Transcript A Lecture on Improve Power Quality Converters

Seminar on
Improved Power Quality
AC-DC Converters with
High Frequency Transformer Isolation
By
Prof. Bhim Singh
Department of Electrical Engineering
Indian Institute of Technology Delhi
Hauz Khas, New Delhi-110016, India
email:[email protected]
Ph.: (91)-011-2659-1045
Classification
Improved Power Quality AC-DC Converters with
High Frequency Transformer Isolation
 The control of DC-DC converter is done such as the
input current wave shaping is achieved for AC-DC
Diode converter.
 The DC-DC converter can be operated in both DCM
and CCM mode.
 The control technique for DCM and CCM are
different.
 It works as voltage follower in DCM mode and there
is no need of input voltage & current sensing for
power factor correction.
Applications
 DC Power Supplies,
 Telecommunication Power Supply,
 Improved Power Factor ballast,
 Power Supplies for equipments like computers,
medical equipments, printers, scanners etc.
 Drives Applications with Power Factor Improvement
at AC side,
 Electrical Welding,
 Lighting such as ballasts, CFL etc.
Single-Phase Buck Boost Flyback
AC-DC Converter
HFT
is
vs
io
Ls
Cs
Co
Cd
Q
+
Vo Load
Single-Phase Buck Forward
AC-DC Converter
HFT
is
vs
Ls
Cs
Lo
io
Co
Cd
Q
+
Vo Load
Single-Phase Buck Push-Pull
AC-DC Converter
HFT
is
vs
Ls
Cs
Cd
Lo
Co
Q1
Q2
io
+
Vo Load
Single-Phase Buck Half-Bridge
AC-DC Converter
HFT
is
vs
Lo
io
Ls
Cd1
Q1
Co
Cs
Cd2
Q2
+
Vo Load
Single-Phase Buck Full Bridge
AC-DC Converter
Ld
is
HFT
io
Ls
Q1
vs
Lo
Cs
Q3
Cd
Co
Q2
Q4
+
Vo Load
Single-Phase Boost Forward
AC-DC Converter
D1
Ld
is
vs
HFT
Lo
Ls
io
D2
Cs
Cd
Q
Co
+
Vo Load
Single-Phase Boost Push-Pull
AC-DC Converter
HFT
is
vs
Lo
io
Ls
Cd
Cs
Ld
Co
+
Q1
Rd
Q2
+
Vo Load
Single-Phase Boost Half-Bridge
AC-DC Converter
Ld
is
vs
HFT
Lo
Ls
Cs
io
Q1
Co
Q2
+
Vo Load
Single-Phase Boost Full Bridge
AC-DC Converter
Ld
is
vs
HFT
Lo
io
Ls
Cs
Q1
Q3
Q2
Q4
Cd
Co
+
Vo Load
Single-Phase Buck-Boost Cuk
AC-DC Converter
is
vs
Ls
L1
Cs
C1
HFT
C2
L2
Co
Q
io
+
Vo Load
Single-Phase Buck-Boost SEPIC ACDC Converter
is
vs
Ls
Ld
Cd
HFT
io
Co
Cs
Q
+
Vo Load
Single-Phase Buck-Boost Zeta
AC-DC Converter
HFT
is
Ls
C1
Lo
io
Q
vs
Cs
Cd
Co
+
Load
Single-phase buck-boost flyback AC-DC
converter in DCM
Single-Phase Buck Boost Flyback AC-DC Converter
Average current mode control in CCM operation
Single-Phase Buck Boost Flyback AC-DC Converter
FLYBACK Converter in DCM
