An unfixed piecewise-optimal reactive power-flow model and its algorithm for AC-DC systems

A novel ac-dc optimal reactive power flow (ORPF) model with the generator capability limits is proposed. The objective is to minimize the total cost of generator reactive and active power outputs paid by an independent transmission company. In the model, the generator operation area is divided into four parts with each one having a different reactive output cost function. The boundaries between the four parts change with operation states of generators and are unfixed. The model is an unfixed piecewise mixed-integer nonlinear programming problem. A heuristic approach is introduced into the interior point method to solve the unfixed piecewise problem. The numerical results of six test systems that range in size from 14 to 2572 buses demonstrate the effectiveness of the proposed method.