Continuous Load Current Mode Analysis of Phase-Controlled
AC to DC Converters.
C.U. Ogbuka, M.Eng.* and M.U. Agu, Ph.D.
Department of Electrical Engineering, University of Nigeria, Nsukka, Nigeria.
E-mail: ucogbuka@yahoo.com
drmarcelagu@yahoo.co.uk
ABSTRACT
In this paper, an insightful analysis of controlled
AC to DC converters operating under continuous
load current mode is presented. The midpoint
converter, as the basic building block of other AC
to DC converter application circuits, is first
analyzed in positive and negative conversion
modes. The full bridge converter, fully controlled,
is shown to comprise a positive and negative
midpoint converter sharing a common AC input
and differentially supplying a common output
load. The analysis results can be used to predict
the output performance of any standard phase
controlled converter application circuit with any
given number of AC input phases and/or output
pulses under continuous load current. The
®
software for simulation is Ansoft SIMPLORER .
(Keyword: AC to DC converter, continuous load,
current mode, midpoint, full bridge)
THE FULLY CONTROLLED MIDPOINT
CONVERTERS
The fully controlled AC to DC midpoint
converters, especially the two and the three pulse
types, constitute the primary units for configuring
or realizing other forms of AC to DC converters.
The midpoint converter has two forms of
connection namely: the positive (forward
connected) converter and the negative (reverse
connected) converter. In phase control, the
control parameter is control delay angle whose
zero point is given by:
t
AC to DC converters are widely applied
industrially, commercially, and domestically. The
AC to DC converter changes AC input
voltage/current to an output with unidirectional
current. The conversion can be controlled or
uncontrolled. When uncontrolled, the switching
semiconductor used is the diode. When
controlled, the switching semiconductor is the
three phase terminal thyristor or transistor. The
thyristor is preferred because of the nature of the
AC input with which thyristor turn-off can be
effected.
The AC to DC converter are of two basic
configurations:
(
0
Where
1
2
1
)
Np
(1)
N p is the converter output pulse number
and the control signal length for continuous gating
is
INTRODUCTION
*
2
. The circuit configurations for two and
Np
three pulse midpoint converter configurations are
as shown in Figure 1.
i g1
io
ig 2
R
T1
T2
vo
L
_v s
_v s
_
_E
Figure 1: Two Pulse Midpoint Positive Converter.
a) The midpoint AC to DC converter
b) The full bridge AC to DC converter
The Pacific Journal of Science and Technology
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–91–
Volume 11. Number 2. November 2010 (Fall)
Where the two sources are displaced by angle
. The source relationships are:
vs
Vm sin t
vs
Vm sin t
Vm sin( t
)
(2)
If the active switches are turned around to have
cathode point at the positive terminal of the
voltage supply, then we have negative AC to DC
converters as shown below for the two and three
pulse configurations.
io
N p is two in eqn 1, so for the two pulse midpoint
converter the zero point of the control delay angle
is zero.
t
ta
0
0
(3)
For the three phase supply, the three pulse
midpoint positive converter is shown below.
io
T1
T2
T3
_v an
_v bn
_v cn
R
T1
T2
vo
L
_v s
_v s
_
_E
Figure 3: Two Pulse Midpoint Negative
Converter.
R
vo
L
_
_E
Figure 2: Three Pulse Midpoint Positive
Converter.
io
R
T1
T2
T3
vo
L
_v an
_v bn
v
_ cn
_
_E
Figure 4: Three Pulse Midpoint Negative
Converter.
The three phase voltage is represented as:
v an
Vm sin t
2
)
3
4
)
3
vbn
Vm sin( t
v cn
Vm sin( t
Np
3 in Equation 1, so for the three pulse
(4)
midpoint converter the zero point of the control
delay angle is
6.
t
0
ta
6
(5)
These are the practical midpoint phase controlled
converters since we have single phase and three
phase systems in the utility supply.
