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(Dave Martindale) wrote:

... You may be better off letting the heat pump run some during the day
to keep the house warm enough so that when the setpoint comes up at 5 PM
(or whenever), the resistance heaters are not used.

Maybe not, in a high-conductance house with a low thermal mass and a long
setback and high-capacity resistance heaters. In the example below, a low-
capacity heat pump barely returns the house to 70 F on a cold day, running
through almost the whole setback time. Heat pumping alone uses 19% more
energy as it slowly raises the house temp from 60 to 70 F with a higher
average setback temp than the same heat pump with a final 8 minute goose
from resistance heaters, just before 5 PM.

20 G=1200'house conductance (Btu/h-F)
30 C=2400'house capacitance (Btu/F)
40 TH=70'normal house temp (F)
50 TS=60'min setback temp (F)
60 SBT=12'setback time (hours)
70 TA=40'outdoor temp (F)
80 RC=C/G'time constant (hours)
90 TC=-RC*LOG((TS-TA)/(TH-TA))'cooling time (hours)
100 TWP=SBT-TC'heat pump warming time (hours)
110 THP=(TH-TS*EXP(-TWP/RC))/(1-EXP(-TWP/RC))'equiv. heat pump temp (F)
120 HPC=(THP-TA)*G'heat pump capacity (Btu/h)
130 COP=3'heat pump COP
140 HPE=HPC*TWP/COP'heat pump energy (Btu elec.)
150 RHC=5*HPC'resistance heat capacity (Btu/h)
160 THR=TA+(RHC+HPC)/G'equiv. resistance + heat pump temp (F)
170 TWR=-RC*LOG((THR-TH)/(THR-TS))'resistance + HP warming time (hours)
180 REE=RHC*TWR'resistance heater energy (Btu elec.)
190 HPA=(TS-TA)*G*(SBT-TC-TWR)'heat pump setback energy (Btu)
200 HPW=HPC*TWR'heat pump warming energy (Btu)
210 HPT=(HPA+HPW)/COP'heat pump total energy (Btu elec.)
220 RET=REE+HPT'total energy with res. assist (Btu elec.)
230 PRINT SBT,TC,TWP,TWR
240 PRINT HPC,RHC,HPE,RET,HPE/RET

setback cooling heat pump warming
hours hours hours hours

12 .8109303 11.18907 .1288909

heat pump resistance Heat pump HP+res HP alone/
Btu/h Btu/h alone Btu Btu (HP+res) Btu

36044.78 180223.9 134435.9 113259.3 1.186974

Nick