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Rule-based thermostat design for night setback of heat pumps
036&5442/90 $3.00 + 0.00 Pergamon Press plc
Energy Vol. 15, No. 11, pp. 935-941, 1990 Printed in Great Britain
ERMOSTAT DFSIGN FOR NIGHT SETBACK OF HEAT PUMPS
ALLEN L. RUTZ+ Battelle 505 King Avenue Columbus. Ohio 43201 and MICHAEL J. MORAN Department of Mechanical Engineering The Ohio State University 206 West 18th Avenue Columbus, Ohio 43210 (Received April 23, 1990) Abstract- We introduce a computer model for testing heat-pump thermostat performance with regard to energy and cost savings due to night setback. Also introduced are two new control strategies for heat-pump night setback: (i) an inexpensive variation of existing control strategies and (ii) a rule-based control strategy using techniques of artificial intelligence. The computer model is based on a transient system model of the residence, heat-pump, and controller, in response to actual weather data. Seasonal energy usage and costs are computed for each control strategy, subject to the effects of variable heat-pump sizing. building thermal inertia, building heat loss, climatic region, and electric rate structure. Results show that night setback can reduce heating season costs in residential heat-pump systems if the control strategy takes into account the characteristics of both the heat-pump system and the building. If these factors are not considered, night setback can increase heat-pump operating costs. The rule-based control strategy consistently provides positive cost savings above other setback methods, and has the added potential of providing diagnostic information about both the heat-pump system and the residence. INTRODUCTION A commonly employed home-heating conservation technique is referred to as night setbackl*z*s and involves lowering the thermostat setpoint at night during the hours of sleep and subsequently raising the setpoint in the morning. Night setback is baaed on the hypothesis that the energy saved during the night, due to the reduced heating load, exceeds the energy required in the morning to reheat the residence. Electric heat-pumps, however, require careful control when using night setback. Because electric heatpumps typically use auxiliary heaters with electric resistance elements to meet high loads, such as those encountered during the morning reheat period, the standard night setback strategy can actually increase the operating cost of the heat-pump. Increased operating costs can also result from night setback if time of day electric rate structures lead to higher charges per kilowatt hour during the morning reheat period than are charged during the nighttime off-peak period. Accordingly, a perceived savings can translate into an actual loss. Several commercially available setback strategies exist for heat-pump thermostats.4*6 Most operate by computing a time at which to start the reheat process, known as the reheat time, usually from IS minutes to 4 hours prior to the time the desired setpoint temperature is to be attained. The performance of these devices varies, and increased complexity does not necessarily result in increased energy efficiency. OBJECTIVES The objectives of this paper are first to introduce a computer model for testing heat-pump thermostat performance with regard to energy and cost savings and then use the model to evaluate the following two new
+ To whom all correspondence should be sent. 935
U
936
L. Rurz and
MICHAEL
J.
MORAN
control strategies for heat-pump night setback: (i) an inexpensive variation of existing control strategies, and (ii) an adaptive, rule-based control strategy using techniques of artificial intelligence (AD6. Discussions of additional setback strategies are given inRef.7.Theenergy and cost savings achieved by the setback strategies are discussed, using the case of no night setback as a baseline. Heat-pump thermostat performance is evaluated using a mathematical model of the residential heat-pump system including the residence, heat-pump, thermostat, weather data, and energy cost data. The model has been developed on the basis of previous field and laboratory investigations, manufacturer’s product descriptions, recorded weather data, and utility rate structures. Thus, the integrated system model (in the form of an interactive computer program) provides a reasonable and validated prediction of the operating characteristics of the home heating system for the purpose of evaluating night setback. The two new setback control strategies have been developed on the basis of observations of the underlying engineering principles involved in heat-pump night setback, then tested and refined using the computer program. To ensure broad applicability of the rule-based algorithm, the energy and cost analysis was performed for residences of varying size and thermal inertia and in four different cities representing different climatic regions of the US and different electric rate structures.’ MATHEMATICAL MODEL DEVELOPMENT A description of the elements of the computer model is presented next. Full details are provided in Ref. 7. her Da$g The Weather Year for Energy Calculation* (WYEC) data from the American Society of Heating, Refrigeration and Air conditioning Engineers (ASHRAE) is used to represent the climatic regions’ listed in Table 1.
Table 1.
Climatic groups and representative cities.
. . wgv Flows The building energy flows are described by a one-node, lumped parameter model, assuming that the temperature of the indoor space T, is uniform throughout, the thermal mass (product of the building mass M and specific heat C,,) is constant, and the overall heat-transfer coefficient U for heat transfer between the building and the ambient environment at temperature T, is constant. The building energy rate balance takes the form
where Q denotes the total rate at which energy is provided to the building by the combined heat-pump system unit (the combination of heat-pump and auxiliary heaters). During cooldown, the heat-pump system is off and Q in Eq.( I) is zero: the building load is met by depleting the energy stored, and the building temperature declines. Denoting the building temperature at an initial time tr by T,, and the temperature at any subsequent time tz by T,,, the time interval required for the building temperature to change from T,, to Tn,, while the ambient temperature remains constant, is then
‘2-G
=
5) ( ”
In(
*Ku-?i T,-T,).
