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. [email protected], [email protected]
com, [email protected] 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 suffer s from the complex computational process es. 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 avoid ing the complex computational problem and hence improve the performance of the photovoltaic inverter generation. The ANN model receives the ?? voltages information at the input side and generates the duty ratios (Ta, Tb, and Tc) 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 M odulation; Inverter Controller.
1. 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 1. The performance of the VSI is highly depends on the pulse width modul ation (PWM) switching control strategy 2. 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 10 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 11 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 1 2, a comparison of the fuzzy logic based SVM for voltage source inverter has been presented. The performance of the developed fuzzy logic (FL) base d 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 13. In this study, the forecasting of the maximum voltages and currents have been achieved using ANN.Alternatively; the ANN can be utilized to improve the performance of the SVM.
In this stud y, a new space vector modulation controller based soft computing-high accuracy implementation of artificial neural network is proposed. This paper includes six sections. Section 2 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. 2.
Conventional Space Vector Modulation The space vector modulation (SVM) is the most common switching controller because of their high efficiency capabilities and easy control 14. The SVM is depended on the three phase quantities which are Va, Vb, and Vc. To simplify the calculations, t he three phases ( Va, Vb, and Vc) can be converted to ?? voltages using Clark’s transformation as , ? ????? ?????? ???????=?? ????cb aVVV// //V V23230 212113 2?? (1) Using the ?? voltages, the reference voltage (Vref) and angular (?) between voltages (V? and V?) can be written as , 22??VVVref+= (2) ? ?? ?? ?? ?=????VVtan1 (3) The output signal is consists from eight vectors which are V0 to V7. The vectors V1, V2, V3, V4, V5, and V6 are known as non- zero vectors whereas the V0 to V7 are known as zero vectors. These eight vectors will form the output signal in a form of hexagon. Hence, the time share (T1 and T2) can be calculated using (Vref) and (?) inside the hexagon. Eight topologies of switches will be realized when (Vref) passes through the sectors which mean one cycle is completed .
3. Devel oped 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 15. Simply, the inputs neurons in the input layer are relay the input signals to the neurons in the hidden layer which i s 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) 16. Since the BP -NN is multi -layered, fully connected, and fe ed 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 weight s. T he 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 resolu tion but they will lead to complex and long computational process. Therefore, s ingle 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, ?=+=Pj jiijjbxvnet1 0 (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 recommend ed function in the hidden layer since its range belong to ( -1,1). The response of the hidden layer using bipolar sigmoid function is describe as,11 2?+=?netjeZ (5) The final layer of the proposed ANN model is the output layer.
The net input of the output layer is written as, ?=+=Mk kjjkkbZwnet1 0 (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, kknet)net(f = (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. 1. The ANN model has two inputs and three outputs. The inputs are the voltages (V? and V?), meanwhile the outputs are the duty ratios (Ta, Tb, and Tc). Hence, the ANN model should be developed to predict the duty ratios (Ta, Tb, and Tc) 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 back-propagation algorithm has been employed to train the ANN model to define the mapping between the inputs (V? and V?) and the output s (Ta, Tb, and Tc). Regarding to the number of the hidden nodes, s mall number of hidden nodes causes high error; mean while 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 s hould 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.Fig. 1. The block diagram of the proposed ANN based SVM for VSI The proposed ANN is depicted in Fig.
2. It consists from three layers; input layer , hidden layer , and output layer which are 2- 10- 3 neurons, respectively. The proposed ANN receives the V? and V? voltages as inputs and generates Ta, Tb, and Tc as output s. Hence, the input of each data sample consists of two input s values (V? and V?) and three output s or target values (Ta, Tb, and Tc). 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 (Ta, Tb, and Tc) after the end of the training proc ess 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) (10)?V?VaTbTcTInput layerHidden layerOutput layer Fig. 2. The architecture of the proposed ANN model5. Results and Discu ssion The performance of the proposed artificial neural network based space vector modulation (ANN-SVM) is investigated using MAT LAB environment and compared with conventional space vector modulation (CON -SVM) . As explained previously, the artificial neural network is trained to generate the duty ratio s (Ta, Tb, and Tc). 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 2E -4. The duty ratios (Ta, Tb, and Tc) 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 (Ta, Tb, and Tc). 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, Fi g. 3 to Fig. 5 responses indicates that the proposed ANN model is significantly robust to realize a favorable response. (a) (b) Fig.
3. Duty ratio (Ta) using (a) conventional and (b) ANN space vector modulation 0.020.030.
522.5x 10-4T ime (s)Duty Ratio0.020.030.040.050.
060.070.08-0.500.511.522.5x 10-4T ime (s)Duty Ratio(a) (b) Fig.
4. Duty ratio (Tb) using (a) conventional and (b) ANN space vector modulation (a) (b) Fig. 5. Duty ratio (Tc) using (a) conventional and (b) ANN space vector modulation 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 Ta, Tb, and Tc for three cycles show very small values which indicate a high performance of the ANN -SVM. 0.020.
511.522.5x 10-4T ime (s)Duty Ratio0.
08-0.500.511.522.5x 10-4T ime (s)Duty Ratio 0.020.030.040.
5x 10-4T ime (s)Duty Ratio0.020.030.040.050.060.
070.08-0.500.511.522.5x 10-4T ime (s)Duty RatioFig. 6.
