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CHAPTER 4

NEURAL NETWORK CONTROLLER FOR HARMONIC

ELIMINATION IN MULTILEVEL INVERTER

4.1 INTRODUCTION

Uninterruptible power supplies (UPSs) are emergency power

sources which have wide spread application in critical equipments, such as

computers, automated process controllers, and hospital instruments. With the

rapid growth in the use of high-efficiency power converters, more and more

electrical loads are nonlinear and generate harmonics. It is a big challenge for

a UPS to maintain a high-quality sinusoidal output voltage under a nonlinear

loading condition.

An NN is an interconnection of a number of artificial neurons that

simulates a biological brain system. It has the ability to approximate an

arbitrary function mapping and can achieve a higher degree of fault

tolerance. NNs have been successfully introduced into power electronics

circuits. For the harmonic elimination of PWM inverters, NN replaced a

large and memory-demanding look-up table to generate the switching angles

of a PWM inverter for a given modulation index (Xiao Sun et al 2002).

4.2 TRAINING METHODS

When an NN is used in system control, the NN can be trained

either on-line or off-line. In on-line training, since the weights and biases of

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the NN are adaptively modified during the control process, it has better

adaptability to a nonlinear operating condition. The most popular training

algorithm for a feed forward NN is back propagation. It is attractive because

it is stable, robust, and efficient. However, the back propagation algorithm

involves a great deal of multiplication and derivation. If implemented in

software, it needs a very fast digital processor. If implemented in hardware, it

results in a rather complex circuitry.

Off-line training of an NN requires a large number of ex ample

patterns. These patterns may be obtained through simulations. Although the

weights and biases are fixed during the control process, the NN is a nonlinear

system that has much better robustness than a linear system. Moreover, the

forward calculation of the NN involves only addition, multiplication, and

sigmoidal-function wave shaping that can be implemented with simple and

low-cost analogue hardware. The fast-response and low-cost implementation

of the off-line trained NN are suitable for UPS inverter applications.

4.3 APPLICATIONS OF NEURAL NETWORKSIN

HARMONICS

The application of ANN is recently growing in power electronics

and drives area. A feed forward ANN basically implements nonlinear input-

output mapping. The computational delay of this mapping becomes large. The

optimal switching pattern Pulse Width modulation (PWM) strategies

constitute the best choice for high power, three-phase, voltage-controlled

inverters and for fixed frequency, fixed-voltage UPS systems. For any chosen

objective function, the optimal switching pattern depends on the desired

modulation index. In the existing practice, the switching patterns are

recomputed for all the required values of this index, and stored in look-up

tables of a microprocessor-based modulator. This requires a large memory

and computation of the switching angles in real time is, as yet, impossible. To

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overcome this problem, attempts were made to use approximate formulas, at

the expense of reduced quality of the inverter voltage. Recently, alternate

methods of implementing these switching patterns have been developed.

Without using a real time solution of nonlinear harmonic elimination

equation, an ANN is trained off-line to output the switching angles for wanted

output voltage. The most disadvantage of this application is the use in training

stage the desired switching angles givenby the solving of the harmonic

elimination equation by the classical method, i.e., the Newton Raphson

method. This algorithm requires starting values for the angles and does not

always converge to the required solution. To give a solution to this problem,

powers electronics researches always study many novel control techniques to

reduce harmonics in such waveforms.

4.4 SELECTIVE HARMONIC ELIMINATION (SHE)STRATEGY

Single phase three level inverter structure is shown in Figure 4.1. It

has 4 switches. When switches S1 and S4 are turned on, the positive half cycle

of the output ac voltage is obtained. The negative half cycle of the ac voltages

are obtained by triggering switches S2 and S3. Various objective functions

can be used in the optimal control of an inverter. For the described study, the

classic harmonic elimination strategy was selected. It consists in determining

s optimal switching angles. The primary angles are limited to the first quarter

cycle of the inverter output line voltage (phase a) Figure4.1. Switching angles

in the remaining three quarters are referred to as secondary angles. The full-

cycle switching pattern must have the half-wave and quarter-wave symmetry

in order to eliminate even harmonics. Hence, the secondary angles are

linearly dependent on their primary counterparts Figure4.2. The resultant

optimal switching pattern yields a fundamental voltage corresponds to a given

value of the modulation index, whereas (s 1) low order, odd, and triple

harmonics are absent in the output voltage.

