L~ARMONIC
CURRENTS GENERATED BY PERSONAL COMPUTERS,
THEIR EFFECTS ON THE POWER SYSTEM AND
METHODS OF HARMONIC REDUCTION;
A Dissertation Presented to
The Faculty of the Russ College of Engineering and
Technology
Ohio University
In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy
by
Hrair
~jntablianl
June, 1994
i
TABLE OF CONTENTS
Page
Chapter One:
Int~oduction
.
Chapter Two: Review of Recent Literature
.
1
8
Chapter Three: The Nature of Harmonic Currents and their
Effects on the Distribution System Neutral Current
3.1
Time-domain Analysis
3.2
Changing the Values of Circuit Parameters
C
12
and L
16
3.3
Harmonic Current Measurement
20
3.4
Time and Frequency Domain Measurements of
Input Currents of PC's
3.4.1 Monitor and Computer Currents Measured
Separately
.
26
3.4.2 Personal Computer Input Current Measurement
Results
3.5
31
The Magnitudes of the Harmonic Currents and
the Neutral Current
23
Chapter Four: Effects of Personal Computer Harmonics on
the Distribution Transformer
4.1
Harmonic Current Effects on Transformer
Losses
4.2
4.3
42
Harmonic Analysis of the Transformer
Circuit
46
Three-phase Transformer Connections
54
ii
Page
Chapter Five: Harmonic Reduction
5.1
Neutral Current Reduction
58
5.2
Common.l y Used Methods of Harmonic
Elimination
5.3
59
A New Single-phase AC to DC Harmonic Reduction
Converter Based on the Voltage-doubler Circuit
5.3.1
Description and Analysis of the
Proposed Circuit
5.3.2
65
Laboratory Verification of the
Propas e d C.i r cui t
72
Chapter Six: Conclusions and Recommendations for Further
Research
78
Appendix 1 The HP 3561A™ Spectrum Analyzer
84
Appendix 2 PSpice Programs_
94
References
Abstract
. . . . . . . . . . ..
102
iii
LIST OF SYMBOLS AND ABBREVIATIONS
Symbol
Description
a
Transformer turns ratio
ac
Alternating current
C
Capacitance
DPF
Displacement power factor
fl
Transformer delta connection
EMI
Electromagnetic interference
dc
Direct current
f
Frequency
fh
Normalized harmonic current
h
Harmonic number
if
I
Current
i1
Transformer primary current
i2
Transformer secondary current
ic
Capacitor current
im
Transformer magnetization current
i2
Resistor current
II
Fundamental current
I
Harmonic current
h
In
Neutral current
Ip
Phase current
Is
Supply current
L
Inductance
pu
Per unit
iv
PEe
Transformer eddy current loss
PF
Power factor
P LL
Transformer total load loss
POS L
Transformer Stray loss
Q
Bipolar transistor
rms
Root mean square
R
Resistance
t}
First conduction period of switch
t2
Secon~
THD
Total harmonic distortion
V,
V
conduction period of switch
Voltage
VC
Capacitor voltage
VH
Higher limit of voltage
v:
Input voltage
VL
Lower limit of voltage
Vo
Output Voltage
~
Radian frequency
y
Transformer wye connection
Z
Impedance
v
LIST OF TABLES
Table
3.1
Page
Magnitudes of harmonic currents of various PC's
in rnA ••.••••••••••••••.••••••••••....•.........
40
4.1
Harmonic composition of non-linear load........
44
4.2
Non-linear load current in pu
45
4.3
Example parameters of equation 4.2
~..
45
vi
LIST OF FIGURES
Figure
Page
1.1 Phase and neutral currents of a balanced
sinusoidal three-phase load
5
1.2 Phase and neutral currents of a balancednon-sinusoidal three-phase load
3.1 Equivalent circuit of bridge rectifier.........
6
12
3.2 Theoretical voltage and current waveforms for
C=0.5 mF, 1=1 mH and R= 100
0...................
13
3.3 Theoretical voltage waveform for C=l mF,
1=1 mH and R=100
0...................... ... . . . . . .
16
3.4 Theoretical current waveform for C=0.5 mF,
1=1 mH and R=100
0..............................
17
3.5 Theoretical current waveform for C=l mF,
1=1 mH and R=100
0..............................
17
3.6 Theoretical current waveform for C=0.5 mF,
1=2 mH and R=100
0..............................
19
3.7 Theoretical voltage waveform for C=0.5 mF,
1=2 mH and R=100
0..............................
20
3.8 Theoretical current waveform for C=0.5 mF,
1=10 mH and R=100
0.............................
21
3.9 Theoretical voltage waveform for C=0.5 mF,
a.............................
21
3.10 A square wave...................................
22
3.11 Magnitude spectrum of a square wave
23
L=10 mH and R=100
vii
Figure
Page
3 .12 Measurement Equipment
.
25
3.13 Measured monitor & computer waveforms of
Compaq Prolinea 4/50
27
™ ••••••••••••••••••••••••••
3.14 Measured monitor & computer current magnitude
spectra of Compaq Prolinea 4/50 ™
.
27
.
28
3.15 Measured monitor & computer current phase
spectra of Compaq Prolinea 4/50 ™
3.16 Measured current waveform of Compaq Prolinea
4/50™
(monitor + computer)
.
29
.
29
.
30
••••••••••••••••••••••••••••••••••••••••
30
3.17 Measured current magnitude spectrum of Compaq
Prolinea 4/50 ™ (moni tor + compu ter)
3.18 Measured monitor current waveform of IBM
PS2/30™
3.19 Measured computer current waveform of IBM
PS2/30 ™
3.20 Measured monitor & computer current phase
spectra of IBM PS2 / 3 0
™
•••••••••••••••••••••••••
3.21 Measured current waveform of Mac IIsi
31
™ ..•.•••.
32
••••••••••••••••••••••••••••••••••••••
32
3.22 Measured current magnitude spectrum of
Mac I I si ™
3.23 Measured current phase spectra of two
Mac IIsi TMI s
33
3.24 Measured current magnitude spectrum of two
Mac IIsi TMI s and that of one Mac IIsi
™
••••••••••
33
viii
Figure
Page
3.25 Measured current waveforms of various PC's
34
3.26 Measured current waveforms of various PC's
35
3.27 Measured current magnitude spectrum of IBM XT
TM
measured current magnitude spectrum of Mac IIsi
3.28 Measured current phase spectrum of IBM XT
TM
measured current phase spectrum of Mac IIsi
3.29 Measured magnitude spectrum of IBM XT
Mac IIsi™ run simultaneously
r
and
'I'M
and
36
TM
and
...................
3.30 Measured magnitude spectrum of IBM XT
r
37
vs.
measured magnitude spectrum of IBM PS2/30
3.31 Measured current phase spectrum of IBM XT
measured current phase spectrum of
36
37
TH
TM
vs.
IBM PS2/ 3 a
TM
38
.....................
38
3.32 Measured magnitude spectrum of IBM XT ™ and
IBM XT™ run simultaneously
4.1 Transformer PSpice model with nonlinear
rectifier load..................................
47
4.2 Transformer current waveforms with ,non-sinusoidal
load obtained by PSpice
48
4.3 Transformer magnitude current spectra with
non-sinusoidal load obtained by PSpice
49
4.4 Measured current waveforms of transformer with
1 PC load
50
4.5 Measured current magnitude spectra of transformer
with 1 PC load..................................
50
ix
Figure
Page
4.6 Phases of i z and i
m
obtained by PSpice
4.7 Measured phases of i z and i
m
.
51
•••••••••••••••••••
52
4.8 Transformer current waveforms with increased
nonsinusoidal load obtained by PSpice
.
53
.
53
4.9 Measured current waveforms of transformer with
3 PC load
4.10 Y-Y connected transformer
.
54
4.11 a-Y connected transformer
.
55
4.12 Current magnitude spectra of Y-Y transformer
56
4.13 Current magnitude spectra of
57
AY transformer
5.1 Transformer with tertiary windings to reduce
the neutral current
.
59
5.2 A parallel-connected series resonant LC filter
in the bridge rectifier circuit
5.3
A
.
60
.
61
series-connected parallel resonant LC filter
in the bridge rectifier circuit
63
5.4 Bridge rectifier circuit with' boost converter
5.5 Input current waveform of the boost converter
obtained by PSpice
.
64
.
65
.
66
5.6 Input current magnitude spectrum of the boost
converter obtained by Pspice
5.7 Schematic of the proposed harmonic reduction
circui t
Figure
Page
5.8 Schematic of uncompensated bridge-rectifier
circui t
67
5.9 Input current waveform of uncompensated bridgerectifier circuit simulated by Pspice
67
5.10 Input current waveform of the proposed circuit
obtained by Pspice
68
5.11 Magnitude spectrum of input current of bridgerectifier obtained by PSpice
70
5.12 Magnitude spectrum of the current of the proposed
harmonic reduction circuit obtained by Pspice
70
5.13 Theoretical current waveform of the proposed
harmonic reduction circuit......................
71
5.14 Laboratory circuit
73
5.15 Control circuit voltages.......................
74
5.16 Laboratory waveform of input current without
harmonic reduction
75
5.17 Measured magnitude spectrum of input current
waveform without harmonic elimination
75
5.18 Laboratory waveform of input current with harmonic
reduction: switch conduction period =1.35 ms
76
5.19 Measured magnitude spectrum of input current
waveform with harmonic elimination: switch
conduction period =1.35
IDS
••••••••••••••••••••••
76
xi
Figure
Page
5.20 Laboratory waveform of lnput current with harmonic
reduction: switch conduction period =0.87 ms
77
5.21 Measured magnitude spectrum of input current
waveform with harmonic elimination: switch
conduction period =0.87 ms
77
1
Chapter One
Introduction
In recent years there has been a growing concern for
power system distortion due to the increasing numbers and
power ratings of non-linear power electronic devices.
Power
system distortion is generally expressed in terms of harmonic
components.
Harmonic currents and/or voltage$ are present on
an electrical system at some mul tiple of the
frequency
(normally 60 Hz).
Typical values
are
fundamental
the
third
harmonic component (180 Hz), the fifth harmonic component (300
Hz), the seventh harmonic component (420 Hz), and so on.
In
converting ac power to dc power a converter chops the ac
current waveform by allowing it to flow only during a portion
of a cycle. The ac current waveform represents a· distorted
sinusoidal waveform that can be separated into its components
using Fourier analysis.
One of the problems caused by harmonic currents is
waveform distortion.
voltage
Other problems due to harmonic currents
are interference with communication signals, excessive losses
and heating in motors and transformers, excessive distribution
neutral current, errors in power measurements, malfunction of
protecti ve relays,
and resonance condi tions a t
a bus tha t
contains a harmonic source and where power factor correction
capacitors are connected.
In addition, a harmonic load can
2
draw power from the supply at a very low
sinusoidal
voltage
systems
the
power factor.
power
factor
at
For
which
equipment operates is given by equation 1.1 where PF is the
power factor, DPF is the displacement power factor, II and Is
are the fundamental and the rms supply currents respectively.
I
PF=_l.DPF
Is
(Eq 1.1)
The DPF is defined as the cosine of the phase angle between
the fundamental components of the supply vol tage and
supply current.
A
the
large harmonic distortion in the supply
current results in a small ratio II/Is and hence a low PF,
even though the DPF might be close to unity.
Power converters (rectifiers and invertors) are major
sources of harmonic currents. These converters can be grouped
according
to
their
harmonic
following categories [1]:
current
behavior
into
the
(i) large power converters such as
high vol tage dc transmission convertors;
(i i)
medi urn size
convertors such as those used in the manufacturing industry
for motor
control;
(iii)
single-phase rectifiers in
has been focused on
low power converters such as the
television sets.
Much attention
large power converters as sources of
harmonics due to the high magnitudes of the currents involved ..
Nevertheless,
harmonics generated by low power converters
become significant when large numbers of converters are used
simultaneously.
3
The major problems associated with the harmonic currents
generated by personal computers are excessive neutral currents
and additional transformer losses in the form of eddy current
losses.
Chapter two gives a brief overview of the recent
Li terature on
this subj ect.
Chapter three identifies the
harmonics in input currents of personal computers and explores
the following:
1. The harmonic currents that are present and their magnitudes
relative to
the fundamental frequency component.
2. The harmonic currents if the
monitor current is measured
separately from the computer.
3. Differences in the harmonic currents among various types of
personal computers.
4.
The
magni tude
magnitude of the
of
the
third harmonic
current
and
the
resulting neutral current.
5. Any cancellations in harmonic currents if various computers
are
active simultaneously.
The power supplies employed in most personal computers are
of the switching mode type. In a switching mode power supply,
the 60 Hz ac voltage is converted into de through a singlephase diode bridge rectifier and the output voltage of the
rectifier is stepped down using a dc to dc converter. The main
advantage
of
the
switching
mode
power
supply
over
the
traditional linear power supply is its high energy efficiency
since the switching elements used (BJTs, MOSFETS) are either
completely off or completely on.
4
The third harmonic current (and other triplen harmonics )
present in the input current of a personal computer is of
utmost concern to the power engineer.
Third harmonic currents
in each phase of a 3-phase system add in phase in the neutral
wire. Balanced non-sinusoidal three-phase loads can result in
significant neutral currents as illustrated in figures 1.1 and
1.2.
The main problem associated wi th excessi ve neutral currents
is the overheating of the neutral wire.
This can be hazardous
in an office building that has computers and other nonlinear
loads and where the neutral conductor is designed to handle
only low levels of neutral currents arising mainly from small
phase imbalances.
In chapter four the impact of harmonic currents of personal
computers on distribution transformer losses
is explored.
Also, the influence of the three-phase transformer connection
on the distribution system neutral current is examined.
distribution
transformer
that
suppli-es
power
to
The
office
buildings is subj ect to the harmonic currents of pe r soria I
computers
resul t
and other electronic
loads.
