Regression model for calculating the base load energy using the utility bills.

NRE 538: Independent Project Submited by- Divyesh Kumar
Calculating Base-load electricity consumption using Utility bills
Abstract:
The research aims to determine if the electricity consumption for the ST. Dana building at University
of Michigan, Ann Arbor, can be calculated by using the utility bills and heating degree days for three
different academic term. ANCOVA analysis, using R statistics, from the available utility bills and the
monthly Heating degree day for past 3 years, showed that there are significant interaction between
the heating degree days and the Winter and Fall academic-terms. However, the analysis failed to
identify any interaction between the heating degree days and the summer term. Dana building’s
base-load electricity consumption was calculated using the regression model for the winter term.
Introduction:
Background: The city of Ann Arbor observes a great variation in temperature and thus the annual
weather pattern. In fact, during the past decade, the monthly average temperature ranged from 15F
to 80F . The seasonal pattern over the decade causes building to annually consume either more or1
less energy. In the year 2006, ST. Dana building rated LEED Platinum which is supposed to function
normally while utilizing the minimal energy. However, since the year 2006 the total energy
consumption of the building hasn’t shown any drastic improvement (see figure 1). One probable
reason might be the variable weather pattern throughout the period.
The energy usage is usually dependent on the outside weather conditions. For instance, a hot summer
of July 2012 recorded 78.9F might be responsible a possible reason to consume more cooling load
electricity as compared to the maximum temperature for the year 2013 recording just 72.9F. Similarly,
an abnormal winter of 2014 will be responsible for more energy usage (mostly natural gas) due to
extra heating systems load compared to any other years in the past (as shown in Figure 1). Hence,
abrupt weather conditions makes difficult to check the performance of building energy consumption
over a period.
Figure 1Annual Electricity Usage (in kWh) for Dana Building, Source: Plant Operations, University of Michigan.
1
As per the Ann Arbor Municipal Airport (KARB), http://forecast.weather.gov/

The performance of a building can be verified if the total annual energy consumption can be broken
down into, firstly, the variable energy consumption due to abnormality of the annual weather, and
secondly, the base-load energy which more or less, remain constant throughout a year. Base-load
electricity of a building is defined as the electricity consumed by appliances which are not affected by
the outside weather condition. For example, the computer systems, lighting systems, refrigerators,
projectors etc. contribute to almost constant annual consumption of electrical energy. These are
essential survival resources for a building and are used continuously over a period of time.
Weather-dependent electrical appliances such as Heating Ventilation and Air Conditioning HVAC
systems, fans, air conditioners or heaters, on the other hand, are used intermittently when the
outside temperature is greater or lesser than the indoor comfort temperature. The energy usage by
any of these weather-dependent appliances contribute towards variable electricity consumption.
Hence, the analysis for the base-load energy will not only confirm the performance of the building but
also help the energy managers to implant and verify the building-retrofit projects, if required.
Tracking building performance by analyzing the base-load consumption will eventually help to bring
building-sustainability.
Interestingly, the Campus Sustainability office at the University of Michigan has set a goal to achieve
25% Green House Gas (GHG) reduction by 2025 . For a long term climate-action plan like GHG
2
reduction, the comparison of base-load energy of a building across the campus, instead of total
energy usage, will help to build a comprehensive strategy.
But the question is, how to estimate base-load energy from a building’s utility bill.
Setting-up the Model: The null hypotheses of the study are that there is no impact of seasonality
(academic term) and the heating degree days on the electricity bill. This can be states as
follows:
Ho1: Dana’s electricity bill has no impact on the Heating degree days,
Ho2: Dana’s electricity bill is independent on the academic terms;and
Ho3: There is no interaction between academic terms and Heating degree days.
Method:
Usually the monthly billing days are not as per the number of days in a month. Instead, the electricity
reading ( as listed in appendix: Table1) were generated and billed for the first working-day of a month.
This was normalised on monthly basis matching with the monthly data for heating degree days.
Ann Arbor’s monthly Heating Degree Days (see appendix for definition)- a measurement designed to
reflect the demand for energy needed to heat a building - which account for the differences in
weather pattern during the past three years, was obtained from the KARB weather station at Ann
Arbor (calculated by www.degreedays.netwith a base temperature of 65F ) .
The past 3 year monthly-electricity bills, culled from the Plant Operation at University of Michigan, are
grouped into the academic terms, that is, winter, fall and summer term (as shown in Appendix table
2
http://sustainability.umich.edu/about/goals

