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A Hybrid Method of CART and Artificial Neural Network for Short Term Load Forecasting in Power Systems
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A Hybrid Method of CART and Artificial Neural Network for Short-term Load Forecasting
in Power SystemsHiroyuki Mori
Dept. of Electronics EngineeringMeiji University
Tama-ku, Kawasaki 214-8571Japan
hmori@isc.meiji.ac.jp
I. Objective
II. Background
III. Case Studies in CEPCO◦ Proposed Method◦ Simulation
IV. Conclusion
Outline
To construct an Intelligent Model for Short-term Load Forecasting
Input data (Rules, Knowledge, Feature Extraction) Output Data
Cause and Effect of Input and Output Data
I. Objective
Nonlinear Large-
Scale
Dynamical
DiscreteStochast
ic
Random-Like
Quasi Periodical
Time-Varian Para metered
2.1 Complexity of Power Systems
Deregulation
Competition
Distributed Generation
Power
networks
(Maximizing Profit while Minimizing
Risk) Uncertainty
2.2 Recent Complexity
Expert Systems (1980~)
Artificial Neural Net (1987~)
Fuzzy Inference (1990~)
Evolutionary Computation or Meta-Heuristics (1990~)
Multi-Agent Systems (1995~)
Data Mining (2000~)
2.3 Trends on Intelligent Systems in IEEE Power Engineering Society
2.4 Intelligent Systems Expert Systems
ANN
Fuzzy
Meta-heuristics
Multi Agent
Data Mining
Inference
Learning
Classification
Optimization
Distributed Systems
Knowledge Discovery
To Understand Complicated Data with Some Rules
To Extract Important Features That are Known and/or Unknown
To Construct More Reasonable Models/Strategies
2.5 Roles of Data Mining
Load Forecasting
Dynamic Security Assessment
Power System Control Center
Data Profiling of Customers, etc.
2.6 What Is Data Mining Used for in Power Systems?
System Operators
III. Case Studies in CEPCO
To Propose a Hybrid Method of Regression Tree and ANN for Short-term Load Forecasting in Electric Power Systems
To Optimize the Structure of the Regression Tree with TS Globally
To Extract Some Simple Rules From Data Set, i.e., Explain the Relationship between Input and Output Data
3.1 Objective
Japan Sea
CEPCO: Chubu Electric Power Co.
Osaka, Nagoya, Tokyo
Pacific Beach
3.2 Where is CEPCO?
Large Factories (Toyota Gr.)
High Humidity
3.3 Regional Features
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)
3.4 Conventional Methods on SLF
Regression Model
ANN Model
Neuro-Fuzzy Model
Fuzzy Inference Model
3.5 Experience of CEPCO on SLF Model
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
3.5 Requirements of Operators for SLF Models
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
◦ (insert equation)
3.6 Short-term Load Forecasting (SLF)
Learning Data Fuzzy ANN y
Learning Data Preprocessor Predictor y
Prediction Model with Preprocessing Technique
3.8 Hint of Prediction Method
Learning Data
Classifier
Cluster 1
Cluster 2
Classifier
Cluster 3
3.9 Proposed Method 1
ANN1y ANN2y AnnMy
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
3.10 Classification as Preprocessor
Data Mining
◦ To Discover Important Rules in Large Data Base
Data Mining
◦ Pattern Recognition
◦ Fuzzy Theory
◦ Decision Tree, etc.
