Cost-effective tariff-aware HVAC coordination in Saudi residential buildings using physics-informed deep reinforcement learning

Abstract

Abstract When multiple On/Off split air-conditioning units in Saudi residential buildings activate simultaneously, the resulting peak demand spike stresses the electrical grid and inflates monthly bills under the kingdom’s two-tier tariff (0.18 SAR/kWh $$\leq$$ 6,000 kWh; 0.30 SAR/kWh above). This paper proposes a Physics-Informed Proximal Policy Optimization (PI-PPO) framework that learns a stationary scheduling policy—time-invariant within a given operating season, so that it applies over an indefinite horizon without re-solving any optimization at each step (a separate policy is trained per representative month to reflect seasonal weather)—to coordinate 18,500 BTU On/Off split units (1.8 kW input, EER 10.25) across multiple zones. Each zone is abstracted as a scheduling task with formally analyzed minimum utilization and feasibility conditions. The model incorporates inter-zone thermal coupling, enabling the scheduler to exploit thermal buffering through shared walls. PI-PPO embeds the zone heat-balance equations directly into the reinforcement learning reward, providing a dense physical signal that guides the agent toward feasible schedules. We evaluate the framework in a lumped-parameter RC thermal simulation of Saudi residential buildings driven by representative diurnal profiles for four months (January, April, July, October). Under a realistic strict comfort band ( $$23{-}25^\circ\textrm{C}$$ ), which reflects occupant expectations in an extreme-heat climate, coordinated scheduling yields modest but consistent cost reductions relative to uncoordinated On/Off thermostatic control—approximately 4.3% for a 5-zone villa in July under the strict comfort band, and only about 1.0% for a larger 20-zone building whose cooling demand approaches thermal saturation; extending the comfort band raises these to roughly 13.4% and 7.8% respectively, as the scheduler reduces consumption billed at the higher tariff tier. Because the Saudi tariff is a two-tier inclining-block structure, the framework produces a tariff-multiplier effect: for buildings whose consumption sits near the 6,000 kWh threshold, a small reduction in energy translates into a proportionally larger reduction in the monthly bill. Our results also delineate the limits of coordination: in thermally saturated hot-climate buildings under a tight comfort band, compressors must run near-continuously, leaving little scheduling slack and correspondingly limited savings. All results are produced by a released, reproducible simulation under the actual Saudi two-tier tariff, a tight comfort band, and a competent baseline, so the reported savings reflect deliberately realistic conditions. We report these bounds together with a component-contribution decomposition of the reward terms and a cross-tariff sensitivity analysis (the operative two-tier step-wise tariff versus linear and exponential alternatives).