Voltage Stability in Electrical Power Systems E-Book

Farid Karbalaei

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 387

Veröffentlichungsjahr: 2022

Beschreibung

Voltage Stability in Electrical Power Systems Explore critical topics and the latest research in voltage stability in electric power systems In Voltage Stability in Electrical Power Systems: Concepts, Assessment, and Methods for Improvement, three distinguished electrical engineers deliver a comprehensive discussion of voltage stability analysis in electrical power systems. The book discusses the concept of voltage stability, effective factors and devices, and suitable system modeling, offering readers an authoritative overview of the subject and strategies to prevent instability in power systems. The authors explore critical topics such as load and load tap changer (LTC) transformer modeling and the impact of distributed generation and transmission-distribution interactions on voltage stability. They also present practical methods to improve voltage stability. Readers will also find: * Thorough introductions to voltage stability, effective factors and devices, and suitable systems modeling * Comprehensive explorations of voltage stability assessment methods, including the continuation power flow methods and PV-curve fitting * In-depth explorations of methods of improving voltage stability, including preventive and corrective methods * Fulsome presentations of measurement-based indices and model-based indices of stability assessment Perfect for engineers and other professionals designing electric power systems, Voltage Stability in Electrical Power Systems: Concepts, Assessment, and Methods for Improvement will also earn a place in the libraries of graduate and senior undergraduate students with an interest in power systems.

Leseprobe

IEEE Press445 Hoes LanePiscataway, NJ 08854

IEEE Press Editorial BoardSarah Spurgeon, Editor in Chief

Jón Atli BenediktssonAnjan BoseAdam DrobotPeter (Yong) Lian    

Andreas MolischSaeid NahavandiJeffrey ReedThomas Robertazzi 

Diomidis SpinellisAhmet Murat Tekalp  

Voltage Stability in Electrical Power Systems

Concepts, Assessment, and Methods for Improvement

Farid Karbalaei

Shahid Rajaee Teacher Training UniversityTehran, Iran

Shahriar Abbasi

Technical and Vocational University of IranKermanshah, Iran

Hamid Reza Shabani

Aalborg UniversityEsbjerg, Denmark

Copyright © 2023 by The Institute of Electrical and Electronics Engineers, Inc. All rights reserved.

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Library of Congress Cataloging‐in‐Publication Data:Names: Karbalaei, Farid, author. | Abbasi, Shahriar (Assistant Professor), author. | Shabani, Hamid Reza, author.Title: Voltage stability in electrical power systems : concepts, assessment, and methods for improvement / Farid Karbalaei, Shahriar Abbasi, and Hamid Reza Shabani.Description: Hoboken, New Jersey : Wiley, [2023] | Includes index.Identifiers: LCCN 2022041340 (print) | LCCN 2022041341 (ebook) | ISBN 9781119830597 (hardback) | ISBN 9781119830641 (adobe pdf) | ISBN 9781119830658 (epub)Subjects: LCSH: Electric power system stability. | Electric power systems–Control.Classification: LCC TK1010 .K367 2022 (print) | LCC TK1010 (ebook) | DDC 621.319–dc23/eng/20220919LC record available at https://lccn.loc.gov/2022041340LC ebook record available at https://lccn.loc.gov/2022041341

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Author Biographies

Farid Karbalaei received BSc degree in power engineering from K. N. Toosi University of Technology, Tehran, Iran, in 1997, and MSc and PhD degrees in power engineering from Iran University of Science and Technology, Tehran, in 2000 and 2009, respectively. Currently, he is an associate professor in Shahid Rajaee Teacher Training University. His research interests are power system dynamics and control, voltage stability and collapse, reactive power control, wind power generation, and optimization methods.