Errors in duty ratios (Ta, Tb, and Tc) 0.020.030.040.
050.060.070.08-505 x 1 0-6Error ( Ta )0.020.030.040.
08-505x 1 0-6Error ( Tb )0.020.030.040.050.
060.070.08-505x 1 0-6T ime (s )Error ( Tc )Three types of indices are used to evaluate the responses of the ANN model as can be shown in Table1. The first index is the root mean square error (RMSE). This index shows very low values which are 8.
1249E -07, 9.2207 E -07, and 7.1081 E -07 for Ta, Tb, and Tc, respectively. The mean absolute error (MAE) are calculated for the Ta, Tb, and Tc as the second index which are 6.3169E -07, 7.0460 E – 07, and 5.2679 E – 07 for Ta, Tb, and Tc, respectively. Finally, the mean error (ME) is used as the third index.
The ME again shows very small values for Ta, Tb, and Tc which are 7.0615 E -08, 5.3579 E -08, and 5.8819 E -08, respectively. The low values from theses indices (RMSE, MAE, and ME) indicate a high accuracy of the proposed ANN -SVM model. Table 1: RMSE, MAE, and ME indices Indices Ta Tb Tc RMSE 8.1249E-07 9.2207 E-07 7.
1081 E -07 MAE 6.3169E-07 7.0460 E-07 5.2679 E -07 ME 7.0615 E -08 5.3579 E -08 5.8819 E -08 For further evaluati on 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 17. Fi g. 7 to Fi g . 9 show the graphical histogram of the errors between the conventional and ANN duty ratios Ta, Tb, and Tc, respectively. The x -axis represents the class boundaries whereas the y -axis represents the frequencies of the class es. The bar in the class becomes hig her 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, t he values of the errors are various from -2.
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 mo del.Fig. 7.
Histogram of the error between the conventional and ANN duty ratio Ta Fig . 8. Histogram of the error between the conventional and ANN duty ratio Tb Fig . 9. Histogram of the error between the conventional and ANN duty ratio Tc -2.5-2-1.
5-1-0.500.511.52x 10-60100020003000400050006000ErrorFrequency-2-10123x 10-60100020003000400050006000ErrorFrequency-2-10123x 10-601000200030004000500060007000ErrorFrequencyThe 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 TH D which mean s increase the quality of the output waveforms. According to the IEEE Std 929 -2000 standard, the value of the measured THD should be less than 5% 18.
Fi g. 10 to Fig. 12 depicted the THD rates of the conventional and ANN space vector modulation for Va, Vb, and Vc respectively.
These figures clearly show that the proposed A NN-SVM model succeed to achieve low THD rates which are 0.40%, 0.49%, and 0.53% for Va, Vb, and Vc respectively . T hus, the proposed ANN -SVM model is implemented successfully with high efficiency.
(a) (b) Fig. 10. THD of the Va using (a) conventional and (b) ANN space vector modulation (a) (b) 0510152000.20.40.
60.81Harmonic orderFundamental (50Hz) = 1.013 , THD= 0.43%Mag (% of Fundamental)0510152000.
18.104.22.168Harmonic orderFundamental (50Hz) = 1.
014 , THD= 0.40%Mag (% of Fundamental)0510152000.20.40.60.
81Harmonic orderFundamental (50Hz) = 1.013 , THD= 0.56%Mag (% of Fundamental)0510152000.20.40.60.
81Harmonic orderFundamental (50Hz) = 1.013 , THD= 0.49%Mag (% of Fundamental)Fig. 11. THD of the Vb using (a) conventional and (b) ANN space vector modulation (a) (b) Fig. 12. THD of the Vc using (a) conventional and (b) ANN space vector modulation Finally, the THD rates are presented in Table 2 to show the difference between the CON -SVM and the ANN -SVM model.
The THD rates in T able 2 show that the ANN-SVM model succeed to accomplish the IEEE Std 929 -2000 standard. Furthermore, the ANN -SVM model gives better results with high quality compar ed to CON-SVM model. Hence, the performance of the proposed system is highly improved. Table 2: The comparison of the THD rates Voltages CON-SVM ANN-SVM ;#55349;;#56393;;#55349;;#56398; 0.
43 0.40 ;#55349;;#56393;;#55349;;#56399; 0.56 0.49 ;#55349;;#56393;;#55349;;#56400; 0.61 0.
53 0510152000.20.40.60.81Harmonic orderFundamental (50Hz) = 1.014 , THD= 0.61%Mag (% of Fundamental)0510152000.
22.214.171.124Harmonic orderFundamental (50Hz) = 1.
014 , THD= 0.53%Mag (% of Fundamental)6. Conclusion This paper presented a new space vector modulation controller based soft computing-high 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? and V? as inputs and generate the duty ratios ( Ta, Tb, and Tc) as outputs . The training data have been generated by simulates the conventional SVM. The ANN model has been trained using Levenberg- Marquardt back-propagation algorithm to draw the mapping between the inputs ( V? and V?) and outputs (Ta, Tb, and Tc). 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 0.40%, 0.49%, and 0.53% for Va, Vb, an d Vc, respectively; whereas the THD values based CON -SVM have been found to be 0.43%, 0.56%, and 0.
61%. 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 ef ficiently used to highly improve the whole system.
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