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The demand for electricity has been rising significantly over the past years and it is expected to rise further in the coming years due to economic and societal development. Smart grid technology is being developed in order to meet the rising electricity requirement. In order for the smart grid to perform its full functions, the Energy Management Systems (EMSs), especially Home Energy Management Systems (HEMS) are essential. It is necessary to understand the energy demand of the loads and the energy supply either from the national grid or from renewable energy technologies. To facilitate the Demand Side Management (DSM), Heat Pumps (HP) and air conditioning systems are often utilised for heating and cooling in residential houses due to their high-efficiency power output and low CO2 emissions. This paper presents a program for a HEMS using a Particle Swarm Optimisation (PSO) algorithm. A HP is used as the load and the aim of the optimisation program is to minimise the operational cost, i.e., the cost of electricity, while maintaining end-user comfort levels. This paper also details an indoor thermal model for temperature update in the heat pump control program. Real measured data from the UK Government's Renewable Heat Premium Payment (RHPP) scheme was utilised to generate characteristic curves and equations that can represent the data. This paper compares different PSO variants with standard PSO and the unscheduled case calculated from the data for five winter days in 2019. Among all chosen algorithms, the Crossover Subswarm PSO (CSPSO) achieved an average saving of 25.61% compared with the cost calculated from the measured data with a short search time of 1576 ms for each subswarm. It is clear from this work that there is significant scope to reduce the cost of operating a HP while maintaining end user comfort levels. [ABSTRACT FROM AUTHOR]