1) for the period 2012-14. Hence, out of total 36 observation, each of the nine observation were
categorised into 3 different academic terms. The separation of the annual bill into the academic
terms will help to identify the energy pattern consumed by the occupants which are students, faculty
and staff of the school.
In order to analyse the correlation with the Dana’s monthly electricity bill (a continuous dependent
variable) with the academic terms (a nominal independent variable) and the Heating degree days
(continuous independent variable) ANCOVA analysis is done as composed in the below diagram.Alpha
(α) is 0.05 for this analysis, and a residual plot was produced to check for equal variances, and a
normality probability plot (NPP) and Shapiro-Wilk test were produced to check for normality of errors.
DiagramShowing the setting up of ANCOVA as a statistical model.
Results:
All four assumptions of ANCOVA were met as follows, so an ANCOVA is the appropriate test: The data
is described by the following parametric linear model:
•Eij = μ + Ti + βi [HDDij] + εij where, E= Monthly Electricity consumption, T = Academic
Terms, HDD = Heating Degree Days, i = Fall, Winter and Summer Terms.
• Each observation was completely independent of other observations.
• The data show equal variance based on the residual plot and normality of errors is achieved
with a Shapiro-Wilk test result of p =0.3173. See Figure 2 and 3 below.
Box-plot Interpretation: The box plot (refer figure 2) indicates variation in the means and the errors
of monthly consumption for three different academic terms. For the period 2012-14, the electricity
consumption for summer term is highest due to increase in the cooling load for the building.
Contrastingly, for the winter the electrical usage has decreased. In fact, the ST. Dana building relies
more on natural gas than electricity during winters.
This is also evident by analysing the error bars as shown in the boxplot. The fall and summer which
covers a wide range of electricity usage as compared to during the winters - indicating that the change
in weather pattern throughout the period of time has least impact on consumption of electricity
during the winters.

Figure 2Box-plot of Monthly Electricity Usage (in kWh) for Dana Building for different academic terms.
The NPP and Normal Q-Q plots: The left part of the graph shows ( refer figure 3) a test of equal
variance (Residuals vs Fitted). Equal variance is verified as the red line sits so close to the horizontal
dashed line in the middle. The right graph shows a test of normality of errors (Normal Q-Q). Although
there is some variation along the normality line, a Shapiro-Wilk tests confirms normality with a
p-value of 0.3173 (p>0.05). Hence, to transformation of data was required.
Figure 3The NPP and Normal Q-Q plots for normalcy test.
ANCOVA Analysis and Coefficients: In the table 1, the null hypothesis H01 was rejected (with p-value =
0.0004, that is > 0.05). However, there is no significant relation between the electricity consumption

with the summer term (p-value=0.190) and the interaction between the Heating degree days and
Summer term , with the p-value 0.534 (>0.05) in determining the electrical consumption.
The table below also suggests that the slopes (Estimated Std.) are different for the each of the
academic term for the period 2012-14 - indicating difference in rate of electric consumption with the
change in term. This is quite evident in the plot drawn for monthly electricity consumption against the
heating degree days.
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 127251.847 5686.863 22.376 < 2e-16 ***
HDD -31.080 7.821 -3.974 0.000410 ***
Term-Summer -9539.572 7121.538 -1.340 0.190456
Term-Winter -35271.496 9561.557 -3.689 0.000891 ***
HDD:Term-Summer -23.682 37.662 -0.629 0.534240
HDD:Term-Winter 27.864 10.906 2.555 0.015936
Table1 The ANCOVA summary for assessing Monthly Electricity consumption with the HDD during each academic term.
Software used: R-statistics.
An adjusted R-squared value of 0.628 was recorded.
The parametric model can be rewritten as following equations ( Refer appendix-metafile for units):
1. ESummer= -54.782 HDD Summer+117712 (refer the yellow-line, figure: 4)
2. EFall = -31.080 HDD Fall+127252; (refer the green-line, figure: 4)and
3. EWinter = -3.2162 HDD Winter+91980 (refer the orange-line, figure: 4)
Base-load Electricity estimate: A gentle slope with a value of 3.21 during the winter term indicates
that there are only few appliances which respond to the increasing heating load. Moreover, the
R-square value for a linear regression between bills and the heating degree days for the winter term is
quite closer to zero (0.029). In other words, the power consumption during the winter term is mostly
due the weather-independent electrical appliances. Accounting for essential weather-independent
appliances can be estimated by studying the energy outline during winter term itself. Hence in order
to remove the dependency of electricity with the heating degree days, the equation 3 should have a
zero β value. So the model predicts that Dana building’s base-load electricity consumption as
91980 kWh per month.

