Power System Wide-area Stability Analysis and Control

By Jing Ma

An essential guide to the stability and control of power systems integrating large-scale renewable energy sources

The rapid development of smart grids and the integration of large scale renewable energy have added daunting new layers of complexity to the long-standing problem of power system stability control. This book offers a systematic stochastic analysis of these nonlinear problems and provides comprehensive countermeasures to improve power system performance and control with large-scale, hybrid power systems.

Power system stability analysis and control is by no means a new topic. But the integration of large scale renewable energy sources has added many new challenges which must be addressed, especially in the areas of time variance, time delay, and uncertainties. Robust, adaptive control strategies and countermeasures are the key to avoiding inadequate, excessive, or lost loads within hybrid power systems. Written by an internationally recognized innovator in the field this book describes the latest theory and methods for handling power system angle stability within power networks. Dr. Jing Ma analyzes and provides control strategies for large scale power systems and outlines state-of-the-art solutions to the entire range of challenges facing today’s power systems engineers.

• Features nonlinear, stochastic analysis of power system stability and control
• Offers proven countermeasures to optimizing power system performance
• Focuses on nonlinear time-variance, long time-delays, high uncertainties and comprehensive countermeasures
• Emphasizes methods for analyzing and addressing time variance and delay when integrating large-scale renewable energy
• Includes rigorous algorithms and simulations for the design of analysis and control modeling

Power System Wide-area Stability Analysis and Control is must-reading for researchers studying power system stability analysis and control, engineers working on power system dynamics and stability, and graduate students in electrical engineering interested in the burgeoning field of smart, wide-area power systems.

• Language: English
• Publisher: Wiley
• Release date: May 10, 2018
• ISBN: 9781119304869

Book preview

About the Author

Professor Jing Ma has been working in this area since 2003. His research mainly concentrates in the area of power system protection and control. A very systematic research and practice on power system wide‐area stability analysis and control, especially the approaches on the small‐signal stability analysis and studies on the novel principle of wide‐area robust and adaptive control, have been carried out over more than 12 years. He was the first to apply Guardian Map Theory, Perturbation Theory, and the Markov Model to fully consider the characteristics of large time‐delay and high uncertainties into the power system stability analysis process. He also invented a variety of robust and adaptive control strategies using the Federated Kalman Filter, Dual Youla Parameterization and Classification, and the Regression Tree to establish a wide‐area control system with high accuracy and efficiency. A series of papers was published in the authoritative journals such as IEEE Transactions on Power Systems and IEEE Transactions on Power Delivery. The work has been widely acknowledged and cited by international peers. Part of his research results was used in many practical engineering projects, which highly accelerate the application and spread of wide‐area control technology. In recent years, he has published more than 30 papers (indexed by SCI), authorized more than 20 patents, and undertaken many major projects in China. For instance, he guided two projects of the National Natural Science Foundation of China to study the Stability and Coordinated Control for a Complicated Power System. He set up an advanced wide‐area protection and control platform for stability analysis of a power system, and pioneered to design and realize the corresponding control techniques. He was also responsible for several projects from governments and enterprises on the study of wide‐area stability analysis and control. He was also a major member of the National Key Research and Development Plan of China on the study of the Wide‐Area Protection and Control for Complicated Power Systems. He cooperated with the China Electric Power Research Institute to guide the exploitation of the integrated protection and control system of substation areas and wide areas. He has been teaching the courses of Power System Automation for years. Many materials of the book have been taught to students and other professionals.

Preface

Power system stability has been a key issue in the three defense lines of power system security defense in China, and has drawn the continuous attention of many researchers. With the large‐scale integration of renewable energy sources and the wide application of power electronic devices, the stability problem caused by grid interconnection has become ever prominent, greatly endangering the safe and stable operation of a power system, even causing blackouts, which result in immeasurable losses to the society and the economy. Therefore, the stability of the power grid under new circumstances and trends requires the in‐depth exploration and research of all electric power practitioners.