Harmonic currents
in the overheating of transformer windings due- to
excessive eddy current losses.
Chapter five briefly outlines methods of neutral current
and harmonic current reduction.
It then introduces a new
single-phase harmonic reduction circuit based on line-
5
0.5
-=
~
0
-0.5
-1
e
2
0
IS
,...
12
10
18
18
Tlrn_ (rna)
0.5
aa
I
0
-0.5
&:5
0
2
0
2
II
10
12
'4
1S
'S
II
10
12
14
18
1S
u
I
0
-0.5
..
-1
"rn_ (rna)
0.5
I
~
0
-o.~
....
-1
0
2
e
e
10
12
14
18
18
Figure 1.1: Phase and neutral currents of a balanced
sinusoidal three-phase load
6
1.5
0.5
-=
I
0
-0.5
-1
~
-1.&5
0
2.
•
•
10
12
1.5
-
0.5
o
-
-0.&5
-
-1.8
o
•
It
•
•
Tl,..,.,.
10
12
115
'8
C,..,.,.)
1.8
,
~
0.11
~
~
I
O~
- 0 . 5 --1
-1.a
0
:&
10
12
, ...
1.
18
1.a
a.a -
i
0
-0.0
-
~
-
I-
-
-,
-1.15
a
•
10
'2
, ....
115
,.
Figure 1 .2: Phase and neutral currents of a balanced nonsinusoidal three-phase load
7
frequency operation using the voltage-doubler circuit with an
addi tional
swi tch.
Theoretical
and
simulation
resul ts
depicting the input current waveform of the new circuit and
its harmonic currents are presented.
Finally,
the proposed
circuit is tested in a laboratory setting and experimental
results are discussed.
In chapter six conclusions are drawn
and recommendations are made for further research.
This dissertation offers three main original contributions
to
understanding
the
harmonic
currents
due
to
computers and their effects on the power system.
contribution
is
the
identification
of
personal
The first
personal
computer
harmonic currents and their roles in generating distribution
system
neutral
con t r i bu t Lon
analysis
of
three).
the
effects
The
second
personal
computer harmonics on the distribution transformer
(chapter
current
the
(chapter
of
four).
is
currents
The third contribution is a new circuit for harmonic
reduction
(chapter five).
based
on
the
voltage-doubler
circuit
8
Chapter Two
Review of Recent Literature
Prior to the development of power electronic convertors
harmonics were associated with electric machines and
transformers.
With the development and increased usage of
rectifiers in power supplies and motor drives, harmonicrelated problems have increased in power systems.
The television set has been a source of harmonic
currents.
capacitor.
It is supplied by a rectifier and a smoothing
Since modern television sets use full-wave
rectification the supply current is rich in odd-order
harmonic currents [2].
The harmonic currents from different
television sets reinforce one another.
At peak viewing
periods such as the Superbowl the harmonics reach 'peak
values and they can have catastrophic consequences on the
neutral conductor and the distribution transformer.
Another source of harmonics is the battery charger for
use with electric vehicles.
Most battery chargers use
controlled or uncontrolled rectifiers with center-tapped
transformers.
The battery charger produces large amounts of
"odd-order harmonics [3].
In common wi th television
receivers and other consumer electronic goods the battery
charger produces high zero sequence triplen harmonic
currents (third, ninth, etc.) which overloads the neutral
9
conductor [3]. Moreover, the phase angles of the harmonic
currents do not vary enough to cause a significant
cancellation when a group of chargers are in operation.
Excessive harmonic currents and hence neutral currents
exist in fluorescent lighting circuits [4].
The harmonic
currents are accounted for by saturation of ballasts and
non-linear lamp arc characteristics.
In a three-phase
system the third harmonic currents are in phase and thus are
added linearly in the neutral conductor.
Measurements on
two building installations has shown that neutral currents
amounted to 75 and 157 percent of the phase currents [4].
To determine the extent of the neutral current problem, a
survey of three-phase computer power system loads was taken
by Liebert Customer Service engineers in 1988 [5].
The
survey included the measurements of the rms phase and
neutral currents at 146 computer sites. The neutral current
is a result of the phase current imbalance and the triplen
harmonic currents.
The neutral current due to phase
imbalance IN (phase-imbalance) is given by [5]:
(Eq.2.1)
where lA' l B and Ie are the magnitudes of the rms phase
currents.
The neutral current due to triplen harmonic
10
currents IN (triplen-currents) can be approximated by equation
2.2 [5]:
.; 2
2
(Eq.
2.2)
I N ( trpilen-currents) = I N - IN (phase-imbalance)
where IN is the neutral current.
For example, if I A=189 A,
I B=193 A, I c=209 A and I N=110 A,
IN(phase-imbalance)
and
IN(triplen-currents)
,=
=
18.33
A
108.6 A
Among the 146 sites surveyed 22.6% of the sites had
neutral current in excess of 100% of the phase current.
is to
It
be noted that this survey did not include building
and office wiring systems which also supply power to
personal computers.
It is well known that switch-mode power supplies can be
designed to provide harmonic-free performance and a great
number of papers have been published dealing with this
subject in the past ten years.
However, in most
applications the economic incentives have not been
sufficient enough to incorporate the harmonic elimination
circuitry in the design [6]. The traditional passive method
of harmonic-reduction of ac to de converters involves
passive series or/and shunt LC filters to reduce the
11
amplitude of one or more of the current harmonics. Of the
active harmonic elimination methods the boost converter
method is considered the most favorable [6]. The weights and
sizes of the components used in the passive method make it
undesirable [1].
A major disadvantage of the active method,
besides its high cost, is the complexity of the control
circuits [7].
12
Chapter Three
The Nature of Harmonic Currents and their Effects on the
Distribution System Neutral Current
3.1: TIME-DOMAIN ANALYSIS
The
equivalent
circuit
of
a
bridge
rectifier
which
represents the input section of a typical power supply
shown in figure 3.1 [8].
voltage and
is
Land C smooth out the output dc
R1 is the load resistance.
L
'--L~~-~
+
======C>
C -'--
i(t)
~ ir(t)
-~
Vs
ic(t) ~
Vc(t)~
-:
RI
Figure 3.1: Equivalent circuit of bridge rectifier
Two modes of operation exist for this circuit. During mode
#1,
the diode is forward biased and the capaci tor charges
through the supply.
During mode #2,
the diode is reverse
biased and the capaci tor discharges through the load.
The
current and voltage waveforms are illustrated in figure 3.2.
13
To find the supply current i(t)
v ; (t),
the
circui t
of
figure
3.1
and the output voltage
is
transient and steady state conditions.
Kirchoff's
examined under hoth
During mode #1, using
laws yields,
d:Zv c ( t) +_1 dvc ( t) +_1 V (t) =_1 V (t)
-d---t-:ZRC
dt
LC c
LC S
(Eq.
3.1)
(Eq.
3.2)
140
<'
~
a
"'D
::J
120
100
80
=c
B'
:::s
60
40
Current
20
0
0
2
3
5
6
7
a
9
10
TIme{msec)
Figure 3.2: Theoretical voltage and current waveforms for
C=O.5 mF, 1=1 mH and R1=100 a
14
In equation 3.2 the second-order differential equation is
solved for vc(t)and from equation 3.1 the response i(t) is
obtained.
The complete response is the sum of the natural
response and the
forced response.
3.3)
(Eq.
where,
(Eq.
3.4)
and
1
a=- 2RC
(Eq.
3.5)
b=~-1c-~
(Eq.
3.6)
2
The constants
K1
and
K2
are determined by applying initial
conditions to-the complete response.
By analyzing the circuit
of figure 3.1 in steady-state the forced response of vc(t) is
obtained as:
15
(Eq.
3.7)
·(Eq.
3.8)
(Eq.
3.9)
where
_
vm4g-vs -
R
-
-
-
-
-
-
-
{ (R-(i)2RCL) 2+ ((i)L) 2
<p=-arctan
.
((i)L)
(R-(i)2 RCL)
During mode #2, the capacitor discharges with a time
constant R x C and
The following initial conditions
find the constants K1 , K2 and K3 :
During mode #1/
Vc{O) = Vc at end of mode #2
<"1(0)
=
0
During mode #2,
Vc{O) = Vc at end of mode #1
are applied in order to
16
3.2: CHANGING THE VALUES OF CIRCUIT PARAMETERS C AND L
In order to reduce the output ripple voltage of a full-
wave rectifier the capacitance of the output filter
capacitor should be increased.
Figure 3.3 shows the output
voltage when the capacitance is doubled to 1 mF. A
comparison of figures 3.2 and 3.3 reveals the reduction in
the ripple voltage.
In addition, increasing the capacitance
makes the input current flatter thus increasing the power
factor.
Figures 3.4 and 3.5 display the input currents of
the rectifier for two different values of C.
120
100
~
80
~
60
~
~
G
:::J
"c
~
D'I
C
::IE
~o ~
-
20
-
~
0
0
2
3
4
5
6
7
8
9
10
Ttme (msec)
Figure 3.3: Theoretical voltage waveform for C=l mF,
1=1 mH and R=lOO 0
17
8
7
6
5
'"
.::s
.,
.a
·c
"0
4
0'
=i
3
2
........--....Io-o-------'
O'------'-----"-----'-""""---.-.......------~--
o
2
3
5
6
7
B
9
10
Tlme(msec)
Figure 3.4: Theoretical current waveform for C=0.5 mF,
L=l mH and R=100 a
7
6
5
g
&)
<4-
""CI
::J
~
c:
D\
D
3
:::Ii
2
O~--"'----""-----~~-~--~-..a..-.~--~--....&.---~---.I
10
2
B
9
o
3
7
5
6
i1rne (rnaec)
Figure 3.5: Theoretical current waveform for C=l mF, L=l mH
and R=lOO C
18
The ripple voltage can be expressed by the following
approximate formula [9]:
I
V=I
fC
(Eq.
3.11)
where
Vr
I
= peak-to-peak ripple voltage
dc load current
f = ripple frequency
C
capacitance
Vr can be expressed in terms of the output voltage Vd c by
substituting for I = Vd c
/
R .
v
V =--E.£.
I
feR
(Eq.
3.12)
For most applications the ripple voltage is considered
small enough when it is less than 10% of the output voltage.
Therefore,
VI
1
-=--=0.1
Vdc res
and
19
c=
1
1
o .1fR O.lx120xlOO
=833uF
The value of C cannot be increased indefinitely because a
large capacitor acts as a constant dc source.
In the
analysis above the upper limit for C was 2 mF.
The inductance of the output filter has a similar impact
on the output voltage and the input current of the bridge
rectifier.
Figure 3.6 shows the input current and figure
3.7 shows the output voltage when L was increased to 2 mH.
7
6
5
g
I)
4
-c
::1
~
c::
C\
D
:5
::i
2
O~_-----_~
o
2
__
__a....Io..-_-"'----_---I._---'----'
~_----'-_~
3
5
6
7
8
9
10
Time (msec)
Figure 3.6: Theoretical current waveform for C=O.5 mF, L=2
mH and R=100 a
20
120
100
~
-§
;t::::
c:
80
80
I:J'
D
::li
40
20
0
0
2
.:5
4
5
6
7
8
9
10
TIme (maec)
Figure 3.7: Theoretical voltage waveform for C=O.5 mF, L=2
mH and R=lOO 0
In addition to decreasing the ripple voltage, increasing
L increases the pulse-width of the input current and hence
decreases its harmonic content.
Figures 3.8 and 3.9 display
the input current and the output voltage respectively for L
= 10 mH.
The value of L is constrained by its physical size
and its cost.
3.3: HARMONIC CURRENT MEASUREMENT
A regularly shaped waveform (such as a square wave) can
be decomposed into its components by using Fourier analysis.
The equation of the harmonic components of a square wave
having an amplitude of 1 and a period T (Figure 3.10) is
21
...
3.5
3
~
-8
:::I
~
"2.5
2
C
at
:i
1.5
0.5
QL.--_ _'--_----"'---_.-.:;;...,j"---_----&_ _----"_ _----"_ _- . L_ _- - L ._ _- - L ._ _- - - '
o
2
5
3
6
7
8
9
10
Time (ms8c)
Figure 3.8: Theoretical Current Waveform for C=0.5 mF, L=10
mH and R=100 a
120
100
~
-8
::::t
~
C
0'
80
60
C
::IE
40
20
0
0
2
4
5
6
7
B
9
10
Time(msec)
Figure 3.9: Theoretical Voltage Waveform for C=0.5 mF,
L=lO mH and R=100 0
22
Vet)
1
+------t------+----t---------t
-1
---=.:>------e:::c=__
Period T
Figure 3.10: A square wave
given by [10]:
Y(t)
=.! [sin(wt) +~sin(3wt)) +~sin5 (wt) +~sin(7wt) + ... ]
n
3
5
7
(Eq. 3.13)
where
w=
2ll / T.
Equation 3.13 represents the Fourier
series of the square wave of figure 3.10.
The frequency
composition of a signal as expressed by Fourier series is
called the frequency spectrum of the signal. The frequency
spectrum of a signal contains both magnitude and phase
23
I Y(t)
I
1.27
1
.42
0.5
.25
.18
I
11
3 f1
I
I
511
7 f1
.14
I
911
f
Figure 3.11: Magnitude spectrum of a square wave
information.
Figure 3.11 shows the magnitude spectrum of
the square wave of figure 3.10 . f 1 is called the
fundamental frequency and is equal to the reciprocal of the
period T of the square wave.
The calculations of the frequency spectra of irregularly
shaped waveforms (such as the input current waveform of a
rectifier) become extremely complex and thus are rarely
made.
Instead, either a spectrum analyzer or a digital data
processing system is used.
The advantages of a signal analyzer over a digital
oscilloscope are its Fast Fourier Transform (FFT) capability
24
and other signal processing capabilities.
