37
CHAPTER 3
DEVELOPMENT OF AN EXPERT SYSTEM TO IDENTIFY
AND ESTIMATE HARMONICS PRODUCED BY POWER
ELECTRONIC CONVERTERS
3.1 INTRODUCTION
The existence of harmonics is one of the significant means of
deteriorating the quality of an electric power supply. In order to fully
understand the problems caused by harmonics, sources of electric power
harmonics needs to be identified and this normally requires power quality
monitoring and analysis. However, monitoring usually generates vast amount
of data which makes manual inspection of the disturbance waveforms a
tedious and time-consuming task. Therefore, it is desirable that the data
collection process is automated such that monitoring equipment not only
captures harmonic waveforms but also performs the task of recognizing the
various types of nonlinear loads present in a system. With such an automated
system, faster and more efficient analysis of the databases can be achieved.
The issue of automatic analysis of various power quality disturbances has
been addressed in the form of the development of expert systems for power
quality event identification or the classification of disturbances such as
transients and voltage sags (Kazibwel and Sendaula 1992). The expert system
for analyzing power system harmonics focuses on symptoms associated with
harmonics related problems and providing possible solutions (Schlabbach
1994, Shipp et al 1995).
38
In this chapter an improved model is proposed to identify the
harmonic distortion produced by the different types of power electronic
converters. The rules are derived to identify harmonics produced by single
phase, three phase fully controlled AC-DC converters, and single phase
voltage source inverters. The proposed model provides automatic and
intelligent identification of harmonic sources originating from power
electronic converters loads by classifying the different types of nonlinear
loads that contribute harmonics to the supply system and then quantifying the
harmonic distortion levels of each type of load. This expert system provides
all the necessary input side and output side parameters that are not available
in the scheme proposed by Azah Mohamed et al (2006). In the development
of the expert system, an important consideration is given to the application of
advance signal processing techniques such as the fractal and fast Fourier
transform (FFT) analyses for characterizing the harmonic signatures of
various types of nonlinear loads. Unique features extracted from the analyses
are in the form of fractal numbers, harmonic distortion levels including
individual harmonic components and total harmonic distortion, crest factor
and power factor. The accuracy of the expert system is illustrated by
comparison with hardware.
3.2 TOOLS FOR ANALYSING HARMONICS
For most conventional analyses, the power system is essentially
modeled as a linear system with passive elements excited by constant
magnitude and constant frequency sinusoidal voltage sources. However, with
the widespread proliferation of power electronics loads nowadays, significant
amounts of harmonic currents are being injected into power systems.
Harmonic currents not only disturb loads that are sensitive to waveform
distortion, but also cause many undesirable effects on power system elements.
As a result, harmonic studies are becoming a growing concern. Harmonics are
39
usually defined as periodic steady state distortions of voltage and/or current
waveforms in power systems. In the harmonic polluted environment, the
theory regarding harmonic quantities needs to be defined to distinguish from
those quantities defined for the fundamental frequency.
3.2.1 Fourier Series and Analysis
The French physicist and mathematician, Joseph Fourier, in his
article ‘Analytic Theory of Heat’ which was published in 1882, first
introduced the theory of the Fourier series. The theory involves expansions of
arbitrary functions in certain types of trigonometric series. It proves that any
periodic function in an interval of time could be represented by the sum of a
fundamental and a series of higher orders of harmonic components at
frequencies, which are integral multiples of the fundamental component. The
series establishes a relationship between the function in time and frequency
domains. A distorted periodic wave can be decomposed into a fundamental
wave and a set of harmonics. This decomposition process is called Fourier
analysis. With this technique the effects of nonlinear elements in power
systems can be analyzed systematically (Chang 1998). A periodic function
can be defined as any function for which
( ) ( )f t f t T (3.1)
for all t. The smallest constant T that satisfies the equation (3.1) is called the
period of the function. By iteration of equation (3.1),
( ) ( ), 0, 1, 2...,f t f t nT n (3.2)
40
Let a function f(t) be periodic with period T, then this function can
be represented by the trigonometric series
) sin cos (
2 1 ) (
1 0 t n b t n a a t f n n n
(3.3)
where )/2( T . A series such as (3.3) is called trigonometric Fourier
series. It can be rewritten as
01
( ) sin( )n nn
f t c c n t
(3.4)
where 2
00
ac , 22nnn bac , and
n
nn b
a1tan
From the equation (3.4), it can be observed that the Fourier series
expression of a periodic function represents a periodic function as a sum of
sinusoidal components with different frequencies. The component of no is
called the nth harmonic of the periodic function. C0 is the magnitude of the dc
component. The component with n=1 is called the fundamental component.
