Fast Calculation of Saddle-Node Bifurcation Point in Islanded Microgrid Based on Levenberg-Marquardt Algorithm

This paper proposes two fast calculation algorithms for the determination of the saddle-node bifurcation point of islanded microgrids, which use bisection search and parabolic approximation respectively. The Levenberg-Marquardt algorithm is applied to obtain the least-squares solution in the infeasible region of power flow equations. The bisection search algorithm uses the least-squares solution to determine whether the current trial step reaches the power flow infeasible region, and finally approaches the saddle-node bifurcation point. The parabolic approximation algorithm performs a parabolic approximation to ‘the least-squares value’ – ‘load margin’ curve in the infeasible region, and the zero point of the curve is corresponding to the required saddle-node bifurcation point. The case analysis shows that the two algorithms proposed in this paper have the advantages of high accuracy, high computational efficiency, and strong robustness.