The use of high-conductivity porous medium is an effective method to enhance the heat transfer rate of phase change material (PCM) in thermal energy storage (TES), reducing the energy consumption of low-carbon buildings. This paper establishes a solid-liquid phase change lattice Boltzmann model of a TES unit and investigates the effects of Rayleigh number, inclination angle, porous array, and porosity. The findings indicate that inserting the porous medium enhances conductive heat transfer and weakens convective heat transfer. When the Rayleigh number is increased from 103 to 104, the liquid fraction increases by 3.0%, while an increase from 104 to 105 only results in a 1.6% increase, suggesting a diminishing effect of increasing the Rayleigh number. Results also show that the inclination angle can be disregarded in this study. Furthermore, increasing the specific surface area enhances conductive heat transfer. However, when the array n is changed to 7, the fastest variation of liquid fraction is obtained among the range from 5 to 9. Increasing the porosity will delay the moment that temperature standard deviation reaches to the maximum, getting the temperature distribution more nonuniform. The findings from this paper are valuable for the design of TES systems in low-carbon buildings. Practical application The porous medium can enhance heat transfer in the phase change process. In the field of low-carbon buildings, porous medium is applied to strengthen the energy storage rate. By investigating the parameters of the Rayleigh numbers, inclination angles, porosities and arrangement of porous medium arrays of the composed energy storage unit, the regularity of the effects on the energy characteristics are obtained, which would provide some valuable practice references for designing these parameters of the energy storage units in the future energy-efficient building sector.