(2)
During reheat, all of the energy needed to return the thermal mass to the original setpoint temperature is supplied to the residence in addition to the building load that exists during the reheat period. The total rate at which energy is provided to the house from the combined heat-pump system while the house is being reheated from initial temperature T,, at time t, to final temperature Tns at time ts is’
Rule-based
thermostat design for night setback of heat pumps
Q =
fJ[r,-l”-K$$],
937
(3)
where
(4)
The climatic regions used in the analysis have already been described. Two building heat loss coefficients, 666.67 Btu/hr-F and 1000 Btu/hr-F, were selected as representative of typical northern and southern loads, respectively.” Two building thermal mass values have been calculated based on approximations of residential mass distribution2 of 6 Ib/sq.ft, residential mass average specific heat of 0.35 Btu/lb-F, and two residence sizes of 1400 square feet and 2800 square feet, yielding approximate building thermal mass values of 3000 Btu/F and 6000 Btu/F. Thermostat Ooeration During reheat, the thermostat calls for energy from the combined heat-pump system according to a recovery Degradation of heat-pump temperature curve specified by the type of setback under consideration. performance due to cycling losses is ignored since all strategies for night setback tend to reduce cycling losses. Ignoring the reduced cycling losses will not significantly impact a comparison of setback strategies and will provide a measure of conservatism in the statement of energy savings due to night setback. Costs Energy cost structures were obtained from utilities located in the cities listed in Table 1 for the winter season (October through May) of 1988/1989, assuming residential usage in all electric homes. Although none of the utilities contacted have time-of-day rates now in place, several indicated that higher electric rates exist for customers with both electric and gas service. Feat-Pumo Performance Heat-pump performance data are provided by the manufacturer in the form of a steady-state heating capacity of the heat-pump alone, QHp, and steady-state coefficient of performance of the heat-pump alone, COP,,, including the degradation of steady-state capacity and coefficient of performance due to defrosting and cycling.“‘ts The coefficient of performance of the auxiliary heaters is taken to be unity. The steady-state coefficient of performance of the combined heat-pump system is therefore COP - COP,
COP = rZOPm%
for QsQ,.
+ l.O(l
-%),
for Q > QBT,
where Q is calculated from Eq.( 1) with dT,/dt - 0. At ambient temperatures below the balance point temperature (the temperature at which the heat-pump capacity equals the steady-state building load, see Fig. l), the heat-pump runs continuously to take maximum advantage of the high heat-pump coefficient of performance COP,, and reduce cycling. Auxiliary heat is invoked to meet only the portion of the load above the heat-pump capacity; then the combined system heat capacity Q equals the building load. This process is characteristic of the operation of high-efficiency heatpumps. At ambient temperatures above the balance point, the heat-pump alone is sufficient to meet the load; thus, COP = COP,, in Eq.(S). At ambient temperatures below the balance point, the system coefficient of performance COP is degraded by the auxiliary heaters to a value less than COP,, as shown by Eq. (5). Therefore, reducing the steady-state building load by lowering the thermostat setpoint results in a lower balance point temperature, effectively raising the operating coefficient of performance of the heat-pump system. stem Model
The input to the computer program consists of specifying the city (climatic region and electric rate structure), the heat-pump (from a range of capacities), the overall building heat transfer coefficient, building thermal mass, normal thermostat setpoint. start time of setback. thermostat setpoint during setback, and end time of setback. Output consists of monthly and seasonal energy usage and costs. A complete listing of the model source code is available.’
938
ALLEN
L.
RWIZand
MI-L
J. MORAN
NEW SETBACK CONTROL STRATEGY DEVELOPMENT Based on observations of the performance of heat-pump systems in actual residences, setback control strategies should take edvantage of the following generalizations: (i) It is preferable to use heat-pump energy (COP,, > 1.0) rdther than resistance heat energy (coefficient of performance = l.O), (ii) Daily ambient temperature variations are typically cyclic with maxima occurring between 11 AM and 4 PM and minima occurring around 6 or 7 AM, (iii) The longer the setback period, the greater the potential for savings. Qne-Hour Stra&gy The first new setback strategy to be introduced is a variation of existing strategies which represents a lowcost alternative to sophisticated controllers, especially for retrofit applications. Rather than resetting the residence temperature abruptly, the heat-pump system is allowed one hour over which to reheat the residence. The temperature is increased linearly over the hour. This strategy, referred to as the One-Hour Strategy, allows the heat-pump to supply a significant portion of the reheat energy, depending on the outdoor temperature, at a higher coefficient of performance than the resistance heat alone provides.