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The harmonic elimination technique is very suitable for inverters

control. By employing this technique, the low THD output waveform without

any filter circuit is possible. Switching devices, in addition, turn on and off

only one time per cycle. Figure 4.2 shows a generalized three-level SHE

PWM waveform, which is synthesized by using the inverter circuit shown in

Figure 4.1. The output waveform is chopped N times per quarter. Each switch

is, therefore, switched N times per cycle to generate such a waveform.

Figure4.1Single phase three-level inverter structure

Figure 4.2Generalized three-level SHE PWM waveform

The Fourier series expansion for the quarter-wave symmetric

waveform as shown in Figure 4.2 is written as follows.

= sin (4.1)

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= ( 1) cos (4.2)

Where, Nis the number of the switching angles per quarter.

k is the switching angles, which must satisfy the following condition

< (4.3)

Vdcis the amplitude of the dc source.

and n is the harmonic order.

From Equation (4.2), the nonlinear equations of SHE PWM

waveform can be written as follows.

cos cos ± cos = = (4.4)

cos 3 cos 3 ± cos 3 = (4.5)

.

.

.

cos cos ± cos = (4.6)

Where, =

In order control the fundamental amplitude and to eliminate the

lower order harmonics, the nonlinear transcendental equations must be solved

and the switching angles 1, 2, …, n are calculated offline to minimize the

harmonics for each modulation index in order to have a total output voltage

with a harmonic minimal distortion rate.

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4.5 ARTIFICIAL NEURAL NETWORK

A typical multilayer ANN is shown in Figure.4.3. It consists of one

input layer, a middle layer and an output layer, where each layer has a

specific function. The input accepts an input data and distributes it to all

neurons in the middle layer. The input layer is usually passive and does not

alter the input data. The neurons in the middle layer act as feature detectors.

They encode in their weights a representation of the features present in the

input patterns. The output layer accepts a stimulus pattern from the middle

layer and passes a result to a transfer function block which usually applies a

nonlinear function and constructs the output response pattern of the network.

The number of hidden layers and the number of neurons in each hidden layer

depend on the network design consideration and there is no general rule for

an optimum number of hidden layers or nodes. The ANN to be used for the

generation of the optimal switching angles has a single input neuron fed by

the modulation index, one hidden layer and s outputs where each output

represents a switching angle.

Figure4.3 A typical multilayer ANN

1x1 1 1

2x2 2 2

nx3

K P

y1

y2

yp

y11

yk1

yk2

ykp

w1k

w12

w11

y12

y1py2p

y21y22

w21

w22

w2k

wn1wn2

wnk

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The output of the neuron is given by the following equation

= ( + ) (4.7)

Where, y - the output of the neuron,

xi - the ith input to the neuron,

wi - the ith connection weight,

wo - the bias weight,

(.) - the transfer function of the neuron,

k - the number of connections with the neurons in the preceding

layer.

Figure4.4 Structure of a single neuron

Figure 4.4 shows the structure of a single neuron. The input signals

x1, x2, … , xk are normally continuous variables. Each of the input signals flows

through a gain or weight. The weights can be positive or negative

corresponding to acceleration or inhibition of the flow of signals. The

summing node accumulates all the input weighted signals and then passes to

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the output through the transfer function which is usually nonlinear, such as

sigmoid, inverse-tan, hyperbolic or Gaussian type. The sigmoid transfer

function used in output layer has the form given by,

( ) = (4.8)

Where is the coefficient or gain which adjusts the slope of the function that

change between the two asymptotic values (0 and +1). The sigmoid function

is nonlinear, monotonic, and differentiable and has the largest incremental

gain at zero signals. In the hidden layer, the Gaussian transfer function has

been used and is given by,

( , ) = ( ) (4.9)

4.6 DIRECT SUPERVISED TRAINING OF ANN FOR SHE

Back Propagation training Algorithm (BPA) is most commonly

used in feed forward ANNs. When a set of input values are presented to the

ANN, step by step calculations are made in the forward direction to drive the

output pattern. A cost functional given by the squared difference between the

net output and the desired net output for the set of input patterns is generated

and this is minimized by gradient descent method altering the weights one at

a time starting from the output layer.