◦ (insert cahrt of Split and Root Node)
3.10 Outline of DM
Growth◦ Minimization of Error after Splitting◦ R(n)=V(n)/V0◦ R(n):Error of Node n◦ V(n): Variance of Learning Data Belonging to Node
n◦ V0: Variance of All Learning Data
Pruning◦ Simple Structure of Regression Tree
Error Estimate◦ Cross-Validation Method
Procedures of Regression Tree
△R(s,t)=R(t)-R(tL)-R(tR)
Where, R(s,t): Degree of Error Reduction in Case where Attribute s at node t, s: Attribute, t: Parent Node, R(t): Sum of Squared Error of Parent Node, R(tL(r)): Error of Left-Side (Right-Side) Child Node
(Insert Chart)
Constructing the Tree
(insert equation)
Where, r: Error, rcv(*): Cross-Validation error, Standard Deviation of Cross-Validation Error, Pruned Tree Number
Pruning
Decision Tree Output Conventional Methods
Classification Qualitative CART, ID3, C4.5
Regression Quantitative CART
Table 1 Difference between Classification and Regression Trees
Drawback of Regression Trees- Classification Accuracy
(Locally Optimal Structure)
Methods Decision Tree Applications Model Structure
Wehenkel, ‘94[A1]
Classification Transient Stability
Local
Rovnyak, ‘94[A2]
Classification Transient Stability
Local
Proposed Regression Load Forecasting
Global
Table 2 Difference between Conventional and Proposed Decision Trees
[A1] Wehenkel, et. Al., “Decision Tree Based Transient Stability Method a Case Study,” IEEE Trans. on Power Systems, Vol. 9, No. 1, pp. 459-469, Feb. 1994[A2] Rovnyak, et. Al., “Decision Tree for Real-time Transient Stability Prediction,” IEEE Trans. On Power Systems, Vol. 9, No. 3, pp. 1417-1426, Aug. 1994.
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
3.11 Meta-Heuristics
Methods Analogies
Parameters
Solution Accuracy
CPU-Time
Probability
SA Annealing -cooling schedule-temperature
Less Slower X
GA Natural Selection
-population-crossover-mutation
Less Slow X
TS Adaptive Memory
-tabu length
More Fast
Table 3 Comparison of Meta-Heuristic Methods
Adaptive Memory (Tabu List)
Only One Parameter (Tabu Length)
No Use of Random Numbers
Transition Type Algorithm
3.12 Tabu Search (TS)
(insert image)
(a) neighborhood search◦ Red (Fixed Attribute): Blue (Free Attribute) Tabu
List (b) Tabu List
Fig. 15 Concept of Tabu Search
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
3.13 Proposed Method 2
(insert image)
(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
(insert image)
(a) phase 1, (b) phase 2
Fig. 17 Constructing Process of Proposed Regression Tree
Locally Optimal Structure
TS Solution: Splitting Attribute
Cost Function: (insert equation)
(insert graph)
Fig. 18 Transfer of Splitting Attribute to TS Solution
Constructing Tree Structure with TS
Fig. 19 Flowchart of Proposed Regression Tree
Start Set Initial Conditions Generate New Solutions (Combinations of Input Variables) Evaluate Cross-Validation Errors of New Solutions (Calculate Split Value?) (Pruning) Select Best Solution Terminated? Stop
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 Table 4 Parameters of MLP
3.13 Simulation
Method Learning Rate
Momentum Term
Iterations
Hidden Unit
Proposed Method
0.01 0.6 10000 5
CART-MLP
0.02 0.1 10000 5
MLP 0.9 0.5 30000 5
No. Input Variables
A Day of the Week d+1
B Predicted Max Temperature
C Predicted Min Temperature
D Predicted Average Temperature
E Predicted Min Humidity
F Predicted Discomfort Index
G Max Load day d
H Dif between max load on days d and d-1
I Dif between avg temp
J Avg of max load
k Avg of avg temp
Table 5 Eleven Input Variables
(Insert graphs)
Fig. 20 Comparison of Errors for Proposed and Conventional Methods
(insert decision tree)
Fig. 21 Example of Split Conditions Close to Root Node
(Insert decision tree)
Fig. 22 Optimal Regression Tree
(Insert decision tree)
Fig. 22 Regression Tree of CART
N(t) Rule
4 T(AV,d+1)> 28.05 CL(md)> 0.845
Note L(md): Max Load on Day d
Table 6 Rule Assigned to Terminal Node 4
Methods Tree (sec) MLP (sec)
Proposed 17760 2.7
CART-MLP 7 4.3
MLP 27.6
Table 7 Computational Time of Each Method
Computer: FUJITSU S-7/7000U Model 45SPECint_rate 95:422 (296MHz)SPECfp_rate 95:561 (296MHz)
(insert graph)
Fig. 24 Comparison of Regression Tree of the Proposed Method and CART-MLP
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 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
V. Conclusion
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.421-426, Columbus, USA, Jan. 2001
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. 1948-1953, Tuscon, AZ, U.S.A, Oct. 2001
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.623-624, New York, NY, USA, Jan. 2002
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. 2003
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.287-294, Springer, Berlin, Germany, Nov. 2003
References
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