An Analytical Formula for Small Signal Stability Sensitivity Using SDP Dual
IEEE TRANSACTIONS ON POWER SYSTEMS(2024)
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.
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Key words
Stability criteria,Numerical stability,Power system stability,Sensitivity,Thermal stability,Mathematical models,Indexes,Small-signal stability,stability sensitivity,Lyapunov equation,SDP,duality
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