Rule-Based StraAza The second new strategy is considerably more complex in that it uses an adaptive, rule-based algorithm, the rules of which are developed based on the generalizations listed previously. The rules and their form of implementation are outlined next with an idealized representation of the rule-based strategy shown in the top portion of Fig. 1, giving the reheat time for four distinct intervals of ambient temperature. Comoutation of the Maximum Reheat Time A longer reheat period allows the heat-pump to provide energy at a higher coefficient of performance than would be realized when using resistance heat alone. On the other hand, a longer reheat period entails a greater building load during the reheat period. Accordingly, there is a tradeoff which places an upper limit on the reheat time. This is the maximum reheat time, t,. Using the mathematical model described previously, the following expression has been developed for the cases under consideration:
where T,, is the set point temperature and t,, is in hours. Equation (6) shows quantitatively that as the thermal mass of the residence increases t,, increases to accommodate the proportionally larger reheat load. Likewise, as the temperature difference to be overcome by reheat increases, t,, increases. As the overall heat transfer coefficient increases, however, t,, decreases, thus emphasizing the increased benefit of setback for residences with large heat losses. For the cases considered, t,, is generally between 2.5 and 5.0 hours. Commutation of the Minimum Reheat Time The minimum reheat time tInin is used in situations of very cold outdoor ambient temperatures, shown in interval 4 of Fig. 1, when the burlding load is large and the combined heat-pump coefficient of performance is near unity. The parameter tmin is a function of the capacity of the auxiliary heaters and the reheat load at the design ambient temperature. Fifteen minutes (0.25 hr) is a representative value, based on typical residential system-design guidelines.” Determination if the Heat-Puma Alone Can Suoolv all of the Reheat Eneray The energy rate required to reheat the house is given by Eq. (3). If the heat-pump, without the auxiliary heaters, can reheat the residence within the maximum reheat time, then the reheat time is set equal to $,a. the time required for the heat-pump to reheat the residence. Equation 2 is used to make this calculation with thp = ts - tt, T,, = the house temperature at the initiation of reheat, T,, = the house temperature at the end of reheat, and TA = the ambient temperature, which is allowed to vary once an hour. The linear variation shown in interval 1 of Fig. 1 gives an idealized representation of thp as a function of ambient temperature. . . .. COP) for SUDD~VIQ~ When the Auxrltarv Heaters are Reauired. We Dete rmine COPL (the mmrmum mtable Reheat The minimum acceptable COP for supplying reheat energy provides a standard by which to determine if it makes more sense to chose tmin for the reheat time or to reheat over a longer time. COPL varies, depending on the capacity of the heat-pump in relation to the magnitude of the building load. Using the mathematical model described previously, the following expression has been derived from the cases under consideration: COPL = COPB -0.2. COPL > 1.05,
(7)
where COPB is the coefficient of performance corresponding to the balance point temperature of the heat-
939
Rule-based thermostat design for night setback of heat pumps pump subjected to the current steady-state building load. COPL is restricted to a,minimum ensure a value greater than unity, the coefficient of performance of the auxiliary heaters.
value of 1.05 to
Iv the &gggt Enerav while Ooeratmn At or Above CO& If this condition is met, then the time for the heat-pump and auxiliary heater, operating at COPL. to reheat the houss (tCoPL) is ca!culated. If toopI, is less than t,,, then the reheat time is increased to equal t,,, shown in interval 2 of Fig.1. If, however, tooF.,, is greater than t,,, the reheat time varies linearly from t,_ to tmin, as shown in interval 3 of Fig. 1.
-f-
4+ REHEAT TIME (Hours)
Cold
Warm \
Heat Pump Capacity BTU/HR
0
l-
Balance’Point Temperature
Setpoint Temperature
AMBIENT TEMPERATURE
Fig. 1. A rule-based reheat example. RESULTS The final form of the rule-based setback strategy provides energy and cost savings in a full spectrum of heat-pump operating scenarios, including the effects of climatic region, heat-pump sizing, building heat loss coefficient, and building thermal mass. The savings achieved by the rule-based strategy consistently exceed that of present, commercially-available controllers. Table 2 shows the seasonal energy and cost summary results for an Atlanta residence. Table 3 shows monthly energy summaries which correspond to the conditions presented in Table 2.
t See rule-based strategy description in text.
940
&NL.RVIZmd
Table
~~HAELJ.
MORAN
2. Example seasonal result for Atlanta: U = 1000, MCp = 6000, set-point temperature = 65 F, set-back temperature = 55 F, set-back start at 10 pm, set-back ended at 6 am.
NO SETBACK STANDARD SETBACK ONE-HOUR SETBACK COMMERCIAL SETBACK RULE-BASED SETBACK
Table
3.
