (PDFs), 17 Problem formulation constraints, 184 distribution function, 185 exIWO, 185 IWO, 185 objective function, 184 reactive power, 185 Problem statement DG and SOP modeling, 181 DG modeling, 182 network reconfiguration, 183 power flow equations, 182 SOPs, 182, 183

Q Quantitative risk assessment (QRA), 20

R Radio-frequency identification (RFID), 216 Raspberry Pi monitoring system, 219 Regulation control schemes AGC, 197 DG, 196 generator prime, 198 island mode, 197 large signal analysis, 197 mathematical model, 198 microgrid, 197 regulation characteristics, 199 signal analysis, 196 Renewable energy, 1, 2, 8, 191 Renewable generation, 225 Renewable Portfolio Standards (RPS), 224 Reverse power flow, 168 Risk analysis approach definition, 20 distribution power, 21 operational performance, 21 stochastic process, 21 Risk-based analysis method, 23

Index Risk indices, 25 Risk visualization, 22 Root mean square (RMS), 41

S Segment-wise hosting capacity levels, 162 Semiconductor switches, 49 Sensitivity analysis, 158 Seoul National University (SNU), 213 Simplified distribution feeder model, 166 Simulation results, 129 Simulation test, 24 Single distribution feeder model, 174 Single feeder test network, 173 Small signal analysis, 206, 210, 211 DG, 207 PID controllers, 207 single area system, 207 voltage magnitude, 206 Smart grids, 2 Social welfare, 131, 132 Soft open points (SOP), 182 Solar deployment, 156 Solar energy, 53 Solar irradiation, 64 Solar irradiation data, 63 Solar irradiation values, 79 Solar photovoltaic sources, 70 Solar photovoltaic system, 54 Solar photovoltaics (PV), 53 connections, 159 distribution network, 151 and DNSPs, 150 feeder, 160 feeder voltage violation, 155 hosting capacity, 150 linear function, 169 load profiles, 152 location, 158 LV distribution networks, 150 mathematical models, 172 MCS method, 157 network planning perspective, 157 and non-dispatchability, 149 penetration levels, 152 POC, 168 power generation, 170 principles, 166 radial feeders, 151 solar customer, 152 solar penetration levels, 155

253 stochastic analysis framework, 154 test network, 152, 160 two-feeder network, 160 voltage drop, 171 Solar power penetration, 198 Solar PV hosting capacity, 150 Sparse grid technique, 19, 20 Static hosting capacity, 51 Static planning approach, 228 Steady-state frequency deviation, 201 Stochastic and feeder level, 175 Stochastic evaluation, 157 Stochastic parameter variation, 56 Stochastic solar PV generation, 150 Storage sizing framework approximation method, 97 BESS, 95 BESS capacity, 94 optimization models, 95 valid generated scenarios, 97 Storage system, 6 Supervisory control and data acquisition (SCADA), 62 Supply function equilibrium (SFE), 122 System Advisor Model (SAM) software, 155 System evaluation analytical solution, 16 classical tensor, 19 hypothesis testing, 19 nonintrusive method, 16, 17, 19 procedures, 16 uncertain quantities, 16 uncertainties, 16

T Total annual cost (TAC), 101 Total harmonic distortion (THD), 49 analysis, 82 biofuel-powered generator, 82 33-bus distribution system, 77, 82 buses, wind speed, 71 estimation, 56 injection condition, 70 values, solar irradiation and load, 70 wind speed, 74, 81 Transmission congestion, 131 Transmission-constrained market, 137 Transmission network congestion, 130 Transmission system operators (TransCo), 146 Two-feeder network, 162, 164

254 Typhoon hardware in loop (HIL) application, 58 CLOSE mode, 62 compilation and model execution, 61 configuration, 60 emulator, 60 FPGA-based, 61 library, 61 model settings, 62 parameters, 58 SCADA, 62 switching element, 59 Typhoon HIL emulator, 59 Typhoon HIL simulation, 50 Typhoon HIL simulators, 58 Typhoon HIL402 emulator, 59

U Upper level (UL) problem, 229

Index V Valve-regulated lead-acid (VRLA), 114 Voltage harmonic distortion, 37 Voltage phasor diagram, 37 Voltage rise, 5–8, 38, 41, 152, 168 Voltage source converter (VSC), 209

W Weibull distribution function, 56 Wind energy conversion system (WECS), 52, 56 Wind speed data, 64 Wind technology, 114 Wind turbine, 52

Z ZnBr battery technology, 116