Context-Aware Parameter Estimation for Forecast Models in the Energy Domain

1. Context-Aware Parameter Estimation for Forecast Models in the Energy Domain Lars Dannecker1,2, Robert Schulze1, Matthias Böhm2, Wolfgang Lehner2, GregorHackenbroich1 1SAP Research Dresden,2Technische Universität Dresden

2. Agenda Forecasting in the Energy Domain Context-Aware Forecast Model Repository Experimental Evaluation Summary and Future Work

3. Forecasting in the Energy Domain

4. ForecastingProcess 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 ε ε Base Component Trend Component Season Component

5. European Energy Market Market Organizer • 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 TSO TSO BG2 BG3 BG1 Balancing Forecasting Aggregation Demand Supply

6. 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 Appendingnew values over time • Optimal parameters change and reoccur over time • Multiple local minima in parameter space • Continuous forecast model evaluation • Efficient forecast model adaptation

7. Context-Aware Forecast Model Repository

8. 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

9. Basic Idea • Case-Based Reasoning = Learning how to solve new problems from past experience • Energy domain: Seasonal reoccurring contexts  Reuse previousforecastmodels • 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 Continuous Insertions Continuous Forecasts Time series Current Forecast Model 1. Model Evaluation Forecast Error Calculation Updating trigger Revise Retain 2. Parameter Storing and Retrieval Retain Insert Problem-Solution Case Base Retrieve Model History Tree Retrieve Distance Compuation Starting Values for Estimation 3. Parameter Re-Estimation Revise Start Values Local Search Global Search Retrieve Updated Parameters

10. 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 <7 ≥ 7 temperature hour <11.3 <8 ≥ 8 ≥11.3 year mean year hour <500 <2005 ≥ 2005 ≥ 2004 <2004 <10 ≥ 10 ≥ 500 year ≥ 2008 <2008 1. Traverse to leaf node 2. Insert 3.  True/Split 4. Chose attributewithhighest 5. Split

11. Parameter Retrieval 4 3 2 A B D E F G H I J K M N 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 0.25 0.9 R 1. Traverse to corresponding leaf node I U Find O as nearest neighbor H K Find P as nearest neighbor G J T 0.65 Q 2. Bob-test with  False  Ascent F 0.4 M 3. Bob-test with cyclical  True  Descent B E O Find R as nearest neighbour P A N x D 4. Bob-test with  False 0.35 0.65 0.75

12. 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 Old subsequence 1 Old subsequence 2 Current subsequence

13. NOTE: (Delete this element) Sample of title slide image. See SAP Image Library for other available images. Experiments

14. 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 Athlon4850e (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

15. Results: TripleSeasonal 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

16. 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

17. Summary and Future Work

18. 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

19. Thank You! Contact information: Lars Dannecker SAP Research Dresden lars.dannecker@sap.com