MONTH October November December January February March April
May
MO
ENERGY SAVINGS (a)
TOTAL ENERGY (Btu)
STRATEGY
3.4673+07 3.4863+07 3.292E+07 3.2323+07 3.2143+07
0.00 -0.55 5.05 6.77 7.30
TOTAL COST (S) 633.31 636.86 605.02 595.29 592.38
usage
thly ene
9~
NO SETBACK
STANDARD SETBACK
1475 4058 7433 8697 7009 3996 1544 456
1605 4183 7299 8533 6883 4167 1698 489
COST SAVINGS (2) 0.00 -0.56 4.47 6.00 6.46
? for
Atlanta
RULE-BASED SETBACK 1325 3870 7080 8293 6674 3821 1436 401
1264 3755 7020 8213 6608 3703 1361 383
1266 3734 6990 8146 6560 3689 1359 382
DISCUSSION Night setback in residential heat-pump systems can significantly reduce heating season costs if the control strategy governing night setback takes into account the operational characteristics of heat-pump systems, The relativemagnitudeofthesavingsfromheat-pumpnightsetback, however,issignificantlyaffected bythehouse building characteristics, as follows. (i) The larger the steady-state heat loss U from a residence, the better the potential savings from night setback. (ii) The larger the house thermal mass MC, the poorer the potential savings from night setback. Large heat losses may be the result of poor insulation, large infiltration, or a large amount of external surface area. Large thermal mass may be due to the large size of the house or a large amount of furnishings in the house. The two conclusions above therefore indicate that night setback savings in a large, well-insulated house are not as significant as the savings in a small, poorly-insulated house located in the same climatic region. The One-Hour option described is attractive to the retrofit market since it does not require replacing the existing thermostat. Instead, a device that simply manipulates the temperature control lever of the existing thermostat could be used. A functionally similar device that moves the thermostat temperature control lever in a matter of seconds rather than an hour exists now for gas furnace thermostats, and can be purchased in many hardware stores for around $30. The rule-based algorithm presented here requires knowledge of both the building energy use parameters and the heat-pump operating characteristics. Although this information is not normally known to a controller, it can be derived by a thermostat equipped with an outdoor temperature sensor, a timer, and microprocessing power.’ An additional feature of the rule-based control strategy that can be used to advantage in modern buildings, including the smart-house concept, is to provide diagnostics of the heat-pump system and residence. The controller could, for example, detect an increase in the overall heat transfer coefficient of the house, possibly due to increased infiltration. Increases in infiltration can be caused by a number of factors’ that are correctable if the homeowner is aware that action is required. Heat-pump system performance degradation can also be monitored by the controller, alerting the homeowner that service is required, and serving the dual functions of both maintaining peak heat-pump performance and extending the heat-pump life. The rule-based strategy presented in this analysis by no means precludes more elaborate schemes. The increased savings potential shown by using AI techniques should,however, serve to motivate further investigation of the application of these techniques to nondeterminate engineering problems, and the computer program’ may be used as a basis for analyzing additional control schemes.
Rule-based thermostat design for night setback of heat pumps
COP COPliP
COPL COPB dT,/dt M CP QHP
Q
kOPL
.
‘mu
h tn-in
TH TA T #P
U
941
NOMENCLATURE coefficient of performance of tile &i&ined system (heat-pump plus auxiliary heater) coefficient of performance of the heat-pump alone minimum acceptable coefficient of performance for reheat coefficient of performance at the balance point temperature rate of change of the indoor temperature as a function of time (F/hr) thermal mass of the residence (Btu/F) capacity of the heat-pump alone (Btu/hr) combined heat-pump system capacity (Btu/hr) time for the heat-pump system, operating at COPL. to reheat (hr) maximum reheat time (hr) time for the heat-pump alone to reheat (hr) minimum reheat time (hr) indoor temperature (F) outdoor ambient temperature (F) thermostat setpoint temperature (F) overall heat transfer coefficient (Btu/hr-F) REFERENCES G. R. Schade, ASHRAE Trans. 88-1, 786 (1978). A. 0. Backus, ASHRAE Trans. 88-1, 467 (1982). E.L. Vine, Energy, 11 811 (1986). Honeywell Product Literature, Model T861 I Chronotherm III(TM) Heat Pump Thermostat, Honeywell, Inc., Golden Valley, MN (1987).
5.
Harper-Wyman IL (1988).
Technical Bulletin, “Computed Recoverya(
6.
E. Rich, Artificial Intellieence,
7.
A.L. Rutz, “Evaluation of Residential Heat Pump Energy and Cost Savings for Four Night Setback Strategies,” MSc. Thesis, Department of Mechanical Engineering, The Ohio State University, Columbus, Ohio (1989).
8.
L. W. Crow, ASHRAE Trans. 87-1, 896 (1981).
9.
B. Andenson,
10.
S.G. Talbert, A.L. Rutz, and C.E. French, ASHRAE Trans. 93-2, 1091 (1987).
11.
R.S. Miller and H. Jaster, “Performance of Air-Source Heat Pumps,” EPRI Report EM-4226, General Electric Company, Schenectady, New York (1985).
12.
“Federal Register,” Appendix M. 44, 1 (Thursday, December 27, 1979).
13.
Bryant Product Literature, “Split-System Heat Pump Units, Model 541C,” Bryant Air Conditioning, Indianapolis, IN (1988).
14.
mHandbook,
McGraw-Hill,
Harper-Wyman
Company, Hinsdale,
New York (1983).
W.L. Carroll, and M.R. Martin, ASHRAE Trans. 91-2b, 183 (1985).