Challenges usually come with innovation and opportunities. With the development and wide application of PMU technology, wide‐area information from WAMS has provided abundant synchronous and dynamic information for the stability analysis and control of a large complex power grid. It is an issue of great theoretical value and practical significance in the smart grid research to combine PMU technology with stability control, so that the safety of the power grid can be guaranteed to most users. Currently, many problems in wide‐area stability control are yet to be solved. For example, it is the basis and premise of wide‐area stability control to conduct system stability identification, instability mode identification, and stability region calculation in a complex time‐varying grid with time delay and uncertainties. Meanwhile, it is the goal and task of wide‐area stability control to design reasonable and effective robust and adaptive control strategies to solve the problems of lack‐of‐control, over‐control, and out‐of‐control in the power grid. By summarizing the existing research achievements and learning from the advantages and disadvantages of traditional stability control, this book conducts a prospective discussion on the key techniques in wide‐area stability control, such as wide‐area signal monitoring, wide‐area stability analysis, and wide‐area control strategies, etc. The discussion is centered on research achievements of the author, and is presented in great breadth and depth, endeavoring to point out the evolving direction of wide‐area stability control.

The author strives to make the basic theories simple and the formula derivations precise and complete. On this basis, through a large number of case studies, rigorous verification that fits the engineering practice is carried out concerning the wide‐area stability control schemes introduced in the book. It should be noted that, since wide‐area stability control is still developing, the contents in this book may not be the final solutions. For the issues that have not gained unified understanding, the author has put forward distinct viewpoints in the book. It is the author’s sincere hope that readers will be inspired by this book to pursue better achievements in their research. Due to limited space, references are provided for the issues that cannot be discussed in detail, so that readers could study them in depth.

This book is readable by graduate students in universities, technical personnel in research institutes, and professionals with certain theoretical knowledge and practical experience in their research on wide‐area stability control and relevant technological innovations. Mistakes are inevitable in the book and any criticism from readers will be welcome.

This work is supported by National Natural Science Foundation of China (No. 51277193), the Chinese University Scientific Fund Project (No. 2014ZZD02), Beijing Metropolis Beijing Nova program (Z141101001814012), the Excellent Talents in Beijing City (2013B009005000001), and the Fund of Fok Ying Tung Education Foundation (141057).

Jing Ma

Beijing, China

2016

1

Basic Theories of Power System Security Defense

1.1 Introduction

A power system is a large‐scale system with wide geographical distribution, large numbers of components, and fast dynamic response. Disturbance on one single component may quickly spread to the whole system. The most important task in power system design and operation is to analyze the transient and dynamic behaviors of the power system under different levels of disturbance and then determine the appropriate control strategies and corresponding measures.

Ever since the 1960s, large area blackouts have occurred from time to time, causing huge economic losses. The 8–14 blackout in the eastern North American power grid that occurred in 2003 has inspired a worldwide wave of research on the prevention of large power grid blackouts. The 2012 India blackout triggered the largest scale of blackout in human history. With the integration of large‐scale renewable energy sources, the power grid operating mode has become changeable. The integration of distributed generation and micronetworks and self‐healing control has caused the distribution network to be changeable, even in configuration. Besides, the application of power electronic devices introduces a large number of nonlinear controlled components to the grid, which causes power grid stable operation and control to be increasingly difficult. Therefore, there is an urgent need to study the security defense of a large power grid.

Power system personnel in China have conducted a lot of research to ensure the safe and stable operation of the power system, and have put forward three defense lines in a power system to deal with serious faults. The first defense line ensures that the system has a certain degree of safety margin in normal operating condition, does not lose the power source and load, and maintains stable operation when nonserious faults occur. The second defense line ensures that system stability is not destroyed and faults do not expand when relatively serious faults occur. The third defense line ensures that the system does not collapse and that large‐area blackout does not occur in the case of extremely serious faults.

