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Context-Aware Parameter Estimation for Forecast Models in the Energy Domain Lars Dannecker1,2, Robert Schulze1, Matthias Böhm2, Wolfgang Lehner2, Gregor Hackenbroich1 1SAP Research Dresden, 2Technische Universität Dresden
Agenda
1.
Forecasting in the Energy Domain
2.
Context-Aware Forecast Model Repository
3.
Experimental Evaluation
4.
Summary and Future Work
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2
Forecasting in the Energy Domain
Forecasting Process and Characteristics
Predicting the Future ! Quantitative model describing historic time series behavior ! Uses parameters to represent specific characteristic ! Estimated model mathematically calculates future behavior
Specific Characteristics… …for energy time series • • • • •
ε
Xt = "
yt + (1 # " )(X t #1 + bt #1 ) Base Component It #S
Multi-Seasonality Dependence on external influences bt = $(X t # X t #1 )+ (1 # $)bt #1 Evolving over time X Negligible linear trend It = % t + (1 # % )It #S Xt Continuous stream of measurements
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!
ε
Trend Component Season Component
4
European Energy Market Market Organizer TSO
Balancing Energy Demand and Supply
TSO BG2
BG1
Balancing Forecasting
Aggregation
BG3
Guarantee stable grids ! Energy Demand has to be satisfied ! Penalties for oversupply ! Day-Ahead & intraday market ! Integration of more RES in power mix " Accurate predictions at any point in time
Renewable Energy Sources (RES) Increasing support
Supply © 2011 SAP AG. All rights reserved.
Demand
! Depending on uncertain influences ! Not plannable like traditional power " Accurate prediction for next day RES supply necessary
5
Energy Data Management for Evolving Time Series $"
Energy Data Management Analytics close to the data
!#," !#+" !#*" !#)"
>/?/@:A:?"
! Quick reactions to changing time series ! Always up-to-date forecasts
!#(" !#'" !#&" !#%"
Appending new values over time
!#$"
">BC4B7E1F4G"
%! !, -9 :; -$ ,"
:= -! '" %! !+ -
BHD7CDI"
$% $$
Į', ȕ¶, Ȗ¶, VWDWH¶
Forecast Model (Į, ȕ, Ȗ, state)
Model Update
'& '% '$
3 Į, ȕ, Ȗ Time Series
Time Series 1
Subsection 3.3
012,3
Subsection 3.2 Model Evaluation 2 Techniques
Error Metric (SMAPE)
Model Adaptation Techniques ,-./.
New Measurements (consumption/ production)
$# $!
'#
! !"#
'!
!"$
#& #%
!"%
#$
!"&
## !"' !"# !"( !"+ !"& !"* !"% !") !"$
!
,-425
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6
Context-Aware Forecast Model Repository
Context of Energy Time Series
Influences for Supply and Demand ! Time series development influenced by background processes ! Changing context causes changes demand and supply behavior ! Calendar: Special Days, Season ! Meteorological: Wind speed, Temp. ! Economical: Population
Context Drift Different types of drifting context ܥଶ !
ܥଵ !
ܥଶ !
ܥଵ !
ܥଶ !
ܥଵ ! ܥଵ !
ܥଶ !
ݖ௧ !
ܥଶ !
ܥଵ !ܥଵ !
ܥଶ !
ܥଵ !
ܥଶ !
ܥଶ !
! ܥ ܥଵ !ଶ ܥଵ !
ݖ௧ ! ܥଵ !
!ݐ
© 2011 SAP AG. All rights reserved.
ݖ௧ ! ܥଶ !
ܥଶ !
ܥଵ ! !ݐ
ܥଶ !
ܥଵ !
ܥଶ !
ܥଵ ! ܥଵ !
ܥଶ !
ܥଵ ! ܥଵ ! !ݐ
ܥଶ ! ܥଵ !
8
ܥଶ !
ܥଶ
Basic Idea Case-Based Reasoning = LearningContinuous how toInsertions solve new problems from past experience Continuous Forecasts Energy domain: Seasonal reoccurring contexts ! Reuse previous forecast models Time series zt +1 = f ({ pi }) ! Retain: Save old parameter combinations with their respective context Current Forecast Model Model Evaluation ! Retrieve: Search1.repository for a context most similar to the current context ! Revise: Use parameter combinations of similar context as input for optimization Forecast Error Calculation
Revise
Updating trigger
2. Parameter Storing and Retrieval
Retain
Insert Retrieve
Problem-Solution Case Base
Retrieve
Retain
{p } { pi }i { pi } Model History Tree
Distance Compuation Starting Values for Estimation 3. Parameter Re-Estimation
Revise
Local Search
Start Values Global Search
Retrieve
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Updated Parameters
9
Parameter Insertion day
Tree Structured Repository ! Decision nodes: Splitting attribute, splitting value ! Leaf nodes: Set of parameter combinations, end index ! Splitting attributes chosen using Partial Interquartil Range (PIQR) ! Split via partitioning median