1985 Fun&tBg.&&, Chapters 23,24, and 25, ASHRAE, Atlanta, GA (1985).
Energy Vol. 15, No. 11, pp. 935-941, 1990 Printed in Great Britain
ERMOSTAT DFSIGN FOR NIGHT SETBACK OF HEAT PUMPS
ALLEN L. RUTZ+ Battelle 505 King Avenue Columbus. Ohio 43201 and MICHAEL J. MORAN Department of Mechanical Engineering The Ohio State University 206 West 18th Avenue Columbus, Ohio 43210 (Received April 23, 1990) Abstract- We introduce a computer model for testing heat-pump thermostat performance with regard to energy and cost savings due to night setback. Also introduced are two new control strategies for heat-pump night setback: (i) an inexpensive variation of existing control strategies and (ii) a rule-based control strategy using techniques of artificial intelligence. The computer model is based on a transient system model of the residence, heat-pump, and controller, in response to actual weather data. Seasonal energy usage and costs are computed for each control strategy, subject to the effects of variable heat-pump sizing. building thermal inertia, building heat loss, climatic region, and electric rate structure. Results show that night setback can reduce heating season costs in residential heat-pump systems if the control strategy takes into account the characteristics of both the heat-pump system and the building. If these factors are not considered, night setback can increase heat-pump operating costs. The rule-based control strategy consistently provides positive cost savings above other setback methods, and has the added potential of providing diagnostic information about both the heat-pump system and the residence. INTRODUCTION A commonly employed home-heating conservation technique is referred to as night setbackl*z*s and involves lowering the thermostat setpoint at night during the hours of sleep and subsequently raising the setpoint in the morning. Night setback is baaed on the hypothesis that the energy saved during the night, due to the reduced heating load, exceeds the energy required in the morning to reheat the residence. Electric heat-pumps, however, require careful control when using night setback. Because electric heatpumps typically use auxiliary heaters with electric resistance elements to meet high loads, such as those encountered during the morning reheat period, the standard night setback strategy can actually increase the operating cost of the heat-pump. Increased operating costs can also result from night setback if time of day electric rate structures lead to higher charges per kilowatt hour during the morning reheat period than are charged during the nighttime off-peak period. Accordingly, a perceived savings can translate into an actual loss. Several commercially available setback strategies exist for heat-pump thermostats.4*6 Most operate by computing a time at which to start the reheat process, known as the reheat time, usually from IS minutes to 4 hours prior to the time the desired setpoint temperature is to be attained. The performance of these devices varies, and increased complexity does not necessarily result in increased energy efficiency. OBJECTIVES The objectives of this paper are first to introduce a computer model for testing heat-pump thermostat performance with regard to energy and cost savings and then use the model to evaluate the following two new
+ To whom all correspondence should be sent. 935
U
936
L. Rurz and
MICHAEL
J.
MORAN
control strategies for heat-pump night setback: (i) an inexpensive variation of existing control strategies, and (ii) an adaptive, rule-based control strategy using techniques of artificial intelligence (AD6. Discussions of additional setback strategies are given inRef.7.Theenergy and cost savings achieved by the setback strategies are discussed, using the case of no night setback as a baseline. Heat-pump thermostat performance is evaluated using a mathematical model of the residential heat-pump system including the residence, heat-pump, thermostat, weather data, and energy cost data. The model has been developed on the basis of previous field and laboratory investigations, manufacturer’s product descriptions, recorded weather data, and utility rate structures. Thus, the integrated system model (in the form of an interactive computer program) provides a reasonable and validated prediction of the operating characteristics of the home heating system for the purpose of evaluating night setback. The two new setback control strategies have been developed on the basis of observations of the underlying engineering principles involved in heat-pump night setback, then tested and refined using the computer program. To ensure broad applicability of the rule-based algorithm, the energy and cost analysis was performed for residences of varying size and thermal inertia and in four different cities representing different climatic regions of the US and different electric rate structures.’ MATHEMATICAL MODEL DEVELOPMENT A description of the elements of the computer model is presented next. Full details are provided in Ref. 7. her Da$g The Weather Year for Energy Calculation* (WYEC) data from the American Society of Heating, Refrigeration and Air conditioning Engineers (ASHRAE) is used to represent the climatic regions’ listed in Table 1.
Table 1.
Climatic groups and representative cities.
. . wgv Flows The building energy flows are described by a one-node, lumped parameter model, assuming that the temperature of the indoor space T, is uniform throughout, the thermal mass (product of the building mass M and specific heat C,,) is constant, and the overall heat-transfer coefficient U for heat transfer between the building and the ambient environment at temperature T, is constant. The building energy rate balance takes the form
where Q denotes the total rate at which energy is provided to the building by the combined heat-pump system unit (the combination of heat-pump and auxiliary heaters). During cooldown, the heat-pump system is off and Q in Eq.( I) is zero: the building load is met by depleting the energy stored, and the building temperature declines. Denoting the building temperature at an initial time tr by T,, and the temperature at any subsequent time tz by T,,, the time interval required for the building temperature to change from T,, to Tn,, while the ambient temperature remains constant, is then
‘2-G
=
5) ( ”
In(
*Ku-?i T,-T,).
