INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR 721302, DECEMBER 27-29, 2002
711
Performance Evaluation of Single Phase Three Level
H-Bridge Converter
D.P. Kothari, Bhim Singh and Ashish Pandey
Abstract- This paper presents the performance analysis of single phase H-bridge AC-DC boost converters for bi-directional
power flow require d in Adjustable Speed Drives (ASD),
Uninterruptible Power Supplies (UPS), and Battery Energy
Storage Systems (BESS) etc. The detailed modeling along with
control algorithm for this AC-DC converter is carried out with a
view of proper design of such systems. Simulation results
demonstrating fast response and improved power quality in
terms of reduced harmonics in AC mains current, high powerfactor and well regulated DC output voltage are given for the
change of load on the proposed AC-DC converter system.
Index Terms-Power-factor Correction, AC-DC boost converter,
Power Quality and PWM Control
I. INTRODUCTION
Single-Phase AC-DC boost converters with bi -directional
power flow is widely used in Adjustable Speed Drives
(ASDs) for traction, line interactive Uninterruptible Power
Supplies (UPS), Battery Energy Storage System (BESS) for
load leveling, battery charging for electric vehicles and power
conditioning, utility interface with renewable energy sources
such as solar photo-voltaic (PV) etc [1-51]. These AC-DC
converters provide high power quality in terms of low value
of total harmonic distortion of AC mains current, high powerfactor, well regulated DC output voltage and fast response
compared to conventional rectifiers realized using thyristors
and diodes.
One of the major reason for a remarkable development in
these boost converters is due to advancement in self
commutating devices namely for small power rating,
MOSFETs 1have unsurpassed performance because of high
switching rate with negligible losses. In medium power
rating, IGBTs are considered ideal device for these with
PWM technology. In high power rating GTO are normally
used in multilevel modes with low switching frequency for
reducing the switching losses. Many manufacturers are
developing IPM (Intelligent Power Modules) of the selfcommutating devices to provide cost effective and compact
structure of these boost converters. Another break-through
has been in these converters because of fast response Hall
effect voltage and current sensors, isolation amplifiers
normally required for the feedbacks used in the control of
these AC-DC converters to provide a high level of dynamic
and steady state performance. Many manufacturers such as
Prof. D.P. Kothari and Mr. Ashish Pandey are in Center for Energy Studies
and Prof. Bhim Singh is Deptt. of Electrical Engineering, IIT Delhi, Hauz
Khas New Delhi-110016(bsingh@ee.iitd.ac.in).
ABB, LEM, Analog Devices and others, are offering these
sensors at competitive low prices.
Another major push in the technology of the boost AC -DC
converters has been due to revolution in microelectronics.
Because of high volume requirement, a number of
manufacturers such as Unitrode, Analog Devices, Siemens
etc. have developed dedicated ICs for the cost effective,
reliable and compact solution to control these converters.
Moreover, high-speed micro controllers and DSPs are
available at reasonable low cost. Many processors are
developed to give direct PWM outputs with fast software
algorithm normally used in these converters, which reduces
the hardware drastically. With these dedicated processors, it
is now possible to implement new and improved control
algorithms of real time control to provide fast dynamic
response of these converters. Starting with conventional PI
controller, sliding mode, fuzzy logic and neural network
based controllers have been employed in the control of these
converters.
A number of configurations of these boost AC-DC converters
have been developed to meet the exact requirements of
widely varying applications. However, majority of them has
employed either PWM technology [3-37] or multilevel [2,3851] control to reduce harmonics and effective control of these
converters in wide varying ratings with suitable solid-state
self-commutating devices. Multilevel AC-DC boost
converters have been developed in cascaded, flying capacitor
and diode clamped configurations [2] to reduce size,
switching losses along with improved power quality at AC
mains and DC output. In light of increasing potential
applications of these boost bi-directional AC-DC converters,
this work is aimed to investigate the performance of a basic H
bridge configuration out of these converters to demonstrate
the improved power quality and fast response capability of
these bidirectional AC-DC boost converters.
