Ser TH1 ~ 2 1 d National Research Comeil national

no. 910 I$ Council Canada de recherches Canada cop 2

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A "MODIFIED" BIN METHOD FOR ESTIMATING

ANNUAL HEATING ENERGY REQUIREMENTS OF

RESIDENTIAL AIR SOURCE HEAT PUMPS

by RLD. Cane

Published in ASHRAE Journal VoL 21, No. 9, September 1979 p. 60.63

* DBR Paper No. 910

Division of Building Research

Price $1.00 OTTAWA NRCC 18354

7

SOMMAIRE, --

L'auteur dgcrit une mEthode de compartimentation modifige pour la prgdiction des besoins gnerggtiques des pompes 5 chaleur rgsidentielles 5 source agrienne. A l'aide d'un exemple, il compare la mEthode proposge 2 celle recomrnandee par llASHRAE. L'auteur compare ensuite les rgsultats avec les besoins GnergGtiques rGels enregistrgs dans une habitation identique 5 celle consid6rse dans l'exemple. La msthode modifige donne des rgsultats beaucoup plus proches de la consommation observEe que la methode normalisge de 1'ASHRAE.

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REQUIREMENTS OF RESIDENTIAL AIR SOURCE HEAT PUMPS

R.L.D. Cane*

ABSTRACT

This article outlines a "modified" bin method for predicting

heating energy requirements of residential air-source heat

pumps. An illustrative example compares the proposed method

with that recommended by ASHRAE. The results are then compared

with the actual monitored heating energy requirement of a house

identical to the one considered in the example. The "modified"

bin method prediction is much closer to the observed con-

sumption than the result of the standard ASHRAE method.

The bin method outlined in the ASHRAE Handbook (Systems 1976 - Chapter 43) overestimates the amount of purchased heating energy needed in

reasonably well insulated dwellings because it erroneously assumes that

purchased heat is needed whenever the out side temperature is below 18.3OC

(6S°F). The "modified" bin method presented here treats internal and

solar heat gains separately from heat loss and thereby determines the

"break even" temperature below which the heating system needs to operate

This will automatically lead to elimination of the bin hours that occur

in the non-heating months of the year.

"Research Officer, Energy and Services Section, Division of Building

Research, National Research Council of Canada, Ottawa, Canada KIA OR6

Estimating Heat Loss

A recent publication1 out lined a technique for estimating the "net"

seasonal heat loss of the various components of a building's outer shell.

The "net" heat loss values were determined by using a computer to evaluate

the annual heating requirements of a "standard" and a "modified"

bungalow exposed to "testf1 year weather cycles for several locations

across Canada. The consequence of increasing the area of windows and

walls and varying the orientation of various components was examined in

detail. The effect of exterior colour of walls and roofs was also

evaluated.

Rather than applying a single degree day correction factor, CD, to

the total heat loss rate, it was thought that each building component

could be modified by a reduction factor derived from Ref. 1. To

quantify the reduction factors, it was necessary to estimate the heat loss

in the absence of solar effects on external surfaces. For example, in

the case of walls, solar absorptivity (a ) values of 0.45 and 0.90 were S

used in Ref. 1 for light and dark surfaces respectively. The heat loss

factor for the case as = 0 could be found by extrapolation. The result is

illustrated in Fig. 1. The north-facing vertical surface was used as it

was thought that the correction would be small and hence reduce the error

in the estimate. The heat loss factors obtained in this manner could

then be compared with the values for cases of non-zero a . The ratio of S

the heat loss factor for any other surface color to the value for a

perfectly white opaque surface (aS = 0) is referred to as the seasonal

heat loss reduction factor (SHLRF). This same procedure was applied to

ceilings and windows. The SHLRF values are then multiplied by the design

heat loss rate for the various components to obtain the adjusted heat

loss rate as follows:

QL (i) = [Hwall0SHLRF + H w ceiling

SHLRF C

- 1 . + . . . . . . . . . . . . . . l o ( At,) (Tindoor-Tmean (i) 1

The SHLRF applies to all above-grade portions of walls including doors W

and foundation. For below-grade portions of walls and the basement

floor the SHLRF is assumed equal to 1. The seasonal heat loss reduction

factors for walls, windows and ceilings are shown in Fig. 2.

