模型的快速降阶技术

Technology on fast order reduction of model

为快速进行模型的降阶,结合平衡截断(Balanced Truncation,BT)方法和特征正交分解(Proper Orthogonal Decomposition,POD)方法提出一种模型降阶方法.该方法采用频域POD快照矩阵低阶逼近系统的可控、可观Gram矩阵;通过奇异值分解(Singular Value Decomposition,SVD)提取BT+POD模态,对低能量模态截断形成降阶子空间,并将其映射到全阶系统,从而形成基于状态空间的降阶模型(Reduced Order Model,ROM);该模型就成为全阶模型(Full Order Model,FOM)的ROM.通过对阶数n=406的LTI SISO系统和阶数n=9的2区间电力系统进行的验证表明,在保留BT方法输入输出平衡特性的基础上,该方法效率高于BT方法.

To perform the order reduction of model quickly,a method is proposed combined with Balanced Truncation（BT） and Proper Orthogonal Decomposition（POD）.The snapshot matrix of POD in frequency domain is used to obtain the low-order approximations to the controllable and observable Gram matrixes of the system;the BT ＋ POD modes are extracted by Singular Value Decomposition（SVD）,the reduced order subspace is generated by truncating low-energy modes and projected to the full order system,and so the Reduced Order Model（ROM） based on state space is constructed;so the model becomes the ROM of Full Order Model（FOM）.An LTI SISO system with order n = 406 and an doubleinterval electric power system with order n = 9 are used to verify the validation of the method,and the results indicate that the method retains the balance characteristics of input and output of BT method and is more efficient than BT method.