1、2010 ASHRAE 639ABSTRACT Robust statistical regression models of commercial and industrial building energy use can be created as a function of outdoor air temperature, occupancy, production and/or other independent variables. These regression models have many uses, including forecasting energy use, b
2、enchmarking, identi-fying savings opportunities, and measuring energy savings from a normalized baseline. When evaluating facilities with this method, monthly utility bills are commonly used as source data because of their widespread availability and accuracy. Monthly energy data, however, provides
3、less resolution than higher frequency daily or even hourly data.This paper examines whether regression models of monthly energy use can be used to predict daily energy use, and by extension whether the time scale of the data affects efforts to understand a buildings fundamental energy performance. T
4、o do so, the paper compares daily-energy and monthly-energy regression models for four commercial and industrial facili-ties. The model coefficients of the daily- and monthly-energy regressions closely match each other for three of the four facil-ities, and thus can be used interchangeably. However,
5、 one of the facilities has different occupancy schedules on weekdays and weekends, and the monthly model cannot predict daily energy use in this case. The generality of these case study results was investigated in this paper by comparing outdoor air based regression models of simulated daily and mon
6、thly energy use. The results indicate that the variation in energy use caused by variable solar radiation, outdoor air humidity, and heat loss to the ground is larger at the daily time scale than the monthly time scale. However, these drivers are sufficiently correlated with outdoor air temperature
7、so that the overall predictive ability of outdoor air temperature based models is still quite good. In addition, the results in this paper indicate that although build-ing energy use is driven by factors that change on the sub-hourly time scale, these effects are fairly evenly distributed over time;
8、 thus, models based on longer time scale data can accurately characterize a buildings energy use.INTRODUCTIONWith rising energy prices and increased incentives for buildings to be energy-efficient, it becomes increasingly important to profile building energy performance. A building energy performanc
9、e profile can be created by regressing build-ing energy use as a function of independent variables, such as weather or occupancy rate, that affects energy consumption. The resulting regression profile provides a robust character-ization of building performance, and can be used for: Benchmarking to c
10、ompare the energy performance of similar-type buildings or to compare the energy perfor-mance of a building over time after removing the effects of changing weather and other energy drivers (Patil et al., 2005; Seryak and Kissock, 2005; Kissock and Mul-queen, 2008).Energy Use Breakdowns to disaggreg
11、ate building energy use into weather-dependent energy use, weather-independent energy use, and energy use that fluctuates with other variables (Kissock and Eger, 2007).Identifying Energy Saving Opportunities by compar-ing profiles against expected profiles and identifying outlying data (Raffio et al
12、., 2007).Profiling and Forecasting Daily Energy Use with Monthly Utility-Data Regression ModelsKevin Carpenter, PE Kelly Kissock, PhD, PEAssociate Member ASHRAE Member ASHRAEJohn Seryak, PE Satyen MorayAssociate Member ASHRAEKevin Carpenter is an energy engineer at CLEAResult Consulting in El Paso,
13、TX. Kelly Kissock is a professor in the Department of Mechan-ical and Aerospace Engineering at the University of Dayton, Dayton, OH. John Seryak is president and lead engineer at Go Sustainable Energy in Columbus, OH. Satyen Moray is a senior engineer at ERS, Inc. in Haverhill, MA.AB-10-0262010, Ame
14、rican Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions (2010, Vol. 116, Part 2). For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs pri
15、or written permission.640 ASHRAE TransactionsEnergy Budgeting to determine future energy use and cost at different seasons of the year and for changing independent variables, such as occupancy rates.Measuring Energy Savings by comparing performance profiles before and after building energy upgrades
16、and modifications (Claridge et al., 1992; Kissock et al., 1998; Kissock and Eger, 2008).Government and utility energy-efficiency programs commonly require building energy use to be profiled in accor-dance with International Performance Measurement and Veri-fication Protocol (IPMVP) methods when dete
17、rmining energy savings from comprehensive building system upgrades or multiple energy-efficiency measures (EVO, 2007). Building energy regression models, which are a function of outdoor temperature, can satisfy the IPMVP requirements and accu-rately calculate energy savings. In addition, ASHRAE Guid
18、e-line 14-2002: Measurement of Energy and Demand Savings uses outdoor air temperature based regression models as the basis for the Whole Building Approach of measuring savings (ASHRAE, 2002). The form and use of these regression models is described by Kissock et al. (2003) and Haberl et al. (2003).