(2)
During reheat, all of the energy needed to return the thermal mass to the original setpoint temperature is supplied to the residence in addition to the building load that exists during the reheat period. The total rate at which energy is provided to the house from the combined heat-pump system while the house is being reheated from initial temperature T,, at time t, to final temperature Tns at time ts is’
Rule-based
thermostat design for night setback of heat pumps
Q =
fJ[r,-l”-K$$],
937
(3)
where
(4)
The climatic regions used in the analysis have already been described. Two building heat loss coefficients, 666.67 Btu/hr-F and 1000 Btu/hr-F, were selected as representative of typical northern and southern loads, respectively.” Two building thermal mass values have been calculated based on approximations of residential mass distribution2 of 6 Ib/sq.ft, residential mass average specific heat of 0.35 Btu/lb-F, and two residence sizes of 1400 square feet and 2800 square feet, yielding approximate building thermal mass values of 3000 Btu/F and 6000 Btu/F. Thermostat Ooeration During reheat, the thermostat calls for energy from the combined heat-pump system according to a recovery Degradation of heat-pump temperature curve specified by the type of setback under consideration. performance due to cycling losses is ignored since all strategies for night setback tend to reduce cycling losses. Ignoring the reduced cycling losses will not significantly impact a comparison of setback strategies and will provide a measure of conservatism in the statement of energy savings due to night setback. Costs Energy cost structures were obtained from utilities located in the cities listed in Table 1 for the winter season (October through May) of 1988/1989, assuming residential usage in all electric homes. Although none of the utilities contacted have time-of-day rates now in place, several indicated that higher electric rates exist for customers with both electric and gas service. Feat-Pumo Performance Heat-pump performance data are provided by the manufacturer in the form of a steady-state heating capacity of the heat-pump alone, QHp, and steady-state coefficient of performance of the heat-pump alone, COP,,, including the degradation of steady-state capacity and coefficient of performance due to defrosting and cycling.“‘ts The coefficient of performance of the auxiliary heaters is taken to be unity. The steady-state coefficient of performance of the combined heat-pump system is therefore COP - COP,
COP = rZOPm%
for QsQ,.
+ l.O(l
-%),
for Q > QBT,
where Q is calculated from Eq.( 1) with dT,/dt - 0. At ambient temperatures below the balance point temperature (the temperature at which the heat-pump capacity equals the steady-state building load, see Fig. l), the heat-pump runs continuously to take maximum advantage of the high heat-pump coefficient of performance COP,, and reduce cycling. Auxiliary heat is invoked to meet only the portion of the load above the heat-pump capacity; then the combined system heat capacity Q equals the building load. This process is characteristic of the operation of high-efficiency heatpumps. At ambient temperatures above the balance point, the heat-pump alone is sufficient to meet the load; thus, COP = COP,, in Eq.(S). At ambient temperatures below the balance point, the system coefficient of performance COP is degraded by the auxiliary heaters to a value less than COP,, as shown by Eq. (5). Therefore, reducing the steady-state building load by lowering the thermostat setpoint results in a lower balance point temperature, effectively raising the operating coefficient of performance of the heat-pump system. stem Model
The input to the computer program consists of specifying the city (climatic region and electric rate structure), the heat-pump (from a range of capacities), the overall building heat transfer coefficient, building thermal mass, normal thermostat setpoint. start time of setback. thermostat setpoint during setback, and end time of setback. Output consists of monthly and seasonal energy usage and costs. A complete listing of the model source code is available.’
938
ALLEN
L.
RWIZand
MI-L
J. MORAN
NEW SETBACK CONTROL STRATEGY DEVELOPMENT Based on observations of the performance of heat-pump systems in actual residences, setback control strategies should take edvantage of the following generalizations: (i) It is preferable to use heat-pump energy (COP,, > 1.0) rdther than resistance heat energy (coefficient of performance = l.O), (ii) Daily ambient temperature variations are typically cyclic with maxima occurring between 11 AM and 4 PM and minima occurring around 6 or 7 AM, (iii) The longer the setback period, the greater the potential for savings. Qne-Hour Stra&gy The first new setback strategy to be introduced is a variation of existing strategies which represents a lowcost alternative to sophisticated controllers, especially for retrofit applications. Rather than resetting the residence temperature abruptly, the heat-pump system is allowed one hour over which to reheat the residence. The temperature is increased linearly over the hour. This strategy, referred to as the One-Hour Strategy, allows the heat-pump to supply a significant portion of the reheat energy, depending on the outdoor temperature, at a higher coefficient of performance than the resistance heat alone provides.
