Robust and distributed state estimation for power systems
Date of Issue2017-09-18
School of Electrical and Electronic Engineering
Nanyang Technological University
Power system state estimation (PSSE) plays an important role in power system operation. The Gaussian noise assumption is commonly made in PSSE. However, this assumption is only an approximation to reality. Outliers that are far away from the expected Gaussian distribution function can give rise to erroneous estimation results. Robust estimators such as Quadratic-Constant (QC), Quadratic-Linear (QL), Square-Root (SR), Multiple-Segment (MS) and Schweppe-Huber Generalized-M (SHGM) have been introduced in the literature to solve the outlier problem in power systems. In this thesis, an analytical equation is derived using the Influence Function (IF), a tool from robust statistics, to calculate approximately the variances of the estimates of these robust estimators. This variance formula has many advantages: (i) It can be used to express the variance of state estimate as a function of measurement variances thus enabling the selection of sensors for specified estimator precision; (ii) It can be used to design an optimal estimator; (iii) Although numerical methods can also be used to find variance, the derived equation as a mathematical function is more insightful and requires less computational effort. For robust PSSE, this thesis proposes a robust estimator based on the maximum likelihood criterion, and a noise model with t-distribution probability density function (pdf). The thick tail property of t-distribution down weights outliers so that the proposed estimator is robust to outliers. Instead of solving the optimization problem numerically, the IF is employed to give an approximate solution to reduce computational load. In addition, a robust estimator based on the moving horizon estimation (MHE) technique is proposed for PSSE. This robust estimator is called re-weighted MHE. The proposed estimator reduces its sensitivity to the outliers by updating their error covariances in real time and then uses these re-weighted error covariances for robust PSSE. Compared with other robust state estimators such as MS and Least Absolute Value (LAV) estimator, one advantage of the proposed estimator is that it can directly incorporate constraints on the states to mitigate the outliers. If Phasor Measurement Units (PMUs) are used, the measurement model becomes linear. Then the proposed estimator can be formulated as a quadratic programming (QP) and solved by Alternating Direction Method of Multipliers (ADMM) algorithm efficiently. When the measurement model is nonlinear, the iterated RMHE (iRMHE) algorithm is proposed. Finally, the centralized estimator is not applicable when the size of power system becomes very large. Two distributed versions of the proposed robust estimator based on MHE are considered: distributed MHE (DMHE) and partitioned MHE (PMHE). For DMHE, each local area will obtain the states of the whole system. It is suitable for the advanced applications such as wide-area monitoring systems (WAMSs) that require the system-wide state to be available to all the regional transmission organizations (RTOs). For PMHE, each local area only uses its local measurements and the states of border buses exchanged from its neighborhoods. It solves a smaller optimization problem to obtain the states of local states. Therefore, the communication load and computational load are reduced.