One component of heat loss that remains to be included in Q (i) is L

the infiltration heat loss. In calculating design heat loss, infiltration

is typically assumed to be between 0.75 and 1.25 air changes per hour. 2

However, at other than design conditions it is highly unlikely that the

air change rate is greater than 0.5 in reasonably tight construction.

There is evidence to suggest that a more representative average value

(particularly new electrically heated homes) might be anywhere from 0.2

to 0.5 air changes per hour.3 The choice of a design infiltration rate

and a seasonal rate must be made after careful examination of the

experimental data now available. 2

The final equation for the adjusted heat loss rate is:

QL (i! = [ (Hwall *SHLRF + H *SHLRFw + .............a 1

W 1

wal l2 2

..... + Hfloor -1 + H *SHLRF + H 1 cei 1 ing c window

Estimating Heat Gains

In the previous section, the SHLRF for windows was set equal to 1

for the purpose of calculating the total heat loss rate. In this

s e c t i o n , t h e s o l a r hea t ga in w i l l be c a l c u l a t e d s e p a r a t e l y .

The d i f f e r e n c e between t h e n e t hea t l o s s and t h e hea t l o s s f o r a

p e r f e c t l y white opaque window ( i . e . , SHLRFwindow

=1) r e p r e s e n t s t h e t o t a l

u se fu l s o l a r hea t gain per u n i t a r e a of window f o r t h e hea t ing season.

This ' u s e f u l ' s o l a r hea t ga in (from Fig. 2) i s summed over a l l f e n e s t r a -

t i o n a r e a s a s fo l lows:

- - " ga in a l l wiidows ( ga in A window 1

S S j j

The fol lowing should be noted when cons ider ing i n t e r n a l h e a t ga ins

from household e l e c t r i c i t y use and occupancy.

(1) A l l e l e c t r i c a l energy consumed by appl iances and l i g h t s w i th in t h e

hea ted space, dur ing t h e h e a t i n g season, i s assumed t o c o n t r i b u t e an

equiva len t amount of hea t f o r space hea t ing . This does no t apply

t o a l l c a ses , a s , f o r example, when water i s hea ted on t h e element

of a cooking range and subsequent ly poured down t h e d r a i n , bu t it

should be s u f f i c i e n t l y accu ra t e f o r e s t ima t ion purposes.

( 2 ) For domestic ho t water h e a t e r s (assumed e l e c t r i c ) and a s s o c i a t e d

plumbing, standby l o s s e s r ep re sen t approximately 20% of t h e t o t a l

e l e c t r i c a l energy consumption f o r hea t ing t h e water a c t u a l l y used. 4

Half of t h e remaining 80% i s assumed t o be l o s t down t h e d r a i n .

Thus approximately 60% of t h e energy used f o r domestic ho t water

hea t ing i s u s e f u l h e a t ga in t o t h e space dur ing t h e h e a t i n g season.

( 3 ) The occupany p a t t e r n f o r t h e household must be assumed. For

example, based on an average occupancy of 2, f o r 12 hours , a t 65

wa t t s pe r occupant, t h e r e s u l t i n g hea t ga in i s approximately

The information regarding household electricity use for appliances,

lights and domestic hot water heating is available from electric utility 5

surveys. One survey indicated the following average consumption data: 2 so 46 4

(a) Domestic hot water heating = 5000 kW*h/yr 2 7P - (b) Appliances and lights = 7500 kW-h/yr (Muu;XhJi 1 9 7

A~WRM) + L'b I?-\ 3 klyL/t..

