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| Optimization of Winding Block Washer Structure for Oil Immersed Transformers Based on Radial Basis Function Response Surface Model with Whale Optimization Algorithm Hyper-Parameters Optimization |
| Liu Gang1, Gao Chenglong1, Hu Wanjun1, Liu Yunpeng1, Li Lin2 |
1. Hebei Provincial Key Laboratory of Power Transmission Equipment Security Defense North China Electric Power University Baoding 071003 China;
2. State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources North China Electric Power University Beijing 102206 China |
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Abstract High hot spot temperature (HST) can seriously affect the stability of transformer operation. The structure of the transformer winding block washers plays a key role in the distribution of oil flow between windings, indirectly affecting the heat dissipation capacity of the windings. In order to improve the stability of transformer operation, this article takes reducing the winding HST as the optimization objective, and uses radial basis function (RBF) response surface model (RSM) to optimize the size of winding block washers, improve oil flow distribution, and achieve better heat dissipation. To the problem of empirical selection of hyper-parameters in the construction of traditional RBF RSM, this paper introduces the whale optimization algorithm (WOA) to determine the optimal hyper-parameters of the RBF RSM. The WOA-RBF RSM is proposed to optimize the size of winding block washers to improve the fitting accuracy and optimization ability of the RSM.
Firstly, use the Workbench platform to parameterize the block washers' size with a two-dimensional eight-zone winding with non-split turn model based on an actual large oil immersed transformer. Secondly, the optimization variable was determined to be the lengths of 7 block washers. The range of changes in block washers' length was determined, aiming to avoid oil flow dead zones. Use Latin hypercube sampling (LHS) to obtain the data set, and obtain the corresponding HST response values of the relevant data set through mutual calls between Matlab and Workbench, forming the final sample set. Thirdly, based on the existing sample set, a RBF RSM was established using the newrb function provided by Matlab. Combining WOA and cross validation ideas, hyper-parameters were optimized for the two hyper-parameters in the newrb function: spread (expansion speed) and MN (maximum number of neurons). Finally, the final RBF RSM was constructed based on the optimal hyper-parameters, and intelligent algorithms were used to obtain the optimal block washers' size scheme and the corresponding minimum HST.
The effectiveness of the non-split turn model used was verified by comparing the flow and temperature results of the split and the non-split turn model. The optimized results based on the WOA-RBF RSM were compared with those before optimization. The HST decreased by 3.81℃ and the maximum temperature rise decreased by 13.42%. Moreover, the optimized block washers' size not only reduced the HST, but also effectively ameliorated the phenomenon of excessive local temperature rise in winding various zones. To verify the accuracy of the optimization results by WOA-RBF, the results were compared with the optimization results of the genetic algorithm (GA). The optimal solution trends of the two methods were consistent, and the optimal HST value difference was only 0.05℃. The block washers' sizes obtained by the two methods were the two optimal credible solutions of the multi-solution problem. The reliability of the optimization results obtained by WOA-RBF was verified. Meanwhile, the efficiency of WOA-RBF is 13.41 times that of GA, indicating that the WOA-RBF method is an accurate and efficient method to solve the optimization problem of winding block washers' size. Simultaneously, this article also compared the WOA with grid search (GS) optimization method and fixed hyper-parameter method from the perspective of hyper-parameter optimization. The average root mean square error (RMSE) and average optimization error of GS-RBF and fixed parameter RBF are 1.12 times, 4.52 times and 1.67 times, 2.56 times higher than those of WOA-RBF, respectively. In the case of superior fitting and optimization accuracy, the optimization efficiency of WOA was 3.13 times than that of GS method, which verified the feasibility of applying WOA to hyper-parameter optimization design.
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Received: 04 July 2023
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2024, Vol. 39 