average input current over a switching cycle is given as:
i1 
1
I pk D
2
(1)
where I is the peak of input current (that’s switch current) and D
is the duty ratio. From Fig.1b I is given as:
pk
pk
I pk 
DTs
v1r
Lm
(2)
where v1r is rectified input voltage and L is transformer
magnetizing inductance referred to primary. From eqns (1) and (2),
the input current is as:
m
D 2 Ts
i1 
v1r
2Lm
(3)
Single-Phase Buck Boost Flyback AC-DC Converter
Design of Flyback Converter in DCM
Equation (3) presents nicely PFC operation in DCM. It is clear that
if duty cycle and switching frequency is kept constant, then input
current is a linear function of input voltage. Eqn. (3) can be written
as:
i1  I1 sint
(4)
where, v1r  V1 sint
(5)
V1D 2 Ts
I1 
2Lm
(6)
Since input inductor current is nothing but the rectified ac mains
current, thus from Eqn. (4), it is clear that by keeping the duty
cycle and switching frequency constant, the average input current
in flyback converter in DCM follows the input voltage exactly thus
emulating a resistor and is known as voltage follower technique.
Therefore, flyback converter behaves as an ideal current shaper,
and performs current shaping automatically with no control when
operating in DCM.
Single-Phase Buck Boost Flyback AC-DC Converter
Design of Flyback Converter in DCM
The design of the converter depends whether it is working in
discontinuous or continuous conduction mode.
The transfer function of the flyback converter in DCM is given as:
Vo 
Dv1r
D1 n
(7)
where n is the turn ratio. From Fig. 1b, for DCM operation, the
condition is:
D  D1  1
(8)
From Eqns. (7) and (8), for the desired maximum duty ratio at
minimum input voltage, turn ratio can be obtained by satisfying
following inequality as:
n
D V1
(1  D) Vo
(9)
Single-Phase Buck Boost Flyback AC-DC Converter
Design of Flyback Converter in DCM
In order to ensure DCM of operation at maximum load, following
condition must be satisfied
Lm 
R L min
1 V
4fs (  o ) 2
n V1min
(10)
where V is the peak value of minimum input voltage. RL min is the
minimum value of load resistance and f is the switching frequency.
Output capacitor is selected on the basis of maximum peak-to-peak
ripple in output voltage ( r ) as:
1 min
s
v
Co 
Vo
rvRL
(11)
Single-Phase Buck Boost Flyback AC-DC Converter
Design of Flyback Converter in DCM and CCM
Stresses on semiconductor devices in DCM can be given by
following equations,
Peak current through switch is given as:
V DT
I

