(372o) Optimal Energy Storage in Batteries: A Convex Formulation for Definition of Charge/Discharge Schedules

As technologies for systems for energy storage mature, consumers may take advantage of differential price signals to self-store energy when its grid-price is low and convert it back when the grid-price is high. This strategy has been proposed as a way of balancing consumption and supply of energy in modern renewable-based electricity markets, as at a grid level, companies face the problem of having a non-programmable supply of energy, but a quite defined consumption pattern. In addition, compared to demand response energy self-storage is a superior strategy, as it does not disrupt consumers’ habits. Because of their simplicity, batteries are usually the first choice for small/medium scale storage. Wide adoption of this strategy requires that over the long term, savings due to displacement of the time that energy is consumed (aka energy arbitrage), are larger than the purchase cost of the battery and accessories.

In this work, we propose a convex optimization problem to define the charge/discharge schedule of a battery, under the assumption that the user will employ it to defer grid-energy consumption under a Time-of-Use (TOU) pricing. The model takes as parameters: the consumption pattern, the tariff schedule, efficiencies for charge and discharge, and, to preserve the life of the battery, includes maximum and minimum bounds for the state of charge values. Apart from being a convex formulation, that guarantees convergence to the global optimum, the model has the novelty of including the degradation of the battery, which has effects on the economics of the process due to a shortage in both battery lifetime and performance. For modelling the degradation, we considered a term proportional to the battery’s total energy throughput, and a term proportional to the charge/discharge rates. The decision variables of the model are hourly charge/discharge powers and the state of health (SoH) fraction that is lost by the battery at each time. For the objective function we considered a compound function which accounted for the cost of replacement of the battery, measured indirectly by the capacity lost in each charge/discharge cycle, and a term that accounted for the money saved by taking advantage of the TOU pricing.

The optimization problem was implemented in GAMS and solved with IPOPT. We employed literature data of new Li-ion batteries SoH losses for different charge/discharge rates to estimate degradation parameters. The simulations were run using California complex tariffs/schedules with several time steps during a single day and seasonal variation, the Uruguayan simple 2-3 step tariffs, and different assumed initial battery prices. Our results indicate that in complex tariffs optimal schedules depend on the battery cost, whereas in simple tariffs there is a limiting battery price for which operation is not worth as the degradation cost associated with turning on the battery surpasses savings due to energy arbitrage. Still, even if the battery price is below this limit positive NPVs are not guaranteed. Simulations to calculate maximum battery prices that may result in positive NPVs were run assuming simple tariff schedules: in the scenarios considered maximum battery values should be in the order of 150 USD/kWh.

Note: The results that will be presented in this talk were partially published in Processes 2018, 6(10), 204; https://doi.org/10.3390/pr6100204