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Probabilistic forecasting of
peak electricity demand
Rob J Hyndman
Joint work with Shu Fan
Probabilistic forecasting of peak electricity demand 1
Outline
1 The problem
2 The model
3 Forecasts
4 Challenges and extensions
5 Short term forecasts
6 Evaluating probabilistic forecasts
7 MEFM package
8 References and resources
Probabilistic forecasting of peak electricity demand The problem 2
The problem
We want to forecast the peak electricity
demand in a half-hour period in twenty years
time.
We have fifteen 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?
Probabilistic forecasting of peak electricity demand The problem 3
The problem
We want to forecast the peak electricity
demand in a half-hour period in twenty years
time.
We have fifteen 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?
Probabilistic forecasting of peak electricity demand The problem 3
South Australian demand data
Probabilistic forecasting of peak electricity demand The problem 4
South Australian demand data
Probabilistic forecasting of peak electricity demand The problem 4
Black Saturday →
The heatwave
Probabilistic forecasting of peak electricity demand The problem 5
The heatwave
Probabilistic forecasting of peak electricity demand The problem 5
The heatwave
Probabilistic forecasting of peak electricity demand The problem 5
South Australian demand data
Probabilistic forecasting of peak electricity demand The problem 6
SA State wide demand (summer 2015)
SAStatewidedemand(GW)
1.01.52.02.53.0
Oct Nov Dec Jan Feb Mar
South Australian demand data
Probabilistic forecasting of peak electricity demand The problem 6
Temperature data (Sth Aust)
Probabilistic forecasting of peak electricity demand The problem 7
Temperature data (Sth Aust)
Probabilistic forecasting of peak electricity demand The problem 8
10 20 30 40
1.01.52.02.53.03.5
Time: 12 midnight
Temperature (deg C)
Demand(GW)
Workday
Non−workday
Demand boxplots (Sth Aust)
Probabilistic forecasting of peak electricity demand The problem 9
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Mon Tue Wed Thu Fri Sat Sun
1.01.52.02.53.03.5
Time: 12 midnight
Day of week
Demand(GW)
Demand densities (Sth Aust)
Probabilistic forecasting of peak electricity demand The problem 10
1.0 1.5 2.0 2.5 3.0 3.5
01234
Density of demand: 12 midnight
South Australian half−hourly demand (GW)
Density
Outline
1 The problem
2 The model
3 Forecasts
4 Challenges and extensions
5 Short term forecasts
6 Evaluating probabilistic forecasts
7 MEFM package
8 References and resources
Probabilistic forecasting of peak electricity demand The model 11
Predictors
calendar effects
prevailing and recent weather conditions
climate changes
economic and demographic changes
changing technology
Modelling framework
Semi-parametric additive models with
correlated errors.
Each half-hour period modelled separately for
each season.
Variables selected to provide best
out-of-sample predictions using cross-validation
on each summer.
Probabilistic forecasting of peak electricity demand The model 12
Predictors
calendar effects
prevailing and recent weather conditions
climate changes
economic and demographic changes
changing technology
Modelling framework
Semi-parametric additive models with
correlated errors.
Each half-hour period modelled separately for
each season.
Variables selected to provide best
out-of-sample predictions using cross-validation
on each summer.
Probabilistic forecasting of peak electricity demand The model 12
Monash Electricity Forecasting Model
y∗
t = yt/¯yi
yt denotes per capita demand (minus offset) at
time t (measured in half-hourly intervals);
¯yi is the average demand for quarter i where t
is in quarter i.
y∗
t is the standardized demand for time t.
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Probabilistic forecasting of peak electricity demand The model 13
Monash Electricity Forecasting Model
Probabilistic forecasting of peak electricity demand The model 14
Monash Electricity Forecasting Model
Probabilistic forecasting of peak electricity demand The model 14
Annual model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
log(¯yi) = log(¯yi−1) +
j
cj(zj,i − zj,i−1) + εi
First differences modelled to avoid
non-stationary variables.
Predictors: Per-capita GSP, Price, Summer CDD,
Winter HDD.
Probabilistic forecasting of peak electricity demand The model 15
Annual model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
log(¯yi) = log(¯yi−1) +
j
cj(zj,i − zj,i−1) + εi
First differences modelled to avoid
non-stationary variables.
Predictors: Per-capita GSP, Price, Summer CDD,
Winter HDD.
Probabilistic forecasting of peak electricity demand The model 15
Annual model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
log(¯yi) = log(¯yi−1) +
j
cj(zj,i − zj,i−1) + εi
First differences modelled to avoid
non-stationary variables.
Predictors: Per-capita GSP, Price, Summer CDD,
Winter HDD.
zCDD =
summer
max(0, ¯T − 17.5)
¯T = daily mean
Probabilistic forecasting of peak electricity demand The model 15
Annual model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
log(¯yi) = log(¯yi−1) +
j
cj(zj,i − zj,i−1) + εi
First differences modelled to avoid
non-stationary variables.
Predictors: Per-capita GSP, Price, Summer CDD,
Winter HDD.
zHDD =
winter
max(0, 19.5 − ¯T)
¯T = daily mean
Probabilistic forecasting of peak electricity demand The model 15
Annual model
SA summer cooling degree days
Year
scdd
2002 2004 2006 2008 2010 2012 2014
300400500600700
SA winter heating degree days
800850
Probabilistic forecasting of peak electricity demand The model 16
Annual model
Variable Coefficient Std. Error t value P value
∆gsp.pc 2.02 5.05 0.38 0.711
∆price −1.67 0.68 −2.46 0.026
∆scdd 1.11 0.25 4.49 0.000
∆whdd 2.07 0.33 0.63 0.537
GSP needed to stay in the model to allow
scenario forecasting.
All other variables led to improved AICC.
Probabilistic forecasting of peak electricity demand The model 17
Annual model
Variable Coefficient Std. Error t value P value
∆gsp.pc 2.02 5.05 0.38 0.711
∆price −1.67 0.68 −2.46 0.026
∆scdd 1.11 0.25 4.49 0.000
∆whdd 2.07 0.33 0.63 0.537
GSP needed to stay in the model to allow
scenario forecasting.
All other variables led to improved AICC.
Probabilistic forecasting of peak electricity demand The model 17
Annual model
Variable Coefficient Std. Error t value P value
∆gsp.pc 2.02 5.05 0.38 0.711
∆price −1.67 0.68 −2.46 0.026
∆scdd 1.11 0.25 4.49 0.000
∆whdd 2.07 0.33 0.63 0.537
GSP needed to stay in the model to allow
scenario forecasting.
All other variables led to improved AICC.
Probabilistic forecasting of peak electricity demand The model 17
Annual model
Probabilistic forecasting of peak electricity demand The model 18
Year
Annualdemand
1.01.21.41.61.82.0
2002 2004 2006 2008 2010 2012 2014
Actual
Fitted
Monash Electricity Forecasting Model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Calendar effects
“Time of summer” effect (a regression spline)
Day of week factor (7 levels)
Public holiday factor (4 levels)
New Year’s Eve factor (2 levels)
Probabilistic forecasting of peak electricity demand The model 19
Monash Electricity Forecasting Model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Calendar effects
“Time of summer” effect (a regression spline)
Day of week factor (7 levels)
Public holiday factor (4 levels)
New Year’s Eve factor (2 levels)
Probabilistic forecasting of peak electricity demand The model 19
Monash Electricity Forecasting Model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Calendar effects
“Time of summer” effect (a regression spline)
Day of week factor (7 levels)
Public holiday factor (4 levels)
New Year’s Eve factor (2 levels)
Probabilistic forecasting of peak electricity demand The model 19
Monash Electricity Forecasting Model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Calendar effects
“Time of summer” effect (a regression spline)
Day of week factor (7 levels)
Public holiday factor (4 levels)
New Year’s Eve factor (2 levels)
Probabilistic forecasting of peak electricity demand The model 19
Fitted results (Summer 3pm)
Probabilistic forecasting of peak electricity demand The model 20
0 50 100 150
−0.40.00.4
Day of summer
Effectondemand
Mon Tue Wed Thu Fri Sat Sun
−0.40.00.4
Day of week
Effectondemand
Normal Day before Holiday Day after
−0.40.00.4
Holiday
Effectondemand
Time: 3:00 pm
Monash Electricity Forecasting Model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Temperature effects
Ave temp across two sites, plus lags for
previous 3 hours and previous 3 days.
Temp difference between two sites, plus lags
for previous 3 hours and previous 3 days.
Max ave temp in past 24 hours.
Min ave temp in past 24 hours.
Ave temp in past seven days.
Each function estimated using boosted regression splines.
Probabilistic forecasting of peak electricity demand The model 21
Monash Electricity Forecasting Model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Temperature effects
Ave temp across two sites, plus lags for
previous 3 hours and previous 3 days.
Temp difference between two sites, plus lags
for previous 3 hours and previous 3 days.
Max ave temp in past 24 hours.
Min ave temp in past 24 hours.
Ave temp in past seven days.
Each function estimated using boosted regression splines.
Probabilistic forecasting of peak electricity demand The model 21
Monash Electricity Forecasting Model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Temperature effects
Ave temp across two sites, plus lags for
previous 3 hours and previous 3 days.
Temp difference between two sites, plus lags
for previous 3 hours and previous 3 days.
Max ave temp in past 24 hours.
Min ave temp in past 24 hours.
Ave temp in past seven days.
Each function estimated using boosted regression splines.
Probabilistic forecasting of peak electricity demand The model 21
Monash Electricity Forecasting Model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Temperature effects
Ave temp across two sites, plus lags for
previous 3 hours and previous 3 days.
Temp difference between two sites, plus lags
for previous 3 hours and previous 3 days.
Max ave temp in past 24 hours.
Min ave temp in past 24 hours.
Ave temp in past seven days.
Each function estimated using boosted regression splines.
Probabilistic forecasting of peak electricity demand The model 21
Monash Electricity Forecasting Model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Temperature effects
Ave temp across two sites, plus lags for
previous 3 hours and previous 3 days.
Temp difference between two sites, plus lags
for previous 3 hours and previous 3 days.
Max ave temp in past 24 hours.
Min ave temp in past 24 hours.
Ave temp in past seven days.
Each function estimated using boosted regression splines.
Probabilistic forecasting of peak electricity demand The model 21
Monash Electricity Forecasting Model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Temperature effects
Ave temp across two sites, plus lags for
previous 3 hours and previous 3 days.
Temp difference between two sites, plus lags
for previous 3 hours and previous 3 days.
Max ave temp in past 24 hours.
Min ave temp in past 24 hours.
Ave temp in past seven days.
Each function estimated using boosted regression splines.
Probabilistic forecasting of peak electricity demand The model 21
Monash Electricity Forecasting Model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Temperature effects
Ave temp across two sites, plus lags for
previous 3 hours and previous 3 days.
Temp difference between two sites, plus lags
for previous 3 hours and previous 3 days.
Max ave temp in past 24 hours.
Min ave temp in past 24 hours.
Ave temp in past seven days.
Each function estimated using boosted regression splines.
Probabilistic forecasting of peak electricity demand The model 21
Monash Electricity Forecasting Model
Temperature effects
6
k=0
fk,p(xt−k) + gk,p(dt−k) + qp(x+
t ) + rp(x−
t ) + sp(¯xt)
+
6
j=1
Fj,p(xt−48j) + Gj,p(dt−48j)
xt is ave temp across two sites at time t;
dt is the temp difference between two sites at
time t;
x+
t is max of xt values in past 24 hours;
x−
t is min of xt values in past 24 hours;
¯xt is ave temp in past seven days.
Probabilistic forecasting of peak electricity demand The model 22
Monash Electricity Forecasting Model
Temperature effects
6
k=0
fk,p(xt−k) + gk,p(dt−k) + qp(x+
t ) + rp(x−
t ) + sp(¯xt)
+
6
j=1
Fj,p(xt−48j) + Gj,p(dt−48j)
xt is ave temp across two sites at time t;
dt is the temp difference between two sites at
time t;
x+
t is max of xt values in past 24 hours;
x−
t is min of xt values in past 24 hours;
¯xt is ave temp in past seven days.
Probabilistic forecasting of peak electricity demand The model 22
Monash Electricity Forecasting Model
Temperature effects
6
k=0
fk,p(xt−k) + gk,p(dt−k) + qp(x+
t ) + rp(x−
t ) + sp(¯xt)
+
6
j=1
Fj,p(xt−48j) + Gj,p(dt−48j)
xt is ave temp across two sites at time t;
dt is the temp difference between two sites at
time t;
x+
t is max of xt values in past 24 hours;
x−
t is min of xt values in past 24 hours;
¯xt is ave temp in past seven days.
Probabilistic forecasting of peak electricity demand The model 22
Monash Electricity Forecasting Model
Temperature effects
6
k=0
fk,p(xt−k) + gk,p(dt−k) + qp(x+
t ) + rp(x−
t ) + sp(¯xt)
+
6
j=1
Fj,p(xt−48j) + Gj,p(dt−48j)
xt is ave temp across two sites at time t;
dt is the temp difference between two sites at
time t;
x+
t is max of xt values in past 24 hours;
x−
t is min of xt values in past 24 hours;
¯xt is ave temp in past seven days.
