A range of methods for
electrical consumption
forecasting
Energy Systems Week
April 22th:
Xavier Brossat EDF/RD/Dpt OSIRIS
1- -
A range of methods for electrical consumption
forecasting.
For Electricité de France the forecast of electricity consumption is a fundamental problem which has been studied for the
last twenty years. It is necessary to be able to provide customers and at the same time, optimize the production at different
horizons of time.
Results of operating models that use non linear regression or ARMAX methods are satisfying with a current accuracy of
1.5% for the forecast of the following day.
But, they have to be continually fitted to be adapted to some very difficult periods of time and to the change of
consumption.
For a few years, due to the new competitive environment, the electrical load curve has become less regular. Its shape and
level which depended essentially on climatic exogenous variables has become more affected by economical and ecological
variables. The data is not always available and the time series used are often short.
So, we have tried to apply the following alternative methods to answer to problems like adaptivity, nonstationarity,
parsimony, lack of data, necessity of forecast interval.
In this presentation we will display the operating models and those different classes of models which we applied to
electrical consumption forecast. For each model we will present the method used, we will show some practical results and
we will discuss the benefits and drawbacks of it.(adaptive Kalmann, GAM, combining algoritms, KWF, Bayesian
Methods, ..)
Energy management
Supply-side uncertainties
G=D
Investment decisions
Fuel supplies
System flexibilities
Nuclear maintenance
scheduling
Long-term
Medium-term
20-50 years
1-5 years
Structuring of
customer contracts
Long-term
demand
Demand-side uncertainties
Stock management
(H2O, Nuclear, large
combustion plants,
etc.)
Daily generation plans
THF, H2O
maintenance
Control and
management of
market risks
Strategy for the use of
load-sheds and gas
contracts
Intra-day redeclarations
Market
arbitrages
Short-term
1 hour – 1 day
Load-shedding,
Load forecasts nominations
R&D skills and Energy Management
Management of market risks
Financial mathematics, optimisation, risk
management,
Portfolio structuring
Optimisation, quantitative
economics, energy markets,
econometrics
Statistics, optimisation, econometrics,
energy markets
Energy markets and
unknown factors
Portfolio
optimisation
Portfolio
management
Optimisation, electricity
generation, gas logistics
Statistics, probabilities, load
forecasts
Load forecasting
A common background: information technology
Outline
1. Some Charateristics of
electrical consumption in
France
2. Operational Model and his
limits
3. A range of methods for
electrical consumption
forecasting.
4. Future Work
5- -
Some charateristics of
electrical
consumption in
France
6- -
Electricity demand data
Various seasonal
components.
High dependency
on climate
Other interspersed
punctual events.
7- -
Some characteristics of French electricity
consumption : annual cycle
Daily Energy (Normal Temperature and nebulosity) from 2004/09/01to 2008/08/31
Special days and events:
Christm
as
From 2006/09/01 to 2007/08/31
Mai
Augu
st
Some characteristics of French electricity
consumption : temperature’s effect in winter
du 05 au 11 novembre 2007
du 12 au 18 novembre 2007
Some characteristics of French electricity consumption :
special days and events
August, 15th
Christmas
January, 1st
Montday to
Friday
Saturday
Sunday
10
30/11/2009
2/7/2009
15/2/2009
25/9/2008
21/4/2008
2/12/2007
1/7/2007
15/2/2007
11/10/2006
26/4/2006
9/1/2006
25/7/2005
17/3/2005
18/11/2004
18/6/2004
11/2/2004
7/10/2003
16/4/2003
19/12/2002
1/9/2002
-4000
-2000
400
0
600
P-Pchap
1000
1200
1600
Economic crisis
800
1400
4000
RMSE horaire en MW
2000
The economic crisis has an impact on French
consumption on the period 2007-2009
2002
2003
2004
2005
0
10
20
Instant
2006
2007
2008
30
40
A good quality of forecast
Problem studied during these last 25 years
