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 Tamb > -5°C,
and the efficiency increases with Tamb. 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.
Figure 2. Space-Conditioning and Water Heating Modes
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 . The system provides 10.5 kW (3 tons) of cooling at the standard
test condition, Tamb
= 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 Tamb
40°C, with a speed range of 30 < Wc
< 120 Hz. The isentropic
efficiency is taken from a 10.5 kW Dorin compressor and expressed as a function
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, TCO2 > TH2O or
air + 2°C, was enforced for the counter-flow water and indoor air heat exchangers.
For the air-conditioning season, the Tevap is maintained at 13.5°C
by modulating blower speed to meet sensible heat ratio target of 0.75 .
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 .
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
Figure 3. Water Heating Costs
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 Tamb
> 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 < Tamb
< 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 < Tamb
< 20°C. In the fourth
strategy, tandem operation between space heating and water heating cycles
is employed when -4 < Tamb
< 15°C. At Tamb
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 Tamb > 29°C (Pdis > 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 Tamb, 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 Tamb, which is inefficient.
At Tamb < 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 Tamb < 26°C,
meeting the daily cooling load in less than 24 hr. At Tamb = 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 Tamb < 20°C, the outdoor air is the sole heat source
for heating water and air. During the ventilation range, 15 < Tamb < 20°C,
the CO2 system is used only as a water heat pump. When space heating
demands start at Tamb < 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 < Tamb < 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.
Figure 4. Discharge and Suction Pressures
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
> 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
mass flow decreases along with the temperature difference
between the water inlet temperature and that of the CO2
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.
The optimal operating and control strategies appear to be more complex,
but this is partly an artifact of the need to make specific assumptions for
initial cycle analysis. In practice, the selection of sensors will determine
the complexity of the control system.