Probabilistic forecasting of peak electricity demand The model 22
Monash Electricity Forecasting Model
Temperature effects
6
k=0
fk,p(xt−k) + gk,p(dt−k) + qp(x+
t ) + rp(x−
t ) + sp(¯xt)
+
6
j=1
Fj,p(xt−48j) + Gj,p(dt−48j)
xt is ave temp across two sites at time t;
dt is the temp difference between two sites at
time t;
x+
t is max of xt values in past 24 hours;
x−
t is min of xt values in past 24 hours;
¯xt is ave temp in past seven days.
Probabilistic forecasting of peak electricity demand The model 22
Fitted results (Summer 3pm)
Probabilistic forecasting of peak electricity demand The model 23
10 20 30 40
−0.4−0.20.00.20.4
Temperature
Effectondemand
10 20 30 40
−0.4−0.20.00.20.4
Lag 1 temperature
Effectondemand
10 20 30 40
−0.4−0.20.00.20.4
Lag 2 temperature
Effectondemand
10 20 30 40
−0.4−0.20.00.20.4
Lag 3 temperature
Effectondemand
10 20 30 40
−0.4−0.20.00.20.4
Lag 1 day temperature
Effectondemand
10 15 20 25 30
−0.4−0.20.00.20.4
Last week average temp
Effectondemand
15 25 35
−0.4−0.20.00.20.4
Previous max temp
Effectondemand
10 15 20 25
−0.4−0.20.00.20.4
Previous min temp
Effectondemand
Time: 3:00 pm
Half-hourly models
log(y∗
t ) = f(calendar effects, temperatures) + et
Data split into working/non-working days, and
into night/day/evening (6 subsets).
Separate model for each half-hour period within
each subset (96 models).
Same predictors used for all models in a subset.
Predictors chosen by cross-validation on last
two summers.
Each model is fitted to the data twice, first
excluding the last summer and then excluding
the previous summer. Average out-of-sample
MSE calculated from omitted data.
Probabilistic forecasting of peak electricity demand The model 24
Half-hourly models
log(y∗
t ) = f(calendar effects, temperatures) + et
Data split into working/non-working days, and
into night/day/evening (6 subsets).
Separate model for each half-hour period within
each subset (96 models).
Same predictors used for all models in a subset.
Predictors chosen by cross-validation on last
two summers.
Each model is fitted to the data twice, first
excluding the last summer and then excluding
the previous summer. Average out-of-sample
MSE calculated from omitted data.
Probabilistic forecasting of peak electricity demand The model 24
Half-hourly models
log(y∗
t ) = f(calendar effects, temperatures) + et
Data split into working/non-working days, and
into night/day/evening (6 subsets).
Separate model for each half-hour period within
each subset (96 models).
Same predictors used for all models in a subset.
Predictors chosen by cross-validation on last
two summers.
Each model is fitted to the data twice, first
excluding the last summer and then excluding
the previous summer. Average out-of-sample
MSE calculated from omitted data.
Probabilistic forecasting of peak electricity demand The model 24
Half-hourly models
log(y∗
t ) = f(calendar effects, temperatures) + et
Data split into working/non-working days, and
into night/day/evening (6 subsets).
Separate model for each half-hour period within
each subset (96 models).
Same predictors used for all models in a subset.
Predictors chosen by cross-validation on last
two summers.
Each model is fitted to the data twice, first
excluding the last summer and then excluding
the previous summer. Average out-of-sample
MSE calculated from omitted data.
Probabilistic forecasting of peak electricity demand The model 24
Half-hourly models
log(y∗
t ) = f(calendar effects, temperatures) + et
Data split into working/non-working days, and
into night/day/evening (6 subsets).
Separate model for each half-hour period within
each subset (96 models).
Same predictors used for all models in a subset.
Predictors chosen by cross-validation on last
two summers.
Each model is fitted to the data twice, first
excluding the last summer and then excluding
the previous summer. Average out-of-sample
MSE calculated from omitted data.
Probabilistic forecasting of peak electricity demand The model 24
Half-hourly models
x x1 x2 x3 x4 x5 x6 x48 x96 x144 x192 x240 x288 d d1 d2 d3 d4 d5 d6 d48 d96 d144 d192 d240 d288 x+
x− ¯x dow hol dos MSE
1 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.037
2 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.034
3 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.031
4 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.027
5 • • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.025
6 • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.020
7 • • • • • • • • • • • • • • • • • • • • • • • • • • 1.025
8 • • • • • • • • • • • • • • • • • • • • • • • • • • 1.026
9 • • • • • • • • • • • • • • • • • • • • • • • • • 1.035
10 • • • • • • • • • • • • • • • • • • • • • • • • 1.044
11 • • • • • • • • • • • • • • • • • • • • • • • 1.057
12 • • • • • • • • • • • • • • • • • • • • • • 1.076
13 • • • • • • • • • • • • • • • • • • • • • 1.102
14 • • • • • • • • • • • • • • • • • • • • • • • • • • 1.018
15 • • • • • • • • • • • • • • • • • • • • • • • • • 1.021
16 • • • • • • • • • • • • • • • • • • • • • • • • 1.037
17 • • • • • • • • • • • • • • • • • • • • • • • 1.074
18 • • • • • • • • • • • • • • • • • • • • • • 1.152
19 • • • • • • • • • • • • • • • • • • • • • 1.180
20 • • • • • • • • • • • • • • • • • • • • • • • • • 1.021
21 • • • • • • • • • • • • • • • • • • • • • • • • 1.027
22 • • • • • • • • • • • • • • • • • • • • • • • 1.038
23 • • • • • • • • • • • • • • • • • • • • • • 1.056
24 • • • • • • • • • • • • • • • • • • • • • 1.086
25 • • • • • • • • • • • • • • • • • • • • 1.135
26 • • • • • • • • • • • • • • • • • • • • • • • • • 1.009
27 • • • • • • • • • • • • • • • • • • • • • • • • • 1.063
28 • • • • • • • • • • • • • • • • • • • • • • • • • 1.028
29 • • • • • • • • • • • • • • • • • • • • • • • • • 3.523
30 • • • • • • • • • • • • • • • • • • • • • • • • • 2.143
31 • • • • • • • • • • • • • • • • • • • • • • • • • 1.523
Probabilistic forecasting of peak electricity demand The model 25
Half-hourly models
Probabilistic forecasting of peak electricity demand The model 26
60708090
R−squared
Time of day
R−squared(%)
12 midnight 6:00 am 9:00 am 12 noon 3:00 pm 6:00 pm 9:00 pm3:00 am 12 midnight
Half-hourly models
Probabilistic forecasting of peak electricity demand The model 26
Demand (January 2015)
Date in January
SAdemand(GW)
012345
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Actual
Predicted
Temperatures (January 2015)
)
40
temp_23090
temp_23083
Half-hourly models
Probabilistic forecasting of peak electricity demand The model 26
Half-hourly models
Probabilistic forecasting of peak electricity demand The model 26
Half-hourly models
Probabilistic forecasting of peak electricity demand The model 26
Predictions adjusted for
saturated usage.
Outline
1 The problem
2 The model
3 Forecasts
4 Challenges and extensions
5 Short term forecasts
6 Evaluating probabilistic forecasts
7 MEFM package
8 References and resources
Probabilistic forecasting of peak electricity demand Forecasts 27
Peak demand forecasting
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Multiple alternative futures created:
Calendar effects known;
Future temperatures simulated
(taking account of climate change);
Assumed values for GSP, population and price;
Residuals simulated
Probabilistic forecasting of peak electricity demand Forecasts 28
Peak demand backcasting
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Multiple alternative pasts created:
Calendar effects known;
Past temperatures simulated;
Actual values for GSP, population and price;
Residuals simulated
Probabilistic forecasting of peak electricity demand Forecasts 28
Peak demand backcasting
Probabilistic forecasting of peak electricity demand Forecasts 29
PoE (seasonal interpretation, summer)
Year
PoEDemand(total)
2.42.62.83.03.23.43.63.8
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
10 %
50 %
90 %
q
q
q
q
q q
q
q
q
q
q
q
q
q
Peak demand backcasting
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Multiple alternative pasts created:
Calendar effects known;
Past temperatures simulated;
Actual values for GSP, population and price;
Residuals simulated
Probabilistic forecasting of peak electricity demand Forecasts 30
Peak demand forecasting
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Multiple alternative futures created:
Calendar effects known;
Future temperatures simulated
(taking account of climate change);
Assumed values for GSP, population and price;
Residuals simulated
Probabilistic forecasting of peak electricity demand Forecasts 30
Peak demand forecasting
Probabilistic forecasting of peak electricity demand Forecasts 31
Population
Year
000'spersons
2000 2005 2010 2015 2020 2025 2030 2035
16002000
base
low
high
GSP
Year
$million
2000 2005 2010 2015 2020 2025 2030 2035
2000035000
base
low
high
Price
Year
c/kWh
2000 2005 2010 2015 2020 2025 2030 2035
1520253035
base
low
high
Peak demand distribution
Probabilistic forecasting of peak electricity demand Forecasts 32
Seasonal POE levels (summer)
Year
PoEDemand
2.02.53.03.54.04.5
2002 2005 2008 2011 2014 2017 2020 2023 2026 2029 2032 2035
q
q
q
q q
q
q
q
q
q
q
q
q
10 % POE
50 % POE
90 % POE
Actual annual maximum
Seasonal block bootstrapping
Conventional seasonal block bootstrap
Same as block bootstrap but with whole years as the
blocks to preserve seasonality.
But we only have about 10–15 years of data, so there is a
limited number of possible bootstrap samples.
Double seasonal block bootstrap
Suitable when there are two seasonal periods (here we
have years of 151 days and days of 48 half-hours).
Divide each year into blocks of length 48m.
Block 1 consists of the first m days of the year, block 2
consists of the next m days, and so on.
Bootstrap sample consists of a sample of blocks where
each block may come from a different randomly selected
year but must be at the correct time of year.
Probabilistic forecasting of peak electricity demand Forecasts 33
Seasonal block bootstrapping
Conventional seasonal block bootstrap
Same as block bootstrap but with whole years as the
blocks to preserve seasonality.
But we only have about 10–15 years of data, so there is a
limited number of possible bootstrap samples.
Double seasonal block bootstrap
Suitable when there are two seasonal periods (here we
have years of 151 days and days of 48 half-hours).
Divide each year into blocks of length 48m.
Block 1 consists of the first m days of the year, block 2
consists of the next m days, and so on.
Bootstrap sample consists of a sample of blocks where
each block may come from a different randomly selected
year but must be at the correct time of year.
Probabilistic forecasting of peak electricity demand Forecasts 33
Seasonal block bootstrapping
Conventional seasonal block bootstrap
Same as block bootstrap but with whole years as the
blocks to preserve seasonality.
But we only have about 10–15 years of data, so there is a
limited number of possible bootstrap samples.
Double seasonal block bootstrap
Suitable when there are two seasonal periods (here we
have years of 151 days and days of 48 half-hours).
Divide each year into blocks of length 48m.
Block 1 consists of the first m days of the year, block 2
consists of the next m days, and so on.
Bootstrap sample consists of a sample of blocks where
each block may come from a different randomly selected
year but must be at the correct time of year.
Probabilistic forecasting of peak electricity demand Forecasts 33
Seasonal block bootstrapping
Conventional seasonal block bootstrap
Same as block bootstrap but with whole years as the
blocks to preserve seasonality.
But we only have about 10–15 years of data, so there is a
limited number of possible bootstrap samples.
Double seasonal block bootstrap
Suitable when there are two seasonal periods (here we
have years of 151 days and days of 48 half-hours).
Divide each year into blocks of length 48m.
Block 1 consists of the first m days of the year, block 2
consists of the next m days, and so on.
Bootstrap sample consists of a sample of blocks where
each block may come from a different randomly selected
year but must be at the correct time of year.
Probabilistic forecasting of peak electricity demand Forecasts 33
Seasonal block bootstrapping
Conventional seasonal block bootstrap
Same as block bootstrap but with whole years as the
blocks to preserve seasonality.
But we only have about 10–15 years of data, so there is a
limited number of possible bootstrap samples.
Double seasonal block bootstrap
Suitable when there are two seasonal periods (here we
have years of 151 days and days of 48 half-hours).
Divide each year into blocks of length 48m.
Block 1 consists of the first m days of the year, block 2
consists of the next m days, and so on.
Bootstrap sample consists of a sample of blocks where
each block may come from a different randomly selected
year but must be at the correct time of year.
Probabilistic forecasting of peak electricity demand Forecasts 33
Seasonal block bootstrapping
Conventional seasonal block bootstrap
Same as block bootstrap but with whole years as the
blocks to preserve seasonality.
But we only have about 10–15 years of data, so there is a
limited number of possible bootstrap samples.
