1. Chapter 10: ANNUAL ENERGY ESTIMATION METHODS
Agami Reddy (rev Dec 2017)
1) Single measure methods
- Degree day method for heating and cooling
- Variable base degree day method
- Model for generating monthly HDD
- Analyzing design alternatives
2) Bin methods
- Standard bin method
- Model for generating monthly bin data
- Modified bin method
3) Inverse modeling and utility bill analysis
HCB 3- Chap 10: Annual Energy Estimation

2. Annual or Seasonal Energy Calculation
The annual energy consumption Qyr (heating and cooling) is
needed to determine operating cost (and evaluate payback)
(10.1)
Two of the most widely used hand-calculations are:
- Single measure methods (there are a few variants)
- Multiple measure methods (there are a few variants)
HCB 3- Chap 10: Annual Energy Estimation

3. Single Measure Methods
Application to residential and light commercial buildings with simple HVAC equipment where energy use is primarily driven by building loads
Relies on one weather datum
Three Methods:
- Degree Day for heating energy use-
Heating Degree Day (HDD)
- Degree Day for cooling energy use-
Cooling Degree Day (CDD)
- Equivalent Full Load Hour (EFLH) for cooling energy use
Not treated
HCB 3- Chap 10: Annual Energy Estimation

4. Balance Point Temperature
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5. HCB 3- Chap 10: Annual Energy Estimation
Degree Day (DD) Method
Annual (or monthly) energy consumption of a building is proportional to the annual (or monthly) degree day of the location
Specific to a selected Base (or balance) Temperature
Degree Day for one month or whole year:
where To is the daily average outdoor air temperature, oC or °F
N is the total days in the year (or month)
DD has an unit of °C-day (or oF-day)
Degree Days are often tabulated at 18.3o C or 65o F base temperature
"+" means that only positive values are to be counted
Heating season:
Eq. (10.7)
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FIGURE 10.1 Annual heating degree-days (K-days)
for the United States, for base of 65°F (18.3°C).
HCB 3- Chap 10: Annual Energy Estimation

8. Degree Day Method for Heating
Annual heating consumption is directly determined as:
(10.9)
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10. Cooling Degree Day (CDD)
Cooling season:
(10.10)
Cooling DD (CDD) can be estimated knowing HDD from:
(10.11)
From Table 10.1,
For Phoenix, annual average outdoor temperature Tav= 70o F
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Caution: CDD method does not work as well as HDD method due to such effects
as solar loads, varying Ktot (window opening) or constant efficiency of cooling device
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Variable Base Degree Day
Newer homes tend to have higher internal loads and lower Ktot
So the traditional Tb of 18.3o C or 65o F
does not apply to newer homes. So we need curves such as shown
Figure 10.3 Annual heating degree-days
HDD (Tbal) as function of Tbal.
(a) For New York, with labels  h/year for 5°F
bin centered at the point
(b) For Denver, Houston, and
Washington, DC, degree-days only.
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The CDD curves for
any variable base
temperature can
be generated from
climatic data
HCB 3- Chap 10: Annual Energy Estimation

14. Erbs et al. Empirical Correlation
allows HDD to be computed knowing only
monthly mean dry-bulb temperature of the location
(10.17) SI
(10.18)
HCB 3- Chap 10: Annual Energy Estimation

15. Erbs et al. Empirical Correlation contd…
(10.19)
(10.20)
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Data
needed
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Site: New York City
 Reference design (design 1): 
U values of opaque surfaces equivalent to 0.10 m (4 in) of fiberglass for walls
and 0.15 m (6 in) for roof;
conductivity of fiberglass k = W/(m. K) [0.10 Btu/(h. ft.°F)];
double-glazed windows with U = 3.0 W/(m2 .K) [0.53 Btu/(h. ft2 .°F)].
HCB 3- Chap 10: Annual Energy Estimation

