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 Pad´e 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.

Orbiting Optimization Model for Tracking Voltage Security Region Boundary in Bulk Power Grids

A voltage security region(VSR)is a powerful tool for monitoring the voltage security in bulk power grids with high penetration of renewables.It can prevent cascading failures in wind power integration areas caused by serious over or low voltage problems.The bottlenecks of a VSR for practical applications are computational efficiency and accuracy.To bridge these gaps,a general optimization model for tracking a voltage security region boundary(VSRB)in bulk power grids is developed in this paper in accordance with the topological characteristics of the VSRB.First,the initial VSRB point on the VSRB is examined with the traditional OPF by using the base case parameters as initial values.Then,the rest of the VSRB points on the VSRB are tracked one after another,with the proposed optimization model,by using the parameters of the tracked VSRB point as the initial value to explore its adjacent VSRB point.The proposed approach can significantly improve the computational efficiency of the VSRB tracking over the existing algorithms,and case studies,in the WECC 9-bus and the Polish 2736-bus test systems,demonstrate the high accuracy and efficiency of the proposed approach on exploring the VSRB.