Double seasonal block bootstrap
Suitable when there are two seasonal periods (here we
have years of 151 days and days of 48 half-hours).
Divide each year into blocks of length 48m.
Block 1 consists of the first m days of the year, block 2
consists of the next m days, and so on.
Bootstrap sample consists of a sample of blocks where
each block may come from a different randomly selected
year but must be at the correct time of year.
Probabilistic forecasting of peak electricity demand Forecasts 33
Seasonal block bootstrapping
Conventional seasonal block bootstrap
Same as block bootstrap but with whole years as the
blocks to preserve seasonality.
But we only have about 10–15 years of data, so there is a
limited number of possible bootstrap samples.
Double seasonal block bootstrap
Suitable when there are two seasonal periods (here we
have years of 151 days and days of 48 half-hours).
Divide each year into blocks of length 48m.
Block 1 consists of the first m days of the year, block 2
consists of the next m days, and so on.
Bootstrap sample consists of a sample of blocks where
each block may come from a different randomly selected
year but must be at the correct time of year.
Probabilistic forecasting of peak electricity demand Forecasts 33
Seasonal block bootstrapping
Probabilistic forecasting of peak electricity demand Forecasts 34
Actual temperatures
Days
degreesC
0 10 20 30 40 50 60
10152025303540
Bootstrap temperatures (fixed blocks)
Days
degreesC
0 10 20 30 40 50 60
10152025303540
Bootstrap temperatures (variable blocks)
40
Seasonal block bootstrapping
Problems with the double seasonal bootstrap
Boundaries between blocks can introduce large
jumps. However, only at midnight.
Number of values that any given time in year is
still limited to the number of years in the data
set.
Probabilistic forecasting of peak electricity demand Forecasts 35
Seasonal block bootstrapping
Problems with the double seasonal bootstrap
Boundaries between blocks can introduce large
jumps. However, only at midnight.
Number of values that any given time in year is
still limited to the number of years in the data
set.
Probabilistic forecasting of peak electricity demand Forecasts 35
Seasonal block bootstrapping
Variable length double seasonal block
bootstrap
Blocks allowed to vary in length between m − ∆
and m + ∆ days where 0 ≤ ∆ < m.
Blocks allowed to move up to ∆ days from their
original position.
Has little effect on the overall time series
patterns provided ∆ is relatively small.
Use uniform distribution on (m − ∆, m + ∆) to
select block length, and independent uniform
distribution on (−∆, ∆) to select variation on
starting position for each block.
Probabilistic forecasting of peak electricity demand Forecasts 36
Seasonal block bootstrapping
Variable length double seasonal block
bootstrap
Blocks allowed to vary in length between m − ∆
and m + ∆ days where 0 ≤ ∆ < m.
Blocks allowed to move up to ∆ days from their
original position.
Has little effect on the overall time series
patterns provided ∆ is relatively small.
Use uniform distribution on (m − ∆, m + ∆) to
select block length, and independent uniform
distribution on (−∆, ∆) to select variation on
starting position for each block.
Probabilistic forecasting of peak electricity demand Forecasts 36
Seasonal block bootstrapping
Variable length double seasonal block
bootstrap
Blocks allowed to vary in length between m − ∆
and m + ∆ days where 0 ≤ ∆ < m.
Blocks allowed to move up to ∆ days from their
original position.
Has little effect on the overall time series
patterns provided ∆ is relatively small.
Use uniform distribution on (m − ∆, m + ∆) to
select block length, and independent uniform
distribution on (−∆, ∆) to select variation on
starting position for each block.
Probabilistic forecasting of peak electricity demand Forecasts 36
Seasonal block bootstrapping
Variable length double seasonal block
bootstrap
Blocks allowed to vary in length between m − ∆
and m + ∆ days where 0 ≤ ∆ < m.
Blocks allowed to move up to ∆ days from their
original position.
Has little effect on the overall time series
patterns provided ∆ is relatively small.
Use uniform distribution on (m − ∆, m + ∆) to
select block length, and independent uniform
distribution on (−∆, ∆) to select variation on
starting position for each block.
Probabilistic forecasting of peak electricity demand Forecasts 36
Seasonal block bootstrapping
Probabilistic forecasting of peak electricity demand Forecasts 37
Actual temperatures
Days
degreesC 0 10 20 30 40 50 60
10152025303540
Bootstrap temperatures (fixed blocks)
Days
degreesC
0 10 20 30 40 50 60
10152025303540
Bootstrap temperatures (variable blocks)
Days
degreesC
0 10 20 30 40 50 60
10152025303540
Seasonal block bootstrapping
Probabilistic forecasting of peak electricity demand Forecasts 37
Outline
1 The problem
2 The model
3 Forecasts
4 Challenges and extensions
5 Short term forecasts
6 Evaluating probabilistic forecasts
7 MEFM package
8 References and resources
Probabilistic forecasting of peak electricity demand Challenges and extensions 38
Challenges
Some judgmental adjustments are done to
account for demand response activity.
We have a separate model for PV generation
based on solar radiation and temperatures. But
limited PV data available, so PV adjustments
are probably inaccurate.
Difficult to account for new technology such as
local storage intended to flatten demand.
Climate change effect is assumed additive at
all temperature levels — probably simplistic.
Probabilistic forecasting of peak electricity demand Challenges and extensions 39
Challenges
Some judgmental adjustments are done to
account for demand response activity.
We have a separate model for PV generation
based on solar radiation and temperatures. But
limited PV data available, so PV adjustments
are probably inaccurate.
Difficult to account for new technology such as
local storage intended to flatten demand.
Climate change effect is assumed additive at
all temperature levels — probably simplistic.
Probabilistic forecasting of peak electricity demand Challenges and extensions 39
Challenges
Some judgmental adjustments are done to
account for demand response activity.
We have a separate model for PV generation
based on solar radiation and temperatures. But
limited PV data available, so PV adjustments
are probably inaccurate.
Difficult to account for new technology such as
local storage intended to flatten demand.
Climate change effect is assumed additive at
all temperature levels — probably simplistic.
Probabilistic forecasting of peak electricity demand Challenges and extensions 39
Challenges
Some judgmental adjustments are done to
account for demand response activity.
We have a separate model for PV generation
based on solar radiation and temperatures. But
limited PV data available, so PV adjustments
are probably inaccurate.
Difficult to account for new technology such as
local storage intended to flatten demand.
Climate change effect is assumed additive at
all temperature levels — probably simplistic.
Probabilistic forecasting of peak electricity demand Challenges and extensions 39
Implementation
Probabilistic forecasting of peak electricity demand Challenges and extensions 40
Our model is used for long-term forecasting in:
Victoria’s Vision 2030 energy plan;
all regions of the National Energy Market;
South Western Interconnected System
(WA);
some local distributors.
Implementation
Probabilistic forecasting of peak electricity demand Challenges and extensions 40
Our model is used for long-term forecasting in:
Victoria’s Vision 2030 energy plan;
all regions of the National Energy Market;
South Western Interconnected System
(WA);
some local distributors.
It is also used for short-term
forecasting comparisons in:
all regions of the
National Energy Market.
Outline
1 The problem
2 The model
3 Forecasts
4 Challenges and extensions
5 Short term forecasts
6 Evaluating probabilistic forecasts
7 MEFM package
8 References and resources
Probabilistic forecasting of peak electricity demand Short term forecasts 41
Short-term forecasts
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Simulating temperatures and residuals is ok for
long-term forecasts because short-term
dynamics wash out after a few weeks.
But short-term forecasts need to take account
of recent temperatures and recent residuals
due to serial correlation.
Short-term temperature forecasts are available.
Probabilistic forecasting of peak electricity demand Short term forecasts 42
Short-term forecasts
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Simulating temperatures and residuals is ok for
long-term forecasts because short-term
dynamics wash out after a few weeks.
But short-term forecasts need to take account
of recent temperatures and recent residuals
due to serial correlation.
Short-term temperature forecasts are available.
Probabilistic forecasting of peak electricity demand Short term forecasts 42
Short-term forecasts
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Simulating temperatures and residuals is ok for
long-term forecasts because short-term
dynamics wash out after a few weeks.
But short-term forecasts need to take account
of recent temperatures and recent residuals
due to serial correlation.
Short-term temperature forecasts are available.
Probabilistic forecasting of peak electricity demand Short term forecasts 42
Short-term forecasting model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures,
lagged demand) + et
Lagged demand inputs
Demand in last 3 hours and last 3 days;
Maximum demand in past 24 hours;
Minimum demand in past 24 hours;
Average demand in past 7 days
Each function is estimated using boosted regression splines.
Probabilistic forecasting of peak electricity demand Short term forecasts 43
Short-term forecasting model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures,
lagged demand) + et
Lagged demand inputs
Demand in last 3 hours and last 3 days;
Maximum demand in past 24 hours;
Minimum demand in past 24 hours;
Average demand in past 7 days
Each function is estimated using boosted regression splines.
Probabilistic forecasting of peak electricity demand Short term forecasts 43
GEFCom2012
Probabilistic forecasting of peak electricity demand Short term forecasts 44
GEFCom2012
Probabilistic forecasting of peak electricity demand Short term forecasts 44
Methods published in
IJF, April 2014.
Outline
1 The problem
2 The model
3 Forecasts
4 Challenges and extensions
5 Short term forecasts
6 Evaluating probabilistic forecasts
7 MEFM package
8 References and resources
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 45
Forecast accuracy measures
MAE: Mean absolute error
MSE: Mean squared error
MAPE: Mean absolute percentage error
¯ Good when forecasting a typical future value
(e.g., the mean or median).
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 46
Forecast accuracy measures
MAE: Mean absolute error
MSE: Mean squared error
MAPE: Mean absolute percentage error
¯ Good when forecasting a typical future value
(e.g., the mean or median).
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 46
Forecast accuracy measures
MAE: Mean absolute error
MSE: Mean squared error
MAPE: Mean absolute percentage error
¯ Good when forecasting a typical future value
(e.g., the mean or median).
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 46
Forecast accuracy measures
MAE: Mean absolute error
MSE: Mean squared error
MAPE: Mean absolute percentage error
¯ Good when forecasting a typical future value
(e.g., the mean or median).
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 46
Forecast accuracy measures
MAE: Mean absolute error
MSE: Mean squared error
MAPE: Mean absolute percentage error
¯ Good when forecasting a typical future value
(e.g., the mean or median).
¯ Useless for evaluating forecast percentiles
(probability of exceedance values) and forecast
distributions.
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 46
Evaluating forecast distributions
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 47
PoE (seasonal interpretation, summer)
Year
PoEDemand(total)
2.42.62.83.03.23.43.63.8
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
10 %
50 %
90 %
q
q
q
q
q q
q
q
q
q
q
q
q
q
Evaluating forecast distributions
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 47
PoE (seasonal interpretation, summer)
Year
PoEDemand(total)
2.42.62.83.03.23.43.63.8
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
10 %
50 %
90 %
q
q
q
q
q q
q
q
q
q
q
q
q
q
12 out of 13 above 90% PoE
6 out of 13 above 50% PoE
2 out of 13 above 10% PoE
Forecast scoring
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 48
0 1 2 3 4 5 6
Demand distribution
Demand (GWh)
Forecast scoring
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 48
0 1 2 3 4 5 6
Demand distribution
Demand (GWh)
50%
50% PoE
Forecast scoring
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 48
0 1 2 3 4 5 6
Demand distribution
Demand (GWh)
50%
50% PoE
Score for 50% PoE
Forecast scoring
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 48
0 1 2 3 4 5 6
Demand distribution
Demand (GWh)
50%
50% PoE
Score for 50% PoE
Equivalent to
absolute error
Forecast scoring
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 49
0 1 2 3 4 5 6
Demand distribution
Demand (GWh)
Forecast scoring
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 49
0 1 2 3 4 5 6
Demand distribution
Demand (GWh)
10%
10% PoE
Forecast scoring
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 49
0 1 2 3 4 5 6
Demand distribution
Demand (GWh)
10%
10% PoE
Score for 10% PoE
Forecast scoring
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 50
0 1 2 3 4 5 6
Demand distribution
Demand (GWh)
Forecast scoring
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 50
0 1 2 3 4 5 6
Demand distribution
Demand (GWh)
75%
75% PoE
Forecast scoring
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 50
0 1 2 3 4 5 6
Demand distribution
Demand (GWh)
75%
75% PoE
Score for 75% PoE
Forecast scoring
Let Qt(1), . . . , Qt(99) be the PoEs of the forecast
distribution for probabilities 1%,. . . ,99%. Then the
score for observation y is
S(Qt(i), yt) =
1
100
i(Qt(i) − yt) if yt < Qt(i)
1
100
(100 − i)(yt − Qt(i)) if yt ≥ Qt(i)
Scores are averaged over all observed data for
each i to measure the accuracy of the forecasts
for each percentile.
Average score over all percentiles gives the
best distribution forecast.
Takes account of how far PoEs are exceeded.
