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| An Optimized 3-D Hybrid Thermal Network Order Reduction Model for Power Modules Based on Branch Value Delivery Algorithm and Self-Pruning Strategy |
| Liu Xuanyi1, Geng Jianghai1, Wang Ping1, Hou Sizu2, Lin Jiehui1 |
1. Key Laboratory of Power Transmission and Transformation Equipment Safety Defense of Hebei Province North China Electric Power University Baoding 071003 China;
2. Hebei Provincial Key Laboratory of Electric Power Internet of Things Technology North China Electric Power University Baoding 071003 China |
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Abstract As the core component of power conversion equipment, power modules have driven the development of motor drives, renewable energy generation, energy storage, and high-voltage direct current transmission. However, trends toward higher power and current densities have increased chip heat generation, posing challenges to their reliable operation. Existing thermal models that neglect thermal coupling exhibit limited accuracy. In contrast, methods that rely on thermal diffusion angles to determine thermal coupling and construct thermal network models are computationally cumbersome. Therefore, it is imperative to develop an efficient technique.
First, Fourier’s law of heat conduction was used to establish a finite-element heat-conduction model of the power module, and the original data required to construct the thermal network model were obtained. During the parameter identification process, four sets of finite-element simulation data under different boundary conditions were used to determine the optimal parameter combinations for thermal conductivity and thermal capacity. A branch-value delivery algorithm and a self-pruning strategy were introduced to account for thermal coupling among multi-layer structures within the power module. The branch value delivery algorithm reduced the computational time required by traditional methods and enhanced modeling efficiency by optimizing the calculation of the thermal conductivity matrix. The self-pruning strategy eliminated redundant branches through two pruning steps, further simplifying the thermal network model.
The model optimized using the proposed strategy was verified through low- and high-frequency performance tests. The experimental results show that under low-frequency-response conditions, the junction- temperature prediction error of the optimized thermal network model at each time point is lower than that of the unoptimized model. The error decreased from -1.98 K to 0.69 K, and the root mean square error also decreased to 0.72 K. In the high-frequency response test, the average error percentage of the optimized model decreased from -1.96% to -0.21%, and the standard deviation decreased from 0.18 K to 0.1 K. In addition, compared with the optimization strategy based on the thermal diffusion angle, computational efficiency increased by 70.3% and the average error decreased by 54.9%.
This paper proposes a method for constructing a 3-D hybrid thermal network model that accounts for thermal coupling among temperature nodes in a multi-layer structure via a branch-value delivery algorithm and a self-pruning strategy. The proposed method avoids the complex calculation process. Based on the branch-value delivery algorithm, the optimized thermal network model can be constructed via two self-pruning processes. This method offers a new approach to improving the efficiency and accuracy of the thermal network model for power modules. Future research can focus on the proposed strategy across different thermal network structures and operating conditions to enable its practical applications.
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Received: 03 July 2025
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2026, Vol. 41 
