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Apart from this introductory chapter, there are 13 chapters devoted to state of the art in this vibrant area.

In Chapter 2, Eduardo Caro and Araceli Hernández discuss a mathematical programming approach to state estimation in power systems. They focus on WLS, least absolute value (LAV), quadratic constant, and quadratic linear criterions, among others. Additionally, the statistical correlation among measurements is analyzed and included, enhancing both estimation accuracy and the bad data identification capabilities. All procedures are illustrated by simple but insightful examples.

From a computational perspective, quadratic constant and LAV techniques perform faster than the conventional WLS estimator, saving up to 75% CPU time (compared with the WLS method directly solved as an optimization problem). On the other hand, mathematical programming formulation of some estimators (such as least median of squares and least trimmed of squares approaches) encounter non‐convexities and a significant number of binary variables, resulting in higher computational burdens.

If the measurement set is corrupted with errors that the χ² test cannot detect, WLS estimation results quality deteriorates, providing the worst estimation quality (if LMS and LTS approaches are not considered). It is observed that QL and QC techniques outperform the rest of estimators, followed by LMR procedure. As expected, the authors report that their computational experiments reported in this chapter suggest that alternative estimators are potential substitutes for traditional WLS method. The state of the art of current nonlinear optimization solvers and recent advances in computational equipment allows using robust estimators in real electric energy systems.

Chapter 3 draws on two bodies of knowledge – electric power engineering and network (graph) theory – to develop and apply a new failure network, an application of line outage distribution factors. Here Hyde M. Merrill and James W. Feltes present an approach to measure how susceptible is an electric power system to cascading outages (stress) that lead to blackouts. The problem is defined in the context of a new perspective of the electric power system. A failure network is defined, based on well‐known line outage distribution factors. Following the practice of network (graph) theory, the structure and properties of this network are analyzed with metrics that measure stress (susceptibility to cascading outages). The metrics can be applied in real‐time operations or in planning to identify vulnerability to cascading. Three studies are described, two on very large North American systems, the other on the smaller national system of Peru. New insights are presented, and a new class of power system options is identified, to reduce susceptibility to cascading rather than to increase transfer capability.

The ideas have application in planning as well as in real time. For operations, it depends, as Schweppe expected, on data from a state estimator. But the additional computations go far beyond simply calculating flows and injections using Ohm's and Kirchhoff's laws.

The authors of Chapter 4, “Model‐Based Anomaly Detection for Power System State Estimation”, Aditya Ashok, Manimaran Govindarasu, and Venkataramana Ajjarapu, recognize that state estimators depend on SCADA measurements from the various remote substations, which introduces several vulnerabilities due to malicious cyberattacks. The security and resiliency of the power system state estimator are important since its output is used by several other network applications in the EMS such as real‐time CA, power markets, etc. While SE is designed to detect and recover from some degree of bad data injected due to measurement errors, or even measurement loss due to telemetry issues, they could be impacted by malicious cyberattacks causing loss of observability, operational, and market impacts. A holistic approach to attack‐resilient SE should involve a combination of attack‐resilient planning approaches to improve attack prevention capabilities in conjunction with attack‐resilient anomaly detection and robust SE formulations to improve attack detection and mitigation resulting in a defense‐in‐depth architecture.

This chapter starts with a broad survey of relevant state‐of‐the‐art literature that addresses the vulnerability of SE to stealthy false data injection attacks and topology‐based attacks. This is followed by a review of some offline attack prevention approaches to enhance the redundancy of SE against those stealthy cyberattacks and online techniques for attack detection and mitigation that address anomaly detection, bad data detection, and other formulations of SE. A model‐based anomaly detection approach uses short‐term load forecasts, generation schedules, and available secure PMU data to detect anomalies due to stealthy cyberattacks. This approach is complementary to traditional bad data detection methods in SE to detect stealthy cyberattacks. This chapter offers some insights into the performance of the proposed anomaly detection approach using a case study on the IEEE 14‐bus system. Finally, this chapter provides a summary of the contributions and promising directions for emerging research topics that show promise for the future including PMU‐based linear state estimator, integrated hybrid SE formulations with PMU data and SCADA, robust and dynamic SE formulations, and MTD‐based approaches for SE that leverage redundancy and randomization of measurements.

