Observability of Power-Distribution Systems

The motivation for and the goals of the development of a distribution system’s state estimation are presented. A short description of the evolution of power-distribution systems for unidirectional to bidirectional power flows, which are characterized by distributed energy resources and flexible loads, is presented. We reveal the major challenges that the grids of the future will be facing and count the number of potential applications that can be implemented in a closely monitored distribution grid. The chapter concludes with a short overview of all the sections.

The positioning of state estimation (SE) in the context of signal processing and its relation to power systems are presented in this chapter. As SE is already universally adopted in power-transmission networks and is making its way into power-distribution networks, the main differences between the two networks are described, and the main challenges of introducing SE into distribution systems are highlighted. Different types of estimators are reviewed, namely, MLE, WLS, LAV, and SHGM, based on projection statistics. Besides their statistical efficiency, the used estimators are also classified in terms of their robustness. In addition, models for three-phase underground cables, overhead lines, transformers, tap changers, and voltage regulators are reviewed. For transformers and voltage regulators, different connections are considered. A unified three-phase branch model as a generalization of the existing three-phase line models is presented. It enables the modeling of voltage regulators or tap changers and three-phase conductors or transformers on the same branch without the introduction of an extra support bus. Thus, the system’s dimension, i.e., the size of the problem, is not increased in the modeling phase and so the computer program’s design is simplified with this model.

Methods for the numerical solution of different state estimators are reviewed in this chapter. The MLE and WLS estimators can be solved directly using the Gauss–Newton or Newton–Raphson method, while the SHGM can be solved using the IRLS, which also leverages the Gauss–Newton method. We show that with the Gauss–Newton or Newton–Raphson method, the least squares problem with the normal equations can be successfully solved. Since the normal equations have a significant effect on the conditioning of the system, Hachtel’s augmented-matrix method that mitigates the intrinsic ill-conditioning of the normal equations was reviewed. In addition, in this chapter the implementation and performance evaluation of different state estimation methods on the proposed unified three-phase branch model is also presented. In order to apply the numerical solution to our problem, first, the partial derivatives with respect to the state variables were calculated. Numerical simulations were performed for all estimators, with different measurement configurations on the IEEE test feeder networks with 13 and 123 buses.

In this chapter, the local sensitivities of the estimated state variables with respect to the uncertain line lengths and inaccurate (pseudo-) measurements in a three-phase distribution network for different measurement configurations and different estimators are investigated. The approach with a perturbation of the KKT conditions, which is agnostic to the choice of the estimator, is presented and implemented. The analysis was performed for a full three-phase branch-network model. The implemented estimators were the LAV, WLS, and SHGM. Based on the results and the selected optimization criterion, the optimal estimator is proposed.

The content of this book, devoted to state estimation in distribution systems, is recapitulated in this chapter. The main outcomes are summarized. In addition, future research directions are presented.