CHAPTER 4 MONITORING OF POWER SYSTEM VOLTAGE STABILITY THROUGH ARTIFICIAL NEURAL NETWORK TECHNIQUE

53 CHAPTER 4 MONITORING OF POWER SYSTEM VOLTAGE STABILITY THROUGH ARTIFICIAL NEURAL NETWORK TECHNIQUE 4.1 INTRODUCTION Due to economic reasons arising out of deregulation and open market of electricity, modern day power systems are being operated closer to their stability limits. Power system voltage stability is one of the challenging problems faced by the utilities. Online voltage stability monitoring is becoming an integral part of the modern day Energy Management Systems (EMS). There has been works reported in the literature on the use of analytical methods to monitor voltage stability of a power system on a real time basis. The methods are generally complex in nature and pose considerable computational burden on the EMS. An important issue with the use of analytical methods is the computational time, even with the state-of-the art processors. ANNs have gained widespread attention from researchers in recent years as a tool for online voltage stability assessment. Due to the non-linear nature of the voltage stability assessment problem, neural networks are better than conventional analytical methods for voltage stability monitoring. There are many works reported on online voltage stability monitoring in the literature, exploring the capability of the ANN to approximate the functional relationship between a voltage stability indicator and the measurable power

54 system parameters that affect the chosen voltage stability index. A major limitation of the use of ANN for online voltage stability monitoring arises due to the fact that the functional relationship itself gets changed from one topology to the other. A scheme for real-time assessment of voltage stability of a power system for single contingency using a single ANN is presented in this research work. A single Feed Forward Back Propagation Network (FFBPN) with minimal neurons is used to provide an estimate of the line stability index for various load conditions. Selected load variations are used as the input to the FFBPN and the available line stability factor is used as an indicator to the voltage stability of the system. The proposed scheme has the ability to get adaptive training when subjected to any new training pattern. The online voltage stability monitoring scheme is applied to the IEEE 14 bus and the IEEE 30 bus power system, and the test results are presented. 4.2 PROPOSED ANN STRUCTURE The development of tools for voltage stability assessment and control to help operators in control centers has attracted ever-increasing attention. Information such as voltage-weak buses/areas is becoming vitally important to voltage stabilization and control of modern power systems. As mentioned above, ANN has emerged as powerful tool in power system analysis. The scheme uses a feed forward network employing a back propagation learning algorithm. The network is made up of sets of nodes arranged in layers. The output of one layer is passed to the next layer through connection weights that control the gain of amplification. The input to a hidden layer or to the output layer is the sum of weighted outputs from the nodes of the previous layer.

55 The back propagation algorithm acquires its name from the fact that during learning, information is propagated back through the network to adjust the connection weights. Back propagation algorithm minimizes the mean squared error between the desired output and the output of the ANN using a gradient descent method of optimization. Training is achieved through the adjustment of weights to reduce the mean squared error while achieving a balance between the ability to recognize a pattern used for training and the ability to identify correctly an unknown pattern. Over training can result in good training error, but can result in poor error during testing. Back propagation neural network can sometimes converge to a local minimum during training. The chances of reaching a local minimum can be reduced by randomly presenting the input data using shuffle and deal techniques. Adaptive learning rates can shorten the training time. The most common learning rules in back propagation is the Delta rule. The rule is given in equation (4.1). ' W W 1*e*I 2*M (4.1) where, W - Old weights W - New weights e - Error M - Momentum I - Inputs 1, 2 - Learning coefficients

56 Back propagation neural networks require a large number of training epochs in order to converge below and acceptable error tolerance. However, this type of network is usually preferred for its reliability during testing. 4.2.1 Input Layer One of the key issues in such applications is that how to select limited variables, with salient features as the input information of the neural network, to represent the power system operating conditions in a large-scale power system. Theoretical studies and utility experiences all indicate that voltage collapse is mainly driven by heavy loading and / or by system contingencies. Comprehensive analysis of the behavior of power system variables under voltage instability indicate that the following two types of variables are important, and can be used as the input to the neural network: Voltage stability assessment requires identification of the collapse point based on load variation commonly employing a property such as singularly of the load flow Jacobian at the collapse point. Hence it can be considered as a mapping of the control variables to the state variables given in equation (4.2). P,V,,P,Q,q v,,q,and flows g g (4.2) d d c g The reactive generation reserve, flows on interface tie lines or major power carriers participating bus / branches contribute heavily to voltage collapse. Hence, we can consider this is a mapping of