(12)
L
1
s
swpk
m
Peak voltage across switch is given as:
Vswpk  V1  nVo
(13)
Similarly, peak current through diode is as:
I diopk
n 2 Vo D1Ts

Lm
(14)
and peak voltage across the diode can be given as:
Vdiopk 
V1
 Vo
n
(15)
Single-Phase Buck Boost Flyback AC-DC Converter
Design of Flyback Converter in DCM and CCM
For CCM operation, the transfer function is given as:
Vo 
Dv1r
(1 - D)n
(16)
Thus in a similar manner as in DCM, for desirable maximum duty
ratio, the turn ratio is determined. However, magnetizing
inductance of the transformer is defined by satisfying the following
inequality [6]:
Lm 
R L max
V
4fs ( o ) 2
V1min
(17)
Referring Fig. 2b, switch current at half of the ripple is given as:
I swh 
Pomax
V1min ηDmax
(18)
Single-Phase Buck Boost Flyback AC-DC Converter
Design of Flyback Converter in DCM and CCM
From Fig 2b, switch peak current for ripple
I sw
is given as:
I sw
2
(19)
V1min D maxTs
Lm
(20)
I swpk  I swh 
where ,
ΔIsw 
Switch RMS current is given as:
1 2
2
I swRMS  D max [Iswpk
 ΔI sw I swpk  ΔI sw
3
(21)
Similarly diode current at half of the ripple is given as:
I dh 
I o max
(1  Dmax )
From Fig 2b, diode peak current for ripple
I dpk  I dh 
I d
2
(22)
I d
is given as:
(23)
where,
I d 
Vo (1  Dmax )Ts
L2
(24)
Single-Phase Buck Boost Flyback AC-DC Converter
Specifications
Input: V1  220VRMS , 50Hz, Single-Phase AC Supply
Output: Vo  110V , Po  1kW, Output voltage-ripple less than 2%
Switching frequency fs  ( s / 2 )  50kHz
Design parameters for DCM
Transformer turn ratio (n) 1.5:1, Magnetizing inductance L m  50H , L f  1mH,
C f  800nF and Co  15mF.
Single-Phase Buck Boost Flyback AC-DC
Converter
Source voltage and
current in DCM at
100% load
Steady state output
voltage in DCM at
100% load
Single-Phase Buck Boost Flyback AC-DC
Converter
Source voltage and
current in CCM at
100% load
Steady state output
voltage in CCM at
100% load
Single-Phase Buck Boost Flyback AC-DC Converter
TABLE I
Comparisons of Flyback Converter Operation in DCM and CCM
DCM Operation
CCM Operation
Quantity
10% Load 100% Load
10% Load 100% Load
Input Current THD
12%
5.1%
11%
4.4%
PF
0.981
0.997
0.989
0.998
Output Ripple
0.55%
1.73%
0.52%
1.45%
Normalized Current Peak
of Switch
Average
(pu)
RMS
25.1
6.73
6.53
2.60
0.93
0.71
0.54
0.67
2.87
1.62
1.35
1.14
Normalized Current Peak
of Diode
Average
(pu)
RMS
14.5
9.76
10.13
3.95
1.13
1.48
1.29
1.16
5.27
2.86
2.57
1.90
Control Technique
Voltage Mode Control
Average Current Control
Size of Converter
Small
Large
Circuit Simplicity
Simple
Complex
Single-Phase Buck Boost Flyback AC-DC Converter
Vs (V),
is(A)
Vdc (V)
Idc
(A)
Test results of AC mains voltage, AC mains current, output DC voltage and output
DC current waveform of AC-DC flyback converter for load perturbation response on
equivalent resistive load (60W to 200W to 60W). (Scale on X-axis 1div=20ms, Yaxis channel-1 1div =85V, channel-2 1div =5A, channel-3 1div= 100V, channel-4
1div= 2A)
Single-Phase Buck-Boost Cuk AC-DC Converter
in DCM
Single-Phase Cuk AC-DC Converter
Inductors voltage and current waveforms in DCM
Single-Phase Cuk AC-DC Converter
CCM operation
Single-Phase Cuk AC-DC Converter
Inductors voltage and current waveforms in CCM
Single-Phase Cuk AC-DC Converter in
DCM Operation
To simplify the analysis, all quantities are referred to the primary side of the
transformer. Volt-second balance on the inductor gives following equality:
vo ' d

(1)
v1r d1
where v o ' and v1r are output voltage (referred to primary) and rectified input
voltage respectively. d is the duty ratio and d1 is the off period of switch, during
which inductor currents decrease linearly.
Assuming 100% efficiency for simplification, the current ratio is:
i1
d

(2)
i 2 ' d1
where i1 and i 2 ' are the input inductor current and output inductor current referred
to primary side of the transformer.
Single-Phase Cuk AC-DC Converter in
DCM
First stage of Operation
When switch is on, two inductor currents increase linearly with the voltage
across them equal to input voltage. The equations of input and output inductor
currents for the interval 0  t  dTs (referring to Fig. 1b(i)) are given by:
v
i1  i  1r t
L1
v
i 2 '  i  1r t
L2 '
(3)
(4)
where i is the minimum input inductor current.
Second Stage of Operation
When switch is off, inductor currents decrease linearly with voltage across them
equal to output voltage. Referring to Fig. 1b(ii) and Fig. 1c, inductor currents are
given by:
v '
v
i1   o t  1r dTs  i
L1
L1
v '
v
i 2 '   o t  1r dTs  i
L2 '
L2 '
(5)
Single-Phase Cuk AC-DC Converter in
DCM
Third stage of Operation
This is the stage when the diode current is zero.
Averaged input and output inductor currents over a switching period can be
given by [1]:
v1r
i1 
dTs (d  d1 )  i
2L1
v1r
i2 '
dTs (d  d1 )  i
2L2 '
(7)
(8)
Sum of the input and output inductor currents is given by:
i1  i 2 ' 
1 v1r
 d 
dTs 1  1 d
2 L eq
d

