Modified parameter optimization of distribution transformer design using covariance matrix adaptation evolution strategy

Optimal transformer design (TD) is a complex multi-modal, multi-objective, mixed-variable and non-linear problem. This paper discusses the application of Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for distribution TD, minimizing four objectives; purchase cost, total life-time cost, total mass and total loss individually. Two independent variables; voltage per turn and type of magnetic material are proposed to append with the usual TD variables, aiming at cost effective, reduced weight, and energy efficient TD. Three case studies with three sets of TD vectors are implemented on 400 KVA, 20/0.4 KV transformer to demonstrate the superiority of Modified Design Variables (MDV), in terms of cost savings, material savings, and loss reduction. Simulation results of CMA-ES provide better TD on comparison with conventional transformer design procedure, branch and bound algorithm tailored to a mixed-integer non-linear programming, Self Adaptive Differential Evolution (SaDE), and real coded GA (RGA). Statistical analysis has proven the faster convergence and consistency of CMA-ES. Moreover, NSGA-II is applied for solving multi-objective TD optimization problem with the aim of providing tradeoff between conflicting TD objectives.