CHAPTER 6 BACK PROPAGATED ARTIFICIAL NEURAL NETWORK TRAINED ARHF

95 CHAPTER 6 BACK PROPAGATED ARTIFICIAL NEURAL NETWORK TRAINED ARHF 6.1 INTRODUCTION An artificial neural network (ANN) is an information processing model that is inspired by biological nervous systems such as brain process information. The most basic functions of the brain are replicated by this model. The key element of ANN is the novel structure of its information processing system. The network is composed of a large number of highly interconnected processing elements (neurons) working in parallel to solve a specific problem. Through a learning process ANN can be configured for a specific application, such as pattern recognition or data classification, etc. This learning process in biological systems involves adjustments to the synaptic connections that exist between the neurons. The same process is undergone in ANN for obtaining solutions to complex problems. The neural network research is aimed to perform various computational tasks at faster rate than traditional systems. Neural networks learn by example and they cannot be programmed to perform a specific task. Artificial neural networks perform various tasks such as Identification and control, Pattern-matching and classification,

96 Sequence recognition, Medical diagnosis, etc. 6.2 NEURAL NETWORK AND THEIR ARCHITECTURES ANNs composes large number of highly interconnected parallel configured processing units called nodes or neurons. A connection link is provided between each and every neuron. Each connection link is associated with weights which contain information about the input signal. This information is used by the neuron net to solve a particular problem. ANNs is characterized by their ability of memorization and generalization of training patterns or data similar to that of a human brain. Since ANN tries to replicate the working nature of brain, it has the capability to model networks of original neurons as found in the brain. Thus, the ANN processing elements are called neurons or artificial neurons. Each neuron has its own internal state and it is the function of inputs received by the neuron. This activity level of neuron is called the activation function. It can be transmitted to other neurons one at a time and thus all neuron receives the activation signal. In order to depict the basic operation of a neural net, I 1, I 2 are considered as a set of neurons. Here I 1 and I 2 are input neurons which transmit signals, and O is the output neuron which receives signals. Input neurons I 1 and I 2 are connected to the output neuron O, over a weighted interconnection links (w 1 and w 2 ) as shown in Figure 6.1. The net input for the simple neuron net architecture can be calculated in the following way,

97 y in = - a 1 w 1 + a 2 w 2 (6.1) where a 1 and a 2 are the activation functions of input neurons I 1 and I 2, i.e., the output of input signals. The output O can be obtained by applying activations over the net input, i.e., the functions of the net input, O = f (O in ) (6.2) Output = function (net input calculated) I 1 w 1 Inputs O Output I 2 w 2 Net Input (o in ) Figure.6.1 Architecture of a neuron function. The function to be applied over the net input is called activation Figure 6.2 shows a mathematical representation of the artificial neuron. In this model, the net input is elucidated as O in = a 1 w 1 + a 2 w 2 +...+ a n w n (6.3) n i1 a i w i where i represents the i th applied over it to calculate the output. processing element. The activation function is

98 Figure 6.2 Mathematical structure of artificial neuron namely, The architectures of ANN are specified by three basic entities The interconnections The training or learning rules adopted for updating and adjusting the connection weights Their activation functions. 6.2.1 Connections between neurons In ANN processing elements are arranged in layers such that each processing element output is found to be connected through weights to the other processing elements. The interconnections of the neurons are essential for an ANN. It should be noted that the function of each processing element in an ANN can be specified only after knowing the point of origination and termination of a neuron. The arrangement of neurons to form layers and the connection link formed between layers is called the network architecture. There exist five basic types of neuron connection architectures. They are, 1. Single layer feed-forward network, 2. Multilayer feed-forward network,