Rule-Based StraAza The second new strategy is considerably more complex in that it uses an adaptive, rule-based algorithm, the rules of which are developed based on the generalizations listed previously. The rules and their form of implementation are outlined next with an idealized representation of the rule-based strategy shown in the top portion of Fig. 1, giving the reheat time for four distinct intervals of ambient temperature. Comoutation of the Maximum Reheat Time A longer reheat period allows the heat-pump to provide energy at a higher coefficient of performance than would be realized when using resistance heat alone. On the other hand, a longer reheat period entails a greater building load during the reheat period. Accordingly, there is a tradeoff which places an upper limit on the reheat time. This is the maximum reheat time, t,. Using the mathematical model described previously, the following expression has been developed for the cases under consideration:
where T,, is the set point temperature and t,, is in hours. Equation (6) shows quantitatively that as the thermal mass of the residence increases t,, increases to accommodate the proportionally larger reheat load. Likewise, as the temperature difference to be overcome by reheat increases, t,, increases. As the overall heat transfer coefficient increases, however, t,, decreases, thus emphasizing the increased benefit of setback for residences with large heat losses. For the cases considered, t,, is generally between 2.5 and 5.0 hours. Commutation of the Minimum Reheat Time The minimum reheat time tInin is used in situations of very cold outdoor ambient temperatures, shown in interval 4 of Fig. 1, when the burlding load is large and the combined heat-pump coefficient of performance is near unity. The parameter tmin is a function of the capacity of the auxiliary heaters and the reheat load at the design ambient temperature. Fifteen minutes (0.25 hr) is a representative value, based on typical residential system-design guidelines.” Determination if the Heat-Puma Alone Can Suoolv all of the Reheat Eneray The energy rate required to reheat the house is given by Eq. (3). If the heat-pump, without the auxiliary heaters, can reheat the residence within the maximum reheat time, then the reheat time is set equal to $,a. the time required for the heat-pump to reheat the residence. Equation 2 is used to make this calculation with thp = ts - tt, T,, = the house temperature at the initiation of reheat, T,, = the house temperature at the end of reheat, and TA = the ambient temperature, which is allowed to vary once an hour. The linear variation shown in interval 1 of Fig. 1 gives an idealized representation of thp as a function of ambient temperature. . . .. COP) for SUDD~VIQ~ When the Auxrltarv Heaters are Reauired. We Dete rmine COPL (the mmrmum mtable Reheat The minimum acceptable COP for supplying reheat energy provides a standard by which to determine if it makes more sense to chose tmin for the reheat time or to reheat over a longer time. COPL varies, depending on the capacity of the heat-pump in relation to the magnitude of the building load. Using the mathematical model described previously, the following expression has been derived from the cases under consideration: COPL = COPB -0.2. COPL > 1.05,
(7)
where COPB is the coefficient of performance corresponding to the balance point temperature of the heat-
939
Rule-based thermostat design for night setback of heat pumps pump subjected to the current steady-state building load. COPL is restricted to a,minimum ensure a value greater than unity, the coefficient of performance of the auxiliary heaters.
value of 1.05 to
Iv the &gggt Enerav while Ooeratmn At or Above CO& If this condition is met, then the time for the heat-pump and auxiliary heater, operating at COPL. to reheat the houss (tCoPL) is ca!culated. If toopI, is less than t,,, then the reheat time is increased to equal t,,, shown in interval 2 of Fig.1. If, however, tooF.,, is greater than t,,, the reheat time varies linearly from t,_ to tmin, as shown in interval 3 of Fig. 1.
-f-
4+ REHEAT TIME (Hours)
Cold
Warm \
Heat Pump Capacity BTU/HR
0
l-
Balance’Point Temperature
Setpoint Temperature
AMBIENT TEMPERATURE
Fig. 1. A rule-based reheat example. RESULTS The final form of the rule-based setback strategy provides energy and cost savings in a full spectrum of heat-pump operating scenarios, including the effects of climatic region, heat-pump sizing, building heat loss coefficient, and building thermal mass. The savings achieved by the rule-based strategy consistently exceed that of present, commercially-available controllers. Table 2 shows the seasonal energy and cost summary results for an Atlanta residence. Table 3 shows monthly energy summaries which correspond to the conditions presented in Table 2.
t See rule-based strategy description in text.
940
&NL.RVIZmd
Table
~~HAELJ.
MORAN
2. Example seasonal result for Atlanta: U = 1000, MCp = 6000, set-point temperature = 65 F, set-back temperature = 55 F, set-back start at 10 pm, set-back ended at 6 am.
NO SETBACK STANDARD SETBACK ONE-HOUR SETBACK COMMERCIAL SETBACK RULE-BASED SETBACK
Table
3.