L1L2 '
L

where, eq L  L '
1
2
(9)
(10)
Single-Phase Cuk AC-DC Converter in
DCM
By substituting the expression in eqn. (2) in to eqn. (9), we get:
 d  1 v1r
 d 
i1 1  1  
dTs 1  1 d
d  2 L eq
d 


(11)
After simplification it gives:
v1r d 2 Ts
i1 
2Leq
(12)
It can be written as:
i1  I1 sint
(13)
where, v1r  V1 sint
(14)
V1d 2Ts
I1 
2Leq
(15)
Single-Phase Cuk AC-DC Converter
Average and peak currents in the semiconductors
and input inductor
Average current ( i sw av ) and peak current ( i sw pk ) of the MOSFET switch over a
switching cycle are as:
v
i sw av  1r
L eq
 d 2Ts 
  (I
1max  I 2max ' ).d


2 

(16)
i sw pk  (I1max  I 2max ' )
(17)
where I1max and I 2max ' are the maximum value of input inductor current and output
inductor current (referred to primary) respectively.
Average current ( i d av ' ), and peak current ( i d pk ' ) of the diode (all referred to
primary) are as:
v
i d av '  o
L eq
 d 2 Ts 

  (I
1max  I 2max ' ).(1- d)
 2 


i d pk '  (I1max  I 2max ' )
(18)
(19)
Single-Phase Cuk AC-DC Converter
Average and peak currents in the semiconductors
and input inductor
Peak voltage across switch ( Vsw pk ) and diode ( Vd pk ' ) (referred to primary) is
given as:
Vsw pk  Vd pk '  Vinmax  Vo '
(20)
The average current ( i L1av ) and RMS current ( i L1rms ) of input inductor are as:
2I
i L1av  1max
(21)
π
I
i L1rms  1max
2
(22)
Single-Phase Cuk AC-DC Converter
Design Description in DCM and CCM
Step 1: Conversion ratio
Defining the dc voltage conversion ratio (M) as,
V
M o
(23)
v1r
where, v1r  V1 sint
(24)
For t  90 , conversion ratio is obtained as the first step of the design. Here V1 is
the peak value of input voltage.
Step 2: Condition for operation in DCM and CCM
Design must ensure the DCM operation, for which following inequality must
hold good:
Ke 
1
2(M  n)2
where K e is the conduction parameter and n is the transformer primary to
secondary turn ratio.
(25)
Design Description in DCM and CCM
For CCM, following condition must be satisfied to ensure the continuous
conduction mode of operation:
1
Ke 
(26)
2(M  n)2
K e is calculated for minimum value of M which occurs at minimum output
voltage and maximum input voltage in CCM for given range of specification.
Step 3: Equivalent inductance ( Leq ) which is the parallel combination of L1 and
L 2 ' , is given as:
L eq 
K e R L Ts
2
(27)
where R L is the load resistance.
Step 4: Duty Ratio
The duty ratio for the given power (load resistance) in DCM is obtained by:
d  2M K e
(28)
Design Description in DCM and CCM
Step 5: L1 and L 2 ' Design
L1 can be obtained by considering the specified maximum current ripple for
DCM as:
2Leq
L1 
(29)
dri
where ri is p.u. ripple current.
L 2 ' can be obtained using expressions for L1 and Leq in eqns. (29) and (10)
respectively.
Similarly, for CCM L1 and L 2 ' can be obtained by specified maximum current
ripple allowed and eqn. (10).
Design Description in DCM and CCM
