4.4 Simulation and Results
4.4.3 Determination of Performance Indices
Table 4.9: Feature selected using IGWO for contingency analysis using P IV Q
System Initial Feature Set F Si
Final Selected Feature Set F Sf1
Dimensionality Reduction (%)
IEEE 30-Bus System
PG1:6, QG1:6, PD1:20, QD1:20
(Total: 52 features)
PG1, QG3, QG4, QG5, QG6, PD3, PD5, QD4
(Total: 8 features)
84.6
IEEE 39-Bus System
PG1:10, QG1:10 PD1:21, QD1:21 (Total: 62 features)
PG10, QG1, QG3, QG4, QG6, QG8, QG10, PD3,
PD8, QD19, QD23 (Total: 11 features)
82.25
k-Nearest Neighbor (KNN) [252], a common and simple method is used for classi- fication. KNN is a supervised learning algorithm that classifies an unknown sample based on the majority of the k-nearest neighbor category. Classifiers do not use any model for k-nearest neighbors and are determined solely based on the minimum dis- tance from the query instance to the training samples. The KNN method is simple and easy to implement hence it is used for a classification and to ensure the goodness of the selected features.
(A.4) RBFNN-2 forP IV Q determination using data set with IGWO based fea- ture selection.
(B) IEEE 39-bus 10-generator power system
(B.1) FFNN-1 forP IM V A determination using data set with IGWO based fea- ture selection.
(B.2) FFNN-2 forP IV Qdetermination using data set with IGWO based feature selection.
(B.3) RBFNN-1 for P IM V A determination using data set with IGWO based feature selection.
(B.4) RBFNN-2 forP IV Q determination using data set with IGWO based fea- ture selection.
For the above mentioned FFNN-1 and RBFNN-1 networks, the number of inputs is same as the number of the features in the selected feature set as per Table 4.8 and for FFNN-2 and RBFNN-2 networks, the number of inputs is same as the number of the features in the selected feature set as per Table 4.9 for IEEE 30-bus power system and IEEE 39-bus power system. The value of PIs are output of ANNs. Different type of FFNNs combinations have been investigated with different combination of the hidden layers and trained using Levenberg-Marquardt Algorithm (LMA). Several RBFNNs have been investigated with different values of Gaussian spread parameter.
The results of the investigation for FFNN and RBFNN are summarized in Tables 4.10, 4.12 and Tables 4.11, 4.13 respectively. After the determination of the PI value, the next step to find out the contingency class on the basis of their PI values.
The average error of test results obtained for IEEE 30-bus system from the FFNN and RBFNN for P IM V A and P IV Q respectively are shown in Tables 4.10 and 4.11.
From these tables, following observations can be made for the 30-bus test system.
• For P IM V A determination the average training error and average testing er- ror of FFNN are 1.8126% and 2.6184% respectively. Whereas the average training error and average testing error of RBFNN are 1.0277% and 1.3751%
respectively.
Table 4.10: Average error of test results proposed from FFNN classifier for P IM V AandP IV Qwith IGWO based feature selection (IEEE 30-Bus Test System)
Sr. No.
Architecture h1-h2-h3-o or h1-h2-o
Number of features selected
Total Number of Sample
Number of Sample Error (%) Train Set Test Set Train Set Test Set
A.1 (P IM V A)
30-15-10-1 9 4170 3500 670 1.2412 1.9451
30-15-10-1 9 4170 3000 1170 2.3142 3.0145
30-10-10-1 9 4170 3500 670 1.0241 2.0941
30-10-10-1 9 4170 3000 1170 2.6712 3.420
Average Error (%) 1.8126 2.6184
A.2 (P IV Q)
30-15-10-1 8 4170 3500 670 2.4147 2.6411
30-15-10-1 8 4170 3000 1170 2.1434 2.6524
30-10-10-1 8 4170 3500 670 1.2457 1.9876
30-10-10-1 8 4170 3000 1170 2.0142 2.6521
Average Error (%) 1.9545 2.4833
Table 4.11: Average error of test results proposed from RBFNN classifier for P IM V AandP IV Qwith IGWO based feature selection (IEEE 30-Bus Test System)
Sr. No.
Network (Spread Constant)
Number of features selected
Total Number of Sample
Number of Sample Error (%) Train Set Test Set Train Set Test Set
A.3 (P IM V A)
N1(8) 9 4170 3500 670 1.1103 1.8465
N2(9) 9 4170 3000 1170 1.0120 1.3451
N3(7) 9 4170 3500 670 1.0314 1.2147
N4(9) 9 4170 3000 1170 0.9571 1.0942
Average Error (%) 1.0277 1.3751
A.4 (P IV Q)
N5(10) 8 4170 3500 670 1.0245 1.1278
N6(8) 8 4170 3000 1170 1.3256 1.4547
N7(9) 8 4170 3500 670 1.9854 1.9949
N8(7) 8 4170 3000 1170 1.4512 1.9875
Average Error (%) 1.4466 1.6412
• For P IV Q determination the average training error and average testing error of FFNN are 1.9545% and 2.4833% respectively. Whereas the average training error and average testing error of RBFNN are 1.4466% and 1.6412% respec- tively.