Postal Address: Faculty of Electrical Engineering, Shahid Rajaee Teacher Training University, Lavizan, Tehran, Iran. Phone: [phone], Email: [email protected] (Corresponding author)

Shahriar Abbasi received BSc and MSc degrees in power engineering from Shahid Rajaee Teacher Training University Tehran, Iran, in 2008 and 2011, respectively. He received PhD degrees in power engineering from Razi University, Kermanshah, Iran, 2018. Currently, he is an assistant professor in Technical and Vocational University of Iran, Kermanshah Branch. His research interests are power system planning, uncertainty modeling, voltage stability and collapse, wind power generation, and optimization methods.

Postal Address: Technical and Vocational University of Iran, Kermanshah Branch, Kermanshah, Iran. Phone: [phone], Email: [email protected]

Hamid Reza Shabani received the MS degree in power electrical engineering from Shahid Rajaee Teacher Training University (SRTTU), Tehran, Iran, in 2014. Also, he received the PhD degree from Iran University of Science and Technology (IUST), Tehran, Iran, in 2021. His thesis title in the PhD program was “evaluation of large‐disturbance rotor angle instability in the modern power systems, with high‐Penetration of wind power generation.” He currently works as a postdoctoral researcher at Aalborg University (AAU Energy) in the Esbjerg Energy Section. His main research interests include power system stability, power system dynamic and control, and renewable energies.

Postal Address: The Faculty of Engineering and Science (AAU Energy), Aalborg University, 6700 Esbjerg, Denmark. Phone: [phone], Email: [email protected]

Preface

Voltage instability has been considered about 60 years ago and is still a major cause of blackouts in electrical power systems. So far, extensive studies have been conducted on this topic and the result of which is publication of thousands of articles and a few number of books. The articles cover a wide range of subjects related to voltage stability, including proper system modeling for voltage stability studies, online and offline voltage stability assessment methods, and methods to prevent voltage instability, which include two sets of preventive and emergency methods.

Being familiar with the all above‐mentioned subjects is necessary for power engineers because effective prevention of voltage instability necessitates timely detection of it. Timely detection also requires knowledge of the mechanism of voltage instability and proper modeling of the system. Since voltage instability is a local phenomenon, contrary to rotor instability, many methods of detecting and preventing voltage instability are performed locally. Therefore, in addition to the engineers working in the system control center, all power engineers in local control centers should be fully familiar with this field.

Good understanding of issues related to voltage stability requires reading hundreds of articles. Due to the fact that articles do not have educational purpose, it is difficult to fully understand, summarize, and relate them together. Therefore, a book that presents all the above subjects in a complete, arranged and comprehensible way is needed; so that it first explains the necessary fundamentals (which is not done in articles) then presents the related subjects in an appropriate classification and sequence. The aim of this book is to present all the voltage stability subjects so that readers with the level of bachelor information can use it well. Of course, the state‐of‐the art on voltage stability is introduced in it to be useful for university professors, master and doctoral students.

This book consisted of three parts. The contents of these parts can be summarized as follows:

The Part I: Concept of Voltage Stability, Effective Factors and Devices, and Suitable System Modeling consisted of four chapters. In Chapter 1, the concept of voltage instability and its types are first described. Then how long‐term instability and voltage drop occur due to the activities of tap changers and thermostatic loads are illustrated. The occurrence of short‐term voltage instability due to the presence of induction motors is also described. In this chapter, by simulating on a simple system, the importance of loadability limit increase in maintaining voltage stability is shown. The concept of exiting from attraction region and the importance of timely performing of emergency measures are also explained by simulation. The purpose of this chapter is to familiarize the reader quickly and in general (not in full detail) with the concept and causes of voltage instability as well as how to prevent it from occurring.

In Chapter 2, different dynamic and static load models used in references to analyze voltage stability are introduced. These models represent the behavior of integrated loads seen from different buss of the power system. In short‐term voltage stability analysis, the dynamic behavior of load is simulated as the dynamic model of induction motor. Hence, a part of the third chapter is devoted to presenting the algebraic and differential relations of induction motor. Another part of this chapter introduces the types of tap changers and modeling transformers with variable tap. In references, there are two models to represent variable tap transformers. The difference between these two models is in the side that the equivalent impedance of transformer is seen from it. The simulations verify that these two models lead to different values for the system loadability limit. Given the importance of determining the correct (real) loadability limit in voltage stability studies, selection of the proper model is very important. This is discussed in this chapter.

