2011-2012 Lecture 16 - The Degree-Day Method and Inverse Modeling PDF

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Energy Efficient Buildings The Degree-Day Method and Inverse Modeling Introduction The principles used in creating spreadsheet simulation models that calculate heating and cooling energy use for each hour during a year can also be used in less computationallyintensive methods of calculating annual energy use. The best of these methods is called the degree-day method. In addition to being less computationally intensive, the degreeday method supports inverse modeling, in which building performance coefficients are extracted from actual energy use data. Inverse modeling is one of the most powerful tools available for analyzing and improving the energy efficiency of existing buildings. This chapter describes the degree-day method and inverse modeling.

The Degree Day Method The degree-day method uses the concept of overall heating coefficient and cooling coefficients of a building to calculate annual heating and cooling energy use. To illustrate how to build a degree-day model, consider my house. Overall UA Values The UA values for my house when I moved in for summer and winter were:

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Btu Btu UA hr⋅° F hr⋅° F Win ter ( Frac Tot ) Summer ( Frac Tot ) 170 ( 33%) ( UA ) walls= A walls ÷ R walls =1802÷10 . 62= 170 ( 22% ) 147 ( 19% ) 147 ( 28% ) ( UA ) win= A win ÷Rwin =221 ÷1. 5= 58 ( 7% ) 58 ( 11% ) ( UA ) ceil = A ceil ÷R ceil =953 ÷16 . 4= UA

¿

0 ( 0% ) ( UA ) inf =N V ρ c p =1 . 0×14005 ×.018 = 252 ( 32% ) 147 ( 28% ) ( UA ) ground =( UA ) ground ÷2 =293÷2= 147 ( 19% ) Btu Btu 522 ( UA ) tot = 774 hr⋅° F hr⋅° F

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The internal heat gains from people, electricity and solar gain through the windows were: ¿

Qpeople,sen =4×210=840 ¿

Qelec =5,500

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[ ] Btu hr

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1 h kWh Btu Btu × ×3,413 =2,143 yr kWh 8,760 yr hr

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¿

Q sol,win ( I Nov − Mar )=[ A winE I E + A winS I S + A winW I W + A winN I N ]×SHGC =[ ( 45× 446) +( 83 ×811) +( 27 ×427 ) +( 68×278 ) ]× ¿

Qsol,sum=assume same from exterior shading ¿

¿

¿

¿

Qin ternal gains =Qpeople+Q elec +Q sol=840 +2,143 + 3,191= 6,174

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. 65 Btu =3,191 hr 24

[ ] Btu hr

Balance Temperature A steady-state energy balance on the house during winter gives: ¿

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¿

¿

Toa 

¿

Q ig

Qi g +Q fur −Q UA =Q i g +Qfur −UA (T ia −T oa ) =0

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T ia

Q UA



Q fur

Next, define the “balance-point temperature” as the outside air temperature when the house needs no heating. To calculate the balance temperature, set Qfur to zero and replace Toa with Tbal. Doing so gives: ¿

Qi g Qig +Q fur −UA ( T ia−T bal ) =0 → T bal=T ia − UA ¿

¿

¿

Qi g

6174 =64 . 0 ° F =72− T bal,w =T ia,w − 774 ( UA ) w ¿

For my house:

Q 6174 =64 . 2° F T bal,s=T ia,s− i g =76− 552 ( UA )s

This means: Whenever Toa < 64.0°F, my house needs heating Whenever Toa > 64.2°F, my house needs cooling Calculating Degree Days In ancient times, average daily temperatures were readily available, but hourly temperatures were not. Thus, it was common to use average daily temperatures to estimate heating and cooling energy use. To estimate annual heating energy use, sum the difference between the balance and average daily outdoor air temperatures for all days during the year when Toa < Tbal. Doing so gives the heating degree days per year for a given location and balance temperature.

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365

HDD( T bal ) =∑ (T bal−T oa,i ) + = Heating ` Degree ` Days i=1

For house in this example with Tbal,h = 64.0 F, and using average daily temperatures from Daytdyus.dat, the annual heating degree days are:

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HDD( T bal −64 . 0° F ) =5,356

° F⋅day yr

]

To estimate cooling energy, calculate the cooling degree days by summing the difference between the balance and average daily outdoor air temperatures for all days during the year when Toa > Tbal. 365

CDD ( T bal ) =∑( T oa,i−T bal) + = Cooling ` Degree ` Days i=1

For the house in this example with Tbal,c = 64.2 F, and using average daily temperatures from Daytdyus.dat, the annual cooling degree days are:

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CDD ( T bal =64 . 2° F )=959

° F⋅day yr

]

Calculating Annual Furnace & Air Conditioning Energy Use The annual heat supplied by the furnace and cooling energy removed from the house by the air conditioner can be calculated using the overall UA value and heating and cooling degree days. ¿