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Figure4.5 Direct Supervised Training of ANN for SHE

Figure4.6 ANN set for the Selective Harmonic Elimination

Figure 4.6 shows an ANN with a single input neuron fed by the

modulation index, l hidden neurons and s outputs each representing a

switching angle. The network was training using the Back Propagation

Algorithm (BPA). The training data extracted from the optimal switching

ANN

7 level

inverter

BPA

Selective

Harmonic

Elimination

Switching signal

generator

m1

2

s

1d

2d

ds

aSbScS

anVbnVcnV

1 1

1m

2 2

l S

2w

lw

1w

1lv

lsv

1

2

s

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angles, designated by 1 to s as functions of the modulation index m.

Equation 4.10 gives the outputs of the ANN shown in Figure4.6.

= , , = 1, … , (4.10)

4.7 INDIRECT SUPERVISED TRAINING OF ANN FOR SHE

In this case, the neural network is trained to generate the switching

angles in a way to eliminate the first harmonics without the knowledge of the

desired switching angles given by the Newton Raphson method. The problem

which arises in this indirect learning paradigm is that the desired outputs of

the ANN, i.e. optimal angles, are unknown. To avoid this problem, we will

insert in series with the ANN the equivalent nonlinear system equations.

Therefore, instead of the minimization of the error between the switching

angles given by the ANN and the wished switching angles often unknown, we

will minimize the error at the output of the nonlinear system equation of the

harmonics to be eliminated. Figure 4.7 shows the diagram of the indirect

training strategy of artificial neuron networks used for harmonics elimination.

When the desired precision is obtained the output of the ANN is used to

generate the control sequence of the inverter.

Figure 4.7 Indirect Training of ANN for Selective Elimination Harmonic

ANN7-level

Inverter

BPA

( )H

Switchingsignal

generatorm

1

2

s

aSbScS

anVbnVcnV

/ 4

1dh

2 0dh0dsh

1h

sh

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The ANN is trained by the back-propagation algorithm of the error

between the desired solutions of the nonlinear system equations to eliminate

the first harmonics and the output of this equation using the switching angle

given by the ANN.

4.8 BACK PROPAGATION NETWORK (BPN) FOR HARMONIC

ELIMINATION

The network to be utilized for the technique is depicted in

Figure 4.8. It consists of one input layer, one hidden layer and an output layer.

Switching angles are given as inputs and their harmonic voltages are taken as

outputs.

Figure 4.8 The network structure

The input layer, hidden layer and output layer of the network

consists of lN , hidN and 12HN neurons, respectively. To train the network,

Nhid

V3

21NN2 h

hidw

2N2 hidw

1N2 hidw

w222

w221 21N21 hw

w211

21Nh

hidN1w

w22w21

w12

1

2

w11

hidN2w

1

1

Input layer Hidden layer Output layer

2

1

2

w212 V1

hNV

Nl

2

lN

1N lw

2Nlw

hidlNNw

21N22 hw

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an appropriate dataset needs to be generated from the dataset D and it is

shown in Figure 4.9.

)1()1()1( 1)1(1101

12)1(112012

11)1(111011

flff

l

l

NNNN

N

N

FNN

FN

FN

FN

FF

FN

FF

fHff

H

H

VVV

VVV

VVV

)1()1()1( 31

23212

13111

)2()2()2( 2)1(1202

22)1(122022

21)1(121021

flff

l

l

NNNN

N

N

FNN

FN

FN

FN

FF

FN

FF

fHff

H

H

VVV

VVV

VVV

)2()2()2( 31

23212

13111

()()( )1(10

2)1(2120

1)1(1110

INfIlIN

fIINfI

IlII

IlII

NNNNNNN

NNNN

NNNN

FNN

FN

FN

FN

FF

FN

FF

INfHIN

fIN

f

H

H

VVV

VVV

VVV

)()()( 31

23212

13111

Figure 4.9 The dataset trainD used to train the network

4.9 TRAINING ALGORITHM FOR HARMONIC ELIMINATION

The entire dataset is given as input to the neural network and

trained well using Back Propagation (BP) algorithm. The training process is

described below.

