Heat pumps have the potential to reduce CO2 emissions due to building heating when compared to fossil-based heating (e.g. natural gas, oil, wood), specifically when used in regions with low-CO2 electrical generation. In many regions, emissions from the electric grid tend to peak during peak demand periods due to the dispatching of fossil-based generation. The design of buildings as distributed thermal storage units can act to diminish the peaks in the grid, reduce the overall CO2 emissions from residential heating, increase the utilization of low-CO2 technologies (nuclear, hydro, wind, solar, etc....), while maintaining the thermal comfort of the occupants. This study is concerned with how thermal energy storage can be integrated into heat pump systems to improve demand flexibility, and ultimately allow the heating system to remain off during peak periods. Heat pumps tend to operate under a limited temperature range, which limits the energy storage density of water as a thermal storage medium. Phase change materials (PCM) can be used as thermal storage, and they benefit from the ability to maintain a high energy density under limited temperature conditions. The challenge is that PCMs have a relatively low thermal conductivity which can limit the rate of charging and discharging of the stored thermal energy. In the current state-of-the-art literature, there is no standard methodology to size PCM thermal energy storage units for heat pump systems. This study presents novel results that compare numerical and analytical predictions of a hybrid PCM-water thermal storage tank, and proposes a reduced analytical methodology for sizing PCM thermal storage tanks for heat pumps used for demand side management. System-level numerical simulations, considering the transient complexities of the melting and solidification process in a system environment, are compared against a simplified analytical predictions of thermal storage performance. Storage tanks containing 75% PCM modules of 2 cm thickness were able to reduce storage volume by over three-fold of water-only storage operating under a Delta T=10 degrees C. Peak periods ranging between 2 and 6 h in a residential household were sustained when the appropriate storage volume is used. Analytical methods for estimating the required volume are presented that ease the storage sizing and discuss the expected benefits and their limitation. (C) 2019 Elsevier B.V. All rights reserved.