Chapter 3 deals with modeling of synchronous generator and two types of distributed generation sources (FSIG‐ and DFIG‐based wind turbines). The modeling degree should be chosen according to the intended type of study. In this chapter, suitable models for studying each type of voltage instability (long term and short term) are presented.

Chapter 4 explains the importance of concurrent modeling of distribution and transmission networks in assessing voltage stability. This is shown that sometimes, separate modeling of distribution and transmission networks causes a significant error in determining the voltage stability limit. Also in this chapter, the effect of the presence of distributed generation (DG) sources on voltage stability is investigated. These sources, which are mainly connected to distribution networks, up to the condition have different effects on voltage stability.

The Part II: Voltage Stability Assessment Methods, includes the Chapters 5–9. This Part of the book is dedicated to voltage stability assessment methods. Voltage stability assessment is performed for several purposes. One of them is determination of the voltage stability margin, which is calculated for both the current (no‐contingency) system and probable contingencies. What is important in calculating the voltage stability margin is speed and accuracy of the calculation. Since the determination of the stability margin must be repeated every few minutes, its calculation for a large number of probable contingencies is possible only if the calculation time be very short while maintaining the required accuracy. For this, the methods of continuation power flow (CPF) and PV‐curve fitting are presented, which are discussed in Chapters 5 and 6.

Voltage stability margin shows the level of system stability in the face of various contingencies. It does not directly provide information about the vulnerable points of system as well as the important elements in instability occurrence. This information, which helps operators to decide about taking the voltage instability preventive methods, is obtained by voltage stability indices. A number of voltage stability indices are calculated based on the system model. These indices help a lot in defining and ranking the critical contingencies, as well as in determining the necessary actions after each contingency occurrence. Another set of indices uses only variables measured at different points of system and does not require the system model. These indices can be used to quickly identify the current status of system and early detection of voltage instability. Also, when voltage stability assessment requires dynamic analysis and time simulation, the voltage stability indices can be used to reduce the required simulation time. These indices are all introduced in Chapters 7 and 8, and the advantages and applications of each one are stated.

In Chapter 9, the machine learning‐based methods to assess and monitor voltage stability of power system are introduced. General topologies of these methods and their capabilities were introduced. These methods are categorized in five methods. For each method, a table including input(s), output(s), used technique, and case study is presented.

In the Part III of this book: Methods of Preventing Voltage Instability, the methods to prevent voltage instability are discussed. All actions used to prevent voltage collapse are divided into two categories: preventive and emergency. The purpose of preventive actions is to increase the voltage stability margin of the power system. Increasing the voltage stability margin is considered for both the current (no‐contingency) system and probable contingencies. Therefore, these actions are applied when the system is stable, but there is a small distance between the current operating point and the voltage stability limit. The purpose of determining preventive actions is to improve system stability with the least measures (especially with the minimum load shedding).

The emergency actions are performed when the system becomes unstable due to one or more contingencies, and if these actions are not applied, a voltage collapse will occur in a few moments or minutes. In determining the emergency actions, the speed of calculations is very important because the later these actions are applied, voltage stability maintenance is possible with more actions.

Some of the voltage stability studies are devoted to methods for determining preventive and emergency actions, which are discussed in Chapters 10 and 11.

Farid Karbalaei, Shahriar Abbasi and Hamid Reza Shabani Tehran

Part IConcept of Voltage Stability, Effective Factors and Devices, and Suitable System Modeling

1How Does Voltage Instability Occur?

