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NỘI DUNG GỒM 9 CHƯƠNG:Chapter 1. Mathematical Background and State of the Art. Chapter 2. Static State Estimation. Chapter 3. Load Modeling for ShortTerm Forecasting. Chapter 4. Fuzzy Regression Systems and Fuzzy Linear Models. Chapter 5. Dynamic State Estimation. Chapter 6. Load Forecasting Results Using Static State Estimation. Chapter 7. Load Forecasting Results Using Fuzzy Systems. Chapter 8. Dynamic Electric Load Forecasting. Chapter 9. Electric Load Modeling for LongTerm Forecasting.
[...]... estimation Reviewing the literature to introduce different techniques developed for short-term load forecasting Explaining the merit of each technique used in the estimation of load forecasting and suitable places for implementation In this chapter, we also try to compare different techniques used in electric load forecasting 1.2 Matrices and Vectors A matrix is an array of elements [1] The elements of... 7 5 4 an1 an2 anm In shorthand,  à A ¼ aij nÂm i ¼ 1, , n j ¼ 1, , m Copyright © 2010 by Elsevier Inc All rights reserved DOI: 10.1016/B978-0-12-381543-9.00001-4 ð1:2Þ 2 Electrical Load Forecasting: Modeling and Model Construction Note that the determinant is also an array of elements with n rows and n columns (always square) and has a value The matrix does not have a value but has... of the two matrices is given by C ¼AþB ð1:11aÞ where the elements of the matrix C are given by cij ¼ aij þ bij for all i, j For example, if 2 A¼ 4 3 5 0 1 ! and B¼ À1 0 2 4 À2 3 ! ð1:11bÞ 4 Electrical Load Forecasting: Modeling and Model Construction then " ð 3 þ 2Þ ð0 þ 4Þ ð 4 þ 0Þ ð 5 À 2 Þ ! 1 5 4 C¼ 4 3 4 # ð1 þ 3Þ C¼ 1.3.2 ð 2 À 1Þ Matrix Subtraction (Difference) The subtraction (difference) of... commute, but if AB ¼ BA, we say that A and B commute If A and B are of the order n  n, then AB, BA will be of the order n  n For example, ! 1 3 2 A¼ 5 6 7 ð2Â3Þ 2 3 2 3 B ¼ 41 55 4 2 ð3Â2Þ 6 Electrical Load Forecasting: Modeling and Model Construction Then AB will be AB2Â2 1 ¼ 5 but BA will be 2 BA3Â3 2 ¼ 41 4 2 ! 2 3 2 4 1 6 7 4 3 3 13 55 ¼ 44 2 3 3 1 55 5 2 2 ! 17 2 ¼ 4 26 7 14 3 6 22 59 24 33 24 !... 0:125 0:91667 À0:54166 Some properties of the matrix inverse are AAÀ1 ¼ AÀ1 A ¼ I À À1 ÁÀ1 A ¼A ð1:22Þ ð1:23Þ If A and B are square matrices and are nonsingular, then ðABÞÀ1 ¼ BÀ1 AÀ1 ð1:24Þ 8 Electrical Load Forecasting: Modeling and Model Construction 1.4 Rank of a Matrix The rank of a matrix A is the maximum number of linearly independent columns of A, or it is the order of the largest nonsingular matrix... the rank of a matrix Given an nÂm matrix A, 1: Rank of A ¼ Rank of AT ð1:25Þ 2: Rank of A ¼ Rank of AAT ð1:26Þ 3: Rank of A ¼ Rank of AT A ð1:27Þ The rank of a matrix is of great importance in electric load forecasting using the static estimation algorithms 1.5 Singular Matrix If A is a square matrix, and if the determinant of A equals zero (i.e., jAj ¼ 0), then the matrix A is called a singular matrix... ViT Ui ¼ 1; j ¼ 1, , n ð1:32Þ ViT Uj ¼ 0; j ¼ 1, , n ð1:33Þ 1.7 Diagonalization Consider now the matrix product e ¼ U À1 AU A ð1:34Þ Using equation (1.30), we have e ¼ VAU A ð1:35Þ 10 Electrical Load Forecasting: Modeling and Model Construction In terms of eigenvectors, we have e ¼ V ½AU1 , AU2 , , AUn A ð1:36Þ Using equation (1.28), we obtain e ¼ V ½λU1 , λU2 , , λUn A Substituting... given by ! 1 U1 ¼ 1 Following the same steps, we obtain the second eigenvector as ! À1 U2 ¼ 1 and hence the matrix U is given by ! 1 À1 À1 T ¼ ½U1 U2 ¼ 1 1 Thus, ! 0:5 þ0:5 T¼ À0:5 0:5 11 12 Electrical Load Forecasting: Modeling and Model Construction Therefore, the transformed matrix A is given by ! ! 0:5 0:5 À2 1 1 e ¼ TAT À1 ¼ A À0:5 0:5 1 À2 1 ! À1 À1 ¼ 1 À2 0 À1 ! 1.8 Partitioned Matrices Partitioning... ¼ Im By solving the preceding equations, we can obtain W ¼ AÀ1 À AÀ1 BY À1 Y ¼ ÀðD À CAÀ1 BÞ CAÀ1 À1 Z ¼ ðD À CAÀ1 BÞ À1 X ¼ ÀAÀ1 BðD ÀCAÀ1 BÞ provided that the matrix A is nonsingular 14 Electrical Load Forecasting: Modeling and Model Construction Example 1.2 Consider the matrix F given by 2 2 61 F¼6 43 0 3 4 2 5 2 4 1 À2 3 À1 À2 7 7 05 3 F can be partitioned as shown Thus, we can find ! ! 2 À3 2... 1 vector, A is an n  n matrix, B is an n  1 vector, and C is 1  1 vector Example 1.3 Given the function fðx,yÞ ¼ 2x2 þ 4xy À y2 ¼ 0 we need to write this function in a quadratic form 16 Electrical Load Forecasting: Modeling and Model Construction We define the vector ! x X¼ y Then 2 2 y 2 À1 fðx, yÞ ¼ ½ x ! x y ! FðxÞ ¼ X T AX where 2 A¼ 2 2 À2 ! Example 1.4 To obtain the quadratic form for the . Electric Load Forecasting. ” The main objectives of this chapter are as follows: • A one-year long-term electric power load- forecasting problem is introduced as a first step for short-term load forecasting. • A. left and right type (LR-type). Chapter 3, Load Modeling for Short-Term Forecasting. ” This chapter pro- poses different load models used in short-term load forecasting for 24 hours. • Three models. functions, for load parameters, are used—namely, triangular membership and trapezoidal membership functions. The problem of load forecasting in this book is restricted to short-term load forecasting and