A Hybrid Method of CART and Artificial Neural Network for Short-term term Load Forecasting in Power Systems

Transcription

1 A Hybrid Method of CART and Artificial Neural Network for Short-term term Load Forecasting in Power Systems Hiroyuki Mori Dept. of Electrical & Electronics Engineering Meiji University Tama-ku, Kawasaki Japan

2 OUTLINE I. Objective II. Background III. Case Studies in CEPCO Proposed Method Simulation IV. Conclusion

3 I. OBJECTIVE To Construct an Intelligent Model for Short-term term Load Forecasting -Rules -Knowledge -Feature Extraction.. Input Data? Output Data Fig. Cause and Effect of Input and Output Data

4 2.1. Complexity of Power Systems Time-Variant Parametered Nonlinear Large-Scaled Quasi Periodical Power Systems Dynamical Random-Like Stochastic Discrete Fig. Characteristics of Power System Problems

5 Deregulation Maximizing Profit while Minimizing Risk Competition Power Networks Uncertainty Distributed Generation Fig. 3 Recent Complexity of Power Systems

6 2.3 Trends on Intelligent Systems in IEEE Power Engineering Society Expert Systems(1980~) Artificial Neural Net(1987~) Fuzzy Inference(1990~) Evolutionary Computation or Meta-Heuristics(1990~) Multi-Agent Systems(1995~) Data Mining(2000~)

7 2.4 Intelligent Systems Expert Systems Inference ANN Learning Fuzzy Classification Meta-heuristics Multi Agent Optimization Distributed Systems Data Mining Knowledge Discovery Fig. 4 Research Activities of Intelligent Systems in IEEE PES

8 2.5 Roles of Data Mining To Understand Complicated Data with Some Rules To Extract Important Features That are Known and/or Unknown To Construct More Reasonable Models/Strategies

9 2.6 What Is Data Mining Used for in Power Systems? Load Forecasting Dynamic Security Assessment Power System Control Center Data Profiling of Customers, etc.

10 Large Data Base Complexity System Operators Feature Extraction Uncertainty Fig. 5 Environment of Power System Operators

11 3.1. OBJECTIVE

12 3.2 Where is CEPCO? Japan Sea Chubu Electric Power Co. Osaka Nagoya Tokyo Pacific Ocean Fig. 7 Territory of CEPCO

13 3.3 Regional Features Large Factories(Toyota Gr.) High Humidity

14 3.4 Conventional Methods on SLF Kalman Filtering (Toyoda, 70) Regression Model (Asbury, 75) ARIMA Model (Hagan, 77) Expert System (Rahman, 88) ANN (El-Sharkawi, 91) Fuzzy Decision Model (Park, 91) Fuzzy Neural Net (Mori, 94) Simplified Fuzzy Inference (Mori, 96) Chaos Time Series Analysis (Mori, 96) DM-Based Approach (Mori, 2001)

15 3.5 Experience of on Regression Model - Fuzzy Inference Model

16 3.5 Requirements of Operators for SLF Models To Enhance the Model Accuracy To Minimize the Maximum Errors To Clarify the Relationship between Input and Output Variables To Validate Their Own Rules To Find out New Rules

17 3.6 Short-term Load Forecasting (SLF) To Play a Key Role in Power System Operation and Planning To Smooth ELD and UC To Make Profit through Deregulated and Competitive Power Markets x d Prediction Model ŷ d+1 Fig. 8 Prediction Model for SLF

18 3.8 Hint of Prediction Method Learning Data Fuzzy ANN ŷ Fig. 9 Example of Fuzzy Neural Net Learning Data Preprocessor Predictor ŷ Fig. 10 Prediction Model with Preprocessing Technique

19 3.9 Proposed Method 1 Preprocessor Cluster 1 ANN 1 Learning Data Classifier Cluster 2 ANN 2 ŷ Cluster M ANN M Fig. 11 Prediction Model of Proposed Method

20 3.10 Classification as Preprocessor -Regression Tree as a DM Tools (To Find out Important Rules) Open Issue - To Focus on Globally Optimal Classification Rather Than Locally Optimal Or Locally Quasi-optimal One

