A New Switching Controller Based Soft Computing-High Accuracy Implementation of Artificial Neural Network

Transcription

1 A New Switching Controller Based Soft Computing-High Accuracy Implementation of Artificial Neural Network Dr. Ammar Hussein Mutlag, Siraj Qays Mahdi, Omar Nameer Mohammed Salim Department of Computer Engineering Techniques, Electrical Engineering Technical College, Middle Technical University, Baghdad, Iraq. Abstract Space vector modulation (SVM) controller is an advanced computation intensive pulse width modulation (PWM) technique. System performance can be accomplished by applying a proper switching technique. To obtain a sinusoidal AC output waveform, the SVM switching technique is widely used and implemented in the inverter control algorithm to reduce harmonics. By controlling the inverter switching scheme, the harmonic content of the output voltage can be minimized. The SVM suffers from the complex computational processes. Therefore, this paper presents a new space vector modulation controller based soft computing-high accuracy implementation of artificial neural network. An artificial neural network (ANN) structure is proposed to identify and estimated the conventional SVM for avoiding the complex computational problem and hence improve the performance of the photovoltaic inverter generation. The ANN model receives the αβ voltages information at the input side and generates the duty ratios (T a, T b, and T c ) as an output. The training data for ANN is generated by simulating the conventional SVM. The total harmonic distortion (THD) rate with ANN and conventional based SVM methods are presented. Three indices namely root mean square error (RMSE), mean absolute error (MAE), and mean error (ME) are used to assessment the performance of the proposed ANN model. Moreover, statistical analysis using histogram method is presented as well for further evaluating. The results show that the proposed ANN model is significantly robust to realize a favorable response compared with the conventional SVM model. Keyword: Soft computing; Artificial Neural Network; Space Vector Modulation; Inverter Controller. IJCSCN February-March 7

2 . Introduction The voltage source inverter (VSI) has been utilized in the last view decades in various applications such as connect the photovoltaic (PV) with load or with utility grid []. The performance of the VSI is highly depends on the pulse width modulation (PWM) switching control strategy []. Therefore, many PWM approaches have been mentioned in the literature review such as carrier based pulse width modulation, sinusoidal pulse width modulation, and space vector modulation (SVM) [3-7]. Among them, the SVM is the dominant switching controller strategy [8]. Its importance comes from it is capable to reduce the harmonic which is one of the most important issues [9]. However, the main drawback of the SVM is the limiting in the inverter switching frequency which comes from the complex computational process conducted by SVM. Therefore, additional memory is required for real time implementation. Gaballah et al. in [] shown a way to decrease the complex computations in SVM and thus applied in real-time. Recently, artificial intelligent systems (AIs) have been reported in the literature to deal with SVM drawbacks. Genetic algorithm (GA) has been used to enhance the performance of the SVM through decreases the complex computational process. The GA based SVM has been utilized in [] to solve the complex online computation. Nonetheless, trap in local minima is the main drawback of the GA. Furthermore, the difficulty of solving the multimodal problems and slow convergence rate are also drawbacks of the GA. Another type of AIs which is fuzzy logic system based SVM has been revealed as well in the last years. In [], a comparison of the fuzzy logic based SVM for voltage source inverter has been presented. The performance of the developed fuzzy logic (FL) based SVM has been compared with conventional SVM. However, the time consumption of the FL tuning is the main drawback. Moreover, the FL can explain the knowledge but cannot learn from the training. To overcome the problem of the artificial intelligent systems, developed machine learning systems have been used. Artificial neural network (ANN) is one of the most important methods in the machine learning systems which has been used in many applications. Tracking of the maximum power based ANN has been proposed in [3]. In this study, the forecasting of the maximum voltages and currents have been achieved using ANN. IJCSCN February-March 7

3 Alternatively; the ANN can be utilized to improve the performance of the SVM. In this study, a new space vector modulation controller based soft computinghigh accuracy implementation of artificial neural network is proposed. This paper includes six sections. Section explains the conventional space vector modulation. Developed artificial neural network model has been introduced in section 3; meanwhile the proposed artificial neural network based SVM has been presented in section 4. Results and discussion has been drawn in section 5. Finally, the conclusion has been portrayed in section 6.. Conventional Space Vector Modulation The space vector modulation (SVM) is the most common switching controller because of their high efficiency capabilities and easy control [4]. The SVM is depended on the three phase quantities which are V a, V b, and V c. To simplify the calculations, the three phases (V a, V b, and V c ) can be converted to αβ voltages using Clark's transformation as, V V α β = 3 / 3 / V / V 3 / V a b c () Using the αβ voltages, the reference voltage (V ref ) and angular (α) between voltages (V α and V β ) can be written as, V ref = + V α V β V α = tan V β α () (3) The output signal is consists from eight vectors which are V to V 7. The vectors V, V, V 3, V 4, V 5, and V 6 are known as non-zero vectors whereas the V to V 7 are known as zero vectors. These eight vectors will form the output signal in a form of hexagon. Hence, the time share (T and T ) can be calculated using (V ref ) and (α) inside the hexagon. Eight topologies of switches will be realized when (V ref ) passes through the sectors which mean one cycle is completed. IJCSCN February-March 7 3

