基于拉格朗日数乘法的高频高压变压器分布电容优化设计

Optimal Design Based on Lagrange Multiplier Approach for Parasitic Capacitance of High Frequency High Voltage Transformers

高频高压变压器在电容器充电电源、脉冲强磁场系统、静电除尘等诸多领域有重要应用,为了提高变压器运行的可靠性,该文以减小高频高压变压器的分布电容和限制其损耗作为设计时的优化目标,并针对此目标提出了一种基于Lagrange数乘法的高频高压变压器分布电容的优化设计方法。并依据此设计方法绕制了一台输入电压500V,输出电压10kV,额定频率15kH z,额定功率为30k V×A的高频高压变压器。对所设计的变压器进行了仿真和实验,得到的分布电容和损耗与理论计算结果一致,且满足绝缘和损耗要求,验证了文中建立的Lagrange模型的准确性。将优化后的变压器与未优化的变压器进行充电对比实验,优化后的变压器充电速度更快,线性度更好,实验结果验证了该优化设计方法的有效性和可行性。

High frequency high voltage（HFHV）transformers are widely used in applications such as capacitor charging power systems（CCPS）, pulsed high magnetic field systems and electrostatic dust collectors etc. In order to minimize the value of the parasitic capacitance as well as the total power loss of the transformer, an innovative optimum design method of HFHV transformers based on Lagrange multiplier approach was presented. A 15 k Hz, 30 k V？A transformer prototype was designed with 500 V input voltage and 10 k V output voltage. The simulation and experiment were given to prove the performance of the transformer prototype.The value of capacitance and loss which meet the loss constraints and insulation requirements are the same to theoretic calculation results. The results verify the accuracy of the Lagrange model established in the paper. In addition,compared with the traditional transformer, the optimized transformer has faster charging speed and better linearity in the charging experiments. The experimental results verify the validity and feasibility of the optimization method.