If it is assumed that electricity consumption is uniform over an n entire year, the heat gain would be 875 kW*h/month based on the data

from Ref. 5. Combining this with the occupancy gain of 50 kW*h/month

yields an internal heat gain of 925 kW-h/month. - - - -- - -

Before the solar and internal gains can be incorporated into a bin

analysis, the length of the heating season must be determined. As a first

step, the months of June, July and August can be excluded. The remaining

months can then be used to calculate the building break even temperature

as follows: L&P--- = kA

TBE = T indoor

H = gain [Hgain s + (Hgain I ) en] - (730 an)-'

The calculated value for the TBE can then be compared with the mean

monthly temperatures for a locale. If the number of months with a mean

monthly temperature less than the T equals the assumed value for n, the BE

value for H is correct. Otherwise, the value for n is changed and a gain

new value for H is calculated. gain

Hours of occurrence of outdoor temperature for the non-heating

months should be excluded from the bins. The breakdown of hourly -

occurrence of outdoor temperature is generally available on a month-by- 6 month basis .

"\

Illustrative Example

The following example illustrates the application of the mcthod.

The characteristics of a two-story single detached house with a heated 2

floor area of 164 m (including basement) are summarized in Table 1. For

this analysis, the house is located in Ottawa, Canada (4673°C days). , ,

Rather than using a single factor C each building component is D' assigned a separate correction factor (SHLRF) derived from the "Net Annual

Heat Loss Factor Method."' The values shown in Table 1, Col. 2, are

obtained from the various SHLRF plots by entering each plot at the degree

days for Ottawa. The bracketed quantity in Col. 2 is the fraction of

the total wall or door area in a particular orientation. The sum of the

products of this value and its SHLRF yield an overall SHLRF to be

multiplied by the Design Heat Loss in Col. 1. Note that a SHLRF of 1 has

been assigned for exposed floor, basement slab and below-grade walls, and

that the below-grade heat loss is assumed constant and independent of

indoor-outdoor temperature difference. A SHLRFI (infiltration) of 0.4

has been used, which is appropriate for tight construction. The

adjusted heat loss values (Col. 3) are summed over all components to yield

an over-all adjusted heat loss characteristic which is analogous to the

ASHRAE H /A CD. t~

Solar heat gains through windows and the internal heat gains remain

to be considered. For this example the useful solar heat gain during the

heating season (Col. 4) is 2230 kW-h. Recall that the internal heat gain

(occupancy and electricity consumed within the heated space) was

calculated to be 925 kW*h/month.

For the Ottawa area, the months of June, July and August are non-

heating months. The total extraneous heat gain (assumed to be constant

over the entire heating season) can be calculated using equation (5).

H = (2230 kW*h + 925 kW*h/month x 9 months) x (730 hour/month x 9 months)-' gain - 7, , 2 1 . 1 - ' b $ ~ d 7 .i'.71*1

=1.6 kW

- 7 - C, ec;k. + U L f i L n L (W + 9. ( L5 . f &

+ d a c t ,Lwu-L rrl w w - h p k * b 5 ' ~ ) . . - .

The next step is fa,compare the new method with the procedure \

recommended by ASHRAE. ~ h ~ ~ b i n calculation using the adjusted heat loss

characteristic from Col. 3 of\,~able 1 is shown in Table 2. For the

ASHRAE method, the design heat'.loss characteristic from Table 1, Col. 1, , --

is first multiplied by the factor C = 0.62, which is appropriate for D

a design outdoor temperature of -13'~.~ The ASHRAE bin calculation is

summarized in Table 3. The characteristics of a commercially available

air source heat pump of 2; ton (9 kW) capacity are used in the example.

Com~arison of the ASHRAE and "Modifiedtt Bin Method

Tables 2 and 3 reveal the basic differences in the two techniques.

Column 1, in both tables, is the number of hours over which the calcula-

tion is made. In Table 2, the months of June, July and August are not

included, which results in 717 fewer hours than Table 3 in the temperature

range 40-65'~. Most of these hours would occur overnight and, thus for

this period would not require heating due to thermal storage effects in

the building (i.e., warm, sunny days, cool nights). Column 10 of Table 3

indicates that 818 kW*h of heating energy would be supplied by the heat

pump in the temperature range 60-65'~; in Table 2 the need for heating

was offset by a combination of solar and internal heat gains.