Step 6: Design of energy transfer capacitor C1
It has great influence on input current waveform. To avoid input current
oscillations at every line half cycle, it is given by:
C1 
1
 r 2 (L1  L 2 ' )
(30)
where,  L   r   s
Resonant frequency (  r ) should lie between line frequency (  L ) and switching
frequency (  s ).
Step 7: Output Capacitor
Output capacitor is chosen according to specified ripple allowed in the output
voltage. It can be achieved by following formula:
Co 
1
 L rv R L min
(31)
where rv is the pu ripple in the output voltage and R Lmin is the minimum load
resistance.
Single-Phase Cuk AC-DC Converter
Specifications
Input: V1  160 270VRMS , 50Hz, Single-Phase AC Supply
Output: Vo  98  132V adjustable with nominal value of 120V , Po  2.6kW
Output voltage-ripple less than 2%
Switching frequency f s  ( s / 2 )  50kHz
Design parameters for DCM mode:
Transformer turn ratio (n) 1:1, L1  1500H , L 2  4.3H , C1  2.5F ,
C2  10F , and Co  30mF.
Single-Phase Buck-Boost Cuk
AC-DC Converter
Source voltage and
current in DCM at
100% load
Steady state output
voltage in DCM at
100% load
Single-Phase Buck-Boost Cuk
AC-DC Converter
Source voltage and
current for 100%
load in CCM
Steady
state
output voltage in
CCM at 100% load
Single-Phase Buck-Boost Cuk
AC-DC Converter
TABLE I
Comparisons of Cuk Converter Operation in DCM and CCM at Full Load
Quantity
DCM Operation
CCM Operation
Input Current THD
5.5%
3.8%
PF
0.998 to 1.0
0.9975 to 1.0
Ripple Factor
1.83%
1.67%
Peak Current Through Device 170A
60A
Control Technique
Voltage Mode Control
Average Current Control
Size of Converter
Small
Large
Circuit Simplicity
Simple
Complex
Single-Phase Buck-Boost Cuk
AC-DC Converter
Vs (V),
is(A)
Vdc
(V)
Idc (A)
Test results of AC mains voltage, AC mains current, output DC voltage and output
DC current waveform of AC-DC cuk converter for load perturbation response on
equivalent resistive load (60W to 200W to 60W). (Scale on X-axis 1div=20ms, Yaxis channel-1 1div =175V, channel-2 1div =5A, channel-3 1div= 100V, channel-4
1div= 1.75A)
Single-Phase SEPIC AC-DC Converter in
DCM
Single-Phase SEPIC AC-DC Converter in
DCM
Single-Phase SEPIC AC-DC Converter
CCM
in
Single-Phase SEPIC AC-DC Converter
CCM
in
Single-Phase SEPIC AC-DC Converter
Specifications
Input: V1  230VRMS , 50Hz, Single-Phase AC Supply
Output: Vo  110V , Po  1.5kW
Output voltage-ripple less than 2%
Switching frequency f s  ( s / 2 )  50kHz
Transformer
turn
ratio
(n)
1:1,
L 2  8.1H , C1  1F , and Co  30mF.
PI controller parameters: gain = 0.308,
time constant = 0.03.
L1  1200H ,
Single-Phase SEPIC AC-DC Converter
DCM
in
Source voltage and
current in DCM at
100% load
Steady state output
voltage in DCM at
100% load
Single-Phase SEPIC AC-DC Converter
CCM
in
Source voltage and
current in CCM at
100% load
Steady state output
voltage in CCM at
100% load
Single-Phase SEPIC AC-DC Converter
TABLE I