Forecasting horizon daily H=1:7*48 half an hour, one week, one
year
A current accuracy of 1. 2% (MAPE) for the forecast of the
following day!
Why more?
Why more ?
Some very difficult periods (winter: with fast changes in temperature,
special days and events: bank holidays, crisis, …)
Due to the new competitive environment, forecasts must be more
accurate.
Therefore customers are able to leave and join the company ( Non
stationarity).
We have do to local forecast
We have to take in account renewable energy, the evolving of uses
We have to evaluate the uncertainties and provide forecast intervals
Uncertainties about customer’s behavior , institutional mechanism, data
acquisition, and socio-economic changes
With keeping the good prediction performance of present methods despite
the changing context (accuracy of 1.2% for the following day).
Why more ?
DATA
Available data is changing :Split between provider and transporter
Difficulties with measuring individual consumption
Short past time series
Different portfolios
Different sampling
New electricity meters : big data flows
Renewable on the network
Portfolio to forecast varies
We have to forecast the consumption of EDF customers instead off
french consumption
Consumption’s process change and can becoming unstationnary
Conso (MW)80000
70000
80000
60000
50000
EDF
France
EDF
France
40000
30000
20000
10000
01/01/05
01/12/04
01/11/04
01/10/04
01/09/04
01/08/04
01/07/04
01/06/04
01/05/04
01/04/04
01/03/04
01/02/04
01/01/04
01/12/03
01/11/03
01/10/03
01/09/03
01/08/03
01/07/03
01/06/03
01/05/03
01/04/03
01/01
01/03/03
01/02/03
01/01/03
00
31/12
Linky
35 millions of smarmeter
EDF R&D : Créer de la valeur et préparer l’avenir - © EDF R&D 2011
Customer’s behavior and use
Multimedia network ( now) Domotic network ( growing)
Production
& Stockage
Client
Charges
Eau Chaude
Compteur
Box
Concentrateur
VE/VEHR
Telco
Distributeur
Fournisseur
(d’énergie, de services)
EDF R&D : Créer de la valeur et préparer l’avenir - © EDF R&D 2011
Internet
Heating pump
La chaleur est prélevée sur l’air extérieur et est restituée sous forme:
d’eau chaude circulant dans les locaux (PAC air/eau)
les émetteurs de chaleur, raccordés sur une boucle d’eau, peuvent être des planchers chauffants, un réseau de
radiateurs et/ou de ventilo-convecteurs.
Plancher chauffant
Radiateur
Ventilo-convecteurs
d’air chaud envoyé dans les locaux (PAC air/air)
les systèmes centralisés avec diffusion d’air chaud dans les faux plafonds par gaines ou par plenum. L’unité extérieure
est reliée à un réseau d’air pulsé. Dans ce cas, le logement est équipé de bouches de soufflage et de grilles de
reprise d’air.
A Key Issue:
How Much Future Energy Efficiency?
Forecast demand can vary substantially from even a single variable, such as
incremental energy efficiency, depending on the how it is incorporated.
SDG&E System Peak Load: Mid-Case Adjusted Forecast
5,500
Without Incremental
Energy Efficiency
5,000
4,500
With Incremental
Energy Efficiency
4,000
3,500
Source: 2009 IEPR Forecast
3,000
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
20
05
20
06
20
07
20
08
20
09
20
10
20
11
20
12
20
13
20
14
20
15
20
16
20
17
20
18
20
19
20
20
Megawatts
10%
Actual
WN Actual
Forecast without Uncommitted EE
Total Adjusted Forecast
Outline
• The Operational
Model and his limits
24 - -
The operational model: model design
Regression model using past values of
France electricity load
Date and calendar events
Outside temperatures in °C
Cloud Cover in octas
Non-linear regression using S.G. Nash’s truncated Newton method
Estimation based on several years with invalidated data:
Breaking periods (summer holidays, Christmas holidays,…)
Bank Holidays
Special events
Pi  Wip i  Wdpi  SpeTari   i
The operational model: the weather independent
part
For Hour h, of the Day d of the Year y :
h, y, day _ type( d ) the load shape depending on the day type of d,
the seasonality for h composed by Fourier series and
dummy variables to cope with Daylight Savings
Sh d 
32000
Weather Independent Part
53000

