Wind power generation has increased in China to achieve the target of decreasing CO2 emissions by 2050, but there are high levels of wind curtailment due to the mismatch between electricity supply and demand. This paper proposes a single-stage air source heat pump coupled with thermal storage for building heating purposes. The main objective is to find the proper system designs and operating strategy, which can help to avoid peak demand periods while obtaining minimized running costs and reduced wind energy curtailment. Dynamic simulations were performed using TRNSYS to investigate its use in a typical office building based on an actual electricity tariff, wind power, and meteorological data. The proper system designs, including the tank size and thermal storage temperature, were determined to maximize the system’s performance. It was found that a proper combination of the two parameters exists for a specific application. Further, results showed that the use of auxiliary electric heating is necessary for single-stage air source heat pumps to participate in a wind curtailment reduction. The operating strategy of the system was also studied. Results indicate that by implementing a proper operating strategy, non-renewable power consumption can be reduced by 11% for the studied building, with a total wind power utilization of 3348 kWh during the heating season while still satisfying the heating demands of users. These findings can contribute to the green and low-carbon development of the building industry and further enhance the grid’s accommodation capacity for renewable energy sources.