4 3. Developed Artificial Neural Network Model The artificial neural network (ANN) is a powerful parallel information processing system which draws the mapping between the inputs and outputs. The ANN consists from the neurons connected by the links which are passing the information from the inputs to the outputs [5]. Simply, the inputs neurons in the input layer are relay the input signals to the neurons in the hidden layer which is connected to the output layer where the final values are generated. Many artificial neural networks (ANNs) have been reported in the literature such as hebb network, adaline network, perceptron network, radial basis function, probabilistic neural network, and back-propagation neural network (BP-NN) [6]. Since the BP-NN is multi-layered, fully connected, and feed forward structure; therefore it is employed in this study. It is simply decrease the mean squared error of the output calculated by the network. Problems in numerous subjects can be solved utilizing the BP-NN. The goal from the training of the neural network is to achieve the response of the training data, additionally, achieve reasonable response to the inputs that are similar to the training data. The training of the BP-NN should passes through three steps which are feedforward of the training data, backpropagation to calculate the error, and update the weights. The appropriate weights for the links are being found after the training process is achieved. Regarding to the hidden layers, increase the number of the hidden layers will increase the resolution but they will lead to complex and long computational process. Therefore, single hidden layer is used in this study to reduce the computational process. Since the proposed system consists from the one hidden layer, the net input of the hidden layer is define as, net j = P j= v ij x i + b j (4) Three types of activation functions have been mentioned in the literatures which are identity function, binary sigmoid function, and bipolar sigmoid function. However, the bipolar sigmoid function is the recommended function in the hidden layer since its range belong to (-,). The response of the hidden layer using bipolar sigmoid function is describe as, IJCSCN February-March 7 4

5 Z j + e = net (5) The final layer of the proposed ANN model is the output layer. The net input of the output layer is written as, net k = M k = w jk Z j + b k (6) Since the target data are continuous rather than binary; the identity function is preferable to use in the output layer in this work. The response of the output layer using identity function is define as, f ( netk ) = net k (7) 4. Proposed Artificial Neural Network Based SVM The block diagram of the proposed ANN based SVM for two-level inverter is shown in Fig.. The ANN model has two inputs and three outputs. The inputs are the voltages (V α and V β ), meanwhile the outputs are the duty ratios (T a, T b, and T c ). Hence, the ANN model should be developed to predict the duty ratios (T a, T b, and T c ) which are compared with sampling period to generate the switching control signals for the VSI. The conventional SVM is used to generate the training data for the ANN model. The Levenberg-Marquardt backpropagation algorithm has been employed to train the ANN model to define the mapping between the inputs (V α and V β ) and the outputs (T a, T b, and T c ). Regarding to the number of the hidden nodes, small number of hidden nodes causes high error; meanwhile large number of hidden neurons causes high generalization error and complex computational process. Therefore, numerous studies have been discussed the optimal number of the nodes in the hidden layer which in turn lead to optimal performance of the ANN. The summery of the theses studies concluded that the best number should be around two to three times of the total number of input and output nodes. Thus, in this study, ten nodes have been used in the hidden layer. IJCSCN February-March 7 5

6 Fig.. The block diagram of the proposed ANN based SVM for VSI The proposed ANN is depicted in Fig.. It consists from three layers; input layer, hidden layer, and output layer which are --3 neurons, respectively. The proposed ANN receives the V α and V β voltages as inputs and generates T a, T b, and T c as outputs. Hence, the input of each data sample consists of two inputs values (V α and V β ) and three outputs or target values (T a, T b, and T c ). The training of the proposed ANN is repeated for all data samples to achieve one epoch. The process of the training will continue until achieve the goal of the error or complete the predefined epochs. Finally, the proposed ANN can be utilized to generate the duty ratios (T a, T b, and T c ) after the end of the training process when it is exposed to new input data. The proposed ANN can be assessment using various error type indices such as root mean square error (RMSE), mean absolute error (MAE), and mean error (ME) which are defined as, (8) (9) () IJCSCN February-March 7 6

