EMF Publications

EMF SR 6 Computation of Electric Power Production Cost with Transmission Constraints

Occasional Paper

Robert L. Earle

Published by
Stanford University, 1996

The production cost in operating an electric power system is the cost of generation to meet the customer load or demand. Production costing models are used in analysis of electric power systems to estimate this cost for various purposes such as evaluating long-term investments in generating capacity, contracts for sales, purchases, or trades of power. A multi-area production costing model includes the effects of transmission constraints in calculating costs. Including transmission constraints in production costing models is important because the electric power industry is interconnected and trades or sales of power amongst systems can lower costs. Moreover, the ongoing deregulation of the power industry and growth of a more open market for power make the need to explicitly account for the effects of transmission on costs more vital.

This thesis develops an analytical model for multi-area production costing. The advantage of this approach is that it explicitly examines the underlying structure of the problems. The major contributions of our research are as follows. First, we develop the multivariate model not just for transportation type of models or electric power network flows, but also for the direct current power flow model. This overcomes the objection that power flows are unrealistically modeled by a transportation network. Most of the competing approaches suffer from this problem. In fact, with the approach developed here, other exogenous restrictions could be placed on the system subject to some conditions. Second, this thesis derives the multi-area production cost curve in the general case. This new result gives a simple formula for determination of system cost and the gradient of cost with respect to transmission capacities. Third, we give an algorithm for generating the non-redundant constraints from a Gale-Hoffman type region. The Gale-Hoffman conditions characterize feasibility of flow in a network. This is useful not only in calculating readability, but it turns out that in order to calculate the system cost we integrate over Gale-Hoffman type regions as well. As a result, for many broad classes of networks, enormous computational effort is saved. We also gather together some existing and new results on Gale-Hoffman regions and put them in a unified framework. Fourth, in order to derive the multi-area production cost curves and also to perform the integration of the multivariate Edgeworth series, an asymptotic series used to represent probability densities, we need wedge shape regions (a wedge is the affine image of an orthant). We give an algorithm for decomposing any polyhedral set into wedges. Fifth, multivariate integration of the normal distribution is a problem with importance in many areas and central to calculation of the production cost. This thesis gives a new method for one-dimensional numerical integration of the trivariate normal. The best methods previously known were only able to reduce the problem to a two dimensional numerical integration.