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], [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 (T

a, 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 V

a, Vb, and

V

c. To simplify the calculations, t he three

phases ( V

a, Vb, and Vc) can be converted to

?? voltages using Clark’s transformation as ,

? ?

?

?

?

? ?

?

?

?

?

? ?

?

?

?

??

?

=

?

? ?

?

?

?c

b aV

V

V

/

/ /

/

V V

2

3

2

3

0 2

1

2

1

1

3 2?

?

(1)

Using the ?? voltages, the reference

voltage (V

ref) and angular (?) between

voltages (V

? and V?) can be written as ,

2

2

?

?V

V

Vref+

=

(2)

? ?

? ?

? ?

? ?

=

?

?

?

?

V

V

tan

1

(3)

The output signal is consists from eight

vectors which are V

0 to V7. The vectors V1,

V

2, V3, V4, V5, and V6 are known as non- zero

vectors whereas the V

0 to V7 are known as

zero vectors. These eight vectors will form

the output signal in a form of hexagon.

Hence, the time share (T

1 and T2) can be

calculated using (V

ref) and (?) inside the

hexagon.

Eight topologies of switches will

be realized when (V

ref) 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,

?

=

+

=

P

j j

i

ij

j

b

x

v

net

1 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,

1

1 2

?

+

=?

net

je

Z

(5)

The final layer of the proposed ANN

model is the output layer. The net input of

the output layer is written as,

?

=

+

=

M

k k

j

jk

k

b

Z

w

net

1 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,

k

knet

)

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 (T

a, Tb, and Tc). Hence,

the ANN model should be developed to

predict the duty ratios (T

a, 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 (T

a, 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

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, 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

?V

aT

bT

cT

Input layerHidden layer

Output layer

Fig. 2. The architecture of the proposed ANN model

5. 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 (T

a, 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 (T

a, 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 (T

a, 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 (T

a) using (a) conventional and (b) ANN space vector modulation

0.020.030.040.050.060.070.08-0.5

0

0.5

1

1.5

2

2.5x 10

-4

T ime (s)

Duty Ratio

0.020.030.040.050.060.070.08-0.5

0

0.5

1

1.5

2

2.5x 10

-4

T ime (s)

Duty Ratio

(a)

(b)

Fig. 4. Duty ratio (T

b) using (a) conventional and (b) ANN space vector modulation

(a)

(b)

Fig. 5. Duty ratio (T

c) 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 T

a, Tb, and Tc for three cycles show very small values

which indicate a high performance of the ANN -SVM.

0.020.030.040.050.060.070.08-0.5

0

0.5

1

1.5

2

2.5x 10

-4

T ime (s)

Duty Ratio

0.020.030.040.050.060.070.08-0.5

0

0.5

1

1.5

2

2.5x 10

-4

T ime (s)

Duty Ratio

0.020.030.040.050.060.070.08-0.5

0

0.5

1

1.5

2

2.5

x 10

-4

T ime (s)

Duty Ratio

0.020.030.040.050.060.070.08-0.5

0

0.5

1

1.5

2

2.5x 10

-4

T ime (s)

Duty Ratio

Fig. 6. Errors in duty ratios (T

a, Tb, and Tc)

0.020.030.040.050.060.070.08

-5

0

5 x 1 0

-6

Error ( T

a )

0.020.030.040.050.060.070.08-5

0

5x 1 0

-6

Error ( T

b )

0.020.030.040.050.060.070.08-5

0

5x 1 0

-6

T ime (s )

Error ( T

c )

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 T

a, Tb, and Tc, respectively.

The mean absolute error (MAE) are calculated for the T

a, Tb, and Tc as the second index which

are 6.3169E -07, 7.0460 E – 07, and 5.2679 E – 07 for T

a, Tb, and Tc, respectively. Finally, the

mean error (ME) is used as the third index. The ME again shows very small values for T

a, Tb,

and T

c 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 T

a, 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 T

a

Fig . 8. Histogram of the error between the conventional and ANN duty ratio T

b

Fig . 9. Histogram of the error between the conventional and ANN duty ratio T

c

-2.5-2-1.5-1-0.500.511.52

x 10

-6

0

1000

2000

3000

4000

5000

6000

Error

Frequency

-2-10123

x 10

-6

0

1000

2000

3000

4000

5000

6000

Error

Frequency

-2-10123

x 10

-6

0

1000

2000

3000

4000

5000

6000

7000

Error

Frequency

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

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 V

a, 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 V

a, Vb, and Vc

respectively . T hus, the proposed ANN -SVM

model is implemented successfully

with

high efficiency.

(a)

(b)

Fig. 10. THD of the V

a using (a) conventional and (b) ANN space vector modulation

(a)

(b)

051015200

0.2

0.4

0.6

0.8

1

Harmonic order

Fundamental (50Hz) = 1.013 , THD= 0.43%

Mag (% of Fundamental)

051015200

0.2

0.4

0.6

0.8

1

Harmonic order

Fundamental (50Hz) = 1.014 , THD= 0.40%

Mag (% of Fundamental)

051015200

0.2

0.4

0.6

0.8

1

Harmonic order

Fundamental (50Hz) = 1.013 , THD= 0.56%

Mag (% of Fundamental)

051015200

0.2

0.4

0.6

0.8

1

Harmonic order

Fundamental (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 V

c 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

051015200

0.2

0.4

0.6

0.8

1

Harmonic order

Fundamental (50Hz) = 1.014 , THD= 0.61%

Mag (% of Fundamental)

051015200

0.2

0.4

0.6

0.8

1

Harmonic order

Fundamental (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 ( T

a, 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

(T

a, 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 V

a, 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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