II. CIRCUIT CONFIGURATIONS
AC-DC bidirectional boost converters are developed in
number of circuit configurations for different power ratings
and to meet other performance requirements of applications
of bidirectional power flow in addition to improved power
quality at input AC mains in terms of high power- factor and
low THD with well regulated output DC voltage. Some of
their applications are battery charging and discharging in line
interactive UPS [11,14,16,25,33], battery energy storage
systems (BESS), transport application such as metro and
traction, ASDs in hoist cranes [5,37,38,40-45]. These
converters are also used for utility interface with nonconventional energy sources such as PVs, winds etc. [9].
These are classified here into two types namely simple bridge
712
NATIONAL POWER SYSTEMS CONFERENCE, NPSC 2002
and multilevel configurations as shown in Figs 1-2. Starting
from basic topology, the other circuits are evolved to enhance
their performance. Primitive topologies are PWM based
voltage source inverter with an input AC filter inductor and
output energy storage capacitor.
Fig 1a shows a half bridge bidirectional boost converter
normally used in small power rating with one leg of H-bridge
and it is controlled in PWM mode for desired power output.
Fig 1b shows classical H-bridge AC-DC converter normally
controlled in unipolar PWM mode for reduced size of AC
inductor with double frequency ripples. Concept of DC link
ripple reduction is also investigated using third active arm as
shown in Figs 1c-1d to improve their performance and
reducing the need of energy storage capacitor at DC link.
Another types of bidirectional boost converters are multilevel
converter as shown in Fig 2.
These converters offer the advantages of low voltage stress
on the switches, reduced losses at reduced switching
frequency for same level of performance in terms of reduced
harmonics and high power-factor at input AC mains and
regulated ripple free DC output voltage at varying loads.
These are classified on the number of levels starting from
three levels as shown in Fig 2a. These are further classified as
diode clamped (Fig 2b), flying capacitor (Fig 2c) and
cascaded (Fig 2d) multilevel bi -directional AC -DC
converters. These converters are developed for higher number
of levels for high voltage and high power applications. It has
been reported that the AC mains current THD can be reduced
below one percent without using PWM control [ ]. Stepped
voltage waveform generated by multilevel converters avoids
higher order harmonics, reduces switch losses and stress on
switching devices and these are most suitable for high power
and high voltage applications. In this paper, a basic H-bridge
topology of these converters (Fig 1b) is modelled and
simulated to demonstrate its enhanced performance in terms
of power quality at input AC mains and output DC loads.
III. CONTROL STRATEGY
Fig.3 shows the block diagram of overall control scheme for
H-bridge, AC-DC converter (Fig. 1b). The sensed DC voltage
of the converter is compared with set reference value in the
error detector. The voltage error is processed in the PI
(proportional-integral) controller. Its output is limited to the
maximum permissible value. This output of the voltage
controller is taken as amplitude of AC mains current. The
unit vector in phase with supply voltage is achieved using
sensed AC voltage. The output of PI controller is multiplied
to unit vector to generate reference sinusoidal supply current
in phase with supply voltage for the unity power factor of the
AC mains. This reference supply current is compared with
sensed AC current in current controller. This current error is
amplified in current controller and output of the current
amplifier is compared with triangular carrier wave to generate
gating signals for the H-bridge VSC. The unipolar control
scheme is used to reduce the harmonics in PWM AC voltage
of the VSC.
IV. MODELING
The proposed H bridge AC-DC bidirectional boost converter
is comprised of the voltage controller, current controller, Hbridge VSC with DC bus having capacitor in parallel with
DC load. All parts are modeled separately and then joined
together in order to simulate the performance of AC-DC
converter.
A. Voltage Controller
P-I (proportional-integral) controller is used to regulate the
DC bus vo ltage of the AC-DC converter. The DC bus voltage
vdc is sensed using a voltage sensor and compared with
sensed DC reference voltage (vdc* ). The resulting voltage
error ve(n) at nth sampling instant is expressed as:
(1)
ve(n) = vdc* - vdc
The output of the PI voltage controller vo(n) at the nth sampling
instant is expressed as:
vo(n)=vo(n-1) +Kp {ve(n) -ve(n-1) }+Ki{ve(n)}
(2)
Where Kp and Ki are proportional and integral gain constants
of the voltage controller. vo(n) and ve(n-1) are the output of the
controller and voltage error at the (n-1) th sampling instant.
