Optimal power flow using a generalized power balance constraint

The paper presents a new method for optimal power flow calculations, using the generalized power balance constraint, obtained from the power flow equations by elimination of all state variables. The reduced optimization problem in the control variables is subsequently decoupled into two stages: a primary stage in the primary control variables (generator active power injections) and a secondary stage mainly in the secondary control variables (generator voltages). The primary stage is solved by economic generation scheduling, where the power system losses are accounted for by the coefficients of the generalized power balance constraint. The secondary stage is solved by linear programming, subject to all power system constraints. The linear programming formulation is such that the solution of the primary stage is maintained, if feasible, or otherwise optimally adjusted. Thus, the method takes full advantage of decoupling, if it is applicable, and otherwise inherently reverts to a coupled approach. A step-limit control strategy successfully damps the oscillations that are always present in successive linear programming, and ensures the optimality and feasibility of the solution.