The Pacific Journal of Science and Technology
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THE FULLY CONTROLLED FULL BRIDGE
CONVERTERS
Although the midpoint AC to DC converter is the
basic building block for realizing other converter
types, its application in industry is limited because
of the severe problems associated with the
presence of DC current in the AC input lines and
the enormous effort it takes in terms of providing
reactive components/equipment to solve the
associated problems.
The concept of full bridge converter usually
made-up of one positive and one negative
converter supplying differential output voltage to
the common load. The circuit configurations are
show below.
–92–
Volume 11. Number 2. November 2010 (Fall)
vs
T1
vs
T3
v an
T1
v bn
T3
v cn
T5
Load
Load
vs
T4
v an
T4
vs
T2
v bn
T6
v cn
T2
Figure 5a: Two Pulse Full Bridge Converter
This Circuit is Analytically Equivalent to the Figure
5b Below.
Figure 6a: Three Phase Full Bridge Converter
The Figure 6a modifies to:
io
T1
T3
io
Load
2v s
T4
T2
T3
T1
T5
z
Figure 5b: Analysis Circuit of Two Pulse Full
Bridge Converter.
Similar argument can be made for three phase
full bridge converter as shown in the figures
below.
The Pacific Journal of Science and Technology
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y
x
T4
Load
T6
T2
Figure 6b: Three Phase Full Bridge Converter
A Typical Representation of the Above Circuit is
Shown Below.
–93–
Volume 11. Number 2. November 2010 (Fall)
io
T3
T1
Midpoint Converters
For the midpoint converter at continuous load
current mode, the converter output voltage v o
T5
a
can be given as:
b
c
Load
v0
T2
T6
T4
(a n cos n t bn sin n t ) Voo
n jN p
Where
Figure 6c: Analysis Circuit of Three Phase Full
Bridge Converter
(7)
j 1, 2 , 3 ,...
N p is the output pulse number for the
midpoint converter and
Voo is the average output
voltage. When generally analyzed, Equation 7
can be simplified as:
Where,
x Van Vbn
Vab
Vm sin t Vm sin( t
3Vm sin( t
y Vbn Vcn Vbc Vm sin( t
)
2
)
(6b)
4
) Vm sin t
3
7
3Vm sin( t
) (6c)
6
Vm sin( t
OPERATIONAL ANALYSIS OF PHASE
CONTROLLED AC TO DC CONVERTERS
N p pulse phase controlled AC to DC
converter operates in two current conduction
modes: Discontinuous Current Mode and
Continuous Current Mode. In most cases, the
conduction mode is continuous load current,
hence this work emphasizes only on this mode of
operation.
The Pacific Journal of Science and Technology
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Vodmn [cos
Vopn ]
n jN p
(8)
j 1, 2 , 3...
For positive midpoint converter where
Negative converters are obtained in the full bridge
configuration by turning the inverter upside down
or by reversing the polarity of all the switches
thereby shifting the respective signals by .
The
v0
(6a)
2
4
) Vm sin( t
)
3
3
3Vm sin( t
z Vcn Van Vca
6
2
)
3
the maximum value of average voltage
Vodmn
Where,
Voo max
N pVmn
sin
Vodmn is
Voo max ,
(9)
Np
, is the control delay angle and
V mn is
th
the amplitude of the AC input per cycle. The n
harmonic amplitude for positive midpoint
converter for n even is derived as:
Vopn
cn sin(n t
n
)
(10a)
And for n odd is derived as:
Vopn
cn cos(n t
Where
n
is the
n
n th
)
(10b)
harmonic voltage phase
angle while
cn [
1
(n 1) 2
1
(n 1) 2
2
cos 2 ]1 / 2 (11)
(n 1)(n 1)
–94–
Volume 11. Number 2. November 2010 (Fall)
For negative midpoint converters,
vo can
be
simplified as:
vo Vodmn cos
Vopn
n jN p
v0
Vodmn [ cos
Vonn ]
n jN p
cos
Vonn
n jN p
j 1, 2 , 3...
j 1, 2 , 3...
