Bi-objective optimization of transcritical CO2 heat pump systems

For the transcritical CO2 heat pump cycle, the gas cooler (GC) pressure can be controlled independently and it can be optimized for optimum COP. Control correlations can be developed offline either based on simulations or experiments or optimization can be done online in real time with continuous pressure and temperature measurements at different locations. The online methods provide more accurate results than the offline correlations, however, they have a long convergence time to the optimum value, especially if the initial GC pressure condition is far away from the optimum. In this paper, we investigate the transcritical cycle as a bi-objective optimization problem where COP and cooling/heating capacity are conflicting objectives with primarily optimizing the GC pressure for maximum cycle COP and maximum cooling or heating capacity which can be useful for transient conditions. The Non-Dominated Sorting Genetic Algorithm (NSGA-II) is used, which generates for different operating conditions the best non-dominated solutions i.e. the Pareto Front that includes the maximum COP, max cooling capacity, and also the intermediate optimum trade-off solutions. The effect on the Pareto Front of each optimization variable; GC outlet temperature, evaporation temperature, evaporator useful superheat, and compressor speed is shown separately, where all except superheat have a significant effect on the Pareto Front. A control methodology is proposed where according to a pre-defined preference, steady-state or transient operation, an optimization parameter is set to either maximize cooling or heating capacity (e.g. obtaining comfort as soon as possible in transient operation), maximize COP (for minimum energy consumption) or operate at a trade-off point as desired. The proposed approach can be applied as an offline control method and it can also be integrated as a hybrid solution with any online optimization method. In both, whenever a new condition is imposed, the offline based bi-objective algorithm will provide a very close estimate of the optimum GC pressure. In a hybrid solution, the online optimizer will then start searching for the true optimum from this very close value and hence reach much faster to the true optimum value. Thus, yielding enhanced capabilities (bi-objective optimization of COP and Q˙c), and in a hybrid solution, additionally further enhanced accuracy (vs offline) with reduced convergence time to the optimum COP and Q˙c (vs online only). A gain to loss ratio in terms of the conflicting objectives (COP and capacity) is presented that can be used as a criteria for deciding whether to move from one solution to another on the Pareto Front.