99 3. Single layer node with its own feedback, 4. Single layer recurrent network, 5. Multilayer recurrent network. The neural nets are basically classified into single-layer or multilayer neural networks. A layer is formed by combining two processing elements with other processing elements through weights. A layer links the input phase with the output phase. These linked interconnections lead to formation of various network architectures. When a layer of the processing units is formed, the inputs can be connected to these units with various weights to give series of outputs. The output is obtained one per each node. Thus, a single-layer feed-forward network is formed as depicted in Figure 6.3. A multilayer feed-forward network (Figure 6.4) is formed by the interconnection of several layers with processing units. The input layer receives the input and transmits to the output layer. The output layer generates the desired output of the network. There is another layer that is formed between the input and output layer is called as hidden layer. This hidden layer has no direct contact with the external background and is internal to the network. An ANN has zero to several hidden layers based on the application. The usage of more number of hidden layers in ANN provides an efficient output response but it lead to complexity of the network. This type of network with more number of layers is called multilayer network. In some cases of applications the network layers are designed such that every output from one layer is connected to each and every node in the next layer.

100 Input layer Output layer I 1 W 11 O 1 W 21 Input Neurons s W 1n W 12 W 22 I 2 O 2 W 2n W 1m Output Neuron s I n W 2m W nm O m Figures 6.3 Single Layer Feed-Forward Network Input layer Hidden layers I 1 Weights H 1 Output layer G 1 O 1 Input Neurons I 2 G 2 H 2 O 2 Output Neurons I n H q G k O m Figures 6.4 Multilayer Feed-Forward Network

101 When the output from output layer is directed back as inputs to same or preceding nodes, then the network is said to be feed-forward network. In these feed-forward networks no neuron in the output layer is an input to a node in the same layer or in the preceding layer. For giving solutions to complex problems, the multilayer feed-forward networks are widely used. Because these network uses many hidden layers and proper training may lead to the specified solution. 6.2.2 Learning methods for training neural network The learning or training is a process by means of that a neural network can be trained to adopt itself to give desired response. This learning makes proper parameter adjustments and thus resulting in target output. The following are the two kinds of broad classifications of learning in ANN. 1. Parameter learning: The weights in the neural network are updated by using this learning. 2. Structure learning: In this learning the total network architecture including the number of processing elements and their connection types are changed. The above two types of learning can be performed simultaneously or separately. Apart from these categories of learning, the general classification of learning in ANN are given as 1. Supervised learning 2. Unsupervised learning 3. Reinforcement learning

102 Though many learning are available, in some cases of problems, the solution by using the supervised learning gives the target output, than the other learning. Since the learning by unsupervised and reinforcement does not provide the proper training for the network to process the input vectors. 6.2.2.1 Supervised learning In the supervised learning, each input vector requires a corresponding target vector, which represents the desired output. The input vector along with target vector is called as training pair. The block diagram of Figure 6.5 depicts the working of a supervised learning network. Desired Output Input NEURAL NETWORK Actual Output Compare Adjustment of weights Error Figure 6.5 Block diagram of Supervised Learning The network is trained precisely about the type of output to be emitted. The input vector for specified application is presented to the network which results in a required output. This obtained output vector is called as actual output vector and is compared with the desired (target) output vector. If there exists a difference between the two vectors an error signal is generated by the network. This error signal is used for adjusting the weights until the actual output matches the target output. In this training, a supervising is done by setting the target output and thus resulting in error minimization. Hence,

103 this type of network training is called as the supervised training methodology. In supervised learning, it is assumed that the correct target output values are known for each input pattern. 6.2.3 Purpose of Activation Functions The output of a network can be derived exactly by the help of an activation function. This function is associated with the input of the processing neuron. The activation function assigns the required operation to the processing neuron in order to get the specified output. This integration function (f) serves to combine activation information from other processing neurons. The response of neurons can be dampened by using the nonlinear activation function and thus it shows that activation stimuli are controllable. The usage of this nonlinear function in multilayer network is more advantageous than single layer network since the output obtained with linear function in multilayer network is same as that of single layer network. Hence due to this reason nonlinear activation functions are widely used in multilayer networks. Sigmoidal functions: This function is widely used in back propagation network because of the relationship between the value of the functions at a point and the value of the derivative at that point. It reduces the computational issues during training. The sigmoidal functions are depicted in Figure 6.6. The sigmoidal function are of two types and are given as Binary sigmoid function: It is also called as logistic sigmoid function or unipolar sigmoid function. The range of this sigmoid function is from 0 to 1.