Cn and n are known as the nth order harmonic magnitude and phase angle,
respectively. The magnitude and phase angle of each harmonic determine the
resulting wave shape of f(t). Equation (3.3) also can be represented by its
complex form as
0( ) jn tn
n
f t c e
(3.5)
where n=0, ±1, ±2, ...
0
2
2
1 ( )T
jn tn
T
c f t e dtT
(3.6)
41
3.2.2 Fourier Transform (FT)
The Fourier transform of a function f(t) is defined as
( ) ( ) j tF f t e dt
(3.7)
and f(t) is called the inverse Fourier transform of F(), which is defined as
1( ) ( )2
j tf t F e d
(3.8)
Equations (3.7) and (3.8) are often called the Fourier transform
pair, and they are used to map any function in the interval of (-∞, ∞) in time
or frequency domain into a continuous function in the inverse domain. The
key property of the Fourier transform is its ability to examine a function or
waveform from the perspective of both the time and frequency domains.
A given function can have two equivalent modes of representations: one is in
the time domain and is called f(t), and the other is in the frequency domain
and is called F(). Equation (3.7) transforms the time function into a
frequency spectrum, and (3.8) synthesizes the frequency spectrum to regain
the time function.
3.2.3 Fast Fourier Transform (FFT) Analysis of Harmonic
Waveform
To characterize the waveforms generated by nonlinear loads, signal
processing of the harmonic load current waveforms need to be performed.
The FFT is one of the traditional techniques widely applied in harmonic
analysis because of its effectiveness in computing harmonic distortion
components of a current waveform (Azah Mohamed et al 2006). The total
42
harmonic distortion (THD), crest factor, distortion or form factor and power
factor which can be computed using FFT analysis are useful factors for
quantifying harmonic distortions. Mathematically, the total harmonic
distortion (THD) in terms of current is given by,
12 2
1
( )nITHD
I (3.9)
where, I1 - Fundamental component of the current
In - Current harmonic component.
The THD normally varies from a few percent to 100% for current
and less than 5% for voltage. In an electrical distribution system, a voltage
THD of 5% or less is considered acceptable. Two other measures of distortion
are the crest and the form factors. The crest factor is the ratio of the peak of a
waveform to its RMS value:
_ ( ) peak
rms
ICrest Factor CF
I (3.10)
where Ipeak - Peak value of the harmonic waveform
Irms - RMS value of the harmonic waveform
The form or distortion factor on the other hand, is the ratio of the
RMS value of a waveform to the RMS of the waveform’s fundamental value
which is given by:
1
_ ( ) rmsIForm Factor FFI
(3.11)
where rmsI = RMS value of a harmonic waveform,
1I = RMS of the waveform’s fundamental value
43
3.3 FRACTAL ANALYSIS OF HARMONIC WAVEFORM
In recent years, fractal techniques have attracted increased attention
as a tool for signal processing. The method has been suggested in many
applications as an alternative for analyzing time-varying signals where other
techniques have not achieved the desired results (Crownover 1995). Fractal
theory is an extension of the classical geometry that can be used to make
precise models of physical structures (Barnsley 1993). Fractal analysis can be
useful for representing the nonlinear load harmonic current waveforms in
terms of fractal features through the computation of fractal numbers. Different
concepts of fractal geometry are available for quantization of chaotic behavior
of nonlinear systems. The fractal technique provides both time and spectral
information of the nonlinear load harmonic patterns. The analysis results
shows that the various harmonic current waveforms can be easily identified
from the characteristics of the fractal features. This investigation proves that
the fractal technique is a useful tool for identifying harmonic current
waveforms and forms a basis towards the development of the harmonic load
recognition system. Apart from increased speed, accuracy or efficiency, the
features of the new method as compared to the other existing techniques are:
1. The approach is able to present both fractals and time
information simultaneously.