22000
17000
12000
0
4
8
12
16
20
24
28
32
36
40

Load (MW)
27000
48000
43000
38000
33000
44
1
DT1
DT2
DT3
DT4
DT5
DT6
DT7
DT8
DT9
DT10
31
DT11
Wip h ,d , y   h , y ,day _ type( d )  S h (d )
S h d   f h d   q h , p
 2m d 
 2m d 
f h d    a m ,h  cos

b

sin
 m,h


365
.
25
365
.
25




m 1
4
61
91
121
151
181
211
Day of the year
241
271
301
331
361
The operational model: the weather dependent
part
Using a temperature felt inside buildings as explanatory variable
Weighted average of instantaneous temperatures and exponentially smoothed
temperature
Influence of cloud cover (lightning, green house effect)
STwh,d , y  (1   h ).Th,d , y   h .ST
(1)
h,d , y
  h .(8  CCh,d , y )
STh(,1d), y  (1   h ).Th,d , y   h .STh(11),d , y
load/instant temperature
load/temperature felt ins. build.
Historical and current ways of forecasting
The operational model: results
Estimation Results
(real temperature)
Middle-Term
Forecast Results
[01/09/2000;31/08/2005]
[01/09/2005;31/07/2006]
RMSE
MAPE
AE
RMSE
MAPE
AE
740 MW
1.12%
-3.6 MW
817 MW
1.16%
27 MW
The operationnal model: comments
This is a sophisticated and efficient model. Take into account
many aspects such as specific periods (Noel, 1 of may,…)
Tricky to fit: a lot of parameters !
Parameters’ estimation by maximum likelihood
Forecast Interval in progress using asymptotic parameters’
uncertainty and boostrap approaches.
For studies: simplified models such as GAM,
Improvement: parsimony , adaptativity, optimization methods?
29
A range of methods
for electrical
consumption
forecasting.
30
Solutions for adapting forecasting methods at EDF
Needs and possible solutions…
Adaptativity
Move of customers
Functional models
GAM
GAM
Modèlesfonctionnels
KWF
Kalman
Kalmann
Mixture of
Mélange
predictors
Désagrégation
Desagregate
Bayésien
Bayesian
Focus on
Individual data
and aggregate
data
Parsimony
a priori
knowledge
Agregats
or
Global signal
uncertainties calculation
Forecast interval
1. State-space Models espace (adaptive Kalman)
Derived from current models (METEHORE, ARMA)
On line parameter identification (those of transfer function climatic data /
consumption
2. Mixture of predictors
Several predictors are used in parallel; Their optimal weighting in the
mixture used for producing the final forecast is calculate by different
algorithms.
3. GAM models ( Generalised Additif Models)
Non parametric approach: more flexibility, less a priori , «we let data speak
for itself »
Efficient algorithms: consumption estimated like a sum of function ( of lead
consumption, temperature fitted by splines).
Well adapted for changes in the load curve
An alternative to current parametrics models used currently
A good tool for studies
4. Functional Models
Load curve is divided into functions These functions are projected in a
wawelet basis. Similitudes between levels of decomposition are used
for forecasting the functions.
Interest
Each curve is an object instead of a time serie
Guaranteed temporal continuity Assurer la continuité temporelle and identify profils and their evolution
in particular for hourly forecasts
Search forms of consumption at different frequencies (Kernel methods and wavelets decomposition).
Alternative to operational models with aim of simplification
Bayesian approach
Methods allowed to combine two kinds of data:
… and adapting forecasts with a priori information:
Prior impact:
A prior distribution (given by the user) is combined with the data of a model to get a posterior
distribution. Probabilistic predictions are derived naturally within the Bayesian workframe
(credible intervals, HPD regions).
Poor historical data case:
In case of too short historical data, usual forecasting methods are ineffective.
The use of a bayesian prior can improve the estimation of a model.
Some forecasting are needed on EDF portfolio subgroups. Some have very poor historical
data. A prior can be built from a model previously estimated on a similar subgroup. One
question is to know if the subgroups are « similar » enough.
A Kernel Wawelet
Functional
approach
KWF
35
Some methods :models
KWF
Let (Zn) be a stationarity functional
valued process.
We predict next segment by
Where (wn,m) is a vector of
weigths that increases when
the segments m and n are
« similar ».
wavelets
MAPE
%
The stationarity assumption
is too strong for the power
demand series.
Some methods :models
How do we compute the dissimilarity?
Monday
WE
After expanding two functions l, m we
compute for each scale j
Wavelets
do discriminate
We then aggregate the scales
We construct the prediction
of wavelet scales using a
kernel function.
KWF
Why stationarity
fails?
2 keys:
 evolving mean level
 existance of groups
MAPE
KWF
8,31%
+ Mean level correction 2,94%
+ Groups
1,64%
Smooth approx.
of day m
Solutions:
Smooth approximation correction
Usage of groups of days
39 - -
Calendar information or unsupervised
learning of classes
Clusturing
Functional Data
Using wavelets
40
CWT and wavelet spectrum
Wavelet spectrum of a
electricity consumtion
during Christmas day
and a summer day.
Different mid frequencies
Wavelet coherence:local correlation of the time-scale representation
of 2 functions
Spectrum smoothed
on time and scale
Wavelet Extended
R2 coefficient
Dissimilarity on a
N time points
and J scales.
42 - -
Wavelet spectrum of mean daily load
Scales are in days
Synthetic data – customers losses (StreamBase)
Mixture of experts
46
Some methods :models
Combining forecasts: an on-line forecasting
problem
Combined
forecast
Individual predictors
Adaptive
Weights
The challenge: reduce the cumulative loss of the combined
forecast, ideally lower than the best expert, or close to the best
expert each time
Some methods :models
Basic ideas, basic algorithms
One parameter:
A kind of « temperature »
parameter
AFTER algorithm: the higher the cumulative loss of a
forecaster the lower the lower is its weight
Some methods :models
French data, combination of opérationnal predictors
Different values of the weights
depending on the « temperature »
parameter
Some methods :models
French data, combination of opérationnal predictors
Different values of the weights
depending on the « temperature »
parameter
Some methods :models
French data set, operational predictors Performances
350
300
250
200
150
100
50
0
-50
-100
1600
Gain : 140 MW
RMSE (MW)
1400
1200
1000
800
600
400
PETRA (938 MW)
CPO (991 MW)
PMIX_opé (924 MW)
PMIX_dyn (784 MW)
Gain de PMIX_dyn/PMIX_opé
EDF R&D – OSIRIS R39 –International Symposium of Forecasting 2010
Présentation des OTM 2009 - Mars 2010
51
Gain (MW)
RMSE mensuels 2008
Some methods :models
Our development/improvements
 Break detection and combining
New algorithms that are able to « follow » the best forecaster when it varies with time
Goude, Y. (2008), "Tracking The Best Predictor With a Detection Based Algorithm", in JSM
Proceedings, Denver, USA.
Goude, Y. (2009), "Adaptive Break Detection and Combining: Application to Electricity Load
Forecast", in JSM Proceedings, Washington, USA.
 Sleeping experts
We suppose that some experts can « sleep » during some period of time
This setting suits particularly well with industrial applications
New forecasters can appear with time
During particularly hard to predict period of time (holidays, banking holidays…) some
experts can’t produce any forecasts
 Online estimation of the mixing parameters
M. Devaine (ENS Paris), Y. Goude (EDF R&D), G. Stoltz (HEC, CNRS),
•
Forecast of the electricity consumption by aggregation of specialized experts; application
to Slovakian and French country-wide hourly predictions‘
Submitted to JRSS –C
Adapted Predictors
Forecast Interval