The average error of test results obtained for IEEE 39-bus system from the FFNN and RBFNN for P IM V A and P IV Q respectively are shown in Tables 4.12 and 4.13.
From these tables, following observations can be made for the 39-bus test system.
Table 4.12: Average error of test results proposed from FFNN classifier for P IM V AandP IV Qwith IGWO based feature selection (IEEE 39-Bus Test System)
Sr. No.
Architecture h1-h2-h3-o or h1-h2-o
Number of features selected
Total Number of Sample
Number of Sample Error (%) Train Set Test Set Train Set Test Set
B.1 (P IM V A)
30-15-10-1 10 4545 3500 1045 1.1142 1.7412
30-15-10-1 10 4545 3000 1545 1.2273 2.5332
30-10-10-1 10 4545 3500 1045 1.1556 2.7423
30-10-10-1 10 4545 3000 1545 2.2547 2.3451
Average Error (%) 1.4379 2.3404
B.2 (P IV Q)
30-15-10-1 11 4545 3500 1045 1.4124 1.7852
30-15-10-1 11 4545 3000 1545 2.3712 2.5423
30-10-10-1 11 4545 3500 1045 1.4278 1.9854
30-10-10-1 11 4545 3000 1545 2.2123 2.4258
Average Error (%) 1.8560 2.1846
• For P IM V A determination the average training error and average testing er- ror of FFNN are 1.4379% and 2.3404% respectively. Whereas the average training error and average testing error of RBFNN are 1.1118% and 1.1604%
respectively.
• For P IV Q determination the average training error and average testing error of FFNN are 1.8560% and 2.1846% respectively. Whereas the average training error and average testing error of RBFNN are 1.1042% and 1.1873% respec- tively.
First, the values of PI are determined, after this classification of the contingency on the basis of their PI values. Neural Network classification task is performed by classifying the contingencies either as secure or insecure in accordance with Table 4.3, that finally gives the ranking for all the contingencies on the basis of their PI values. On the basis of PI values , three different severity levels have been considered that also provides the ranking of the contingencies; Class-I (Highly Critical Contin- gencies), Class-II(Critical Contingencies) and class-III (Non-Critical contingencies).
The output determines whether a pattern belongs to a particular Class: I to III indicating the ranking of contingencies and the system security status. For some line outage, load flow solution failed to converge at some loading condition. Such line outage are placed at the top of the ranking list. Thus contingency screening, ranking and security assessment are performed at the same time.
Table 4.13: Average error of test results proposed from RBFNN classifier for P IM V AandP IV Qwith IGWO based feature selection (IEEE 39-Bus Test System)
Sr. No.
Network (Spread Constant)
Number of features selected
Total Number of Sample
Number of Sample Error (%) Train Set Test Set Train Set Test Set
B.3 (P IM V A)
N1(8) 10 4545 3500 1045 0.9410 1.0345
N2(10) 10 4545 3000 1545 1.1321 1.0514
N3(14) 10 4545 3500 1045 1.0174 1.2143
N4(12) 10 4545 3000 1545 1.3567 1.3415
Average Error (%) 1.1118 1.1604
B.4 (P IV Q)
N5(12) 11 4545 3500 1045 1.0041 1.0249
N6(8) 11 4545 3000 1545 1.0347 1.0894
N7(8) 11 4545 3500 1045 1.1241 1.3210
N8(10) 11 4545 3000 1545 1.2541 1.3142
Average Error (%) 1.1042 1.1873
It is found from the results shown in Table 4.10 to Table 4.13 that RBFNN is better suited for the classification of contingencies as compared with FFNN for both 39-bus and 30-bus power system. So in next step for the classification only RBFNN has been proposed for the contingency analysis.
The RBFNN is selected for on-line contingency assessment and ranking. The normalized values of IGWO based selected features from pre contingent real and reactive power output of generators (PG & QG)and real and reactive demand at all the load buses (PD & QD) are considered as input features for training of the RBFNN. The PIs of the systemP IM V A andP IV Q are taken as the output features.
Single line outage contingencies are considered in this work for online ranking, as they are most frequent in occurrence.
The number of inputs to the network is equal to the number of training features the input feature setF Sf obtained using IGWO for determiningP IM V A andP IV Q. Once the training of the neural network is successfully accomplished, the estimation of PI for unknown load patterns is almost instantaneous.
Each input vector [yi] is of the following form:
[yi] = Selected Final Input Feature Set,F Sf1 or F Sf2 (4.11)
The output vector [yo] of the proposed model determine PIs, as [yo1] = [P IM V A] from RBFNN-1
[yo2] = [P IV Q] from RBFNN-2 )
(4.12)
Since the same contingency, some cases may be critical from P IV Q point of view and non-critical from index P IM V A is used to assess security and similarly for some other cases security margin is found to critical from P IM V A point of view and non0critical from index P IV Q. Therefore,separate ranking is obtained for both indices P IM V A and P IV Q employing two RBFNNs as shown in . For each case, the performance indices are obtained off-line by AC load flow calculation.