This output of the voltage controller, vo(n) is limited to safe
permissible value and resulting limited output is taken as
amplitude of the AC mains current, Ism* .
B. Reference AC Mains Current
From sensed AC mains voltage (Vsm Sin wt), a unit vector
template is estimated by computing its amplitude. The unit
vector is estimated as:
u(t)= vs/Vsm =Sin wt
(3)
This unit vector is multiplied to an estimated amplitude of
AC mains current Ism * . The resulting signal is taken as
reference AC mains current as:
is* =Ism * u(t)=Ism* Sin wt
(4)
C. Current Controller
The carrier based PWM current controller contributes the
switching pattern of the H bridge devices. The current error
in reference and sensed AC mains currents (is* -is) is amplified
and amplified output is compared with carrier triangular wave
to generate gating signals of the devices. The PWM input
voltage of the VSI is expressed as:
va=vdc (SA-SB)
(5)
Where, SA and SB are the switching functions stating the
ON/OFF status of the IGBTs. If SA is one it means upper
device of the left arm of H-bridge is on. If SA is zero then
lower device of the left arm of H-bridge is on. Similarly if SB
is one it means upper device of the right arm of H-bridge is
on. If SB is zero then lower device of the right arm of Hbridge is on. However, either IGBT or paralleled diode will
conduct depending upon the polarity of the AC mains current.
D. H Bridge VS Converter
The H-bridge AC-DC converter is modeled in terms of its
two basic equations on AC as well as DC side. The AC side
volt-ampere equation is as follows:
Rs is +Ls pi s +va = vs
(6)
Where is is AC mains current. vs and va are the AC mains
voltage and PWM voltage of H bridge input, respectively. Rs
INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR 721302, DECEMBER 27-29, 2002
and Ls are the resistance and inductance of the input AC
reactor. The “p” is a time derivative operator (d/dt).
The eqn.(6) may be written as state space equation as:
p is = (vs-va-Rs is)/Ls
(7)
Similarly, DC side basic electrical equation may be written
as:
p vdc= (i dc-iL)/Cdc
(8)
Where vdc is the DC bus voltage across DC capacitor C dc.
The charging current idc and DC load current iL can be
expressed as:
idc = i s (SA-SB)
(9)
iL= vdc/RL
(10)
Where RL is load resistance at the DC bus.
The set of first order differential equations given in (7) and
(8) governs the dynamic model of the AC-DC converter
system. These equations are solved along with other
equations using fourth order Runge-Kutta method to analyze
dynamic and steady state behavior of the proposed AC-DC
converter. A standard FFT package is used to compute
harmonic spectrum and THD of the AC mains current.
VII. REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
V. PERFORMANCE OF AC-DC CONVERTER SYSTEM
[10]
The performance characteristics of proposed H-bridge ACDC converter are shown in Figs. 4-5. Fig. 4 shows the
harmonic spectrum of input AC mains current of H bridge
AC-DC converter excluding fundamental component of it.
The proposed control scheme is able to reduce harmonic level
in AC current well below specified in IEEE-519 standard and
THD of it is only less than 1%. Fig. 5 shows steady state and
dynamic performance of proposed AC-DC converter for
sudden application and removal of DC load. The AC mains
current remains sinusoidal under steady state and dynamic
operating conditions. A small dip in DC bus voltage at load
application and a small rise in its value at removal of load are
observed which recover to reference value within few cycles
of AC mains. The DC bus voltage can be recovered at the
faster rate by tuning the parameters of PI voltage controller
but at the cost of transients in AC mains current. Therefore, a
compromise is made between dynamics of DC bus voltage
and smooth variation in AC mains current in selecting the
parameters of PI voltage controller.
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
VI. CONCLUSIONS
A brief review of single-phase bidirectional AC -DC boost
converters has been made and few circuit configurations of
these converters are presented with a view of selecting a right
topology for a specific application. Performance analysis of a
basic H bridge topology of boost AC-DC bi-directional
converter has been carried out to demonstrate its improved
power quality at input AC mains and DC output. The
proposed control scheme of AC -DC boost converter has been
found effective to reduce THD of AC mains current well
below IEEE-519 standard and to result in smooth, sinusoidal
input AC mains current even under load variations. It has also
been found capable to regulate DC bus voltage with zero
steady state error at different loads.