57 max Qg Q g,criticalflows (Voltage stability margin) Fourteen features extracted from the base case power flow solutions for each contingency and from PV studies of the intact system are used as input to the neural networks. The data was normalized to take values between 0 and 1. 4.2.2 Hidden Layer The number of hidden layers and the number of nodes in each hidden layers are common concerns when dealing with ANNs. It can be argued that a three layered structure (1 input, 1 hidden, 1 output) can form arbitrary complex decision regions and can therefore separate populations of patterns which are intermeshed spatially in pattern space. In our study we use one hidden layer with 3, 5 and 7 hidden nodes. 4.2.3 Output Layer output node is used. In this study we assess the line voltage stability index. Hence one 4.3 SUITABILITY OF ANN FOR VOLTAGE STABILITY MONITORING Compared to the traditional methods, neural network modeling has the following advantages. ANN handles improperly specified form of independent and dependent variables. Also, it requires only a little prior knowledge of the physical background of the processes. It has the ability to make necessary data transformation. ANN has the ability to capture nonlinear pattern and the nonlinearity of relationship. The exact form of this relationship cannot be extracted from the ANN but rather is encapsulated in

58 the stored series of weights and connections between nodes. It has the ability to learn incrementally as new cases added into the model. ANNs do not require complicated programming, logical inference schemes, or the development of complex algorithms to build a successful model. The main advantage is that ANNs are able to model non-linear, dynamic and noisy data. The ability to generalize and its ability in fault tolerance give neural network a competitive edge in dealing with incomplete data and missing values. ANNs also have fault tolerance, meaning that when some of the neuron malfunctions, neural network can still produce approximately correct output. The advancement in computing also helps to make the neural network works faster on its parallel processing. With the adaptive system, neural network changes its structure based on the information that go through network during the learning phase. The standard multi-layer, feed-forward networks are capable of approximating any measurable function to any desired degree of accuracy. The disadvantages of artificial neural networks are: 1) the training neural network is computationally intensive; 2) no global method exists for determining when to stop training and thus overtraining is problematic; 3) sensitive to composition of the training data set; 4) sensitivity of training to initial network parameters; 5) black box models. The voltage stability index is evaluated under normal load conditions and step load varying conditions through ANN with high accuracy and in less time. The online monitoring of voltage stability is easily taken care off by the ANN, as the stability problem involved is non linear. For the IEEE 14 bus and IEEE 30 bus systems the training performance is converged at 11 epochs, 4 epochs, 7 epochs and 7 epochs

59 under load varying conditions and under single line contingency respectively. This is already shown in Figure 4.2, Figure 4.4, Figure 4.6 and Figure 4.8 respectively. As the number of epochs for convergence of error is less the training time is less and the question of over fitting does not arise. 4.4 RESULTS AND ANALYSIS The proposed ANN technique is tested with the standard IEEE 14 bus and IEEE 30 bus systems. The line stability index of all the lines for various load conditions and single line contingency with load variations are obtained through this ANN model. The first five severe lines are identified for the above two conditions. Also, the optimal location for the placement of TCSC is identified. 4.4.1 IEEE 14 Bus System - Analysis under Various Load Conditions Line stability index of each line for IEEE 14 bus system during load variation condition is analyzed through neural network model shown in Figure 4.1. A neural network is modeled for calculating the line stability index value of each line in system during load variations from 50% to 200%. Figure 4.2 shows the training performance of the proposed network. Figure 4.1 Neural network for calculating line stability index under load variations for IEEE 14 bus system Network Parameters: Network type - Feed-forward back propagation network

60 Training function Adaptive learning function Performance function - TRAINLM - LEARNGDM - MSE Number of layers - 2 Transfer function - PURELIN Number of datas generated - 1500 Number of datas used for training - 1350 Number of datas used for testing - 150 Figure 4.2 Training performance of ANN under load variations for IEEE 14 bus system From the results obtained through the ANN, the first five severe lines are identified. Compared with the other lines, the line 4-9 reaches the greatest line stability index during most of the various load condition. So, the line 4-9 is ranked as the most severe line in the system. Ranking of lines under load variation for IEEE 14 bus system is shown in Table 4.1.