2. It is very effective in monitoring time-varying signal dynamics
making it easier to locate the area of interest for proper
investigation.
3. It can be widely applied to localize various disturbance
waveforms for better visualization of the signal characteristics
4. It is a suitable candidate for pattern recognition of the various
load harmonic waveforms.
44
The algorithm has been well tested on data sets ranging from a few
hundreds to tens of thousands of data points. Fractals are often studied with
the aid of fractal dimension. Fractal dimension is a measure of the
“convoluted ness" or “degree of meandering" of the fractal set. The following
method presents a fast and simple way of estimating the fractal dimension of
a waveform (in the plane) (Pe 2003). The term waveform refers to the shape
of a wave, usually drawn as instantaneous values of a periodic quantity versus
time. In practice, a waveform is represented by a finite sample of N points,
,.....1:),( NiyxW ii . To estimate the fractal dimension D of the wave-
form ,.....1:),( NiyxW ii , W is first normalized using the equations
(3.12) and (3.13).
*
max
ii
xxx
(3.12)
* max
max min
ii
y yyy y
(3.13)
Here maxx , maxy denote the maximum values of the numbers xi,
iy respectively, and miny denotes the minimum of the numbers iy . The fractal
dimension D can be estimated using the formula,
*
ln( )1ln(2 )
LDN
(3.14)
where L is the length of the normalized wave-form W, and N* = N - 1. L is
easily calculated by repeated application of the distance formula on ),( **ii yx
and ),( *1
*1 ii yx , 1N,.....2,1ifor , that is
*
* * 2 * * 21 1
1( ) ( )
N
i i i ii
L x x y y
(3.15)
45
The process is quantified in terms of fractal numbers which is
derived using the equation (3.16).
2
1
2
1
N l
j k jj
N l
j l jj
y yF
y y
(3.16)
where, F is the fractal number of thm data set mS containing data points, k and
l are small integer sampling steps size which specifies the time interval
between close data points, such that l is greater than k. For the effectiveness
of the equation, different norms can be selected, however for this particular
work, the Euclidean norm is used due to its simplicity. The fractal number
computation turned out to be more efficient in this case if the ratio l to k is not
an integer. The data points have to be properly classified such that data points
belonging to k-step sampled subsets do not fall into the l-step subsets (Umeh
et al 2004).
3.4 DESIGN OF THE EXPERT SYSTEM FOR
IDENTIFICATION OF HARMONICS
For harmonic measurements of the nonlinear loads, harmonic
waveforms were obtained from single phase full converter (AC-DC), three
phase fully controlled converter (AC-DC), and single phase inverter
(DC-AC). The converters mentioned above were simulated using SIMULINK
in MATLAB. Harmonic measurements were performed to obtain data for
identification of harmonic loads. Hardware circuits are fabricated to verify the
performance of the algorithm developed. The proposed expert system is
designed in such a manner that the user can recognize typical harmonic
46
features of nonlinear loads and its structure is as shown in Figure 3.1. The
system consists of attribute extraction module and expert system development
module. The procedure involved in the development of the expert system is:
1. to determine the type of nonlinear loads.
2. to extract the current signatures or empirical features of the
nonlinear loads using FFT and fractal analyses.
3. to transfer the features in terms of knowledge base into a set of
computer programs.
4. to validate the developed expert model.