A. P. Sakis Meliopoulos, Yu Liu, Sungyun Choi, and George J. Cokkinides propose in Chapter 5 a scheme for real‐time operation and protection of microgrids based on distributed dynamic state estimation (DDSE). First, the DDSE can be used for setting‐less component protection that applies dynamic state estimation on a component under protection with real‐time measurements and dynamic models of the component. Based on the results, the well‐known χ² test yields the confidence level that quantifies the goodness of fit of models to measurements, indicating the health status of the component. With this approach, renewable DERs in microgrids can be protected on an autonomous and adaptive basis. Meanwhile, the estimated state variables of each component are converted to phasor data with time tags and then collected to the DERMS of microgrids. These aggregated phasor data that are once filtered by the DDSE are input to the static state estimator in the DERMS along with unfiltered data sent from conventional meters, relays, and digital fault recorders, ultimately generating real‐time operating conditions of microgrids. This chapter also provides numerical simulations to compare the DDSE‐based approach with conventional centralized state estimation in terms of data accuracy and computational speeds.

Any component in microgrids can be protected by the proposed setting‐less protection method, capable of tracking full dynamic characteristics of a device under protection. This method can provide adaptive protection in microgrids, where unpredictable fault conditions or abnormal states may arise. It is important to point out that the setting‐less protection is fundamentally based on the physical characteristics, thus requiring no additional settings for grid conditions. The authors suggest that the approach also facilitates real‐time operation by reducing the state estimation computation time as well as by enhancing the accuracy of estimation results. In this sense, the DDSE can be of great importance to the real‐time operation and management of microgrids in which the penetration of renewable DERs has recently increased.

In Chapter 6, “Distributed Robust Power System State Estimation” by Vassilis Kekatos, H. Zhu, G. Wang, and Georgios B. Giannakis discuss some of the recent advances in power system state estimation (PSSE). The Cramer–Rao lower bound (CRLB) on the covariance of any unbiased estimator is first derived for the PSSE setup. Following a review of conventual Gauss–Newton iterations, contemporary PSSE solvers leveraging relaxations to convex programs and successive convex approximations are explored. To overcome the high complexity involved, a scheme named “feasible point pursuit”, relying on successive convex approximations is advocated. A decentralized PSSE paradigm is presented to provide the means for coping with the computationally intensive SDP formulations, which is tailored for the interconnected nature of modern grids, while it can also afford processing PMU data in a timely fashion. Novel bad data processing models and fresh perspectives linking critical measurements to cyberattacks on the state estimator are presented. Motivated by advances in online convex optimization, model‐free, and model‐based state trackers, the authors offer a fresh perspective on state tracking under model‐free and model‐based estimators. With the current focus on low‐ and medium‐voltage distribution grids, solvers for unbalanced and multiphase operating conditions are desirable. Smart meters and synchrophasor data from distribution grids (also known as micro‐PMUs) call for new data processing solutions. Advances in machine learning and statistical signal processing, such as sparse and low‐rank models, missing and incomplete data, tensor decompositions, deep learning, nonconvex and stochastic optimization tools, and (multi)kernel‐based learning to name a few, are currently providing novel paths to grid monitoring tasks while realizing the vision of smarter energy systems.

