Problems:
Batteries vs. Power Plants
(This question has little to do with optimization; it's just about the electric power industry). Visit
https://www.midwestiso.org/page/LMP+Contour+Map+%26+Data and look up the 5-minute real-time "LMP" (Locational Marginal Price) at the location DECO.MONROE3 I think that's the large coal-fired power plant in Monroe, MI. The LMP is essentially the Lagrange multiplier for a large NLP; it is also the wholesale price of electricity at that point. I believe the units are $/MWh.
Report the value you find, and the date/time you looked. Also, convert it to cents per kWh. The retail price for electricity (including distribution charges, taxes, etc.) is around 11 cents per kWh, just for comparison.
Also, consider buying an 20-pack of AA batteries for $10.86 (I got the price from walmart.com). Each AA battery contains, let's say, 2500 milli-Amp-hours, which when multiplied by 1.5 volts gives 3.75 Watt-hours.
How much are you paying per kWh?