Figure 1. “Ideal� Simultaneous Air-Conditioning and Water Heating Cycle

This paper presents an idealized residential system that meets domestic water and space conditioning demands (see Figure 1). The ideal system presented heats water to U.S. domestic storage temperatures of 60°C, in addition to meeting residential heating and cooling loads. Using simplified thermodynamic calculations and assumptions, optimal system operation strategies and configurations were identified for both heating and cooling seasons. The results provide a basis for more detailed system simulations that can focus on optimizing actual heat exchanger hardware design.

The optimal operating strategy varies throughout the year because the transcritical CO₂ cycle exhibits a COP-maximizing discharge pressure, with a discharge temperature above or below the desired hot water temperature. Optimization algorithms are used to identify the most efficient operating condition. Water heating costs can be reduced to a third of electric resistance at T_amb > -5°C, and the efficiency increases with T_amb. After reviewing the assumptions made, an overview will be given of the various operation strategies and hardware configurations selected by climate season. Each operating strategy based on ambient climate will be examined in detail. Summaries of system parameters, such as high and low end CO₂ pressures and temperatures, will provide ideal system parameters that provide the starting point for more detailed system simulation and control studies of the space-conditioning and water-heating system.

Assumptions

A number of assumptions were made in order to greatly simplify cycle calculations and the optimizations, which were performed using Engineering Equation Solver (EES). Heating and cooling loads were based on an overall UA value from a moderately insulated house, approximated as linearly dependent on ambient temperature [6]. The system provides 10.5 kW (3 tons) of cooling at the standard test condition, T_amb = 35°C. The heating and cooling lines meet at 18°C, and it is assumed that ventilation suffices between 15°C and 20°C. A minimum water heating capacity of 4 kW is desired, matching common electric resistance heaters that meet the 12.1 kWh/day average U.S. domestic hot water demand in 3 hr. The compressor was sized for maximum displacement at T_amb = 40°C, with a speed range of 30 < W_c < 120 Hz. The isentropic efficiency is taken from a 10.5 kW Dorin compressor and expressed as a function of P_dis/P_suc.

Assumptions for the cooling season are summarized in Figure 2, which shows a CO₂ T-h diagram for simultaneous air conditioning (a/c) and water heating (WH). A pinch limit, T_CO2  > T_H2O or air + 2°C, was enforced for the counter-flow water and indoor air heat exchangers. For the air-conditioning season, the T_evap is maintained at 13.5°C by modulating blower speed to meet sensible heat ratio target of 0.75 [1]. The outdoor coil is cross-flow and assumed large enough to cool CO₂ to a 2°C approach at any ambient air temperature. An internal heat exchanger (IHX), assumed to have 0.9 effectiveness, proves beneficial as cooling loads increase. Pressure drop is neglected in all heat exchangers.

A simplified heat-pump cycle can be used for space heating (SH) or water heating. During heating season, UA = 3.6 was assumed for the outdoor coil, based on an airflow rate and geometry from a previously simulated coil [1]. Space-heating air is supplied to the room at 40°C and returned at 20°C. Water is heated from 17°C supply to 60°C delivery temperatures.

It is recommended that the IHX be bypassed in the heat-pump cycle because the highly superheated suction gas produces a higher compressor discharge temperature that could risk compressor oil breakdown; the impact on COP is negligible.

Overview of Optimized System

Five distinct operating strategies are needed for this optimized system, as will be detailed later in Figure 5. The first two strategies apply to the a/c and WH cycle. For T_amb > 23.5°C, indoor air is the sole heat source for water heating. The water inlet valve to the heater is simply opened for simultaneous air-conditioning and water heating, and closed during a/c-only operation. At 20 < T_amb < 23.5°C, insufficient heat is available in the indoor air; therefore, a combination of indoor and outdoor air heat sources may be used. Thus, a third operation strategy is needed, using the CO₂ system as a water-only heat pump during a/c off-cycle time. The system continues to act as a water heat pump during the ventilation season, 15 < T_amb < 20°C. In the fourth strategy, tandem operation between space heating and water heating cycles is employed when -4 < T_amb < 15°C. At T_amb < -4°C, the system reaches maximum capacity, and space heating loads must be met using a fifth strategy, providing water heat and supplementary space heat with an electric resistance heater.

