Context-Aware Parameter Estimation for Forecast Models in the Energy Domain Lars Dannecker 1,2, Robert Schulze 1, Matthias Böhm 2, Wolfgang Lehner 2, Gregor

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

© 2011 SAP AG. All rights reserved. 2

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


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


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


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


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


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


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



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



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



C1 3 5 2005 324 -12.3 0.684 0.34 16

C2 2 6 2006 648 -4.9 0.673 0.32 104



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


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


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)

Sample of title slide image.

See SAP Image Library for other

available images.


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


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


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


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

Thank You!

Contact information:

Lars DanneckerSAP Research [email protected]

Documents

Context-Aware Parameter Estimation for Forecast Models in the Energy Domain Lars Dannecker 1,2, Robert Schulze 1, Matthias Böhm 2, Wolfgang Lehner 2, Gregor