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 51
Forecast scoring
Let Qt(1), . . . , Qt(99) be the PoEs of the forecast
distribution for probabilities 1%,. . . ,99%. Then the
score for observation y is
S(Qt(i), yt) =
1
100
i(Qt(i) − yt) if yt < Qt(i)
1
100
(100 − i)(yt − Qt(i)) if yt ≥ Qt(i)
Scores are averaged over all observed data for
each i to measure the accuracy of the forecasts
for each percentile.
Average score over all percentiles gives the
best distribution forecast.
Takes account of how far PoEs are exceeded.
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 51
Forecast scoring
Let Qt(1), . . . , Qt(99) be the PoEs of the forecast
distribution for probabilities 1%,. . . ,99%. Then the
score for observation y is
S(Qt(i), yt) =
1
100
i(Qt(i) − yt) if yt < Qt(i)
1
100
(100 − i)(yt − Qt(i)) if yt ≥ Qt(i)
Scores are averaged over all observed data for
each i to measure the accuracy of the forecasts
for each percentile.
Average score over all percentiles gives the
best distribution forecast.
Takes account of how far PoEs are exceeded.
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 51
GEFCom2014
Probabilistic forecasting of demand, price,
wind, and solar.
Rolling forecasts with incremental data update
on a weekly basis.
Forecasts submitted in the form of percentiles
of future distributions.
Evaluation based on quantile scoring.
Prizes for student teams, and for best methods.
Winning methods to be published in the IJF.
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 52
GEFCom2014
Probabilistic forecasting of demand, price,
wind, and solar.
Rolling forecasts with incremental data update
on a weekly basis.
Forecasts submitted in the form of percentiles
of future distributions.
Evaluation based on quantile scoring.
Prizes for student teams, and for best methods.
Winning methods to be published in the IJF.
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 52
GEFCom2014
Probabilistic forecasting of demand, price,
wind, and solar.
Rolling forecasts with incremental data update
on a weekly basis.
Forecasts submitted in the form of percentiles
of future distributions.
Evaluation based on quantile scoring.
Prizes for student teams, and for best methods.
Winning methods to be published in the IJF.
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 52
GEFCom2014
Probabilistic forecasting of demand, price,
wind, and solar.
Rolling forecasts with incremental data update
on a weekly basis.
Forecasts submitted in the form of percentiles
of future distributions.
Evaluation based on quantile scoring.
Prizes for student teams, and for best methods.
Winning methods to be published in the IJF.
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 52
GEFCom2014
Probabilistic forecasting of demand, price,
wind, and solar.
Rolling forecasts with incremental data update
on a weekly basis.
Forecasts submitted in the form of percentiles
of future distributions.
Evaluation based on quantile scoring.
Prizes for student teams, and for best methods.
Winning methods to be published in the IJF.
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 52
GEFCom2014
Probabilistic forecasting of demand, price,
wind, and solar.
Rolling forecasts with incremental data update
on a weekly basis.
Forecasts submitted in the form of percentiles
of future distributions.
Evaluation based on quantile scoring.
Prizes for student teams, and for best methods.
Winning methods to be published in the IJF.
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 52
GEFCom2014
Load forecasting provisional leaderboard
Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 53
Outline
1 The problem
2 The model
3 Forecasts
4 Challenges and extensions
5 Short term forecasts
6 Evaluating probabilistic forecasts
7 MEFM package
8 References and resources
Probabilistic forecasting of peak electricity demand MEFM package 54
MEFM package for R
Available on github:
install.packages("devtools")
library(devtools)
install_github("robjhyndman/MEFM-package")
Package contents:
seasondays The number of days in a season
sa.econ Historical demographic & economic data for
South Australia
sa Historical data for model estimation
maketemps Create lagged temperature variables
demand_model Estimate the electricity demand models
simulate_ddemand Temperature and demand simulation
simulate_demand Simulate the electricity demand for the next
season
Probabilistic forecasting of peak electricity demand MEFM package 55
MEFM package for R
Available on github:
install.packages("devtools")
library(devtools)
install_github("robjhyndman/MEFM-package")
Package contents:
seasondays The number of days in a season
sa.econ Historical demographic & economic data for
South Australia
sa Historical data for model estimation
maketemps Create lagged temperature variables
demand_model Estimate the electricity demand models
simulate_ddemand Temperature and demand simulation
simulate_demand Simulate the electricity demand for the next
season
Probabilistic forecasting of peak electricity demand MEFM package 55
MEFM package for R
Usage
library(MEFM)
# Number of days in each "season"
seasondays
# Historical economic data
sa.econ
# Historical temperature and calendar data
head(sa)
tail(sa)
dim(sa)
# create lagged temperature variables
salags <- maketemps(sa,2,48)
dim(salags)
head(salags)
Probabilistic forecasting of peak electricity demand MEFM package 56
MEFM package for R
# formula for annual model
formula.a <- as.formula(anndemand ~ gsp + ddays + resiprice)
# formulas for half-hourly model
# These can be different for each half-hour
formula.hh <- list()
for(i in 1:48) {
formula.hh[[i]] <- as.formula(log(ddemand) ~ ns(temp, df=2)
+ day + holiday
+ ns(timeofyear, df=9) + ns(avetemp, df=3)
+ ns(dtemp, df=3) + ns(lastmin, df=3)
+ ns(prevtemp1, df=2) + ns(prevtemp2, df=2)
+ ns(prevtemp3, df=2) + ns(prevtemp4, df=2)
+ ns(day1temp, df=2) + ns(day2temp, df=2)
+ ns(day3temp, df=2) + ns(prevdtemp1, df=3)
+ ns(prevdtemp2, df=3) + ns(prevdtemp3, df=3)
+ ns(day1dtemp, df=3))
}
Probabilistic forecasting of peak electricity demand MEFM package 57
MEFM package for R
# Fit all models
sa.model <- demand_model(salags, sa.econ, formula.hh, formula.a)
# Summary of annual model
summary(sa.model$a)
# Summary of half-hourly model at 4pm
summary(sa.model$hh[[33]])
# Simulate future normalized half-hourly data
simdemand <- simulate_ddemand(sa.model, sa, simyears=50)
# economic forecasts, to be given by user
afcast <- data.frame(pop=1694, gsp=22573, resiprice=34.65,
ddays=642)
# Simulate half-hourly data
demand <- simulate_demand(simdemand, afcast)
Probabilistic forecasting of peak electricity demand MEFM package 58
MEFM package for R
plot(ts(demand$demand[,sample(1:100, 4)], freq=48, start=0),
xlab="Days", main="Simulated demand futures")
Probabilistic forecasting of peak electricity demand MEFM package 59
MEFM package for R
plot(ts(demand$demand[,sample(1:100, 4)], freq=48, start=0),
xlab="Days", main="Simulated demand futures")0.61.01.4
Series52
0.51.52.5
Series49
0.51.52.5
Series88
0.61.21.8
0 50 100 150
Series53
Days
Simulated demand futures
Probabilistic forecasting of peak electricity demand MEFM package 59
MEFM package for R
plot(demand$annmax, main="Simulated seasonal maximums",
ylab="GW")
Probabilistic forecasting of peak electricity demand MEFM package 60
MEFM package for R
plot(demand$annmax, main="Simulated seasonal maximums",
ylab="GW")
0 20 40 60 80 100
1.52.02.53.0
Simulated seasonal maximums
Index
GW
Probabilistic forecasting of peak electricity demand MEFM package 60
MEFM package for R
boxplot(demand$annmax, main="Simulated seasonal maximums",
xlab="GW", horizontal=TRUE)
rug(demand$annmax)
Probabilistic forecasting of peak electricity demand MEFM package 61
MEFM package for R
boxplot(demand$annmax, main="Simulated seasonal maximums",
xlab="GW", horizontal=TRUE)
rug(demand$annmax)
1.5 2.0 2.5 3.0
Simulated seasonal maximums
GW
Probabilistic forecasting of peak electricity demand MEFM package 61
MEFM package for R
plot(density(demand$annmax, bw="SJ"), xlab="Demand (GW)",
main="Density of seasonal maximum demand")
rug(demand$annmax)
Probabilistic forecasting of peak electricity demand MEFM package 62
MEFM package for R
plot(density(demand$annmax, bw="SJ"), xlab="Demand (GW)",
main="Density of seasonal maximum demand")
rug(demand$annmax)
1.5 2.0 2.5 3.0 3.5
0.00.40.81.2
Density of seasonal maximum demand
Demand (GW)
Density
Probabilistic forecasting of peak electricity demand MEFM package 62
Outline
1 The problem
2 The model
3 Forecasts
4 Challenges and extensions
5 Short term forecasts
6 Evaluating probabilistic forecasts
7 MEFM package
8 References and resources
Probabilistic forecasting of peak electricity demand References and resources 63
References
¯ Hyndman, R.J. & Fan, S. (2010)
“Density forecasting for long-term peak electricity demand”,
IEEE Transactions on Power Systems, 25(2), 1142–1153.
¯ Fan, S. & Hyndman, R.J. (2012) “Short-term load forecasting
based on a semi-parametric additive model”.
IEEE Transactions on Power Systems, 27(1), 134–141.
¯ Ben Taieb, S. & Hyndman, R.J. (2013) “A gradient boosting
approach to the Kaggle load forecasting competition”,
International Journal of Forecasting, 29(4).
¯ Hyndman, R.J., & Fan, S. (2014).
“Monash Electricity Forecasting Model”. Technical paper.
robjhyndman.com/working-papers/mefm/
¯ Fan, S., & Hyndman, R.J. (2014). “MEFM: An R package imple-
menting the Monash Electricity Forecasting Model.”
