Optimal power flow solutions using the gradient projection method. I. Theoretical basis

The authors look at the application of nonlinear programming, particularly the gradient projection method (GPM), to optimal power flow (OPF) problems. The proposed approach solves a sequence of linearly constrained optimisation problems by the GPM, each of which is iterated with the solution of the nonlinear equations of the constraint set. Among many advantages, the inequality constraints are directly handled in the GPM, without the necessity of artificial methods, such as the penalty function technique and makes it very easy to evaluate the step size. The authors present the theoretical foundations of the GPM in the context of variable reduction techniques and the use of orthogonal transformations to improve the numerical performance of the GPM