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22. Single Measure Methods
Disadvantages:
Suitable for residences and small commercial (one zone) buildings
Assumes continuous and constant building operation over year
Not very appropriate for cooling calculations
– Allows little flexibility for changes in building operation in
Thermostat setback
Occupancy
Equipment
Can not easily capture primary equipment cycling losses over year
Produces results that are within ± 30 % of actual energy usage
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Bin Methods
Simplified Multiple Measure – Basic Bin Method
Gets its name from the way the weather data are put together
Weather data are broken into temperature "bins"
Each "bin" has the cumulative number of hours it has been at a given temperature range over the whole year
Conventional bins are 5 °F
35 – 39 °F
40 – 44 °F
45 – 59 °F…
Calculation done for each bin following:
where Nbin is the number of hours in the temperature interval
(or bin) centered at that temperature
(10.25)
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Fig Bin Data for Denver, CO
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Bin Methods
Advantages over Single Measure Method
Captures temperature dependent information of variation in
Building loads
Equipment loads
Captures load dependent equipment performance
Degradation due to cycling
Fig Variation of
balance point temperature
and internal gains for a
typical house
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Bin Methods
Limitations of Basic Bin Method:
- Balance point temperature is not constant over day
- Solar loads not treated properly
- Latent loads not treated properly
- Does not captures time dependent internal loads: People, lights, equipment
- Improper treatment of time of day variation in HVAC operation
- Failure to separately consider different zones of the building
Modified Bin Method
- Can treat different zones
- Can treat zones with diurnal occupancy
- Solar loads includes as linearized with outdoor temperature
- Considers coincident wet-bulb to treat latent loads
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30. Model for Generating Bin Data
Erbs et al. (1983) have also proposed a correlation method for the monthly cumulative frequency distribution (CFD) of the number of hours in the month below a balance or base temperature Tbal which has been normalized as:
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10.19
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Figure 10.9 Comparison of actual versus empirically generated bin data for New York City for February following Example 10.7
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Inverse Modeling
Approach which uses monitored energy data from the building to develop regression models. They are being used extensively for:
Commissioning tests: to evaluate whether a component or a system is installed and commissioned properly;
Comparison with design intent: to compare actual consumption with design predictions and identify causes of discrepancies,
Demand Side Management (DSM): to predict reduction in electrical costs if certain operational changes are made which alter the buildings loads during on-peak hours of the day;
Operation and maintenance (O&M): to predict energy savings from planned retrofits to building shell and equipment
Monitoring and verification (M&V): to verify, once energy conservation measures are implemented, that the actual savings are consistent with the anticipated savings
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Utility Bill Analysis
FIGURE Variable-base degree-day model identification using electricity utility bills at a hospital. Note that some utility bills have been excluded from the regression due to a degree-day threshold. (a) Left graph shows bills vs. time, (b) right graph shows bills vs. cooling degree-days (Courtesy of Sonderegger, 1998)
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2-P cooling
Single Variate
Change-Point
Models
1-P
3-P heating
3-P cooling
Steady-state, single-variate models appropriate for modeling energy use in residential and commercial buildings- such models can be used to regress utility bills (MMT), as well as daily or hourly energy use
A non-linear modeling approach is needed for 3-P models and higher.
Specialized software has been developed for this purpose
4-P heating
4-P cooling
5-P
Fig
HCB 3- Chap 10: Annual Energy Estimation

37. M&V Requires Modeling
Determining savings from energy conservation measures
Figure 10.14
Scatter plot showing how daily cooling energy use varies with outdoor temperature for a large university building in Texas
The faint dots correspond to initial energy use, while the dark circles correspond to energy use after energy efficiency improvements were made to the building.
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Process of determining the best model fit for a specific project involves fitting all forms of change point models and selecting the one with the least root mean square error (RMSE)
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Outcomes
Be familiar with the general classification of energy estimation methods and advantages of multiple measure methods over single measure methods
Understand the basis of single measure methods, to what types of structures they are applicable and the concept of degree-day
Be able to solve problems involving heating degree-day method (HDD) and cooling degree-day (CDD) method
Familiarity with the Erbs et al. approach to generate monthly HDD for any location
Understand the basis of the bin method and to what type of structures it is applicable
Be able to solve problems involving the basic bin method
Familiar with the Erbs et al. approach to generate monthly bin data for any location
Understand the basis of the modified bin method and its advantage over the bin method
Familiarity with inverse methods and their usefulness applicable to M&V
Understand how the DD concept is used for utility bill modeling
Familiarity with different change point model functional forms and how models are identified from data
HCB 3- Chap 10: Annual Energy Estimation