Shifting residential space heating from the use of gas boilers towards the use of heat pumps is recognized as a method to reduce green house gas emissions and increase energy efficiency and the share of renewable energy sources. Demand response of these systems could aid in reducing peak loads on the electricity grid. Extra flexibility can be added in the form of a thermal energy storage tank. This paper proposes a multi-objective model predictive control strategy for such a system, which takes into account the users energy cost, the environmental impact of energy use and the impact of expanding the electricity generation capacity. This control strategy is used in a case study inspired by the Belgian electricity generation park with 500,000 heat pumps to investigate the effect of the size of a space heating storage tank on consumer cost, energy use and required electricity generation capacity. Results indicate that the proposed demand response strategy reduces the required peak load capacity substantially with only a small increase in costs for the consumer. When adding a large hot water storage tank, the required additional capacity is nearly eliminated. Independently of the required capacity, the controller shifts energy use from peak to base generating plants. Increasing the storage tank size increases the amount of energy that is shifted. However, when demand response is applied by using a space heating storage tank, the costs for the consumer always increase relative to the case without demand response or storage tank. If demand response is desired by the grid operator, heat pump owners should be encouraged to participate by remunerating them for their additional expenses. (C) 2017 Elsevier Ltd. All rights reserved.