This chapter is an overview of the basic theories of power system security defense. First, the basic requirements on power system reliability and the definition and classification of power system stability in China and abroad are introduced. The different types of disturbances that a power system may encounter and their impacts on the system are introduced. In order to ensure the safe and stable operation of a power system, different kinds of protection and control measures should be taken concerning different types of disturbances, including prevention control, emergency control, splitting control, and restoration control.

1.2 Power System Reliability and Stability

1.2.1 Reliability of Power System

The basic function of a power system is to provide all users with a continuous power supply that is in accordance with relevant regulations in power quality (voltage and frequency). Power system reliability is a measure of the capability of the power system to provide users with the required quantity of power of acceptable quality standard continuously, including two aspects: system adequacy and security [1].

1.2.1.1 Adequacy

Adequacy (also known as static reliability) refers to the capability of a power system to provide users with the required quality and quantity of power when the power system is in steady‐state operation and, within the allowed ranges of system component rated capacity, bus voltage, and system frequency, to consider the planned outage and reasonable unplanned outage of system components to the user and provides all of the required electric power and the ability described in reference [1]. Detailed indexes to characterize adequacy are as follows:

LOLD (loss of load probability) refers to the probability that the system cannot meet load demand in a given time interval, that is,

(1.1)

where Pi is the probability of the system being at state i. S is the complete set of system states in which the system cannot meet load demand in the given time interval.

LOLE (loss of load expectation) refers to the expected number of hours or days when the system cannot meet load demand in a given time interval, that is,

(1.2)

where Pi is the probability of the system being at state i, S is the complete set of system states in which the system cannot meet load demand in the given time interval, and T is the number of hours or days in the given time interval.

LOLF (loss of load frequency) refers to the number of times when the system cannot meet load demand in a given time interval, that is,

(1.3)

where Fi is the probability of the system being at state i and S is the complete set of system states in which the system cannot meet load demand in the given time interval.

LOLD (loss of load duration) refers to the average time duration when the system cannot meet load demand in a given time interval, that is,

(1.4)

where LOLE is loss of load expectation and LOLF is loss of load frequency.

EDNS (expected demand not supplied) refers to the expected reduction of load demand power due to generation capacity shortage or power grid constraints in a given time interval, that is,

(1.5)

where Pi is the probability of the system being at state i, Ci is the reduced load power at state i, and S is the complete set of system states in which the system cannot meet load demand in the given time interval.

EENS (expected energy not supplied) refers to the expected reduction of load demand energy due to generation capacity shortage or power grid constraints in a given time interval, that is,

(1.6)

where Pi is the probability of the system being at state i, Fi is the probability of the system being at state i, Di is the time duration (in days) at state i, Ci is the reduced load power at state i, S is the complete set of system states in which the system cannot meet load demand in the given time interval, and T is the number of hours in the given time interval.

1.2.1.2 Security

Security (also known as dynamic reliability) refers to the capability of a power system to endure emergent disturbances such as a short‐circuit fault or unexpected withdrawal of system components. For safe operation of the power system, the following constraints should be satisfied:

Load constraint. For a system containing n nodes, the following power balance equations should be satisfied, that is, the load constraints:

(1.7)

where θi and θj are the phase angles of voltages at node i and node j, respectively, Ui and Uj are the amplitudes of voltages at node i and node j, Pi and Qiare the active and reactive power injections to node i, and Gij and Bij are corresponding elements in the node admittance matrix.

Operation constraint. The node voltage amplitude U, phase angle difference θ, branch power flow S, and generator power P and Q should be within certain ranges:

(1.8)

where the symbols in the upper right corner, l, u, and m, represent the lower limit, upper limit, and maximum value respectively.

The operation constraints are inequalities, which could be integrated into

(1.9)

where U represents the column vector of state variables.

