Seminar on Seminar on Improved Power Quality Improved Power Quality AC-DC Converters with AC-DC Converters with High Frequency Transformer High Frequency Transformer Isolation Isolation By By Prof. Bhim Singh Prof. Bhim Singh Department of Electrical Department of Electrical Engineering Engineering Indian Institute of Technology Indian Institute of Technology Delhi Delhi Hauz Khas, New Delhi-110016, India Hauz Khas, New Delhi-110016, India email:[email protected]email:[email protected]
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Seminar on Improved Power Quality AC-DC Converters with High Frequency Transformer Isolation By Prof. Bhim Singh Department of Electrical Engineering Indian.
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Seminar onSeminar onImproved Power Quality Improved Power Quality AC-DC Converters with AC-DC Converters with
High Frequency Transformer IsolationHigh Frequency Transformer Isolation
ByByProf. Bhim SinghProf. Bhim Singh
Department of Electrical Engineering Department of Electrical Engineering Indian Institute of Technology Delhi Indian Institute of Technology Delhi Hauz Khas, New Delhi-110016, IndiaHauz Khas, New Delhi-110016, India
Single-Phase Buck Boost Flyback AC-DC ConverterFLYBACK Converter in DCM
average input current over a switching cycle is given as:
DI2
1i pk1 (1)
where pkI is the peak of input current (that’s switch current) and D is the duty ratio. From Fig.1b pkI is given as:
1rm
spk v
L
DTI (2)
where 1rv is rectified input voltage and mL is transformer magnetizing inductance referred to primary. From eqns (1) and (2), the input current is as:
1rm
s2
1 v2L
TDi (3)
Single-Phase Buck Boost Flyback AC-DC ConverterDesign 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:
tsinIi 11 (4)
where, tsinVv 11r (5)
m
s2
11 2L
TDVI (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 ConverterDesign 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:
nD
DvV
1
1ro (7)
where n is the turn ratio. From Fig. 1b, for DCM operation, the condition is: 1DD 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:
o
1
V
V
D)(1
Dn
(9)
Single-Phase Buck Boost Flyback AC-DC ConverterDesign of Flyback Converter in DCM
In order to ensure DCM of operation at maximum load, following condition must be satisfied
2
1min
os
minLm
)V
V
n
1(4f
RL
(10)
where min1V is the peak value of minimum input voltage. minLR is the minimum value of load resistance and sf is the switching frequency. Output capacitor is selected on the basis of maximum peak-to-peak ripple in output voltage ( vr ) as:
Lv
oo Rr
V
C (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:
m
s1swpk L
DTVI (12)
Peak voltage across switch is given as: o1swpk nVVV (13)
Similarly, peak current through diode is as:
m
s1o2
diopk L
TDVnI (14)
and peak voltage across the diode can be given as:
o1
diopk Vn
VV (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:
D)n-(1
DvV 1r
o (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]:
2
1min
os
maxLm
)V
V(4f
RL (17)
Referring Fig. 2b, switch current at half of the ripple is given as:
max1min
omaxswh ηDV
PI (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 swI is given as:
2Iswpk
swswh
II
(19)
where ,
m
smax1minsw L
TDVΔI (20)
Switch RMS current is given as: 2swswpksw
2swpkmaxswRMS ΔI
3
1IΔI[IDI (21)
Similarly diode current at half of the ripple is given as:
)1(I
max
max
D
I odh
(22)
From Fig 2b, diode peak current for ripple dI is given as:
2
Idpkd
dh
II
(23)
where,
2
max )1(
L
TDVI so
d
(24)
Single-Phase Buck Boost Flyback AC-DC Converter
Specifications
Input: RMS1 220VV , 50Hz, Single-Phase AC Supply Output: V110Vo , 1kWPo , Output voltage-ripple less than 2% Switching frequency 50kHz)2/(fs s Design parameters for DCM Transformer turn ratio (n) 1.5:1, Magnetizing inductance H50Lm , 1mHL f ,
800nFC f and 15mFCo .