Comparisons of SEPIC Converter Operation in DCM and CCM
DCM Operation
Quantity
10% Load
100% Load
CCM Operation
10% Load
100% Load
Input Current THD
10%
6%
3.8%
8.5%
PF
0.994
0.997
0.998
0.995
Output Ripple
0.22%
1.27%
1.1%
0.1%
Peak
14.50pu
9.84pu
3.24pu
3.14pu
Average
0.76pu
0.77pu
0.71pu
0.78pu
RMS
4.60pu
2.18pu
1.50pu
1.39pu
Peak
15.2pu
10.94pu
3.17pu
3.15pu
Average
1.47pu
1.27pu
0.93pu
0.98pu
RMS
7.22pu
3.34pu
1.68pu
1.56pu
Normalized Current
of Switch
Normalized Current
of Diode
Control Technique
Voltage Mode Control
Average Current Control
Size of Converter
Small
Large
Circuit Simplicity
Simple
Complex
Single-Phase SEPIC AC-DC Converter
Vs (V),
is(A)
Vdc
(V)
Idc
(A)
Test results of AC mains voltage, AC mains current, output DC voltage and output DC
current waveform of AC-DC sepic converter for load perturbation response on
equivalent resistive load (60W to 200W to 60W). (Scale on X-axis 1div=20ms, Y-axis
channel-1 1div =150V, channel-2 1div =5A, channel-3 1div= 100V, channel-4 1div=
1.75A)
Single-Phase Buck-Boost Zeta
AC-DC Converter in DCM
Single-Phase Buck-Boost Zeta
AC-DC Converter in DCM
Single-Phase Buck-Boost Zeta
AC-DC Converter in CCM
Single-Phase Buck-Boost Zeta
AC-DC Converter in CCM
Single-Phase Zeta AC-DC Converter
Specifications
Input: V1  220VRMS , 50Hz, Single-Phase AC Supply
Output: Vo = 48V, Po  1kW, output voltage-ripple less
than 2%
Switching frequency f s  ( s / 2 )  50kHz
Transformer
turn
ratio
(n)
5:1,
inductance Lm =100μH , Lf =3mH , Lo =10mH
C1 =10μF , Co =22mF , and Cf =100nF .
Magnetizing
Single-Phase Buck-Boost Zeta
AC-DC Converter in CCM
Source voltage and
current in DCM at
100% load
Steady state output
voltage in DCM at
100% load
Single-Phase Buck-Boost Zeta
AC-DC Converter in CCM
Source voltage and
current for 100% load in
CCM
Steady state output
voltage in CCM at 100%
load
Single-Phase Zeta AC-DC Converter
Vs (V),
is(A)
Vdc (V)
Idc (A)
Test results of AC mains voltage, AC mains current, output DC voltage and output
DC current waveform of AC-DC zeta converter for load perturbation response on
equivalent resistive load (60W to 200W to 60W). (Scale on X-axis 1div=20ms, Yaxis channel-1 1div =150V, channel-2 1div =3A, channel-3 1div= 100V, channel-4
1div= 1.75A)
Single-Phase Zeta AC-DC Converter
TABLE I
Comparisons of Zeta Converter Operation in DCM and CCM
DCM Operation
Quantity
10% Load
100% Load
CCM Operation
10% Load
100% Load
Input Current THD
11%
4.98%
9.2%
1.36%
PF
0.993
0.9975
0.994
0.998
Output Ripple
0.62%
1.99%
0.67%
1.98%
Peak
9.21
4.15
2.92
1.75
Average
0.92
1.01
0.45
0.62
RMS
2.15
1.71
1.04
0.95
Peak
36.90
20.01
14.6
8.73
Average
4.52
3.02
3.24
3.17
RMS
10.45
5.41
5.37
4.57
Normalized Current
of Switch
Normalized Current
of Diode
Control Technique
Voltage Mode Control
Average Current Control
Size of Converter
Small
Large
Circuit Simplicity
Simple
Complex
References
•
•
•
•
•
•
•
•
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