# Comparison of One- and Two-Variable Linear Regression Models and Classic Energy Intensity for Energy Performance Tracking of Two Manufacturing Sectors

## Abstract

We report manufacturing facilities consumed about 32% of total domestic energy in the United States in 2016. To evaluate the energy savings achieved through the implementation of energy conservation projects and to establish powerful arguments for future projects, accurate energy performance tracking methods are necessary. The classic energy intensity method (i.e., the ratio of annual total energy over annual total production) is the means most widely used to measure savings because it can be understood and calculated easily. This method considers the variation in production rates to some extent; however, it fundamentally assumes facilities' base energy consumption (energy consumption at zero production) to be zero, which rarely holds true. Furthermore, this method does not consider variations in other relevant parameters, such as weather conditions. Therefore, the regression models approach is commonly recommended to track energy performance improvements. However, because it requires more data and statistical expertise, the regression models approach has been adopted by only a few facilities, and many others suspect it is not worth the effort for their specific cases. For this reason, the improved accuracy this approach offers needs to be demonstrated. By analyzing 477 monthly energy (electricity and natural gas) data sets, this study quantitatively comparedmore »

- Authors:

- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- U.S. Department of Energy (DOE), Washington, DC (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE Office of Energy Efficiency and Renewable Energy (EERE), Advanced Manufacturing Office (EE-5A)

- OSTI Identifier:
- 1474575

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Energy Engineering

- Additional Journal Information:
- Journal Volume: 115; Journal Issue: 5; Journal ID: ISSN 0199-8595

- Publisher:
- Taylor & Francis

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION; energy efficiency; energy intensity tracking; energy performance baselining; energy performance tracking; manufacturing facility; linear regression modeling

### Citation Formats

```
Guo, Wei, Wenning, Thomas J., Nimbalkar, Sachin U., Thirumaran, Kiran, Armstrong, Kristina O., and Levine, Eli. Comparison of One- and Two-Variable Linear Regression Models and Classic Energy Intensity for Energy Performance Tracking of Two Manufacturing Sectors. United States: N. p., 2018.
Web. doi:10.1080/01998595.2018.12027705.
```

```
Guo, Wei, Wenning, Thomas J., Nimbalkar, Sachin U., Thirumaran, Kiran, Armstrong, Kristina O., & Levine, Eli. Comparison of One- and Two-Variable Linear Regression Models and Classic Energy Intensity for Energy Performance Tracking of Two Manufacturing Sectors. United States. doi:10.1080/01998595.2018.12027705.
```

```
Guo, Wei, Wenning, Thomas J., Nimbalkar, Sachin U., Thirumaran, Kiran, Armstrong, Kristina O., and Levine, Eli. Wed .
"Comparison of One- and Two-Variable Linear Regression Models and Classic Energy Intensity for Energy Performance Tracking of Two Manufacturing Sectors". United States. doi:10.1080/01998595.2018.12027705. https://www.osti.gov/servlets/purl/1474575.
```

```
@article{osti_1474575,
```

title = {Comparison of One- and Two-Variable Linear Regression Models and Classic Energy Intensity for Energy Performance Tracking of Two Manufacturing Sectors},

author = {Guo, Wei and Wenning, Thomas J. and Nimbalkar, Sachin U. and Thirumaran, Kiran and Armstrong, Kristina O. and Levine, Eli},

abstractNote = {We report manufacturing facilities consumed about 32% of total domestic energy in the United States in 2016. To evaluate the energy savings achieved through the implementation of energy conservation projects and to establish powerful arguments for future projects, accurate energy performance tracking methods are necessary. The classic energy intensity method (i.e., the ratio of annual total energy over annual total production) is the means most widely used to measure savings because it can be understood and calculated easily. This method considers the variation in production rates to some extent; however, it fundamentally assumes facilities' base energy consumption (energy consumption at zero production) to be zero, which rarely holds true. Furthermore, this method does not consider variations in other relevant parameters, such as weather conditions. Therefore, the regression models approach is commonly recommended to track energy performance improvements. However, because it requires more data and statistical expertise, the regression models approach has been adopted by only a few facilities, and many others suspect it is not worth the effort for their specific cases. For this reason, the improved accuracy this approach offers needs to be demonstrated. By analyzing 477 monthly energy (electricity and natural gas) data sets, this study quantitatively compared the accuracy of classic energy intensity, one-variable (production only) linear regression models, and two-variable (i.e., production and weather) linear regression models for two manufacturing sectors (primary metal and transportation equipment manufacturing). Results showed that significant improvements in accuracy were achieved with one-variable regression models when compared with the classic energy intensity method and with two-variable regression models when compared with one-variable regression models. These improvements were demonstrated using the p values of intercept, cooling degree days, and heating degree days. Based on these results, to achieve a good balance between accuracy improvements and resources requirements, one-variable (production only) linear regression models for electricity consumption and two-variable (production and heating degree days) linear regression models for natural gas consumption are recommended for both sectors in the case of limited resources. Lastly, facilities can also use the results to decide which approaches fit better in their cases.},

doi = {10.1080/01998595.2018.12027705},

journal = {Energy Engineering},

number = 5,

volume = 115,

place = {United States},

year = {2018},

month = {8}

}

Works referenced in this record:

##
Applications of artificial neural-networks for energy systems

journal, September 2000

- Kalogirou, Soteris A.
- Applied Energy, Vol. 67, Issue 1-2

##
Measuring industrial energy savings

journal, May 2008

- Kelly Kissock, J.; Eger, Carl
- Applied Energy, Vol. 85, Issue 5

##
Measuring Progress with Normalized Energy Intensity

journal, April 2011

- Lammers, Nathan; Kissock, Kelly; Abels, Brian
- SAE International Journal of Materials and Manufacturing, Vol. 4, Issue 1

##
Artificial neural networks and physical modeling for determination of baseline consumption of CHP plants

journal, August 2014

- Rossi, Francesco; Velázquez, David; Monedero, Iñigo
- Expert Systems with Applications, Vol. 41, Issue 10

##
A Method for Measuring the Efficiency Gap between Average and Best Practice Energy Use: The ENERGY STAR Industrial Energy Performance Indicator

journal, July 2005

- Boyd, Gale A.
- Journal of Industrial Ecology, Vol. 9, Issue 3

##
Mathematical description for the measurement and verification of energy efficiency improvement

journal, November 2013

- Xia, Xiaohua; Zhang, Jiangfeng
- Applied Energy, Vol. 111

##
Industrial energy efficiency: the need for investment decision support from a manager perspective

journal, December 2003

- Sandberg, Peter; Söderström, Mats
- Energy Policy, Vol. 31, Issue 15