Mert Korkali in Chapter 7, “Robust Wide‐Area Fault Visibility and Structural Observability in Power Systems with Synchronized Measurement Units,” presents work merging robust state estimation and optimal sensor deployment with the objective to achieve system‐wide fault visibility and structural observability in modern power systems equipped with wide‐area measurement systems (WAMSs). The first part of this chapter introduces a method that enables synchronized measurement‐based fault visibility in large‐scale power systems. The approach uses the traveling waves that propagate throughout the network after fault conditions and requires capturing arrival times of fault‐initiated traveling waves using synchronized sensors so as to localize the fault with the aid of the recorded times of arrival (ToAs) of these waves. The second part of this chapter is devoted to optimization model for the deployment (placement) of PMUs paving the way for complete topological (structural) observability in power systems under various considerations, including PMU channel limits, zero‐injection buses, and a single PMU failure.

In Chapter 8, authors Junbo Zhao, Lamine Mili, and Massimo La Scala recall that in the power system environment, the distribution of the measurement noise is usually unknown and frequently deviates from the assumed Gaussian distribution model, yielding outliers. Under these conditions, the performance of the current state estimators that rely on Gaussian assumption can deteriorate significantly. In addition, the sampling rates of SCADA and PMU measurements are quite different, causing a time skewness problem. Under the title “A Two‐Stage Robust Power System State Estimation Method with Unknown Measurement Noise,” the authors propose a robust state estimation framework to address the unknown non‐Gaussian noise and the measurement time skewness issue. In the framework, the Schweppe‐type Huber generalized maximum‐likelihood (SHGM) estimator is advocated for SCADA measurement‐based robust state estimation. They show that the state estimates provided by the SHGM estimator follow roughly a Gaussian distribution. This effectively allows combining it with the buffered PMU measurements for final state estimation. Robust Mahalanobis distances are proposed to detect outliers and assign appropriate weights to each buffered PMU measurement. Those weights are further utilized by the SHGM estimator to filter out non‐Gaussian PMU measurement noise and help suppress outliers. Extensive simulation results carried out on the IEEE‐30 bus test system demonstrate the effectiveness and robustness of the proposed method.

Chapter 9 by Ibrahim Omar Habiballah and Yuanhai Xia: “Least‐Trimmed‐Absolute‐Value State Estimator” is intended to improve the accuracy of estimation results considering complex situations induced by multiple types of bad data. In addition to conventional state estimators such as WLS and LAV, other robust estimators are used to detect and filter out bad data. This includes, among many, least median squares and least‐trimmed square estimators. The authors introduce an efficient robust estimator known as least‐trimmed‐absolute‐value estimator. The algorithm arises from the two estimators: LAV and LTS and benefits the merits of both. It can detect and eliminate both single and multiple bad data more efficiently. DC estimation is conducted on 6‐bus system and IEEE 14‐bus system first; then these two systems and the IEEE 30‐bus system are used to conduct AC estimation experiments. Various types of bad data are simulated to evaluate the performance of the proposed robust estimator.

A new probabilistic approach to state estimation in distribution networks based on confidence levels is introduced in Chapter 10. Here, Bernd Brinkmann and Michael Negnevitsky state that their proposal uses the confidence that the estimated parameters are within their constraints as a primary output of the estimator. By using the confidence value, it is possible to combine information about the estimated value as well as the accuracy of the estimate into a single number. Their motivation is that the traditional approach to state estimation only provides the estimated values to the network operator without any information about the accuracy of the estimates. This works well in transmission networks where a large number of redundant measurements are generally available. However, due to economic constraints, the number of available real‐time measurements in distribution networks is usually low. This can lead to a significant amount of uncertainty in the state estimation result. This makes it difficult to adapt the traditional state estimation approach to distribution networks.

A probabilistic observability assessment is also presented in this chapter using a similar probabilistic approach. The traditional approach to observability in distribution networks is limited because even if a network is classified as observable, the state estimation result could be completely decoupled from reality. The presented method on the other hand determines if the state of a distribution network can be estimated with a degree of accuracy that is sufficient to evaluate if the true value of the estimated parameters is within their respective constraints.

This approach has been demonstrated in case studies using real 13‐bus and 145‐bus feeders. The results show that even if a large amount of uncertainty is present in the state estimation result, the proposed approach can provide practical information about the network state in a form that is easy to interpret.

