Electricity Pricing Theory Based on Continuous Time Commodity Model

The recent national conversation on the resiliency of the electric grid and existing RTO/ISO tariffs in U.S. prompt us to re-examine the pricing theories applied in electricity market design. The theory of spot pricing is the basis of electricity market design in many countries, but it has two major drawbacks: one is that it is still based on the traditional hourly scheduling/dispatch model, ignores the crucial time continuity in electric power production and consumption and causes difficulties concerning bidding and operation for market participants; the second is that it assumes that the electricity products are homogeneous in the same trading period and cannot distinguish the base, intermediate and peak power with obviously different technical and economic characteristics. To overcome the shortcomings, this paper presents an new electricity pricing theory based on continuous time commodity model, including spot pricing model and load duration model. The market optimization models under the two pricing mechanisms are established with the Riemann and Lebesgue integrals respectively and the functional optimization problem are solved by the Euler-Lagrange equations to obtain the market equilibria. The feasibility of pricing according to load duration is proved by strict mathematical derivation. Case study shows that load duration pricing can correctly identify and value different attributes of generators, reduce the total electricity purchasing cost, and distribute profits among the power plants more equitably. The theory and methods proposed in this paper will provide new ideas and theoretical foundation for the development of electric power markets.