A Generalized Pattern Search Algorithm Methodology for solving an Under-Determined System of Equality Constraints to achieve Power System Observability using Synchrophasors

Abstract

The impact of the generalized pattern search algorithm (GPSA) on power system complete observability utilizing synchrophasors is proposed in this work. This algorithmic technique is an inherent extension of phasor measurement unit (PMU) minimization in a derivative-free framework by evaluating a linear objective function under a set of equality constraints that is smaller than the decision variables in number. A comprehensive study about the utility of such a system of equality constraints under a quadratic objective has been given in our previous paper. The one issue studied in this paper is the impact of a linear cost function to detect optimality in a shorter number of iterations, whereas the cost is minimized. The GPSA evaluates a linear cost function through the iterations needed to satisfy feasibility and optimality criteria. The other issue is how to improve the performance of convergence towards optimality using a gradient-free mathematical algorithm. The GPSA detects an optimal solution in a fewer number of iterations than those spent by a recursive quadratic programming (RQP) algorithm. Numerical studies on standard benchmark power networks show significant improvement in the maximum observability over the existing measurement redundancy generated by the RQP optimization scheme already published in our former paper.

An enhanced hunter‐prey optimization for optimal power flow with FACTS devices and wind power integration

“…Meta-heuristic approaches have gained widespread popularity as effective strategies for solving real-world problems and finding optimal solutions. Some of the well-known metaheuristic algorithms include the genetic algorithm (GA) and its variants [3][4][5][6][7], Sine Cosine Algorithm (SCA) [8], the Orchard algorithm (OA) [9], Snake Optimizer (SO) [10], Jellyfish Optimizer (JS) [11], Fick's Law Algorithm (FLA) [12], the successive history-based adaptive differential evolutionary (SHADE) [13] algorithm, the enhanced chaotic grasshopper optimization algorithm (ECGOA) [14], the Aphid-Ant Mutualism (AAM) [15], pattern search algorithms (PSA) and their variants [16][17][18][19][20][21][22], among others. In the field of power systems, the optimal power flow (OPF) problem using thermal power generators has been extensively studied, with several meta-heuristic algorithms being applied.…”

Optimal Placement of Measuring Devices for Distribution System State Estimation Using Dragonfly Algorithm

“…Besides that, many papers only target full observability by using measurements such as the phasor measurement unit (PMU). A few of them performed the derivative-free optimization algorithm such as the genetic algorithm (GA) [42] and a heuristic optimization like particle swarm algorithm (PSO) [40,43,44] to optimize the cost function of their proposed problems which is the NoMs. e author of [42] employs a derivative-free optimizer, that is, a generalized pattern search.…”

“…A few of them performed the derivative-free optimization algorithm such as the genetic algorithm (GA) [42] and a heuristic optimization like particle swarm algorithm (PSO) [40,43,44] to optimize the cost function of their proposed problems which is the NoMs. e author of [42] employs a derivative-free optimizer, that is, a generalized pattern search. is algorithm is counted with GA in the MATLAB optimization library regarding the derivative-free optimizers.…”

Allocation of Optimal PMUs for Power System Observability Using PROMETHEE Approach

“…A security-based observability approach for optimal PMU sensor placement is suggested in [40]. A globalized optimization approach, i.e., generalized pattern search algorithm (GPSA) [41], has been implemented for determining the PMU locations in a bounded nonconvex nonlinear framework.…”