Figure 3.1 Structure of the expert system for identification of
harmonics in nonlinear loads
In the implementation of the expert system, considerations are
given to the preparation of data used in the formation of rules and in the
development of the graphical user interface (GUI). The attribute extraction
47
module is meant for pre-processing of the harmonic current waveforms using
FFT and Fractal analysis is shown in Figure 3.2. In the pre-processing stage,
unique characteristic features of harmonic current waveforms are extracted by
means of harmonic decomposition and fractal number computations. The
parameters namely, RMS current, total harmonic distortion, crest factor, form
or distortion factor, percentage of individual harmonic distortions, minimum,
maximum and the average value of the fractal number computations are
computed. The extracted features are then used as inputs into the expert
system.
Figure 3.2 Attribute extraction module
The knowledge base is poised of a set of rules in the form of
expertise knowledge from an elaborate analysis of the extracted features. The
rules are in the form of IF-THEN-ELSE description as suggested by Ibrahim
et al (1999). The ‘IF’ statement developed expert system comprises the
characteristic feature of various single phase nonlinear loads. The THEN part
Fractal Number
Computation
Individual Harmonic distortion calculation
Total Harmonic Distortion
Calculation
Crest factor Calculation
Form factor Calculation
Input to Expert System
Fractal Analysis
Fourier analysis (FFT)
Power Electronic Converter
Harmonic waveform generation
48
consists of a particular load or load composition matching the IF statement,
while the ELSE part acts as activation to the next rule. To formulate rules,
strict threshold values are set for each converter type or each combination of
converters. This is achieved by a comprehensive analysis and comparison of
derived features from each type of nonlinear load. The experimental data for
training and evaluation of the system are acquired by harmonic currents
generated by using the single phase and three phase fully controlled
converters at various firing angle, and single phase voltage source inverter.
Examples of the derived rules for single phase fully controlled
converter are described as follows:
Rule: 1 Firing Angle = 36o
IF
3rd Harm > 5th Harm &
7th Harm < 9th Harm &
13th Harm > 15th Harm &
19th Harm < 21st Harm &
22nd Harm < 20th Harm &
THD >10.95 &
THD < 16.5 &
Crest Factor > 1.43 &
Crest Factor < 1.45 &
Form Factor > 0.7 &
Form Factor <.72 &
Fractal Number Mean > 50 &
Fractal Number Mean < 55
THEN
Single phase full converter RL load at α=36o
49
Rule: 2 α = 60o IF
3rd Harm > 5th Harm &
7th Harm < 9th Harm &
13th Harm > 15th Harm &
19th Harm < 21st Harm &
22nd Harm < 20th Harm &
THD > 31.5 &
THD < 31.7 &
Crest Factor > 1.6 &
Crest Factor < 1.62 &
Form Factor > 0.73 &
Form Factor < 0.75 &
Fractal Number Mean > 45 &
Fractal Number Mean < 50 &
THEN
Single phase full converter RL load at α=60o
3.5 CREATING GRAPHICAL USER INTERFACE
In the MATLAB, Graphical User Interface Development
Environment (GUIDE), provides a set of tools for creating Graphical User
Interfaces (GUIs). These tools greatly simplify the process of designing and
building of GUIs. GUI is developed using the GUIDE layout editor, easily by
clicking and dragging the components such as panels, buttons, text fields,
sliders, menus, and so on into the layout area. To program the GUI, GUIDE
automatically generates an M-file that controls the operation of GUI
(www.mathworks.com). The M-file initializes the GUI and contains a
framework for all the GUI callback the commands that are executed when a
user clicks a GUI component. Using the M-file editor, one can add code to the
callbacks to perform the functions want to do.
50
3.5.1 Graphical User Interface Development Environment (GUIDE)
To start GUIDE, enter guide at the MATLAB command prompt.
This displays the GUIDE Quick Start dialog, as shown in Figure 3.3. From
the Quick Start dialog, one can,
1. Create a new GUI from one of the GUIDE templates - Prebuilt
GUIs that can be modifying for own purposes.
