Multi-Objective Electromagnetic Design Optimization of a Power Transformer Using 3D Finite Element Analysis, Response Surface Methodology, and the Third Generation Non-Sorting Genetic Algorithm

Abstract

This paper presents a multi-objective design optimization of a power transformer to find the optimal geometry of its core and the low- and high-voltage windings, representing the minimum power losses and the minimum core and copper weights. The optimal design is important because it allows manufacturers to build more efficient and economical transformers. The approach employs a manufacturer’s design methodology, which is based on the usage of the laws of physics and leads to an analytical transformer model with the advantage of requiring a low amount of computing time. Afterward, the multi-objective design optimization is defined along with its constraints, and they are solved using the Non-Sorting Genetic Algorithm III (NSGA-III), which finds a set of optimal solutions. Once an optimal solution is selected from the Pareto front, it is necessary to fine-tune it with the 3D Finite Element Analysis (FEA). To avoid the large computing times needed to carry out the 3D Finite Element (FE) model simulations used in multi-objective design optimization, Response Surface Methodology (RSM) polynomial models are developed using 3D FE model transformer simulations. Finally, a second multi-objective design optimization is carried out using the developed RSM empirical models that represent the cost functions and is solved using the NSGA-III. The numerical results of the optimal core and windings geometries demonstrate the validity of the proposed design methodology based on the NSGA-III. The used global optimizer has the feature of solving optimization problems with many cost functions, but it has not been applied to the design of transformers. The results obtained in this paper demonstrate better performance and accuracy with respect to the commonly used NSGA-II.

Analysis of Transformer No-Load Loss Using Finite Element Method Validated by Experimental Tests

“…Finite element method (FEM) is a robust method for solving electromagnetic problems [7], [8] including highly superior numerical accuracy in complex phenomena and electromagnetic field distribution analysis [9], [10]. In addition, FEM can directly obtain the result while avoiding complex modeling processes [11].…”

Cost optimization of oil type distribution transformer using multi-objective genetic algorithm

“…The CFD-EMAG model is used to verify the results in this study. Transformer losses and weight are minimized with NSGA-III, and the results are confirmed by FEA in [4]. The current density and iron cross-section conformity factor of the oil type, 50 kVA, 34.5/0.4 kV transformer is optimized using MATLAB in [5].…”

Transformer Modelling Considering Power Losses Using an Inverse Jiles-Atherton Approach

“…Numerical methods are widely used to solve electromagnetic problems such as the optimal design of electromagnetic devices such as rotating electrical machines and transformers. Although the finite element method (FEM) is a powerful method for solving this type of problems [4,5], it is time consuming and requires high computational resources [6]. In addition, the implementation of realistic hysteresis models in FEM poses important difficulties and increases the computational resources significantly [7].…”