Optimal Battery Charge Scheduling For Revenue Stacking Under Operational Constraints Via Energy Arbitrage

TL;DR

This work tackles optimal revenue stacking through energy arbitrage using battery storage in the Day-Ahead Market under practical constraints. It introduces a MILP framework that accommodates variable charging rates, battery degradation, and availability limits, driven by price forecasts and grid costs. The approach yields 80–90% of the theoretical maximum profits over a year across multiple European markets, with the Python/MILP implementation capable of generating daily schedules efficiently. The study highlights the impact of forecast window length and degradation on profitability and points to machine-learning forecasting as a path to further gains in practice.

Abstract

As the share of variable renewable energy sources increases in the electricity mix, new solutions are needed to build a flexible and reliable grid. Energy arbitrage with battery storage systems supports renewable energy integration into the grid by shifting demand and increasing the overall utilization of power production systems. In this paper, we propose a mixed integer linear programming model for energy arbitrage on the day-ahead market, that takes into account operational and availability constraints of asset owners willing to get an additional revenue stream from their storage asset. This approach optimally schedules the charge and discharge operations associated with the most profitable trading strategy, and achieves between 80% and 90% of the maximum obtainable profits considering one-year time horizons using the prices of electricity in multiple European countries including Germany, France, Italy, Denmark, and Spain.

Figures (8)

• Figure 1: Sample schedule for a 100 kWh battery, assuming no grid cost, a constant charge rate of 0.5W/Wh, and without any limit on the number of charging/discharging cycles
• Figure 2: Charging curve $f_c$ and discharging curve $f_d$ of a lithium-ion battery
• Figure 3: Max. positive SOC change $\overline{\Delta}$ (top) and min. negative SOC change $\underline{\Delta}$ (bottom) in one hour of charge as a function of $\text{SOC}$
• Figure 4: Profit achieved on one-year-long simulations on the 2022 electricity prices of different European countries
• Figure 5: Profit distributions using MILP-P (top) with $l=28$ and MILP-O (bottom) on the German electricity market for the whole year 2022