I want to run a Simulation in Matlab that involves the running costs of an electronic device which consists of the power consumption of this said device. The simulation should run for the next 1-5 years. Since the (daily/monthly/yearly) \$/kWh electricity prices are not constant over time, my thought was to model them using a stochastic process which captures the changes over time. I want to calibrate the parameters of said stochastic process using historical data of $/kWh electricity prices.
Upon my research I found a lot about the modeling of electricity spot prices (e.g. Comparison of Electricity Spot Price Modelling and Risk Management Applications), but from my understanding (and please correct me if I am wrong) electricity spot prices do not reflect/represent \$/kWh electricity prices that I need for the running costs calculations. The explanations about mean-reverting models in different paper of spot price modeling are sound, however I am yet to find something that models \$/kWh electricity prices. I even thought about using Geometric Brownian Motion to simulate it, but in my opinion this would not fit.
Can someone point me in the right direction to a stochastic process that is frequently used to model $/kWh electricity prices and that can be used in my simulation?