(i) Generate arbitrary weights in the interval maxmin,ww and assign it

to neurons of the hidden layer and the outer layer. Assign unity

weight to the neurons of the input layer.

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(ii) Give the training dataset D as input to the network and determine

the BP error as follows

outT VVe (4.11)

In Equation (4.11), TV and outV are the target output and the

network outputs, respectively. From every output neuron of the

network, the elements of outV )( hV can be determined as follows

HidN

nnnhh ywV

1(4.12)

where,

l

jkl

N

j

jnn e

wy

1 1(4.13)

In Equation (4.12) hidN is the number of hidden neurons, nhw is the

assigned weight of the hn link of the network and hV is the

output of the thh output neuron. In Equation (4.13), ny is the output

of the thn hidden neuron.

(iii) On the basis of the obtained BP error, determine the change in

weights as follows

.V. ew out (4.14)

where, the learning rate , normally ranges from 0.2 to 0.5.

(iv) Determine new weights as follows,

www (4.15)

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(v) Repeat the process from step (ii), until BP error gets reduced to a

least value, essentially, the condition to be satisfied is 0.1e .

Once the training process is completed, the network gets well-

prepared to evaluate any given unknown data.

4.10 SIMULATION RESULTS

The implementation of the Neural Network Control technique is

performed in the working platform of MATLAB (version 7.10). The

technique is implemented in such a way that it can eliminate the 3rd order and

5th order harmonics and so it can minimize the total harmonic distortion. The

output voltages of the Three H Bridges are given in Figure 4.10, 4.11 and

4.12.The output voltage performance of the inverter obtained for the

computed optimal switching angles are given in Figure 4.13. Output voltage

Vs time plot is given in Figure 4.14. FFT analysis of inverter output voltage is

shown in Figure 4.15.

Acomparison of the performance of Neural Network Controller and

Fuzzy Logic Controller with respect to the Total Harmonic Distortion

and the computational time with modulation index of 0.5 and sampling

frequency of 200KHzare listed in the Table 4.1. From the results

it is observed that Fuzzy logic controller gives better result than that of

neural network controller for the multilevel inverter considered for

simulation.

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Figure 4.10 Output waveform of inverter bridge 1

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Figure 4.11Output waveform of inverter bridge 2

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Figure 4.12 Output waveform of inverter bridge 3

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Figure 4.13 Output waveform of the Inverter using neural network

controller

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Figure 4.14 Output Voltage Vs Time plot of the Inverter usingneural

network controller

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Figure 4.15 FFT Analysis of Inverter with neural network controller

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Table 4.1 Comparative results of multilevel inverter with Neural

Network and Fuzzy Logic Controller

Methodologies Total harmonic

distortion (THD)

Computational

time in Seconds

Fuzzy Logic 1.8468 0.0795

Neural Network 4.2373 0.2021

BasilM.Saied et al (2008) found 3rd, 5th,7th, 9th and 11th harmonics

with the help of SHE-PWM technique on a single phase 3 level H bridge

inverter using Neural network and Fuzzy Logic. The 3rd and 5th harmonic

voltages for Neural Network controller were reported as 1% and 5%

respectively. Hence it is clear that the proposed Neural Network Controller

used in this thesis gives better result with the THD of 4.2%. Also it is

observed that Fuzzy Logic Controller is more accurate than Neural Network

Controller.

4.11 CONCLUSION

In this chapter, the use of the ANN to solve the selective harmonics

elimination problem in PWM inverters is proposed. This technique allows

successful voltage control of the fundamental as well as suppression of a

selective set of harmonics. The main advantage of the proposed method is

that it requires neither high computing power nor specialized ANN hardware.

The main drawback of this technique lies in the training phase, since, this

phase is quite complex and time consuming. The given simulation results

proving the feasibility of the proposed technique.