Optimal power flow by a nonlinear complementarity method

A nonlinear complementarity method for solving nonlinear optimal power flow problems is presented. This method stems from proposed reformulation of complementarity problems as nonlinear systems of equations which age, in turn, solved by a Newton-type method. To reformulate optimal power flow problems as nonlinear systems of equations we employ a function ψ_μ: ℛ²→ℛ that satisfies the property ψ_μ(a,b)=0⇔a>0, b>0 and ab=μ, for any μ>0. Then, unlike interior-point methods, the new method handles the complementarity conditions for optimality, s_i⩾0, π _i/⩾0 and s_iπ_i=0, without requiring that s_i>0 and π_i>0 be satisfied at every iterate. Numerical results illustrate the viability of the proposed method as applied to several power networks. A comparison with two interior-point algorithms is discussed