19、These regression models have been incorporated into the ASHRAE Inverse Modeling Toolkit (IMT) (Kissock et al., 2002). The regression models described in this paper are iden-tical to those in the recommended in ASHRAE Guideline 14 and the ASHRAE IMT.Generally, the most available source of building en
20、ergy data for creating regression profiles is monthly utility billing data. Because monthly energy data provides less resolution than daily or hourly interval data, one may question the accu-racy of monthly data as the basis of regression profiles. This paper presents both monthly-energy-data regres
21、sion and corresponding daily-energy-data regression profiles for four commercial and industrial facilities to compare the two regres-sion types. Daily, rather than hourly, energy was chosen and is recognized as the preferred method because statistically predicting daily energy requires fewer indepen
22、dent variables to be considered (EVO, 2007) that cause hour-to-hour energy volatility but do not significantly affect overall energy profile. The comparisons between daily-energy and monthly-energy profiles demonstrate whether standard monthly data sets are sufficient to provide robust regression mo
23、dels similar to those generated by daily data sets.REGRESSION METHODOLOGYThe most common regression model used to represent the weather dependency of a buildings energy use is a three-parameter regression. Three-parameter change-point models describe the common situation when cooling (or heating) be
24、gins when the air temperature is more (or less) than the building balance temperature, and non-temperature dependent energy use is constant. For example, consider a building that uses electricity for both air conditioning (i.e. weather-depen-dent) and non-weather-related uses such as lighting and pl
25、ug loads. During cold weather, no air conditioning is necessary, but electricity is still used for lighting/plug loads. As the air temperature increases above some balance-point temperature, air conditioning electricity use increases as the outside air temperature increases (Figure 1a). The regressi
26、on coefficient 1describes non-weather-dependent electricity use; the regression coefficient 2describes the rate of increase of elec-tricity use with increasing temperature; and the regression coefficient 3describes the change-point temperature where weather-dependent electricity use begins. This typ
27、e of model is called a three-parameter cooling (3PC) change-point model. Similarly, when a fuel is used for space conditioning and non-weather-related uses such as domestic hot water, fuel use can be modeled by a three-parameter heating (3PH) change point model (Figure 1b).The functional forms for b
28、est-fit, three-parameter change-point models for cooling energy use, Ec, (3PC) and heating energy use, Eh, (3PH), as a function of outside temperature, T, are:(1)(2)where 1is the constant term, 2is the temperature-dependent slope term, and 3is the temperature change-point.Figure 1 (a) 3PC (cooling)
29、and (b) 3PH (heating) regression models.Ec 12T 3()+=Eh 123T()+=2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions (2010, Vol. 116, Part 2). For personal use only. Additional reproduction, distribution, or transmiss
30、ion in either print or digital form is not permitted without ASHRAEs prior written permission.2010 ASHRAE 641In cases when the same fuel is used for both heating and cooling, a five-parameter (5P) regression model (Figure 2) can be used to represent the weather-dependency of a buildings energy use.