1.1 Introduction

The phenomenon of voltage instability is one of the major problems of today’s power systems. According to the Institute of Electrical and Electronics Engineers (IEEE)/The International Council on Large Electric Systems (CIGRE) definition, voltage stability is the ability of a power system in maintaining an acceptable steady‐state voltage at all buses when subjected to a contingency. The consequence of voltage instability is voltage collapse. Unlike rotor angle instability, which is more related to generator operation, voltage instability depends on the amount and characteristic of loads. For this, voltage instability is also called load instability [1]. Voltage instability is divided into two categories; long term and short term. In the long‐term type, voltage collapse occurs during a process of a few tens of seconds or a few minutes, but in the short‐term voltage instability, the voltage collapse occurs rapidly and within a few seconds.

In general, the reason of voltage instability is the presence of devices whose power consumption is not much dependent on voltage. Voltage drop initially reduces the input power of these devices, but after a few moments or minutes, the reaction of these devices causes their receiving power to increase to a value close to the value before the voltage drop. Power recovery may be done for active power only or for both active and reactive powers. Figure 1.1 conceptually shows the process of recovering the active power of a device when voltage drops. It is observed that at first the power is reduced but in the steady state its value become close to the initial value. Therefore, it is said that this device has the characteristic of constant steady‐state power. In this figure, it is assumed that a constant reduced voltage is applied to the device. Also, the fluctuations of power are ignored when it is recovering. In practice, the voltage of a device decreases as its power consumption increases. In steady‐state conditions, this voltage drop is small, but when voltage instability occurs, power recovery causes a severe voltage drop. A necessary (not sufficient) condition for maintaining voltage stability is that the transfer of the required power to constant power consumers is possible. Otherwise, long‐ or short‐term voltage instability will occur, depending on to the power recovery time constant.

Figure 1.1 Power recovery after voltage drop.

One of the most important devices that create constant power characteristic is load tap changer (LTC) transformer. In most cases, the variable tap is located on the high voltage (HV) side of the transformer. This is due to less current in the HV side, which makes it easier to change the tap. Another reason is the high number of winding turns in the HV side, which makes the voltage regulation more accurate [1]. The tap control system usually controls the voltage of low voltage (LV) side, which has lower short‐circuit level. These devices fix the voltage of LV side, independent of the HV side voltage. By keeping this voltage fixed, the power consumption at the LV side also remains constant. Hence, assuming the transformer losses remain constant, the power received from the HV side is independent of its voltage. Therefore, the load seen from the HV side of the transformer has the characteristic of constant steady‐state power. If the system is stable, voltage and power recovery will be done by tap changer in a few tens of seconds. In addition to tap changer, thermostatically controlled heat loads (TCLs) can also create constant power characteristic. When voltage drops, these loads will remain in the circuit longer because they must produce the necessary heat energy. Therefore, as the voltage decreases, the impedance of a set of these loads decreases. As a result, when the voltage drops, the power consumption by these loads does not change much in the steady state. It is clear that in the early moments of voltage drop, TCLs have an impedance characteristic and a constant power characteristic is created during a process of several minutes.

The main reason of short‐term voltage instability is the presence of induction motor loads. Speed reduction and stalling of these motors lead to sudden increase in their reactive power consumption by them and voltage collapse. After a voltage reduction, initially, the power consumption of an induction motor decreases, but due to decreasing speed and increasing slip, the active power consumed by the motor gradually will increase. The amount of active power increment depends on the type of mechanical load supplied by the motor. The power recovery in induction motors is done quickly in a few seconds. Motor stalling happens when the motor is unable to supply its connected mechanical load. In this chapter, using simulation on simple networks, the procedure of voltage instability occurrence due to the above‐mentioned factors is illustrated.

1.2 Long‐Term Voltage Instability

In this section, using an example, the procedure of voltage instability due to operation of LTCs is shown. Also, the reason of this occurrence is illustrated.

1.2.1 A Simple System

To simulate the occurrence of voltage instability, the simple system of Figure 1.2 is used. In this system, a generator supplies a static load with voltage‐dependent characteristic through two parallel lines and an LTC transformer. For the load, the exponential model according to Eqs. (1.1) and (1.2) is used. In these equations, P0 and Q0 are, respectively, the demanded active and reactive powers of this load at the voltage 1 pu. A complete discussion about load modeling is presented in Chapter 2.