The Fast Fourier
transform is a mathematical algorithm for transforming data
from the time domain into the frequency domain.
First the
time domain data are sampled into discrete data and then the
samples in the time domain are transformed into samples in
the frequency domain by the FFT algorithm.
Because of
sampling some information in the input time domain data are
lost.
However, by spacing the samples close together, an
excellent approximation of the input signal is obtained.
Figure 3.12 shows the equipment (and their setup) used to
measure input current harmonics of personal computer loads.
A 0.015
a shunt is placed in series with the voltage source
to provide a voltage that is proportional to the current.
The voltage across the shunt is fed to the signal analyzer
(HP
3561A~)
that is interfaced with a controller (HP 200™
series personal computer). The controller collects the data
displayed by the signal analyzer and stores it on disk.
The data collected by the HP 200™
series personal
computer was loaded into MATLAB™ and time waveforms and
frequency spectra of the input currents of
personal
computer loads were plotted. Appendix 1 gives a detailed
description of the HP 3561A™ signal analyzer and shows the
BASIC program listings that were run by the HP 200™
series
personal computer for time domain and frequency domain data
acquisitions.
25
p
r------
120 V( )
I
Shunt
supply [_--:---0. 015,---O~hm_ _
---1
personal
computer
load
N
HP 3561A
signal
analyzer
HP-IB bus
HP 200 Series
personal
computer
Figure 3.12: Measurement equipment
26
3.4: TIME AND FREQUENCY DOMAIN MEASUREMENTS OF INPUT
CURRENTS OF PC'S
There are several considerations for the measurement of
the harmonic currents of a personal computer.
Among them is
the role that the monitor plays in shaping the current
waveform of the personal computer.
In addition, it is
important to know what differences are there in the harmonic
currents of personal computers of various makes and models.
Of particular importance are the phase relationships of the
harmonic spectra drawn by individual
personal computers.
3.4.1: MONITOR AND COMPUTER CURRENTS MEASURED SEPARATELY
In order to determine the contribution of the monitor to
the harmonic content of the input current of a personal
computer, the monitor
cur~ent
and the computer current were
measured separately.
Figure 3.13 shows the current
waveforms of the monitor and the computer of a Compaq
Prolinea 4/50™
personal computer.
The current waveforms
of the monitor and of the computer are similar as indicated
by figure 3.13.
Figures 3.14 and 3.15 show the magnitude
spectra and the phase spectra of the monitor and of the
computer currents of a Compaq Prolinea 4/50™
respectively.
PC
There isn't much difference in the phase
angles of the harmonic currents of the monitor and of the
computer to indicate harmonic cancellations.
27
400
300
200
~
-.......
v
100
"!
0
~
-100
I
-200
-300
-400
0
2
8
8
10
12
14
18
18
20
TIme (m.ec)
Figure 3.13: Measured monitor & computer current waveforms
of Compaq Prolinea 4/50(
Monitor .... computer)
90
80
70
l'
~
4D
"0
...
='
-c
00
~
60
50
40
30
20
10
200
400
800
1000
1200
1400
1 600
1800
2000
Frequency (Hz)
Figure 3.14: Measured monitor & computer current magnitude
spectra of Compaq Prolinea 4/50 (
monitor .... computer)
28
200
150
100
d;
~
..........
.!!
50
··.
..
" ':
0
,, ''
,\ ::
,,-, '
0"
.i
-50
'(
-100
~
-150
-200
,
0
100
200
300'
400
.500
600
700
800
900
1000
F,...quency (Hz)
Figure 3.15: Measured monitor & computer current phase
spectra of Compaq Prolinea 4/50 (
monitor .... computer)
Figures 3.16 and 3.17 show the current waveform and the
magnitude spectrum of the Compaq Prolinea
4/50~personal
computer respectively when the monitor and the computer are
supplied simultaneously. These figures confirm the additive
nature of the harmonic currents of the monitor and of the
computer. In order to be able to generalize these results,
the measurements were repeated on several other personal
computers.
Figure 3.18 and 3.19 display the current
waveforms of·the monitor and of the computer of a IBM
PS2/30~
personal computer respectively. Figure 3.20 shows
the phase spectra of these currents.
the Compaq Prolinea
4/50~
As was the case with
personal computer the harmonic
29
800
BOO
400
~
200
~
u
~c:
0
a
-200
D'
::Ii
-400
-600
-BOO
2
0
6
8
12
10
14
16
20
18
Ttme (maec)
Figure 3.16: Measured current waveform of Compaq Prolinea
4/50 (monitor + computer)
160
140
120
i'"""'
II
"C
:2
c:
100
80
0-
D
::IE
60
40
20
0
0
200
400
600
800
1000
1200
1400
1 600
1BOO
2000
Frequency (HZ)
Figure 3.17: Measured current magnitude spectrum of
Compaq Prolinea 4/50 (monitor + computer)
30
currents of the monitor and of the computer are
approximately in phase with one another.
Therefore, it is
safe to consider the monitor an integral part of a personal
computer during harmonic measurements of its input current.
150
100
1
50
""-'"
•
i=-
0
-so
-100
-150
0
2
8
10
12
1....
16
18
20
TIme em.ec)
Figure 3.18: Measured monitor current waveform of IBM
PS2/30
300 r------r-----r-----r-----r----~-____,.--___r_--......._--__r_-____,
200
!
~8'
=-
100
o
-100
-200
__
-300 -----~--......i---""'--
o
2
8
'__--..a.----.&..----A.----4.------I
10
12
16
18
20
nm. (m••c)
Figure 3.19: Measured computer current waveform of IBM
PS2/30
31
200
150
100
i
~
~
50
0
~
~
-50
-100
-150
-200
0
100
200
300
400
500
600
700
BOO
900
1000
Frequency (Hz)
Figure 3.20: Monitor and computer current phase spectra
of IBM PS/30
3.4.2: PERSONAL COMPUTER INPUT CURRENT MEASUREMENT RESULTS
The Input current waveform of a Mac IIsi™ personal
computer is shown in figure 3.21.
Figure 3.22
shows the
magnitude spectrum of the waveform of figure 3.21 obtained
from the spectrum analyzer.
It is evident that large
harmonic components are present in the input current. The
magnitudes of the odd-numbered harmonics up to the eleventh
harmonic (660 hz) are significant.
The dominance of the
odd-numbered harmonic currents is expected since the current
waveform possesses half-wave symmetry.
In waveforms with
half-wave symmetry only the odd-numbered harmonic components
are present.
The current phase spectra of two Mac IIsi™'s
are shown in figure 3.23.
The harmonic currents of two Mac
IIsiTH's are completely in phase and therefore their
magnitudes linearly add to one another as illustrated in
figure 3.24.
32
400
300
200
100
'<
$
(l)
.a
·c
0
:::E
-100
"0
0'
0
-200
-300
-400
4
2
0
B
6
12
10
14
16
18
20
Time (msec)
Figure 3.21: Measured current waveform of Mac IIsi™
120
i-
-
80
-
-
60
-
-
100
i
I)
'"C
.a
-2
D"
c
::IE
-
40
20
o
f\
o
-
n
0-
f\.
200
"400
,,) \A\.I\_A.
600
1\
BOO
J\
1000
1'\
1'\
1 200
'"
1 400
.-
1 600
,......
.-.
1 800
2000
Frequency (Hz)
Figure 3.22: Measured current magnitude spectrum of
Mac IIsi™
33
200
150
100
50
0-
e
It
0
~
C
-c
-50
-100
-150
-200
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Frequency (Hz)
Figure 3.23: Measured current phase spectra of two
Mac IIsi™'s
250
200
1
150
Two
I
cv
"'U
~
·c
0'1
0
::t
One
100
50
OI:ll.A-~-"""'...&...1IIooI----r::a...&......a....ICI""""""'-"""""'-"':..a..--.JI""-'..&..Il--""'~~~~
a
200
400
600
BOO
1000
1200
1 400
-"""
1 600
---.I
1 800
2000
Frequency (HZ)
Figure 3.24: Measured current magnitude spectrum of two
Mac IIsi™'s and that of one Mac IIsi™
34
Figure 3.23 also reveals that the phase angles of
successive harmonic currents have opposite signs.
This is
characteristic of the input currents of all types of
personal computers that were examined.
Figures 3.25 and
3.26 show measured current waveforms of various types of
PC's.
The IBM PS/70™ draws the highest input current with a
peak value of 1 A.
Recent models of PC's (IBM PS/70™, Mac
absorb more power than former models (IBM
IIsi~)
Plus™).
PS/30~,
Mac
This shows a trend towards larger PC's in the
future and hence more harmonic problems can be expected due
to PC's.
800
IBM XT
Mac 11s1
600
400
<'
200
~
IIJ
-0
.a
·c
0'
0
~
0
-200
Mac Plus
-400
-600
-800
0
2
4
6
8
10
12
14
16
18
20
Time (msec)
Figure 3.25: Measured current waveforms of various PC's
35
1500
IBM PS2/70
1000
. . . . ~ IBM XT
500
1
G
0
"'0
.a
'c
0\
C
:::E
-500
-1000
-1500
0
2
6
8
10
12
14
16
18
20
Time (msec)
Figure 3.26: Measured current waveforms of various PC's
When a group of different types of PC's are connected it
is possible that harmonic current cancellations occur.
Figure 3.28 compares the phases of the currents of a Mac
IIsi m and a IBM XT m •
The third, the fifth and the seventh
harmonic currents are in phase and phase shifts occur among
higher harmonic currents.
When a Mac I I s i ™ and a IBM XT™
are active simultaneously, the third, the fifth and the
seventh harmonic components accumulate while in higher order
harmonic components partial cancellations occur.
This can
be verified by comparing the spectra of figures 3.27 and
3.29.
Similar conclusions can be reached when an IBM XT™
and IBM PS/230™ are run simultaneously as illustrated by
figures 3.30, 3.31 and 3.32 .
36
180 r---~---r-----,--~---r-----r--~--.,.------r-----.
¢:==J
160
IBM XT
140
120
<'
,g
100
Mac 1181
ll)
""C
~
'c
0'1
80
0
~
60
40
20
0
200
0
400
600
800
1000
1200
1400
1600
. 1800
2000
Frequency (Hz)
Figure 3.27: Measured current magnitude spectrum of IBM
XT m and measured current magnitude spectrum of Mac IIsi~
200
IBM XT ~
150
----J
v-
Mac 11s1
100
-e
50
~
~
I)
0
"i;I
c:
-c
-50
-100
-150
-200
0
200
400
600
BOO
1000
1200
1400
1600
1800
2000
Frequency (Hz)
Figure 3.28: Measured current phase spectrum of IBM XT™
and measured current phase spectrum of Mac IIsi™
37
300
250
200
1
I)
"0
Z
150
·c
C\
0
~
100
n
50
o
a
~
200
J\
400
1\
f\
600
f\
1\
800
I\.
1000
1\
1200
,"",
1400
.,..
1600
-.
~
1800
2000
Frequency (Hz)
Figure 3.29: Measured current magnitude spectrum of IBM XT™
and Mac IIsi™ run simultaneously
Figure 3.30: Measured current magnitude spectrum of IBM
XT™ and measured current magnitude spectrum of IBM PS/30™
38
200
I<=IBM PS2/30
150
IBM XT ~
100 ~
I
~
,.,
~
,....."
eIi'
50
0~
0
~
~
v
~
~
,
~
"
"""
,/
f""
u
V
I
-50
~
v
~
-100
v
~
200
-
~
:;I
o
-
I-""
V'
~
~
-150
~
L;
~
-400
600
BOO
1000
1200
1400
1 600
1 BOO
2000
Frequency (Hz)
Figure 3.31: Measured current phase spectrum of IBM XT™
and measured current phase spectrum of IBM PS/30™
450
I
II)
400
~
-
350
~
-
300
~
-
250
~
-
-g
:t:
c:
C"
:i
200
'""
n
150
~
100
~
-
50
I-
-
0
0
200
400
600
BOO
1 000
1 200
1 -400
1 600
1 800
2000
Frequency (Hz)
Figure 3.32: Measured current magnitude spectrum of IBM
XT m and IBM PS/30 m run simultaneously
39
It should be noted that during these measurements no
programs were executed on the personal computers.
The
differences in the measurements were insignificant when
programs were executed.
3.5: THE MAGNITUDES OF THE HARMONIC CURRENTS OF PERSONAL
COMPUTERS AND THE NEUTRAL CURRENT
Table 3.1 lists
input current harmonics of various types
of personal computers.
currents
In parentheses are the harmonic
as a percent of the fundamental component of the
current (60 Hz component).
The third harmonic current 1 3
ranges from 74% up to 87% of the fundamental current II.
constitutes from 41 to 67% of II.
Is
The range of 1 7 is
between 16% to 44% of II and the range of 1 9 is from 3% to
21% of II.
Harmonic currents higher than the ninth are
below 10% of II .
The third harmonic current ranges from 74% to 86% of the
fundamental current.
High neutral currents are expected due
to the high magnitudes of the third harmonic currents (and
the magnitudes of higher order triplen harmonic currents)
because they are in phase with each other (zero sequence) in
all three phases of the
power system.
The third harmonic
current is dominant in the neutral conductor because its
magnitude is much larger than the unbalanced portion of the
fundamental current and any other harmonic current.
40
Mac IIsi
I
I
1
3
Is
I 7
I
9
III
I
I
13
1S
IBM XT
IBM PS/30
Mac Plus
IBM PS/70
106.82
165.93
199.02
83.35
541.88
(100%)
(100%)
(100%)
(100%)
(100%)
89.31
122.45
152.63
72.30
458.83
(83.6%).
