In future energy systems with high shares of renewable energy sources, the electricity demand of buildings has to react to the fluctuating electricity generation in view of stability. As buildings consume one-third of global energy and almost half of this energy accounts for Heating, Ventilation, and Air Conditioning (HVAC) systems, HVAC are suitable for shifting their electricity consumption in time. To this end, intelligent control strategies are necessary as the conventional control of HVAC is not optimized for the actual demand of occupants and the current situation in the electricity grid. In this paper, we present the novel multi-zone controller Price Storage Control (PSC) that not only considers room-individual Occupants' Thermal Satisfaction (OTS), but also the available energy storage, and energy prices. The main feature of PSC is that it does not need a building model or forecasts of future demands to derive the control actions for multiple rooms in a building. For comparison, we use an ideal, error-free Model Predictive Control (MPC) and a conventional hysteresis-based two-point control as upper and lower benchmarks, respectively. We evaluate the three controllers in a multi-zone environment for cooling a building in summer and consider two different scenarios that differ in how much the permitted temperatures vary. The results show that PSC strongly outperforms the conventional control approach in both scenarios with regard to the electricity costs and OTS. It leads to 50 % costs reduction and 15 % comfort improvements while the ideal MPC achieves costs reductions of 58 % and comfort improvements of 29 %. Considering that PSC does not need any building model or forecast, as opposed to MPC, the results support the suitability of our developed control strategy for controlling HVAC systems in future energy systems.