21 3. 10 Outline of DM Split Node Root Node Data Mining To Discover Important Rules in Large Data Base Data Mining Methods - Pattern Recognition - Fuzzy Theory - Decision Tree, etc. Fig. 12 Decision Tree

22 Procedures of Regression Tree Growth Minimization of Error after Splitting V ( n) R( n) = Pruning V 0 R(n): Error of Node n V(n): Variance of Learning Data Belonging to Node n V 0 : Variance of All Learning Data Simple Structure of Regression Tree Error Estimate Cross-validation Method (A1)

23 Δ R s, t = R t ( ) R( t ) R( ) L t R (1) No s Yes R (t L ) R (t) R (t R ) Fig. 13 Process of Constructing Tree

24 r(t p )=r CV (t p )+σ(t p ) (2) σ t p : 1 t p : 2 t p : 3 Fig. 14 Pruning Process

25 Table 1 Difference between Classification and Regression Trees Drawback of Regression Trees -Classification Accuracy (Locally Optimal Structure)

26 Table 2 Difference between Conventional and Proposed Decision Trees [A1] [A2] Wehenkel, et. al., Decision Tree Based Transient Stability Method a Case Study, IEEE Trans. on Power Systems, Vol. 9, No. 1, pp , Feb Rovnyak, et. al., Decision Tree for Real-time Transient Stability Prediction, IEEE Trans. on Power Systems, Vol. 9, No. 3, pp , Aug

27 3.11 Meta-Heuristics Definition Iterative Methods That Have Some Heuristics or Simple Rules in Search Process Feature To Aim at Evaluating Highly Accurate Solutions Typical Meta-Heuristic Methods SA, GA & TS

28 Table 3 Comparison of Meta-Heuristic Methods Methods Analogies Parameters Solution Accuracy CPU- Time Probability SA Annealing - Cooling Schedule - Temperature Less Slower GA Natural Selection - Population - Crossover - Mutation Less Slow TS Adaptive Memory - Tabu Length More Fast

29 3.12 Tabu Search(TS) Adaptive Memory (Tabu List) Only One Parameter (Tabu Length) No Use of Random Numbers Transition Type Algorithm

30 (a) Neighborhood Search Fixed Attribute Free Attribute Tabu List Fig. 15 (b) Tabu List Concept of Tabu Search

31 3.13 Proposed Method 2 To Construct the Regression Tree with the Globally Optimal Structure To Combine the Optimal Regression Tree with MLP Optimal Regression Tree To Assign Input Variables to Split Nodes To Globally Optimize Combinations of Input Variables with TS

32 V A V A V C V B (a) Phase 1 (b) Phase 2 V A,V B,V C : Input Variables Used as Split Conditions Fig. 16 Constructing Process by CART Locally Optimal Structure

33 V A V C V A V B V A V B (a) Phase 1 (b) Phase 2 Fig. 17 Constructing Process of Proposed Regression Tree

34 Constructing Tree Structure with TS TS Solution: Splitting Attribute Cost Function: b a c r(t p )=r CV (t p )+σ(t p ) d e b a a b c d e b a Fig. 18 Transfer of Splitting Attribute to TS Solution

35 START Set Initial Conditions Generate New Solutions (Combinations of Input Variables) Evaluate Cross-validation Errors of New Solutions Select Best Solution Calculate Split Value Pruning No Terminated? Yes STOP Fig. 19 Flowchart of Proposed Regression Tree

36 3. 13 SIMULATION Target: One-step- ahead Daily Maximum Load Forecasting Learning Data: Summer Weekdays in June to September 91~ 98 (Except 93 for Unusual Weather Conditions) Test Data: Summer Weekdays in June to September 99 Size of Initial Tree : 31 Splitting Nodes Tabu Length: 12 Conventional Methods: CART-MLP and MLP Methods Table 4 Parameters of MLP Learning Rate Momentum Term Iterations Proposed Method Hidden Unit CART-MLP MLP

