| 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.; 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 problem. The major contributions of our research are as follows. First, we develop the multivariate model not just for transportation type models of electric power network flows, but also for the direct current power flow model. 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. 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, we need wedge shaped regions (a wedge is the affine image of an orthant). We give an algorithm for decomposing any polyhedral set into wedges. Fifth, 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. |