104 It can be defined as 1 f (I) I 1 e (6.4) function is -f(i)] (6.5) Bipolar sigmoid function: This function is defined as I 2 1 e f (I) 1 (6.6) I I 1 e 1 e The sigmoid function range is between -1 and +1. The derivative of this function can be f (I) [1 f (I)][1 f (I)] (6.7) 2 f(i) f(i) 1 1.5 1 0 I 0 I (a) (b) Figure 6.6 (a) Binary sigmoidal function (b) Bipolar sigmoidal function

105 The hyperbolic tangent function and bipolar sigmoid function are closely related to each other and their relation can be depicted as I I e e f (I) (6.8) I I e e 2I 1 e f (I) (6.9) 2I 1 e The derivative of the hyperbolic tangent function is h (I) = [1+h(I)][1-h(I)] (6.10) If a binary data is used in the network, the bipolar sigmoid activation function shall be used after converting that data into bipolar form. 6.2.4 Terms used for ANN Weights: The direct communication link between the neurons in the architecture of ANN is associated with weights. The information about the input signal is contained in the weights and it is used by the network to give solutions for solving the problems. Since there are many such links in a network, the weights are represented as a weight matrix (W). The mathematical formation of this conn T w 1 w11 w1m W (6.11) T w n w n1 w nm where w i = [w i1, w i2,... w im ] T, i=1,2,...n, is the weight vector of processing element and w ij is the w

106 the information of all elements in an ANN and set of W matrices determine set of all possible element configurations for that ANN. Bias: The bias plays a major role in determining the output of the network. The bias included in the network has its impact in calculating the net input. The bias is included by adding a component I 0 = 1 to input vector I. Thus, the input vector becomes I = (1, I 1,... I i,... I n ) (6.12) The bias is considered like another weight, that is w 0j = b j. For a simple network shown in Figure 6.7, the net input to output neuron O j is calculated as follows, I 1 w 1j I 2 w 2j I j w ij O j w nj b j I n -1 Figure 6.7 Inclusion of Bias term for Neuron net

107 o inj I w n i0 a i w ij 0w0j a1w1j a2w2j... anwnj n 0 j aiwij i1 n o b a w (6.13) inj j i1 i ij The bias can be of two types 1. Positive bias 2. Negative bias The positive bias helps in increasing the net input of the network and negative bias helps in decreasing the net input of the network. Thus by using bias the output of the network can be changed. Threshold: It is a value limit set in order to predict the final output of the network. This threshold value is used in the activation function. The calculated net input and this set value is compared to obtain the network output. Each and every application has a threshold limit and based on this value the activation function is defined for that network. According to that function the required output is also calculated. The activation function using threshold can be defined as 1, if net f (net) (6.14) 1, if net w

108 Learning Rate: weight adjustment at each step of training process. The range of learning rate is from 0 to 1and it determines the rate of learning at each time step. Momentum factor: It is added in the weight updating process inorder to have faster convergence. This factor helps in large weight adjustments and hence used in the back propagation network. It should be noted that for using this momentum factor, the weights of the previous training patterns must be saved. Vigilance parameter: The vigilance parameter ( control the degree of similarity required for patterns to be assigned to the 6.3 BACK PROPAGATION ARTIFICIAL NEURAL NETWORK The networks associated with back propagation learning algorithm are called Back Propagation Artificial Neural Networks (BPANNs). It is a popular learning method developed by neural networks. The network with this algorithm gives the alternate way for handling large learning problems and has reawakened the scientific community to the modelling and processing of numerous quantitative phenomena. This algorithm is applied to multilayer feed forward networks with continuous differentiable activation functions. For a given set of training pattern, the algorithm provides a procedure for changing the weights in a BPANN to classify the given input patterns correctly. The basic concept for this weight update algorithm is based on the gradient descent method. In this method, the error is propagated back to the hidden unit through the feed forward layer. The main objective of the network is to train the network in order to achieve a balance between the nets