37 Table 5 Eleven Input Variables No. Input Variables a Day of the Week for Day d+1 b Predicted Maximum Temperature on Day d+1 c Predicted Minimum Temperature on Day d+1 d Predicted Average Temperature on Day d+1 e Predicted Minimum Humidity on Day d+1 f Predicted Discomfort Index on Day d+1 g Maximum Load Day d h Difference between Maximum Load on Days d and d-1 I Difference between Average Temperature on Days d and d-1 j Average of Maximum Load on Days d, d-1 and d-2 k Average of Average Temperature on Days d, d-1 and d-2

38 Proposed Method CART-MLP MLP Average Error (%) Methods Maximum Error (%) Methods Fig. 20 Comparison of Errors for Proposed and Conventional Methods

39 Yes AV T d C No Yes AV T d C No Yes AV T d C No AV T d + 1 : Predicted Average Temperature on Day d+1 Fig. 21 Example of Split Conditions Close to Root Node

40 AV T d + 1 AV AV T d + 1 T d + 1 L M d ΔL M d AV T d + 1 L M d AV T d + 1 AV T d + 1 L M d m H d + 1 L M d AV T d + 1 M T d + 1 M T d + 1 AV T d + 1 m H d + 1 : Predicted Maximum Temperature : Predicted Average Temperature : Predicted Minimum Humidity : Maximum Load Fig. 22 Optimal Regression Tree L M d ΔL M d : Difference between Maximum Load

41 AV T d + 1 AV T d + 1 AV T d + 1 AV T d + 1 L M d AV T d + 1 L M d L M d AV/3 L d AV T d + 1 L M d : Predicted Average Temperature : Maximum Load AV/3 L d : Average of Maximum Load Fig. 22 Regression Tree of CART

42 Table 6 Rule Assigned to Terminal Node 4 d AV 1 T + M L d Note) L M d :Maximum Load on Day d

43 Table 7 Computational Time of Each Method Computer: FUJITSU S-7/7000U MODEL 45 SPECint_rate 95: 422 (296MHz) SPECfp_rate 95: 561 (296MHz)

44 No. of Terminal Nodes Proposed Method Variance Ratio Methods Methods CART-MLP Cross-validation Error Methods Fig. 24 Comparison of Regression Tree of the Proposed Method and CART-MLP

45 V. CONCLUSION 1. This Paper Has Proposed a Hybrid Method of the Optimal Regression Tree and MLP for Short-term Load Forecasting. 2. Tabu Search Is Used to Globally Optimize the Model Structure of the Regression Tree. 3. The Simulation Results Have Shown That the Proposed Method Is More Effective than CART-MLP and MLP in Terms of the Average and the Maximum Errors. 4. The Proposed Method Allows to Clarify the Relationship between Input and Output Variables through the Systematic Rules.

46 References H. Mori and N. Kosemura, "Optimal Regression Tree Based Rule Discovery for Short-term Load Forecasting," Proc. of 2001 IEEE PES Winter Meeting, Vol. 2, pp , Columbus, USA, Jan H. Mori, N. Kosemura, K. Ishiguro and T. Kondo, "Short-term Load Forecasting with Fuzzy Regression Tree in Power Systems," Proc. of 2001 IEEE International Conference on Systems, Man & Cybernetics, pp , Tucson, AZ, U.S.A., Oct H. Mori, N. Kosemura, T. Kondo and K. Numa,"Data Mining for Short-term Load Forecasting," Proc. of 2002 IEEE PES Winter Meeting, Vol. 1, pp , New York, NY, USA, Jan H. Mori and Y. Sakatani, "An Integrated Method of Fuzzy Data Mining and Fuzzy Inference for Short-term Load Forecasting," Proc. of ISAP (CD-ROM), Limnos, Greece, Aug H. Mori, Y. Sakatani, T. Fujino and K. Numa, "An Efficient Hybrid Method of Regression Tree and Fuzzy Inference for Short-term Load Forecasting in Electric Power Systems," A..Lofti and M. J. Garibaldi (Eds.), Applications and Science in Soft Computing, pp , Springer, Berlin, Germany, Nov