Comparison of the linear approximations for the dynamic security region of network-reduction power systems

The dynamic security region (DSR) of bulk power system has been accepted more and more in recent years for providing plenty of security information and good prospect in online application. This paper compares three linear approximations for the dynamic security region of network-reduction power systems. The three 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 L0-linear approximation based on the invariant assumption of the normal vector for the boundary of the stability region corresponding to different control variable. The three linear approximations are all obtained with a same critical point lying just on the boundary of dynamic security region. The critical point is searched with numerical simulation. The accuracy of the three linear approximations is compared, using the linear approximation obtained with the curve fitting approach or the actual boundary of DSR searched as the benchmark. Simulation results in IEEE 3-machine 9-bus system and 10-machine 39-bus New England system show that all the three linear approximations display fairly accurate estimation. Furthermore, from the computational viewpoint, the L-linear and the L0-linear method are two alternative choices to approximate the dynamic security region