Figure 4A plot drawn between Monthly Electricity consumption and heating degree days for the period 2012-12.
Discussion:
By referring the β coefficients, the behaviour of electricity usage are different for different
academic terms. The rate of consumption (or slope) is seen highest for the summer than in the fall
term and lastly for the winter term.In fact, the major heating load is been taken care by consuming
more natural gas than any heating appliances.
Although, by comparing a widely used energy metrics: Energy usage intensity (EUIs), refer appendix
definition, for Dana building with other similar schools within the campus will have no effect on
energy consumption but a slight change in the building attributes such as building functionality,
square footage, occupancy load, even the consumer behavior and time of usage to name few, will
cause enough variation in their total energy usage pattern. Instead, a retrospective energy usage
analysis for the Dana building by using the electricity bill - if compared with other similar schools - will
reduce complexities due to change in physical building attributes. Furthermore, by grouping the
energy usage with academic-term period, that is fall, winter and summer terms, will take into account
for change in occupancy load and the consumer behavior, if any.
The retrospective analysis for the Dana building assumes that there isn’t any major building-functional
change as a the change in number of building occupants is constant throughout an year - irrespective
of any academic terms. The research disregards any annual breaks - specially the Christmas break-
where buildings and its operation are closed almost for a couple of weeks. Hence, a weekly data of
electricity consumption would be more precise to determine the closer base-load electricity results.

References:
● Lean Analysis, Johnson Controls Inc. Sample Lean Analysis by Johnson Controls. [online at
http://www.johnsoncontrols.com/content/us/en/products/building_efficiency/products-and-
systems/building_management/lean.html]
● Energy Star Portfolio Manager, Technical References [online at
portfoliomanager.energystar.gov/pdf/reference/Climate%20and%20Weather.pdf ]
● Abrax Energy, An Introduction to Utility Bill Weather Normalization for Energy Contractors,
[online at
www.abraxasenergy.com/articles/intro-weather-normalization-contractors/#_ftnref7 ]

NRE 538: Independent Project
Appendix:
Definition:
Heating Degree Day (HDD): Degree days below a temperature (also called Heating degree days)
correspond to the cumulative number of degrees by which the mean daily temperature falls below a
given temperature called the "base temperature".
Energy Use Intensity (EUI) for a building: is the measurement used to size up a building's energy
performance. It represents the energy consumed by a building relative to its size and is expressed in
gigajoules per square metre per year.
A building's EUI is calculated as follows:
Total energy consumed in one year (GJ) / total floor space of the building (m2
)
For example, if an 8,000 m2 school consumed 7,000 GJ of energy, its EUI would be 0.88 GJ/m2. A
similarly sized school that consumed 10,000 GJ of energy would have a higher EUI (1.25 GJ/m2) to
reflect its higher energy use. Generally, a lower EUI signifies better energy performance.
Raw Data:
Table 1: S.T. Dana Building, University of Michigan, Electricity bill for the period 2012-2014
Month Term Year
Electric Bill
(kWh per
Bill)
Billing Days
Heating
Degree Days
(in Day-F)
Monthly Electricity
Usage ( in kWh per
Month)
Jul Summer 2014 114,565.00 31 94 114565.00
Aug Summer 2014 121,318.00 30 55 125361.93
Sep Fall 2014 131,254.00 29 220 135780.00
Oct Fall 2014 116,227.00 31 466 116227.00
Nov Fall 2014 99,412.00 28 914 106512.86
Dec Fall 2014 88,195.00 29 993 94277.41
Jan Winter 2014 86,472.00 32 1539 83769.75
Feb Winter 2014 98,895.00 29 1345 95484.83
Mar Winter 2014 85,538.00 28 1168 94702.79
Apr Winter 2014 94,648.00 31 539 91594.84
May Summer 2014 97,001.00 29 259 103690.72
Jun Summer 2014 103,846.00 29 63 107426.90
Jul Summer 2013 118,121.00 31 46 118121.00
Aug Summer 2013 119,199.00 30 70 123172.30
Sep Fall 2013 122,542.00 29 201 126767.59
Oct Fall 2013 100,119.00 31 454 100119.00
Nov Fall 2013 99,211.00 29 849 102632.07

