Comparison of linear approximations for the dynamic security region of power systems

Abstract

This paper compares the performance of three types of linear approximations for the dynamic security region of power system with network-reduction model. The three types of linear approximations are the Q-linear approximation based on the quadratic approximation of stability region, the L-linear approximation based on the linear approximation of stability region and the LO-linear approximation based on the invariant assumption of the normal vector of stability region. The linear approximations are obtained with a critical point just on the boundary of dynamic security region. In the comparison, the linear approximation obtained by the least square curve fitting method is used as the benchmark. Furthermore, for the dynamic security region in low dimension, the figure with the searched critical point is used to directly compare the accuracy of different approaches. Simulations in IEEE 3-machine 9-bus system and 10-machine 39-bus New England system show that, with a given critical point, all the three types of approximations display fairly accurate estimation. Furthermore, from the computational viewpoint, the L-linear and the LO-linear method with less computational burden are two alternative choices to approximate the dynamic security region.