Decomposition of the Estimation and Control Problems in Power Systems

Abstract

The problem of state estimation and subsequent constrained optimization of generator real power outputs in a multi-area power system is considered. Formulations are developed whereby the naturally sparse structure of the system can be utilized by decomposition methods.The estimation phase, in which the nodal voltages and phase angles are determined from noisy measurements on a system of known network structure and parameters, is presented. An original algorithm based on a method of network tearing, is given, in which the system is decomposed into subsystems each of which is solved separately, and subsequently coordinated to achieve an overall sclution. It is shown that the method results in a good approximation to the least squares solution of the nonlinear estimation problem which would be achieved by conventional centralized methods. The results required for the decomposition of electrical networks are derived from algebraic considerations, and a comparison of the computational burden of the centralized and decomposed scheme is made.Integration of the state estimation problem with economic dispatch of the generator real power outputs based on the derived network conditions is obtained by application of the Dantzig-Wolfe decomposition principle. The decomposition results in a set of subproblems, which are linear programs, whose cost functions are modified by intervention parameters given by a master problem. The master problem, which seeks an overall optimum by adjustment of the intervention parameters, is a linear program of transformed variables derived from the current optimal solutions to the subproblems. The algorithm iteratively minimizes the cost of power production subject to constraints which arise from the network state, operational limits, and security of supply considerations.Both the estimation and dispatch phases are shown to lead to a two-level computational scheme which is suitable for implementation in a multi-processor hierarchical system for real time network monitoring and control.Computational experience with several size networks is presented in which the decomposition methods are compared with conventional solution techniques. The decomposition methods are shown to enable a substantial reduction in computer storage and computation time. Even if a parallel processing system is not adopted the proposed techniques will still result in improved computational efficiency in a single processor computer.For the large scale estimation and control problems which occur in modern power systems, decomposition methods are shown to be feasible and desirable. Furthermore the algorithms are found to be rapid enough for real time implementation on a large scale system.