Forecasting electricity demand
1
Forecasting
medium- and long-term
peak electricity demand
Rob J Hyndman
Business & Economic Forecasting Unit
Forecasting electricity demand
The problem
We want to forecast the peak electricity
demand in a half-hour period in ten years
time.
2
Forecasting electricity demand
The problem
We want to forecast the peak electricity
demand in a half-hour period in ten years
time.
We have ten years of half-hourly electricity
data, temperature data and some
economic and demographic data.
2
Forecasting electricity demand
The problem
We want to forecast the peak electricity
demand in a half-hour period in ten years
time.
We have ten years of half-hourly electricity
data, temperature data and some
economic and demographic data.
The location is South Australia: home to
the most volatile electricity demand in the
world.
2
Forecasting electricity demand
The problem
We want to forecast the peak electricity
demand in a half-hour period in ten years
time.
We have ten years of half-hourly electricity
data, temperature data and some
economic and demographic data.
The location is South Australia: home to
the most volatile electricity demand in the
world.
2
Forecasting electricity demand
2
The problem
We want to forecast the peak electricity
demand in a half-hour period in ten years
time.
We have ten years of half-hourly electricity
data, temperature data and some
economic and demographic data.
The location is South Australia: home to
the most volatile electricity demand in the
world.
Sounds impossible?
Forecasting electricity demand
Demand data
Half-hourly demand data for South Australia from 1 July 1997 to 31 March 2007.
Only data from November–March are shown.
3
Forecasting electricity demand
4
Demand data
2.0
1.5
1.0
SA demand (GW)
2.5
South Australian operational demand (summer 06/07)
Nov 06
Dec 06
Jan 07
Feb 07
Mar 07
Half-hourly demand data for South Australia from 1 November 2006 to 31 March 2007.
Forecasting electricity demand
5
Demand data
2.0
1.5
1.0
SA demand (GW)
2.5
SA demand (first 3 weeks of January 2007)
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21
Half-hourly demand data for South Australia
from
1–21 January 2007.
Date in
January
Forecasting electricity demand
6
Demand boxplots
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Fri
Sat
Sun
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1.5
2.0
●
1.0
Demand (GW)
2.5
3.0
Time: 12 midnight
●
Mon
Day of week
Forecasting electricity demand
7
Temperature data
Time: 12 midnight
2.0
1.5
1.0
Non−Olympic Demand (GW)
2.5
Workday
Non−workday
10
20
Temperature (deg C)
30
40
Forecasting electricity demand
Demand drivers
calendar effects
8
Forecasting electricity demand
Demand drivers
calendar effects
prevailing weather conditions (and the
timing of those conditionals
8
Forecasting electricity demand
Demand drivers
calendar effects
prevailing weather conditions (and the
timing of those conditionals
climate changes
8
Forecasting electricity demand
Demand drivers
calendar effects
prevailing weather conditions (and the
timing of those conditionals
climate changes
economic and demographic changes
8
Forecasting electricity demand
Demand drivers
calendar effects
prevailing weather conditions (and the
timing of those conditionals
climate changes
economic and demographic changes
changing technology
8
Forecasting electricity demand
Demand drivers
calendar effects
prevailing weather conditions (and the
timing of those conditionals
climate changes
economic and demographic changes
changing technology
8
Forecasting electricity demand
Demand drivers
calendar effects
prevailing weather conditions (and the
timing of those conditionals
climate changes
economic and demographic changes
changing technology
Modelling framework
Semi-parametric additive models with
correlated errors.
8
Forecasting electricity demand
Demand drivers
calendar effects
prevailing weather conditions (and the
timing of those conditionals
climate changes
economic and demographic changes
changing technology
Modelling framework
Semi-parametric additive models with
correlated errors.
Each half-hour period modelled separately.
8
Forecasting electricity demand
8
Demand drivers
calendar effects
prevailing weather conditions (and the
timing of those conditionals
climate changes
economic and demographic changes
changing technology
Modelling framework
Semi-parametric additive models with
correlated errors.
Each half-hour period modelled separately.
Variables selected to provide best
out-of-sample predictions for 2005/06 summer.
