Closed-form solution for optimal REC reallocation with peak costs

Derive a closed-form solution for the optimal reallocation scheme that minimizes the global renewable energy community (REC) bill when offtake and injection peak fees are included, where the decision variables are per-member allocations of net production and received community production at each market period, bounded by each member’s net consumption or net production and constrained so that total reallocated community production is conserved in each market period.

Background

The paper formulates the optimal reallocation scheme used by the Energy Community Manager (ECM) to minimize the sum of ex-post electricity bills (“global REC bill”) by allocating REC production among members across market periods within a billing period. The objective includes retailer buying/selling costs, REC fees on internal exchanges, and peak offtake/injection fees measured after reallocation. When peak fees are set to zero, the authors show the scheme can be solved by a greedy algorithm. However, with nonzero peak fees, the authors explicitly state that they did not identify any closed-form solution, leaving the problem unresolved.

A closed-form solution in the presence of peak costs would enable faster and more scalable computation of optimal allocations, which is valuable both for real-time community operation and for training reinforcement learning policies that rely on repeated evaluations of the reallocation scheme.

References

Despite our efforts, we did not identify any closed-form solution of the optimal reallocation scheme problem.

— Optimal Control of Renewable Energy Communities subject to Network Peak Fees with Model Predictive Control and Reinforcement Learning Algorithms  (2401.16321 - Aittahar et al., 2024) in Appendix: Illustrative examples of the optimal reallocation scheme, Subsection “REC with peaks costs”