(1.1)

(1.2)

Figure 1.2 Single‐line diagram of a simple system with LTC transformer.

The transformer is modeled as a series leakage impedance and an ideal transformer. Next to the load, there is a compensating capacitor with the admittance 0.45 pu. In this example, the generator is modeled as a constant voltage source, and the voltage V1 is assumed to be 1 pu. Therefore, the dynamic behavior of this system is only due to the operation of LTC. It is assumed that the LTC is installed at the HV side and its value (a) can vary from 0.85 to 1.15 pu in the steps of 0.005 pu (0.5%). The duty of the LTC is maintaining V3 between 0.99 and 1.01 pu. This range is called the LTC dead band. The dead band is always considered larger than LTC steps, usually twice of LTC steps. Otherwise, the LTC changes will not converge to a steady‐state value.

1.2.2 Voltage Calculation

To calculate V3 for different tap values, the equivalent circuit π is used to model LTC transformer [2]. By doing so, the equivalent single‐phase circuit of this system is as shown in Figure 1.3. By changing the tap value, the impedance of the equivalent circuit branches of the transformer changes. In this system, the bus 1 is slack and the buses 2 and 3 are the PQ type. To calculate the voltages, the load flow equations are written and solved with voltage‐dependent load at bus 3. Assuming P0 and Q0 are, respectively, equal to 0.5 and 0.2 pu, the steady‐state tap value becomes 1.00 and the magnitude of voltage V3 is equal to 0.992 (a value between 0.99 and 1.01 pu).

Figure 1.3 Single‐phase equivalent of the system of Figure 1.2.

Assuming the outage of one of the parallel lines, the voltage of bus 2 and consequently the voltage of bus 3 decreases. After this voltage drop, the LTC reduces the tap value installed at the HV side to recover the voltage. The LTC and voltage changes are shown in Figure 1.4. It can be seen that by a few changes of tap value, the voltage of bus 3 is recovered to the desired range.

Figure 1.4 Voltage recovery after line outage.

1.2.3 Illustration of Voltage Collapse

Now with the two parallel lines, the values of P0 and Q0 are increased to 0.83 and 0.33 pu, respectively. In this condition, in steady state, the tap value and voltage of bus 3, respectively, converge to 1.05 and 0.991 pu. Now, with these values for P0 and Q0, and outage of one of the parallel lines, the LTC control system will start reducing its tap value again to recover the voltage of bus 3. But in this case, as shown in Figure 1.5, voltage recovery is not achieved. At the first few steps, the voltage of bus 3 increases by any reduction in the tap. But after these initial steps, any decrease in the tap leads to a voltage drop, which means that the voltage instability has occurred.

Figure 1.5 Voltage instability after line outage.

1.2.4 The Reason of Voltage Collapse Occurrence

The reason of impossibility of voltage recovery is that voltage recovery means the recovery of active and reactive powers to values close to P0 and Q0 (0.83 and 0.33 pu in this example). Therefore, voltage recovery is achieved only when after a line outage, the system be able to deliver these amounts of power to the bus 3. To better understand this subject, the transformer impedance is shifted to its primary side as shown in Figure 1.6. By doing so, the power delivered to the primary side of the ideal transformer is the same as the power delivered to the load. Now, due to the tap operation, the load seen from the primary side of the ideal transformer has the characteristic of constant steady‐state power. Because, regardless of the primary side voltage, the secondary side voltage and consequently its power consumption in steady state is almost constant. (Of course, the steady‐state voltage may vary in the dead band range, causing slight changes in the steady‐state power consumption.) It is obvious that the constant power characteristic will be obtained during a few tens of seconds to a few minutes process, depending on the time delay of the tap changes. In addition to the steady‐state characteristic, there are also some transient characteristics that indicate the momentary relationship between power and voltage in the primary side of the ideal transformer. These characteristics are according to Eqs. (1.3) and (1.4).

(1.3)

(1.4)

Figure 1.6 Transformer impedance transferred to the primary side.

