Some Applications of a New Approach to Loss Minimization in Electrical Utility Systems

In Appendix I, a computational procedure for the solution of economic load dispatching problems is developed. The equations are in generalized form in that the variables at any entering node to the network may be either the vector potential above ground or else the vector current entering the electric network. Generating station losses as well as electric network losses are included. 2. An example is presented in the body of the paper which involves three generators and two loads. The equations presented in Appendix I are adapted to fit this specific problem. In so doing, it was elected to replace the generalized variables by voltages above ground at all entering nodes on the electric network. 3. Numerical results for the example are presented in Appendix II. 4. The method presented in this paper requires the solution of simultaneous algebraicequations, some of which involve nonlinearities. Experience with the example suggests: (a) A Taylor's series expansion technique is applicable; (b) The selection of a starting point, in the multidimensional domain of the variables, that will lie near the point representing the actual solution, is of vital importance in assuring the rapid convergence of the calculations; (c) The selection of such a point may be achieved by computing a common incremental rate Pa' at the generating stations while neglecting the electric network losses, and then computing the electric potentials plus the Lagrange multipliers while assuming equal but unspecified incremental power rates for the generators.