github.com/robjhyndman/MEFM-package
Probabilistic forecasting of peak electricity demand References and resources 64
Some resources
Blogs
robjhyndman.com/hyndsight/
blog.drhongtao.com/
Organizations
International Institute of Forecasters:
forecasters.org
IEEE Working Group on Energy Forecasting:
linkedin.com/groups/
IEEE-Working-Group-on-Energy-4148276
Books
Dickey and Hong (2014) Electric load
forecasting: fundamentals and best practices,
OTexts. www.otexts.org/book/elf
Probabilistic forecasting of peak electricity demand References and resources 65
Some resources
Blogs
robjhyndman.com/hyndsight/
blog.drhongtao.com/
Organizations
International Institute of Forecasters:
forecasters.org
IEEE Working Group on Energy Forecasting:
linkedin.com/groups/
IEEE-Working-Group-on-Energy-4148276
Books
Dickey and Hong (2014) Electric load
forecasting: fundamentals and best practices,
OTexts. www.otexts.org/book/elf
Probabilistic forecasting of peak electricity demand References and resources 65
Some resources
Blogs
robjhyndman.com/hyndsight/
blog.drhongtao.com/
Organizations
International Institute of Forecasters:
forecasters.org
IEEE Working Group on Energy Forecasting:
linkedin.com/groups/
IEEE-Working-Group-on-Energy-4148276
Books
Dickey and Hong (2014) Electric load
forecasting: fundamentals and best practices,
OTexts. www.otexts.org/book/elf
Probabilistic forecasting of peak electricity demand References and resources 65
Some resources
Blogs
robjhyndman.com/hyndsight/
blog.drhongtao.com/
Organizations
International Institute of Forecasters:
forecasters.org
IEEE Working Group on Energy Forecasting:
linkedin.com/groups/
IEEE-Working-Group-on-Energy-4148276
Books
Dickey and Hong (2014) Electric load
forecasting: fundamentals and best practices,
OTexts. www.otexts.org/book/elf
Probabilistic forecasting of peak electricity demand References and resources 65
Some resources
Blogs
robjhyndman.com/hyndsight/
blog.drhongtao.com/
Organizations
International Institute of Forecasters:
forecasters.org
IEEE Working Group on Energy Forecasting:
linkedin.com/groups/
IEEE-Working-Group-on-Energy-4148276
Books
Dickey and Hong (2014) Electric load
forecasting: fundamentals and best practices,
OTexts. www.otexts.org/book/elf
Probabilistic forecasting of peak electricity demand References and resources 65
Some resources
Blogs
robjhyndman.com/hyndsight/
blog.drhongtao.com/
Organizations
International Institute of Forecasters:
forecasters.org
IEEE Working Group on Energy Forecasting:
linkedin.com/groups/
IEEE-Working-Group-on-Energy-4148276
Books
Dickey and Hong (2014) Electric load
forecasting: fundamentals and best practices,
OTexts. www.otexts.org/book/elf
Probabilistic forecasting of peak electricity demand References and resources 65
Some resources
Blogs
robjhyndman.com/hyndsight/
blog.drhongtao.com/
Organizations
International Institute of Forecasters:
forecasters.org
IEEE Working Group on Energy Forecasting:
linkedin.com/groups/
IEEE-Working-Group-on-Energy-4148276
Books
Dickey and Hong (2014) Electric load
forecasting: fundamentals and best practices,
OTexts. www.otexts.org/book/elf
Probabilistic forecasting of peak electricity demand References and resources 65

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Probabilistic forecasting of peak electricity demand

  • 1. Probabilistic forecasting of peak electricity demand Rob J Hyndman Joint work with Shu Fan Probabilistic forecasting of peak electricity demand 1
  • 2. Outline 1 The problem 2 The model 3 Forecasts 4 Challenges and extensions 5 Short term forecasts 6 Evaluating probabilistic forecasts 7 MEFM package 8 References and resources Probabilistic forecasting of peak electricity demand The problem 2
  • 3. The problem We want to forecast the peak electricity demand in a half-hour period in twenty years time. We have fifteen 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? Probabilistic forecasting of peak electricity demand The problem 3
  • 4. The problem We want to forecast the peak electricity demand in a half-hour period in twenty years time. We have fifteen 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? Probabilistic forecasting of peak electricity demand The problem 3
  • 5. South Australian demand data Probabilistic forecasting of peak electricity demand The problem 4
  • 6. South Australian demand data Probabilistic forecasting of peak electricity demand The problem 4 Black Saturday →
  • 7. The heatwave Probabilistic forecasting of peak electricity demand The problem 5
  • 8. The heatwave Probabilistic forecasting of peak electricity demand The problem 5
  • 9. The heatwave Probabilistic forecasting of peak electricity demand The problem 5
  • 10. South Australian demand data Probabilistic forecasting of peak electricity demand The problem 6 SA State wide demand (summer 2015) SAStatewidedemand(GW) 1.01.52.02.53.0 Oct Nov Dec Jan Feb Mar
  • 11. South Australian demand data Probabilistic forecasting of peak electricity demand The problem 6
  • 12. Temperature data (Sth Aust) Probabilistic forecasting of peak electricity demand The problem 7
  • 13. Temperature data (Sth Aust) Probabilistic forecasting of peak electricity demand The problem 8 10 20 30 40 1.01.52.02.53.03.5 Time: 12 midnight Temperature (deg C) Demand(GW) Workday Non−workday
  • 14. Demand boxplots (Sth Aust) Probabilistic forecasting of peak electricity demand The problem 9 qqqq q q q q qq qq q q q q q q qq q q q q q q q q q q q q q q qq q q q q q q q q qq qqq q qq q qqq qqq q q qq q q q q q q qq q q q q qq q q q q qq q q q qq qq q qqq q q q q q q q q q q q q qq qqq qqqq qq q qq q q qq qq q qq q q q qq q q q q q q q q q q q q q qq q q q q q qq q q Mon Tue Wed Thu Fri Sat Sun 1.01.52.02.53.03.5 Time: 12 midnight Day of week Demand(GW)
  • 15. Demand densities (Sth Aust) Probabilistic forecasting of peak electricity demand The problem 10 1.0 1.5 2.0 2.5 3.0 3.5 01234 Density of demand: 12 midnight South Australian half−hourly demand (GW) Density
  • 16. Outline 1 The problem 2 The model 3 Forecasts 4 Challenges and extensions 5 Short term forecasts 6 Evaluating probabilistic forecasts 7 MEFM package 8 References and resources Probabilistic forecasting of peak electricity demand The model 11
  • 17. Predictors calendar effects prevailing and recent weather conditions climate changes economic and demographic changes changing technology Modelling framework Semi-parametric additive models with correlated errors. Each half-hour period modelled separately for each season. Variables selected to provide best out-of-sample predictions using cross-validation on each summer. Probabilistic forecasting of peak electricity demand The model 12
  • 18. Predictors calendar effects prevailing and recent weather conditions climate changes economic and demographic changes changing technology Modelling framework Semi-parametric additive models with correlated errors. Each half-hour period modelled separately for each season. Variables selected to provide best out-of-sample predictions using cross-validation on each summer. Probabilistic forecasting of peak electricity demand The model 12
  • 19. Monash Electricity Forecasting Model y∗ t = yt/¯yi yt denotes per capita demand (minus offset) at time t (measured in half-hourly intervals); ¯yi is the average demand for quarter i where t is in quarter i. y∗ t is the standardized demand for time t. log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Probabilistic forecasting of peak electricity demand The model 13
  • 20. Monash Electricity Forecasting Model Probabilistic forecasting of peak electricity demand The model 14
  • 21. Monash Electricity Forecasting Model Probabilistic forecasting of peak electricity demand The model 14
  • 22. Annual model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et log(¯yi) = log(¯yi−1) + j cj(zj,i − zj,i−1) + εi First differences modelled to avoid non-stationary variables. Predictors: Per-capita GSP, Price, Summer CDD, Winter HDD. Probabilistic forecasting of peak electricity demand The model 15
  • 23. Annual model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et log(¯yi) = log(¯yi−1) + j cj(zj,i − zj,i−1) + εi First differences modelled to avoid non-stationary variables. Predictors: Per-capita GSP, Price, Summer CDD, Winter HDD. Probabilistic forecasting of peak electricity demand The model 15
  • 24. Annual model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et log(¯yi) = log(¯yi−1) + j cj(zj,i − zj,i−1) + εi First differences modelled to avoid non-stationary variables. Predictors: Per-capita GSP, Price, Summer CDD, Winter HDD. zCDD = summer max(0, ¯T − 17.5) ¯T = daily mean Probabilistic forecasting of peak electricity demand The model 15
  • 25. Annual model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et log(¯yi) = log(¯yi−1) + j cj(zj,i − zj,i−1) + εi First differences modelled to avoid non-stationary variables. Predictors: Per-capita GSP, Price, Summer CDD, Winter HDD. zHDD = winter max(0, 19.5 − ¯T) ¯T = daily mean Probabilistic forecasting of peak electricity demand The model 15
  • 26. Annual model SA summer cooling degree days Year scdd 2002 2004 2006 2008 2010 2012 2014 300400500600700 SA winter heating degree days 800850 Probabilistic forecasting of peak electricity demand The model 16
  • 27. Annual model Variable Coefficient Std. Error t value P value ∆gsp.pc 2.02 5.05 0.38 0.711 ∆price −1.67 0.68 −2.46 0.026 ∆scdd 1.11 0.25 4.49 0.000 ∆whdd 2.07 0.33 0.63 0.537 GSP needed to stay in the model to allow scenario forecasting. All other variables led to improved AICC. Probabilistic forecasting of peak electricity demand The model 17
  • 28. Annual model Variable Coefficient Std. Error t value P value ∆gsp.pc 2.02 5.05 0.38 0.711 ∆price −1.67 0.68 −2.46 0.026 ∆scdd 1.11 0.25 4.49 0.000 ∆whdd 2.07 0.33 0.63 0.537 GSP needed to stay in the model to allow scenario forecasting. All other variables led to improved AICC. Probabilistic forecasting of peak electricity demand The model 17
  • 29. Annual model Variable Coefficient Std. Error t value P value ∆gsp.pc 2.02 5.05 0.38 0.711 ∆price −1.67 0.68 −2.46 0.026 ∆scdd 1.11 0.25 4.49 0.000 ∆whdd 2.07 0.33 0.63 0.537 GSP needed to stay in the model to allow scenario forecasting. All other variables led to improved AICC. Probabilistic forecasting of peak electricity demand The model 17
  • 30. Annual model Probabilistic forecasting of peak electricity demand The model 18 Year Annualdemand 1.01.21.41.61.82.0 2002 2004 2006 2008 2010 2012 2014 Actual Fitted
  • 31. Monash Electricity Forecasting Model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Calendar effects “Time of summer” effect (a regression spline) Day of week factor (7 levels) Public holiday factor (4 levels) New Year’s Eve factor (2 levels) Probabilistic forecasting of peak electricity demand The model 19
  • 32. Monash Electricity Forecasting Model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Calendar effects “Time of summer” effect (a regression spline) Day of week factor (7 levels) Public holiday factor (4 levels) New Year’s Eve factor (2 levels) Probabilistic forecasting of peak electricity demand The model 19
  • 33. Monash Electricity Forecasting Model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Calendar effects “Time of summer” effect (a regression spline) Day of week factor (7 levels) Public holiday factor (4 levels) New Year’s Eve factor (2 levels) Probabilistic forecasting of peak electricity demand The model 19
  • 34. Monash Electricity Forecasting Model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Calendar effects “Time of summer” effect (a regression spline) Day of week factor (7 levels) Public holiday factor (4 levels) New Year’s Eve factor (2 levels) Probabilistic forecasting of peak electricity demand The model 19
  • 35. Fitted results (Summer 3pm) Probabilistic forecasting of peak electricity demand The model 20 0 50 100 150 −0.40.00.4 Day of summer Effectondemand Mon Tue Wed Thu Fri Sat Sun −0.40.00.4 Day of week Effectondemand Normal Day before Holiday Day after −0.40.00.4 Holiday Effectondemand Time: 3:00 pm
  • 36. Monash Electricity Forecasting Model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Temperature effects Ave temp across two sites, plus lags for previous 3 hours and previous 3 days. Temp difference between two sites, plus lags for previous 3 hours and previous 3 days. Max ave temp in past 24 hours. Min ave temp in past 24 hours. Ave temp in past seven days. Each function estimated using boosted regression splines. Probabilistic forecasting of peak electricity demand The model 21
  • 37. Monash Electricity Forecasting Model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Temperature effects Ave temp across two sites, plus lags for previous 3 hours and previous 3 days. Temp difference between two sites, plus lags for previous 3 hours and previous 3 days. Max ave temp in past 24 hours. Min ave temp in past 24 hours. Ave temp in past seven days. Each function estimated using boosted regression splines. Probabilistic forecasting of peak electricity demand The model 21
  • 38. Monash Electricity Forecasting Model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Temperature effects Ave temp across two sites, plus lags for previous 3 hours and previous 3 days. Temp difference between two sites, plus lags for previous 3 hours and previous 3 days. Max ave temp in past 24 hours. Min ave temp in past 24 hours. Ave temp in past seven days. Each function estimated using boosted regression splines. Probabilistic forecasting of peak electricity demand The model 21
