Cyber-Physical Power Systems State Estimation

By Arturo Bretas, Newton Bretas, Joao B.A. London Jr and Breno Carvalho

Cyber-Physical Power System State Estimation updates classic state estimation tools to enable real-time operations and optimize reliability in modern electric power systems. The work introduces and contextualizes the core concepts and classic approaches to state estimation modeling. It builds on these classic approaches with a suite of data-driven models and non-synchronized measurement tools to reflect current measurement trends required by increasingly more sophisticated grids. Chapters outline core definitions, concepts and the network analysis procedures involved in the real-time operation of EPS.

Specific sections introduce power flow problem in EPS, highlighting network component modeling and power flow equations for state estimation before addressing quasi static state estimation in electrical power systems using Weighted Least Squares (WLS) classical and alternatives formulations. Particularities of the state estimation process in distribution systems are also considered. Finally, the work goes on to address observability analysis, measurement redundancy and the processing of gross errors through the analysis of WLS static state estimator residuals.

• Develops advanced approaches to smart grid real-time monitoring through quasi-static model state estimation and non-synchronized measurements system models
• Presents a novel, extended optimization, physics-based model which identifies and corrects for measurement error presently egregiously discounted in classic models
• Demonstrates how to embed cyber-physical security into smart grids for real-time monitoring
• Introduces new approaches to calculate power flow in distribution systems and for estimating distribution system states
• Incorporates machine-learning based approaches to complement the state estimation process, including pattern recognition-based solutions, principal component analysis and support vector machines

• Language: English
• Publisher: Elsevier Science
• Release date: May 14, 2021
• ISBN: 9780323903226

Arturo Bretas

Arturo Bretas received the B.Sc. and M.Sc. degrees in Electrical Engineering from the University of Sao Paulo in 1995 and 1998, respectively, and the Ph.D. degree from Virginia Tech in 2001. He is currently a Full Professor with the Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL, USA. His research interests include cyber-physical systems security, smart grids, state estimation, and reliability optimization.

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Chapter 1: State estimation in electric power systems

Abstract

This chapter aims to provide a panoramic view of this book, highlighting the structure and motivation that led the authors to accomplish it by organizing the following sections:

• Section 1.1 Introduction: Briefly describes the importance of the state estimation process for real-time operation of Electric Power Systems (EPSs), presenting concepts and the general nature of this process, contextualizing its development and the need for evolution to keep in line with the new trends and current technologies.

• Section 1.2 Book Organization: Describes its structure.

Keywords

Power systems; Real-time monitoring; State estimation process

This chapter aims to provide an overview of this book, highlighting the structure and motivation that led the authors to accomplish it by organizing the following sections:

•Section 1.1Introduction: Briefly describes the value of the state estimation process for real-time operation of Electric Power Systems (EPSs), presenting concepts and the general nature of this process, contextualizing its development and the need for evolution to keep in line with the new trends and current technologies.

•Section 1.2Book Organization: Describes its structure.

1.1: Introduction

1.1.1: Historical context

At the end of the 1960s, significant changes were made in the philosophy of the operation of EPSs. These were due to the blackouts in the East Coast of the United States, which showed the relevance of issues related to the security of the operation of EPSs. At the same time, the combination of two factors, the difficulty to operate EPSs (increasingly interconnected) and technological advances in computing and telecommunication, allowed the development of functions related to security monitoring and analysis, giving rise to the so-called Security Control or simply Real-Time Operation (Wu et al., 2005).

The initial step for real-time operation is to estimate the current state of the EPS and then determine the appropriate control actions. Once the topology and the parameters of the electrical network have been known, the operational state of an EPS, operating in a sinusoidal steady state, becomes a function of the complex voltages in its buses, since from them it is possible to determine all the other electric quantities of interest (currents and power flows). Thus in this context, the complex voltages in the EPS buses are simply called EPS state variables.

Due to the large size of the EPSs, their state variables are determined by means of telemetry systems, i.e., remote measurements, which are subject to a series of noises due to, for example, the different measurement accuracy of the transformers of the measuring instruments, the secondary circuit of these transformers (wiring and load), and the various measuring devices (transducers, converters, etc.) (Abur and Expósito, 2004). Thus in order to obtain more reliable values for the state variables as required for real-time operation, the measurements must be filtered. In order to perform this task, the control centers have a set of computer programs that are responsible for executing the so-called power system state estimation (PSSE) process.

From the works published by Schweppe et al. in the late 1960s and early 1970s (Schweppe and Wildes, 1970; Schweppe and Rom, 1970; Schweppe, 1970; Schweppe and Handschin, 1974), which outlined various concepts and the general nature of the problem, PSSE became the subject of numerous research. In works such as those published in Coutto Filho et al. (1990); Monticelli (1999); Abur and Expósito (2004), a vast bibliographical revision starting from 1968 is presented.

