Differential evolution solution to transformer no-load loss reduction problem

Abstract

After the completion of core manufacturing and before the assembly of transformer active part, 2N small individual cores and 2N large individual cores are available and have to be optimally combined into N transformers so as to minimise the total no-load loss (NLL) of N transformers. This complex combinatorial optimisation problem is called transformer no-load loss reduction (TNLLR) problem. A new approach combining differential evolution (DE) and multilayer perceptrons (MLPs) to solve TNLLR problem is proposed. MLPs are used to predict NLL of wound core distribution transformers. An improved differential evolution (IDE) method is proposed for the solution of TNLLR problem. The modifications of IDE in comparison to the simple DE method are (i) the scaling factor F is varied randomly within some range, (ii) an auxiliary set is employed to enhance the population diversity, (iii) the newly generated trial vector is compared with the nearest parent and (iv) the simple feasibility rule is used to treat the constraints. Application results show that the performance of the proposed method is better than that of two other methods, that is, conventional grouping process and genetic algorithm. Moreover, the proposed method provides 7.3% reduction in the cost of transformer main materials.