109 ability to respond (memorization) and its ability to give reasonable responses to similar input that is used in training (generalization). The process by which the weights are calculated during the learning period of the network with the back propagation algorithm is different from other networks. It is very difficult to calculate the weights of the hidden layers in multilayer perceptrons with zero output error and when the hidden layers are increased the network training becomes more complex. For updating weights, the error must be calculated. The calculated error is the difference between the actual and the desired (target) output and it can be easily measured at the output layer. But it should be noted that at the hidden layers, there is no direct information of the error. So other techniques should be used to calculate an error at the hidden layer with minimized output error. stages, The training of the Back propagated neural network is done in three 1. The feed-forward of the input training data 2. Back propagation of the error and 3. Updating weights according to error obtained The testing of the BPN involves the computation of feed-forward phase only. There can be more than one hidden layer (more beneficial) but one hidden layer is sufficient. Even though the training is very slow, once the network is trained it can produce its outputs very rapidly. 6.3.1 Architecture of BPANN A back propagation neural network is a multilayer, feed forward neural network consisting of an input layer, a hidden layer and an output layer. The neurons present in the hidden and output layers have biases whose

110 activation is always 1 and those biases also act as weights. Figure 6.8 shows the architecture of BPANN with the information of feed forward and back propagation phase. In the back propagation phase of learning, signals are sent in the reverse direction to the processing elements. The outputs obtained from the network is either binary (0, 1) or bipolar (-1, +1) and so the activation function could be the sigmoid activation function. Input values Input Layer Weight matrix1 Hidden layer Weight matrix 2 Output Layer Output values Figure 6.8 Basic architecture of a back propagated network The notations used in the BPN are, a i - Activation of unit I i, input signal. o i - Activation of unit O j, o j = f(o inj ) w ij - Weight on connection from unit I i to unit O j b j - Bias acting on unit j. Bias has a constant activation of 1.

111 W - Weight matrix, W={ w ij } o inj - Net input to unit O j j - Threshold for the activation of neuron O j. S - Training input vector, S = (s 1,..., s i,..., s n ) T - Training output vector, T = (t 1,..., t i,...,t n ) I - Input vector, I = (I 1,..., I i,...,i n ) w ij - Change in weights, w w (new) w (old) (6.15) ij ij ij - Learning rate for controlling the weight adjustment at each step of training. 6.4 FLOWCHART FOR TRAINING BPANN The flow of the training process is depicted by using the flowchart shown in Figure 6.9. The terms used in the flowchart and in the training algorithm are as follows, I = input training vector ( I 1,... I i,... I n ) d = target output vector (d 1,... d i,... d n ) = Learning rate parameter I i = input unit i. (since the input layer uses identity activation function, the input and output signals here are same) b oj = bias on jth hidden unit b ok = bias on kth output unit c ij = Weight on connection from unit i th to j th Hidden node H j = hidden unit j. The net input to H j is

112 H b I c (6.16) inj 0j i i ij and the output is H j = f(h inj ) (6.17) O k = output unit k. The net input to O k is O ink b0k H jwik (6.18) j and the output is O k = f(o ink ) (6.19) k = error correction weight adjustment for w jk that is due to an error at output unit O k, which is back propagated to hidden units that feed into unit O k j = error correction weight adjustment for c ij that is due to the back propagation of error to hidden unit H j. The binary sigmoidal and bipolar sigmoidal activation functions are the commonly used activation functions because of the following characteristics, Continuity Differentiability Nondecreasing monotony