Forecasting electricity demand
9
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
yt,p denotes demand at time t (measured in
half-hourly intervals) during period p, p = 1, . . . , 48;
Forecasting electricity demand
9
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
yt,p denotes demand at time t (measured in
half-hourly intervals) during period p, p = 1, . . . , 48;
hp (t ) models all calendar effects;
Forecasting electricity demand
9
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
yt,p denotes demand at time t (measured in
half-hourly intervals) during period p, p = 1, . . . , 48;
hp (t ) models all calendar effects;
fp (w1,t , w2,t ) models all temperature effects where
w1,t is a vector of recent temperatures at Kent
Town and w2,t is a vector of recent temperatures at
Adelaide airport;
Forecasting electricity demand
9
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
yt,p denotes demand at time t (measured in
half-hourly intervals) during period p, p = 1, . . . , 48;
hp (t ) models all calendar effects;
fp (w1,t , w2,t ) models all temperature effects where
w1,t is a vector of recent temperatures at Kent
Town and w2,t is a vector of recent temperatures at
Adelaide airport;
zj,t is a demographic or economic variable at time t
Forecasting electricity demand
9
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
yt,p denotes demand at time t (measured in
half-hourly intervals) during period p, p = 1, . . . , 48;
hp (t ) models all calendar effects;
fp (w1,t , w2,t ) models all temperature effects where
w1,t is a vector of recent temperatures at Kent
Town and w2,t is a vector of recent temperatures at
Adelaide airport;
zj,t is a demographic or economic variable at time t
nt denotes the model error at time t.
Forecasting electricity demand
10
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
hp (t ) includes handle annual, weekly and daily seasonal
patterns as well as public holidays:
hp (t ) = `p (t ) + αt,p + βt,p + γt,p + δt,p
`p (t) is “time of summer” effect (a regression spline);
Forecasting electricity demand
10
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
hp (t ) includes handle annual, weekly and daily seasonal
patterns as well as public holidays:
hp (t ) = `p (t ) + αt,p + βt,p + γt,p + δt,p
`p (t) is “time of summer” effect (a regression spline);
αt,p is day of week effect;
Forecasting electricity demand
10
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
hp (t ) includes handle annual, weekly and daily seasonal
patterns as well as public holidays:
hp (t ) = `p (t ) + αt,p + βt,p + γt,p + δt,p
`p (t) is “time of summer” effect (a regression spline);
αt,p is day of week effect;
βt,p is “holiday” effect;
Forecasting electricity demand
10
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
hp (t ) includes handle annual, weekly and daily seasonal
patterns as well as public holidays:
hp (t ) = `p (t ) + αt,p + βt,p + γt,p + δt,p
`p (t) is “time of summer” effect (a regression spline);
αt,p is day of week effect;
βt,p is “holiday” effect;
γt,p New Year’s Eve effect;
Forecasting electricity demand
10
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
hp (t ) includes handle annual, weekly and daily seasonal
patterns as well as public holidays:
hp (t ) = `p (t ) + αt,p + βt,p + γt,p + δt,p
`p (t) is “time of summer” effect (a regression spline);
αt,p is day of week effect;
βt,p is “holiday” effect;
γt,p New Year’s Eve effect;
δt,p is millennium effect;
Forecasting electricity demand
11
Fitted results (3pm)
0.4
0.2
−0.4
0
50
100
150
0.2
0.0
−0.4
Normal
Day before
Holiday
Holiday
Mon
Tue
Wed
Thu
Fri
Day of week
0.4
Day of summer
Effect on demand
0.0
Effect on demand
0.2
0.0
−0.4
Effect on demand
0.4
Time: 3:00 pm
Day after
Sat
Sun
Forecasting electricity demand
12
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
fp (w1,t , w2,t ) =
6
X
fk,p (xt−k ) + gk,p (dt−k ) + qp (xt+ ) + rp (xt− ) + sp (x̄t )
k =0
+
6
X
Fj,p (xt−48j ) + Gj,p (dt−48j )
j=1
xt is ave temp across sites at time t;
Forecasting electricity demand
12
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
fp (w1,t , w2,t ) =
6
X
fk,p (xt−k ) + gk,p (dt−k ) + qp (xt+ ) + rp (xt− ) + sp (x̄t )
k =0
+
6
X
Fj,p (xt−48j ) + Gj,p (dt−48j )
j=1
xt is ave temp across sites at time t;
dt is the temp difference between sites at time t;
Forecasting electricity demand
12
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
fp (w1,t , w2,t ) =
6
X
fk,p (xt−k ) + gk,p (dt−k ) + qp (xt+ ) + rp (xt− ) + sp (x̄t )
k =0
+
6
X
Fj,p (xt−48j ) + Gj,p (dt−48j )
j=1
xt is ave temp across sites at time t;
dt is the temp difference between sites at time t;
xt+ is max of xt values in past 24 hours;
Forecasting electricity demand
12
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
fp (w1,t , w2,t ) =
6
X
fk,p (xt−k ) + gk,p (dt−k ) + qp (xt+ ) + rp (xt− ) + sp (x̄t )
k =0
+
6
X
Fj,p (xt−48j ) + Gj,p (dt−48j )
j=1
xt is ave temp across sites at time t;
dt is the temp difference between sites at time t;
xt+ is max of xt values in past 24 hours;
xt− is min of xt values in past 24 hours;
Forecasting electricity demand
12
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
fp (w1,t , w2,t ) =
6
X
fk,p (xt−k ) + gk,p (dt−k ) + qp (xt+ ) + rp (xt− ) + sp (x̄t )
k =0
+
6
X
Fj,p (xt−48j ) + Gj,p (dt−48j )
j=1
xt is ave temp across sites at time t;
dt is the temp difference between sites at time t;
xt+ is max of xt values in past 24 hours;
xt− is min of xt values in past 24 hours;
x̄t is ave temp in past seven days.