Dec Fall 2013 92,404.00 29 1191 98776.69
Jan Winter 2013 85,675.00 32 1170 82997.66
Feb Winter 2013 96,206.00 29 1098 92888.55
Mar Winter 2013 85,681.00 28 1006 94861.11
Apr Winter 2013 93,525.00 31 616 90508.06
May Summer 2013 101,988.00 29 225 109021.66
Jun Summer 2013 109,340.00 28 76 117150.00
Jul Summer 2012 114,252.00 29 23 126493.29
Aug Summer 2012 116,401.00 31 80 112763.47
Sep Fall 2012 111,349.00 30 223 115188.62
Oct Fall 2012 97,289.00 29 478 103998.59
Nov Fall 2012 90,697.00 31 836 87771.29
Dec Fall 2012 88,018.00 28 946 97448.50
Jan Winter 2012 77,232.00 30 1079 79806.40
Feb Winter 2012 85,957.00 31 934.5 77638.58
Mar Winter 2012 79,556.00 29 458 85042.62
Apr Winter 2012 94,460.00 29 474.5 97717.24
May Summer 2012 87,123.00 30 90.5 90027.10
Jun Summer 2012 103,777.00 30 32 103777.00

Metadata:
Metadata for Project_NRE538.csv

Contact information:

Divyesh Kumar
School of Natural Resources & Environment
University of Michigan
divyeshk@umich.edu

Secondary contacts (GSIs for course):
Justin Burdin (jburdine@umich.edu)

Context:
This dataset is the electricity utility bill collected from the
Plantoperations at University of Michigan for the NRE538 classproject.
measuring popping efficiency of microwave popcorn. The past 3 year
monthlyelectricity bills, culled from the Plant Operation at University of
Michigan, are grouped into the academic terms, that is, winter, fall and summer
term for the period 201214. Hence, out of total 36 observation, each of the
nine observation were categorised into 3 different academic terms.

Ann Arbor’s monthly Heating Degree Days (see appendix for definition) a
measurement designed to reflect the demand for energy needed to heat a building
which account for the differences in weather pattern during the past three
years, was obtained from the KARB weather station at Ann Arbor (calculated by
www.degreedays.net with a base temperature of 65F )
Temporal coverage:
The data covered in experiments are for 2012 to 2014.

Geographic coverage:
The area of study is in ST. Dana Building, University of Michigan, Ann Arbor,
MI, USA
Attributes:

Name Definition Type Units Precision

E Monthly electricity billContinuos kWh 2 decimals
HDD Heating Degree Days Continuos DaysF2 decimals
TERM Academic Terms Discrete

Coding:
energymodelfull = Comparing Electricity consumption with academic terms and
Heating degree days.
R-Code:
Setting-Up and Initial Analysis
read.csv(file="Project_NRE538.csv")
energy=read.csv("Project_NRE538.csv")
attach(energyfullmodel)
summary(energyfullmodel)

Testing for normalcy and comparing the discrete variables
boxplot(kwh.month~Term,which=c(1,1),ylab='Electricity Bill kWh per day')
par(mfrow=c(1,2))
plot(energymodelfull,which=c(1,2))
shapiro.test(resid(energymodelfull))
ANCOVA Analysis
energymodelfull<lm(kwh.month~HDD*Term)
summary(energymodelfull)

Graphing the variables

plot(HDD[Term=='Fall'],kwh.month[Term=='Fall'],xlab='Heating Degree Day per
month',ylab='Monthly Electricity bill in kWh',pch=15,col='green')
points(HDD[Term=='Winter'],kwh.month[Term=='Winter'],pch=16,col='orange')
points(HDD[Term=='Summer'],kwh.month[Term=='Summer'],pch=17,col='yellow')
abline(127251.847,31.080,col='green',lty=1)
abline(91980.351,3.216, col='orange',lty=2)
abline(117712,54.782, col='yellow',lty=4)

Regression model for calculating the base load energy using the utility bills.

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Regression model for calculating the base load energy using the utility bills.