Estimating Transient Stability Regions of Large-Scale Power Systems Part II: Reduced-Order Stability Region with Computational Efficiency

Part II of this paper presents a reduced-order stability region (ROSR) based method to estimate the full-order stability region (FOSR) of a large-scale power system. First, we introduce the definitions of FOSR and ROSR, followed by a comprehensive theory that reveals the relationships between them. Since the full-order system can be rewritten as a standard two timescale model and the reduced-order system is regarded as the slow subsystem of it, the proposed theory is derived based on the idea of singular perturbation. With rigorous mathematical proof, the properties of FOSR and ROSR are revealed. Moreover, a modified Energy Augmented Dynamic (EAD) algorithm and a constrained equidistant projection (CEP) approach are employed to estimate the ROSR and FOSR, respectively. The modified EAD algorithm and CEP form a so-called reduced-order stability region mapping (ROSRM) method. Finally, the proposed ROSRM method is applied to the IEEE 10-machine-39-bus power system, and simulation studies confirm its superiority to the traditional energy function method in terms of computational speed and reliability of results.