Analytical static voltage stability boundary based on holomorphic embedding

Abstract

This paper proposes a novel analytical method to calculate the Static Voltage Stability Boundary (SVSB) for power systems as a hypersurface in a high-dimensional space on power flow solutions. First, the proposed method derives the analytical voltage solution of AC power flows in the form of Multivariate Power Series (MPS) using the Multidimensional Holomorphic Embedding Method (MDHEM). Second, based on the Cauchy-Hadamard theorem, the proposed method is able to derive an analytical expression of the SVSB using the obtained voltage MPS. Besides, a theoretical proof is given in this paper to generalize the proposed method from unidimensional to multidimensional scenarios. In general, the SVSB is found to be analyzable and its analytical expression can be derived offline. Therefore, in the online stage, the proposed method can be used to judge the feasibility of operating conditions very quickly. IEEE 14-bus system, New England 39-bus system, and IEEE 118-bus system are adopted to validate the effectiveness of the proposed method.