HW4 - Long term system planning
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Dec 6, 2023
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ES 300 – Homework 4
Long term system planning
Note:
all data needed to complete this assignment are located in the HW4
Data.xlsx file posted on Moodle.
You are chief demand forecaster at the friendly neighborhood electric utility,
and are trying to build a model that will predict “peak system demand” in the
year 2024. To start with, you have a bunch of historical information for the past
20 years, including peak demand data and records of four other variables that
might help explain how peak demand changes year-to-year. Note that 1 GW =
1000 MW.
You decide to start with some exploratory analysis of the pairwise
relationships between peak demand and the other variables.
Year
Peak
Demand
(GW)
Economic
Index
Population
(million)
Per Capita
Energy use
Metric
Max Average
Daily Temp (F)
2004
19.34
1.10
4.00
1.30
85.46
2005
20.11
1.30
4.08
1.40
86.99
2006
19.83
1.40
4.14
1.40
86.00
2007
20.20
1.50
4.21
1.50
84.47
2008
20.47
1.80
4.27
1.50
86.99
2009
20.70
1.60
4.35
1.40
89.42
2010
20.52
2.67
4.44
1.10
89.42
2011
20.81
1.78
4.55
1.20
90.50
2012
20.20
-0.29
4.64
1.00
86.00
2013
19.78
-2.78
4.72
0.98
86.00
2014
20.81
2.53
4.79
0.98
86.99
2015
20.67
1.60
4.85
0.97
84.47
2016
20.98
2.22
4.90
0.96
86.99
2017
20.49
1.80
4.95
0.94
83.48
2018
20.85
2.00
5.00
0.94
84.56
2019
20.74
2.40
5.06
0.93
83.56
1)
First, create four separate “scatter plots” of peak electricity demand
versus (show them in different graphs). You must label each axis to get
credit!
a.
Economic index
b. Population
c.
Per capita energy use
d.
Maximum average daily temperature
Since no single variable is a perfect predictor of peak demand, you think it would
be wise to create a model that uses information from all four variables to help
predict demand. You use least squares regression to fit the following model.
Y
T
= aw
T
+ bx
T
+ cy
T
+ dz
T
Where,
Y
T
= predicted peak demand in year T (in GW)
w
T
= economic index in year T
x
T
= population in year T
y
T
= per capita energy use in year T
z
T
= maximum average daily temperature in year T
The “best fit” coefficients are found to be:
a = 0.1758
b = 1.344
c = 0.220
d = 0.1595
With your trusty model in hand, you set out to predict future demand. The person
in the cubicle next to you passes you a series of forecasts that describe the state
of the world in the years 2020-2024. Here is what it says:
Year
Economic
Index
Population
(million)
Per Capita
Consumption
Metric
2020
0.90
5.15
0.90
2021
0.95
5.25
0.85
2022
1.00
5.40
0.80
2023
1.05
5.55
0.80
2024
1.10
5.75
0.78
What you don’t know is what the maximum average daily temperature will be in
these future years (no one does!). You decide a reasonable way to look into this
would be to use historical temperature data from 1954-2019:
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2. Look at the historical temperature data listed in the ‘HistoricalTemps’
worksheet (look at the bottom of the screen in Excel), please calculate two
values:
a.
The median (50
th
percentile) temperature. To determine this, put
=MEDIAN(B:B) into any blank cell and press enter.
= 86.09
b.
The 90
th
percentile (i.e., please estimate this as the 7
th
highest
temperature on record). To do this, sort the data by temperatures from
largest to smallest and find the 7
th
highest.
= 88.52
3.
Now you’re ready to use your model to predict the future.
a. First calculate future electricity demand in years 2020-2024 assuming a
median temperature (your answer for 2a).
2020 = 21.01
2021 = 21.14
2022 = 21.34
2023 = 21.55
2024 = 21.82
b.
Next calculate future electricity demand in years 2020-24 assuming a 90
th
percentile temperature (your answer for 2b).
2020 = 21.4
2021 = 21.53
2022 = 21.73
2023 = 21.94
2024 = 22.21
c.
If you want to have enough generation capacity to meet 2024 peak demand
under a 90
th
percentile temperature, how much new capacity
do you need
to build (assuming today the system already has 21 GW of “firm” capacity
installed).
= 1.21
d.
How much new capacity
do you need in order to have a 15% “reserve
margin” (i.e., 115% of 2024 peak demand under a 90
th
percentile), assuming
today the system already has 21 GW of “firm” capacity installed?
=
4.544