Adding water heating to the overall CO₂ system reduces the water heating cost by 2/3 or more compared to the 12 kWh/day needed by electric resistance. Figure 3 shows the cost of adding water heating load to the CO₂ refrigerant system; the incremental COP ranges from 3 to 16. Cost declines with rising evaporating temperature as the outdoor temperature increases. One-stage water heating was found to be optimal or nearly optimal for all seasons, with the CO₂ -to-H2O heat exchanger placed immediately downstream of the compressor. Where the water source is colder, it may be cost-effective to add a pre-heater because a colder heat sink increases cycle efficiency. Water heating times are influenced by compressor speeds, but are always faster than electric resistance.

At T_amb > 29°C (P_dis > 75 bar), there is abundant heat rejection to the air due to the sizable a/c loads, and the COP-maximizing discharge pressure for the a/c only cycle is high enough to heat water to 60°C. Therefore, water heating is free. The 3-hr water heating time constraint determines how much of the high-side refrigerant temperature profile is needed for water heating (4 kW). The rest of the heat is rejected to air in the gas cooler downstream. As a/c load decreases with T_amb, the COP-maximizing high side pressure decreases. When it reaches 75 bar at 29°C, the temperature difference between CO₂ and water approaches the pinching limit and water heating is still free because no extra compressor work is needed. CO₂ flows through the refrigerant side of the water heater continuously, while water flows through it for 3 hr per day and is then shut off for the remaining 21 hr. Rejecting all heat to the water would result in much faster heating times, but it is less efficient because the high-side discharge pressure would be 94.4 bar, regardless of T_amb, which is inefficient.

At T_amb < 29°C, the COP-maximizing discharge pressure at these moderate-load conditions is sufficient for a/c-only, but too low to heat water to 60°C. Therefore, added compression energy is required in order to limit water-heating time to 3 hr. At 26°C, the compressor speed reaches its (lubrication limited) minimum of 30 Hz. Compressor cycling occurs at T_amb < 26°C, meeting the daily cooling load in less than 24 hr. At T_amb = 23.5°C, the air-conditioning and water-heating system runs only 3 hr per day, with all 4 kW of heat rejection going to water heating. As ambient temperature drops and less heat is being removed from the building, the water-heating-only system compensates for the shortfall of the indoor air energy source.

When T_amb < 20°C, the outdoor air is the sole heat source for heating water and air. During the ventilation range, 15 < T_amb < 20°C, the CO₂ system is used only as a water heat pump. When space heating demands start at T_amb < 15°C, water heating at 30 Hz may be performed in tandem with space heating, because heating loads are small at mild temperatures, off-cycle time is abundant. The space heating and water heating (30 Hz) times total 24 hr at 10.2°C.

At -4 < T_amb < 10.2°C, the space and water heating system configurations operate continuously in tandem at a common minimum compressor speed until the compressor reaches the maximum 120-Hz speed limit at around -4°C. Consequently, as compressor speed increases to meet higher space-heating demands on increasingly colder days, the water heating time will decrease.

The cycle state points are dictated by the compressor speed, which determines water and space heating capacity. While the compressor runs at constant speed, the transitions are accomplished by the back-pressure valve adjusting Pdis from approximately 75 to 90 bar in order to maximize COP for space heating and water heating, respectively. Suction and discharge pressures are shown in Figure 4.

Choosing Optimal System Configurations

The total cost of water heating using one- or two-stage water heating strategies is very similar. For two-stage water heating, in which refrigerant flows through a pre-heater downstream of the outdoor coil, system efficiency is increased by the presence of this additional heat sink, saving about 1 kWh/day at T_amb > 28°C. Only in very hot climates would this small benefit offset the cost and complexity of the extra refrigerant circuit through the water heater. Benefits would also be larger in cities where water supply temperature is lower or hot water capacity demands are large. During cooler ambient conditions, there is very little heat rejection to preheat sink because the CO₂ mass flow decreases along with the temperature difference between the water inlet temperature and that of the CO₂ exiting the outdoor coil.

For the heating season, a simultaneous one-stage space heating and water heating strategy was compared to a tandem space heating and water heating operation and was found to save only about 0.5 kWh/day. Tandem mode is more efficient because the discharge pressure can be optimized for space heating and water heating independently.