(73.8%)
(76.7%)
(86.7%)
(84.7%)
65.18
68.03
94.76
55.80
333.54
(61.0%)
(41.0%)
(47 • 6%)
(66.9%)
(61.5%)
40.51
26.71
39.16
36.53
192.04
(37 .9%)
(16.1%)
(19.7%)
(43.8%)
(35.4%)
21.25
5.64
10.39
17.78
(19.9%)
(3.4%)
(5.2%)
(21.3%)
71.18
(13.1%)
8.70
3.98
3.53
3.31
17.75
(8.1%)
(2 .4%)
(1.8%)
(4.0%)
(3 .3%)
2.95
8.46
1.49
4.95
(2 .8%)
(5 .1%)
(0. 7%)
(5 • 9%)
3.46
8.29
2.30
7.51
(3.2%)
(5 • 0%)
(1.1%)
(9.0%)
49.02
(9.0%)
48.01
(8.8%)
Table 3.1: Magnitudes of harmonic currents of various PC'S
in rnA
The IBM XT™ has the lowest
per~ent
third harmonic current
(74%). Since the computer is connected
line-to-neutral in a
3-phase system, the neutral current is approximately equal
to three times the vector sum of the third and ninth
harmonic currents flowing in each phase.
In = 3
(1 3 2
+
1 92 )
1/2
= 3 (122.458 2 +
5.642 2 )
1/ 2
367.764 rnA
41
The phase current is given by:
I P= (I 12 + I 3 2 + I 5 2 +I 7 2 + I 92 + I 11 2 + I 13 2 + I 15 2)
r,
=
In /
1/2
219.226 rnA
Ip
= 1.677
The Mac Plus rn offers the worst case third harmonic
current (87%).
In a similar manner In and I p are obtained.
In
3 (72.303 2 + 17.789 2 )
r,
130.507 rnA
In /
I p = 1.712
1/ 2
223.377 rnA
With a large number of personal computer loads,
the
neutral current is expected to be 1.7 times the phase
current.
It will certainly overload the neutral conductor
that is designed to handle lower currents than the phase
currents.
42
Chapter Four
Effects of Personal Computer
the Distribution
Ha~onic
Currents on
Transfo~er
4.1: HARMONIC CURRENT EFFECTS ON TRANSFORMER LOSSES
The harmonic currents generated by personal computer
loads introduce extra losses in the transformers feeding the
loads.
The additional losses are the results of increased
eddy currents.
The extra transformer losses due to
harmonics require that the transformer be derated so that
the total losses do not exceed the ratings.
According to A
standard c57.110-1986 (A Recommended Practice for
Establishing Transformer capability When Supplying
Nonsinusoidal Load Currents) the total load loss of a
transformer can be divided between winding losses
losses.
and stray
Stray losses are the eddy current losses due to
stray electromagnetic flux in the windings , core and other
structural parts of the transformer.
The total load loss
can be expressed as [11]
Pu = I 2 R +
where
PEe
P~
+
POOL
(Eq. 4.1)
is the loss due to stray electromagnetic flux in
the windings and P OSL is the stray loss in components other
than the windings.
Before going into further details of the
discussion of transformer losses,
should be explained.
eddy current losses
43
Generally, eddy currents are defined as circulating
currents in the magnetic core of a transformer [12].
A
time-changing flux induces voltage within a core in the same
manner as it would in a wire wrapped around that core since
the core (made of iron) is a fairly good conductor.
The
induced voltages cause eddy currents to flow within the core
that result in heating losses in the iron core or eddy
current losses.
equation 4.1.
These losses are represented by P OS L in
Eddy current losses are minimized by
building the core from thin, insulated sheets of iron
("laminations") and thus restricting the flow of eddy
currents.
When an ac current flows through the windings of a
transformer each conductor becomes surrounded by an
electromagnetic field.
Each conductor linked by the time-
changing flux experiences an internal induced voltage that
causes eddy currents to flow in that conductor. The eddy
currents produce additional heating losses in the windings
that are referred to as stray losses.
The eddy current
losses within the transformer windings are represented by
PEe
in equation 4.1.
Harmonic currents cause excessive
eddy current losses in the transformer windings since these
losses are proportional to the square of the currents and
the square of the frequencies.
Although the
loss in
the core (POSL ) is increased as a resul t of nonsinusoidal
44
currents, it is considered less critical than the winding
The maximum per unit load current that ensures that the
losses do not exceed the rated 60 Hz operating conditions of
a transformer is given by equation 4.2 [11].
I
max
1 + PEC-R(PU)
=
(Eq.
Where,
PE~R
4.2)
(pu) is the per unit value of eddy current
loss under rated 60 Hz conditions, h is the harmonic number
and f h is the harmonic component of current divided by the
60 Hz component of current.
The input current waveform of a
group of 30 IBM XT m personal computers is considered as a
load with the following harmonic composition.
1
5.551 A
3
4.626 A
5
3.138 A
7
1.629 A
9
0.610 A
Table 4.1: Harmonic composition of non-linear load
45
The rms current is given by:
I r ms
= (
1 12
+ I 32 + 1 5 2 + 1 7 2 + 1 92 ) 1/ 2 = 8.067 A
The harmonic currents are converted to pu of the rrns
current and the following values are obtained:
r,
h
(pu)
1
0.6939
3
0.5782
5
0.3922
7
0.2036
9
0.0763
Table 4.2: Non-linear load current in pu
If the maximum eddy current loss of the transformer is
15% of the 12 R loss, then PEC- R
=
0.15 pu.
f
hl
f h 2 and f h 2 h 2
are calculated and tabulated as follows:
h
1
0.6939
1
1.000
1.000
1.000
3
0.5782
9
0.8334
0.6945
6.251
5
0.3922
25
0.5652
0.3194
7.9863
7
0.2036
49
0.2934
0.0861
4.2181
9
0.0763
81
0.1100
0.0121
0.9801
2.1121
.E 20.435
~
Table 4.3: Example parameters of equation 4.2
46
The maximum current from equation 4.2 is:
I max
(pu)
=
1 +0.15
=0'.6849
1+20.4350 15
2.1121 ·
I max = O. 6 8 4 9 x 8 A = 5. 4 7 9 A
Thus, the transformer capability is 68 % of its rated
load current capability.
4.2 HARMONIC ANALYSIS OF THE TRANSFORMER CIRCUIT
In order to observe the current waveforms of a
transformer a PSpice model of a transformer is implemented
as shown in figure 4.1.
The nonlinear magnetic transformer
model of Pspice is used.
The B-H characteristics of an
iron-core transformer model in Pspice are analyzed using the
Jiles-Atherton model [13].
An iron-cor.e transformer can be
represented by the following PSpice statements:
Ll 2 0 500
L2 3 0 500
K12 Ll L2 0.9999 CMOD
.MODEL CMOD CORE (AREA=20 PATB=40 GAP=O.l MS=1.6E+5
+ ALPHA=le-3 A=1000 C=0.5 K=1500)
where Ll and L2 specify the number of turns of the primary
and secondary windings of the transformer respectively.
K12
47
•
D2
7
l.1
tmlt
\i.C4I
t..,
•
10
D4
a
Figure 4.1: Transformer PSpice model with nonlinear
rectifier load
is the mutual coupling of the transformer windings and CORE
is the model name for a nonlinear magnetic inductor.
model
parameter~
are defined as follows [13]:
AREA:
Mean magnetic crosi section area in cm2
PATH:
Mean magnetic path length in cm
GAP:
Effective air-gap length in cm
MS:
Magnetic saturation in Aim
ALPHA:
Mean field parameter
A:
Shape parameter
c:
Domain wall-flexing constant
K:
Domain wall-pinning constant
The
48
Program 1 of appendix 2 shows a copy of the Pspice
program that was used.
the primary(i 1 )
,
Figure 4.2 shows the waveforms of
the secondary (i z ) and the magnetization (i m)
currents of the transformer under a nonsinusoidal rectifier
load (input section of a switch-mode power supply). The
magnetization current i m is equal to the difference i 1
-
i2-
Figure 4.3 shows the magnitude spectra of these waveforms_
20
15
10
s
5
G)
"C
:::3
~
0
C
0-
0
:E
-5
-10
-15
-20
0
5
10
15
20
25
30
35
Time (msec)
Figure 4.2: Transformer current waveforms with
nonsinusoidal load obtained by PSpice
40
49
15
12
s
-II:::J
~
10
1m
0-
0
:2
5
......
.wo
O"------............-----~~--...--.L.I~-...I.--
o
100
150
200
250
300
350
~-.....L------'
450
500
Frequency (Hz)
Figure 4.3: Transformer magnitude current spectra with
nonsinusoidal load obtained by PSpice
In order to confirm the PSpice results of figures 4.2 and
4.3, measurements were taken on a lab transformer supplying
power to a IBM
XT~.
The transformer is rated at 600 VA and
has several isolated windings rated at voltages
and 120 V.
6, 60, 110
The primary winding of the transformer was a 120
V winding and so was the secondary winding.
Figures 4.4 and
4.5 display the results of these measurements.
50
200
100
!
t)
a
'0
:2
c::
C'
0
:5
-100
-200
-300
a
5
10
15
25
20
30
35
40
Time (msec)
Figure 4.4: Measured current waveforms of transformer with
1 PC load
180
:J
140
120
~
1m'
100
J
80
:i
eo
c:
at
Ll
12
40 .
20
0
0
50
100
150
200
250
300
350
~oo
....50
F.... qu.ncy (Hz)
Figure 4.5: Measured current magnitude spectra of
transformer with 1 PC load
500
51
In both the simulated and the experimental spectra
(figures 4.3 and 4.5) i
contains lower harmonics than i 2 •
1
The relationship between these currents is the following.
( Eq. 4. 3 )
Where, a is the turns ratio of the transformer windings.
There are cancellations in the harmonic currents of i
2
and
i m • Figures 4.6 and 4.7 show the phase angles of i 2 and i m
for the simulated and the experimental results respectively.
For harmonic currents
higher than the fundamental current
the phase shifts between i 2 and i m are greater than 100
degrees.
200
·,· ..,,,,
·,· ,
,· ·
· ·,
,,· ,,
,12
150
r-'
100
~
t
.-,
,, ,
,, ,,
.
60
.
0
-50
-100
-150
0
~.J¢==::J 1m
·· .
·.
, ,,
, ,
,"'_,,
60
,,
100
160
200
2&0
300
350
400
460
Frequency (Hz)
Figure 4.6: Phases of i 2 and
1m
obtained by PSpice
eoc
52
200
::¢==:JImr:
..
..
150
100
""":-
.
!
•
I
•
I
,
I
I
•
I
I
I
•
•
I
I
,
I
I
I
I2
SO
.i i,
I
I
I
I
..
..
0
e-
.i
-50
I
I
'
'-"'"
.
-100
I
I
I
-1~
-200
I
0
I
L.-J
00
100
1 eo
200
260
.300
3GO
400
460
f!»OO
Frequeney (Hz)
Figure 4.7: Measured phases of
12
and i m
The magnitude of i m is comparable to the magnitude of i 2
because the transformer is lightly loaded.
It is expected
that as the load increases the magnitude of
12
increases yet
the magnitude of i m does not change significantly and this
fact is verified by figures 4.8 and 4.9.
The amount of
loading and the value of the turns ratio determine the
extent of harmonic cancellations between i 2 and i m •
The
magnetization current which contains odd order (3rd, 5th,
7th etc.) harmonic currents is considered a source of
harmonic currents to the distribution system.
applied voltage to a transformer goes
When the
above the rated
voltage the level of transformer saturation
increases and
the magnetization current i m increases dramatically.
53
20
15
10
5
~
&)
~
.a
0
"2
CJl
0
:s
-5
-10
-15
TIme (msec)
Figure 4.8: Transformer current waveforms with
increased nonsinusoidal load obtained by PSpice
8OO------......---,...------r----.----~-~-----,
600
400
!
200
-400
-600
-800...----------"""--------'----"""----'-----"
o
5
10
15
25
30
35
40
20
TIme (msec)
Figure 4.9: Measured current waveforms of transformer
with 3 PC load
54
Under a fairly sinusoidal load a transformer should not be
overexcited to keep down the levels of the harmonic currents
due to saturation.
However, when the load is highly
nonsinusoidal operating the transformer above its rated
voltage will partially reduce the harmonic components of the
primary current and thus have beneficial effects.
4.3: THREE-PHASE TRANSFORMER CONNECTIONS
The primary and the secondary windings of a three-phase
transformer can be connected in either a Y or a 4.
This
gives a total of four possible connections for a three-phase
transformer: Y-Y, Y-4, 4-Y, and 4-4.
Figures 4.10 and 4.11
show the connections of a Y-Y and a 4-Y transformer
respectively.
a
b
c
~
-,
~
I
I~
",
a1
b1
n
c1
Figure 4.101 Y-Y connected transformer
55
C-~J
n
b
Figure 4.11:
~-y
connected transformer
A three-phase transformer model of PSpice is obtained by
connecting three single-phase transformers whose supply
voltages are 120 electrical degrees apart. Program 2 of
appendix 3 shows the PSpice program that was used to
simulate a Y-Y connected transformer feeding a nonlinear
rectifier load.
Figure 4.12 shows the current magnitude
spectra of the secondary current i 2 and the neutral current
in of a Y-Y connected transformer.
The neutral current is
obtained by adding the secondary phase currents vectorially.
As expected, a large neutral current exists that consists of
triplen harmonic currents.
Figure 4.13 shows the primary
line {i 1 } and phase (i p ) current magnitude spectra of a
a-Y
56
transformer.
Unlike the phase current, the line current
does not contain third harmonic components.
circulating phase currents in the
additional heating
~
winding
inside the transformer.
However, the
cause
Therefore, the
neutral current can be avoided by connecting one or both
windings of the transformer in delta.
.
10 - -........----......---.op----.--...,...-----,.--....---~--....------.
8~
!'·I~I2
I
··
·
I
I
Y==::J
I
I
$
6~
In
"B•
~
·c
If
2
4~
.:" ..
I,
2~
~ ~
~I
50
100
150
.'
Ito
I \
\.