(15a)
(12)
j 1, 2 , 3...
th
The n
harmonic amplitude for negative
midpoint converter for n even is derived as:
vo Vodmn 2 cos
Vonn
It is to be noted that the magnitude of DC
c n sin(n t
n
)
(13a)
component
And for n odd is derived as:
Vonn
c n cos(n t
Where Vodmn ,
, and
n
)
(13b)
c n are as earlier defined.
vo
ve Converter
vo
Figure 7: Conceptual Circuit of Full Bridge AC to
DC Converter.
Where,
vo
vo
for either positive or
(14)
The Pacific Journal of Science and Technology
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.
Vopn Vonn
(16)
For n even,
c n [sin( n t
n
) sin(n t
n
n
)] (17a)
)
(17b)
For n odd
cn [ cos(n t
n
) cos(n t
n
)]
(18)
The implication of this is that the full bridge
configuration eliminates odd harmonics even
when present in the midpoint converters that
make it up, but doubles the amplitude of the even
harmonics.
For the full bridge converter, the maximum value
of average voltage:
are obvious from the figure above
as the output voltage of the positive and the
negative converters respectively. From the above
analysis for the positive and the negative midpoint
converters,
2Vodmn cos
The nth harmonic amplitude for the full bridge
converter is:
Vonf
0
vo
and
Vodmn cos
2c n sin(n t
ve Converter
vo
j 1, 2 , 3...
bridge converter to become
Vonf
Full bridge AC to DC converters are made-up of
positive and negative midpoint converters as
shown below.
vo
(15b)
negative midpoint converters is doubled in the full
Full Bridge Converter
vo
(Vopn Vonn )
n jN p
Voo max
2Vodmn
2Vmn N p
sin
Np
(19)
–95–
Volume 11. Number 2. November 2010 (Fall)
Parallel operation of full bridge converters is also
obtainable to achieve 12-pulse and, indeed, other
multpulse
converter
configurations.
A
freewheeling diode can also be connected across
the converter load.
b. Three pulse AC/DC converter (positive
and negative) with
van
230 2 sin t
®
vbn
230 2 sin( t
2
)
3
®
vcn
230 2 sin( t
4
)
3
SIMPLORER SIMULATION OF SAMPLE AC
TO DC CONVERTERS UNDER DIFFERENT
OPERATION CONDITIONS
SIMPLORER ,
a
trademark
of
Ansoft
Corporation, is a simulation package for electric
circuit simulations that allows you to easily and
quickly model all components of your application.
You can design and model with electric and
electronic facts; control and mechanical
components; discontinuous processes; and
controls with electric circuits, block diagrams, and
state graph components.
c.
Six pulse (3-phase full bridge) both
positive and negative with input as
vab
415 2 sin t
vbc
415 2 sin( t
2
)
3
vbc
415 2 sin( t
4
)
3
®
The task of simulation using SIMPLORER
involves creation of project using SSC
Commander, creation of model using the
graphical
input
tool
schematic
or
the
®
SIMPLORER text editor, evaluation and analysis
of result using the simulator data and Day Post
Processor applications, respectively
In this section, various configurations of AC to DC
converter
are
simulated
using
Ansoft
®
SIMPLORER for the two-pulse, three pulse, and
the six-pulse converter. Both the positive
converter
and
the
negative
converter
arrangements are investigated.
I.
The load is 50 resistor with both
positive and negative converter
II.
Series combination of 10
resistor,
60mH inductance, and 120V EMF with
positive converter only.