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 IComparisons of Flyback Converter Operation in DCM and CCM
Quantity
DCM Operation CCM Operation
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 of Switch(pu)
Peak 25.1 6.73 6.53 2.60
Average 0.93 0.71 0.54 0.67
RMS 2.87 1.62 1.35 1.14
Normalized Current of Diode(pu)
Peak 14.5 9.76 10.13 3.95
Average 1.13 1.48 1.29 1.16
RMS 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
Test results of AC mains voltage, AC mains current, output DC voltage and output 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 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, Y-equivalent resistive load (60W to 200W to 60W). (Scale on X-axis 1div=20ms, Y-axis channel-1 1div =85V, channel-2 1div =5A, channel-3 1div= 100V, channel-4 axis channel-1 1div =85V, channel-2 1div =5A, channel-3 1div= 100V, channel-4 1div= 2A)1div= 2A)
Vs (V),
is(A)
Vdc (V)
Idc (A)
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:
11r
o
d
d
v
'v (1)
where 'vo and 1rv 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:
12
1
d
d
'i
i (2)
where 1i and 'i2 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 sdTt0 (referring to Fig. 1b(i)) are given by:
tL
vii
1
1r1 (3)
t'L
vi'i
2
1r2 (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:
idTL
vt
L
'vi s
1
1r
1
o1 (5)
idT'L
vt
'L
'v'i s
2
1r
2
o2
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]:
i)d(ddT2L
vi 1s
1
1r1 (7)
i)d(ddT'2L
v'i 1s
2
1r2 (8)
Sum of the input and output inductor currents is given by:
dd
d1dT
L
v
2
1'ii 1
seq
1r21
(9)
where, 'LL
'LLL
21
21eq
(10)
Single-Phase Cuk AC-DC Converter in DCM
By substituting the expression in eqn. (2) in to eqn. (9), we get:
dd
d1dT
L
v
2
1
d
d1 1
seq
1r11
i (11)
After simplification it gives:
eq
s2
1r1 2L
Tdvi (12)
It can be written as: tsinIi 11 (13)
where, tsinVv 11r (14)
eq
s2
11 2L
TdVI (15)
Single-Phase Cuk AC-DC Converter Average and peak currents in the semiconductors
and input inductor Average current ( avswi ) and peak current ( pkswi ) of the MOSFET switch over a switching cycle are as:
).d'I(I2
Td-
L
vi 2max1max
s2
eq
1ravsw
(16)
)'I(Ii 2max1maxpksw (17) where 1maxI and 'I2max are the maximum value of input inductor current and output inductor current (referred to primary) respectively. Average current ( 'i avd ), and peak current ( 'i pkd ) of the diode (all referred to primary) are as:
d)-).(1'I(I2
Td
L
v'i 2max1max
s2
eq
oavd
(18)
)'I(I'i 2max1maxpkd (19)
Single-Phase Cuk AC-DC Converter Average and peak currents in the semiconductors
and input inductor
Peak voltage across switch ( pkswV ) and diode ( 'V pkd ) (referred to primary) is
given as: 'VV'VV oinmaxpkdpksw (20)
The average current ( avL1i ) and RMS current ( rmsL1i ) of input inductor are as:
π
2Ii 1max
avL1 (21)
2
Ii 1max
rmsL1 (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,
1r
o
v
VM (23)
where, tsinVv 11r (24) For 90t , conversion ratio is obtained as the first step of the design. Here 1V 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:
2en)2(M
1K
(25)
where eK is the conduction parameter and n is the transformer primary to secondary turn ratio.
Design Description in DCM and CCM
For CCM, following condition must be satisfied to ensure the continuous conduction mode of operation:
2en)2(M
1K
(26)
eK 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 ( eqL ) which is the parallel combination of 1L and 'L2 , is given as:
2
TRKL sLe
eq (27)
where LR is the load resistance. Step 4: Duty Ratio The duty ratio for the given power (load resistance) in DCM is obtained by:
eKM2d (28)
Design Description in DCM and CCM
Step 5: 1L and 'L2 Design 1L can be obtained by considering the specified maximum current ripple for
DCM as:
i
eq1 dr
2LL (29)
where ir is p.u. ripple current. 'L2 can be obtained using expressions for 1L and eqL in eqns. (29) and (10)
respectively. Similarly, for CCM 1L and 'L2 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:
)'L(L
1C
212
r1
(30)
where, srL 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:
minLvLo Rr
1C
(31)
where vr is the pu ripple in the output voltage and minLR is the minimum load resistance.
Single-Phase Cuk AC-DC ConverterSpecifications
Input: RMS1 270V160V , 50Hz, Single-Phase AC Supply
Output: 132V98Vo adjustable with nominal value of 120V , 2.6kWPo Output voltage-ripple less than 2%
Switching frequency 50kHz)2/(fs s Design parameters for DCM mode: Transformer turn ratio (n) 1:1, H1500L1 , H4.3L2 , F2.5C1 ,
F10C2 , and 30mFCo .
