双有源桥型变换器电磁暂态等效算法稳定性及截断误差分析

高频隔离型双有源桥(dual active bridge,DAB)变换器是电力电子变压器(power electronic transformer,PET)的核心设备之一。其中,高频链的存在以及高开关频率特性,使得PET电磁暂态仿真效率较低。该文对先前研究提出的DAB型变换器积分解耦算法进行稳定性与截断误差分析,以提高该方法的可信度。首先,建立DAB简化电路并列写其状态方程;其次,选取特殊对称矩阵,利用Lyapunov直接法分析前向欧拉、梯形积分和积分解耦方法下连续系统与离散系统的稳定性,计算不同积分方法的局部截断误差,建立相对均方根误差作为全局误差的衡量指标;并结合实际变压器参数取值,分析不同积分方法对仿真步长的约束;最后,在PSCAD/EMTDC中,进行稳定性与误差验证。结果表明,积分解耦法和梯形积分法的稳定性与截断误差均不会对仿真步长产生附加约束。

Stability and Truncation Error Analysis of Electromagnetic Transient Equivalent Algorithm for Dual Active Bridge Converter

The high-frequency isolated dual active bridges converter(DAB) are core equipment of the power electronic transformers(PET). It has been well-known that the electromagnetic transient(EMT) simulation of PET time inefficient due to the existence of the high-frequency links and the large node counts inside each power module. In this paper, the stability and truncation error of the integration decoupling algorithm for DAB type converter were analyzed. First, a simplified circuit of DAB with its equation of state were given. Second, the Lyapunov direct method with a special symmetric matrix was used to analyze the stability of continuous and discrete systems under Forward Euler(FE), Trapezoidal Rule(TR) and integral decoupling(ID) methods. Third, the local truncation error of TR and ID methods was calculated and the relative root mean square error was established as a measure of global error. Fourth, the constraint effect of different integration methods on the simulation step size was analyzed considering the actual transformer parameter value. Finally, stability and error verification were performed in PSCAD/EMTDC. The results show that the stability and truncation error of the ID and TR method will not impose additional constraints on the simulation step size.