Empirical Gramian balanced reduction of nonlinear power system model
Zhao Hongsha · Dianli zidonghua shebei · 2014
The empirical Gramian balanced reduction method is proposed to reduce the dimensionality and complexity of nonlinear multi-machine power system model,which projects the high-dimensional nonlinear dynamic model to a low-dimensional subspace to obtain a reduced model while retains the original dynamic behaviors of its inputs and outputs. Its implementation is as followings:build the nonlinear dynamic model of power system;obtain the empirical controllable and observable Gramian matrices based on the simulative samples and experiential samples;calculate the transformation matrix T based on the obtained Gramian matrices to get the balanced model of original system and its empirical controllable and observable Gramian matrices;decomposite the singular values of obtained Gramian matrices of the balanced model to get the Hankel singular values;determine the subspace dimension according to the obtained Hankel singular values to get the reduced model. Simulation is carried out for an actual 20-generator nonlinear power system as an example and the simulative results show its dimension is reduced from 120 to 50 while its stability and the dynamic behaviors of its inputs and outputs are kept,verifying the effectiveness of the empirical Gramian balanced reduction method applied in the reduction of nonlinear power system model.