In this article a model of the electric power consumption in a multi-area power system is derived. The model is based on stochastic differential equations to mimic the stochastic behavior of electric power consumption in large systems. The developed model considers correlations between the consumptions in the different areas. A numerical example showing how to find the parameters of the process will be given. The load data used in the numerical example is hourly energy consumption data for the Nordic countries: Sweden, Norway, and Finland.