EDF R&D – OSIRIS R39 –International Symposium of Forecasting 2010
52
Using Bayesian
approach
53
Management of Uncertainty
Forecast Intevals




Residuals
Mixture of predictors
Bayesian
KWF
Need to be valid and adapted to the problem
RESIDUALS
A confidence interval for the prediction on the
KWF model
The vector of weights w induces a
probability distribution
●The KWF predictor is the mean of
this empirical distribution
●The CI can be obtained (at least
pointwisely) using the quantiles of this
distribution
●The quantiles are estimated using
bootstrap resampling.
●The sampling probabilities are given
by w.
●Corrections need to be made in order
to cope with the non stationarity of the
●
Numerical results
●
●
●
We test our approach on J+1
forescast during one year of the
daily load curve at EDF.
For each day, we compute the
mean coverage of the interval.
The empirical mean coverage
are 89 %, 85 % and 80 % for
the CI of announced level
95 %, 90 % and 80 %
respectively.
Antoniadis, Brossat, Cugliari & Poggi (2013)
preprint hal.archives-ouvertes.fr/hal-00814530
Future Work
62
Future Work:
Prospective methods
 Consumption’s Changes:
Abrupt changes (customers losses, unusual meteorological events):
Evolving in the uses: heating pump, Sterling motors, battery, micro generation
Demand respons services: pilot hot water heater,electric car recharge, contracted
interruption
Smartgrid
Local forecast
Renewable
Global optimization vs local optimization
 Methods Changes
Parsimonious models (simplicity allows adaptivity?) Regime switching
Vectorial models Dimension reduction (factor models…)
Clusturing, On line clusturing
Multiscale -Mixt Models High dimension
Reactive power forecast
Non stationnary,locally stationnary processes,
Simulation of the uses
Mixture of experts with adapted experts
Future Work:
 Probalistic forecasts
Do we need a new model for that (ex: quantile modelization)? Can we use
our actual models?
Parametric vs nonparametric, time series bootstrap…
Distinguishing and quantifying the different uncertainties from data to
forecast:
Adapted with needs of provider , of optimization
Uncertainties on the consumption linked with physical uncertainties