Simulation Task
0
For control delay angle
display output voltage
a. Two-pulse
vo
and
3
In each case, the output voltage of the desired
load is the parameter of interest.
for:
AC/DC
vs
230 2 sin t
f
50H Z for
converter
both
negative converters.
where
positive
The Pacific Journal of Science and Technology
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(input
and
–96–
Volume 11. Number 2. November 2010 (Fall)
Simulation Results
Two Pulse Rectif ier (Delay Angle=0, Duty Cy cle=0.5) Positiv e Conv erter
Two Pulse Rectif ier (Delay Angle=0, Duty Cy cle=0.5) Negativ e Conv erter
0.8k
E1.V [V]
0.8k
0.6k
0.4k
D3
PWM
0.2k
E1.V [V]
0.6k
PWM
D1
S3
PW M3
S1
PW M1
0.4k
0.2k
0
PWM
R1
R := 50
PWM
PW M1
PW M3
S1
S3
D3
D1
-0.2k
0
R := 50
-0.4k
R1
-0.6k
0
2.5m
5m
7.5m
10m
13m
15m
18m
0.7k
R1.V [V]
S4
PWM
PWM
PW M2
2m
4m
6m
8m
10m 12m 14m 16m
20m t [s]
0.1k
D4
0.5k
S2
0
S2
PW M2
PW M4
0.6k
S4
-0. 8k
PWM
PW M4
PWM
-0. 6k
21m t [s]
D2
D4
-0. 4k
E1
-0.8k
E1
-0. 2k
R1.V [V]
0
D2
-0. 1k
0.4k
-0. 2k
0.3k
-0. 3k
Switches
S1
S2
S3
S4
0.2k
Switches
S1
S2
S3
S4
Phase Shif t
0
0
180
180
0.1k
0
-0.1k
0
2.5m
5m
7.5m
10m
13m
15m
18m
Phase Shif t
180
180
360
360
-0. 4k
-0. 5k
-0. 6k
-0. 7k
21m t [s]
0
Two Pulse Rectif ier (Delay Angle=pi/3, Duty Cy cle=0.5) Positiv e Conv erter
2m
4m
6m
8m
10m 12m 14m 16m
20m t [s]
Two Pulse Rectif ier (Delay Angle=pi/3, Duty Cy cle=0.5) Positiv e Conv erter
0.8k
0.8k
E1.V [V]
E1.V [V]
0.6k
0.6k
D1
D1
0.4k
D3
PWM
PW M 1
S1
PW M3
0
S3
-0. 2k
E1
-0. 4k
D2
PW M 4
S4
PWM
-0. 4k
E2
-0. 8k
0
-0. 8k
2m
4m
6m
8m
10m
12m
14m
16m
18m 20m t [s]
S2
PW M 2
VM1
-0. 6k
D2
0
PWM
-0. 2k
EMF := 120
D4
-0. 6k
PWM
S4
PWM
PW M4
0.7k
R1.V [V]
4m
6m
8m
10m
12m
14m
16m
18m 20m t [s]
0.7k
PW M2
VM1.V [V]
0.6k
0.5k
Switches
S1
S2
S3
S4
0.5k
Phase Shif t
60
60
240
240
2m
S2
0.6k
Switches
S1
S2
S3
S4
0
V
L := 60m
L1
E1
D4
+
S3
PW M1
R := 50
R1
0.2k
PWM
PWM
PW M 3
0.4k
R1
R := 50
0.2k
PWM
S1
D3
0.4k
0.3k
Phase Shif t
60
60
240
240
0.4k
0.3k
0.2k
0.1k
0.2k
0
0.1k
-0. 1k
0
-0. 2k
0
-0. 1k
0
2m
4m
6m
8m
10m
12m
14m
16m
2m
4m
6m
8m
10m
12m
14m
16m
18m 20m t [s]
18m 20m t [s]
Figure 8: Simulation Results for Sample Two Pulse AC to DC Converters.
