Stochastic Processes wtih respect to the electric load demand
Your analysis is correct as far as it goes.

You could probably make a model that's much closer to being ergodic, if you're willing to declare some external factors (such as folks' bedtimes, temperature, and external lighting) as known inputs rather than as intrinsic elements of your random process.  I suspect that's an uphill battle (how do you deal with holidays, and post-holiday hangovers?), but you should certainly be able to get things a lot closer if you were motivated.