2. Open an existing GUI. It can be selected one of these options,
clicking OK opens the GUI in the Layout Editor
Figure 3.3 Graphical User Interface Development Environments
(GUIDE) quick start
3.5.2 Layout Editor
When open a GUI in GUIDE, it is displayed in the Layout Editor,
which is the control panel for all of the GUIDE tools. The following figure
shows the Layout Editor with a blank GUI template. Layout the GUI by
dragging components, such as push buttons, pop-up menus and axes from the
51
component palette at the left side of the Layout Editor into the layout area.
For example, drag a push button into the layout area; it appears in the layout
area Figure 3.4 shows the layout editor -control panel.
Figure 3.4 Layout editor-control panel
3.5.3 Running a Graphical User Interface (GUI)
To run a GUI, select Run from the tools menu, or click the run
button on the toolbar. This displays the functioning GUI outside the Layout
Editor ( ). GUIDE stores a GUI in two files, which are generated the first
time saved or run the GUI: A figure file, with extension.fig, which contains a
complete description of the GUI layout and the components of the GUI: push
buttons, menus, axes, and so on. The M-file with an extension.m, which
contains the code and callbacks that are controls the Graphical User Interface
(GUI). When the GUI is laid out in the Layout Editor, work is stored in the
FIG-file. When the GUI is programmed, work is stored in the M-file.
52
After laying out GUI, program the GUI M-file using the M-file
editor. GUIDE automatically generates this file from the first time save or run
the GUI. The GUI M-file
1. Initializes the GUI.
2. Contains code to perform tasks before the GUI appears on the
screen, such as creating data or graphics.
3. Contains the callback functions that are executed each time a
user clicks a GUI component.
Initially, each callback contains just a function definition line. Then
use the M-file editor to add code that makes the component function the way
want it to. To open the M-file, click the M-file Editor icon on the Layout
Editor Toolbar.
3.5.4 Development of Graphical User Interface
A graphical user interface (GUI) program has been developed in
MATLAB to allow communication between a user and the expert system.
Initially, an input current waveform or voltage waveform is generated using
Simulink model. The developed Graphical User Interface model is shown in
Figure 3.5. The interface illustrates the entire identification process
dynamically in which at a click of the “RUN” button, the load composition
exhibits the characteristic features of the input current waveform together
with a display of harmonic attributes of waveform. The displayed attributes
include the individual harmonic contents from third harmonic up to the
twenty-third harmonic, the current THD, crest factor, form factor, power
factor, RMS values of source voltage and output voltage and RMS values of
source current and output current. By selecting the “FFT plot” button, a FFT
analysis of the current waveform is performed; crest factor, form factor,
53
power factor and FFT plot are displayed. Likewise, by selecting the “Fractal”
button fractal plot and fractal numbers are displayed.
Figure 3.5 The developed expert system output model
3.6 TESTING OF THE EXPERT SYSTEM, RESULTS AND
DISCUSSION
The developed expert system model identifies and estimates the
harmonic levels for different types of nonlinear loads from its distorted supply
current and load voltage. The expert system is tested for single phase, three
phase fully controlled converters and single phase voltage source inverter.
The simulation results are compared with the developed hardware
experimental results for the following cases.
3.6.1 Single Phase Fully Controlled Converter Feeding RL Load
The single phase fully controlled converter feeding RL load with
the following specifications is considered for testing: Supply Voltage (Vs)
=230V, Firing Angle =36o, Load Resistance(R) =153 Ω, Load Inductance
54
(L)=0.328H. The simulink model for the single phase fully controlled
converter is shown in Figure 3.6. The results of the developed Graphical User
Interface are shown in Figure 3.7. The hardware test setup is shown in
Figure 3.8. The supply current waveform and harmonic spectrum of the
hardware is shown in Figure 3.9 and Figure 3.10 respectively. Comparative
results of simulation and hardware are shown in Table 3.1. Table 3.2
represents the comparison of important parameters for different firing angles.