MONTH October November December January February March April
May
MO
ENERGY SAVINGS (a)
TOTAL ENERGY (Btu)
STRATEGY
3.4673+07 3.4863+07 3.292E+07 3.2323+07 3.2143+07
0.00 -0.55 5.05 6.77 7.30
TOTAL COST (S) 633.31 636.86 605.02 595.29 592.38
usage
thly ene
9~
NO SETBACK
STANDARD SETBACK
1475 4058 7433 8697 7009 3996 1544 456
1605 4183 7299 8533 6883 4167 1698 489
COST SAVINGS (2) 0.00 -0.56 4.47 6.00 6.46
? for
Atlanta
RULE-BASED SETBACK 1325 3870 7080 8293 6674 3821 1436 401
1264 3755 7020 8213 6608 3703 1361 383
1266 3734 6990 8146 6560 3689 1359 382
DISCUSSION Night setback in residential heat-pump systems can significantly reduce heating season costs if the control strategy governing night setback takes into account the operational characteristics of heat-pump systems, The relativemagnitudeofthesavingsfromheat-pumpnightsetback, however,issignificantlyaffected bythehouse building characteristics, as follows. (i) The larger the steady-state heat loss U from a residence, the better the potential savings from night setback. (ii) The larger the house thermal mass MC, the poorer the potential savings from night setback. Large heat losses may be the result of poor insulation, large infiltration, or a large amount of external surface area. Large thermal mass may be due to the large size of the house or a large amount of furnishings in the house. The two conclusions above therefore indicate that night setback savings in a large, well-insulated house are not as significant as the savings in a small, poorly-insulated house located in the same climatic region. The One-Hour option described is attractive to the retrofit market since it does not require replacing the existing thermostat. Instead, a device that simply manipulates the temperature control lever of the existing thermostat could be used. A functionally similar device that moves the thermostat temperature control lever in a matter of seconds rather than an hour exists now for gas furnace thermostats, and can be purchased in many hardware stores for around $30. The rule-based algorithm presented here requires knowledge of both the building energy use parameters and the heat-pump operating characteristics. Although this information is not normally known to a controller, it can be derived by a thermostat equipped with an outdoor temperature sensor, a timer, and microprocessing power.’ An additional feature of the rule-based control strategy that can be used to advantage in modern buildings, including the smart-house concept, is to provide diagnostics of the heat-pump system and residence. The controller could, for example, detect an increase in the overall heat transfer coefficient of the house, possibly due to increased infiltration. Increases in infiltration can be caused by a number of factors’ that are correctable if the homeowner is aware that action is required. Heat-pump system performance degradation can also be monitored by the controller, alerting the homeowner that service is required, and serving the dual functions of both maintaining peak heat-pump performance and extending the heat-pump life. The rule-based strategy presented in this analysis by no means precludes more elaborate schemes. The increased savings potential shown by using AI techniques should,however, serve to motivate further investigation of the application of these techniques to nondeterminate engineering problems, and the computer program’ may be used as a basis for analyzing additional control schemes.
Rule-based thermostat design for night setback of heat pumps
COP COPliP
COPL COPB dT,/dt M CP QHP
Q
kOPL
.
‘mu
h tn-in
TH TA T #P
U
941
NOMENCLATURE coefficient of performance of tile &i&ined system (heat-pump plus auxiliary heater) coefficient of performance of the heat-pump alone minimum acceptable coefficient of performance for reheat coefficient of performance at the balance point temperature rate of change of the indoor temperature as a function of time (F/hr) thermal mass of the residence (Btu/F) capacity of the heat-pump alone (Btu/hr) combined heat-pump system capacity (Btu/hr) time for the heat-pump system, operating at COPL. to reheat (hr) maximum reheat time (hr) time for the heat-pump alone to reheat (hr) minimum reheat time (hr) indoor temperature (F) outdoor ambient temperature (F) thermostat setpoint temperature (F) overall heat transfer coefficient (Btu/hr-F) REFERENCES G. R. Schade, ASHRAE Trans. 88-1, 786 (1978). A. 0. Backus, ASHRAE Trans. 88-1, 467 (1982). E.L. Vine, Energy, 11 811 (1986). Honeywell Product Literature, Model T861 I Chronotherm III(TM) Heat Pump Thermostat, Honeywell, Inc., Golden Valley, MN (1987).
5.
Harper-Wyman IL (1988).
Technical Bulletin, “Computed Recoverya(
6.
E. Rich, Artificial Intellieence,
7.
A.L. Rutz, “Evaluation of Residential Heat Pump Energy and Cost Savings for Four Night Setback Strategies,” MSc. Thesis, Department of Mechanical Engineering, The Ohio State University, Columbus, Ohio (1989).
8.
L. W. Crow, ASHRAE Trans. 87-1, 896 (1981).
9.
B. Andenson,
10.
S.G. Talbert, A.L. Rutz, and C.E. French, ASHRAE Trans. 93-2, 1091 (1987).
11.
R.S. Miller and H. Jaster, “Performance of Air-Source Heat Pumps,” EPRI Report EM-4226, General Electric Company, Schenectady, New York (1985).
12.
“Federal Register,” Appendix M. 44, 1 (Thursday, December 27, 1979).
13.
Bryant Product Literature, “Split-System Heat Pump Units, Model 541C,” Bryant Air Conditioning, Indianapolis, IN (1988).
14.
mHandbook,
McGraw-Hill,
Harper-Wyman
Company, Hinsdale,
New York (1983).
W.L. Carroll, and M.R. Martin, ASHRAE Trans. 91-2b, 183 (1985).
1985 Fun&tBg.&&, Chapters 23,24, and 25, ASHRAE, Atlanta, GA (1985).