Currently, the PSSE process has already been consolidated as a basic procedure necessary for real-time operation of EPSs. However, due to the development of new equipment and electrical devices associated with the so-called smart grids (advanced measurement structures, intelligent meters, synchronized phasor measurements, etc.), the paradigms of the operation of EPSs expand and require the PSSE process to evolve to keep in line with the new trends.

In view of the previous, in order to work with the operation of EPSs, understanding the problems and suggesting solutions, the professionals of the area must have the theoretical background necessary to understand the functioning of the entire PSSE process. In this sense, it is important to highlight that, although several scientific articles have dealt specifically with several problems related to the PSSE process, relatively few published books cover all the stages involved in this process.

This was the main motivation for writing this book, which aims to present, in a didactic way and with the depth necessary for the training and specialization of electrical engineers, all stages of the PSSE process, based on several scientific articles published during the last decades dealing with specific issues in this process.

1.1.2: The process of PSSE

The first stage of the conventional PSSE process consists in obtaining the system topology with the correct location of the meters available in the so-called bus-branch model (which corresponds to the single-line diagram of the system), which is performed from logical measurements, obtained continuously consisting of status of switches and circuit breakers, as well as information about the type and location of the meters installed in the system (information modeled at the bus section level, that is, in the physical representation of the elements of the system).

Once the system topology is obtained in the bus-branch model, the second step of the process is to verify if it is possible, through the available set of analog measurementsa, to determine all system state variables. If so, the system is said to be observable. Otherwise, the lack of measurements can be met by pseudo-measurementsb, through which the entire system will become observable.

Since the system is observable, from the topology of the system and its parametersc stored in the database of the control centers, as well as the set of analog measurements available, the state estimation itself will be carried out in Step 3 of the process.

It is worth mentioning that the state estimator used in Step 3 can be dynamic or static. In the case of the dynamic estimatord, the variations of the quantities of interest, relative to the variable time, are considered in the network modeling. On the other hand, in the static estimator, the network model used is static, translating into a photograph of the system at a fixed time-instant. Thus the mathematical behavior of the electric system is translated using only nonlinear algebraic equations, without the use of differential equations. This book will focus mainly on the static state estimator, since it is the most used in current real-life applications. However, Chapter 8 will be dedicated to dynamic state estimation.

Because the analog measurements used in the PSSE process are not exact, the estimation of the unknown state variables will be also inexact. It can be said then that the PSSE process consists of finding the best estimate of the unknown state variables. For this, of the many existing statistical criteria, the one that has been used the most in the PSSE process is the Weighted Least Squares (WLS), which was originally formulated in Schweppe and Wildes (1970).

When the errors in the measurements are Gaussian, the classical WLS Estimator works very well, failing, however, in the occurrence of one or more gross errors (GEse). Among the causes of GEs, we can highlight analog-to-digital conversion errors and errors in the telemetering communication channels, or even cyber-attacks (Liu et al., 2009).

In the case of single GE, that is, when only one measurement has GE, or multiple noninteracting GEsf, the classical WLS estimator associated with techniques for processing GEs from the residual analysis perform well. However, it may fail in the following situations (Abur and Expósito, 2004): GEs associated to measurements with low redundancyg; multiple interactive GEs; and GEs in measurements that are highly influential, that is, they attract the convergence of the state estimation process, traditionally called leverage point measurements (Monticelli, 2000). One should observe that although some works on such refer to error, they want to say residual, because the classical WLS works with residual only and not with error, which are different quantities (Bretas et al., 2013).

It should be noted that due to the previously cited problems, statistically more robust state estimators were applied in EPS, such as the Weighted Least Absolute Value (WLAV) method (Irving et al., 1978; Kotiuga and Vidyasagar, 1982). The WLAV estimator was shown to be more robust than the WLS associated with residual analysis techniques in the presence of single and multiple GEs. However, the WLAV also fails in the occurrence of GE in one or more measures of leverage point (Falcão and Assis, 1988). In order to overcome the problems caused by the measurements classified as leverage points with GEs, the estimator based on the Weighted Least Median of Squares (WLMS) method was proposed for EPS (Mili et al., 1991). This estimator was the first proposed statistically robust estimator that can identify GEs in measurements classified as points of leverage. However, such an estimator requires a combinatorial search, making it impracticable for real-time application in large EPS (Falcão and Arias, 1994; Monticelli, 2000).

Due to the practical unfeasibility of the WLMS estimator, and due to the simplicity of the formulation and the ease of computer implementation of the WLS estimator, associated to the analysis of the residuals of the measurements, the latter is the estimator that is most used in real-life applications and most studied in academia.

After the considerations in the previous paragraphs, in the fourth stage of the PSSE process, GEs are processed, that is, the procedure for detecting, identifying, and eliminating GE-carrying measurements (or the effect of these measurements). If any measurement is detected with GE, after processing of Step 4, Step 3 is performed again to obtain state variables without the effect of the erroneous measurements. The PSSE process ends when, after an estimate, no measurement is detected with GE. One should observe again that great majority of previously presented and implemented real-life solutions are using the residuals to detect GEs.