113 6.4.1 Training algorithm adopted for BPANN The back propagation learning algorithm can be outlined in the following three phases of algorithm. They are as follows, Feed forward Phase Back propagation of error Weight and bias updation Step 0: Step 1: Step 2: Initialize weights and learning rate to some random values. Perform Steps 2-9 when stopping condition is false. Perform Steps 3-8 for each training pair. 6.4.1.1 Feed forward Phase of network Step 3: Step 4: Each input unit receives input signal x i and it is send to the hidden unit (i = 1 to n). The net input of each Hidden unit H j (j =1to p) is calculated H b I c (6.20) inj 0j i i ij Calculate output of the hidden unit by applying its activation functions over H inj H j = f(h inj ) (6.21) and send the obtained output signal from hidden unit to the input of output layer units. Step 5: For each output unit O k (k = 1 to m), calculate the net input p O b H w (6.22) ink 0k j1 j ik

114 and apply the activation function to compute output signal O k = f(o ink ) (6.23) 6.4.1.2 Calculation of Back propagation error in the network Step 6: Target pattern for each output unit O k (k =1 to m) is received corresponding the error correction factor is computed, k = (d k O k ) f (O ink ) (6.24) According to error correction factor the change in weights and bias are updated and is given as jk = k H j (6.25) 0k = k (6.26) k to the hidden layer backwards. Step 7: Each hidden unit (H j, j = 1 to p) sums its delta inputs from the output units, m inj kw jk (6.27) k1 inj inj ) to calculate the error term j = inj f (H inj ) (6.28) bias, j, update the change in weights and ij = j I i (6.29) oj = j (6.30)

115 6.4.1.3 Weight and bias updation in network Step 8: Update the bias and weights for each output unit O k (k =1 to m) w jk(new) = w jk(old) jk (6.31) b 0k(new) = b 0k(old) 0k (6.32) Update the bias and weights for each hidden unit (H j, j = 1 to p) c ij(new) = c ij(old) ij (6.33) b oj(new) = b oj(old) oj (6.34) Step 9: Check for the stopping condition. When the actual output equals the target output or if required epochs reached, the stopping condition is checked. The weights in this algorithm are changed immediately after a training pattern is presented. This is an incremental approach for updation of weights but it is different from another training called batch mode training where the weights are changed only after all the training patterns are presented. Another drawback of this batch mode training is it needs additional storage for the immediate weight updation. Since the back propagation learning algorithm implements gradient descent method it converges with nearest minimum error. This is possible only when the relation existing between the input and the output training patterns is deterministic. Thus error surface is also deterministic. If the error surface is random in nature, the algorithm based on gradient descent method helps to get out of local minima. It also updates the weights of the network within the required learning rate and minimizes the problems due to lack of proper convergence.

116 Initialization phase Start Initialize the weights C For each training pair I, t NO B YES Input signal I i received Transmitted to Hidden layer units Calculate the hidden Layer output (H j ) Send H j to the output layer Target pair d k enters Calculate the output layer output (O k ) A Output calculation phase Figure 6.9 Adaptive Learning Algorithm of BPN

117 Error derivation phase A Compute error correction factor between output & hidden (f k ) Derive the weight and bias correction term Weight and bias updation phase j j change the weight and bias Updated weight and bias on Output unit w jk(new), b ok (New) Updated weight and bias on Hidden unit c ij(new), b oj (New) C NO If target epochs reached or d k = O k YES B Stop Figure 6.9 (Continued)

118 6.4.2 Factors needed for convergence of BPANN The training and convergence of the BPANN are based on various learning factors such as weights initialization, the type of learning rate, the weight updation rule, the size and nature of the training patterns, and the architecture of network. Initial weights: The initialization of weights is an important factor for determining the convergence of network. The weights are initialized at small random values inorder to have faster convergence. Since the sigmoidal activation functions are widely used in this network, the weight cannot be initialized to high values. Because the activation functions get saturated from initial stage itself and may have the problems due to local minima. The range of weight (w ij ) used for initialization is given in the following equation. 3, p 3 i p i (6.35) where p i is the number of processing elements j that feed forward to processing element i. The weights connecting input neurons to the hidden neurons are obtained by the equation. cij(old) cij(new) (6.36) c (old) j where c j is the average weight calculated for all values of i, and the scale 1/n (n is the number of the input neurons and P is the number of hidden neurons). convergence of BPANN. A larger learning rate may result in overshooting

