Long-term Equilibrium in Electricity Markets with Renewables and Energy Storage Only

Guillaume Tarel, Magnus KorpÄs, and Audun Botterud

September 2022

In this paper, we study the optimal generation mix in power systems where only two technologies are available: variable renewable energy (VRE) and electric energy storage (EES). By using a net load duration curve approach, we formulate a least-cost optimization model in which EES is only limited by its power capacity. We solve this problem analytically and find least-cost and market equilibrium conditions that lead to the optimal capacities of VRE and EES. We show that, mathematically, an electricity price structure that depends on the period of the year (i.e. EES charging or discharging, VRE curtailment, load shedding) and on investments costs leads to cost recovery for VRE and EES. We show that when EES is the marginal technology (either charging or discharging) the price must be non-zero. More specifically, the equilibrium prices during EES charge or discharge are functions of the EES and VRE fixed costs. We confirm our analytical findings using a numerical model. We argue that, although the system we study is hypothetical and simplified, our findings provide insights and research directions for how to recover fixed costs in a future electricity market based on VRE and EES only.

Keywords: electricity markets, optimality conditions, market equilibrium, variable renewable energy, energy storage system, duration curve model