Influence of Load Curve Slope on Clearing Prices of Continuous-Time Commodity Electricity Market

With the increasingly large-scale integration of renewable energies, the existed electricity markets are faced with new challenges. The recent national conversation on the resiliency of the electric grid and existing RTO/ISO tariffs in U.S. also prompt us to re-examine the electricity market design. The electricity markets in Australia and Europe have problems also. 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, and thus has difficulties in dealing with the crucial time continuity in electric power production / consumption; 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 different technical and economic characteristics. To overcome the shortcomings, a new electricity pricing theory based on continuous time commodity model is proposed by the authors, 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 market equilibria are obtained by solving the Euler-Lagrange equations of the related functional optimization problems. The feasibility of pricing according to load duration is proved by both strict mathematical derivation and case study, which can correctly identify and value different attributes of generators and increase market efficiency. In particular, the influence of load curve slope on clearing prices under the two pricing mechanisms are analyzed.