119 and oscillation, while a lower learning rate leads to slower learning of the -3 to 10. Momentum: The momentum factor is added with the normal gradient descent method inorder to have larger learning rate without convergence. This factor can be used with either pattern by pattern updating or batch-mode updating. The weight updation formula with momentum factor is given by the following equations. w (t 1) w jk (t) kh j wij(t) w jk (t 1 (6.37) jk ) w jk(t 1) c (t 1) c jk(t) jii cij(t) c jk(t 1 (6.38) jk ) c jk(t 1) Generalization: When trainable parameters are more for the given amount of training data, the network shows overtraining. On the other hand for small number of trainable parameters, the network fails to learn the training data and performs poorly. For improving the generalization of network, the input space of the pattern is changed. This can be done by introducing the variations in the input space without altering the output components. The back propagation network is the best network for generalization. Number of training data and hidden layer nodes: The entire input space should be covered by training data. For multilayer feed forward networks there exists many numbers of hidden layers. The number of hidden units depends up on the application to be used and it should be determined.

120 6.5 IMPLEMENTATION OF BACK PROPAGATED NEURAL NETWORK BASED ACTIVE REGENERATIVE HARMONIC FILTER For improving the performance and obtaining better results in harmonic elimination, the neural based current controller (Maurizio Cirrincione et al. 2009) is implemented. The training of the network layer gives the required mitigation of harmonics. For obtaining the required harmonics reduction, back propagated neural network is used. These networks are purely based on supervisory training. It uses gradient descent method of training instead of steepest descent method since the adjustment for required output can be done continuously during the training process. The standard steepest descent is always used due to the constant learning rate throughout the training. But the total performance of this algorithm is very sensitive to the proper setting of the learning rate. It is not practical to determine the optimal setting for the learning rate before training, and so the performance will be better if the learning rate changes during training process (Li Xia et al. 2011). For improving the performance, the learning rate is allowed to change during the training process (Julio Viola et al. 2007). This adaptive learning rate attempts to keep the learning step size as large as possible while keeping the learning stable. The flow of adaptive training algorithm for the Back Propagated Artificial Neural Network (BPANN) is shown in the flowchart of Figure 6.9. The proposed ARHF with the trained BPANN is depicted in Figure 6.10 (Pinheiro et al. 1996).

121 Figure 6.10 Proposed ARHF with neural network trainer 6.5.1 Simulation and its Outputs The MATLAB simulink model is used to model the two types of nonlinear loads with inclusion of Back propagated neural network for controlling active regenerative harmonic filter. The Nonlinear Load 1and 2 are simulated with the ARHF as shown in Figures 6.11 and 6.12.

Figure 6.11 Simulation circuit of Nonlinear Load 1 with Neural Network 122

123 Figure 6.12 Simulation circuit of Nonlinear Load 2 with Neural Network The multilayer feed forward back propagated neural network is implemented in the simulation. After simulation of both loads, the magnitudes of harmonics are reduced. The individual network layers incorporated in the MATLAB simulink model are shown in Figure 6.13(a) and (b). The integration of the neural network layers is shown in Figure 6.13(c). The sigmoidal activation function is selected and it works on the given input to give the particular order harmonic reduction. The training is done for 84 epoches for getting the best harmonic elimination (Figure 6.13(d)). The FFT window shown in Figures 6.14 and 6.15 gives the source current with reduced THD i for both loads.