7 Hidden layer Input layer Output layer T a V α T b V β T c Fig.. The architecture of the proposed ANN model IJCSCN February-March 7 7

8 5. Results and Discussion The performance of the proposed artificial neural network based space vector modulation (ANN-SVM) is investigated using MATLAB environment and compared with conventional space vector modulation (CON-SVM). As explained previously, the artificial neural network is trained to generate the duty ratios (T a, T b, and T c ). To achieve the best results, the ANN is trained using back-propagation method. Since the frequency used in this study is 5 khz, thus the duty ratios are various from zero to E-4. The duty ratios (T a, T b, and T c ) corresponding to the conventional and ANN space vector modulation are depicted in Fig. 3 to Fig. 5. These figures show three cycles of the duty ratios (T a, T b, and T c ). They are clearly showed that the responses of the ANN-SVM are stable and very similar to the responses of the CON-SVM without any negative impact such as oscillation. Moreover, the response of the ANN-SVM distinctly succeeds to track the exact CON- SVM. Hence, Fig. 3 to Fig. 5 responses indicates that the proposed ANN model is significantly robust to realize a favorable response. Duty Ratio.5 x Duty Ratio.5 x Time (s) (a) Time (s) (b) Fig. 3. Duty ratio (T a ) using (a) conventional and (b) ANN space vector modulation IJCSCN February-March 7 8

9 Duty Ratio.5 x Duty Ratio.5 x Time (s) (a) Time (s) Fig. 4. Duty ratio (T b ) using (a) conventional and (b) ANN space vector modulation (b) Duty Ratio.5 x Duty Ratio.5 x Time (s) (a) Time (s) Fig. 5. Duty ratio (T c ) using (a) conventional and (b) ANN space vector modulation (b) Fig. 3 to Fig. 5 do not clearly show how the ANN-SVM response is close from the CON- SVM response. For that reason, the errors between the CON-SVM response and ANN-SVM response are drawn in Fig. 6. The errors of T a, T b, and T c for three cycles show very small values which indicate a high performance of the ANN-SVM. IJCSCN February-March 7 9

10 Error ( T a ) 5 x Error ( T b ) 5 x Error ( T c ) 5 x Time (s) Fig. 6. Errors in duty ratios (T a, T b, and T c ) IJCSCN February-March 7

11 Three types of indices are used to evaluate the responses of the ANN model as can be shown in Table. The first index is the root mean square error (RMSE). This index shows very low values which are 8.49E-7, 9.7 E -7, and 7.8 E -7 for T a, T b, and T c, respectively. The mean absolute error (MAE) are calculated for the T a, T b, and T c as the second index which are 6.369E-7, 7.46 E -7, and E -7 for T a, T b, and T c, respectively. Finally, the mean error (ME) is used as the third index. The ME again shows very small values for T a, T b, and T c which are 7.65 E-8, E-8, and E-8, respectively. The low values from theses indices (RMSE, MAE, and ME) indicate a high accuracy of the proposed ANN-SVM model. Table : RMSE, MAE, and ME indices Indices T a T b T c RMSE 8.49E E E-7 MAE 6.369E E E-7 ME 7.65 E E E-8 For further evaluation for the performance of the proposed ANN-SVM, the histogram statistical analysis is used which is the most popular statistical analysis. It describes the feature representation and frequency distribution [7]. Fig. 7 to Fig. 9 show the graphical histogram of the errors between the conventional and ANN duty ratios T a, T b, and T c, respectively. The x-axis represents the class boundaries whereas the y-axis represents the frequencies of the classes. The bar in the class becomes higher when the numbers of the points are high; meanwhile the bar becomes lower when the numbers of the points are low. It is important to show that the measured values by the ANN-SVM model are compatible with the measured values by the CON-SVM. The graphical of the histogram analysis show that the values based ANN-SVM model are comparable with those values CON-SVM where a very small errors have been found. Most of the errors values are found to be in the middles bars which are the lowest error bars. Furthermore, the values of the errors are various from -.5E-6 to 3E-6 which are very small values. Moreover, the distributions of the errors are very close to normal distribution. This finding shows high accuracy and performance of the proposed ANN-SVM model. IJCSCN February-March 7

