Power-current hybrid rectangular formulation for interior-point optimal power flow

A non-linear interior-point optimal power flow algorithm based on power-current hybrid mismatch formulation in rectangular coordinates is proposed. In the proposed algorithm, all buses are divided into two types: the buses with non-zero injections and the buses with zero injections. For the buses with non-zero injections, power flow equations are presented by power mismatch formulation. For the buses with zero injections, power flow equations are presented by current mismatch formulation. The proposed power-current hybrid formulation combines the advantages of both power mismatch and current mismatch formulations. For the buses with zero injections, the proposed hybrid formulation shares the advantages of current mismatch formulation: first-order derivatives of power flow equations become constants, second-order derivatives of power flow equations become zeros so that Jacobian and Hessian matrices of power flow equations are easier to compute. The hybrid mismatch formulation is also easier to handle the buses with non-zero injections than current mismatch formulation. Numerical studies on various testing systems indicate that the proposed hybrid formulation has better convergence performance and computational efficiency, especially for large-scale optical power flow problems with a large percentage of zero-injection buses.