Modeling and analysis of bistable behavior in a transcritical heat pump

Effective marketing motivates this control study to understand the multiplicity of stable solutions in a transcritical heat pump where in prototype units two steady states exist (very efficient, and inefficient). Control oriented modelling, originating from first principles highlights the state-dependent heat transfer coefficient in the evaporator dynamics as a contributing cause to this bistable phenomena. Specifically, the bilinear nature of the controlled gas cooler and its coupling to the dynamic nonlinearity in the evaporator induces a system-wide bifurcation in the equilibrium conditions. Model results are presented to illustrate this, along with steady-state and dynamic data to confirm the accuracy of the model.