31、The functional form for a five-parameter change-point model for energy use, E, is:(3)where 1is the constant term, 2is the cooling tempera-ture-dependent slope term, 3is the cooling temperature change-point, 4is the heating temperature-dependent slope term, and 5is the heating temperature change-poin
32、t.These regression models can be used in conjunction with commonly-known methods of calculating building heating and cooling energy use such as the heating degree-day (HDD) and cooling degree-day (CDD) methods. In the HDD method, heating degree-days are calculated by summing the difference between h
33、eating change-point temperature and average daily outdoor temperature for all heating days of the year. A build-ings annual heating energy use is then calculated by multi-plying heating degree-days by the buildings heat loss coefficient, divided by heating system efficiency (ASHRAE, 2009). A heating
34、 regression model is thus useful because it finds change-point temperature (3) and the quantity heat loss coefficient divided by heating system efficiency (as the 2term). The CDD method calculates a buildings annual cool-ing energy use in a similar fashion, and applicable terms can be found using a
35、cooling regression model.MONTHLY AND DAILY ENERGY USE REGRESSIONS MODELSThe following four case studies compare regression models of monthly and daily energy use data. The monthly-energy regression models are created from monthly utility data and aver-age monthly outdoor air temperature during each
36、monthly billing cycle. Monthly utility data is normalized to an average daily value by dividing the total monthly energy use by the number of days in the billing cycle. The daily-energy regression models are created from daily energy use data and daily average outdoor air temperature over the same p
37、eriod. Temperature data was taken from an online daily temperature archive (Kissock, 1999), and a statistical software program (Kissock, 2005) was used to create each of the following regressions. Case Study #1: Grocery StoreThis first case study is from a grocery store in New Hamp-shire. The store
38、has lighting that is on during store hours, refrigeration that operates continuously year-round, and a rooftop air conditioning system for summer space cooling. Figure 3(a) shows the stores monthly electrical energy plotted versus monthly average outdoor air temperature for a 12-month period. Each s
39、quare in the graph represents one month of energy use and average outdoor temperature. Figure 3(b) shows the analogous plot of 365 days of daily electrical energy use plotted against average daily outdoor air temperature over the same period as the monthly data. The line through each data set is a b
40、est-fit 3PC regression model. Table 1 presents the parameters of the monthly-energy and daily-energy regression models and their differences. It is apparent that the differences between the parameters in the two regression models are very small.Case Study #2: Plastics Manufacturing PlantFigure 4(a)
41、shows the monthly steam energy use plotted against monthly average outdoor air temperature for a large plastics plant in Rhode Island, and Figure 4(b) shows the anal-ogous plot of daily steam energy use against average outdoor temperature over the same period. The steam plant for the facility operat
42、es continuously to serve year-round process heating loads and to provide space heating during winter. The line through each data set is a best-fit 3PH regression model. Data from 25 consecutive months were plotted and modeled.Table 2 presents the parameters of the monthly-energy and daily-energy reg
43、ression models and their differences. It is apparent that the differences between the parameters of the two regression models are very small.Case Study #3: High-Rise Apartment BuildingThis next case study is from a high-rise apartment build-ing in New York City that uses natural gas for three primar
44、y purposes: 1) winter space heating, 2) domestic hot water heat-ing, and 3) fuel for an engine that drives the buildings chiller for summer space cooling. Due to gas use for both heating and cooling, a five-parameter regression is best suited to represent this buildings energy-usage. Figure 5(a) sho
45、ws monthly natu-ral gas plotted against average monthly outdoor air tempera-ture, and Figure 5(b) presents the analogous plot of daily natural gas use against average outdoor temperature over the same period. The line through each data set is a best-fit 5P regression model. Data for 12 consecutive m
46、onths were plot-ted and modeled.Table 3 presents the parameters of the monthly- and daily-energy regression models and their differences. As before, it is apparent that the differences between the parameters of the two regression models are very small.E 12T 3()+45T()+=Figure 2 5P regression model.20
47、10, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions (2010, Vol. 116, Part 2). For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHR
48、AEs prior written permission.642 ASHRAE TransactionsConstant energy term = 2,504 kWh/dayTemperature-dependent slope = 70.85 kWh/dayCTemperature change-point = 14.0C (57.2F)R2=0.89(a) Monthly Regression (b) Daily RegressionConstant energy term = 2,485 kWh/dayTemperature-dependent slope = 68.28 kWh/da
49、yCTemperature change-point = 13.8C (56.9F)R2=0.69Figure 3 Grocery store electrical energy 3PC regressions.Table 1. Grocery Store Monthly- and Daily-Energy Regression Parameters3PC Regression TermMonthly-Energy RegressionDaily-Energy RegressionDifference (Monthly minus Daily)Constant Energy Term (kWh/day) 2,504 2,485 0.8%Temperature-Dependent Slope (kWh/day-C) 70.85 68.28 3.6%Temperature Change-Point (oC) 14.0oC (57.2oF) 13.8oC (56.9oF) 0.2oC2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, I