The Pacific Journal of Science and Technology
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–97–
Volume 11. Number 2. November 2010 (Fall)
Three Pulse AC/DC Conv erter (Delay Angle=pi/3, Duty Cy cle=1/3) Negativ e Conv erter
Three Pulse AC/DC Conv erter (Delay Angle=0, Duty Cy cle=1/3) Positiv e Conv erter
0.4k
0.4k
PW M1
PW M3
PW M2
PWM
PWM
E1.V [V]
E2.V [V]
E3.V [V]
0.3k
PWM
S3
S2
R1
S3
PW M2
-0. 1k
S2
0.1k
S1
PWM
0
D2
0.2k
PW M1
0.1k
S1
D3
PWM
0.2k
D1
R := 50
E1
E3
E2
PW M3
-0. 3k
R1
R := 50
-0.2k
-0.3k
0
2m
4m
6m
8m
10m
12m
14m
16m
-0.4k
18m 20m t [s]
0
E3
E2
50
R1.V [V]
Switches
S1
S2
S3
0
-50
-0. 1k
Switches
S1
S2
S3
0
-0.1k
PWM
-0. 2k
D3
-0. 4k
E1
E1.V [V]
E2.V [V]
E3.V [V]
0.3k
D2
D1
Phase Shif t
270
30
150
Phase Shif t
30
150
270
2m
4m
6m
8m
10m 12m 14m 16m 18m 20m t [s]
0.34k
R1.V [V]
0.32k
0.3k
0.28k
-0. 15k
0.26k
-0. 2k
0.24k
-0. 25k
0.22k
0.2k
-0. 3k
0.18k
-0. 35k
0
2m
4m
6m
8m
10m
12m
14m
16m
18m 20m t [s]
0.16k
0
2m
4m
6m
8m
10m 12m 14m 16m 18m 20m t [s]
Three Pulse AC/DC Conv erter (Delay Angle=pi/3, Duty Cy cle=1/3) Positiv e Conv erter
Three Pulse AC/DC Conv erter (Delay Angle=0, Duty Cy cle=1/3) Negativ e Conv erter
0.4k
PW M2
PW M1
PWM
PWM
PW M3
E1.V [V]
E2.V [V]
E3.V [V]
0.3k
PWM
0.2k
0.4k
D1
D2
D3
PWM
0.1k
PW M2
S1
S2
S3
0.1k
V
-0.2k
0
VM1
-0.1k
PWM
S2
0.2k
+
PW M3
-0.1k
S1
R1
R := 10
L1
L := 60m
S3
PWM
0
E1.V [V]
E2.V [V]
E3.V [V]
0.3k
PW M1
E1
E2
E3
E4
EMF := 120
-0.2k
-0.3k
-0.3k
-0.4k
D1
D2
R1
D3
-0.4k
0
0
2m
4m
6m
8m 10m 12m 14m 16m
-0.16k
E1
E2
E3
2m
4m
6m
8m 10m 12m 14m 16m
20m t [s]
20m t [s]
R := 50
R1.V [V]
-0.18k
-0.2k
-0.22k
Switches
S1
S2
S3
Phase Shif t
90
210
330
0.35k
0.3k
VM1.V [V]
0.2k
0.1k
-0.24k
-0.26k
Switches
S1
S2
S3
Phase Shif t
210
330
90
0
-0.28k
-0.3k
-0.1k
-0.32k
-0.2k
-0.34k
0
2m
4m
6m
8m 10m 12m 14m 16m
20m t [s]
0
2m 4m
6m 8m 10m 12m 14m 16m
20m t [s]
Figure 9: Simulation Results for Sample Three Pulse AC to DC Converters.