713
[20]
[21]
[22]
[23]
[24]
IEEE Recommended Practices and Requirements for Harmonics
Control in Electric Power Systems, IEEE Std. 519, 1992.
J. S. Lai and F. Z. Peng, “Multilevel converters- A new breed of power
converters,” IEEE Transactions on Industry Applications, Vol. 32,
No.3, pp. 509-517, May/June 1996.
H. Kielgas and R. Nill, “Converter propulsion systems with three-phase
induction motors for electric traction vehicles,” IEEE Trans. Industry
Applications, vol. IA-16, pp. 222-233, March/April 1980.
O. Stihi and B. T. Ooi, “A single-phase controlled-current PWM
rectifier,” IEEE Trans. Power Electron., vol. 3, pp. 453-459, October
1988.
T. Hashimoto and S. Sone, “PWM converter-inverter system for AC
supplied train,” in Proc. MLRE’89, 1989, pp. 93-97.
J.T. Boys and A.W. Green, “Current-forced single-phase reversible
rectifier,” IEE Proc. vol. 136, pp. 205-211, September 1989.
K. Thiyagarajah, V. T. Ranganathan and B. S. Ramakrishna Iyengar,
“A high switching frequency IGBT PWM rectifier/inverter system,”
IEEE Trans. Power Electron., vol. 6, pp.576-584, Oct. 1991.
V. R. Kanetkar and G. K. Dubey, “Economical single phase current
controlled unipolar and bi-directional voltage source converters,” in
Proc. IEEE PESC’93, 1993, pp. 862-867.
H. S. Kim, G. H. Choe, G. J. Yu and J. S. Song, “Analysis of bidirectional PWM converter for application of residential solar air
conditioning system,” in Proc.IEEE WCPEC’1994, pp.1069-1072.
T. Shimizu, T. Fujita, G. Kimura and J. Hirose, “Unity-power-factor
PWM rectifier with DC ripple compensation,” in Proc. IEEE
IECON’94, 1994, pp. 657-662.
C. Chen and D. M. Divan, “Simple topologies for single phase AC line
conditioning,” IEEE Trans. Industry Applications, vol. 30, pp. 406-412,
March/April 1994.
G. V. Covic, G. L. Peters and J. T. Boys, “An improved single phase to
three phase converter for low cost AC motor drives,” in Proc. IEEE
PEDS’95, 1995, pp. 549-554.
F. Flinders and W. Oghanna, “Simulation of a complex traction PWM
rectifier using SIMULINK and the dynamic node technique,”in Proc
IEEE IECON’97, 1997, pp. 738-743.
I. Ando, I. Takahashi, Y. Tanaka and M. Ikehara, “Development of a
high efficiency UPS having active filter ability composed of a three
arms bridge,” in Proc. IEEE IECON’97, 1997, pp. 804-809.
F. Flinders and W. Oghanna, “The characteristics of a new model based
controller for single-phase PWM rectifier,” in Proc. IEEE IECON’97,
1997, pp. 895-900.
W. J. Ho, J. B. Lio and W. S. Feng, “A line-interactive UPS structure
with built-in vector-controlled charger and PFC,” in Proc. IEEE
PEDS’97, 1997. pp. 127-132.
D. Maischak, “A novel control strategy for IGBT -four-quadrant
converters,” in Proc. EPE’97, 1997, pp. 3.179-3.183.
W. Runge, “Control of line harmonics due to four-quadrant-converter
in AC tractive stock by means of filter and transformer,” in Proc.
EPE’97, 1997, pp. 3.459-3.464.
B. Dobrucky, J. Kyyra, V. Racek, M. Hukel and J. Dubovsky,
“Improvement of performance of four quadrant converter using
unidirectional DC link inductor,” in Proc. EPE’97, 1997, pp. 3.4654.469.
S. Pirog, “PWM rectifier and active filter with sliding mode control,” in
Proc. EPE’97, 1997, pp. 3.831-3.836.
