Residential heat pump as flexible load for direct control service with parametrized duration and rebound effect

This paper addresses the problem of an aggregator controlling residential heat pumps to offer a direct control flexibility service. The service consists of a power modulation, upward or downward, that is activated at a given time period over a fixed number of periods. The service modulation is relative to an optimized baseline that minimizes the energy costs. The load modulation is directly followed by a constrained rebound effect, consisting of a delay time with no deviations from the baseline consumption and a payback time to return to the baseline state. The potential amount of modulation and the constrained rebound effect are computed by solving mixed integer linear problems. Within these problems, the thermal behavior of the building is modeled by an equivalent thermal network made of resistances and lumped capacitances. Simulations are performed for different sets of buildings typical of the Belgian residential building stock and are presented in terms of achievable modulation amplitude, deviations from the baseline and associated costs. A cluster of one hundred ideal buildings, corresponding to retrofitted freestanding houses, is then chosen to investigate the influence of each parameter defined within the service. Results show that with a set of one hundred heat pumps, a load aggregator could expect to harvest mean modulation amplitudes of up to 138 kW for an upward modulation and up to 51 kW for a downward modulation. The obtained values strongly depend on the proposed flexibility service. For example, they can decrease down to 2.6 kW and 0.4 kW, respectively, if no rebound effect is allowed.