Economic operation of power systems: Insight and efficiency gained by geometric representations

The economic scheduling of generation in power systems was traditionally performed by solving the equations of coordination while satisfying the constraint of power balance between load and total generation. Later, optimal load flow programs were developed to take into account generator voltages as control variables and different operational constraints. There is continuing interest in developing and improving these techniques. The present paper gives a unifying view of the above problems by a geometrical representation of the cost function by ellipsoids in the multi-dimensional space of generator powers. The power balance or load flow constraints are represented by a hypersurface and the optimum results as the point of tangency of these surfaces. The conclusions consist of recommendations for efficient computation of optimal load flows.