A least squares solution for optimal power flow sensitivity calculation

A least-squares-based algorithm is proposed that is suitable for post optimal power flow (OPF) sensitivity calculations. It computes Lagrange multipliers. The algorithm involves the formulation of a Lagrangian which includes the appropriate objective function and all the enforced constraints. By applying the Kuhn-Tucker conditions, the derivatives of the Lagrangian at the solution with respect to free variables provide a set of over-determined equations for the Lagrange multipliers. A least-squares estimation of the Lagrange multipliers with the over-determined set of equations is used. The mathematical formulation of the least-squares problem for the sensitivity calculation is presented. A computationally efficient method of solving the normal equation is derived. Special care has been taken to accurately model all controls and all operating and security constraints. The algorithm has been tested on a reasonably large system. The results indicate the validity of the approach