Multi-objective optimal control of an air-to-water heat pump for residential heating

Abstract

The current study investigates the optimal operation of an air-to-water heat pump system. To this end, the control problem is formulated as a classic optimal control or dynamic optimization problem. As conflicting objectives arise, namely, minimizing energy cost while maximizing thermal comfort, the optimization problem is tackled from a multi-objective optimization perspective. The adopted system model incorporates the building dynamics and the heat pump characteristics. Because of the state-dependency of the coefficient of performance (COP), the optimal control problem (OCP) is nonlinear. If the COP is approximated by a constant value, the OCP becomes convex, which is easier to solve. The current study investigates how this approximation affects the control performance. The optimal control problems are solved using the freely available Automatic Control And Dynamic Optimization toolkit ACADO. It is found that the lower the weighting factor for thermal discomfort is, the higher the discrepancy is between the nonlinear and convex OCP formulations. For a weighting factor resulting in a quadratic mean difference of 0.5°C between the zone temperature and its reference temperature, the difference in electricity cost amounts to 4% for a first scenario with fixed electricity price, and up to 6% for a second scenario with a day and night variation in electricity price.