Dynamic simulation of a transcritical CO2 heat pump with vapor injection in reciprocating compressors (Voorhees cycle) under off-design operating conditions

Transcritical CO2 heat pumps equipped with vapor injection in the cylinder of a reciprocating compressor (Voorhees cycle) are a promising low-carbon heating technology, but their off-design behavior and optimal control have not been investigated so far. This paper presents a dynamic model of a CO2 heat pump based on a Flash-Tank Vapor Injection Voorhees cycle, developed in the Simulink/Simscape environment. The reciprocating compressor, equipped with a solenoid injection valve, is represented by a customized Simscape component in which the volumetric efficiencies, the discharge enthalpy, and the mechanical power are evaluated by an Artificial Neural Network (ANN) trained on a detailed lumped-parameter compressor model; this decouples the fast compressor cycle from the slower thermodynamic cycle and enables stable coupled simulation. An Extremum Seeking Control (ESC) algorithm is implemented to track the gas cooler pressure that maximizes the Coefficient of Performance in real time, without a plant model. Across six off-design boundary conditions spanning both directions of variation of each external variable, the ESC identifies the optimum within 0.5 % of the brute-force maximum, and the resulting trends of intermediate pressure, COP, and flash-tank vapor quality agree with previously published steady-state results, confirming the internal consistency of the model and its suitability for optimal control of transcritical Voorhees heat pumps.