1.2.2 Stability of Power System

The modern power system is a large and complex dynamic system, the basic requirement of which is security and stability. The high‐dimensional characteristics of models, the uncertainty of system operation mode, the strong nonlinearity of components and the randomness of disturbance all make the mechanism of the power system stability very complicated. With the interconnection of large‐scale power grids, the wide application of flexible AC transmission technology such as HVDC and FACTS, and the gradual increase of renewable energy integration, the analysis of power system dynamic mechanism, and power system stability analysis and control have become more and more difficult.

Power system stability can be summarized as the capability of a system to maintain at the equilibrium state under given initial conditions or to restore to an allowed equilibrium state after disturbance occurs. Through classification and definition, a general understanding of power system stability can be gained, including the characteristics of different types of stability, the causes, and the relationship between them. In the 1960s and before, it was customary to divide power system stability into static stability and dynamic stability. In 1981, the Institute of Electrical and Electronic Engineers (IEEE) proposed a new classification and definition of power system stability at the winter session of the IEEE power engineering seminar (PES) [2–5]:

Static stability/small disturbance stability. For a certain steady‐state operation state, if the system is static‐stable, then when a small disturbance occurs the system will be restored to an operation state the same or close to the predisturbance operation state.

Transient stability/large disturbance stability. For a certain steady‐state operation state and a certain disturbance, if the system is transient stable, then when such disturbance occurs, the system could be restored to an acceptable steady‐state operation state.

In August 2004, IEEE published the latest definition and classification of power system stability formulated by the CIGRE 38th Committee and the IEEE Dynamic Behavior Committee joint group. In the new classification method, power system stability is divided into three different forms of stability – power angle stability, voltage stability, and frequency stability, according to the reflection of power system instability characteristics in the three operation variables. Each form of stability is then divided into small disturbance stability and large disturbance stability. The connection between short‐term stability/long‐term stability and the above forms of stability is established. The classification of power system stability is shown in Figure 1.1 [6,7].

Flow chart of the classification of power system stability by IEEE/CIGRE starting from angle stability, to frequency stability, to voltage stability, to short-term stability, and to long-term stability.

Figure 1.1 Classification of power system stability by IEEE/CIGRE.

According to the size of disturbance, the physical properties that lead to instability mode, flow, and time span, etc. IEEE/CIGRE divides power system stability into power angle stability, frequency stability and voltage stability:

Power angle stability. This refers to the capability of synchronous generators in an interconnected system to maintain synchronous operation after disturbance occurs. It depends on the ability of the electromagnetic torque and mechanical torque of each synchronous generator to maintain/restore balance.

Small disturbance power angle stability is the capability of a power system to maintain synchronous operation under small disturbances, which is determined by the initial operating state of the system. Small disturbance problems usually have to do with lack of oscillation damping. Local problems usually involve rotor angle oscillation between certain generator and other parts of the system. Global problems are caused by the interaction between large generator clusters, which involve oscillation between the generator cluster in one region and the generator cluster in another region; thus they have complex characteristics obviously different from those of local oscillation.

Large disturbance power angle stability or transient stability usually refers to the capability of a power system to maintain synchronous operation under severe disturbances (such as a transmission line short‐circuit fault), which depends on the initial state of the system and the severity of the disturbance. Power system instability is usually caused by a lack of synchronous torque, which leads to the formation of nonperiodic angle separation and is reflected in first swing instability.

Voltage Stability. This refers to the capability of a power system to maintain the static voltage of all buses after disturbance occurs in a given initial state. It depends on the ability of the power system to maintain/restore the balance between system load demand and load supply. Voltage instability is reflected in the continuous decline or rise of the voltages of some buses, and the consequence may be losing the load of a region, or even a power outage due to cascading failure caused by protection tripping.

Voltage stability can also be divided into large disturbance voltage stability and small disturbance voltage stability, which describe the capability of a power system to maintain the static voltage under large disturbances (such as system fault or loss of generator or line) and small disturbances (such as slight variations of load), respectively. The forms of voltage stability are affected by the interaction between system and load characteristics, discrete and continuous control, and protection.

