context-aware parameter estimation for forecast models in the energy domain lars dannecker 1,2,...
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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
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Agenda
1. Forecasting in the Energy Domain
2. Context-Aware Forecast Model Repository
3. Experimental Evaluation
4. Summary and Future Work
Forecasting in the Energy Domain
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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• Multi-Seasonality
• Dependence on external influences
• Evolving over time
• Negligible linear trend
• Continuous stream of measurements
X t y t
It S
1 X t 1 bt 1
bt X t X t 1 1 bt 1
It X t
X t 1 It S
Base Component
Trend Component
Season Component
εε
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European Energy Market
Market Organizer
TSO TSO
BG2 BG3
SupplyDemand
Balancing
Forecasting Aggregation
BG1
Balancing Energy Demand and Supply
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 Depending on uncertain influences Not plannable like traditional power
Accurate prediction for next day RES supply necessary
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Energy Data Management for Evolving Time Series
Energy Data Management
Analytics close to the data Quick reactions to changing time series Always up-to-date forecasts
Appending new values over time Optimal parameters change and reoccur over time Multiple local minima in parameter space Continuous forecast model evaluation Efficient forecast model adaptation
Context-Aware Forecast Model Repository
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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
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Case-Based Reasoning = Learning how to solve new problems from past experienceEnergy domain: Seasonal reoccurring contexts Reuse previous forecast models Retain: Save old parameter combinations with their respective context Retrieve: Search repository for a context most similar to the current context Revise: Use parameter combinations of similar context as input for optimization
Basic Idea
Problem-SolutionCase Base
Start Values
Updating trigger
Continuous Insertions Continuous Forecasts
Updated Parameters
})({1 it pfz Time series
Current Forecast Model
3. Parameter Re-Estimation
Global SearchLocal Search
Forecast Error Calculation
Retrieve
Retain
Starting Values for Estimation
2. Parameter Storing and Retrieval
1. Model Evaluation
Model History Tree
}{ ip}{ ip}{ ip
Insert
Retrieve
Distance Compuation
Revise Retain
Revise
Retrieve
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Parameter Insertion
ContextSummary Parameters End Index
day hour year mean temperature p1 p2 K
C1 3 5 2005 324 -12.3 0.684 0.34 16
C2 2 6 2006 648 -4.9 0.673 0.32 104
C3 5 5 2008 112 12.5 0.623 0.38 573
C4 4 8 2009 272 7.3 0.629 0.41 692
day
temperature
≥ 7<7
<11.3
hour
<10 ≥ 10
≥11.3<8hour
≥ 8
year
<2004 ≥ 2004year
<2005 ≥ 2005mean
<500
≥ 500
ContextSummary Parameters End Index
day hour year mean temperature p1 p2 K
C1 3 5 2005 324 -12.3 0.684 0.34 16
C2 2 6 2006 648 -4.9 0.673 0.32 104
C3 5 5 2008 112 12.5 0.623 0.38 573
C4 4 8 2009 272 7.3 0.629 0.41 692
C5 4 1 2009 291 30.3 0.636 0.31 1024
ContextSummary Parameters End Index
day hour year mean temperature p1 p2 K
C1 3 5 2005 324 -12.3 0.684 0.34 16
C2 2 6 2006 648 -4.9 0.673 0.32 104
C3 5 5 2008 112 12.5 0.623 0.38 573
C4 4 8 2009 272 7.3 0.629 0.41 692
C5 4 1 2009 291 30.3 0.636 0.31 1024
PIQR 0.33 0.28 0.46 0.27 0.35
ContextSummary Parameters End Index
day hour year mean temperature p1 p2 K
C1 3 5 2005 324 -12.3 0.684 0.34 16
C2 2 6 2006 648 -4.9 0.673 0.32 104
ContextSummary Parameters End Index
day hour year mean temperature p1 p2 K
C1 5 5 2008 112 12.5 0.623 0.38 573
C2 4 8 2009 272 7.3 0.629 0.41 692
C3 4 1 2009 291 30.3 0.636 0.31 1024
year
<2008 ≥ 2008
1. Traverse to leaf node
2. Insert
4. Chose attribute with highest
5. Split
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
3. True/Split
€
c = 5 ≥ 4 = cmax ?