~
200
250
JOO
350
400
450
500
Frequency (Hz)
Figure 4.12: Current magnitude spectra of Y-Y transformer
57
t·
··,· <;:=::J II
···
·
···
I
20
s
15
•
"!
...,
-c
aD
~
Ip
10
O.....-----..-........-
o
50
100
................." "---.......150
200
250
......
- - - - . l L . . . o - -.......~-""-----'
300
3SO
~
450
500
Frequency (Hz)
Figure 4.13: Current magnitude spectra of
on delta side
~-y
transformer
58
Chapter Five
Harmonic Reduction
5.1: NEUTRAL CURRENT REDUCTION
High neutral currents in a power system can overload the
neutral conductor.
One way to minimize the neutral current
is to keep the load as balanced as possible.
Thus, the
neutral current due to the load imbalance is kept at a
minimum.
However the neutral current due to the triplen
harmonic currents still exists.
To reduce the neutral current in a 3-phase system, a
transformer with tertiary windings [5] can be employed in
such a way that the tertiary and the secondary currents are
antiphase as shown in the circuit arrangement of figure 5.1.
The dots on the transformer windings describe the polarities
of the voltages and currents on the secondary side with
respect to the voltages and currents on the primary side.
So, if the primary current of the transformer flows into the
dotted end of the primary winding, the secondary current
will flow out of the dotted end of the secondary winding.
Therefore, with the dot configuration shown in figure 5.1
the phase currents of the secondary windings flow into the
common point of the Y-connection and the tertiary currents
flow out of the common point. Thus, the neutral currents i
and i n2 are 180 degrees out of phase and hence cancel each
other out provided that the secondary and the tertiary
windings of the transformer are loaded equally.
In most
n1
59
applications adding tertiary windings is not feasible since
the arrangement of figure 5.1 is relatively expensive.
~p
al
Inl
~-
I
a
,-
-~
(-("
,\
c---:
,~~
~)
j
.v-~~
b
9~
/J
)
bl
\..::J
l~
p
cl
I
'<,
'",=:,
a2
'~ ~/
."./
.\
I
I
§!
-:=
In2
1
L
b2
-----,._-,"--
c2
Figure 5.1: Transformer with tertiary windings to reduce
the neutral current
5.2: COMMONLY USED METHODS OF HARMONIC ELIMINATION
There are several methods of reducing the harmonic
currents in a single-phase ac to dc converter.
Conventional
passive filters can be used to eliminate the harmonics
selectively[Key].
Figure 5.2 shows a parallel-connected
60
series resonant LC filter where Ls is the series inductance
of the supply.
The impedance of the filter branch as a
function of frequency is given by equation 5.2:
Z(w) =jw£l+ . 1
]Wei
(Eq.
5.1)
(Eq.
5.2)
which can be expressed as:
Z(w) = w2~lCl-l
Jwei
The impedance approaches zero when
~
= l/J (Ll C1).
So,
if it is required to filter the third harmonic current the
frequency is tuned to
~
=3 x 2x60.
The filter branch acts
as a short circuit and prevents the third harmonic load
01
D2
+
Ls
Vout
c
RI
D4
Filter
Figure 5.2: A parallel-connected series resonant LC filter
in the bridge rectifier circuit
61
current from flowing in the supply.
Several filter branches
can be used each tuned to a different frequency to filter
out the undesired harmonic currents.
The filter can also be
connected in series with the supply as shown in figure 5.3
[6].
The series-connected parallel resonant LC filter is
tuned to present an infinite impedance to the harmonic
current component to be filtered.
is needed to decrease oscillations.
The added resistance R1
The admittance of the
filter branch is given by equation 5.3 :
(Eq.
5.3)
Filter
"
"\..
C1
II
D1
D2
L1
c
RI
D4
Figure 5.3: A series-connected parallel resonant LC filter
in the bridge rectifier circuit
62
which can be expressed as:
(Eq.
5.4)
The impedance of the branch circuit is equal to the
reciprocal of the admittance and is given by:
(Eq.
5.5)
When the frequency equals the resonant frequency
~
= l/J (Ll Cl), the impedance equals the resistance R1 •
Without the resistor the impedance approaches infinity at
the resonant frequency.
The voltage ratings of the passive filter components must
be equal to the voltage of the supply.
In addition, their
current ratings should be equal to the highest supply
current.
This rating requirements make the sizes, the
weights, and the costs of the components high.
Therefore,
passive filters are undesirable.
There are several active methods of harmonic elimination.
The active circuit shapes the distorted input current
waveform to approximate a sinusoidal waveform.
The three
63
active circuits of harmonic elimination are the buck, boost,
and the buck-boost converters.
Among the active
methods
the boost method is most promising[6] .
The harmonic components of the supply current can be
eliminated by inserting a boost stage in the input section
of the power supply as shown in figure 5.4.
The boost
converter converts a low dc voltage to a high dc voltage.
When the switch is on the diode is reverse biased and the
inductor L 1 gets charged., When the switch is off both the
inductor and the supply charge the capacitor through the
01
C1
II
Boost Converter
Figure 5.4: Bridge rectifier circuit with boost
converter
64
diode D5.
The switch is operated at much higher frequencies
than the supply frequency.
Figure 5.5 shows the input
current waveform of the boost circuit simulated by PSpice at
a frequency of 2 KHz (program 4 of appendix 2 shows the
PSpice program that was used).
The input current .waveform
contains the switching frequency ripple.
frequency magnitude spectrum
The input current
is shown in figure 5.6.
The
harmonics are reduced significantly when using the boost
converter.
Active circuits are operated at switching
frequencies of 20 KHz to 100 KHz [6].
When operated at
these high frequencies the input current waveform will
resemble a sinusoidal waveform closely and the harmonic
8.CA . . , . . . - - - - - - - - - - - - - - - - - - - - - - - - - - - - ,
4.CA
OA
-4.OA
-8.QA
5ms
10 ms
15 ms
20ms
Time
Figure 5.5: Input current waveform of the boost converter
obtained by PSpice
65
6.OA . , - - - - - - - - - - - - - - - - - - - - - - - - - - - ,
4.OA
aOA
2.OA
1.OA
A
A
0A~----~~-,.u----..u..---...:I----........._---~---~-~----I_'_r_~---uJ
OH
O.8KH
1.2KH
1.6KH
2.OKH
Frequenc,y
Figure 5.6: Input current magnitude spectrum of the boost
converter obtained by PSpice
currents will almost disappear.
The boost
converter is
significantly smaller than the passive filters and has a
better performance.
However, its control circuit is complex
and it has a high EMI (electromagnetic interference)
switching frequency component that must be filtered.
5.3: A NEW SINGLE-PHASE AC TO DC HARMONIC REDUCTION
CONVERTER BASED ON THE VOLTAGE-DOUBLER CIRCUIT
5.3.1: DESCRIPTION AND ANALYSIS OF THE PROPOSED' CIRCUIT
A new harmonic reduction circuit is proposed that is
based on the voltage-doubler circuit as shown in figure 5.7.
The new circuit has an additional switch that is operated on
66
D1
...
L1
C1
Q.5rnF
Vout
RI
swttotl
OJ
C2
D4
200 ohrne
D.5rnF
Figure 5.7: Schematic of the proposed harmonic reduction
circuit
line frequency (60 Hz).
When the switch is open the circuit
acts as a full-wave bridge rectifier. During each half-cycle
a pair of diodes conduct until the dc output voltage rises
above the supply voltage. When the switch is closed the
circuit acts as a voltage-doubler rectifier each capacitor
getting
charg~d
to approximately the peak of the ac voltage.
To better understand the operation of the new circuit the
circuit of the uncompensated bridge rectifier is considered
first as shown in figure 5.8.
A PSpice analysis of the
circuit of figure 5.8 was performed (PSpice program 5 in
appendix 2 shows the program code).
Figure 5.9 shows the
PSpice results of the input current waveform of the bridge
67
Dt
D2
+
Lt
Vout
C
Va
1 mF
AI
1210
2JDO ohm.
D4
Figure 5.8: Schematic of uncompensated bridge-rectifier
circuit
~QA +--------+--------+--------+--------+--------+--------+--------+--------~---+
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
+
1.QA -+-I
I
I
I
I
I
I
I
I
I
I
I
O.QA
I
-+-----I
I
I
I
I
I
I
I
I
I
-1.QA
+
t
I
I
:
I
I
I
I
I
I
I
-2.OA
I
+-- ------+----.- ---+- ----- --+--------+----- ---+------- -+-- - - - ---+--- -- - --+----+
QJns
4ms
ems
12ms
te ms
Tme
Figure 5.9: Input current waveform of uncompensated
bridge-rectifier circuit simulated by PSpice
68
rectifier circuit.
The current pulsewidth of figure 5.9
can be increased by stepping up the supply voltage before
the current starts to flow and after the current becomes
zero. This is achieved by operating the circuit of figure
5.7 as a voltage-doubler (switch is closed) outside the
normal current conduction times.
The switch is opened
during the normal current conduction time and the circuit
operates as an ordinary bridge rectifier.
Figures 5.10
shows the simulated results of the input current waveform
when the new scheme is used(PSpice program 6 in appendix 2) .
Switch closed
+I - - - - - - - -+
2.OA
II
I
"
- -- --
.
-+~-
- - - - -+ - - - - - - - -+- - - - - - - -+---- -- - -+- - - - - - - -+- - - - - - - -+- - - +
.
I
.
.
,
•
.
<"-
:'~
I
I
I
1.OA
+.
I
I
O.OA
I
l
.
.
.
.
.
.
.
.
.
I
II
I
I
:
I
I
I
.+
I
::
:
!
.
:
:
I.
t2
t1·
./
.
switch open
:
I
I
:
l
·1.~
r.
-2.OA
+------ --+--------+-- -- ---+--- -- ---+--------+--- ---- -+- --- - - --+-- - -- - --+-- - +
4me
8ma
l2ms
lema
I
:
Figure 5.10: Input current waveform of the proposed
circuit obtained by Pspice
69
The durations of the conduction periods (t 1 and t 2 in
figure 5.10) of the switch can be determined either by
performing a PSpice simulation (program 5) or a theoretical
analysis of the bridge rectifier circuit (section 3.1) and
reading the zero crossings of the input current.
Figures
5.11 and 5.12 show the input current magnitude spectra of
the bridge rectifier circuit and the new voltage-doubler
circuit obtained by Pspice.
It is obvious from these
figures that the harmonic content of the input current
decreases significantly with the new circuit.
A measure of
the current distortion is the total harmonic distortion
(THD) and is defined as [8]
~~
L.J I
THD%=100
2
h
(Eq.
5.6)
h=2
II
The current shown in figure 5.11 has a THD of
the current of figure 5.12 has a THD of
69.5% while
39.4%. Moreover,
the third harmonic component of the current is reduced from
.615 A to .21 A , a reduction of
The analysis of section 3.1
65.8%.
can be extended to the
proposed voltage-doubler circuit by choosing the appropriate
capacitance and initial conditions.
First, the circuit is
analyzed as a voltage-doubler with C=0.5 mF.
Near the end
of the first conduction period the analysis is switched to
70
'.OA
+ - - - - - - - - - - - - - -.;.-- - - - - - - - - - - - - +- - - - - - - - - - - - - - -+- - - - - - - - - - - - - - -+-- - - - - - - - - - - - --+I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
O.SA
I
I
+
+
I
I
I
I
I
I
I
I
I
I
I
I
I
I
+
I
O.8A
I
+
I
I
I
I
I
I
I
I
I
I
I
I
I
I
+
+
:
:
:
O.2A -+-
4-
~~
I
I
I
I
:
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
,
,
O.CA
O.OKH
O.2KH
O.4KH
O.6KH
O.6KH
1.0KH
o
Frequency
Figure 5.11: Magnitude spectrum of input current of
bridge-rectifier obtained from PSpice
1.M +, - - - - - - - - - - - - - - -+- - - - - - - - - - - - - - -+- - - - - - - - - - - - - - -+- - - - - - - - - - - - - - -+- - - - - - - - - - - - - - -+-I
,
I
I
I
I
I
I
I
I
I
I
I
I
I
I
O.SA
I
+
+
I
I
I
I
I
I
,
I
0.6A -+-I
I
I
,
,
I
I
I
I
0.4A
t
I
I
I
I
I
I
I
I
0.2A
+,
,
I
I
I
I
I
I
o.QA
I
o.OKH
O.2KH
o.4KH
O.6KH
0.8KH
1.OKH
D
Frequency
Figure 5.12: Magnitude spectrum of the current of the
proposed harmonic reduction circuit obtained from PSpice
71
the bridge-rectifier by dividing the capacitance by two (two
capacitors in series) and using double the output voltage as
an initial condition.
When the current reaches zero the
analysis is switched back to the voltage-doubler circuit.
The input current waveform of the new harmonic reduction
circuit is shown in figure 5.13.
It resembles the
simulation results of figure 5.10 closely.
L== 10 mH. C==0.5 mF, R==200 ohms
1.6
1.4
1.2
...-..
~
...
'-'"
c:
e
O.B
~
:::I
u
0.6
0.4
0.2
0
0
2
4
5
6
7
B
9
Time (msec)
:Figure 5.13: Theoretical current waveform of the proposed
harmonic reduction circuit
72
5.3.2: LABORATORY VERIFICATION OF THE PROPOSED CIRCUIT
A prototype circuit as shown in figure 5.14 is developed
to verify the operation of the proposed circuit.
The
control circuit uses a window comparator that gives an
output high when the input voltage falls between preset
lower and upper limi ts VL and VH •
The signals of Vi n l VL , VH
and Va are shown in figure 5.15.
The npn transistor Q2 in
the power circuit is used as a switch during the positive
half-cycle and is controlled by Vo. A pnp transistor (not
shown in figure 5.14) is connected back-to-back to Q2 and
performs the switching function during the negative halfcycle.
