油浸式变压器绕组瞬态温升降阶快速计算方法

Reduced Order Calculation Method of Steady Temperature Rise of Oil Immersed Power Transformer

油浸式电力变压器绕组温升监测是保证其安全稳定运行的重要手段。为了改善采用有限元方法计算油浸式电力变压器绕组瞬态温升时存在效率不高的问题,提出一种结构保留的本征正交分解(SPOD)与离散经验插值方法(DEIM)相结合的计算策略。首先,该文采用最小二乘有限元法(LSFEM)与迎风有限元法(UFEM)构建变压器绕组瞬态温升计算控制方程;其次,针对控制方程的特点,引入SPOD方法,通过将采样时间内的计算结果构成快照矩阵,建立降阶模型,降低有限元刚度矩阵的计算阶数,提高求解有限元方程的效率;然后,为了改善本征正交分解方法对于非线性问题效率提升不高的缺陷,结合DEIM算法,对有限元方程中的非线性项进行插值处理,从而减少每一时步形成总体刚度矩阵的时间,进一步提高总体计算效率。为了验证文章所提算法的精确性及高效性,根据油浸式电力变压器绕组的基本特点,建立了单分区分匝绕组传热模型,对其瞬态传热过程进行计算,结果表明:基于SPOD-DEIM的有限元降阶计算能够在保证精度的前提下有效提高计算效率,与全阶计算结果相比,流场与温度场的计算误差均不超过1.5%,且计算效率提升5.1倍。同时,为了充分说明SPOD-DEIM算法在工程应用中的价值,该文基于110 kV变压器绕组搭建了温升实验平台,建立了八分区分匝绕组数值计算模型,对算法的精度、效率及工程应用价值进行了验证及讨论,计算及实验结果表明:精度方面,降阶计算较全阶计算的瞬态全过程计算误差小于2.5%,且与实验结果相比,误差不超过5.41K;效率方面,降阶计算的全过程计算时间为54.28 h,与全阶计算相比,计算效率提升至10.57倍,与商业仿真软件Fluent相比,效率提升至6.37倍,充分说明所提算法的高效性及工程应用价值,为大型电力设备快速仿真提供新思路。

In order to improve the efficiency problem of using finite element method to calculate the transient temperature rise of oil immersed power transformer windings,this paper proposes a calculation strategy that combines structure preserved property orthogonal decomposition(SPOD)with discrete empirical interpolation method(DEIM).Firstly,the article uses the least squares finite element method(LSFEM)and upwind finite element method(UFEM)to construct the control equation for calculating the transient temperature rise of transformer windings.The finite element method combined with LSFEM-UFEM can accurately obtain the flow field and temperature field distribution during the transient temperature rise change process of the winding;However,in practical engineering applications,the mesh size and number of nodes of the model are generally large,and using finite element method to solve faces the problem of high time cost.Therefore,in order to reduce the computational scale and improve computational efficiency,the article introduces a reduction method based on the characteristics of the control equation.The traditional POD method usually decomposes the entire dataset and only reflects the statistical characteristics of the dataset,However,the inability to preserve physical features results in low interpretability of the reduced order model.Therefore,this article adopts a reduced order calculation strategy of"data structure preservation"to improve the efficiency of solving finite element equations;At the same time,in order to improve the efficiency improvement of the intrinsic orthogonal decomposition method for nonlinear problems,the DEIM algorithm is combined to interpolate the nonlinear terms in the finite element equation,thereby reducing the time for forming the overall stiffness matrix at each step and further improving the overall computational efficiency.In order to verify the accuracy and efficiency of the algorithm proposed in the article,a single zone split turn winding heat transfer model was established and its transient heat transfer process was calculated.The results showed that the finite element reduced order calculation based on SPOD-DEIM can effectively improve the calculation efficiency while ensuring accuracy.Compared with the full order calculation results,the calculation errors of the flow field and temperature field are not more than 1.5%,and the calculation efficiency is increased by 5.1 times.At the same time,in order to fully demonstrate the value of SPOD-DEIM algorithm in engineering applications,the article built a temperature rise test platform based on 110 kV transformer windings,and established an eight zone split turn winding numerical calculation model to verify and discuss the accuracy,efficiency,and engineering application value of the algorithm.The calculation and experimental results show that in terms of accuracy,the transient whole process calculation error of reduced order calculation is less than 2.5%compared to full order calculation,and compared with experimental results,The error shall not exceed 5.41 K;In terms of efficiency,the entire process calculation time of reduced order calculation is 54.28 h,which increases the calculation efficiency to 10.57 times compared to full order calculation and 6.37 times compared to commercial simulation software Fluent.This fully demonstrates the efficiency and engineering application value of the algorithm proposed in this article.