An Incomplete Observability-Constrained PMU Allocation Problem by Using Mathematical and Evolutionary Algorithms

Abstract

The purpose of this paper is to introduce several optimization algorithms that can be used to address optimization models in the power network, where the level of observability may be either complete or incomplete. These algorithms include discrete, continuous and metaheuristic methods. Initially, the optimization problem is approached by implementing a zero-one mixed integer linear program solved by several methods, including branch and bound revised simplex and primal dual-simplex in combination with interior point algorithms. To solve the problem of depth-one-unobservability (DoOU), a nonlinear program is proposed using Sequential Quadratic Programming (SQP), Interior-Point methods (IPMs) or YALMIP\\s branch-and-bound algorithm. Additionally, the paper proposes the use of metaheuristic algorithms, such as Genetic Algorithms (GAs) and Binary Particle Swarm Optimization (BPSO), to solve optimization problems under incomplete observability. The proposed algorithms are tested using simulations on IEEE standard systems to illustrate their efficiency and reliability in solving the optimization problem under partial observability. Overall, the paper concludes that these algorithms can efficiently lead to the optimum point in a reasonable runtime. Hence, this work examines the problem of putting a restricted PMUs number to make the DoOU and to give a feedback to the state estimation routine accuracy.