Space cooling is the main contributor to high electrical power demand in summer. This research investigates the effect of adding a phase change thermal energy storage unit (PCTSU) to an air source heat pump (HP) cooling system. The HP model improves on an existing model in the simulation software library to simulate the HP performance. The PCTSU performance is simulated using a newly developed two-dimensional transient heat transfer model, which is experimentally validated against available experimental results. The cooling system is operated in three modes to satisfy the space cooling demand of a 7.6 stars house in the City of Adelaide, Australia. The PCTSU is charged by the HP when outdoor temperature is relatively low and discharged either whenever space cooling is required during the day (mode M2) or during the peak period only (mode M3). The simulation is conducted for the whole cooling season, and the cooling energy and electricity usage performances of the system with a PCTSU (modes M2 and M3) are compared with those of the system without a PCTSU (mode M1). A sensitivity analysis reveals that the PCTSU performance is slightly sensitive to the uncertainties of melting temperature of the phase change material and to the inlet temperature of the heat transfer fluid. The PCTSU provides 25% and 13% of the cooling energy and requires 11% and 6% of the electrical energy usage for charging by the HP in modes M2 and M3 respectively. Both electricity usage and demand tariffs are considered, and the cost savings are 14% and 7% in the former and 14% and 13% in the latter, in modes M2 and M3 respectively. The cost analysis indicates that techno-economic benefits of using PCTSUs should be carefully analysed. Appropriate economic incentives are needed to accelerate the uptake of thermal storage for space cooling applications to reduce high electrical power demand and help to avoid the need to further increase the grid capacity.