We formulate generation capacity portfolio planning in the power grid as a least-cost optimization problem and derive analytical expressions for the optimality conditions for dispatchable generation, variable renewable energy (VRE), and energy storage systems (EES) using a generalized net load duration curve approach. This is done for different operational strategies for EES with and without VRE in the system. For all studied combinations of technologies and operational strategies, we show that all units, including VRE and EES, recover their costs and maximize their profits in the system optimum, for an ideal short-term electricity market based on marginal cost and scarcity pricing. We verify the analytical findings through a numerical example, which shows that the general net load duration curve approach gives identical results to a standard capacity expansion model with sequential operation of the generation and ESS units, under the assumption of limited power capacity but infinite energy capacity of EES. The results highlight that the net load duration curve models presented in this paper can be a useful supplement to more detailed simulation studies of markets with high penetration of VRE and EES, to better understand the underlying factors that determines the optimal capacity mix and profitability of each technology in energy-only electricity markets.
Keywords: electricity markets, optimality conditions, market equilibrium, variable renewable energy, energy storage system, duration curve model