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° F⋅day Btu hr MMBtu ×5356 × 24 =99 .5 hr⋅° F yr day yr ¿ ° F⋅day Btu hr MMBtu ×959 ×24 = 12. 7 QAC,sen =( UA )s ×CDD=552 hr⋅° F day yr yr Qfur= ( UA )w ×HDD=774

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Assuming the furnace is 80% efficient and the COP of the air conditioner is 3.0, the annual furnace fuel and air conditioner electricity use are about:

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(UA )W 99 .5 MMBtu =124 ×HDD= 0 . 8 yr E FUR ¿ (UA )S 12. 7 ×CDD = W E,AC = E AC 3 . 0×3,412(Btu/kWh ) ¿

Qng,fur =

MMBtu yr

] ]

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MMBtu kWh =1,174 yr yr

Base 65-F Degree Days

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In this example, both the heating and cooling balance temperatures were about 64 F. This result is typical of many houses. So typical, that it is common to assume the balance temperature is 65 F and calculate degree days based on this assumption. Base 65-F heating and cooling degree days for a given time period are often posted on the internet and reported by weather services. The loss of accuracy from using base 65 F degree days to calculate energy use depends on the difference between the actual building balance temperature and the assumed 65 F balance temperature.

Inverse Modeling Now, take DD models of natural gas and electrical energy use and imagine what XY graphs of natural gas versus outdoor air temp and electricity versus outdoor air temp should look like.

For my house, the actual graphs look like this.

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Lonsdale Gas Use vs. Outdoor Air Temperature

With January gas use removed. Lonsdale Electricity Use vs. Outdoor Air Temperature

With August electricity use removed from regression.

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These graphs were created by: Ascii data file of 13 months of ng and elec use from bills AscII data file of actual avg daily temps from same period as utility bills from www.engr.udayton.edu/weather Combining data files in “Energy Explorer” Software Modeling NG vs Temp with “3PH” model Modeling Elec vs Temp with “3PC” model Next, compare calculated coefficients and energy use to actual building coefficients and energy use as derived from statistical analysis of the measured natural gas and electricity use. Heating Tbalance Tbal,h (measured) = 63 F Tbal,h (calculated) = 64 F Measured and calculated are very close. UA (UA/Mfur )(meas) = 6.96(ccf/monthsF) UA (meas) = 6.96 (ccf/mof) Mfur\ UA (meas) = 6.96 (ccf/mof) x .80 x 100,000(Btu/ccf) x (mo/(8760/12)hr) UA (meas) = 763 (Btu/hrF) UA (calculated) = 774(Btu/hrF) Measured and calculated are very close.

Qng,fur Qng, hotwater (meas) = 15.0 ccf/month Qng, hw(meas) 15.0(ccf/month) x (12 months/yr) x (100,000 Btu/ccf) Qng, hw (meas) = 18.0 mmBtu/yr Qng,(meas) = 1,345 ccf/yr x 100,000(Btu/ccf) = 135 (mmBtu/yr) Qng, hw (meas) = 18.0 (mmBtu/yr) Qng, fur (meas) = Qng – Qng, hw = (135 – 18.0) (mmBtu/yr) = 117 (mmBtu/yr) Qng, fur (calc) = 124 (mmBtu/yr) Measured and calculated are very close, especially considering December data not included in measured results Cooling Tbalance Tbal, c (measured) = 61.5 F Tbal, c (calculated) = 64.2 F Measured and calculated are very close. UA

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UA/COP (meas) = 35.5 (kwh/monthF) UA (meas) 35.5 (kwh/Mof)(3.0)3413 (Btu/kwh)(MO/(8760/12)hr) UA (meas) 498 (Btu/hf) UA (calc) = 522 (Btu/hf) Measured and calculated are very close. Welec, ac Welec, other (meas) = 464 (kWh/mo) x 12 (mo/yr) = 5569kwh Welec, tot (meas) = 6,082 kWh Welec, ac (meas) = 6,082 – 5,568 = 514 (kWh/yr) Welec, ac (calc) = 1,174 kWh/yr Results consistent considering Welec, ac (meas) ≈850 (kWh/yr) if here for July/Aug This example shows the power of the degree-day modeling approach. Simple calculations of UA, Tbal, HDD, CDD can accurately predict natural gas and electrical energy use. Forward and Inverse Modeling Traditional “forward” modeling is: Estimated physical characteristics of building + Estimated weather Data  Estimated Energy use But one can also do “inverse” modeling to estimate physical characteristics of building: Estimated characteristics of building  Actual weather + Actual Energy Use

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Simulated Natural Gas Use for House with (Tset = 72 ) and (Tset = 72 F from 8 am to 10 pm and Tset = 60 F from 11 pm to 7 am)

Simulated Natural Gas Use for House with (Inf = 0.8 ACH, Rwall = 4, Rceil = 16) and (Inf = 0.4 ACH, Rwall = 14 and Rceil = 26)

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Simulated Natural Gas Use for House with (Vhw = 5 gal/hr, Thw = 140 F) and (Vhw = 3 gal/hr, Thw = 120 F)

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