The seasonal performance factor (SPF) is 15% higher when determined

by the ASHRAE method than by the modified bin method. The ASHRAE method

predicts a heating energy consumption and savings over resistance heating,

74% and 108% higher than that obtained by the modified method. This

would lead to a substantial over-estimation of the economic benefit of

the heat pump.

The house in this example is one of four in an energy conservation

project located near Ottawa jointly sponsored by the National Research

Council of Canada and the Housing and Urban Development Association of

Canada. The monitored results from an occupied dwelling indicate that

the heating energy supplied by an electric furnace to this dwelling is

approximately 10,500 kW*h per year. This is in good agreement with the

predictions by the modified bin method (11,523 kW-h), but is much less

than the 20,070 kW-h indicated by the standard ASHRAE method.

Although not used in the example bin calculations, it is recommended

that part load correction factors be used. 8'9 In well insulated houses,

the heat pump balance point is considerably below the accepted 25'-35'F

range, resulting in many hours of operation at a reduced load factor.

This would result in a reduction in the SPF from that calculated here.

Conclusions

The proposed bin method using SHLRFs and a separate accounting for

solar and internal gains provides an accurate estimate of heat loss and

hence heat pump energy consumption in well insulated residential

construction.

The continued use of all hours of occurrence of outdoor temperature

below 18.3"C ( 6 5 O ~ ) without regard to time of year is not appropriate.

The outdoor temperature data are published in Canada in a format that

allows separation of the hours on a month-by-month basis. If the

proposed method is used, the bins should include heating season hours of

occurrence from the thermostat set point down, since the solar and

internal gains are treated separately (Table 2).

Acknowledeement

The author wishes to acknowledge the helpful discussions with his

colleague, G.P. Mitalas, whose work provided the basis for the SHLRF values.

This paper is a contribution from the Division of Building Research,

National Research Council of Canada and is published with the approval

of the Director of the Division.

Nomenclature

A window

j

H gain I

H gain

S j

H gain

n

4, ( i )

SHLRFc

SHLRFI

SHLRF W

2 2 - ne t a r e a of window j (m o r f t )

- design heat l o s s r a t e f o r c e i l i n g (kW)

- design hea t l o s s r a t e f o r basement f l o o r (kW)

- t o t a l monthly i n t e r n a l heat gain ( e l e c t r i c a l and occupancy)

(kW0h/month) 2 - use fu l s o l a r heat gain f o r window j (kW-h/m )

- average hea t gain ( i n t e r n a l and s o l a r ) assumed constant (kW)

- design heat l o s s r a t e by i n f i l t r a t i o n (kW)

- design heat l o s s r a t e f o r wall (kW)

- design heat l o s s r a t e f o r window (kW)

- length of heat ing season (months)

- adjus ted heat l o s s r a t e , b in i (kW)

- seasonal heat l o s s reduction f a c t o r f o r c e i l i n g

- seasonal heat l o s s reduction f a c t o r f o r i n f i l t r a t i o n

- seasonal hea t l o s s reduct ion f a c t o r f o r wall

- outdoor temperature a t which heat gains j u s t o f f s e t heat

l o s s (OC o r OF)

- design indoor temperature (OC o r OF)

- mean outdoor temperature i n b in i (OC o r OF)

- design indoor-outdoor temperature d i f fe rence (deg C o r deg F)

- design indoor - mean outdoor temperature i n bin i (deg C o r deg F)

- s o l a r a b s o r p t i v i t y of surface

References

1. G.P. Mitalas. Net Annual Heat Loss Factor Method for Estimating Heat

Requirements of Buildings. Nat. Res. Council of Canada, Div. Bldg. Res.

Bldg. Res. Note 117, 1976.

2. ASHRAE Handbook; 1977 Fundamentals - Chapter 21. American Society of

Heating, Refrigerating and Air-conditioning Engineers.

3. G.T. Tamura and A.G. Wilson. Air Leakage and Pressure Measurements of

Two Occupied Houses. ~ S H ~ A E Journal, Vol. 5, No. 12, 1963.

4. Canadian Standards Associdtion. Performance Requirements for Electric

Storage-Tank Water Heaters. CSA Standard C191-1973, June 1973.