  • 39. Monash Electricity Forecasting Model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Temperature effects Ave temp across two sites, plus lags for previous 3 hours and previous 3 days. Temp difference between two sites, plus lags for previous 3 hours and previous 3 days. Max ave temp in past 24 hours. Min ave temp in past 24 hours. Ave temp in past seven days. Each function estimated using boosted regression splines. Probabilistic forecasting of peak electricity demand The model 21
  • 40. Monash Electricity Forecasting Model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Temperature effects Ave temp across two sites, plus lags for previous 3 hours and previous 3 days. Temp difference between two sites, plus lags for previous 3 hours and previous 3 days. Max ave temp in past 24 hours. Min ave temp in past 24 hours. Ave temp in past seven days. Each function estimated using boosted regression splines. Probabilistic forecasting of peak electricity demand The model 21
  • 41. Monash Electricity Forecasting Model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Temperature effects Ave temp across two sites, plus lags for previous 3 hours and previous 3 days. Temp difference between two sites, plus lags for previous 3 hours and previous 3 days. Max ave temp in past 24 hours. Min ave temp in past 24 hours. Ave temp in past seven days. Each function estimated using boosted regression splines. Probabilistic forecasting of peak electricity demand The model 21
  • 42. Monash Electricity Forecasting Model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Temperature effects Ave temp across two sites, plus lags for previous 3 hours and previous 3 days. Temp difference between two sites, plus lags for previous 3 hours and previous 3 days. Max ave temp in past 24 hours. Min ave temp in past 24 hours. Ave temp in past seven days. Each function estimated using boosted regression splines. Probabilistic forecasting of peak electricity demand The model 21
  • 43. Monash Electricity Forecasting Model Temperature effects 6 k=0 fk,p(xt−k) + gk,p(dt−k) + qp(x+ t ) + rp(x− t ) + sp(¯xt) + 6 j=1 Fj,p(xt−48j) + Gj,p(dt−48j) xt is ave temp across two sites at time t; dt is the temp difference between two sites at time t; x+ t is max of xt values in past 24 hours; x− t is min of xt values in past 24 hours; ¯xt is ave temp in past seven days. Probabilistic forecasting of peak electricity demand The model 22
  • 44. Monash Electricity Forecasting Model Temperature effects 6 k=0 fk,p(xt−k) + gk,p(dt−k) + qp(x+ t ) + rp(x− t ) + sp(¯xt) + 6 j=1 Fj,p(xt−48j) + Gj,p(dt−48j) xt is ave temp across two sites at time t; dt is the temp difference between two sites at time t; x+ t is max of xt values in past 24 hours; x− t is min of xt values in past 24 hours; ¯xt is ave temp in past seven days. Probabilistic forecasting of peak electricity demand The model 22
  • 45. Monash Electricity Forecasting Model Temperature effects 6 k=0 fk,p(xt−k) + gk,p(dt−k) + qp(x+ t ) + rp(x− t ) + sp(¯xt) + 6 j=1 Fj,p(xt−48j) + Gj,p(dt−48j) xt is ave temp across two sites at time t; dt is the temp difference between two sites at time t; x+ t is max of xt values in past 24 hours; x− t is min of xt values in past 24 hours; ¯xt is ave temp in past seven days. Probabilistic forecasting of peak electricity demand The model 22
  • 46. Monash Electricity Forecasting Model Temperature effects 6 k=0 fk,p(xt−k) + gk,p(dt−k) + qp(x+ t ) + rp(x− t ) + sp(¯xt) + 6 j=1 Fj,p(xt−48j) + Gj,p(dt−48j) xt is ave temp across two sites at time t; dt is the temp difference between two sites at time t; x+ t is max of xt values in past 24 hours; x− t is min of xt values in past 24 hours; ¯xt is ave temp in past seven days. Probabilistic forecasting of peak electricity demand The model 22
  • 47. Monash Electricity Forecasting Model Temperature effects 6 k=0 fk,p(xt−k) + gk,p(dt−k) + qp(x+ t ) + rp(x− t ) + sp(¯xt) + 6 j=1 Fj,p(xt−48j) + Gj,p(dt−48j) xt is ave temp across two sites at time t; dt is the temp difference between two sites at time t; x+ t is max of xt values in past 24 hours; x− t is min of xt values in past 24 hours; ¯xt is ave temp in past seven days. Probabilistic forecasting of peak electricity demand The model 22
  • 48. Fitted results (Summer 3pm) Probabilistic forecasting of peak electricity demand The model 23 10 20 30 40 −0.4−0.20.00.20.4 Temperature Effectondemand 10 20 30 40 −0.4−0.20.00.20.4 Lag 1 temperature Effectondemand 10 20 30 40 −0.4−0.20.00.20.4 Lag 2 temperature Effectondemand 10 20 30 40 −0.4−0.20.00.20.4 Lag 3 temperature Effectondemand 10 20 30 40 −0.4−0.20.00.20.4 Lag 1 day temperature Effectondemand 10 15 20 25 30 −0.4−0.20.00.20.4 Last week average temp Effectondemand 15 25 35 −0.4−0.20.00.20.4 Previous max temp Effectondemand 10 15 20 25 −0.4−0.20.00.20.4 Previous min temp Effectondemand Time: 3:00 pm
  • 49. Half-hourly models log(y∗ t ) = f(calendar effects, temperatures) + et Data split into working/non-working days, and into night/day/evening (6 subsets). Separate model for each half-hour period within each subset (96 models). Same predictors used for all models in a subset. Predictors chosen by cross-validation on last two summers. Each model is fitted to the data twice, first excluding the last summer and then excluding the previous summer. Average out-of-sample MSE calculated from omitted data. Probabilistic forecasting of peak electricity demand The model 24
  • 50. Half-hourly models log(y∗ t ) = f(calendar effects, temperatures) + et Data split into working/non-working days, and into night/day/evening (6 subsets). Separate model for each half-hour period within each subset (96 models). Same predictors used for all models in a subset. Predictors chosen by cross-validation on last two summers. Each model is fitted to the data twice, first excluding the last summer and then excluding the previous summer. Average out-of-sample MSE calculated from omitted data. Probabilistic forecasting of peak electricity demand The model 24
  • 51. Half-hourly models log(y∗ t ) = f(calendar effects, temperatures) + et Data split into working/non-working days, and into night/day/evening (6 subsets). Separate model for each half-hour period within each subset (96 models). Same predictors used for all models in a subset. Predictors chosen by cross-validation on last two summers. Each model is fitted to the data twice, first excluding the last summer and then excluding the previous summer. Average out-of-sample MSE calculated from omitted data. Probabilistic forecasting of peak electricity demand The model 24
  • 52. Half-hourly models log(y∗ t ) = f(calendar effects, temperatures) + et Data split into working/non-working days, and into night/day/evening (6 subsets). Separate model for each half-hour period within each subset (96 models). Same predictors used for all models in a subset. Predictors chosen by cross-validation on last two summers. Each model is fitted to the data twice, first excluding the last summer and then excluding the previous summer. Average out-of-sample MSE calculated from omitted data. Probabilistic forecasting of peak electricity demand The model 24
  • 53. Half-hourly models log(y∗ t ) = f(calendar effects, temperatures) + et Data split into working/non-working days, and into night/day/evening (6 subsets). Separate model for each half-hour period within each subset (96 models). Same predictors used for all models in a subset. Predictors chosen by cross-validation on last two summers. Each model is fitted to the data twice, first excluding the last summer and then excluding the previous summer. Average out-of-sample MSE calculated from omitted data. Probabilistic forecasting of peak electricity demand The model 24
  • 54. Half-hourly models x x1 x2 x3 x4 x5 x6 x48 x96 x144 x192 x240 x288 d d1 d2 d3 d4 d5 d6 d48 d96 d144 d192 d240 d288 x+ x− ¯x dow hol dos MSE 1 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.037 2 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.034 3 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.031 4 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.027 5 • • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.025 6 • • • • • • • • • • • • • • • • • • • • • • • • • • • 1.020 7 • • • • • • • • • • • • • • • • • • • • • • • • • • 1.025 8 • • • • • • • • • • • • • • • • • • • • • • • • • • 1.026 9 • • • • • • • • • • • • • • • • • • • • • • • • • 1.035 10 • • • • • • • • • • • • • • • • • • • • • • • • 1.044 11 • • • • • • • • • • • • • • • • • • • • • • • 1.057 12 • • • • • • • • • • • • • • • • • • • • • • 1.076 13 • • • • • • • • • • • • • • • • • • • • • 1.102 14 • • • • • • • • • • • • • • • • • • • • • • • • • • 1.018 15 • • • • • • • • • • • • • • • • • • • • • • • • • 1.021 16 • • • • • • • • • • • • • • • • • • • • • • • • 1.037 17 • • • • • • • • • • • • • • • • • • • • • • • 1.074 18 • • • • • • • • • • • • • • • • • • • • • • 1.152 19 • • • • • • • • • • • • • • • • • • • • • 1.180 20 • • • • • • • • • • • • • • • • • • • • • • • • • 1.021 21 • • • • • • • • • • • • • • • • • • • • • • • • 1.027 22 • • • • • • • • • • • • • • • • • • • • • • • 1.038 23 • • • • • • • • • • • • • • • • • • • • • • 1.056 24 • • • • • • • • • • • • • • • • • • • • • 1.086 25 • • • • • • • • • • • • • • • • • • • • 1.135 26 • • • • • • • • • • • • • • • • • • • • • • • • • 1.009 27 • • • • • • • • • • • • • • • • • • • • • • • • • 1.063 28 • • • • • • • • • • • • • • • • • • • • • • • • • 1.028 29 • • • • • • • • • • • • • • • • • • • • • • • • • 3.523 30 • • • • • • • • • • • • • • • • • • • • • • • • • 2.143 31 • • • • • • • • • • • • • • • • • • • • • • • • • 1.523 Probabilistic forecasting of peak electricity demand The model 25
  • 55. Half-hourly models Probabilistic forecasting of peak electricity demand The model 26 60708090 R−squared Time of day R−squared(%) 12 midnight 6:00 am 9:00 am 12 noon 3:00 pm 6:00 pm 9:00 pm3:00 am 12 midnight
  • 56. Half-hourly models Probabilistic forecasting of peak electricity demand The model 26 Demand (January 2015) Date in January SAdemand(GW) 012345 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Actual Predicted Temperatures (January 2015) ) 40 temp_23090 temp_23083
  • 57. Half-hourly models Probabilistic forecasting of peak electricity demand The model 26
  • 58. Half-hourly models Probabilistic forecasting of peak electricity demand The model 26
  • 59. Half-hourly models Probabilistic forecasting of peak electricity demand The model 26 Predictions adjusted for saturated usage.
  • 60. Outline 1 The problem 2 The model 3 Forecasts 4 Challenges and extensions 5 Short term forecasts 6 Evaluating probabilistic forecasts 7 MEFM package 8 References and resources Probabilistic forecasting of peak electricity demand Forecasts 27
  • 61. Peak demand forecasting log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Multiple alternative futures created: Calendar effects known; Future temperatures simulated (taking account of climate change); Assumed values for GSP, population and price; Residuals simulated Probabilistic forecasting of peak electricity demand Forecasts 28
  • 62. Peak demand backcasting log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Multiple alternative pasts created: Calendar effects known; Past temperatures simulated; Actual values for GSP, population and price; Residuals simulated Probabilistic forecasting of peak electricity demand Forecasts 28
  • 63. Peak demand backcasting Probabilistic forecasting of peak electricity demand Forecasts 29 PoE (seasonal interpretation, summer) Year PoEDemand(total) 2.42.62.83.03.23.43.63.8 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 10 % 50 % 90 % q q q q q q q q q q q q q q
  • 64. Peak demand backcasting log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Multiple alternative pasts created: Calendar effects known; Past temperatures simulated; Actual values for GSP, population and price; Residuals simulated Probabilistic forecasting of peak electricity demand Forecasts 30
  • 65. Peak demand forecasting log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Multiple alternative futures created: Calendar effects known; Future temperatures simulated (taking account of climate change); Assumed values for GSP, population and price; Residuals simulated Probabilistic forecasting of peak electricity demand Forecasts 30
  • 66. Peak demand forecasting Probabilistic forecasting of peak electricity demand Forecasts 31 Population Year 000'spersons 2000 2005 2010 2015 2020 2025 2030 2035 16002000 base low high GSP Year $million 2000 2005 2010 2015 2020 2025 2030 2035 2000035000 base low high Price Year c/kWh 2000 2005 2010 2015 2020 2025 2030 2035 1520253035 base low high
  • 67. Peak demand distribution Probabilistic forecasting of peak electricity demand Forecasts 32 Seasonal POE levels (summer) Year PoEDemand 2.02.53.03.54.04.5 2002 2005 2008 2011 2014 2017 2020 2023 2026 2029 2032 2035 q q q q q q q q q q q q q 10 % POE 50 % POE 90 % POE Actual annual maximum
  • 68. Seasonal block bootstrapping Conventional seasonal block bootstrap Same as block bootstrap but with whole years as the blocks to preserve seasonality. But we only have about 10–15 years of data, so there is a limited number of possible bootstrap samples. Double seasonal block bootstrap Suitable when there are two seasonal periods (here we have years of 151 days and days of 48 half-hours). Divide each year into blocks of length 48m. Block 1 consists of the first m days of the year, block 2 consists of the next m days, and so on. Bootstrap sample consists of a sample of blocks where each block may come from a different randomly selected year but must be at the correct time of year. Probabilistic forecasting of peak electricity demand Forecasts 33
