A Semi-smooth Projected Levenberg-Marquardt Power Flow Method to Cope With the Constraints Exchange Issue

In the conventional power flow (PF) calculation, when using the PV-PQ bus switching to deal with the problem of the generator buses reactive power limits violation for power systems, this method may cause the power flow calculation to fail. If using the Fischer-Burmeister (FB) function to handle constraint exchange issues, then using the Newton-Raphson (NR) method to solve PF, this operation will lead to a slow convergence. In this paper, a semi-smooth projected Levenberg-Marquardt (PLM) power flow method based on the FB function to deal with the constraints exchange issues is proposed. This method can change the search direction when the constraint exchange positions are at sharp corners, and adjust the size of the trust region to prevent the power flow from divergence due to excessive step size in the iterative process, thus improving convergence and reliability. Furthermore, the traditional power flow calculation method is sensitive to the initial value, which may cause the PF divergence, however the method of PLM proposed in this paper is globally convergent, which is not sensitive to the initial value. Numerical tests implemented on a small 3-bus network and a modified IEEE 118-bus system show that the proposed method is more efficient and robust than existing methods.