5. V.S. Manian and A. Juchymenko. Energy Usage and Relative Utilization

Efficiencies of Oil-, Gas-, and Electric-Heated Single-Family Homes.

ASHRAE Trans. Vol. 81, Part 2, 1975.

6. Environment Canada. Atmospheric Environment Service. Hourly Data

Summaries, July 1967.

7. ASHRAE Handbook; Systems 1976 - Chapter 43. American Society of

Heating, Refrigerating and Air-conditioning Engineers.

8. C.E. Bullock and W.R. Reedy. Heat Pump Cyclic Performance and Its

Influence on Seasonal Operation. Procs. 3rd Annual Heat Pump

Technology Conference. April 10-11, 1978, Oklahoma State Univ.,

Stillwater, Oklahoma.

9. G.E. Kelly and J. Bean. Dynamic Performance of a Residential

Air-to-Air Heat Pump. Nat. Bur. Stds., Thermal Engineering Section,

Center for Building Technology NBS Building Science Series 93, 1977.

TABLE 1

SUMMARY OF APPLICATION OF NEW METHOD

(1) (2) (3) (41 ( 5 1

Design Heat Seasonal Useful Below-

Loss Rate Heat Loss Adjusted S o l a r Grade Area I n s u l a t i o n , * (HL/AtD) ** Reduct ion Heat Loss Heat Heat

Building Component m Nominal Factor Rate ( a L / ~ t D ) Gain Loss W/"C (SHLRF ) w/"C kW*h k W

Ce i l ing 59.4 R5.6 11.6 0.68 7.9

Walls ( facing) : N 30.0 R3.5 0.96(0.18) (windows S 43.0 " 39.0 o.81[ 0.67(0.26) 31.6 excluded) E 43.6 " (To ta l ) 0.84 (0.26) (Total )

W 48.8 I ' 0.84(0.29)

Windows ( facing) : N 5 .9 T r i p l e Glazed S 5 . 8 " 33.2 1 .0 33.2 E 0 .9 I t (To ta l ) (Tota l ) W 0 .0 "

Doors (facing) : N 1 . 9 I n s u l . Door 5 .8 0.96(0.61) 5 . 3 [windows Plus Storm O.gl [ excluded) E 1 .2 " (To ta l ) 0.84(0.39)

Exposed Floor 3.7 R3.5 1.1 1.0 1.1

Basement xal 1 8 .9 R1.8 4.2 0.81 3.4 (above- grade ; windows excluded) A + & v * + * L ~ jy ' = I 7 9 -

51.k - I n f i l t r a t i o n - - 93.3 37.3 Lnur i % ~ L~,,.,, $ v ~ . 8

(0.75 a. c / h r ) - (0.3 a . c / h r ) r

Total heat loss r a t e , W/*C rn

y * . 2 2 \ I

I Basement slab*** 52.0 n i l 5 .4 W/m 1.0 5.4 W/m 1 58 Basement wal l f** 2~79- \I, - I 0.95

(below-grade) 62.3 R1.8 10.75 I T 1 . O 10.75 I '

2 2 3 0 r f l ? L '"L L'L = 2479 .q * R value i s i n SI u n i t s (mul t ip ly by 5.67 f o r R va lue i n B r i t i s h Uni t s ) % - p ~ a p w . 4 b.3)

s 3 ** A t = 47.2 C deg [72- (-131 - E5 .F F 6.1 Z 'L *** D ' 3 2 3 0 Belou grade h e a t l o s s assumed cons tan t and independent of outdoor temperature

1

ht&% &XI141

.c-J- @ !A '3.L" $ TABLE 2 , f < (;.. .J-F 1 MODIFIED BIN METHOD

k,!

