I am trying to come up with an equation for electricity storage in buildings, establishing a relationship between cost ($) and size/power (MW). Would it be merely a function of size (Cost = X * size) or would there also be a "fixed" term (Cost = Y + X*size)? Initially the sizes would be 2, 4 and 6 MW and I have no restrictions on the technology/type of battery.
On an specific basis, it depends on the type of technology considered, e.g compressed air, batteries, flywheels and its installation cost as well as on the ratio between power and energy capacity in the given application according to the "Y + X*size" relation. However, the relationship with the application demand seems to be "X*size"-like. Annex 2 in this reference may bring some ideas about the matter,
http://www.irena.org/-/media/Files/IRENA/Agency/Publication/2017/Oct/IRENA_Electricity_Storage_Costs_2017.pdf
There is a relatively fixed cost from packaging/machining/connecting a system, a variable cost w.r.t. capacity, and a variable cost w.r.t. recharge rate and power generation (which themselves can be decoupled in a very few technologies). In some applications like Li-ion batteries the capacity and power density are closely coupled with relatively narrow parameter space, while in applications like flow batteries. There's overall a lot of parameter space, so one way of approaching it could be to pick a desired end capability and hard-stop specifications (e.g. requirements for 1 MW min power density and 4 MWh capacity, effectively no limit on footprint/volumetric energy density) and then go fitting technologies to that. Then, once there's a clear outlier or you have a close couple of candidates, you could vary the technology within the sub-class to better fit (e.g. trade-off of capex and lifetime for a desired cycle depth).
Depends upon the source from where the charging current is taken. Check literature explaining Electric Vehicles getting charged from Grid.
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