In the power circuit the ac supply voltage was set at 30
V instead of 120 V in order not to exceed the ratings of the
components that were available.
The shape of the input
current should not be affected by this because the
magnitudes of the harmonics would be off by a constant
factor.
In addition, to keep the control circuit simple the
control voltage v o
had half-wave symmetry i.e. the
conduction periods of the switch were chosen to be equal.
The harmonic components of the input current would be lower
in magnitude if this simplification was not made.
Time waveforms were measured in the laboratory using an
HP Signal Analyzer (HP 3561A). Figure 5.16 shows the time
waveform of the input current for the bridge-rectifier
circuit and figure 5.17 shows its magnitude spectrum. As can
73
1111
LM741C
IN5212
11
•
SK312A
a
_
CONTROL CIRCUIT
D4
u
..
+
C1
CUInF
....
It-
1BJ
SK3929
•
CI
JIll
Unf
01, 02, 03, 04, IN5212
POWER CIRCUIT
Figure 5.14: Laboratory circuit
74
be seen in figure 5.17 the harmonic content of the input
current is quite high.
Figures 5.18 and 5.19 show the
corresponding waveforms of the proposed harmonic reduction
circuit.
In figure 5.19, there is a significant reduction
in the harmonic components of the input current in
particular the third harmonic current.
The THDs of figures
5.17 and 5.19 are 70.1% and 30.7% respectively.
conduction time of the switch is lowered from t 1
If the
=
1.35
IDS
to t 1 = 0.87 ms the results of figures 5.20 and 5.21 are
obtained.
The spectrum of figure 5.21 has a higher harmonic
content than the spectrum of figure 5.19 .
Figure 5.15: Control circuit voltages
75
600
400
.~
......,
200
Q)
0
"C
:;]
~
c
C'
c
:1:
-200
-400
-600
a
2
4
10
B
6
12
14
16
Time ems)
Figure 5.16: Laboratory waveform of input current without
harmonic reduction
180
160
140
~
~
.......,
tJ
120
100
""C
::::J
+J
-2
at
c
::I:
80
60
40
20
0
0
100
200
300
400
500
600
700
800
900
1000
Frequency (Hz)
Figure 5.17: Measured magnitude spectrum of input current
waveform without harmonic elimination
76
600
400
W
200
~
CD
"0
::J
a
:t=
c
0'
D
::E
-200
-400
-600
0
2
4-
10
B
6
12
14
16
TIme (ms)
Figure 5.18: Laboratory waveform of input current with
harmonic reduction: switch conduction period = 1.35 IDS
300,...-----r------,..----yo----,----r----r------"T----r----,-----,
250
,......
-c
E
'-"
200
G)
"U
:J
......,
150
·c
0\
0
~
100
50
........
O~..J.-~-
o
100
----&-..a...--.......-.t~
200
300
...........~--~_..._---'-...._--..l..._........_...._..._ _.-_.......
400
500
600
700
800
900
_
1000
Frequency (Hz)
Figure 5.19: Measured magnitude spectrum of input current
waveform with harmonic elimination: switch conduction
period = 1.35 ms
77
400
~
200
'-'
Q)
0
"'C
:::s
~
c
0'
0
~
-200
-400
-600
4
2
0
10
8
6
12
14
16
Time (ms)
Figure 5.20: Laboratory waveform of input current with
harmonic reduction: switch conduction period = 0.87 ms
300
,..------.,.-----r-----,----..,..-------,r-------,-----r----.---oor----,
250
,.......
200
-c
E
'-'
G)
-0
::3
...,
150
·c
0\
C
~
100
50
OClo..-...L-I..-.L_---oL.....L.L..--L.I_...&..L.a..----t...Jo.-~I....-..L....I..lI..._L-J..-__LU_~~_Ir.._-L....:a...I._.~---I.~--'-........,
o
100
200
300
400
500
600
700
800
900
1000
Frequency (Hz)
Figure 5.21: Measured magnitude spectrum of input current
waveform with harmonic elimination: switch conduction
period = 0.87 ms
78
Chapter Six
Conclusions and Recommendations for Further Research
The switch-mode power supply used in personal computers draws
a nonlinear current that is rich in harmonic currents.
A
high
density of switch-mode power supply loads results in tDe
overloading of the neutral conductor and the overheating of the
distribution transformer.
Due to the highly nonsinusoidal nature of the input current
waveform (figure 3.21) of
a personal computer high amplitudes of
harmonic currents are generated (figure 3.22).
currents are of odd-order
the input current waveform.
These harmonic
because of the half-wave symmetry of
The magnitudes of the harmonic
currents up to the eleventh harmonic current are significant.
Although personal computers have similar input current waveforms
(figure 3.25 & 3.26), these waveforms are not exactly identical.
The slight differences in the current waveforms are due to the
.
.
differences in the values of the output filter parameters (L and
C) of the power supplies.
The input currents of personal computers are accounted for by
the input current of the monitor and the input current of the
computer.
The input currents of the monitor and the computer
have $imilar waveforms (figure 3.13).
In addition there isn't
enough diversity in the phase angles (figure 3.15) of the
harmonic currents of the monitor and the computer to indicate
harmonic current cancellations.
Therefore, the monitor
79
contributes evenly to the harmonic currents of the personal
computer and should be considered an integral part of the
personal computer.
The phase angles of the harmonic currents of the input
currents of different personal computers (figure .3.28) do not
vary enough to cause significant harmonic current cancellations.
The third, the fifth and the seventh order harmonics in different
types of personal computers strongly reinforce one another.
There are some cancellations in the higher-order harmonics but
these are insignificant because of the very low magnitudes of the
high-order harmonic currents.
Therefore, the magnitudes of the
harmonic currents in a computer center or an office building
increase proportionately with the number of personal computers.
The range of the third harmonic current is from 74% to 87% of
the fundamental current in eight types of personal computers
(table 3.1).
Due to the additive nature of the third harmonic
currents, large neutral currents are generated in a three-phase
distribution system feeding the personal computer loads.
Where
personal computers make up the majority of the loads, the neutral
current will be as high as 1.7 times the phase currents even if
the phase currents are balanced.
In an office building or a computer center where personal
computers exist in large numbers, the third harmonic current can
possibly overheat the neutral wire and can cause fires.
An
immediate method of dealing with high neutral currents involves
80
monitoring the neutral current.
To prevent potential hazards
overcurrrent relays can be installed on the neutral conductor.
Another method is to size the neutral conductor to twice the size
of the phase current or to run a second conductor in parallel to
share the neutral current.
The harmonic currents generated by personal computers create
additional losses in the distribution transformer.
The increased
losses are eddy current losses that are proportional to the
squares of the frequencies of the harmonic currents.
losses increase the
oper~ting
These
temperature of the transformer and
require derating the transformer to a fraction of its capacity.
The design of a transformer can be changed to make it capable
of handling nonlinear loads.
A more practical approach would be
to derate the transformer. IEEE std. c57.110-1986 describes
methods for calculating the capacity of a transformer for a given
harmonic load [11].
Running the transformer in excess of its
capability limits its service length and may result in its
failure.
Circuit breakers that respond to the rms currents may
not be able to
pro~ect
the transformer and other protective
devices such as temperature sensors should be used.
Although transformers in general are considered sources of
harmonic distortion, they can act as filters to nonlinear loads.
The phase angles of the magnetization current harmonics oppose
the phase angles of the load current harmonics and hence lead to
harmonic cancellations (figure 4.6).
During light loads a
81
,
transformer supplying a nonsinusoidal load will have a primary
current that is lower in harmonic content than the load current.
Out of the four possible three-phase transformer connections, the
4-Y connection prevents the harmonic currents from propagating
into the primary side of the transformer and ,hence limits the
effects of the harmonic currents on the distribution system.
Among the harmonic elimination methods the passive method is
less advantageous than the active methods.
The passive method
requires relatively large inductors and capacitors to reduce the
low-frequency harmonic currents.
Active methods of harmonic
reduction use circuits that are smaller and lighter.
Chapter
five describes a new harmonic reduction ac-to-dc' converter based
on a line-frequency voltage-doubler circuit with a switch.
Simulation and experimental waveforms of the supply current are
presented.
The current harmonics are reduced substantially by
carefully closing and opening a switch during half a cycle, thus
increasing the pulsewidth of the current.
The total harmonic
distortion THD of the input current is reduced significantly and
so is the magnitude of the third harmonic current.
The advantages of this ac-to-dc harmonic reduction converter
over the high-frequency boost converter are its low cost, high
reliability and simplicity of control.
The disadvantage is its
inability to eliminate the harmonics completely.
The proposed
method of harmonic reduction can be applied to loads of a wide
power range.
In situations where the load is highly variable a
controller can be added that detects the zero crossings of the
82
current and can set the firing angles of the switch for maximum
harmonic reduction.
The harmonic current measurements and analysis in this work
can be extended to include other switch-mode power supply loads.
Among these loads are laser printers, photocopiers and fax
machines.
The phase relationships of the harmonic currents of
these loads with the harmonic currents of personal computers can
be made.
In addition, the nature of harmonic currents of
fluorescent lamps can be determined and compared with the
harmonic currents of switch-mode power supply loads in order to
obtain an overall picture of the harmonic current problem in an
office building.
It is recommended that a statistical method for calculating
the harmonic current magnitudes of a group of personal computers
be explored.
The harmonic currents of a group of personal
computers in a lab or an office can be monitored.
Using a
spectrum analyzer the harmonic current levels can be measured at
certain intervals
over several days.
(e~g.
15 minutes) at the same time of the day
The measurements can also include the phase
angles of the harmonic currents.
After the data is collected
statistical models can be formed to predict the harmonic current
levels and to gather other useful statistical information.
Oversizing the neutral conductor
to overcome the neutral
current problem due to triplen harmonic currents is only a
partial solution.
Adding a tertiary transformer winding to
eliminate the neutral current is not practical and is extremely
83
expensive.
New methods of neutral current elimination should be
explored that take cost and practicality into consideration.
One
such alternative could be harmonic current injection.
IEEE standard c57.110-1986 [11] uses approximate methods to
determine the eddy current losses of a transformer due to
harmonic currents.
A more sophisticated computer analysis is
required for the precise determination of the eddy current
losses.
Furthermore, measurements should be taken on a
transformer that is subjected to harmonic currents to validate
the analysis.
Further research is required to find the most appropriate
means of overcoming the problems caused by personal computer
harmonics.
It is well known that switch-mode power supplies can
be designed to provide harmonic-free performance.
However,
manufacturers of power supplies and personal computers have been
hesitant to include harmonic-reduction circuits in their designs
mainly because of economics.
Standards should be developed to
divide the burden of cleaning power system harmonic current
pollution between manufacturers and utilities.
84
APPENDIXl:
THE HP 3561A™ SPECTRUM ANALYZER
GENERAL FEATURES OF THE HP 3561Arn
The HP model 3561A™ is a signal analyzer covering the
frequency range 0 to 100 KHz.
Its capabilities include
time, magnitude and phase displays.
The display formats
include the display of single traces and the simultaneous
display of two traces in a top-bottom format.
Both linear
and logarithmic scaling of the display is available.
All the measurement functions of the HP 3561A™ are
programmable via the Hewlett-Packard Interface Bus
{HP-IB™).
The HP-IB™
links the
HP
3561A™ to desktop
computers, minicomputers and other HP-IB™ controlled
instruments to form automated measurement systems.
Each HP-IB™ device has an address; the address of the
3561A~
signal analyzer is 711.
HP
Data and instructions are
transferred between devices on the HP-IB™.
These
instructions or commands may be sent to the HP 3561A™ by a
controller(e.g. HP 200™ series personal computer) through
the use of BASIC instructions.
For example the BASIC
command
OUTPUT 711i"SP10KHZi"
sets the frequency span of the signal analyzer to 10 KHz.
This is the equivalent of manually pressing a front panel
key on the HP 3561A™.
85
ACCESSING DATA FROM THE HP3561Arn
The HP 3561Arn uses binary data transfers to speed up the
transfer time.
When transferred in binary format, data is
attached to a header containing information about the HP
3561A~
configuration. There are two types of traces in the
HP3561A~:
time traces that are 399 words (798 bytes) in
length and magnitude or phase traces that are 401 words (802
bytes) in length.
These traces occupy 1028 bytes of memory
with the following formats:
Time domain traces:
Byte:
1 -2
Data:
2 number
bytes
3 - 6
7 - 804
2 length 789 data
bytes: 2
bytes
unused bytes
805 - 806 807 - 1028
2 unused
bytes
222 header
bytes
Frequency domain traces:
Byte:
1 - 2
3 - 4
5 - 806
807 - 1028
Data:
2 number
, bytes
2.1ength
bytes
802 data
bytes
222 .ne ade r
bytes
The ·DSTB (dump selected trace binary) command transmits
trace data in binary format over the HP-IB™.
The following
program illustrates how a data header is accessed for a time
domain trace using the DSTB command.
86
10
20
ASSIGN
ASSIGN
30
40
REAL
50
60
70
OUTPUT
TRANSFER
CONTROL
ENTER
@Anz to 711
@Tag to BUFFER [1028]iFORMAT OFF
Start t
@Anzi"DSTB"
@Anz to @Tag; END , WAIT
@Taq,5i806+147
@Taq;Start_t
Line 10 creates an I/O path to Hp
3561A~
Line 20 creates an I/O path to the buffer that will receive
the trace data.
Line 30 declares "Start t" as a real variable.
Line 40 instructs the HP 3561A™ to prepare to transfer the
time domain trace in binary format.
Line 50 causes the trace data and the header data to be
loaded into the buffer.
transfer
be
At this point the data
is complete, but the data is not usable; it must
read into a variable.
Line 60 reads the buffer at location "806+147" where "806"
indicates the beginning of the header and "175" the
offset byte.