The classical formulation of the PSSE process is based on the assumptions that the network configuration (obtained in Step 1) and the parameters used in the models representing the elements of the electrical network are correct. However, these assumptions are often not true. Thus in addition to the GEs, the PSSE process is still subject to two other types of errors. These are error caused by erroneous information of some parameter of the electrical network, known as parameter error (PE), and error due to erroneous information about the status (open or closed) of a switch and/or circuit breaker in Step 1, known as topological error (TE). The effect of TEs and PEs on the PSSE process is drastic, usually intolerable, and several researches have been developed to address these errors.

Although the generation, transmission, and distribution of electric energy usually occur through three-phase systems, in the classical formulation of the PSSE process it is considered the hypothesis of a balanced system. That is, it is considered that the loads are balanced, and the networks are symmetrical, where the electric quantities in the phases have the same magnitude, but with a phase angle difference of 120° between them. Thus most of the studies developed in the context of PSSE make use of the model per-phase, or single-phase (positive sequence model), suitable for most transmission systems, which is the focus of this book.

It should also be pointed out that in the classical formulation of the PSSE process only the unsynchronized logical and analog measurements provided by the Supervisory Control and Data Acquisition (SCADA) system are considered.

1.2: Organization of the book

In order to ease the understanding of all stages of the PSSE process, as well as some problems related to this process and the proposed solutions already presented, this book is divided into nine chapters, where the Introduction corresponds to the first one. In order to make the text more clear, page footers with explanatory notes will be used in all chapters, defining or explaining the meaning of terminologies common to the area to which they refer to.

The chapters were elaborated following a logical sequence. In the meantime, they were organized to allow independent reading, according to the interest of the reader.

Chapter 2 of this book presents concepts, definitions, and procedures of network analysis involved in the real-time operation of EPSs. The chapter describes all stages of the PSSE process, especially Step 1, since the others will be dealt with in detail in the next chapters of this book. The chapter ends discussing the effect of TEs and PEs and the inclusion of Synchronized Phasor Measurements (SPMs) in the PSSE process. Finally, some practical problems are proposed.

Chapter 3 reviews the basic formulation of the power flow problem in EPS. This chapter also deals with the modeling of the electrical components of the network and the power flow equations that are also used in the formulation of the state estimation process. Finally, some theoretical and real-life application problems are proposed.

Chapter 4 deals with the third stage of the conventional PSSE process, that is, the state estimation itself. After the presentation of basic definitions, the formulations of the WLS state estimator are presented in the coupled, decoupled, and linear versions. Next, it is introduced the hybrid WLS estimator, which is the WLS estimator that allows the simultaneous processing of SCADA measurements and SPMs, as well as estimators statistically more robust than the WLS estimator. At the end of this chapter are some problems to assist in understanding the operation of the WLS Estimator.

Chapter 5 focuses on the qualitative characteristics of measurement sets in the context of static state estimation in EPSs, which refer to the analyses of observability and redundancy of measurements. Concepts, definitions, and some methods already developed to perform these analyses are presented in a detailed way considering the single-phase modeling of the power grid, the existence of only SCADA measurements. This is because most of the estimators and methods developed for observability and redundancy analysis work on these considerations. However, the methods that will be presented in this chapter for analysis of observability and redundancy of measurements can be extended to consider the three-phase modeling of the network as well as the existence of SCADA measurements and SPM, as will be discussed in the last sections of this chapter. At the end of this chapter are some problems to assist in understanding aspects related to the qualitative characteristics of measurement sets in the context of static state estimation in EPSs.

Chapter 6 covers the fourth step of the conventional PSSE process, the GE processing step, which is performed after processing the first three steps of the PSSE process, as presented in Chapter 2. This chapter presents definitions and the necessary theoretical basis for the understanding of the classical methodologies developed for GE processing from the WLS estimator residuals analysis. After presenting these methodologies, the chapter also provides some examples and exercises to enable a better understanding for GEs detection, identification, and elimination from the WLS estimator residuals analysis.

Chapter 7 describes the fundamentals of the innovation methodology, as well as its application in the processing of errors in the PSSE process. The chapter also provides some problems to enable a better understanding of the information presented.

Chapter 8 addresses the dynamic state estimation (DSE) problem, based on the Kalman filter (KF) formulation. The chapter presents the asymmetry index for anomaly detection and identification (in the context of DSE, suddenly large load changes as well as measurement GEs are named as anomaly). The chapter presents further several simulation results validating the presented anomaly detection model.

Chapter 9 presents the core ideas of data-driven state estimator solutions. Linear regression models are introduced, as well as machine-learning approaches used to estimate the gross errors on measurements. Hybrid data-driven physics-model-based solutions are further discussed. Problems concerning real-life applications are introduced.

The book also has two appendices, one with the definitions of statistical robustness and breakdown point and the other with answers to the exercises proposed in the book chapters.

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