61 Table 4.1 Ranking of first five severe lines under load variations for IEEE 14 bus system Rank of line Bus From To 1 4 9 2 5 6 3 1 2 4 7 8 5 12 13 4.4.2 IEEE 14 Bus System - Analysis with TCSC In this work, TCSC having the reactance value of X c = 0.05 pu is installed on the severe lines one by one which are ranked in Table 4.1. The line stability index of all the lines in the system is calculated and their results are shown in Table 4.2. Table 4.2 Line stability index for each line of IEEE 14 bus system with TCSC Bus Line stability index with TCSC in line From To 4-9 5-6 1-2 7-8 12-13 1 2 0.1194 0.1209 0.2170 0.0783 0.1195 1 5 0.0145 0.0145 0.0141 0.0149 0.0145 2 3 0.3192 0.3176 0.3211 0.0536 0.3190 2 4 0.0300 0.0299 0.0303 0.0300 0.0300 2 5 0.0118 0.0118 0.0120 0.0118 0.0118 3 4 0.0326 0.0325 0.0327 0.0292 0.0326 4 5 0.0029 0.0029 0.0029 0.0028 0.0029 4 7 0.0000 0.0000 0.0000 0.0000 0.0000 4 9 0.1331 0.1462 0.1463 0.1290 0.1463

62 Table 4.2 (Continued) Bus Line stability index with TCSC in line From To 4-9 5-6 1-2 7-8 12-13 5 6 0.1387 0.0925 0.1389 0.0805 0.1384 6 11 0.0155 0.0155 0.0155 0.0155 0.0155 6 12 0.0179 0.0179 0.0179 0.0179 0.0179 6 13 0.0337 0.0338 0.0337 0.0338 0.0337 7 8 0.1539 0.1566 0.1542 0.1122 0.1543 7 9 0.0263 0.0263 0.0263 0.0258 0.0263 9 10 0.0208 0.0208 0.0208 0.0204 0.0208 9 14 0.0623 0.0623 0.0623 0.0613 0.0623 10 11 0.0151 0.0151 0.0151 0.0149 0.0151 12 13 0.0929 0.093 0.0929 0.0929 0.0994 13 14 0.0797 0.0801 0.0797 0.0796 0.0797 When compared with TCSC in other lines, the stability index values for more number of lines are found to have the least value with TCSC in line 7-8. It shows that the stability levels of more number of lines are improved after placing TCSC in line 7-8. So, line 7-8 is the most optimal placement for inserting TCSC. 4.4.3 IEEE 14 Bus System - Analysis under Single Line Contingency with Various Load Conditions Line stability index of each line for IEEE 14 bus system under single line contingency with load variations is analyzed through neural network model shown in Figure 4.3. A neural network is modeled for calculating the line stability index value of each line in system under single line contingency with load variation from 50% to 200% in steps of 10%. Figure 4.4 shows the training performance of the proposed network.

