Power Flow Analytical Solutions and Multi-Dimensional Voltage Stability Boundaries Based on Multivariate Quotient-Difference Method

This paper proposes a novel Multivariate Quotient-Difference (MQD) method to obtain the approximate analytical solution for AC power flow equations. Therefore, in the online environment, the power flow solutions covering different operating conditions can be directly obtained by plugging values into multiple symbolic variables, such that the power injections and consumptions of selected buses or areas can be independently adjusted. This method first derives a power flow solution through a Multivariate Power Series (MPS). Next, the MQD method is applied to transform the obtained MPS to a Multivariate Padé Approximants (MPA) to expand the Radius of Convergence (ROC), so that the accuracy of the derived analytical solution can be significantly increased. In addition, the hypersurface of the voltage stability boundary can be identified by an analytical formula obtained from the coefficients of MPA. This direct method for power flow solutions and voltage stability boundaries is fast for many online applications, since such analytical solutions can be derived offline and evaluated online by only plugging values into the symbolic variables according to the actual operating conditions. The proposed method is validated in detail on New England 39-bus and IEEE 118-bus systems with independent load variations in multi-regions.