Forecasting electricity demand
12
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
fp (w1,t , w2,t ) =
6
X
fk,p (xt−k ) + gk,p (dt−k ) + qp (xt+ ) + rp (xt− ) + sp (x̄t )
k =0
+
6
X
Fj,p (xt−48j ) + Gj,p (dt−48j )
j=1
xt is ave temp across sites at time t;
dt is the temp difference between sites at time t;
xt+ is max of xt values in past 24 hours;
xt− is min of xt values in past 24 hours;
x̄t is ave temp in past seven days.
Forecasting electricity demand
12
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
fp (w1,t , w2,t ) =
6
X
fk,p (xt−k ) + gk,p (dt−k ) + qp (xt+ ) + rp (xt− ) + sp (x̄t )
k =0
+
6
X
Fj,p (xt−48j ) + Gj,p (dt−48j )
j=1
xt is ave temp across sites at time t;
dt is the temp difference between sites at time t;
xt+ is max of xt values in past 24 hours;
xt− is min of xt values in past 24 hours;
x̄t is ave temp in past seven days.
Each function is smooth and estimated using regression splines.
−8
−4
0
0
Lag 5 temp differential
4
Lag 1 temp differential
5
−10
−10
25
−5
−5
0
Lag 6 temp differential
0
5
Previous max temp
35
Lag 2 temp differential
5
35
15
5
−10
−10
25
10
20
Lag 3 temp differential
−5
−5
0
0
5
Lag 1 day temp differential
5
0.0 0.2 0.4
Effect on demand
−0.4
25
0.0 0.2 0.4
Effect on demand
15
−0.4
0.0 0.2 0.4
Effect on demand
−0.4
35
0.0 0.2 0.4
15
0.0 0.2 0.4
Lag 5 temperature
Effect on demand
35
Effect on demand
Lag 1 temperature
−0.4
Last week average temp
25
−0.4
15
0.0 0.2 0.4
35
Effect on demand
Lag 4 temperature
25
−0.4
0.0 0.2 0.4
Effect on demand
−0.4
15
0.0 0.2 0.4
−5
35
Effect on demand
25
0.0 0.2 0.4
Effect on demand
0.0 0.2 0.4
Effect on demand
−0.4
Temperature
−0.4
15
−0.4
25
0.0 0.2 0.4
Effect on demand
15
−0.4
0.0 0.2 0.4
Effect on demand
−0.4
25
0.0 0.2 0.4
0.0 0.2 0.4
Effect on demand
−0.4
15
−0.4
Effect on demand
0.0 0.2 0.4
Effect on demand
−0.4
0.0 0.2 0.4
0.0 0.2 0.4
−0.4
0.0 0.2 0.4
Effect on demand
−0.4
Effect on demand
−0.4
Effect on demand
0.0 0.2 0.4
Effect on demand
−0.4
Forecasting electricity demand
13
Fitted results (3pm)
Time: 3:00 pm
Lag 2 temperature
35
15
Lag 3 temperature
Lag 1 day temperature
35
15
Previous min temp
30
−10
−8
25
−5
−4
35
Lag 2 day temperature
25
35
Temperature differential
0
0
5
Lag 4 temp differential
4
Forecasting electricity demand
14
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
Other variables described by linear
relationships with coefficients c1 , . . . , cJ .
Forecasting electricity demand
14
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
Other variables described by linear
relationships with coefficients c1 , . . . , cJ .
Estimation based on annual data.
Forecasting electricity demand
14
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
Other variables described by linear
relationships with coefficients c1 , . . . , cJ .
Estimation based on annual data.
Forecasting electricity demand
14
Equations
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
Other variables described by linear
relationships with coefficients c1 , . . . , cJ .
Estimation based on annual data.