€
PIQR =
˜ a 3 − ˜ a 1
2
⎛
⎝ ⎜
⎞
⎠ ⎟
aN − a1
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Parameter Retrieval
xA
B
D
E
F
G
H
I
JK
OP
Q
R
T
U
N
M
O=(0.9,0.25) P=(0.85,0.2)
R=(0.75,0.95) Q=(0.85,0.55)
U=(0.95,0.85)T=(0.93,0.75)
1. Traverse to corresponding leaf node
Find R as nearest neighbour
Find O as nearest neighbor
Find P as nearest neighbor€
a2
€
a1 = 0.65
€
a2 = 0.65
€
a1 = 0.9
€
a2 = 0.4
€
a1 = 0.35
€
a1 = 0.25
A B D E F G H I J K M N
€
a1 = 0.7
0.25 0.9
0.4
0.65
0.35 0.65
€
a10.75
2. Bob-test with False Ascent
€
a1 = 0.7
3. Bob-test with cyclical True Descent
€
a2 = 0.4
4. Bob-test with False
€
a1 = 0.65
1
2
34
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Optimization
Subsequence Similarity Find parameters that are associated with most similar time series shape Using Pearson Cross Correlation Coefficient
Subsequent Parallel Optimization Parallel local and global parameter optimization Local: Nelder Mead; Global: Simulated Annealing Results from local optimization directly used Parallel global search to consider areas not covered Global search continues after local search finished Quick accuracy recovery + global coverage
Current subsequenceOld subsequence 2Old subsequence 1
€
RZ ′ Z τ( ) =zi − z ( )
i=1
N −τ
∑ ′ z i+τ − ′ z ( )
σ z2σ ′ z
2
Experiments
NOTE: (Delete this element)
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Settings
DataSets UK National Grid: Aggregated Demand United Kingdom MeRegio: MeRegio project data 86 single customer demand NREL Wind: Aggregated data from US wind parks CRES PPV: Single appliance photovoltaic supply
Forecast Models Triple Seasonal Exponential Smoothing (5 parameters) EGRV multi-equation autoregressive model (up to 31 parameters
Comparison Scenario Time vs. Accuracy against 4 common approaches
Error Metric Symetric Mean Absolute Percentage Error (SMAPE)
Plattform AMD Athlon 4850e (2.5 GHz), 4GB RAM, Windows 7 Visual C++ 2010
Subsequent Parallel Optimization Parallel local and global parameter optimization Results from local optimization directly used Parallel global search to consider areas not covered Global search continues after local search finished Quick accuracy recovery + global coverage
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Results: Triple Seasonal Exponential Smoothing
TS-Exponential Smoothing Small number of parameters, quick to estimate MHT quickly reaches good accuracy Our method is not superior on all data sets Large result divergence for other approaches MHT overhead: Eval (100 models) 4 msec, 20000 models 0.6 sec
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Results: EGRV Model (Energy Domain Specific)
EGRV Large number of parameters, hard to estimate MHT achieved best results on all data sets Difference between best and worst approach much larger MHT better suited for more complex models MHT overhead: Eval (100 models) 6 msec, 20000 models 1.1 sec
Summary and Future Work
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Summary & Future Work
Problem
• Evolving energy time series require efficient forecast model estimation
Summary
• Time series context influences time series development
• Case-based reasoning approach
• Store previous forecast model parameters for reuse with similar contextual situation
• Tree organized Context-Aware Forecast Model Repository
• Retrieve parameter by comparing current context to past context
• Parameters serve as input for optimization approaches
Future Work
• Evaluate accuracy for approach without subsequent optimization
• Order attributes in tree using information criterion
• Further parallelization