Problem
We want to study the possibility to buy a battery system to store some power when possible. This will allow to satisfy power demand when solar and wind are not enough available and hydro power alone is not enough. Moreover, it reduces the risk to not satisfy the demand in case of a generator failure. Batteries can have various capacities. From a market study, we consider that 2500 euros per kWh is a relevant average price. The battery technology have a lifetime of about 18 months, considering hourly charge and discharge cycles. The electric components used to store the power (between the generators and the battery system and from the battery and the power delivery sink) have a global efficiency of 88%.
This new battery within the grid may allow to shutdown the most expensive generators when enough power has been stored. Nevertheless, we want to keep at least 25kWh in the battery at the end of the 24 hours. With historical data about wind and solar conditions, we have globally excellent production conditions about 22% of the time (ie. >75% of maximum power) and bad conditions about 15% of the time (ie <30% of maximum power). The demand given for 24h can be considered of an average demand over the year. Season effects are neglected in this analysis.
Define the mathematical problem allowing to size battery storage and solve it using python (scipy optimize)
Update your model to optimize the energy production taking into account this new battery using Python