Frequency stability. This refers to the capability of a system to maintain the frequency within the allowed limit by adjusting the output of the system hot spares or automatically removing part of the load when serious disturbances (such as generator tripping, system splitting, loss of a large load, etc.) occur and result in active power imbalance. Frequency instability is reflected in the tripping of protection devices of the generator or load due to continuous declining or swing of frequency.

At the same time, based on long‐time design, operation, and research experience, power system personnel in China proposed a definition and classification of power system stability suitable for the actual power system in China, as shown in Figure 1.2.

Flow chart of the classification of power system stability by industry standard DL755‐2001 starting from angle stability, to frequency stability, to voltage stability, and to short and long-term stability.

Figure 1.2 Classification of power system stability by industry standard DL755‐2001.

The overall framework and main concept of two definition and classification methods are basically the same. A comparison between the two methods is shown in Table 1.1. The main difference is as follows. For power angle stability, in addition to the three short‐term stability processes IEEE/CIGRE proposes, that is, nonperiodic instability, periodic instability, and transient instability, DL755‐2001 gives the definition of large disturbance dynamic stability, which refers to the capability of a power system to maintain relatively long‐term power angle stability under the effects of slow automatic regulation and control devices when a large disturbance occurs. For voltage stability, IEEE/CIGRE considers that the small disturbance voltage stability includes a short‐term process and a long‐term process, but DL755‐2001 considers that a small disturbance voltage stability mainly refers to static voltage stability and does not include a long‐term process such as a chain reaction.

Table 1.1 Comparison between two stability classification standards.

1.3 Three Defense Lines in the Power System

1.3.1 Classification of Disturbance in the Power System

Power system security and stability guidelines DL 755‐2001 classifies large disturbances into three categories according to the severity degree [8], and puts forward corresponding security and stability requirements:

Category I – single‐element fault disturbance

Any line single‐phase instantaneous grounding fault with successful reclosing.

Any line single‐phase permanent fault with unsuccessful reclosing or nonfault three‐phase disconnection without reclosing in double‐circuit or multiple‐circuit lines or loop network of the same voltage level.

Any line three‐phase fault and disconnected without reclosing in double‐circuit or multiple‐circuit lines or loop network of the same voltage level.

Any generator tripping or loss of excitation.

Any transformer in the receiving system fault and out of service.

Abrupt change of any large load.

Any AC tie line fault or nonfault disconnection without reclosing.

DC transmission line unipolar fault.

Category II – severe single‐element fault disturbance

Single‐circuit line single‐phase permanent fault with unsuccessful reclosing or nonfault three‐phase disconnection without reclosing.

Single‐phase grounding fault with unsuccessful reclosing occurring simultaneously on two different‐name phases of double‐circuit lines on the same tower and double‐circuit lines three‐phase tripped off.

DC transmission line bipolar fault.

Any bus fault.

Category III – multiple severe fault disturbances

Switch refusing to operate in the case of a fault.

Relay protection/automatic device maloperation or refusing to operate in the case of a fault.

Failure of an automatic regulation device.

Multiple faults.

Loss of a large‐capacity power plant.

Other accidental factors.

1.3.2 Power System Operation State

A power system is a nonlinear dynamic system with structure, parameter, and dynamic uncertainties. The operating conditions of a power system are generally described with three groups of equations: one group of differential equations describing the dynamic behavior of the power system components and control devices, and the other two groups of algebraic equations forming the equality and inequality constraints of power system operation, respectively.

The equality constraints represent the balance between system total power generation and total load capacity; the inequality constraints represent certain system variables, such as voltage and current, that must not exceed the maximum limits of physical devices. According to whether the constraints are satisfied, system operation can be divided into five states, as shown in Figure 1.3 [9].

Cycle diagram illustrating the conversion relationship between the power system operation states starting from normal state, to alert state, to emergency state, to extreme emergency state, to recovery state.