63 Figure 4.3 Neural network for calculating line stability index under single line contingency with load variations for IEEE 14 bus system Network Parameters: Network type - Feed-forward back propagation network Training function - TRAINLM Adaptive learning function - LEARNGDM Performance function - MSE Number of layers - 2 Transfer function - PURELIN Number of datas generated - 320 Number of datas used for training - 288 Number of datas used for testing - 32 Figure 4.4 Training performance of ANN for IEEE 14 bus system under single line contingency with load variations

64 From the results obtained through the ANN, the first five severe single line contingencies are identified. Compared with the other lines, the line 7-8 reaches the highest line stability index values during most of the various load condition with single line contingency condition. So, the line 7-8 is ranked as the most severe line contingency in the system. Ranking of lines under single line contingency with load variation for IEEE 14 bus system is shown in Table 4.3. Table 4.3 Ranking of single line contingency with load variations for IEEE 14 bus system Ranking of single line Bus contingency From To 1 7 8 2 7 9 3 2 4 4 5 6 5 1 5 4.4.4 IEEE 30 Bus System - Analysis under Various Load Conditions Line stability index of each line for IEEE 30 bus system during load variation condition is analyzed through neural network model shown in Figure 4.5. The neural network is modeled for calculating the line stability index value of each line in the system during load variation from 50% to 200%. Figure 4.6 shows the training performance of the proposed ANN. Figure 4.5 Neural network for calculating line stability index under load variations for IEEE 30 bus system

65 Network parameters: Network type Training function Adaptive learning function - Feed-forward back propagation network - TRAINLM - LEARNGDM Performance function - MSE Number of layers - 2 Transfer function - PURELIN Number of datas generated - 1500 Number of datas used for training - 1350 Number of datas used for testing - 150 Figure 4.6 Training performance of ANN under load variations for IEEE 30 bus system From the results obtained through this neural network, the first five severe lines are identified. Compared with the other lines, the line 6-10

66 reaches the greatest line stability index during most of the various load condition. So, it is ranked as the most severe line in the system. Ranking of first five severe lines for IEEE 30 bus system with load variation is shown in Table 4.4. Table 4.4 Ranking of first five severe lines under load variations for IEEE 30 bus system Rank of line Bus From To 1 6 10 2 2 5 3 9 11 4 12 13 5 4 12 4.4.5 IEEE 30 Bus System - Analysis with TCSC In this work, TCSC having the reactance value of X c = 0.05 pu is installed on the severe lines one by one which are ranked in Table 4.4. The line stability index of all lines in the system is calculated and their results are shown in Table 4.5. Table 4.5 Line stability index for each line of IEEE 30 bus system with TCSC Bus Line stability index with TCSC in line From To 6-10 2-5 9-11 12-13 4-12 1 2 0.0800 0.0765 0.0811 0.0492 0.0821 1 3 0.0092 0.0091 0.0092 0.0089 0.0092 2 4 0.0120 0.0119 0.0120 0.0127 0.0120

67 Table 4.5 (Continued) Bus Line stability index with TCSC in line From To 6-10 2-5 9-11 12-13 4-12 3 4 0.0027 0.0027 0.0027 0.0027 0.0027 2 5 0.1291 0.0990 0.1309 0.0815 0.1313 2 6 0.0000 0.0000 0.0000 0.0000 0.0000 4 6 0.0000 0.0000 0.0000 0.0000 0.0000 5 7 0.0565 0.0569 0.0565 0.0591 0.0565 6 7 0.0391 0.0390 0.0392 0.0395 0.0392 6 8 0.0588 0.0577 0.0567 0.027 0.0563 6 9 0.0000 0.0000 0.0000 0.0000 0.0000 6 10 0.3691 0.3693 0.3361 0.3739 0.3691 9 11 0.1014 0.1142 0.1143 0.1287 0.1146 9 10 0.0672 0.0676 0.0676 0.0680 0.0676 4 12 0.0752 0.0752 0.0753 0.0763 0.0605 12 13 0.0440 0.0464 0.0468 0.0585 0.0375 12 14 0.0182 0.0183 0.0183 0.0184 0.0182 12 15 0.0149 0.0149 0.0149 0.015 0.0148 12 16 0.0158 0.0158 0.0158 0.0159 0.0158 14 15 0.0408 0.0409 0.0409 0.0411 0.0408 16 17 0.0484 0.0485 0.0485 0.0488 0.0485 15 18 0.0073 0.0073 0.0073 0.0073 0.0073 18 19 0.0205 0.0205 0.0205 0.0207 0.0205 19 20 0.0022 0.0022 0.0022 0.0023 0.0022 10 20 0.0065 0.0065 0.0065 0.0066 0.0065 10 17 0.0205 0.0206 0.0206 0.0207 0.0206 10 21 0.0374 0.0376 0.0376 0.0378 0.0376

