Covariance Matrix Adaptation Evolutionary Strategy for the Solution of Transformer Design Optimization Problem

Transformer design (TD) is a complex multi-variable, non-linear, multi-objective and mixed-variable problem. This paper discusses the application of Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) for distribution TD, minimizing three objectives; purchase cost, total life-time cost 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 and energy efficient TD. Three case studies with three sets of TD vectors are implemented to demonstrate the superiority of CMA-ES and modified design variables (MDV), in terms of cost savings and loss reduction. Fourth case study depicts the accuracy, faster convergence and consistency of CMA-ES. Effectiveness of the proposed methodologies has been examined with a sample 400KVA 20/0.4KV transformer design. Simulation results show that CMA-ES with MDV provide the best solution on comparison with conventional TD procedure and, Branch and bound algorithm for TD optimization problem.