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,
