Wrobel, Andrzej Jerzy
(2006)
The formal theory of pricing and investment for electricity.
PhD thesis, London School of Economics and Political Science (United Kingdom).
Abstract
The Thesis develops the framework of competitive equilibrium in infinitedimensional commodity and price spaces, and applies it to the problems of electricity pricing and investment in the generating system. Alternative choices of the spaces are discussed for two different approaches to the price singularities that occur with pointed output peaks. Thermal generation costs are studied first, by using the mathematical methods of convex calculus and majorisation theory, a.k.a. rearrangement theory. Next, the thermal technology, pumped storage and hydroelectric generation are studied by duality methods of linear and convex programming. These are applied to the problems of operation and valuation of plants, and of river flows. For storage and hydro plants, both problems are approached by shadowpricing the energy stock, and when the given electricity price is a continuous function of time, the plants' capacities, and in the case of hydro also the river flows, are shown to have definite and separate marginal values. These are used to determine the optimum investment. A shortrun approach to longrun equilibrium is then developed for pricing a differentiated good such as electricity. As one tool, the WongViner Envelope Theorem is extended to the case of convex but nondifferentiable costs by using the shortrun profit function and the profitimputed values of the fixed inputs, and by using the subdifferential as a multivalued, generalised derivative. The theorem applies readily to purely thermal electricity generation. But in general the shortrun approach builds on solutions to the primaldual pair of plant operation and valuation problems, and it is this framework that is applied to the case of electricity generated by thermal, hydro and pumpedstorage plants. This gives, as part of the longrun equilibrium solution, a sound method of valuing the fixed assetsin this case, the river flows and the sites suitable for reservoirs.
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