Extended opportunity cost model to find near equilibrium electricity prices under non-convexities

Abstract

This paper finds near equilibrium prices for electricity markets with non-convexities due to binary variables, in order to reduce the market participants’ opportunity costs, such as generators’ unrecovered costs. The opportunity cost is defined as the difference between the profit when the instructions of the market operator are followed and when the market participants can freely make their own decisions based on the market prices. We use the minimum complementarity approximation to the minimum total opportunity cost model, from previous research, with tests on a much more realistic unit commitment model than in previous research, including features such as reserve requirements, ramping constraints, and minimum-up and -down times. The developed model incorporates flexible price-responsive demand, as in previous research, but since not all demand is price responsive, we consider the more realistic case that total demand is a mixture of fixed and flexible. Another improvement over previous minimum total opportunity cost research is computational: whereas the previous research had nonconvex terms among the objective function’s continuous variables, we convert the objective to an equivalent form that contains only linear and convex quadratic terms in the continuous variables, thus allowing for efficient optimization by CPLEX.We compare the unit commitment model with the standard social welfare optimization version of unit commitment, in a series of sensitivity analyses, varying flexible demand to represent varying degrees of future penetration of electric vehicles and smart appliances, different ratios of generation availability, and different values of transmission line capacities to consider possible congestions. The minimum total opportunity cost and social welfare solutions are mostly very close in different scenarios, except in some extreme cases; the obtained solution has smaller opportunity costs than social welfare, at very little cost in reduction of social welfare; and solution times of the minimum total opportunity cost model are longer, due to a larger model size, but the times are still very quick for practical use.