Abstract
A fundamental planning problem is considered for an air-to-air heat pump system which is composed of compressor, indoor and outdoor coils, fans, expansion valve, and so forth. First, physical relationships of the objective system are formulated mathematically by investigating heat cycle and mass flew relationships of the system. Then, a multiobjective optimal planning problem is formulated by assuming full and partial loads for space heating and air-cooling. In this optimization problem, the following two mutually incommensurable designing objectives are formulated as objective functions; i.e., (a) to minimize the total cost of equipment necessary to construct the heart pump system, and (b) to minimize the annual amount of energy consumption necessary to drive the system. As constraints in the optimization procedure, following several conditions are considered: 1) Heat cycle and mass flow relationships of the system corresponding to each load level for air-conditioning. 2) Constraints concerning permissible level of noise generated from indoor and outdoor fans. 3) Some additional constraints concerning upper and lower limits of refrigerant's temperatures at several cycle points so as to avoid the generation of frost at the evaporator and so forth. In the above-mentioned optimization problem, the following two cases are investigated concerning control methods of the system for partial loads. Case-A: In this case, an inverter is assumed to be installed to control the system for partial loads. In this system, the discharge amount of refrigerant is changed by the compressor's volume control, and air-flow capacity of both indoor and outdoor fans are also assumed to be controlled. Case-B: In this case, the system is operated for partial loads by adopting a simple on-off control device. By involving the system's optimal operational problem for partial loads, the optimal system's designing problem is formulated as a multiobjective nonlinear optimization problem. By adopting both the weighting method and the generalized reduced gradient algorithm, the set of Pareto optimal solutions is derived for two cases concerning system's control mentioned above. In other words, the design variables concerning system's construction are determined optimally together with optimal control policy for partial loads. Through a numerical study by using the optimal planning method proposed here, it is ascertained that two design objectives investigated here are obviously conflicting to each other, and the designer can determine design variables rationally by analyzing the trade-off relationship between design objectives mentioned above. It is also recognized the advantageous point of control Case-A compared with Case-B though the cost is still high to equip an inverter control device into the system. Through this numerical calculation, both validity and effectiveness are ascertained of the optimal planning method proposed here compared with the conventional trial-and-error designing method.
