Electricity Market Theory Based on Continuous Time Commodity Model
📝 Abstract
The recent research report of U.S. Department of Energy prompts 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 does not treat the inter-temporal constraints seriously; the second is that it assumes that the electricity products are homogeneous in the same dispatch period and cannot distinguish the base, intermediate and peak power with obviously different technical and economic characteristics. To overcome the shortcomings, this paper presents a continuous time commodity model of electricity, 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 equation to obtain the market equilibria. The feasibility of pricing according to load duration is proved by strict mathematical derivation. Simulation results show 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.
💡 Analysis
The recent research report of U.S. Department of Energy prompts 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 does not treat the inter-temporal constraints seriously; the second is that it assumes that the electricity products are homogeneous in the same dispatch period and cannot distinguish the base, intermediate and peak power with obviously different technical and economic characteristics. To overcome the shortcomings, this paper presents a continuous time commodity model of electricity, 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 equation to obtain the market equilibria. The feasibility of pricing according to load duration is proved by strict mathematical derivation. Simulation results show 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.
📄 Content
Electricity Market Theory Based on Continuous Time Commodity Model
Haoyong Chen1, Lijia Han2
1Institute of Power Economics and Electricity Markets, South China University of Technology,
Guangzhou 510641, China. Email: eehychen@scut.edu.cn
2Mathematical & Physical Science School, North China Electric Power University,
Beijing 102206, China. Email: hljmath@ncepu.edu.cn
Abstract
The recent research report of U.S. Department of Energy prompts 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 does not treat the intertemporal constraints seriously; the second is that it assumes that the electricity products are homogeneous in the same dispatch period and cannot distinguish the base, intermediate and peak power with obviously different technical and economic characteristics. To overcome the shortcomings, this paper presents a continuous time commodity model of electricity, 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 equation to obtain the market equilibria. The feasibility of pricing according to load duration is proved by strict mathematical derivation. Simulation results show 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.
Keyword: Electricity markets, Spot pricing, Load duration, Functional optimization
- Introduction In the letter of United States Secretary of Energy Rick Perry (Perry [2017]) to Federal Energy Regulatory Commission (FERC) on September 28, 2017, it is addressed that short-run markets may not provide adequate price signals to ensure long-term investments in appropriately configured capacity. Also, resource valuations tend not to incorporate superordinate network and/or social values such as enhancing resilience into resource or wires into investment decision making. The increased important of system resilience to overall grid reliability may require adjustments to market mechanisms that enable better valuation. This conclusion is quoted from Quadrennial Energy Review (QER [2017]). Furthermore, the current wholesale market price formation rules are also doubted. Rick Perry urges FERC to take immediate action to ensure that the reliability and resiliency attributes of generation with on-site fuel supplies are fully valued and develop new market rules that will achieve this urgent objective. In the U.S. Department of Energy’s Staff Report to the Secretary (DOE [2017]), the problems with the current wholesale electricity markets and the relationship to reliability/resilience of power grids are investigated and several important findings are reported. It is suggested that FERC should expedite its efforts with states, RTO/ISOs, and other stakeholders to improve energy price formation in centrally-organized wholesale electricity markets. Energy price formation reform is supported after several years of fact finding and technical conferences. DOE staff identified several research topics including market structure and pricing mechanism for enabling equitable, value-based remuneration for desired grid attributes. The definition of electricity commodity model, cost structure and price formation mechanism are the most basic problems regardless of market structure. As the physical indifference (electricity produced by the power plants cannot be separated once injected into the power grid), and the existence of the complex physical network (power system), electricity becomes the world’s most complex commodity. So the definition and pricing theory of electricity commodity are not so obvious. Spot Pricing of Electricity published in 1988 by Prof. F. C. Schweppe of the Massachusetts Institute of Technology is the classic literature of electricity pricing theory and became the theoretical basis of spot electricity market design in different countries (Schweppe [1988]). Electricity price theory research should be divided into two parts, namely, electricity cost analysis (that is, what is a reasonable price) and electricity price formation mechanism in electricity markets. In the ideal electricity market, the clearing price should be equal to the marginal cost of power plants and marginal utility of power users. The theory of spot pric
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