The Pacific Journal of Science and Technology
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–98–
Volume 11. Number 2. November 2010 (Fall)
Six Pulse Rectif ier (Delay Angle=0, Duty Cy cle=1/3) Positiv e Conv erter
PW M1
PW M3
PWM
Six Pulse Rectif ier (Delay Angle=0, Duty Cy cle=1/3) Positiv e Conv erter
PW M1
PW M5
PWM
0.6k
PWM
PW M5
PW M3
PWM
E1.V [V]
E2.V [V]
E3.V [V]
PWM
0.6k
PWM
0.4k
0.2k
D1
S1
E1
D5
S5
S3
D3
0
E1
-0.2k
R1
R := 50
E2
-0. 2k
L1
L := 60m
1.1k
+
V
-0. 4k
VM1
-0. 6k
20m t [s]
0 2m 4m 6m 8m 10m 12m 14m 16m
D2
E3
0
S5
S3
E2
0 2m 4m 6m 8m 10m 12m 14m 16m
D6
D5
-0.4k
-0.6k
D4
S1
0.2k
R := 10
R1
D1
D3
E1.V [V]
E2.V [V]
E3.V [V]
0.4k
D4
E3
R1.V [V]
D6
20m t [s]
EMF := 120
D2
1.1k
1k
VM1.V [V]
1k
S4
S6
S2
S4
0.9k
PWM
PWM
PWM
PW M6
PW M4
Switches
S1
S2
S3
S4
S5
S6
S6
S2
0.9k
PWM
PWM
PW M2
0.8k
Phase Shif t
60
120
180
240
300
360
PW M4
0.6k
0.5k
2m 4m 6m 8m 10m 12m 14m 16m
PW M2
0.8k
Switches
S1
S2
S3
S4
S5
S6
0.7k
0
PWM
PW M6
20m t [s]
Phase Shif t
60
120
180
240
300
360
0.7k
0.6k
0.5k
0 2m 4m 6m 8m 10m 12m 14m 16m
20m t [s]
Six Pulse Rectif ier (Delay Angle=pi/3, Duty Cy cle=1/3) Positiv e Conv erter
Six Pulse Rectif ier (Delay Angle=pi/3, Duty Cy cle=1/3) Positiv e Conv erter
0.6k
PW M 1
PW M 3
E1.V [V]
E2.V [V]
E3.V [V]
PW M 5
PW M3
PWM
PWM
PW M5
PWM
0.4k
PWM
PWM
PW M1
0.6k
PWM
0.2k
D1
D3
0
R := 0.8
R1
D1
D3
E1
S1
S5
L1
L := 15m
+
S5
S3
0
-0. 4k
-0. 6k
0
2m
4m
6m
8m 10m 12m 14m 16m
20m t [s]
R1
R := 50
E2
V
VM 1
D4
D6
D2
EMF := 40
VM1.V [V]
D4
E3
D6
D2
0
S4
S6
S2
S2
PW M 6
PWM
4m
6m
8m 10m 12m 14m 16m
20m t [s]
PWM
R1.V [V]
PWM
0
PW M4
PW M 2
Switches
S1
S2
S3
S4
S5
S6
2m
0.6k
0.5k
PWM
PWM
-0. 6k
0.2k
0.1k
S6
S4
-0. 2k
-0. 4k
0.3k
PWM
PW M 4
S1
E1
E2
E3
D5
0.2k
-0. 2k
D5
S3
E1.V [V]
E2.V [V]
E3.V [V]
0.4k
Phase Shif t
120
180
240
300
360
60
-0. 1k
-0. 2k
0
2m
4m
6m
8m 10m 12m 14m 16m
20m t [s]
PW M6
Switches
S1
S2
S3
S4
S5
S6
PW M2
Phase Shif t
120
180
240
300
360
60
0.4k
0.3k
0.2k
0.1k
0
-0. 1k
0
2m
4m
6m
8m 10m 12m 14m 16m
20m t [s]
Figure 10: Simulation Results for Sample Six Pulse AC to DC Converters.
CONCLUSION
A detailed and an insightful analysis of controlled
AC to DC converters operating under continuous
load current have been presented in this paper.
The derived equations, in general form, can be
used for a phase controlled AC to DC converter of
any output voltage pulse number and therefore of
any AC input phase number.
