Optimal coordination of multiple price-maker electricity storage units for price arbitrage
Solà Vilalta, Albert
Decarbonization of the electricity supply via the integration of renewable generation poses significant challenges for electric power systems, but also creates new market opportunities. Electric energy storage can take advantage of these opportunities while providing flexibility to power systems that can help address these challenges. This thesis is concerned with the optimal coordination of multiple price-maker electric energy storage units that cooperate to maximize their total profit from price arbitrage. The case of a single unit has already been considered in the literature, where an efficient algorithm to solve one-unit problems is provided. The contribution of this thesis is the study of the multiple storage units case. This problem is interesting because, in practice, the total storage capacity in an electric power system is distributed across several storage units. As we show with a counterexample, multiple storage units cannot, in general, be aggregated into a single storage unit. The price-maker assumption introduces a nonlinearity to the problem. This nonlinearity complicates the interactions between the storage units because the action taken by a storage unit affects the price of electricity seen by all storage units. We propose two novel solution methods for the optimal control of multiple price-maker electric energy storage units that cooperate to maximize their total profit from price arbitrage. These new methods tackle the nonlinearity introduced by the price-maker assumption and can handle positive and negative electricity prices. Both methods exploit on the fly time decompositions that only need limited future price information, similar to the decomposition in time provided by the one-unit algorithm from the literature. The first solution method computes solutions that satisfy Lagrangian Sufficiency Conditions for optimality using a nested search on Lagrange multipliers and associated solutions. The decomposition in time obtained by the method is driven by the storage unit with the largest energy to power ratio. In principle, this solution method is suitable for any number of units, but, in practice, the nested structure results in prohibitive computational times for three or more units. Furthermore, including round-trip efficiencies or leakage of the storage units in this method is challenging and threatens convergence even in the case of two units. The second solution method combines a decomposition by unit and a decomposition in time. The decomposition by unit is based on the Alternating Direction Method of Multipliers and breaks the problem into several one-unit subproblems. Every subproblem is solved using the efficient one-unit algorithm from the literature that exploits an on the fly decomposition in time, and this results in a time decomposition for the whole solution method. It can account for round-trip efficiencies and leakage of the storage units because the decomposition by unit reduces it to solving several one-unit problems iteratively. Our numerical experiments show very promising performance in terms of accuracy and computational time. In particular, they suggest that computational time scales linearly with the number of storage units.