Transcritical CO2 heat pumps (TCHPs) are regarded as an efficient and low-carbon solution for heating and hot water supply; however, their performance is highly dependent on appropriate control strategies under wide variations in ambient and water temperatures. In this study, a numerical investigation of a TCHP system operating under the original control strategy was first conducted for ambient temperatures ranging from −25 °C to 35 °C and outlet water temperatures from 30 °C to 70 °C. Based on the analysis, an optimal discharge pressure library control strategy considering segmented outlet water temperatures and multiple practical constraints (OPL-SWMC) is proposed. By optimizing the water tank configuration, the control strategies for cyclic and direct heating modes are unified, which simplifies system operation and control implementation. The effectiveness of the proposed OPL-SWMC strategy is further evaluated through a comparative study between fuzzy PID and conventional PID controllers. The results indicate that the OPL-SWMC strategy achieves a maximum coefficient of performance (COP) of 3.15, representing a 22.0% improvement compared with the original cyclic heating mode. In addition, the fuzzy PID controller significantly shortens the settling time of the discharge pressure to its optimal setpoint. Compared with the conventional PID controller, the settling time is reduced by 31.0%, 22.3%, and 30.2% at ambient temperatures of −25 °C, 15 °C, and 35 °C, respectively. Overall, the proposed OPL-SWMC strategy demonstrates robust operational stability and improved dynamic performance, providing a practical and effective control solution for TCHP systems operating under wide temperature conditions.
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