基于多物理场仿真和VIKOR决策的干式铁心电抗器多目标优化

损耗和金属导体用量是干式铁心电抗器优化设计过程中需要考虑的关键因素，为有效降低损耗和成本，该文提出基于多物理场仿真和VIKOR决策的干式铁心电抗器多目标优化方法。首先以干式铁心电抗器为研究对象，建立磁场-流场-温度场模型，将磁场计算获得的铁心和线圈损耗密度作为热源，经过流-热耦合计算得到电抗器温度分布；建立磁场-结构场模型，将基于磁场计算得到的电磁力作为应力项，计算得到铁心及线圈振动位移分布，通过有限元仿真与拉丁超立方试验设计相结合的方法，得到不同结构参数下铁心电抗器温升与振动位移结果。为进一步简化优化流程，采用灵敏度分析方法进行参数降维，针对关键参数建立设计参数与温升、振动之间的代理模型，并采用多目标遗传算法得到满足电抗器性能要求的Pareto前沿解集。考虑到电抗器金属导体用量与损耗之间相互冲突，引入VIKOR综合决策方法，在确定优化目标权重的基础上，计算Pareto解集的利益比率大小，以最小利益比率确定最优设计参数组合，最后通过仿真验证优化设计方法的正确性。优化后的铁心电抗器与优化前相比，在损耗增加4.4%的情况下，铁心和线圈金属导体用量分别减少了3.0%和16.6%，同时温升及振动在满足设计要求的基础上分别降低了7.4%和16.7%。所提方法可以有效提升电抗器性能，为电抗器优化设计提供指导。

Multi-objective Optimization of the Dry Core Reactor Based on Multi-physical Field Simulation and VIKOR Decision

The loss and the amount of metal conductor are the key factors to be considered in the optimization design of dry-core reactor. In order to effectively reduce the loss and cost, this paper proposes a multi-objective optimization method for dry-core reactor based on multi-physical field simulation and VIKOR decision. Firstly, the dry-core reactor is taken as the research object, and the magnetic field-flow field-temperature field model is established. The core and coil loss density obtained from the magnetic field calculation is used as the heat source, and the reactor temperature distribution is obtained through the fluid-thermal coupling calculation; The magnetic field-structure field model is established, and the electromagnetic force calculated based on the magnetic field is taken as the stress item to obtain the vibration displacement distribution of the core and coil. The temperature rise and vibration displacement results of the core reactor under different structural parameters are obtained by combining the finite element simulation and Latin hypercube test design. In order to further simplify the optimization process, the sensitivity analysis method is used to reduce the dimension of parameters, the proxy model between design parameters and temperature rise and vibration is established for key parameters, and the multi-objective genetic algorithm is used to obtain the Pareto frontier solution set that meets the performance requirements of the reactor. Considering the conflict between the amount of metal conductor and the loss of the reactor, the VIKOR comprehensive decision method is introduced. On the basis of determining the weight of the optimization objective, the benefit ratio of Pareto solution set is calculated, and the optimal design parameter combination is determined by the minimum benefit ratio. Finally, the correctness of the optimization design method is verified by simulation. Compared with the optimized core reactor, the consumption of iron core and coil metal conductors decreased by 3.0% and 16.6% respectively when the loss increased by 4.4%, and the temperature rise and vibration decreased by 7.4% and 16.7% respectively on the basis of meeting the design requirements. The proposed method can effectively improve reactor performance and provide guidance for reactor optimization design.