Figure 3.6 Simulink model for the single phase fully controlled converter
Figure 3.7 Results of the developed graphical user interface for single
phase fully controlled converter
55
Figure 3.8 Hardware test setup of single phase fully controlled converter
Figure 3.9 Supply current waveform of single phase fully controlled converter
Figure 3.10 Harmonic spectrum of supply current of single phase fully controlled converter
56
Table 3.1 Comparative results of harmonic levels in single phase fully
controlled converter for a firing angle α=36o
Harmonic Order Power GUI
in MATLAB Real time
PQA* Expert System
(GUI)# THD % 26.00 23.4 24.61
Fundamental 100.00 100.00 100.00 3 25.71 21.20 16.58 5 3.30 8.00 2.75 7 1.21 4.20 1.35 9 0.69 2.80 0.52
11 0.52 1.40 0.68 13 0.38 1.00 0.15 15 0.52 0.70 0.30 17 0.14 0.30 0.17 19 0.13 0.70 0.18 21 0.15 0.80 0.15 23 0.13 0.80 0.21
*Power Quality Analyzer Readings
#-Develop Graphical User Interface Results
Table 3.2 Comparison of performance parameters in single phase
fully controlled converter
Sl. No.
Performance Parameter
Firing Angle (in degrees) 18o 36o 54o 72o
Expert System
Hardware Results
Expert System
Hardware Results
Expert System
Hardware Results
Expert System
Hardware Results
1. THD 11.95 10.80 24.61 23.40 32.63 31.10 40.23 39.10 2. Crest Factor 1.26 1.64 1.26 1.64 1.38 1.78 1.62 2.01 3. Power Factor 0.95 0.94 0.93 0.94 0.86 0.84 0.78 0.76
The total harmonic distortion of the single phase fully controlled
converter for the expert system is 24.61% and for the developed hardware is
23.4% according to Table 3.1. The important performance parameters of the
57
converter are compared in Table 3.2 and the readings are very close to the
hardware results. Hence the results obtained in the simulation and hardware is
found to be satisfactory.
3.6.2 Three Phase Fully Controlled Converter Feeding Resistive
Load
The three phase fully controlled converter feeding resistive load
with the following specifications is considered for testing: SupplyVoltage
(Vs) =400 V, Firing Angle =30o, Load Resistance(R) = 1000 Ω. The simulink
model for the three phase fully controlled converter is shown in Figure 3.11.
The results of the developed Graphical User Interface are shown in
Figure 3.12. The hardware test setup is shown in Figure 3.13. The supply
current waveform of the hardware is shown in Figure 3.14. Comparative
results of simulation and hardware are shown in Table 3.3. Table 3.4
represents the comparison of important parameters for different firing angles.
Figure 3.11 Simulink model for the three phase fully controlled converter
58
Figure 3.12 Results of the developed graphical user interface for three
phase fully controlled converter
Figure 3.13 Hardware test setup of three phase fully controlled converter
59
Figure 3.14 Supply current waveform of the three fully controlled
converter (for firing angle α=30o)
Table 3.3 Comparative results of harmonic levels in three phase fully controlled converter for a firing angle α=30o
Harmonic Order Power GUI in Matlab
Real time PQA*
Expert System (GUI)#
THD % 37.82 34.11 33.92 Fundamental 100.00 100.00 100.00
3 0.01 0.14 0.01 5 28.28 26.32 27.67 7 14.70 12.92 12.30 9 0.01 0.14 0.01
11 12.67 10.96 10.45 13 9.29 8.21 7.89 15 0.01 0.14 0.01 17 8.65 6.92 7.30 19 6.94 6.14 5.86 21 0.01 0.14 0.01 23 6.64 5.53 5.25
* - Power Quality Analyzer Readings
#-Develop Graphical User Interface Results
60
Table 3.4 Comparison of performance parameters of three phase fully
controlled converter
Sl. No.
