Economic nonlinear MPC for a population of thermostatically controlled loads

Thermostatically controlled loads, including heat pumps, electrical space heaters, air-conditioners, electrical boilers, and refrigerators, have a large potential to provide regulation services to energy systems. In this paper, we design a price-responsive control system for aggregating and coordinating a population of thermostatically controlled loads, each with a relatively small power consumption. The goal is to shift electricity consumption of the whole group to the periods with low electricity prices. Model predictive control is an advanced control method, which can naturally include electricity price and weather forecasts as well as the dynamics of the loads into the control problem. The main challenge is to find an accurate aggregate model describing demand response of the population. The proposed solution is a nonlinear modification of bin state transition model, which is further used for formulating nonlinear mixed integer optimization problem. The control objective is to minimize operational cost of the population. As a case study, we consider a population of electrical space heaters. The numerical simulations demonstrate the accuracy of the obtained model and that the proposed control system reduces the operational cost up to 20%, whereas the customer comfort is not compromised.