Power System State Estimation and Forecasting

This chapter presents initially historical references to the electric industry and constructs a connection with power system state estimation (SE). Power network operating modes and their associated controls are characterized. Also, the chapter delineates the main aspects of SE, including the origins of the estimation theory remoting to Gauss’s thoughts, the genesis of SE, the characterization of the power system state of interest, the purposes/advantages, and the modularity of SE (network configuration, measuring system observation capability evaluation, state forecasting, state filtering, and input data validation). The computational implementation of a friendly educational tool for SE named State Estimation Educational (SEE) tool—a free, open-source Web application available at https://​seet.​mbrown.​com.​br/​—is also discussed. This chapter ends with a description of the content of the book’s chapters, which align with SE modules.

This chapter starts with an analogy between a frequent medical practice procedure (physical examination) and the state estimation process; it is made with pedagogical motivation to facilitate the understanding of conceptual/methodological aspects explored ahead. The chapter gives the fundamentals of least squares estimation and the different forms (linear, nonlinear, coupled, decoupled, fast decoupled) of the weighted least squares (WLS) power system static state estimation (SSE). Also, mathematical approaches different from the classical industrial standard WLS are addressed. The uncertainty propagation in the WLS process is commented on. Illustrative examples percolate through the chapter. In the end, advanced topics are pointed out, and problems are proposed. A list of references completes the chapter as a guide to further reading.

This chapter presents the rudiments of the schemes devoted to processing the network statuses of circuit breakers/switches, which is necessary for describing the grid connectivity and transforming the bus-section/circuit breaker representation into the bus-branch model required for power system state estimation (SE) and other network analysis functions. Substation bus configurations (radial, two buses, breaker-and-a-half, and ring bus) are addressed. Also, the problem of detecting/identifying network configuration errors—categorized as reported network changes that did not occur (type A) or appeared network changes are unreported (type B)—is addressed here. These errors involve the inclusion/exclusion of network elements, depending on whether they relate to false closed/open status information. The influence of network configuration errors in the SE process is indicated. Advanced topics, a list of problems, and references close the chapter.

This chapter provides the elements necessary to characterize the observation capability of measuring systems designed to serve the power system state estimation (SE) function. Two main approaches to the observability analysis problem, segmented into numerical and topological, are addressed. The numerical approach involves matrix manipulation, performing straightforward floating-point arithmetic operations with routines already present in estimation process calculations. On the other hand, the topological methods are based on the graph theory. They are adequate from the conceptual perspective since the observability problem is considered structural natured, i.e., dependent on the grid topology and the type/placement of measurements. Illustrative examples of the numerical and topological approaches are included. The chapter contains a section on advanced topics and ends with proposed problems. A list of references is included.

This chapter concerns the evaluation of the strength of a measuring system known as criticality analysis, whose objective is to identify the elements minimally critical to network observability. The term critical conveys the idea of decisive importance, the belief of what things are essential, crucial, and indispensable for a given purpose (observability), supported by a careful judgment on the severity of consequences for power system state estimation (SE). Criticality analysis identifies which measurements taken individually or forming groups that participate in SE are indispensable in case their unavailability makes the grid unobservable. Data unavailability may happen by accident, programmed maintenance, cyberattack, or chance. Criticality analysis is vital since a SE crash can lead system operators to make decisions based on incomplete or incorrect information, leading to suboptimal or dangerous outcomes. The chapter includes illustrative examples of criticality analysis considering the measurements as a primary element of the study and measuring units (i.e., the aggregate of devices deployed at substations). Advanced topics and proposed problems, followed by a list of references, close the chapter.

This chapter is devoted to evincing the negative impact that corrupted measurements can produce in power system state estimation (SE) and how to deal with it. Statistical tests performed on the weighted least squares (WLS) objective function and estimation residuals are presented. Maximum likelihood-type estimators, those capable of resisting the influence of outliers, are also addressed. The optimized measurement placement problem regarding both observability/criticality analysis is formulated. The simulation of gross error measurements and how to handle them are illustrated in several examples. Advanced topics indicate that forecasting-aided state estimation (FASE) and phasor-aided state estimation (PHASE) approaches are pointed out to facilitate BD processing. Also, the SE vulnerability to cyberattacks is commented on. Problems are proposed at the end of the chapter.

This chapter deals with the problem of integrating forecasting techniques with power system state estimation (SE) algorithms. Forecasting-aided state estimation (FASE) has been proposed as an attractive alternative to overcome some issues in the traditional SE. Different strategies for creating a forecasting step in the SE process are devised. Modeling aspects regarding the establishment of a discrete-time state transition model are addressed. Concerning data validation, an innovation analysis is advocated. An example elucidates its application. The innovation is determined by the difference between a measurement just received and its forecasted value. The chapter can be seen as a guide to using a predictive database to enhance the estimation process, regarding, for instance, observability and extended WLS SE filtering. Throughout the chapter, main achievements of the FASE approach are addressed. The chapter ends with a section on advanced topics followed by proposed problems and a list of references.

This chapter explores the idea that synchrophasors contribute to increasing data redundancy for SE, making their incorporation into existing SCADA-based estimators indisputable. SCADA (supervisory control and data acquisition) measurements are complemented by synchrophasors, i.e., bus voltages (magnitudes and phase angles) and branch currents (real and imaginary parts), available employing PMUs, sited at designated buses in the network. Two schemes are presented: (a) combine conventional with phasor measurements and process them by adopting a single (hybrid) estimator, and (b) take conventional and phasor measurements as individual sets and process them separately using two estimators. A data validation/diagnosis scheme is based on a residual analysis, such as the innovation analysis performed in forecasting-aided state estimators. An illustrative example showing the processing of spurious SCADA measurements is presented. Advanced topics, proposed problems, and references are at the end of the chapter.

This chapter describes algorithms for network parameter estimation and detection/identification of possible errors. The concepts of irrelevant branches and barely relevant branches are adopted. The parameter error processing performed by methods that explore these concepts is based on thoroughly chosen recorded measurement scans in which redundancy is sufficiently high. Considered a matter of great significance for improving the reliability of SE results, this functionality can also be a way of cleaning the network parameter database shared by all EMS applications. A didactic example of the parameter estimation problem using the irrelevant branch method is presented. Advanced topics on the subject are pointed out. Proposed problems are included, and a list of references is provided.

This chapter expresses the author’s viewpoints on SE, backed up by many years of research. The difficulties of implementing power system state estimation (SE) are discussed. SE’s characteristics, standing as the pinnacle of complexity and unprecedented challenges, unmatched by any other applications of estimation theory created, are gathered. Aspects such as residual analysis, detectability and identifiability of bad data, criticality analysis, forecasting-aided state estimation, and accessibility of synchrophasors to enhance redundancy are issues addressed. A list of references finishes the chapter.