  • 69. Seasonal block bootstrapping Conventional seasonal block bootstrap Same as block bootstrap but with whole years as the blocks to preserve seasonality. But we only have about 10–15 years of data, so there is a limited number of possible bootstrap samples. Double seasonal block bootstrap Suitable when there are two seasonal periods (here we have years of 151 days and days of 48 half-hours). Divide each year into blocks of length 48m. Block 1 consists of the first m days of the year, block 2 consists of the next m days, and so on. Bootstrap sample consists of a sample of blocks where each block may come from a different randomly selected year but must be at the correct time of year. Probabilistic forecasting of peak electricity demand Forecasts 33
  • 70. Seasonal block bootstrapping Conventional seasonal block bootstrap Same as block bootstrap but with whole years as the blocks to preserve seasonality. But we only have about 10–15 years of data, so there is a limited number of possible bootstrap samples. Double seasonal block bootstrap Suitable when there are two seasonal periods (here we have years of 151 days and days of 48 half-hours). Divide each year into blocks of length 48m. Block 1 consists of the first m days of the year, block 2 consists of the next m days, and so on. Bootstrap sample consists of a sample of blocks where each block may come from a different randomly selected year but must be at the correct time of year. Probabilistic forecasting of peak electricity demand Forecasts 33
  • 71. Seasonal block bootstrapping Conventional seasonal block bootstrap Same as block bootstrap but with whole years as the blocks to preserve seasonality. But we only have about 10–15 years of data, so there is a limited number of possible bootstrap samples. Double seasonal block bootstrap Suitable when there are two seasonal periods (here we have years of 151 days and days of 48 half-hours). Divide each year into blocks of length 48m. Block 1 consists of the first m days of the year, block 2 consists of the next m days, and so on. Bootstrap sample consists of a sample of blocks where each block may come from a different randomly selected year but must be at the correct time of year. Probabilistic forecasting of peak electricity demand Forecasts 33
  • 72. Seasonal block bootstrapping Conventional seasonal block bootstrap Same as block bootstrap but with whole years as the blocks to preserve seasonality. But we only have about 10–15 years of data, so there is a limited number of possible bootstrap samples. Double seasonal block bootstrap Suitable when there are two seasonal periods (here we have years of 151 days and days of 48 half-hours). Divide each year into blocks of length 48m. Block 1 consists of the first m days of the year, block 2 consists of the next m days, and so on. Bootstrap sample consists of a sample of blocks where each block may come from a different randomly selected year but must be at the correct time of year. Probabilistic forecasting of peak electricity demand Forecasts 33
  • 73. Seasonal block bootstrapping Conventional seasonal block bootstrap Same as block bootstrap but with whole years as the blocks to preserve seasonality. But we only have about 10–15 years of data, so there is a limited number of possible bootstrap samples. Double seasonal block bootstrap Suitable when there are two seasonal periods (here we have years of 151 days and days of 48 half-hours). Divide each year into blocks of length 48m. Block 1 consists of the first m days of the year, block 2 consists of the next m days, and so on. Bootstrap sample consists of a sample of blocks where each block may come from a different randomly selected year but must be at the correct time of year. Probabilistic forecasting of peak electricity demand Forecasts 33
  • 74. Seasonal block bootstrapping Conventional seasonal block bootstrap Same as block bootstrap but with whole years as the blocks to preserve seasonality. But we only have about 10–15 years of data, so there is a limited number of possible bootstrap samples. Double seasonal block bootstrap Suitable when there are two seasonal periods (here we have years of 151 days and days of 48 half-hours). Divide each year into blocks of length 48m. Block 1 consists of the first m days of the year, block 2 consists of the next m days, and so on. Bootstrap sample consists of a sample of blocks where each block may come from a different randomly selected year but must be at the correct time of year. Probabilistic forecasting of peak electricity demand Forecasts 33
  • 75. Seasonal block bootstrapping Probabilistic forecasting of peak electricity demand Forecasts 34 Actual temperatures Days degreesC 0 10 20 30 40 50 60 10152025303540 Bootstrap temperatures (fixed blocks) Days degreesC 0 10 20 30 40 50 60 10152025303540 Bootstrap temperatures (variable blocks) 40
  • 76. Seasonal block bootstrapping Problems with the double seasonal bootstrap Boundaries between blocks can introduce large jumps. However, only at midnight. Number of values that any given time in year is still limited to the number of years in the data set. Probabilistic forecasting of peak electricity demand Forecasts 35
  • 77. Seasonal block bootstrapping Problems with the double seasonal bootstrap Boundaries between blocks can introduce large jumps. However, only at midnight. Number of values that any given time in year is still limited to the number of years in the data set. Probabilistic forecasting of peak electricity demand Forecasts 35
  • 78. Seasonal block bootstrapping Variable length double seasonal block bootstrap Blocks allowed to vary in length between m − ∆ and m + ∆ days where 0 ≤ ∆ < m. Blocks allowed to move up to ∆ days from their original position. Has little effect on the overall time series patterns provided ∆ is relatively small. Use uniform distribution on (m − ∆, m + ∆) to select block length, and independent uniform distribution on (−∆, ∆) to select variation on starting position for each block. Probabilistic forecasting of peak electricity demand Forecasts 36
  • 79. Seasonal block bootstrapping Variable length double seasonal block bootstrap Blocks allowed to vary in length between m − ∆ and m + ∆ days where 0 ≤ ∆ < m. Blocks allowed to move up to ∆ days from their original position. Has little effect on the overall time series patterns provided ∆ is relatively small. Use uniform distribution on (m − ∆, m + ∆) to select block length, and independent uniform distribution on (−∆, ∆) to select variation on starting position for each block. Probabilistic forecasting of peak electricity demand Forecasts 36
  • 80. Seasonal block bootstrapping Variable length double seasonal block bootstrap Blocks allowed to vary in length between m − ∆ and m + ∆ days where 0 ≤ ∆ < m. Blocks allowed to move up to ∆ days from their original position. Has little effect on the overall time series patterns provided ∆ is relatively small. Use uniform distribution on (m − ∆, m + ∆) to select block length, and independent uniform distribution on (−∆, ∆) to select variation on starting position for each block. Probabilistic forecasting of peak electricity demand Forecasts 36
  • 81. Seasonal block bootstrapping Variable length double seasonal block bootstrap Blocks allowed to vary in length between m − ∆ and m + ∆ days where 0 ≤ ∆ < m. Blocks allowed to move up to ∆ days from their original position. Has little effect on the overall time series patterns provided ∆ is relatively small. Use uniform distribution on (m − ∆, m + ∆) to select block length, and independent uniform distribution on (−∆, ∆) to select variation on starting position for each block. Probabilistic forecasting of peak electricity demand Forecasts 36
  • 82. Seasonal block bootstrapping Probabilistic forecasting of peak electricity demand Forecasts 37 Actual temperatures Days degreesC 0 10 20 30 40 50 60 10152025303540 Bootstrap temperatures (fixed blocks) Days degreesC 0 10 20 30 40 50 60 10152025303540 Bootstrap temperatures (variable blocks) Days degreesC 0 10 20 30 40 50 60 10152025303540
  • 83. Seasonal block bootstrapping Probabilistic forecasting of peak electricity demand Forecasts 37
  • 84. Outline 1 The problem 2 The model 3 Forecasts 4 Challenges and extensions 5 Short term forecasts 6 Evaluating probabilistic forecasts 7 MEFM package 8 References and resources Probabilistic forecasting of peak electricity demand Challenges and extensions 38
  • 85. Challenges Some judgmental adjustments are done to account for demand response activity. We have a separate model for PV generation based on solar radiation and temperatures. But limited PV data available, so PV adjustments are probably inaccurate. Difficult to account for new technology such as local storage intended to flatten demand. Climate change effect is assumed additive at all temperature levels — probably simplistic. Probabilistic forecasting of peak electricity demand Challenges and extensions 39
  • 86. Challenges Some judgmental adjustments are done to account for demand response activity. We have a separate model for PV generation based on solar radiation and temperatures. But limited PV data available, so PV adjustments are probably inaccurate. Difficult to account for new technology such as local storage intended to flatten demand. Climate change effect is assumed additive at all temperature levels — probably simplistic. Probabilistic forecasting of peak electricity demand Challenges and extensions 39
  • 87. Challenges Some judgmental adjustments are done to account for demand response activity. We have a separate model for PV generation based on solar radiation and temperatures. But limited PV data available, so PV adjustments are probably inaccurate. Difficult to account for new technology such as local storage intended to flatten demand. Climate change effect is assumed additive at all temperature levels — probably simplistic. Probabilistic forecasting of peak electricity demand Challenges and extensions 39
  • 88. Challenges Some judgmental adjustments are done to account for demand response activity. We have a separate model for PV generation based on solar radiation and temperatures. But limited PV data available, so PV adjustments are probably inaccurate. Difficult to account for new technology such as local storage intended to flatten demand. Climate change effect is assumed additive at all temperature levels — probably simplistic. Probabilistic forecasting of peak electricity demand Challenges and extensions 39
  • 89. Implementation Probabilistic forecasting of peak electricity demand Challenges and extensions 40 Our model is used for long-term forecasting in: Victoria’s Vision 2030 energy plan; all regions of the National Energy Market; South Western Interconnected System (WA); some local distributors.
  • 90. Implementation Probabilistic forecasting of peak electricity demand Challenges and extensions 40 Our model is used for long-term forecasting in: Victoria’s Vision 2030 energy plan; all regions of the National Energy Market; South Western Interconnected System (WA); some local distributors. It is also used for short-term forecasting comparisons in: all regions of the National Energy Market.
  • 91. Outline 1 The problem 2 The model 3 Forecasts 4 Challenges and extensions 5 Short term forecasts 6 Evaluating probabilistic forecasts 7 MEFM package 8 References and resources Probabilistic forecasting of peak electricity demand Short term forecasts 41
  • 92. Short-term forecasts log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Simulating temperatures and residuals is ok for long-term forecasts because short-term dynamics wash out after a few weeks. But short-term forecasts need to take account of recent temperatures and recent residuals due to serial correlation. Short-term temperature forecasts are available. Probabilistic forecasting of peak electricity demand Short term forecasts 42
  • 93. Short-term forecasts log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Simulating temperatures and residuals is ok for long-term forecasts because short-term dynamics wash out after a few weeks. But short-term forecasts need to take account of recent temperatures and recent residuals due to serial correlation. Short-term temperature forecasts are available. Probabilistic forecasting of peak electricity demand Short term forecasts 42
  • 94. Short-term forecasts log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures) + et Simulating temperatures and residuals is ok for long-term forecasts because short-term dynamics wash out after a few weeks. But short-term forecasts need to take account of recent temperatures and recent residuals due to serial correlation. Short-term temperature forecasts are available. Probabilistic forecasting of peak electricity demand Short term forecasts 42
  • 95. Short-term forecasting model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures, lagged demand) + et Lagged demand inputs Demand in last 3 hours and last 3 days; Maximum demand in past 24 hours; Minimum demand in past 24 hours; Average demand in past 7 days Each function is estimated using boosted regression splines. Probabilistic forecasting of peak electricity demand Short term forecasts 43
  • 96. Short-term forecasting model log(yt) = log(¯yi) + log(y∗ t ) log(¯yi) = f(GSP, price, HDD, CDD) + εi log(y∗ t ) = f(calendar effects, temperatures, lagged demand) + et Lagged demand inputs Demand in last 3 hours and last 3 days; Maximum demand in past 24 hours; Minimum demand in past 24 hours; Average demand in past 7 days Each function is estimated using boosted regression splines. Probabilistic forecasting of peak electricity demand Short term forecasts 43
  • 97. GEFCom2012 Probabilistic forecasting of peak electricity demand Short term forecasts 44
  • 98. GEFCom2012 Probabilistic forecasting of peak electricity demand Short term forecasts 44 Methods published in IJF, April 2014.