Figure 1.3 Conversion relationship between power system operation states.

The power system operation state can be divided into a normal state and an abnormal state. The normal state can be further divided into the safety state and the alert state and the abnormal state can be further divided into the emergency state and the restoration state. The operation of a power system includes all these states and the mutual transfer between them.

The safety state refers to when system frequency, node voltages, and the load of each component are all within the allowed ranges, and a general small disturbance does not cause the system to break from the normal operation state.

The alert state refers to when the overall system is still within the safe operation range, but the operating parameters of certain components or regions are close to the threshold values; thus any new disturbance will cause the system to enter the emergency state. For a power system in the alert state, preventive control measures should be taken for the system to remain in the safe state.

The emergency state refers to when a disturbance occurs in the power system in the normal operation state (including load fluctuation and various kinds of fault), and the power balance between the power source and load is destroyed, causing system frequency and node voltage to deviate more than the allowed values, or the load of components to exceed the limit of safe operation. For a power system in the emergency state, all kinds of corrective and stability control measures should be taken to restore the system to the normal operation state.

The restoration state refers to when a power system is split into a number of local systems and part of the systems cannot ensure normal power supply to users, although the other systems could maintain the normal operation state; or when the system is not split but cannot ensure normal power supply to all users and part of the load has been cut off. If a power system in the emergency state cannot be restored to the normal operation state by taking corrective and stability control measures, emergency control measures should be taken to minimize the impact on users. Then restoration control measures should be taken according to the need to restore the system to its normal operation state.

1.3.3 Three Defense Lines in Power System Stability Control

As a result of long‐term operation experience and lessons from power blackout accidents at home and abroad, the power system in China has produced a set of principles and experiences for the configuration of system security defense measures. It is clearly pointed out in Power system security and stability guidelines DL 755‐2001 and Power system security and stability control technology guidelines DL/T 723‐2000 that the power system should appropriately set three defense lines according to the severity and probability of different faults to cope with corresponding faults. The technical and structural characteristics of each defense line should adapt to its function, as shown in Figure 1.4.

Three defense lines (defense lines I, II, and III) in power system safety and stability control labeled system states, status feature, and defense.

Figure 1.4 Three defense lines in power system safety and stability control.

In Power system security and stability guidelines DL 755‐2001, the security and stability standard for a power system to enable it to bear large disturbances is established, which divides the capability of a power system to bear large disturbances into three levels [10]:

Security and stability standard level I. When large disturbance category I occurs in a power system in the normal operation mode, protection, switches, and reclosing all operate correctly. The power system should maintain stable operation and a normal power supply without taking stability control measures. Other components should remain within the accident overload capacity and no cascading tripping should occur.

Security and stability standard level II. When large disturbance category II occurs in a power system in the normal operation mode, protection, switches, and reclosing all operate correctly. The power system should maintain stable operation, and if necessary stability control measures such as generator tripping and load shedding could be taken.

Security and stability standard level III. When large disturbance category III occurs in a power system in the normal operation mode and system stability is destroyed, measures must be taken to prevent the system from collapsing, to avoid long‐time blackout and disastrous power outage for most important users (including the station service power supply), and to minimize the loss of load. The power system should be restored to the normal operation state as soon as possible.

Correspondingly, in order to ensure the safe and stable operation of a power system, a complete secondary defense system should also include three defense lines:

Defense line I. Defense line I ensures that the power system could maintain normal operation and meet the security requirements under large disturbance category I. The measures taken include a primary system facility and a secondary protection device. The primary system should establish a reasonable grid structure, be equipped with a complete power facility, and arrange reasonable operation modes. The secondary system should be equipped with relay protection devices with good performance that could isolate faults immediately and restrict the development of faults.

Power system security and stability control defense line I is to clear fault components immediately and prevent faults from expanding. It mainly consists of relay protection devices with good