Line 70 reads the data beginning at byte 981 (806+175) into
the variable "Start ttl
Program 1 is the BASIC program used to transfer time
domain traces from the HP
3561A~
into files on disk.
It
reads the trace data and places it in an array "Time data".
The array "Time data" is saved in a file named "TIME1" and a
graphical display of the trace is obtained on the HP 200™
series computer for verification purposes.
87
Program 1: Reads a time trace
10
20
30
40
50
This program reads data from the time trace of HP
3561 A and associated header to obtain calibrated time
data. The data is placed in the Time data(400) array,
and is scaled and formatted. The array Time data is
saved into a file named "TIME1".
-
52
60
70
80
90
92
OPTION BASE 1
!Select a default lower array bound of 1
ASSIGN @Anz To 711
! Create an I/O path to HP 3561 A
ASSIGN @Tag To BUFFER [1028]iFORMAT OFF
! Create an I/O path to a 1028 byte
! buffer; transfer data in binary format
94
96
!
! Declare variables, arrays
!
98
100
110
120
130
140
150
160
162
164
166
170
180
190
200
202
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
INTEGER Trace type,Raw data(400)
REAL start_t,Stop_t,Cenetr_t,Time-per_div
REAL Volts full
REAL X,T~ dat~(400)
!
OUTPUT @Anzi"DSTB"
! Dump trace and header data
TRANSFER @Anz To @TAgiEND,WAIT ! Initiate the transfer
! to the buffer; wait until
! all the data has been
! transferred
LOCAL @Anz
!
! Read the data and the header; the header is offset by
! 806 bytes
,
CONTROL @Tag,Si4
! Position to buffer byte 4
ENTER @TagiRaw data(*)
! and read the data
!
-
CONTROL @Taq,5i806+14S!Position to buffer header offset
ENTER @TaqiTrace type ! by 145 bytes to read trace type
IF Trace type<2 THEN
! if not time trace send error
BEEP
_.
! message and quit
PRINT "not time data"
GOTO 820
END IF
!
CONTROL @Tag,5i806+147 !Position to buffer offset byte
ENTER @TaqiStart t
! 147 and read start time
!
-
CONTROL @Tag,5i806+155
ENTER @taqiStop t
Position to buffer offset byte
! 1.55 and read stop time
CONTROL @taq,5i806+163
Position to buffer offset byte
!
-
88
400
410
420
430
440
450
460
470
480
490
500
510
520
530
540
550
560
570
580
582
584
590
591
592
594
595
596
597
598
600
610
620
630
631
632
634
633
640
650
660
670
680
690
700
702
710
720
722
730
740
,
ENTER @tagiCenter t
-
! 163 and read center time
CONTROL @taq,5i806+171 !Position to buffer offset byte
ENTER @tagiTimeyer_div
! 171 and read time/dive
!
CONTROL @taq,5i806+179
ENTER @taqiVolts full
!Position to buffer offset byte
! 179 and read volts full scale
!
!
! Scale data to -128 to +127 range
,
Factor=Volts full/32768
FOR 1=1 TO 399
CONTROL @Taq,5i2*I+5
ENTER @Tag iRaw data (I)
IF Raw data(I»128 THEN Raw data(I)=Raw data(I)-256
NEXT I!
- -
MAT Time data=Raw data*(Factor) ! Copy the scaled raw
! data array into time data
! array
,
! Convert into rnA
!
Factor1=(1000/0.015)
! 0.015 is the shunt resistance
FOR 1=1 TO 400
Time data(I)=Time data(I)*Factorl
NEXT-I
!
-
Find the array maximum
Find the array minimum
Maxi=MAX(Time data(*»
~ni=MIN(Time-data(*»
IF
~ni=Maxi
THEN STOP
!
CREATE ASCII "TlME1", 50 !Create an ASCII file of length
ASSIGN @Path To "TIMEl" ! 50i Create an I/O path to
! filei
OUTPUT @PathiTime data(*) ! Transfer array to file
!
! Plot the
-
data
!
GCLEAR
Clear the graphics display
GINIT
Setup the graphics display
GRAPHICS ON
VIEWPORT 60,120,40,80 I Define area of screen for
I display
!
WINDOW 0,400,Mini,Maxi
I
Define values for ends of
! the axis
FRAME
! Draw a frame around the graphics
PRINT "max+value",Maxi
! print a summary of the data
89
750
760
770
780
790
800
810
820
830
PRINT "min-value",Mini
PRINT "start time",Start t
PRINT "stop time" ,Stop tMOVE 1,Time data(l) !-Move the pen to the first point
FOR "I=! TO 400
DRAW I,Time data (I)
Plot the data
NEXT I
STOP
END
Program 2
was used to transfer magnitude frequency
domain traces into files on disk.
In program 2 the raw data
is transferred into the array "Mag_data".
The data is
scaled using a conversion factor of 0.005 dB and then it is
converted to unitless from decibels.
saved into a file named "MAG!".
Finally, the data is
Program 3 transfers phase
frequency domain traces into files.
The raw data is moved
to array "Phase data" and is scaled by a factor of 0.1
degrees.
90
Program 2: Reads a magnitude trace
1
2
5
This program reads data from the frequency magnitude
trace of HP 3561 A and associated header to obtain
calibrated magnitude data. The data is placed in the
Mag data(402) array, and is scaled and formatted.
The-array, Nmag data(402} is saved into a file named
6
"MAGI" •
3
4
10
20
30
40
42
44
50
52
54
60
70
71
80
90
100
110
120
130
131
132
133
134
135
136
137
140
150
160
161
162
163
164
165
166
167
168
169
170
180
190
-
OPTION BASE 1
!Select a default lower array bound
ASSIGN @Anz TO 711
ASSIGN @Tag TO BUFFER [1028];FORMAT OFF
! Create an I/O path to a 1028 byte
! buffer; transfer data in binary
!
! Declare variables, arrays
!
INTEGER Raw data(402)
REAL Mag data (402) ,Nmag data(402)
REAL Center_f,Fre~span-
!
!
!
OUTPUT @Anzi"DSTB"
!Dump trace and header data
CONTROL @Taq,3i1
TRANSFER @Anz TO @TagiCOUNT 1028,WAIT! Initiate the
! transfer to the buffer; wait until
! all the data has been transferred
!
LOCAL @Anz
!
! Read the data and the header; the header is offset by
! 806 bytes
!
CONTROL @Taq,5i5
! Position to buffer byte 5
ENTER @TagiRaw data(*)
! and read the data
!
-
CONTROL @Tag,5i806+147 !Position to buffer offset byte
ENTER @TagiCenter f
!147 and read center frequency
!
CONTROL @Tag,5i806+155 !Position to buffer offset byte
ENTER @TagiFre~span
! 155 and read frequency span
!
!scale data by multiplying by a factor of 0.005 dB
!copy the scaled raw data array into mag. data array
!
MAT
!
Mag_data=Raw_data*(.OOS)
91
200
202
210
220
230
240
250
251
252
253
254
255
256
270
280
290
300
301
302
303
304
305
306
307
310
320
330
340
342
350
352
360
370
380
381
382
390
400
410
420
421
422
423
430
440
! convert decibel data to unitless data
! default display unit is dB
!
FOR 1=1 TO 401
Nmaq data(I)=10.0 A(Mag data(I)/20.0)
NEXT-I
!
! convert into rnA
!
Factor=(1000/0.015)
! 0.015 is the shunt resistance
FOR I=l TO 401
Nmag data(I)=Nmaq data(I)*Factor
NEXT-I
!
Maxi=MAX(Nmag data(*»
! Find the array maximum
Mini=MIN(Nmaq-data(*»
! Find the array minimum
!
CREATE ASCII "MAG1",50
!Create an ASCII file of
ASSIGN @Path To "MAG1"
!length 50; Create an r/o path
OUTPUT @PathiNmag data(*)! to file; Transfer array to
- ! file
!
! Plot the data
!
GCLEAR
! Clear the graphics display
GINIT
! Setup the graphics display
GRAPHICS ON
VIEWPORT 60,120,40,80! Define area of screen for
! display
WINDOW 0,400,~ni,Maxi ! Define values for ends of
! the axis
FRAME
! Draw a frame around the graphics
PRINT "max value=",Maxi ! print a summary of the data
PRINT "min value=",Mini
PRINT "center freq.=",Center f
PRINT "freq. span=" ,FreCLspan
MOVE 1,Nmag data (1) ! Move the pen to the first point
FOR I=l TO 401
DRAW I,Nmag data (I) ! Plot the data
NEXT I
PRINT
PRINT
PRINT
STOP
END
92
Program 3: Reads a phase trace
1
2
3
4
5
6
10
20
30
40
42
44
50
52
54
60
70
71
80
90
100
110
120
130
131
132
133
134
135
136
137
140
150
160
161
162
163
165
166
167
168
169
1"'.0
172
174
175
176
178
This program reads data from the frequency phase
trace of HP 3561 A and associated header to obtain
calibrated phase data. The data is placed in the
Phase data(402) array, and is scaled and formatted.
The array Phase data(402) is saved into a file named
"PHASE1".
OPTION BASE 1
!Select a default lower array bound
ASSIGN @Anz TO 711
ASSIGN @Taq TO BUFFER [1028]iFORMAT OFF
! Create an I/O path to a 1028 byte
! buffer; transfer data in binary
!
! Declare variables, arrays
!
INTEGER Raw data (402) , Phase offset
REAL Phase data(402)·
-
REAL
Center_f,Fre~span
!
!
!
OUTPUT @Anzi"DSTB"
!Dump trace and header data
CONTROL @Taq,3i1
TRANSFER @Anz TO @TagiCOUNT 1028,WAIT! Initiate the
! transfer to the bufferi wait until
! all the data has been transferred
!
LOCAL @Anz
!
! Read the data and the header; the header is offset by
! 806 bytes
!
CONTROL @Taq,5i5
! Position to buffer byte 5
ENTER @TaqiRaw data(*)
! and read the data
!
CONTROL @Taq,5i807
! Position to buffer byte 807
ENTER @TaqiPhase offset ! and read phase offset
!.
CONTROL @Taq,5i806+147 !Position to buffer offset byte
ENTER @TaqiCenter f
!147 and read center frequency
!
CONTROL @Taq,5i806+155 !Position to buffer offset byte
ENTER @Tag iFre~span
! 155 and read frequency scan
!
! scale data by multiplying by a factor of 0.1 degrees
! add phase offset and copy raw data array into phase
! data array
!
93
180
181
182
183
184
185
186
187
188
189
191
200
280
290
300
301
302
303
304
305
306
307
310
320
330
340
342
350
352
360
362
364
370
3 80
381
382
390
400
410
420
421
422
423
430
440
MAT
MAT
Phase data=Raw data*(.l)
Phase data=Phase_data+(Phase_offset)
!
! Check for undefined values
!
FOR 1=1 TO 401
IF Phase data(I)<-3000
Phase data(I)=O
END IF
NEXT I
THEN
!
!
Maxi=MAX(Phase data(*»
~ni=MIN(Phase-data(*»
!
Find the array maximum
Find the array minimum
-
CREATE ASCII "PHASE1",50
Create an ASCII file of
ASSIGN @Path To "PHASE1" !length 50; Create an I/O path
OUTPUT @Path;Phase data(*) ! to file; Transfer array to
- ! file
!
! Plot the
!
data
GCLEAR
! Clear the graphics.display
GINIT
! Setup the graphics display
GRAPHICS ON
VIEWPORT 60,120,40,80! Define area of screen for
! display
WINDOW 0/400,Mini,Maxi ! Define values for ends of
! the axis
FRAME
! Draw a frame around the graphics
PRINT "Phase offset=",Phase_offset ! print a sununary of
! the data
PRINT "max value=" , Maxi
PRINT "min value=" , ~ni
PRINT "center freq.=",Center f
PRINT "freq. span=" , FreCl...span
MOVE 1,Phase data(l) ! Move the pen to the first point
FOR 1=1 TO 40"1
DRAW I,Phase data (I) ! Plot the data
NEXT I
PRINT
PRINT
PRINT
STOP
END
94
APPENDIX 2: PSPICE PROGRAMS
PROGRAMS FOR TRANSFORMER CIRCUIT ANALYSIS
PSpice program 1
* This program performs a transient analysis of a single phase
* transformer with a nonlinear rectifier load.
*
.OPTIONS RE1T01=0.1 ITL5=0 ITL4=500
*
Input AC Voltage of 250 V peak
VIN 0 1 SIN ( 0 250 60Hz)
*
Series resistor of 10 ohms
Rl 1 2 10
*
Transformer inductor 11 of 500 turns
Ll 2 0 500
*
Transformer inductor L2 of 500 turns
L2 3 0 500
*
Transformer inductor. coupling coefficient of .9999
K12 L1 L2 0.9999 CMOD
*
Model parameters for nonlinear magnetic transformer
*
AREA
Mean magnetic cross section in cm2
*
PATH
Mean magnetic path length in em
*
GAP
Effective air-gap length in em
*
MS
Magnetic saturation in Aim
*
ALPHA = Mean field parameter
*
A
Shape parameter
*
C
= Domain wall=flexing constant
*
K
= Domain wall-pinning constant
.MODEL CMOD CORE (AREA=20 PATH=40 GAP=O.l MS=1.6E+5 ALPHA=le-3
+ A=lOOO C=0.5 K=1500)
*
*
*
*
Full-Wave bridge rectifier load
diodes
d2 5 0 diode
d4 5 3 diode
dl 3 6 diode
d3 0 6 diode
.model diode d
*
output inductor of ImH
L3 6 7 1rnH
*
output capacitor Cd of 1 mF
cd 7 5 ImF
*
load Resistor of 10 ohms
Rl 7 5 10
*
transient analysis from 0 to Is in steps of 1ms
.TRAN 1ms Is Os 1ms
. PROBE
.END
95
PSpice program 2
* This program performs a transient analysis of a three phase
* y - Y connected transformer with nonlinear rectifier loads.
