基于特征矩阵分区等值和自适应插值切换的有源配电网多速率并行仿真方法

A Multi-Rate Parallel Simulation Method for Active Distribution Network Based on Characteristic Matrix Partition Equivalence and Adaptive Interpolation Switching

现代有源配电网呈现复杂多变、多时间尺度的特征,采用单一仿真速率难以同时兼顾计算效率与精度,对此该文提出基于特征矩阵分区等值和自适应插值切换的有源配电网多速率并行仿真方法。首先,构建系统状态空间矩阵,并基于状态矩阵特征值的量级将系统拆分为多个动态特性差异的子系统,通过将系统的状态矩阵进行分块等效,实现子区域在小步长时刻的独立仿真解算与在大步长时刻的等效补偿,在保证仿真精度的基础上大幅降低了系统仿真规模;然后,针对各区域间数据交互不同步问题,通过倍率步长相量法分析线性插值误差产生原理及主要影响因素,并提出基于二阶泰勒展开式的多步自适应插值仿真算法,可以根据系统频率与仿真步长需求调节相关插值参数,显著降低插值误差;最后,采用改进型IEEE 123节点配电网算例,通过分区等值/插值计算与仿真结果的对比,验证了所提多速率并行仿真方法的可行性与有效性。

With the rapid development of power electronics technology and increasing penetration of distributed generations,modern active distribution networks exhibit complex dynamic characteristics due to the multiple time scales of system operation,which poses challenges to the simultaneous demand of computational efficiency and accuracy in the conventional simulation method with a single simulation-rate.This paper proposes a multi-rate parallel simulation method based on the characteristic matrix partition equivalence and adaptive interpolation switching.Firstly,a state space matrix is constructed for the whole active distributed system,and the system is divided into multiple subsystems with different dynamic characteristics based on the magnitude of the eigenvalues of the state matrix and their corresponding natural frequencies.The iterative computation of the high-speed subsystem is equivalently calculated within a certain period of time through binomial expansion and multidimensional matrix summation formulas,and then the block equivalence of the system's state matrix is achieved.This method transforms the original full-region state quantity iterative computation into the independent simulation solutions for subregions at small step sizes and equivalent compensation at large step sizes,simplifying the original high-order matrix iterative computation to the low-order matrix iterative computation,thereby significantly reducing the simulation complexity while ensuring simulation accuracy.For the problem of asynchronous data interaction between regions,the error generation principle and main influencing factors of the traditional linear interpolation method are analyzed through the magnification step length vector method.Based on the second-order Taylor expansion,the interpolation algorithm is improved by introducing undetermined coefficients.A multi-step adaptive interpolation simulation algorithm is proposed,which can adjust relevant interpolation parameters according to the system frequency and simulation step length requirements,significantly reducing interpolation errors.Finally,using the improved IEEE 123 node distribution network example,the feasibility and effectiveness of the proposed multi-rate parallel simulation method are verified through the comparison of partition equivalence/interpolation calculations and simulation results.The specific innovations of this article are as follows:Based on the discrete state space matrix,the system is considered as a multiple-rate counterpart due to different dynamic characteristics,and then the influence of coupling between fast and slow system regions on the accuracy of multi-rate simulation is evaluated through diagonalizing the matrix.The equivalent decoupling of the partitioned subsystem models is implemented to achieve independent resolution of subregions in small steps and equivalent compensation in large steps,significantly reducing the computational load while ensuring simulation accuracy.For the problem of asynchronous data interaction in multi-rate regions,the error caused by the conventional linear interpolation methods are analyzed by using the magnification step length vector method,and the relationships between the error and the system frequency and step length are also derived.Based on the second-order Taylor expansion,a multi-rate multi-step adaptive interpolation algorithm is proposed,which adjusts the interpolation algorithm parameters according to the simulation requirements for the first time to meet the minimum error condition,and performs optimal switching among multiple interpolation algorithms to improve the inter-region interaction coordination and simulation accuracy.Through simulation comparison,the following conclusions can be drawn:(1)This method evaluates the impact of fast and slow partition coupling on the accuracy of multi rate simulation numerical values,and decouples the subsystem model equivalently to achieve independent solution of the subregion in small steps and equivalent compensation in large steps,reducing the order of the state iteration matrix during simulation and significantly improving efficiency while ensuring computational accuracy.(2)On the basis of analyzing the principle and influencing factors of linear interpolation errors,an adaptive interpolation switching simulation algorithm is proposed.Relevant interpolation parameters are adjusted according to the system frequency and simulation step size requirements,and interpolation algorithm optimization is carried out to improve the accuracy and stability of parallel simulation.