68 Table 4.5 (Continued) Bus Line stability index with TCSC in line From To 6-10 2-5 9-11 12-13 4-12 10 22 0.0000 0.0000 0.0000 0.0000 0.0000 21 22 0.0000 0.0000 0.0000 0.0000 0.0000 15 23 0.0149 0.0150 0.0150 0.0151 0.0150 22 24 0.0023 0.0023 0.0023 0.0023 0.0023 23 24 0.0301 0.0301 0.0301 0.0303 0.0302 24 25 0.0000 0.0000 0.0000 0.0000 0.0000 25 26 0.0481 0.0482 0.0482 0.0486 0.0482 25 27 0.0000 0.0000 0.0000 0.0000 0.0000 28 27 0.0000 0.0000 0.0000 0.0000 0.0000 27 29 0.0182 0.0182 0.0182 0.0184 0.0182 27 30 0.0568 0.0568 0.0569 0.0574 0.0569 29 30 0.0432 0.0433 0.0433 0.0437 0.0434 When compared with TCSC in other lines, the stability index values for more number of lines are found to have the least value with TCSC in line 6-10. It shows that the stability levels of more number of lines are improved after placing TCSC in line 6-10. So, line 6-10 is the most optimal placement for inserting TCSC 4.4.6 IEEE 30 Bus System - Analysis under Single Line Contingency with Various Load Conditions Line stability index of each line for IEEE 30 bus system under single line contingency with load variations is analyzed through neural network model shown in Figure 4.7. The neural network is modeled for calculating the line stability index value of each line in the system for single

69 line contingency and with load variations from 50% to 200% in steps of 10%. Figure 4.8 shows the training performance of the proposed ANN. Figure 4.7 Neural network for calculating line stability index under single line contingency with load variations for IEEE 30 bus system Network Parameters: Network type - Feed-forward back propagation network Training function - TRAINLM Adaptive learning function - LEARNGDM Performance function - MSE Number of layers - 2 Transfer function - PURELIN Number of datas generated - 656 Number of datas used for training - 590 Number of datas used for testing - 66 Figure 4.8 Training performance of ANN for IEEE 30 bus system under single line contingency with load variations

70 From the results obtained through this neural network, the first five severe single line contingencies are identified. Compared with the other lines, the line 9-11 reaches the highest line stability index values during most of the various load with single line contingency. So, the line 9-11 is ranked as the most severe line contingency in the system. Ranking of lines under single line contingency with load variations for IEEE 30 bus system is shown in Table 4.6. Table 4.6 Ranking of single line contingency with load variations for IEEE 30 bus system Ranking of single line Bus contingency From To 1 9 11 2 12 13 3 25 26 4 1 2 5 1 3 4.5 SUMMARY A study on the voltage stability for load variation and single line contingency with load variations has been presented in this chapter. The use of FFBPN with minimal number of neurons for voltage stability assessment and enhancement has been presented in this work. This proposed ANN identi es the severe lines and the information about the rank of lines with respect to the line voltage stability index for both conditions. The effectiveness of this method has been demonstrated on the IEEE 14 bus and IEEE 30 bus systems. The computation time is very small for ANN and it

71 gives high accurate values of the line voltage stability index. The test results under both conditions show that the method could be applied to practical systems to provide power system operators with useful information about voltage stability and its improvement. This method does not involve complex and sophisticated matrix computation. This method is able to identify the most stressed line. Based on the ranking of lines under load variations, this work has identified the optimal location of TCSC among the severe lines. It has been identi ed that TCSC can be placed optimally in line 7-8 for the IEEE 14 bus system. The line 6-10 is the most optimal line for placement of TCSC in the IEEE 30 bus system. Also, it is found that the voltage stability is improved by placing the TCSC at optimal location.