一种多时间尺度线性系统模型降阶的误差预测方法

An Error Prediction Method of Model Order Reduction for Multi-Time Scale Linear System

传统线性系统的数学模型降阶方法,无法预测降阶所引起的系统状态变量动态特性的时域误差,这将导致降阶模型与原始模型状态变量的动态特性差异大,而无法用于系统分析。因此,在传统奇异摄动模型降阶方法基础上,提出一种基于L2范数的线性系统模型降阶的误差预测方法。解析推导了忽略快动态、固定慢动态降阶引起的系统状态变量动态特性的相对误差计算公式,构建了单台发电机供电的交流电力系统、三台发电机供电的直流电力系统的多时间尺度数学模型,并对它们进行了模型降阶和误差预测。仿真结果验证了所提误差预测方法的正确性。

The conventional methods of order reduction model for linear system cannot predict the time domain error of dynamic behaviors of state variables between the original and reduced models,so the reduced models derived by conventional methods maybe not suitable for analyzing the system performances because of the large variation between the reduction model and origin model. To solve this problem,this paper has proposed a L2 norm-based error prediction method for error prediction which is based on the conventional singular perturbation model order reduction method. The relative error calculation formula of the dynamic characteristic of the system state variable is deduced which ignore the variation caused by fast dynamic and fixed slow dynamic reduction. Then,the multi-time scale mathematical models of an AC system powered by one generator and a model of a DC system powered by three generators are built. They are reduced and the consequent errors are predicted. The simulation results demonstrate the effectiveness and accuracy of the proposed method.