A semi-empirical approach to performance mapping for load-based testing of air conditioners and heat pumps

Reliable performance representations are essential for realistic sizing, control, and digitalization of Heating, Ventilation, and Air Conditioning (HVAC) systems. However, conventional fixed-speed rating procedures do not capture control-driven behavior, while purely empirical or theoretical models often fail to balance accuracy, generalizability, and experimental effort. This study proposes a semi-empirical framework to map the performance of reversible air conditioners characterized through emulator-type load-based testing. The methodology combines first and second laws of thermodynamics with experimentally derived functionals of compressor efficiency, heat exchanger thermal conductances, and residual losses. Dynamic characteristics observed under load-based operation, including cycling and partial-load modulation, are embedded into the model through load-dependent auxiliary relations. Using only cooling/heating load, outdoor temperature, and indoor temperature set-point as inputs, the model estimates COP in both cooling and heating modes with deviations below 10%, achieving average errors around 3% in the eight-coefficient configuration. Increasing model complexity yields limited additional benefit, demonstrating that accurate and generalizable performance maps can be constructed from a reduced experimental dataset.