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| Fast Updating Method for Reduced-Order Model of Transformer Winding Temperature Field Based on Matrix Low-Rank Decomposition |
| Yang Fan1, Wu Tao1, Hao Hanxue1, Li Xing2, Jiang Jinyang3 |
1. State Key Laboratory of Power Transmission Equipment Technology Chongqing University Chongqing 400044 China;
2. College of Automation Engineering Nanjing University of Aeronautics and Astronautics Nanjing 210016 China;
3. Chongqing Electric Power Research Institute State Grid Chongqing Electric Power Company Chongqing 400015 China |
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Abstract The temperature state of transformer winding affects its operating life directly, so researchers have widely discussed how to achieve continuous and accurate calculations of the temperature field of transformer winding. The model orderreduction technique is currently the mainstream solution, and existing methods generally adopt singular value decomposition (SVD) of the initial snapshot matrix to obtain the modes, keeping the modes unchanged and continuously using them. During the operation of transformers, due to the dynamic changes in operating conditions, the modes will also change accordingly, resulting in a significant decrease in the computational accuracy of the static reduced order models (ROM).
It is difficult to fully consider various operating conditions when building the initial snapshot set, and it can lead to high computational costs in the offline phase. Continuously updating the initial snapshot matrix and performing SVD operations when new snapshots are available is a solution. Still, the high computational cost of SVD can cause ROM to lose its speed advantage. This paper proposed a low-cost method for updating modes and subsequently updating ROM based on matrix low-rank decomposition. Firstly, when a new snapshot is available, it is added to the initial snapshot matrix, and the snapshot matrix update is represented using matrix low-rank decomposition. Then, the solution of updating the modes directly from the SVD results of the initial snapshot matrix and the new snapshot was established. Only low computational cost SVD operation was required for low dimensional matrices, without the need for high computational cost SVD of the new snapshot matrix. Furthermore, sparse measurements of winding temperature were used to determine the modal coefficients and form a dynamic ROM. Finally, numerical calculations and transformer scaling prototype experiments verified the method’s effectiveness.
The results indicate that during the transformer’s operation, the proper orthogonal decomposition (POD) modes of its winding temperature field dynamically change, and it is necessary to update the modes of the ROM when new snapshots are available to suppress the increase in calculation errors of the ROM. The error of the proposed method for updating the temperature field modes of transformer winding is at the level of 10-8, and the single update takes 0.71 seconds for a grid-scaleofmillions, which is 239 times faster than traditional methods. In numerical experiments, the calculation error is reduced by a maximum of 1.92 K compared to the static ROM, with only a 0.016-second increase in single-step computation time. In the temperature rise test of the transformer scale prototype, the maximum computational error is 2.59 K, and the single-step computation time is 0.018 5 seconds, effectively avoiding the accuracy decline caused by modes change during transformer operation while maintaining computation speed at the second level. For calculating transformer winding temperature fields under varying load rates, only one mode update is required within each load rate interval. Increasing the number of mode updates will not lead to a further significant reduction in errors due to information redundancy. This research provides a solution for achieving continuous and accurate transformer winding temperature field calculations using ROMs.
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Received: 25 December 2024
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2025, Vol. 40 
