An Analytical Formula for Stability Sensitivity Using SDP Dual

TL;DR

This paper derives an analytical formula for stability sensitivity in power systems using SDP duality, offering more accurate and efficient evaluation compared to traditional methods.

Contribution

It introduces a novel analytical approach for stability sensitivity analysis in power systems based on SDP duality, reducing computational effort.

Findings

Enhanced accuracy of stability sensitivity evaluation

Reduced computational burden compared to numerical methods

Validated with microgrid case studies

Abstract

In this letter, we analytically investigate the sensitivity of stability index to its dependent variables in general power systems. Firstly, we give a small-signal model, the stability index is defined as the solution to a semidefinite program (SDP) based on the related Lyapunov equation. In case of stability, the stability index also characterizes the convergence rate of the system after disturbances. Then, by leveraging the duality of SDP, we deduce an analytical formula of the stability sensitivity to any entries of the system Jacobian matrix in terms of the SDP primal and dual variables. Unlike the traditional numerical perturbation method, the proposed sensitivity evaluation method is more accurate with a much lower computational burden. This letter applies a modified microgrid for comparative case studies. The results reveal the significant improvements on the accuracy and computational efficiency of stability sensitivity evaluation.