*Months of June , J u l y and August excluded

Energy Adjusted Below Heating

Ave . Energy Outdoor Heat Grade Building Ave . Consumed Energy

Power Consumed by Temp. Loss Supp 1 i e d Number Heat Heat Heating Heat Pump Input t o by Range, Res is tance by O F

of ( 6 L / ~ t D x d ~ ~ Y LOSS, Gain, Required, Capaci ty , Heat Pump, Heat Pump, Heate rs , System, Hours* k~ kW kW kW k W k W kW*h k W * h kW-h

65-69 215 0.20 60-64 293 0.53 55-59 398 0.87 50-54 475 1.20 45-49 491 1 .53 40-44 554 1.87 35- 39 668 2.20 30- 34- _ 728 2.53

h i 0.0 12.6 4.2 0 0 0 0 .0 11.7 4.0 0 0 0 0.22 10.8 3.8 3 1 0 8 7 0.55 9 .9 3 .7 98 0 261 0.88 9 .1 3.4 161 0 432 1.22 8 .2 3 .3 272 0 676 1.55 7 .3 3 .1 440 0 1035 1.88 6 .6 3.0 622 0 1369

,Z -29 _ - 5SIj 2 . 7 , , 0,25 1.60 2.22 6.0 2.9 - 575 D - - 1190 -

20-24 46 7 3.20 15- 19 383 3.53 10-14 348 3.87 5-9 2 75 4.20 0-4 210 4.53

-5 - -1 145 4.87 -10 - -6 8 3 5.20 -15 - -11 4 1 5.53 -20 - -16 15 5.87

2.55 5.6 2.8 595 0 1191 2.88 5 .2 2.7 573 0 1103 3.22 4 .8 2.6 607 0 1120 3.55 4 . 3 2.6 590 0 976 3.88 3 .9 2.5 522 0 815 4.22 3 .3 2.4 348 133 6 12 4.55 2 .7 2 .3 19 1 153 378 4.88 2 .3 2 .1 8 6 106 200 5.22 2.0 1 .9 2 8 48 78

6325 Y \ 5739 440 11523

2.87 + '9s - 1.10 2 2 ;r

2 2 2 , 5 3 ( 0 = 1\90 kvL Heating Energy Suppl ied by System J

L o k u i> 2,l--f- SPF = = 1.9 55 \ iqo \, , 1.9 kd =r 575 k'+JL Energy Consumed+ Energy Consumed -

b by Heat Pump by Res is tance Heaters

Energy Saving over Res is tance Heating = 5344 kW*h

k

*

N O ; ,&d U'L- 4 - I 1 A& *--+ TABLE 3

I ASHRAE B I N METHOD

C 13 (21 . (31 (41 ( 5 3 16 3 (73 (8) (9 ) (10) ',

Energy Heating

Outdoor Heat Consumed Energy Building Ave. Power Consumed by Suppl ied

Res is tance by

55-59 692 0.39 $4

50-54 633 0 . 84 r.lL

540 45-49 1 . 16 1 , ~ 1139 ':c\ x 565 40-44 1 .49 ' ,a \

35-39 670 1.81 2.14 1849 2.70

728 30- 34 2.14 2,*& 2249 ? ~ t z

25-29 5 36 2 .46 2.1s 1828 . ' "

20-24 467 2 . 78 3.11 1742 \ t a b 15-19 383 3. 11 3.43 1555 lL77

10-14 348 3.43 3.15 1524 ' " 3 1 1292 ~ 3 % ;

?'J.,Q - --- .- ~ ~- - .- 4.":.Qe.- fq%o . /- ----- . .,. . .~- - n -5 - -1 145 4.34 " ' 4 767 YLL

-10 - -6 83 4 - 7 3 .a ' s 471 i:"F -15 - -11 4 1 5.05 ',7

15 -20 - -16 5.37 5-30

7042 7855 1099 " ' 20020 2x49

+,o~&!3'?5 = 5.63 Heating Energy Suppl ied by System

5.03n2to = b5L kwt* 2 + 4

SPF = = 2.2 h,?. 3.9 r&?'o - gJq kuh

%'- 1 0 5 b - S I 9 = 2 3 1 kvk - Energy Consumed + Energy Consumed 3 .9 l co~ = 2 .5 by Heat Pump by Res is tance Heaters

~ . 5 ~ 2 1 , 3 = 525 kwh 1322k Energy Saving over Res is tance Heating = 11116 kW-h

* A l l 12 months included

Z

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