The objectives of this work are: (a) to present a new system for building heating which is based on underground energy storage, (b) to develop a mathematical model of the system, and (c) to optimise the energy performance of the system. The system includes Photovoltaic Thermal Hybrid Solar Panels (PVT) panels with cooling, an evacuated solar collector and a water-to-water heat pump. Additionally, storage tanks, placed underground, are used to store the waste heat from PVT panels cooling. The thermal energy produced by the solar collectors is used for both domestic hot water preparation and thermal energy storage. Both PVT panels and solar collectors are assembled with a sun-tracking system to achieve the highest possible solar energy gain. Optimisation of the proposed system is considered to achieve the highest Renewable Energy Sources (RES) share during the heating period. Because the resulting optimisation problem is nonlinear, the classical gradient-based optimisation algorithm gives solutions that are not satisfying. As alternatives, three heuristic global optimisation methods are considered: the Genetic Algorithm (GA), the Particle Swarm Optimisation (PSO) algorithm, and the Jaya algorithm. It is shown that the Jaya algorithm outperforms the GA and PSO methods. The most significant result is that 93% of thermal energy is covered by using the underground energy storage unit consisting of two tanks.