124 (a) Neural network Layer 1 (b) Neural network Layer 2 (c) Integration of Layers (1 and 2) (d) Epoches carried out in training Figure 6.13 Implementation of BPANN in simulation

125 Figure 6.14 Simulated Nonlinear Load 1 with BPANN (THD i =1.53%) Figure 6.15 Simulated Nonlinear Load 2 with BPANN (THD i =3.84%)

126 The gradient descent method of training algorithm is adopted for this network and it controls the regenerative converter switching (Mumcu et al. 2001) there by controlling the generation of harmonics. FFT analysis shows the meticulous harmonic elimination by the usage of back propagation neural network. The derived harmonic profiles are tabulated and their performance is validated. By using the adaptive training algorithm for the Back Propagated Artificial Neural Network, the utility is protected from the issues created by nonlinear loads. The devastating effects created by all types of nonlinear loads can be lucratively reduced by the use of ANN controller. The input current THD of the nonlinear loads obtained before mitigation are THD i =89.54% (NL1) and THD i =190.55% (NL2) respectively. After the use of this adaptive Back Propagated Artificial Neural Network with ARHF, the current THD for NL1 and NL2 are reduced. The FFT profile of harmonic orders obtained after simulation is comparatively low as described in the standards like IEEE 519-1992. The reduced source current THDs by the BPANN based active regenerative filtering are depicted in Figure 6.14 for NL1 and in Figure 6.15 for NL2 and they are THD i (NL1) = 1.53% THD i (NL2) = 3.84% 6.6 VALIDATION AND DISCUSSION OF SIMULATED RESULTS The MATLAB simulation of the nonlinear loads is done with FFT analysis of source current. The two cycles of the utility current is observed and the harmonic profiles of nonlinear loads (NL1 and NL2) are tabulated. By the simulation, the magnitude of the current THD for both types of nonlinear loads is taken with the even and odd harmonic orders. The harmonic orders taken for the nonlinear loads before compensation are shown in Table 6.1. Figure 6.16 gives the bar chart of the harmonic orders plotted with its

127 magnitude in percentage (%). The harmonic orders upto the 19 th order including even and odd orders is plotted in the chart which gives a clear picture of harmonics content in the utility. The compensation of source current starts with the instantaneous p- q theory based current controller. The additional use of high pass filter with this controller mitigates the higher order harmonics. The graphs in Figures 6.17 and 6.18 depict the reduced magnitude of harmonics obtained after the usage of p-q theory based controller with and without high pass filter. The plotted chart also indicates the performance of this controller with the uncompensated profile of both loads. The harmonic orders like H 3, H 5, H 7,.etc., upto H 19 are reduced by this controller and further reduction is also done by addition of HPF with it. For improving the efficiency of active regenerative filtering the artificial intelligence techniques are introduced. The fuzzy logic controller is first checked with the proposed filtering to reduce the harmonics pollution. The fuzzy tuned controller provides fine tuning for reducing the harmonics compared to the classical methods. The results obtained by usage of fuzzy tuned controller are shown in Figure 6.19. The comparison chart for p-q theory based controller and fuzzy logic controller is shown in Figure 6.20. This validates the performance of fuzzy logic controller in harmonic limitation. To obtain the best power quality at the utility, the back propagated neural network is implemented and results are taken. The uncompensated source profile comparison with BPANN is given in Figure 6.21 for NL1 and NL2. Figure 6.22 shows the results of neural network based controller over p- q theory based control. The optimized intelligent controller is predicted in Figure 6.23 for both types of nonlinear loads. All controllers performances are compared in Figure 6.24 and the best performing controller for the harmonics suppression in both loads is explained in conclusion.

