This paper examines a Renewable Energy Community (REC) made up of 10 dwellings that collectively self-consume energy produced by a photovoltaic field connected to a water purifier. Each dwelling heat demand is satisfied by means of Heat Pump (HP) coupled with Thermal Energy Storage (TES), which can be managed to perform load shifting and increase collective-self-consumption (CSC). Techno-economic analyses are performed accounting for HPs' COP variation with temperature and part load operations, as well as TES heat dispersion. A new centralised control strategy for HPs is proposed and a sensitivity analysis is performed to assess the impact of varying TES system capacity. The results show that the centralised strategy can increase the CSC by 12-30%, with TES sizes of 100-1000 litres respectively. But the electricity consumption of HPs increases by 2-5% due to higher storage system temperatures causing worse average COPs by 2.3-0.6% and higher thermal losses by 29-58%. As a result, REC's energy independence rise, as does the amount of CSC incentives, but electricity bills also increase. Comparing these trends shows that CSC incentives should be adjusted according to energy prices to ensure cost-effective outcomes for all stakeholders and encourage the adoption of similar centralised control strategies.