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A range of methods for electrical consumption forecasting Energy Systems Week April 22th: Xavier Brossat EDF/RD/Dpt OSIRIS

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, ..)

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Energy management

Supply-side uncertainties Investment decisions Fuel supplies System flexibilities Nuclear maintenance scheduling Long-term 20-50 years Medium-term 1-5 years Structuring of customer contracts Long-term demand Demand-side uncertainties G = D Stock management (H2O, Nuclear, large combustion plants, etc.) Daily generation plans Control and management of market risks THF, H2O maintenance Intra-day redeclarations Market arbitrages Short-term 1 hour – 1 day Load forecasts Load-shedding, nominations Strategy for the use of load-sheds and gas contracts

R&D skills and Energy Management

Management of market risks Financial mathematics, optimisation, risk management, Portfolio structuring Optimisation, quantitative economics, energy markets, econometrics Portfolio management Optimisation, electricity generation, gas logistics Portfolio optimisation Statistics, optimisation, econometrics, energy markets Energy markets and unknown factors Statistics, probabilities, load forecasts Load forecasting A common background: information technology

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Outline

1.

2.

3.

4.

Some Charateristics of electrical consumption in France Operational Model and his limits A range of methods for electrical consumption forecasting.

Future Work

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Some charateristics of electrical consumption in France

Electricity demand data

Various seasonal components.

High dependency on climate Other interspersed punctual events.

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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

The economic crisis has an impact on French consumption on the period 2007-2009

Economic crisis 0 10 20 2002 2003 2004 2005 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 60000 50000 40000 30000 20000 10000 0 0 01/01 31/12 EDF EDF France France

EDF R&D : Créer de la valeur et préparer l’avenir - © EDF R&D 2011 19

Linky 35 millions of smarmeter

Customer’s behavior and use

Multimedia network ( now) Domotic network ( growing)

Concentrateur

Compteur Box

Client

Eau Chaude

Charges Production & Stockage VE/VEHR Telco Distributeur Fournisseur (d’énergie, de services)

EDF R&D : Créer de la valeur et préparer l’avenir - © EDF R&D 2011 20

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.

5,500

SDG&E System Peak Load: Mid-Case Adjusted Forecast

Without Incremental Energy Efficiency 5,000 10% 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 Actual WN Actual Forecast without Uncommitted EE Total Adjusted Forecast

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Outline

•

The Operational Model and his limits

The operational model: model design

Outside temperatures in °C 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,…)

P

i



Wip

i



Wdp

i



SpeTar

i

 

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,

S h

the seasonality for h composed by Fourier series and dummy variables to cope with Daylight Savings 32000 27000 22000 17000 12000 0 DT1 4 DT2 8 DT3 12 DT4 16 DT5 20 DT6 24 28 DT7 32 DT8 36 DT9 40 DT10 44 DT11  

Weather Independent Part

53000 48000 43000 38000 33000 1 31 61 91 121 151 181 211

Day of the year

241 271 301 331 361

Wip S h d h

  ,

d

, 

y f h



f



h



d h

  ,

y

 ,

day q

_

h

,

type

(

d p

)

m

4   1

a m

,

h

 cos 

S h

(

d

) 2 

md

365 .

25 

b m

,

h

 sin 2 

md

365 .

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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)

STw h

,

d

,

y

 ( 1  

h

).

T h

,

d

,

y

 

h

.

ST h

, ( 1 )

d

,

y

 

h

.( 8 

CC h

,

d

,

y

)

ST h

, ( 1 )

d

,

y

 ( 1  

h

).

T h

,

d

,

y

 

h

.

ST h

(  1 ) 1 ,

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

740 MW

MAPE

1.12%

AE

-3.6 MW

RMSE

817 MW

MAPE

1.16%

AE

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?

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A range of methods for electrical consumption forecasting.

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Solutions for adapting forecasting methods at EDF

Needs and possible solutions…

Adaptativity Move of customers Parsimony Kalman Kalmann Mixture of predictors Functional models GAM GAM KWF

Agregats

or

Global signal

uncertainties calculation Focus on Individual data and aggregate data a priori knowledge 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

in particular for hourly forecasts and identify profils and their evolution 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

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Some methods :models

KWF

Let (Z n ) be a stationarity functional valued process.

We predict next segment by Where (w n,m ) is a vector of weigths that increases when the segments

m

« similar ».

and

n

are 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

compute for each scale

j

we 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 KWF

MAPE

8,31% + Mean level correction 2,94% + Groups 1,64% Smooth approx.

Solutions:

of day m 

Smooth approximation correction



Usage of groups of days Calendar information or unsupervised learning of classes

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Clusturing Functional Data Using wavelets

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CWT and wavelet spectrum

41 - Different mid frequencies Wavelet spectrum of a electricity consumtion during Christmas day and a summer day.

Wavelet coherence:local correlation of the time-scale representation of 2 functions

Spectrum smoothed on time and scale Wavelet Extended R 2 coefficient Dissimilarity on a N time points and J scales.

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Wavelet spectrum of mean daily load Scales are in days

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Synthetic data – customers losses (StreamBase)

Mixture of experts

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Some methods :models

Combining forecasts: an on-line forecasting problem

Individual predictors Adaptive Weights Combined forecast 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

Gain : 140 MW EDF R&D – OSIRIS R39 –International Symposium of Forecasting 2010 1600 1400 1200 1000 800 600 400

RMSE mensuels 2008

PETRA (938 MW) PMIX_opé (924 MW) Gain de PMIX_dyn/PMIX_opé CPO (991 MW) PMIX_dyn (784 MW) 51 350 300 250 200 150 100 50 0 -50 -100

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

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Management of Uncertainty Forecast Intevals

    Residuals Mixture of predictors Bayesian KWF Need to be valid and adapted to the problem 56 - -

RESIDUALS

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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 functional time series.

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

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Future Work

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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