Figure 6.16 Uncompensated harmonic profiles for NL1 and NL2 128

129 Figure 6.17 Comparison chart for NL1 and NL2 with p-q Theory based controller (without HPF)

130 Figure 6.18 Harmonic profiles for NL1 and NL2 with p-q Theory based controller (with HPF)

Figure 6.19 FFT profiles for NL1 and NL2 with Fuzzy Logic Controller 131

132 Figure 6.20 Fuzzy Logic controller comparison with p-q theory based controller (NL1 and NL2)

133 Figure 6.21 FFT profiles for NL1 and NL2 with BPANN trained controller

134 Figure 6.22 BPANN trained controller with p-q theory based controller (NL1 and NL2)

Figure 6.23 Comparison of FLC and BPANN (NL1 and NL2) 135

136 (a) All controllers comparison of THD i for NL1 (b) All controllers comparison of THD i for NL2 Figure 6.24 Comparison of THD i for NL1 and NL2 Table 6.1 gives the complete FFT profiles of all loads with uncompensation and also compensation provided by p-q theory based current controller, fuzzy tuned controller and back propagated neural network based current controllers. The lucrative reduction of odd order harmonics is predicted clearly for all type of controllers. The reduced harmonic orders show that the best harmonic limitation is provided by artificial neural network

137 than other types of controllers. The harmonic orders in this table also validate the results provided by active regenerative harmonic filter during mitigation of source current harmonics for both types of nonlinear loads. Table 6.1 Harmonic Values obtained from the Simulation S.NO. Non Linear Load 1 Non Linear Load 2 Controller p-q Harmonic Without controller Order controller without HPF p-q Without controller FLC ANN controller with HPF p-q p-q controller controller FLC ANN without with HPF HPF H1. 100 100 100 100 100 100 100 100 100 100 H2. 0.67 0.05 0.05 0.11 0.04 0.04 0.76 0.72 0.18 0.03 H3. 77.01 5.31 5 5.19 1.1 95.36 20.23 19.13 3.08 2.66 H4. 0.31 0.02 0.02 0.04 0.02 0.07 0.13 0.13 0.09 0.02 H5. 42.6 2.94 2.76 2.8 0.63 86.83 4.22 3.99 1.85 1.59 H6. 0.09 0.01 0.01 0.01 0.01 0.1 0.25 0.24 0.06 0.01 H7. 11.6 0.8 0.75 0.69 0.44 75.21 2.83 2.67 1.32 1.13 H8. 0.18 0.01 0.01 0.03 0.01 0.11 0.07 0.06 0.05 0.01 H9. 5.71 0.39 0.37 0.43 0.34 61.78 1.42 1.34 1.02 0.88 H10. 0.1 0.01 0.01 0.01 0.01 0.11 0.15 0.14 0.04 0.01 H11. 8.21 0.57 0.53 0.54 0.27 48.09 1.04 0.98 0.84 0.72 H12. 0.06 0 0 0.01 0.01 0.1 0.04 0.04 0.03 0.01 H13. 2.78 0.19 0.18 0.14 0.23 35.87 0.7 0.66 0.71 0.61 H14. 0.11 0.01 0.01 0.02 0 0.08 0.11 0.1 0.03 0 H15. 2.5 0.17 0.16 0.19 0.2 26.92 0.52 0.49 0.61 0.53 H16. 0.05 0 0 0.01 0 0.08 0.03 0.03 0.02 0 H17. 3.37 0.23 0.22 0.21 0.17 22.43 0.41 0.39 0.54 0.46 H18. 0.05 0 0 0.01 0 0.08 0.08 0.08 0.02 0 H19. 0.9 0.06 0.06 0.03 0.16 21.45 0.3 0.29 0.49 0.41 The Table 6.2 gives the Total current Harmonic Distortion obtained by the use of ARHF with all the controllers. The reduced THD i is obtained for the application of BPANN with the regenerative converter compared to the other conventional controllers. The values of source current THDs are also within the stringent limits of the standards.

138 Table 6.2 THD i obtained from the Simulation CONTROLLERS NONLINEAR NONLINEAR LOAD1 LOAD2 Uncompensated THD i =89.54 % THD i = 190.55% p-q theory based controller THD i = 6.17% THD i = 20.98% p-q theory based controller with HPF THD i = 5.81% THD i =19.84% Fuzzy Logic Controller THD i = 6.00% THD i = 4.47% Back Propagation Neural Network trained controller THD i = 1.53% THD i = 3.84%