The premise of “Advanced Distribution System State Estimation in Multi‐Area Architectures” is that distribution grids are characterized by a very large number of nodes and different voltage levels. Moreover, different portions of the system can be operated by different distribution system operators. In this context, multi‐area approaches can be indispensable key tools to perform DSSE efficiently. Chapter 11 by Marco Pau, Paolo Attilio Pegoraro, Ferdinanda Ponci, and Sara Sulis presents state of the art, challenges, and novel approaches for multi‐area state estimation (MASE) in distribution systems. A new methodology, based on a two‐step procedure, is presented in detail. This procedure is designed to accurately estimate the status of a large‐scale distribution network, relying on a distributed measurement system in a multi‐area framework. Criteria for the sub‐area's division are presented along with the issues, requirements, and challenges of estimation steps. Benefits of the use of synchronized measurements obtained by phasor measurement units (PMUs) in terms of the accuracy and efficiency enhancements in the estimation results are presented and discussed.

Chapter 12 by Ye Guo, Lang Tong, Wenchuan Wu, Hongbin Sun, and Boming Zhang is under the title “Hierarchical Multi‐Area State Estimation” and is motivated by the need for a coordinated state estimator for multi‐area power systems. Of course, the proposed method should provide the same state estimate as a centralized estimator but solved in a distributed manner. In this chapter, the authors review earlier relevant work in the field, including two‐level single‐iteration estimators, inter‐area Gauss–Newton methods and intra‐area Gauss–Newton methods. In particular, the authors focus on recently published work where local system operators communicate their sensitivity functions to the coordinator. These sensitivity functions fully represent local optimal conditions, and consequently, this method has improved rate of convergence.

The application of parallel processing for static/dynamic state estimation is motivated by the desire for faster computation for online monitoring of the system behavior. In Chapter 13, Hadis Karimipour and Venkata Dinavahi investigate the process of accelerating static/dynamic estimation for large‐scale networks.

In the first part, using an additive Schwarz method, the solution of each subsystem is carried out by using the conventional numerical techniques and exchanging the boundary data among subsystems. To increase the accuracy a slow coherency method was used to decide the domain decomposition. In addition, load balancing by distributing equal workload among processors is utilized to minimize inter‐processor communication. The advantages of the proposed approach over existing approaches include reducing execution time by splitting equal amount of work among several processors, minimizing the effect of boundary buses in accuracy and not requiring major changes in existing power system state estimation paradigm. Next, the proposed method is implemented in massively parallel architecture of GPU. As shown in the results, the advantage of utilizing GPU for parallelization is significant when the size of the system is increased.

The proposed method is general and can be extended to any number of GPUs connected in a cluster. Results show that more GPUs can reduce expected computation time. Result comparisons verified the accuracy and efficiency of the proposed method. In addition, the performance of the slow coherency method as the partitioning tool was analyzed, and it was concluded that for different fault locations in the system, results derived from this method had lower amounts of error.

Chapter 14 is “Dishonest Gauss Newton Method‐Based Power System State Estimation on a GPU”, by Md. Ashfaqur Rahman and Ganesh Kumar Venayagamoorthy. The authors acknowledge that real‐time power system control requires accelerating the computation processes. While many methods to speed up the computational process are available, it is worthwhile to explore current parallel computation technology to develop faster estimators. The authors use the term “dishonest Gauss Newton method,” but the technique is based on the PARTAN (short for Parallel tangent). Their study concerns a graphics processing unit (GPU) implementation. As the method is not explored extensively in the literature, its accuracy is investigated first. Then different aspects of the parallel implementation are explained. It takes a few hundreds of microseconds for IEEE 118‐bus systems, which are found to be the fastest in the existing reported times. For very large systems, the required configuration of a GPU and the corresponding time are also estimated. Finally, the distributed method‐based parallelization is also implemented.