A Jacobian-free Newton-GMRES(m) method with adaptive preconditioner and its application for power flow calculations

In this paper, an adaptive preconditioner is constructed for Jacobian-free Newton-GMRES(m) [JFNG(m)] methods, which is devised for solving coordination equations in distributed simulations of power systems. The preconditioner is updated during both Newton iterations and GMRES iterations by means of a rank-one update algorithm. The proposed preconditioned JFNG(m) is applied to power flow calculations for test. The results show that the adaptive preconditioner can enhance convergence of Newton-GMRES(m) iteration schemes greatly and has stronger robustness compared with other precondition methods. Moreover, the proposed method has strong parallelism and scalability, which makes it feasible to solve distributed simulation problems of power systems.