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| An Adaptive Simulation Method for Power Electronics Systems Based on Stiffness Detection |
| Yu Zhujun1, Zhao Zhengming1,2, Shi Bochen1, Xu Han1, Jia Shengyu1 |
1. State Key Laboratory of Control and Simulation of Power Systems and Generation Equipment Department of Electrical Engineering Tsinghua University Beijing 100084 China;
2. Sichuan Energy Internet Research Institute Tsinghua University Chengdu 610213 China |
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Abstract The high-efficiency simulation tool plays an important role in designing and analyzing power electronics systems. Meanwhile, modeling the parasitic elements to analyze their influences on system reliability and performing parameter sweep for optimal design have become trends in practical applications. However, the mathematical properties of the system can become complicated and may alternate between being stiff or non-stiff. In this situation, using a single forward or backward integration method cannot achieve the highest efficiency, which brings great challenges for simulation tools. A recently developed discrete-state event-driven (DSED) framework can achieve accurate and efficient simulation of power electronics systems and has shown great advantages over commercial software. However, it cannot automatically identify the mathematical properties of the system, so much space remains for improvement when dealing with complex simulation scenarios. This paper proposes an adaptive simulation method for power electronics systems based on stiffness detection. It can always select the better numerical solver during the simulation process with low extra cost, greatly improving the simulation efficiency.
Firstly, the optimal scenarios of different numerical algorithms in power electronics system simulation are analyzed. This paper points out that only when the step size is limited by the stability rather than the accuracy of the numerical method, the stiffness of the system will bring extra difficulty for simulation. Therefore, whenever the switching event happens in power electronics systems, the high-order explicit numerical method with high accuracy should be chosen as the initial solver. After the free responses have decayed to the steady state, the low-order implicit numerical method with a large stability region should be selected.
Secondly, the criterion to detect stiffness and automatically switch between different methods is constructed. The flexible-adaptive discrete-state (FA-DS) method under the DSED framework is chosen as the solver for non-stiff situations. It is a single-step variable-order variable-step method. The backward discrete-state event-driven (BDSED) method is chosen as the solver for stiff situations. It is based on the backward difference formula (BDF), a multi-step variable-order variable-step method. The adaptive solver uses the FA-DS solver as the initial solver after each switching event. Only when the order of the FA-DS solver has reached the highest order and the following calculation point is far away from the next discrete switching event, the detection will be started. Then, the adaptive solver estimates the maximum possible step size of the BDSED using the historical values and the Newton interpolation formula. If it is larger than the current step size, the BDSED solver will be used in the remaining interval until the next switching event. The computational cost of the detection is very low compared with the numerical integration process. Thus, the proposed method can always find the optimal solver to improve the overall simulation efficiency without much extra cost.
The proposed method analyzes the high-frequency voltage oscillations in a 10 kV-2 MW four-port power electronics transformer. The adaptive solver is implemented under the DSED framework. The simulation results are compared with those by commercial software, the DSED framework with a single FA-DS solver and the DSED framework with a single BDSED solver. With the same level of accuracy, it achieves about 4-fold speed-up, which confirms its accuracy and efficiency.
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Received: 06 January 2023
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2023, Vol. 38 