  • 99. Outline 1 The problem 2 The model 3 Forecasts 4 Challenges and extensions 5 Short term forecasts 6 Evaluating probabilistic forecasts 7 MEFM package 8 References and resources Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 45
  • 100. Forecast accuracy measures MAE: Mean absolute error MSE: Mean squared error MAPE: Mean absolute percentage error ¯ Good when forecasting a typical future value (e.g., the mean or median). Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 46
  • 101. Forecast accuracy measures MAE: Mean absolute error MSE: Mean squared error MAPE: Mean absolute percentage error ¯ Good when forecasting a typical future value (e.g., the mean or median). Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 46
  • 102. Forecast accuracy measures MAE: Mean absolute error MSE: Mean squared error MAPE: Mean absolute percentage error ¯ Good when forecasting a typical future value (e.g., the mean or median). Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 46
  • 103. Forecast accuracy measures MAE: Mean absolute error MSE: Mean squared error MAPE: Mean absolute percentage error ¯ Good when forecasting a typical future value (e.g., the mean or median). Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 46
  • 104. Forecast accuracy measures MAE: Mean absolute error MSE: Mean squared error MAPE: Mean absolute percentage error ¯ Good when forecasting a typical future value (e.g., the mean or median). ¯ Useless for evaluating forecast percentiles (probability of exceedance values) and forecast distributions. Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 46
  • 105. Evaluating forecast distributions Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 47 PoE (seasonal interpretation, summer) Year PoEDemand(total) 2.42.62.83.03.23.43.63.8 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 10 % 50 % 90 % q q q q q q q q q q q q q q
  • 106. Evaluating forecast distributions Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 47 PoE (seasonal interpretation, summer) Year PoEDemand(total) 2.42.62.83.03.23.43.63.8 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 10 % 50 % 90 % q q q q q q q q q q q q q q 12 out of 13 above 90% PoE 6 out of 13 above 50% PoE 2 out of 13 above 10% PoE
  • 107. Forecast scoring Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 48 0 1 2 3 4 5 6 Demand distribution Demand (GWh)
  • 108. Forecast scoring Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 48 0 1 2 3 4 5 6 Demand distribution Demand (GWh) 50% 50% PoE
  • 109. Forecast scoring Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 48 0 1 2 3 4 5 6 Demand distribution Demand (GWh) 50% 50% PoE Score for 50% PoE
  • 110. Forecast scoring Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 48 0 1 2 3 4 5 6 Demand distribution Demand (GWh) 50% 50% PoE Score for 50% PoE Equivalent to absolute error
  • 111. Forecast scoring Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 49 0 1 2 3 4 5 6 Demand distribution Demand (GWh)
  • 112. Forecast scoring Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 49 0 1 2 3 4 5 6 Demand distribution Demand (GWh) 10% 10% PoE
  • 113. Forecast scoring Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 49 0 1 2 3 4 5 6 Demand distribution Demand (GWh) 10% 10% PoE Score for 10% PoE
  • 114. Forecast scoring Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 50 0 1 2 3 4 5 6 Demand distribution Demand (GWh)
  • 115. Forecast scoring Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 50 0 1 2 3 4 5 6 Demand distribution Demand (GWh) 75% 75% PoE
  • 116. Forecast scoring Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 50 0 1 2 3 4 5 6 Demand distribution Demand (GWh) 75% 75% PoE Score for 75% PoE
  • 117. Forecast scoring Let Qt(1), . . . , Qt(99) be the PoEs of the forecast distribution for probabilities 1%,. . . ,99%. Then the score for observation y is S(Qt(i), yt) = 1 100 i(Qt(i) − yt) if yt < Qt(i) 1 100 (100 − i)(yt − Qt(i)) if yt ≥ Qt(i) Scores are averaged over all observed data for each i to measure the accuracy of the forecasts for each percentile. Average score over all percentiles gives the best distribution forecast. Takes account of how far PoEs are exceeded. Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 51
  • 118. Forecast scoring Let Qt(1), . . . , Qt(99) be the PoEs of the forecast distribution for probabilities 1%,. . . ,99%. Then the score for observation y is S(Qt(i), yt) = 1 100 i(Qt(i) − yt) if yt < Qt(i) 1 100 (100 − i)(yt − Qt(i)) if yt ≥ Qt(i) Scores are averaged over all observed data for each i to measure the accuracy of the forecasts for each percentile. Average score over all percentiles gives the best distribution forecast. Takes account of how far PoEs are exceeded. Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 51
  • 119. Forecast scoring Let Qt(1), . . . , Qt(99) be the PoEs of the forecast distribution for probabilities 1%,. . . ,99%. Then the score for observation y is S(Qt(i), yt) = 1 100 i(Qt(i) − yt) if yt < Qt(i) 1 100 (100 − i)(yt − Qt(i)) if yt ≥ Qt(i) Scores are averaged over all observed data for each i to measure the accuracy of the forecasts for each percentile. Average score over all percentiles gives the best distribution forecast. Takes account of how far PoEs are exceeded. Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 51
  • 120. GEFCom2014 Probabilistic forecasting of demand, price, wind, and solar. Rolling forecasts with incremental data update on a weekly basis. Forecasts submitted in the form of percentiles of future distributions. Evaluation based on quantile scoring. Prizes for student teams, and for best methods. Winning methods to be published in the IJF. Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 52
  • 121. GEFCom2014 Probabilistic forecasting of demand, price, wind, and solar. Rolling forecasts with incremental data update on a weekly basis. Forecasts submitted in the form of percentiles of future distributions. Evaluation based on quantile scoring. Prizes for student teams, and for best methods. Winning methods to be published in the IJF. Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 52
  • 122. GEFCom2014 Probabilistic forecasting of demand, price, wind, and solar. Rolling forecasts with incremental data update on a weekly basis. Forecasts submitted in the form of percentiles of future distributions. Evaluation based on quantile scoring. Prizes for student teams, and for best methods. Winning methods to be published in the IJF. Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 52
  • 123. GEFCom2014 Probabilistic forecasting of demand, price, wind, and solar. Rolling forecasts with incremental data update on a weekly basis. Forecasts submitted in the form of percentiles of future distributions. Evaluation based on quantile scoring. Prizes for student teams, and for best methods. Winning methods to be published in the IJF. Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 52
  • 124. GEFCom2014 Probabilistic forecasting of demand, price, wind, and solar. Rolling forecasts with incremental data update on a weekly basis. Forecasts submitted in the form of percentiles of future distributions. Evaluation based on quantile scoring. Prizes for student teams, and for best methods. Winning methods to be published in the IJF. Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 52
  • 125. GEFCom2014 Probabilistic forecasting of demand, price, wind, and solar. Rolling forecasts with incremental data update on a weekly basis. Forecasts submitted in the form of percentiles of future distributions. Evaluation based on quantile scoring. Prizes for student teams, and for best methods. Winning methods to be published in the IJF. Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 52
  • 126. GEFCom2014 Load forecasting provisional leaderboard Probabilistic forecasting of peak electricity demand Evaluating probabilistic forecasts 53
  • 127. Outline 1 The problem 2 The model 3 Forecasts 4 Challenges and extensions 5 Short term forecasts 6 Evaluating probabilistic forecasts 7 MEFM package 8 References and resources Probabilistic forecasting of peak electricity demand MEFM package 54
  • 128. MEFM package for R Available on github: install.packages("devtools") library(devtools) install_github("robjhyndman/MEFM-package") Package contents: seasondays The number of days in a season sa.econ Historical demographic & economic data for South Australia sa Historical data for model estimation maketemps Create lagged temperature variables demand_model Estimate the electricity demand models simulate_ddemand Temperature and demand simulation simulate_demand Simulate the electricity demand for the next season Probabilistic forecasting of peak electricity demand MEFM package 55
  • 129. MEFM package for R Available on github: install.packages("devtools") library(devtools) install_github("robjhyndman/MEFM-package") Package contents: seasondays The number of days in a season sa.econ Historical demographic & economic data for South Australia sa Historical data for model estimation maketemps Create lagged temperature variables demand_model Estimate the electricity demand models simulate_ddemand Temperature and demand simulation simulate_demand Simulate the electricity demand for the next season Probabilistic forecasting of peak electricity demand MEFM package 55
  • 130. MEFM package for R Usage library(MEFM) # Number of days in each "season" seasondays # Historical economic data sa.econ # Historical temperature and calendar data head(sa) tail(sa) dim(sa) # create lagged temperature variables salags <- maketemps(sa,2,48) dim(salags) head(salags) Probabilistic forecasting of peak electricity demand MEFM package 56
  • 131. MEFM package for R # formula for annual model formula.a <- as.formula(anndemand ~ gsp + ddays + resiprice) # formulas for half-hourly model # These can be different for each half-hour formula.hh <- list() for(i in 1:48) { formula.hh[[i]] <- as.formula(log(ddemand) ~ ns(temp, df=2) + day + holiday + ns(timeofyear, df=9) + ns(avetemp, df=3) + ns(dtemp, df=3) + ns(lastmin, df=3) + ns(prevtemp1, df=2) + ns(prevtemp2, df=2) + ns(prevtemp3, df=2) + ns(prevtemp4, df=2) + ns(day1temp, df=2) + ns(day2temp, df=2) + ns(day3temp, df=2) + ns(prevdtemp1, df=3) + ns(prevdtemp2, df=3) + ns(prevdtemp3, df=3) + ns(day1dtemp, df=3)) } Probabilistic forecasting of peak electricity demand MEFM package 57
  • 132. MEFM package for R # Fit all models sa.model <- demand_model(salags, sa.econ, formula.hh, formula.a) # Summary of annual model summary(sa.model$a) # Summary of half-hourly model at 4pm summary(sa.model$hh[[33]]) # Simulate future normalized half-hourly data simdemand <- simulate_ddemand(sa.model, sa, simyears=50) # economic forecasts, to be given by user afcast <- data.frame(pop=1694, gsp=22573, resiprice=34.65, ddays=642) # Simulate half-hourly data demand <- simulate_demand(simdemand, afcast) Probabilistic forecasting of peak electricity demand MEFM package 58
  • 133. MEFM package for R plot(ts(demand$demand[,sample(1:100, 4)], freq=48, start=0), xlab="Days", main="Simulated demand futures") Probabilistic forecasting of peak electricity demand MEFM package 59
  • 134. MEFM package for R plot(ts(demand$demand[,sample(1:100, 4)], freq=48, start=0), xlab="Days", main="Simulated demand futures")0.61.01.4 Series52 0.51.52.5 Series49 0.51.52.5 Series88 0.61.21.8 0 50 100 150 Series53 Days Simulated demand futures Probabilistic forecasting of peak electricity demand MEFM package 59
  • 135. MEFM package for R plot(demand$annmax, main="Simulated seasonal maximums", ylab="GW") Probabilistic forecasting of peak electricity demand MEFM package 60
  • 136. MEFM package for R plot(demand$annmax, main="Simulated seasonal maximums", ylab="GW") 0 20 40 60 80 100 1.52.02.53.0 Simulated seasonal maximums Index GW Probabilistic forecasting of peak electricity demand MEFM package 60
  • 137. MEFM package for R boxplot(demand$annmax, main="Simulated seasonal maximums", xlab="GW", horizontal=TRUE) rug(demand$annmax) Probabilistic forecasting of peak electricity demand MEFM package 61
  • 138. MEFM package for R boxplot(demand$annmax, main="Simulated seasonal maximums", xlab="GW", horizontal=TRUE) rug(demand$annmax) 1.5 2.0 2.5 3.0 Simulated seasonal maximums GW Probabilistic forecasting of peak electricity demand MEFM package 61
  • 139. MEFM package for R plot(density(demand$annmax, bw="SJ"), xlab="Demand (GW)", main="Density of seasonal maximum demand") rug(demand$annmax) Probabilistic forecasting of peak electricity demand MEFM package 62
  • 140. MEFM package for R plot(density(demand$annmax, bw="SJ"), xlab="Demand (GW)", main="Density of seasonal maximum demand") rug(demand$annmax) 1.5 2.0 2.5 3.0 3.5 0.00.40.81.2 Density of seasonal maximum demand Demand (GW) Density Probabilistic forecasting of peak electricity demand MEFM package 62
  • 141. Outline 1 The problem 2 The model 3 Forecasts 4 Challenges and extensions 5 Short term forecasts 6 Evaluating probabilistic forecasts 7 MEFM package 8 References and resources Probabilistic forecasting of peak electricity demand References and resources 63
  • 142. References ¯ Hyndman, R.J. & Fan, S. (2010) “Density forecasting for long-term peak electricity demand”, IEEE Transactions on Power Systems, 25(2), 1142–1153. ¯ Fan, S. & Hyndman, R.J. (2012) “Short-term load forecasting based on a semi-parametric additive model”. IEEE Transactions on Power Systems, 27(1), 134–141. ¯ Ben Taieb, S. & Hyndman, R.J. (2013) “A gradient boosting approach to the Kaggle load forecasting competition”, International Journal of Forecasting, 29(4). ¯ Hyndman, R.J., & Fan, S. (2014). “Monash Electricity Forecasting Model”. Technical paper. robjhyndman.com/working-papers/mefm/ ¯ Fan, S., & Hyndman, R.J. (2014). “MEFM: An R package imple- menting the Monash Electricity Forecasting Model.” github.com/robjhyndman/MEFM-package Probabilistic forecasting of peak electricity demand References and resources 64
  • 143. Some resources Blogs robjhyndman.com/hyndsight/ blog.drhongtao.com/ Organizations International Institute of Forecasters: forecasters.org IEEE Working Group on Energy Forecasting: linkedin.com/groups/ IEEE-Working-Group-on-Energy-4148276 Books Dickey and Hong (2014) Electric load forecasting: fundamentals and best practices, OTexts. www.otexts.org/book/elf Probabilistic forecasting of peak electricity demand References and resources 65
  • 144. Some resources Blogs robjhyndman.com/hyndsight/ blog.drhongtao.com/ Organizations International Institute of Forecasters: forecasters.org IEEE Working Group on Energy Forecasting: linkedin.com/groups/ IEEE-Working-Group-on-Energy-4148276 Books Dickey and Hong (2014) Electric load forecasting: fundamentals and best practices, OTexts. www.otexts.org/book/elf Probabilistic forecasting of peak electricity demand References and resources 65
  • 145. Some resources Blogs robjhyndman.com/hyndsight/ blog.drhongtao.com/ Organizations International Institute of Forecasters: forecasters.org IEEE Working Group on Energy Forecasting: linkedin.com/groups/ IEEE-Working-Group-on-Energy-4148276 Books Dickey and Hong (2014) Electric load forecasting: fundamentals and best practices, OTexts. www.otexts.org/book/elf Probabilistic forecasting of peak electricity demand References and resources 65
  • 146. Some resources Blogs robjhyndman.com/hyndsight/ blog.drhongtao.com/ Organizations International Institute of Forecasters: forecasters.org IEEE Working Group on Energy Forecasting: linkedin.com/groups/ IEEE-Working-Group-on-Energy-4148276 Books Dickey and Hong (2014) Electric load forecasting: fundamentals and best practices, OTexts. www.otexts.org/book/elf Probabilistic forecasting of peak electricity demand References and resources 65
  • 147. Some resources Blogs robjhyndman.com/hyndsight/ blog.drhongtao.com/ Organizations International Institute of Forecasters: forecasters.org IEEE Working Group on Energy Forecasting: linkedin.com/groups/ IEEE-Working-Group-on-Energy-4148276 Books Dickey and Hong (2014) Electric load forecasting: fundamentals and best practices, OTexts. www.otexts.org/book/elf Probabilistic forecasting of peak electricity demand References and resources 65
  • 148. Some resources Blogs robjhyndman.com/hyndsight/ blog.drhongtao.com/ Organizations International Institute of Forecasters: forecasters.org IEEE Working Group on Energy Forecasting: linkedin.com/groups/ IEEE-Working-Group-on-Energy-4148276 Books Dickey and Hong (2014) Electric load forecasting: fundamentals and best practices, OTexts. www.otexts.org/book/elf Probabilistic forecasting of peak electricity demand References and resources 65
  • 149. Some resources Blogs robjhyndman.com/hyndsight/ blog.drhongtao.com/ Organizations International Institute of Forecasters: forecasters.org IEEE Working Group on Energy Forecasting: linkedin.com/groups/ IEEE-Working-Group-on-Energy-4148276 Books Dickey and Hong (2014) Electric load forecasting: fundamentals and best practices, OTexts. www.otexts.org/book/elf Probabilistic forecasting of peak electricity demand References and resources 65