Variable
Intercept
Gross State Product
Lag Price
Cooling Degree Days
Coefficient
−0.13981
0.01684
−0.04957
0.36300
Std. Error
0.04338
0.00108
0.00727
0.01716
t value
−3.222
15.649
−6.818
21.157
P value
0.018094
0.000004
0.000488
0.000001
Forecasting electricity demand
15
Actual
Fitted
1.45
1.40
1.35
1.30
1.25
Annual demand
1.50
1.55
Predictions
1998
2000
2002
Year
2004
2006
Forecasting electricity demand
15
Predictions
80
75
70
65
R−squared (%)
85
90
95
R−squared
12 midnight 3:00 am
6:00 am
9:00 am
12 noon
Time of day
3:00 pm
6:00 pm
9:00 pm 12 midnight
Forecasting electricity demand
15
Predictions
1.0
1.5
2.0
2.5
3.0
Actual demand
1998
2000
2002
2004
2006
Time
1.0
1.5
2.0
2.5
3.0
Predicted demand
1998
2000
2002
2004
2006
Forecasting electricity demand
15
2.0
1.5
1.0
Actual demand
2.5
3.0
Predictions
1.0
1.5
2.0
Predicted demand
2.5
3.0
Forecasting electricity demand
16
Peak demand forecasting
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
Multiple alternative futures created by
resampling residuals using a seasonal
bootstrap;
Forecasting electricity demand
16
Peak demand forecasting
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
Multiple alternative futures created by
resampling residuals using a seasonal
bootstrap;
generating simulations of future
temperature patterns based on seasonally
bootstrapping past temperatures (with
some adjustment for extremes and climate
change);
Forecasting electricity demand
16
Peak demand forecasting
log(yt,p ) = hp (t ) + fp (w1,t , w2,t ) +
J
X
cj zj,t + nt
j =1
Multiple alternative futures created by
resampling residuals using a seasonal
bootstrap;
generating simulations of future
temperature patterns based on seasonally
bootstrapping past temperatures (with
some adjustment for extremes and climate
change);
using assumed values for GSP and Price.
Forecasting electricity demand
17
Peak demand distribution
Demand
1.4
Base
0.8
0.6
0.2
0.4
Density
1.0
1.2
2007/2008
2008/2009
2009/2010
2010/2011
2011/2012
2012/2013
2013/2014
2014/2015
2015/2016
2016/2017
2017/2018
W)5
6
0.0
5
1
2
3
Demand (GW)
4
5
Forecasting electricity demand
17
Peak demand distribution
Annual maximum
Base demand
1.0
0.5
Density
1.5
2007/2008
2008/2009
2009/2010
2010/2011
2011/2012
2012/2013
2013/2014
2014/2015
2015/2016
2016/2017
2017/2018
W)6
6
0.0
5
3
4
5
Demand (GW)
6
Forecasting electricity demand
17
3.0
3.5
4.0
90%
50%
10%
2%
●
●
●
●
●
●
●
2.5
Prob of exceedance in one year
Peak demand distribution
●
●
●
2000
2005
2010
Year
2015
Forecasting electricity demand
Conclusions
We have forecast the extreme upper tail in ten
years time using only ten years of data!
18
Forecasting electricity demand
Conclusions
We have forecast the extreme upper tail in ten
years time using only ten years of data!
This method has now been adopted for the official
South Australian peak electricity demand forecasts.
18
Forecasting electricity demand
Conclusions
We have forecast the extreme upper tail in ten
years time using only ten years of data!
This method has now been adopted for the official
South Australian peak electricity demand forecasts.
We hope to extend method to Victoria in next year.
18
Forecasting electricity demand
Conclusions
We have forecast the extreme upper tail in ten
years time using only ten years of data!
This method has now been adopted for the official
South Australian peak electricity demand forecasts.
We hope to extend method to Victoria in next year.
Method could also be used for short-term demand
forecasting, if we add a model for correlated
residuals.
18
Forecasting electricity demand
Conclusions
We have forecast the extreme upper tail in ten
years time using only ten years of data!
This method has now been adopted for the official
South Australian peak electricity demand forecasts.
We hope to extend method to Victoria in next year.
Method could also be used for short-term demand
forecasting, if we add a model for correlated
residuals.
Provides way to analyse probability of coincident
peaks across different interconnected markets.
18
Forecasting electricity demand
Conclusions
We have forecast the extreme upper tail in ten
years time using only ten years of data!
This method has now been adopted for the official
South Australian peak electricity demand forecasts.
We hope to extend method to Victoria in next year.
Method could also be used for short-term demand
forecasting, if we add a model for correlated
residuals.
Provides way to analyse probability of coincident
peaks across different interconnected markets.
Could be extended to whole year, providing
probabilistic forecasts of total energy requirements.
18
Forecasting electricity demand
Conclusions
We have forecast the extreme upper tail in ten
years time using only ten years of data!
This method has now been adopted for the official
South Australian peak electricity demand forecasts.
We hope to extend method to Victoria in next year.
Method could also be used for short-term demand
forecasting, if we add a model for correlated
residuals.
Provides way to analyse probability of coincident
peaks across different interconnected markets.
Could be extended to whole year, providing
probabilistic forecasts of total energy requirements.
An R package and a paper will (eventually) appear
at www.robhyndman.info
18