A load that has a transient characteristic in addition to the steady‐state characteristic is called a dynamic load. In the above‐mentioned example, the load seen from the primary side of the transformer is a dynamic load. The power variations of dynamic loads due to voltage change, in addition to the steady‐state term, have a transient term. Now, due to the constant steady‐state power characteristic, a stable operating point is achieved only when it is possible to deliver power to the demanded load. For this reason, in many references, the maximum loadability of a power system is introduced as the long‐term voltage stability limit.

Occurrence of voltage instability implies that the active and reactive powers of 0.83 and 0.33 pu are definitely more than the maximum powers that can be transferred to the primary side of the ideal transformer. Figure 1.7 shows the voltage variations versus the active power variations received at the primary side of the ideal transformer before and after the line outage. In drawing these curves, the variation of the transformer series impedance due to the tap changes is neglected. The error of this approximation is very small since the transformer impedance is connected in series with the line impedance. These curves, which are widely used in power system voltage stability studies, are called power voltage (PV) curves [3]. Usually, these curves are drawn with constant power factors. The power factor in Figure 1.7 is chosen based on the active and reactive powers of the load and the reactive power produced by the capacitor at voltage 1 pu. It can be seen that the maximum transferable active power after line outage is equal to 0.75 pu, which is less than the power required to voltage recovery (0.83 pu). In Figure 1.7, along with the PV curves, the transient characteristics of the active power seen from the primary side of the ideal transformer are plotted. These characteristics are obtained for different tap values. The intersection points of the transient characteristics with the PV curves are the active power and voltage values for different tap values. As can be seen, as the tap decreases, the intersection point moves toward the point of maximum transferable power (the nose of PV curve). Until the intersection point reaches the nose of PV curve, any tap reduction will increase the received power by the load. Due to the voltage‐dependent characteristic of the load, increasing the received power means increasing the voltage V3, although the voltage decreases. After crossing the nose of PV curve, the power and voltage V3 will reduce after each tap reduction. Therefore, the nose of the PV curve is also called the collapse point.

Figure 1.7 The PV curves seen from the primary side of the ideal transformer of Figure 1.6.

Figure 1.8 shows the PV curves with different power factors of the load. It is shown that the more lead characteristic of the load, i.e. the more reactive power compensation, the higher maximum loadability, and also the higher collapse point voltage. If the reactive power compensation level is not high, the voltage of collapse point will be low (even about 0.5 pu). However, if the reactive power compensation level is high, the collapse point voltage may even reach values higher than 0.9 pu. Given that the operating voltage of the system is usually in the range of 0.95–1.05 pu, if the compensation level is low, then there will be a large distance between the operating range and the collapse point. Under these conditions, the probability of long‐term voltage instability is very low. But if the level of compensation is high, the operating range is close to the collapse point. Hence, it is found that the long‐term voltage instability is the problem of power systems that have been highly compensated.

Figure 1.8 The PV curves with different power factors of load.

1.2.5 The Importance of Timely Emergency Measures

The Figure 1.7 illustrates that the inability of LTC in maintaining voltage appears when it is not possible to transfer the needed power to a bus whose voltage is controlled. Therefore, as this will be shown in future chapters, the basis of all voltage instability preventing methods is increasing the maximum loadability level of the power system. This increase is usually done by measures such as increasing the voltage of the generators, connecting the capacitors, and removing the reactors. If increasing the loadability level be not sufficient, the last measure is to reduce the system load. The important point is that the above measures can be effective when applied in a timely manner. The later the measures, the more measures must be taken to maintain voltage stability. To explain this, let us assume that there is another capacitor with susceptance 0.20 pu in bus 3 that connects when needed (Figure 1.9). By connecting this capacitor, it is possible to maintain the voltage stability of the system. Because, as shown in Figure 1.10, the maximum transferable power of the system when the capacitor is connected and one of the parallel lines is removed becomes more than the demanded power. In this figure, similar to Figure 1.7, the dashed‐line curves are the load transient characteristics seen from