*
.OPTIONS RELTOL=O.1 ITL5=0 ITL4=500
Transformer phase A
*
*
*
VINI
*
Rl 1
Input Voltage of 200 V
1 0 SIN ( 0 200 60Hz 0 0 0 )
Series resistor of 10 ohms
2 10
*
Transformer Inductors of 500 turns
Ll 2 0 500
L2 3 10 500
*
Link Resistor between 11 and L2
Rlink 10 0 lE+6
*
Inductor Coupling Kl = 0.9999
Kl Ll L2 0.9999 CMOD
*Model for CMOD
.MODEL CMOD CORE (AREA=20 PATH=40 GAP=O.1 MS=I.6E+5 ALPHA=le-3
+ A=1000 C=0.5 K=1500)
*
Full-Wave Bridge Rectifier load
*
diodes
d2 5 10 diode
d4 5 3 diode
dl 3 6 diode
d3 10 6 diode
.model diode d
*
output inductor of ImH
L3 6 7 ImH
*
output capacitor Cd of 1 mF
cdl 7 5 ImF
*
load resistor of 10 ohms
Rll 7 5 10
*
*
*
*
Transformer phase B
Input Voltage of 200 V at phase angle -120 degrees
VIN2 11 0 SIN ( 0 200 60Hz 0 0 -120)
*
Series resistor of 10 ohms
Rl1 11 12 10
*
Transformer Inductors of 500 turns
L11 12 0 500
L12 13 10 500
*
Inductor Coupling K2 = 0.9999
K2 Ll1 L12 0.9999 CMOD
*
. Full-Wave Bridge Rectifier load
*
diodes
d12 15 10 diode
96
d14 15 13 diode
d11 13 16 diode
d13 10 16 diode
output inductor of ImH
*
L13 16 17 ImH .
*
output capacitor Cd of 1 mF
cd2 17 15 ImF
load Resistor of 10 ohms
*
R12 17 15 10
*
*
*
*
VIN3
*
Transformer phase C
Input Voltage of 200 V at phase angle 120 degrees
21 0 SIN ( 0 200 60Hz 0 0 120)
Series resistor of 10 ohms
R21 21 22 10
Transformer Inductors of 500 turns
*
L21 22 0 500
L22 23 10 500
Inductor Coupling K3 = 0.9999
*
K3 L21 L22 0.9999 CMOD
*
*
Full-Wave Bridge Rectifier load
diodes
*
d22 25 10 diode
d24 25 23 diode
d21 23 26 diode
d23 10 26 diode
output inductor of ImH
*
L23 26 27 1mH
capacitor Cd of 1 rnF
*
cd3 27 25 ImF
load Resistor of 10 ohms
*
R13 27 25 10
Transient Analys.is from 1 illS to 500
*
.TRAN 1ms 500ms Os 1ms
. PROBE
.END
IDS
97
PSpice program 3
* This program performs a transient analysis of a three phase
* a - Y connected transformer with nonlinear rectifier loads.
*
.OPTIONS RELTOL=O.l ITL5=0 ITL4=500
*
*
Transformer phase A
*
Input Voltage of 200 V
VINI 1 10 SIN ( 0 200 60Hz 0 0 0 )
*
Series resistor of 5 ohms
Rl 1 2 5
*
Link Resistor between Ll and L2
Rlink 10 0 lE+6
*
Transformer Inductors of 500 turns
Ll 2 50 500
12 3 0 500
Rsl 50 22 5
Inductor Coupling Kl = 0.9999
*
Kl Ll 12 0.9999 CMOD
*Model for CMOD
.MODE1 CMOD CORE (AREA=20 PATH=40 GAP=O.1 MS=1.6E+5 ALPHA=le-3
+ A=1000 C~0.5 K=1500)
*
Full-Wave Bridge Rectifier load
*
diodes
d2 5 0 diode
d4 5 3 diode
dl 3 6 diode
d3 0 6 diode
.model diode d
output inductor of ImH
*
L3 6 7 lrnH
*
capacitor Cd of 1 mF
cd1 7 5 ImF
load Resistor of 10 ohms
*
R11 7 5 10
*
*
Transformer phase B
*
Input Voltage of 200 V at phase angle of -120 degrees
VIN2 11 10 SIN ( 0 200 60Hz 0 0 -120)
*Series resistor
Rl1 11 12 5
*
Transformer Inductors
Lll 12 52 500
L12 13 0 500
Rs2 52 2 5
*
Inductor Coupling
K2 111 L12 0.9999 CMOD
*
Full-Wave Bridge Rectifier LOAD
*
diodes
98
d12
d14
dll
d13
15 0 diode
15 13 diode
13 16 diode
o 16 diode
output inductor
*
L13 16 17 1mH
capacitor Cd of 1 rnF
*
cd2 17 15 1mF
load Resistor
*
R12 17 15 10
*
*
*
Transformer Phase c
Input voltage of 200 V at 120 degrees
VIN3 21 10 SIN ( 0 200 60Hz 0 0 120)
*
Series resistor
R21 21 22 5
*
Transformer Inductors
L21 22 51 500
L22 23 0 500
Rs3 51 12 5
*
Inductor Coupling
K3 L21 L22 0.9999 CMOD
*
Full-Wave Bridge Rectifier load
*
diodes
d22 25 0 diode
d24 25 23 diode
d21 23 26 diode
d23 0 26 diode
*
output inductor
L23 26 27 1mH
*
capacitor Cd of 1 mF
cd3 27 25 1mF
*
load Resistor
R13 27 25 10
*
Transient analysis from 1 ms to 500 ms
.TRAN 1rns 500ms Os 1ms
. PROBE
.END
99
PROGRAMS FOR HARMONIC ELIMINATION CIRCUIT ANALYSIS
PSpice program 4
* This program performs a transient analysis of a bridge
* rectifier with a boost stage (figure 5.3). The switch of the
* boost converter is operated at a frequency of 2 KHz
*
.options RELTOL=O.Ol 1TL5=0 1TL4=50
*
diodes
d2 a 2 diode
d4 a 1 diode
*
Supply Voltage of 120v at 60Hz
vi 1 2 sin (0 120 60HZ)
*
diodes
dl 1 3 diode
d3 2 3 diode
.model diode d
*
voltage controlled switch
81·4 0 8 0 SMOD
.MODEL SMOD VSWITCH (RON=lE-12 ROFF=lE+12 VON=5 VOFF=O)
VC 8 a PULSE (0 5 Oms 0 0 200us O.5ms)
*
output inductor
Ll 3 4 15mH
* diode
d5 4 5 diode
*
capacitor Cd of 0.5 mF
cd 5 0 0.5mF
*
load Resistor
Rl 5 a 200
*
transient analysis from 100 illS to 120 illS
.tran O.lms 120ms lOOms 0.5ms
.probe
.four 60HZ i(vi)
.end
100
PSpice program 5
* This program performs a transient analysis of a basic bridge
* rectifier circuit
*
(figure 5.10).
.options RELTOL=O.Ol ITL5=O
diodes
d2 2 0 diode
d4 2 1 diode
*
Supply Voltage of 120v at 60Hz
vi 10 0 sin (0 120 60HZ)
*
Supply Series Inductor
11 10 1 10mH
* diodes
d1 1 3 diode
d3 0 3 diode
.model diode d
*
capacitors Cd of 1 mF
cl 3 6 0.5mF
c2 6 2 0.5mF
*
load Resistor
rl 3 2 200
*
transient analysis from 200 ms to 300ms
.tran O.05ms 300ms 200ms O.lms
.four 60hz i(vi)
.probe
.end
*
101
PSpice program 6
* This program performs a transient analysis of the proposed
* harmonic reduction circuit of figure 5.9.
*
.options RELTOL=O.Ol ITL5=O
*
diodes
d2 2 0 diode
d4 2 1 diode
*
Supply Voltage of 120v at 60Hz
vi 10 0 sin (0 120 60HZ)
*
Supply Series Inductor
11 10 1 lOmH
*
diodes
dl 1 3 diode
d3 0 3 diode
.model diode d
*
Switch conduction times t1=2.1 s , t2=2.0 s
Sl 0 6 8 0 SMOD
.MODEL SMOD VSWITCH (RON=lE-6 ROFF=lE+6 VON=5 VOFF=O)
VC 8 9 PULSE (0 5 Oms 0 0 2.1ms 8.333ms)
Vel 9 0 PULSE (0 5 6.2ms 0 0 2.0ms 8.333ms)
*
capacitors Cl and C2 of 0.5 mF
c1 3 6 O.5mF
c2 6 2 0.5mF
*
load Resistor
rl 3 2 200
*
transient analysis from 200ms to 300ms
.tran O.OSms 300ms 200ms O.lms
.four 60hz i(vi)
.probe
.end
102
References
[1]
Arrillaga J., Bradley D.A., Bodger P.S., Power System
Harmonics, ,John Wiley & Sons, 1985.
[2]
Shepherd W., Zand P., Energy Flow and Power Factor in
Nonsinusoidal Circuits, Cambridge University Press, 1979.
[3] Orr J., Oberg K., "Current Harmonics Generated by a
Cluster of Electric Battery Chargers," IEEE Trans. Ind.
Appl., No.3, PP 691 - 700, March 1982.
[4] Liew A., "Excessive Neutral Currents in Three Phase
Fluorescent Lighting Circuits," IEEE Trans. Ind. Appl.,
Vol.25, No.4, PP 776 - 782, July/Aug. 1989.
[5] Gruzs T., "A Survey of Neutral Currents in Three-phase
Computer Systems," IEEE Trans. Ind. Appl., Vol. 26, No.4, PP
719 - 725, July/Aug. 1990.
[6] Key T.S., Lai, Jih-Sheng , "Comparison of Standards and
Power supply Design Options for Limiting Harmonic Distortion
in Power Systems," IEEE Trans. on Industry Applications,
·VOL. 29, NO.4, PP. 688-695, July/Aug. 93.
103
[7]
Kelly A.W, Hallouda M.A., Doore M.D., Nance J.L., "Near-
uni ty-power-factor Single-phase AC-to-DC Converter using a
Phase-controlled Rectifier," Proceedings of the 1992 Applied
Power Electronics· Conference, Feb. 92, Boston, MA.
[8]
Mohan N., Undeland T.M., Robbins W. P., Power Electronics:
Converters, Applications and Design,
John Wiley & Sons, New
York, 1989.
[9]
Malvino A.P., Electronic Principles, Macrnillan/McGraw-
Hill, 1991.
[10] Kreysig E., Advanced Engineering Mathematics, John Wiley
& Sons, 1988.
[11]IEEE Recommended Practice for Establishing Transformer
Capability When ,Supplying Nonsinusoidal Load Currents.
ANSI/IEEE C57.110-1986 .
[12]
McPherson G., An Introduction to Electrical Machines and
Transformers, John Wiley & Sons, 1981.
[13]
Rashid M.H., Spice For Circuits And Electronics Using
PSpice,
Prentice-Hall Inc. , 1990.
104
[14] IEEE Guide for Harmonic Control and Reactive Compensation
of Static Power Converters, IEEE standard 519, 1981.
[15]
J.
Subjak, J. Mcquikin,
Measurements,
"Harmonics - Causes, Effects,
and Analysis : An update," IEEE Trans.
Ind.
Appl., Vol. 26, No.5, PP 1034 - 1042, Nov./Dec. 1990.
[16] J. Winn, D. Crow, "Harmonic Measurements Using a Digital
Storage Oscilloscope," IEEE Trans . Ind. Appl., Vol. 25. No.4,
PP 783 - 788, July/Aug. 1989.
[17] l1.A. Geisler, "Predicting Power Factor and Other Input
Parameters for Switching Power Supplies," Proceedings of the
1990 Applied Power Electronics Conference, March 90, Dallas,
Texas.
[18]
P.N. Enjeti,
R. Martinez,
"A High Performance Single
Phase AC to DC Rectifier with Input Power Factor Correction,"
Proceedings of the 1993 Applied Power Electronics Conference,
March 93, San Diego, California.
105
[19]
Aintablian H.O., Hill H.W., Jr., "Harmonic Currents of
Personal
System
Computers
Neutral
Applications
and
t hei r
Current,"
Society
Effects
on
Proceedings
Annual
Meeting,
,
H. W. ,
the
of
Distribution
the
Industrial
93,
Oct.
Toronto,
Ontario.
[20]
Aintablian
H. o.
Hill
Jr. ,
"The
Effects
of
Harmonic Currents of Personal Computers on the Distribution
Transformer, "
Proceeding,s
of
the
North
American
Power
Symposium, Oct. 92, Reno, Nevada.
[21]
Aintablian H.O., Hill H.W., Jr., "Harmonic Currents of
Personal
Computers
and
System Neutral
Current."
Conference
of
Power
Vancouver,
Be.
their
Effects
Proceedings
Systems
and
on
of
the
the
Distribution
International
Engineering,
Aug.
92,
Abstract
Aintablian, Hrair, Ohannes Ph.D. June 1994
Electrical and Computer Engineering
Harmonic Currents Generated by Personal Computers, their
Effects on the Power System and Methods of Harmonic
Reduction (105 pp.)
Director of Dissertation: H.W.Hill Jr.
The switching mode power supplies used in personal
computers are major sources of harmonic currents. Measured
and calculated waveforms and harmonic levels of input
currents of various types of personal computers are
presented. Harmonic currents of a group of personal
computers reinforce each other. Neutral currents resulting
from the addition of triplen harmonics are analyzed and
recommendations are made to safeguard against potential
problems.
The impact of personal computer harmonic currents
on distribution transformer losses are explored.
Harmonic
currents result in the overheating of transformer due to
excessive eddy current losses.
In addition, the influence
of three-phase transformer connection on the distribution
system neutral current is examined. In the past ten years
several methods of power factor improvement through harmonic
elimination have been developed that use high frequency