In this paper, the authors propose a novel model order reduction method integrating evolutionary and conventional approaches for higher-order linear time-invariant single-input–single-output (SISO) and multi-input–multi-output (MIMO) dynamic systems. The proposed method makes use of a differential evolution algorithm with enhanced mutation operation for the determination of reduced order model (ROM) denominator polynomial coefficients. In addition, an improved multi-point Padé approximation method is used to determine the optimal ROM numerator polynomial coefficients. The optimum property of the ROM is measured by minimising the integral square of the step response error between the original high-order dynamic system and the ROM. In the case of the MIMO system reduction approach, an optimal ROM transfer function matrix is determined by minimising a single objective function. This objective function is defined by a linear scalarising of the multi-step error function matrix components $$ \left( {E_{ij} } \right) $$ E ij . The proposed method guarantees the preservation of the stability, passivity and accuracy of the original higher-order system in the ROM. The proposed method is validated by applying it to a ninth-order SISO system, as well as to the tenth- and sixth-order linearised single-machine infinite-bus power system model with and without an automatic excitation control system. The simulation results and the comparison of the integral square error and impulse response energy values of the ROM demonstrate the dominance of the proposed method over the latest reduction methods available in the literature.

中文翻译：

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使用增强的 DE 算法和改进的 MPPA 方法的线性时不变系统的最优模型逼近

在本文中，作者针对高阶线性时不变单输入单输出 (SISO) 和多输入多输出 (MIMO) 动态系统提出了一种新的模型降阶方法，该方法集成了进化方法和传统方法。所提出的方法利用具有增强变异操作的差分进化算法来确定降阶模型(ROM)分母多项式系数。此外，改进的多点Padé近似方法用于确定最佳ROM分子多项式系数。通过最小化原始高阶动态系统与 ROM 之间阶跃响应误差的积分平方来衡量 ROM 的最佳性能。在 MIMO 系统缩减方法的情况下，通过最小化单个目标函数来确定最佳 ROM 传递函数矩阵。该目标函数由多步误差函数矩阵分量 $$ \left( {E_{ij} } \right) $$ E ij 的线性标量定义。所提出的方法保证了ROM中原始高阶系统的稳定性、无源性和准确性。通过将其应用于九阶 SISO 系统以及具有和不具有自动励磁控制系统的十阶和六阶线性化单机无限母线电力系统模型，对该方法进行了验证。仿真结果以及 ROM 的积分平方误差和脉冲响应能量值的比较证明了所提出的方法相对于文献中可用的最新减少方法的优势。