The Pacific Journal of Science and Technology
http://www.akamaiuniversity.us/PJST.htm
It can be seen from the simulation results of
figures 8 to10 that for any given control delay
angle
the outputs of the negative converters
are shifted by 180º in phase from the output of
the corresponding positive converters and that
the positive converters have an average positive
output voltage while the negative converters have
an average negative output voltage. The output
pulse numbers of 2, 3, and 6 are also observed in
Figures 8, 9, and 10, respectively.
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Volume 11. Number 2. November 2010 (Fall)
The energy storage ability of the inductors is also
evident in the circuit configuration with RLE loads
where the output voltage has both the positive
and the negative components; this is very much
in accordance with relevant theory. Note is also
taken that the output voltage is at a constant
value of E or zero in the RLE or R load
configurations respectively throughout the delay
period.
The analysis results can be used to predict the
output performance of any standard phase
controlled converter application circuit with any
given number of AC input phases and/or output
pulses under continuous load current. The
®
software for simulation, Ansoft SIMPLORER , is
demonstrated to be very useful for the purpose of
simulation of power electronic circuits and
systems. It is therefore, highly, recommended that
researchers and students of power electronic
should utilize this software in the design process
of power electronic circuits.
ABOUT THE AUTHORS
Engr. Cosmas Uchenna Ogbuka, received his
B.Eng. (First Class Honors) and M.Eng. Degrees
(Distinction) in 2004 and 2009, respectively, in the
Department of Electrical Engineering University of
Nigeria, Nsukka where he presently works as a
Lecturer/Research Student.
His research
interests are in adjustable speed drives,
microgrids, power electronics, and dispersed
generation.
Engr. Prof. Marcel U. Agu, obtained his B.Sc. in
Electrical Engineering in 1974 in the University of
Nigeria, Nsukka. He also received his M.A.Sc.
and Ph.D. in 1978 and 1982, respectively, in
Power Electronics from the University of Toronto
Canada. He is a Professor in the Department of
Electrical Engineering University of Nigeria,
Nsukka. His research interests are in power
electronic circuits and electric drives.
SUGGESTED CITATION
REFERENCES
1.
Agu, M.U. 1997. „„A Generalized Conceptual
Analysis of Phase-Controlled AC to DC Converters
Under Continuous Load Current Mode‟‟. Electric
Power Engineering Conference (EPEC97):
University of Nigeria, Nsukka. 119-129.
2.
Ming-Tsung, T. and W.I. Tsai. 1999. „„Analysis and
Design of Three-Phase AC-to-DC Converters With
High Power Factor and Near-Optimum
Feedforward‟‟. IEEE Transactions on Industrial
Electronics. 46(3):535-543.
3.
Dewan, S.B. and A. Straughen. 1978 Power
Semiconductor Circuits. John Wiley: New York,
NY.
4.
Machhopadhyay, S. 1978. „„A New Concept for
Improving the Performance of Phase Controlled
Converters‟‟. IEEE Trans. on Indu. Appl.
1A(14):594-603.
5.
Dubey, G.K., S.R. Doradla,, A. Joshi, and R.M.K.
Sinha. 1986. Thyristorized Power Controllers.
Wiley Eastern: Delhi, India.
6.
Agu, M.U. 2008 „„Advanced Power Electronic EEE
612‟‟. Unpublished Lecture Notes, Department of
Electrical Engineering University of Nigeria,
Nsukka.
Ogbuka, C.U. and M.U. Agu. 2010. “Continuous
Load Current Mode Analysis of Phase-Controlled
AC to DC Converters.” Pacific Journal of Science
and Technology. 11(2):91-100.
Pacific Journal of Science and Technology
The Pacific Journal of Science and Technology
http://www.akamaiuniversity.us/PJST.htm
–100–
Volume 11. Number 2. November 2010 (Fall)