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
Steady state output voltage in CCM at 100% load
Source voltage and current for 100% load in CCM
Single-Phase Buck-Boost Cuk AC-DC Converter
TABLE IComparisons 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
Test results of AC mains voltage, AC mains current, output DC voltage and output 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 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, Y-equivalent resistive load (60W to 200W to 60W). (Scale on X-axis 1div=20ms, Y-axis channel-1 1div =175V, channel-2 1div =5A, channel-3 1div= 100V, channel-4 axis channel-1 1div =175V, channel-2 1div =5A, channel-3 1div= 100V, channel-4 1div= 1.75A)1div= 1.75A)
VVs s (V)(V), ,
iiss(A)(A)
VVdc dc (V)(V)
IIdc dc (A)(A)
Single-Phase SEPIC AC-DC Converter in
DCM
Single-Phase SEPIC AC-DC Converter in
DCM
Single-Phase SEPIC AC-DC Converter inCCM
Single-Phase SEPIC AC-DC Converter inCCM
Single-Phase SEPIC AC-DC Converter
Specifications
Input: RMS1 230VV , 50Hz, Single-Phase AC Supply
Output: V110Vo , kW5.1Po
Output voltage-ripple less than 2%
Switching frequency 50kHz)2/(fs s
Transformer turn ratio (n) 1:1, H1200L1 ,
H1.8L2 , F1C1 , and 30mFCo .
PI controller parameters: gain = 0.308,
time constant = 0.03.
Single-Phase SEPIC AC-DC Converter in DCM
Source voltage and current in DCM at 100% load
Steady state output voltage in DCM at 100% load
Single-Phase SEPIC AC-DC Converter in CCM
Source voltage and current in CCM at 100% load
Steady state output voltage in CCM at 100% load
Single-Phase SEPIC AC-DC ConverterTABLE I
Comparisons of SEPIC Converter Operation in DCM and CCM
Quantity
DCM Operation CCM Operation
10% Load 100% Load 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%
Normalized Current of Switch
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
Normalized Current of Diode
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
Control Technique Voltage Mode Control Average Current Control
Size of Converter Small Large
Circuit Simplicity Simple Complex
Single-Phase SEPIC AC-DC Converter
Test results of AC mains voltage, AC mains current, output DC voltage and output 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 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 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= channel-1 1div =150V, channel-2 1div =5A, channel-3 1div= 100V, channel-4 1div= 1.75A)1.75A)
VVs s (V)(V), ,
iiss(A)(A)
VVdc dc (V)(V)
IIdc dc
(A)(A)
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 ConverterSpecifications
Input: RMS1 220VV , 50Hz, Single-Phase AC Supply
Output: Vo = 48V, 1kWPo , output voltage-ripple less
than 2%
Switching frequency 50kHz)2/(fs s
Transformer turn ratio (n) 5:1, Magnetizing
inductance mL =100μH , fL =3mH , oL =10mH
1C =10μF , oC =22mF , and fC =100nF .
Single-Phase Buck-Boost Zeta AC-DC Converter in CCM
Steady state output voltage in DCM at 100% load
Source voltage and current in DCM at 100% load
Single-Phase Buck-Boost Zeta AC-DC Converter in CCM
Steady state output voltage in CCM at 100% load
Source voltage and current for 100% load in CCM
Single-Phase Zeta AC-DC Converter
IIdc dc (A)(A)
Test results of AC mains voltage, AC mains current, output DC voltage and output 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 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, Y-equivalent resistive load (60W to 200W to 60W). (Scale on X-axis 1div=20ms, Y-axis channel-1 1div =150V, channel-2 1div =3A, channel-3 1div= 100V, channel-4 axis channel-1 1div =150V, channel-2 1div =3A, channel-3 1div= 100V, channel-4 1div= 1.75A)1div= 1.75A)
VVs s (V)(V), ,
iiss(A)(A)
VVdc dc (V)(V)
Single-Phase Zeta AC-DC ConverterTABLE I
Comparisons of Zeta Converter Operation in DCM and CCM
Quantity
DCM Operation CCM Operation
10% Load 100% Load 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%
Normalized Current of Switch
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
Normalized Current of Diode
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
Control Technique Voltage Mode Control Average Current Control
Size of Converter Small Large
Circuit Simplicity Simple Complex
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