Analysis of PDG, Penalty-BFGS and KKT in Economic Dispatch Problems

Abstract

For the past several decades, Economic Dispatch problem has been a hot topic in the field of mathematics. In general, Economic Dispatch problem can be regarded as a quadratic optimization problem in power system. This paper utilized projected gradient descent algorithm, penalty-BFGS algorithm and KKT conditions method, which can be used to minimize the cost function with equality constraints and inequality constraints, with an attempt to explain and address Economic Dispatch problem. Based on the three methods above, the corresponding results are presented and analyzed. The results demonstrated that the three algorithms have different performances. Each can solve the quadratic problem with efficiency to different degrees. Keywords- Economic dispatch; Non-linear optimization; PGD algorithm; BFGS algorithm; KKT conditions.