To mitigate stress imposed on power grids by air source heat pumps (ASHP) during peak electricity demand periods, a time-phase operated heat pump heating system integrated with phase change heat storage was proposed and developed. A control strategy coupling the phase change temperature of the heat storage module (Tp) with indoor temperature (Ti) was implemented using a PLC-based control module. System performance, under heat storage, heat release, and heating-only modes was experimentally evaluated across multiple operating condition. Continuous dynamic experiments over several days were conducted to determine temperature thresholds of the heat storage module and analyze system dynamic behavior, energy efficiency, and temperature stability. Results demonstrate that the proposed system provides stable and continuous heating, maintaining indoor temperatures within 18.0-20.0°C. The heat storage module showed stable heat storage and release performance within 40.0-44.0°C. The actual operating temperature threshold was lower than the material phase change temperature due to thermal resistance. During peak electricity demand periods, household heating can be achieved exclusively by the heat storage module, resulting in near-zero electricity consumption. During mid-peak periods, the heat pump operates in heating-only mode for approximately 35% of the total operating time. The proposed system demonstrates strong robustness during 72 h of continuous operation, improving heating stability by 40% during peak periods and reducing the daily operating time of the heat pump by 25%. Economic analysis indicates that the proposed system achieves a cost reduction of 19% compared with conventional ASHP systems, highlighting its potential for practical application.