Performance Parameter
Firing Angle (in degrees) 0o 30o 45o 60o
Expert System
Hardware Results
Expert System
Hardware Results
Expert System
Hardware Results
Expert System
Hardware Results
1. THD 11.95 10.80 24.61 23.40 32.63 31.10 40.23 39.10 2. Crest Factor 1.26 1.64 1.26 1.64 1.38 1.78 1.62 2.01 3. Power Factor 0.95 0.94 0.93 0.94 0.86 0.84 0.78 0.76
The total harmonic distortion of the three phase fully controlled
converter for the expert system is 33.92% and for the developed hardware is
34.11% according to Table 3.3. The important performance parameters of the
converter are compared in Table 3.4 and the readings are very close to the
hardware results. Hence the results obtained in the simulation and hardware is
found to be satisfactory.
3.6.3 Single Phase Voltage Source Inverter Feeding Resistive Load
The single phase voltage source inverter feeding resistive load with
the following specifications is considered for testing: Supply Voltage (Vs)
=230V DC, Load Resistance(R) = 400 Ω. The simulink model for the single
phase is voltage source inverter shown in Figure 3.15. The hardware test setup
is shown in Figure 3.16. The results of the developed Graphical User Interface
are shown in Figure 3.17. The output voltage wave form and harmonic
spectrum of the hardware is shown in Figures 3.18 and 3.19 respectively.
Comparative results of simulation and hardware are shown in Table 3.5.
61
Figure 3.15 Simulink model for the single phase voltage source inverter
Figure 3.16 Hardware test setup for the single phase voltage source
inverter
62
Figure 3.17 Results of the developed graphical user interface for single
phase voltage source inverter
Figure 3.18 Output voltage waveform of the single phase voltage source
inverter
63
Figure 3.19 Harmonic spectrum of the output voltage waveform of the single phase voltage source inverter
Table 3.5 Comparative results of individual harmonic levels of single
phase voltage source inverter
Harmonic Order Power GUI in Matlab
Real time PQA*
Expert System (GUI)#
THD % 46.25 47.00 46.89 Fundamental 100.00 100.00 100.00
3 33.34 33.33 33.28 5 20.00 20.00 20.02 7 14.29 14.30 14.26 9 11.12 11.10 11.13
11 9.10 9.10 9.13 13 7.71 7.70 7.69 15 6.68 6.70 6.72 17 5.90 5.90 5.90 19 5.28 5.20 5.21 21 4.78 4.70 4.73 23 4.37 4.30 4.32
* - Power Quality Analyzer Readings
#-Develop Graphical User Interface Results
64
The total harmonic distortion of the single phase voltage source
inverter for the expert systems is 46.89% and for the developed hardware is
47.00% according to Table 3.5. Hence the results obtained in the simulation
and hardware is found to be satisfactory.
3.7 CONCLUSION
In this chapter, an improved model is proposed to identify the
harmonic distortion produced by the different types of power electronic
converters. The rules are derived to identify harmonics produced by single
phase, three phase fully controlled AC-DC converters, and single phase
voltage source inverters. The proposed model provides automatic and
intelligent identification of harmonic sources originating from power
electronic converters loads by classifying the different types of nonlinear
loads that contribute harmonics to the supply system and then quantifying the
harmonic distortion levels of each type of load. FFT and Fractal analyses of
the current waveforms of the nonlinear loads have been carried out to obtain
the harmonic characteristic features of the loads. Each type of load is
represented by its total harmonic distortion, crest factor, form factor, power
factor, individual harmonic distortions with respect to fundamental and the
average value of the fractal number. The process of identifying the various
types of nonlinear loads is automated by developing a rule-based expert
system. The system is verified and found to be accurate in identifying the
respective nonlinear load type from the observed hardware current/voltage
waveform. The developed expert system also incorporates a graphical user
interface program, which can be used in a user-friendly and interactive
environment.