基于本征正交分解和克里金代理模型的油浸式变压器绕组温度场快速计算方法

doi:10.19595/j.cnki.1000-6753.tces.240544

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摘要

为了快速获得各种工况下油浸式电力变压器绕组的温度分布与热点,该文提出了一种基于本征正交分解（POD）与克里金代理模型（KSM）相结合的快速计算方法。首先,基于POD降阶方法对变压器温度场的离散方程组进行降阶,得到降阶模态系数矩阵;其次,根据不同变压器工况对绕组温度场的影响程度选取重要工况参数,通过拉丁超立方采样形成工况参数矩阵即样本空间;然后,基于KSM方法构建样本空间与对应模态系数的代理模型,跳过对全阶模型的复杂非线性计算,以绕组工况为输入得到模态系数,结合模态高效重构温度场;最后,为验证该方法的有效性及与现有方法相比的优越性,分别用该方法与现有方法对110 kV油浸式变压器绕组八分区仿真模型与绕组温升实验测量数据进行对比分析。算例表明,该文所提方法对于相关测试工况的计算偏差更低,计算精度更高,且计算效率有较大幅度的提升,充分表明了该方法的有效性与优越性。该文所提变压器稳态温度场计算方法可为变压器数字化运维提供技术支撑。

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关键词 ：油浸式电力变压器, 温度场, 本征正交分解, 克里金代理模型

Abstract：

In order to quickly obtain the temperature distribution and hot spots of the windings of oil immersed power transformers under various operating conditions, this paper proposes a fast calculation method based on the combination of the proper orthogonal decomposition (POD) and Kriging surrogate model (KSM). Firstly, based on the POD reduction method, the discrete equation system of the transformer temperature field was reduced. Through eigenvector decomposition, a set of orthogonal eigenvectors and corresponding eigenvalues were obtained, and these eigenvectors were arranged in descending order according to the size of the eigenvalues. A small number of optimal modes were selected to approximate the full order model, thereby reducing the model order and accelerating the solution speed; Secondly, analyzed the factors affecting the hot spot temperature of transformer windings, determined important operating parameters, and formed an operating parameter matrix or sample space through Latin hypercube sampling; Then, taking the operating parameters as input and modal coefficients as output, 50 sets are taken as the training set in the sample space. Based on the KSM method, a surrogate model was constructed for the sample space and corresponding modal coefficients. Equ.(13) in the text is the specific function expression of the surrogate model. This method uses the Kriging function to describe the correlation between data points by constructing a covariance function, which can accurately predict the data values of unknown points. Faced with the temperature field problem of windings under new operating conditions, the corresponding POD modal coefficients can be obtained through a surrogate model, and the full field data can be quickly obtained through modal reconstruction, bypassing the complex nonlinear calculation of the full order model and achieving rapid calculation of transformer winding temperature. Finally, to verify the effectiveness of the method, an eight zone numerical heat transfer model for the winding of a 110 kV oil immersed transformer was established, and the algorithm was compared with the calculation results of the simulation software Fluent. The results show that for the selected 50 test conditions, the maximum average absolute error is 1.19℃ and the maximum relative error is 2.79%. In terms of computational efficiency, the method proposed in this paper improves the computational efficiency to 13.39 times that of the full order model. If preprocessing time is not considered, it only takes 0.006 seconds to calculate the corresponding results for a certain condition. To verify the engineering application value of the method proposed in this paper, a temperature rise experimental platform based on product level oil immersed transformer winding structure was constructed. The temperature rise of the winding under certain operating conditions was measured and recorded, and the algorithm calculation results were compared with the experimental results. The calculation errors were all within an acceptable range, verifying the engineering application value of the POD-KSM reduced order model. At the same time, to demonstrate the superiority of the proposed method compared to existing methods, error analysis was conducted on the simulation and experimental results. The results showed that the proposed method outperformed existing methods in terms of computational accuracy and efficiency. The calculation method for steady-state temperature field of transformers proposed in this article can provide technical support for digital operation and maintenance of transformers.

Key words： Oil immersed power transformer temperature field proper orthogonal decomposition Kriging surrogate model

收稿日期: 2024-04-08

PACS:

TM411

基金资助:

国家自然科学基金联合基金（U23B20135）和河北省“三三三人才工程”（C20231116）资助项目

通讯作者: 刘刚男,1985年生,副教授,硕士生导师,研究方向为电气设备多物理场建模及仿真、电力系统时域仿真和电磁场理论及其应用。E-mail：liugang_em@163.com

作者简介: 张志宇男,2000年生,硕士研究生,研究方向为变压器多物理场仿真及降阶计算。E-mail：faculty0627@163.com

引用本文:

张志宇, 寇家俊, 张重远, 杜振斌, 刘刚. 基于本征正交分解和克里金代理模型的油浸式变压器绕组温度场快速计算方法[J]. 电工技术学报, 0, (): 2492931-2492931. Zhang Zhiyu, Kou Jiajun, Zhang Zhongyuan, Du Zhenbin, Liu Gang. A Fast Calculation Method for Temperature Field of Oil Immersed Transformer Windings Based on Proper Orthogonal Decomposition and Kriging Surrogate Model. Transactions of China Electrotechnical Society, 0, (): 2492931-2492931.

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https://dgjsxb.ces-transaction.com/CN/10.19595/j.cnki.1000-6753.tces.240544 https://dgjsxb.ces-transaction.com/CN/Y0/V/I/2492931

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