12 Frequency Error x -6 Fig. 7. Histogram of the error between the conventional and ANN duty ratio T a Frequency Error x -6 Fig. 8. Histogram of the error between the conventional and ANN duty ratio T b Frequency Error x -6 Fig. 9. Histogram of the error between the conventional and ANN duty ratio T c IJCSCN February-March 7

13 The last assessment is conducted based on the quality of the output waveforms. One of the criterions that is used to show the quality of the output waveforms is the total harmonic distortion (THD). The researches aims always to decrease the value of the THD which means increase the quality of the output waveforms. According to the IEEE Std 99- standard, the value of the measured THD should be less than 5% [8]. Fig. to Fig. depicted the THD rates of the conventional and ANN space vector modulation for V a, V b, and V c respectively. These figures clearly show that the proposed ANN-SVM model succeed to achieve low THD rates which are.4%,.49%, and.53% for V a, V b, and V c respectively. Thus, the proposed ANN-SVM model is implemented successfully with high efficiency. Fundamental (5Hz) =.3, THD=.43% Fundamental (5Hz) =.4, THD=.4% Mag (% of Fundamental) Harmonic order Mag (% of Fundamental) Harmonic order 5 (a) (b) Fig.. THD of the V a using (a) conventional and (b) ANN space vector modulation Fundamental (5Hz) =.3, THD=.56% Fundamental (5Hz) =.3, THD=.49% Mag (% of Fundamental) Mag (% of Fundamental) Harmonic order 5 5 Harmonic order (a) (b) IJCSCN February-March 7 3

14 Fig.. THD of the V b using (a) conventional and (b) ANN space vector modulation Fundamental (5Hz) =.4, THD=.6% Fundamental (5Hz) =.4, THD=.53% Mag (% of Fundamental) Mag (% of Fundamental) Harmonic order Harmonic order (a) (b) Fig.. THD of the V c using (a) conventional and (b) ANN space vector modulation Finally, the THD rates are presented in Table to show the difference between the CON- SVM and the ANN-SVM model. The THD rates in Table show that the ANN-SVM model succeed to accomplish the IEEE Std 99- standard. Furthermore, the ANN-SVM model gives better results with high quality compared to CON-SVM model. Hence, the performance of the proposed system is highly improved. Table : The comparison of the THD rates Voltages CON-SVM ANN-SVM V a.43.4 V b V c.6.53 IJCSCN February-March 7 4

15 6. Conclusion This paper presented a new space vector modulation controller based soft computinghigh accuracy implementation of artificial neural network to solve the complexity in the computational process of the SVM. The modified ANN model has been train to receive the voltages V α and V β as inputs and generate the duty ratios (T a, T b, and T c ) as outputs. The training data have been generated by simulates the conventional SVM. The ANN model has been trained using Levenberg-Marquardt backpropagation algorithm to draw the mapping between the inputs (V α and V β ) and outputs (T a, T b, and T c ). Three indices namely root mean square error (RMSE), mean absolute error (MAE), and mean error (ME) have been used to assessment the response of the ANN model. These indices show very low values which demonstrate the robustness of the ANN-SVM model. The quality of the output waveforms signals based ANN-SVM have been calculated using total harmonic distortion (THD). The THD values based ANN-SVM have been found to be.4%,.49%, and.53% for V a, V b, and V c, respectively; whereas the THD values based CON-SVM have been found to be.43%,.56%, and.6%. This finding show that the performance of the VSI based ANN- SVM has been significantly improved by decrease the THD and decrease the complex computational processes as well. Finally, statistical analysis using histogram method has been employed for further evaluation. The histogram method show a normal data distribution and very small error values. Thus, the proposed ANN model can be efficiently used to highly improve the whole system. References [] H. Shareef, A. Mohamed, A. H. Mutlag. Current Control Strategy for a Grid Connected PV System Using Fuzzy Logic Controller. 4 IEEE International Conference on Industrial Technology (ICIT), Feb. 6 - Mar., 4, Busan, Korea. [] A. H. Mutlag, A. Mohamed, H. Shareef. A Nature-Inspired Optimization-Based Optimum Fuzzy Logic Photovoltaic Inverter Controller Utilizing an ezdsp F8335 Board. Energies, vol. 9, no., pp. 3, 6. [3] Zhou K, Wang D. Relationship between spacevector modulation and three phase carrierbased PWM: a comprehensive analysis. IEEE Trans Ind Appl ;49(): [4] Kwasinski A, Krein PT, Chapman PL. Time domain comparison of pulse-width modulation schemes. IEEE Power Electron Lett 3;(3):64 8. IJCSCN February-March 7 5

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