Application of non-linear programming for large-scale AC-DC power flow analysis

This paper proposes a robust, non-divergent model for large-scale AC-DC power flow analysis. By introducing relaxation variables into power flow equations, the conventional power flow model is turned into a non-linear programming model to minimize the L₂ norm of the relaxation variables subject to operation constraints and DC station control modes. The interior point method (IPM) is used to solve the model. Due to the special structure of the proposed model, the size of coefficient of correction equations in the IPM can be reduced to the same as Jacobian in the conventional Newton method. Further, the coefficient is symmetrical positive-definite with a diagonal perturbation, which leads to a better convergence than Newton direction. The model and algorithm proposed also have the following features: (1) no special initial value is needed; (2) strong robustness for power grids with plenty of small/negative impedance; (3) applicable for searching a desirable operation point by appropriate settings of inequality constraints; (4) striving for ultimate close to power flow solution avoiding to stop too early at a local minimizer. Numerical simulations on a 6527 buses power grid in China with 8 HVDC lines show that the proposed model has robust convergent property in the feasible region, around the boundary of the feasible region and even beyond the feasible region of power flow.