V. R. Kanetkar and G. K. Dubey, “Current controlled boost-type
single-phase voltage source converters for bi-directional power flow,”
IEEE Trans. Power Electron., vol. 12, pp. 269-277, March 1997.
V. R. Kanetkar and G. K. Dubey, “Series equivalence/operation of
current-controlled boost-type single-phase voltage source converters
for bi-directional power flow,” IEEE Trans. Power Electron., vol. 12,
pp. 278-286, March 1997.
Y. Nishida, O. Miyashita, T. Haneyoshi, H. Tomita and A. Maeda, “A
predictive instantaneous-current PWM controlled rectifier with ACside harmonic current reduction,” IEEE Trans. Ind. Electron., vol. 44,
pp. 337-343, June 1997.
J. Carter, C. J. Goodman and H. Zelaya, “Analysis of the single-phase
four-quadrant PWM converter resulting in steady-state and small-signal
dynamic models,” IEE Proc.-Electr. Power Appl., vol. 144, no. 4, pp.
241-247, July 1997.
714
[25] N. Hirao, T. Satonaga, T. Uematsu, T. Kohama, T. Ninomiya and M.
Shyama, “Analytical considerations on power loss in a three-arm-type
uninterruptible power supply,” in Proc. IEEE PESC'98, 1998, pp.
1886-1891.
[26] D. Shmilovitz, D. Czarkowski, Z. Zabar and S. Y. Yoo, “A novel
single -stage unity power factor rectifier/inverter for UPS applications,”
in Proc. IEEE INTELEC'98, 1998. pp. 762-769.
[27] R. Srinivasan and R. Oruganti, “A unity power factor converter using
half-bridge boost topology,” IEEE Trans. Power Electron., vol. 13, pp.
487-500, June 1997.
[28] D. Shmilovitz, D. Czarkowski, Z. Zabar and S. Zou, “A novel
reversible boost rectifier with unity power factor,” in Proc. IEEE
APEC'99, 1999, pp. 363-368.
[29] B. R. Lin and H. H. Lu, “Implementation of non-deterministic PWM
for inverter drives,” in Proc. IEEE ISIE'99, 1999, pp. 813-818.
[30] T. Shimizu, Y. Jin and G. Kimura, “DC ripple current reduction on a
single -phase PWM voltage source rectifier,” in Proc. IEEE IAS'99,
1999, pp. 810-817.
[31] D. Shmilovitz, D. Czarkowski, Z. Zabar and S. Zou, “A simplified
controller for a half-bridge boost rectifier,” in Proc. IEEE APEC'00,
2000, pp. 452-455.
[32] D. K. Jackson and S. B. Leeb, “A power factor corrector with bidirectional power transfer capability,” in Proc. IEEE PESC'00, 2000,
vol. I, pp.365-370.
[33] M. Ashari, C.Y. Nayar and S. Islam, “An improved in-line
uniterruptable power supply system,” in Proc. IEEE ICHQP'00, 2000,
pp.548-553.
[34] I. Kasikci, “A new method for power factor correction and harmonic
elimination in power systems,” in Proc. IEEE ICHQP'00, 2000, pp.
810-815.
[35] M. Ohshima and E. Masada, “The P, Q controllable domain of a single
phase PWM converter to preserve sinusoidal AC current waveform,”
IEEE Trans. Power Electron., vol. 15, pp. 485-494, May 2000.
[36] S. J. Chiang, “Design and implementation of a single phase three-arms
rectifier inverter,” IEE Proc.-Electr. Power Appl., vol.147, no.5,
pp.379-384, Sept. 2000.
[37] H. J. Ryoo, J. S. Kim, G. H. Rim, Y. J. Kim, M. H. Woo and C. Y.
Won, “Unit power factor operation of parallel operated AC to DC
PWM converter for high po
[38] wer traction application,” in Proc. IEEE PESC'01, 2001, pp. 631-636.
[39] H. Stemmler, “Power Electronics in electric traction applications,”in
Proc. IEEE IECON’93, 1993, pp. 707-713.
[40] C. Osawa, Y. Matsumoto, T. Mizukami and S. Ozaki, “A state-space
modeling and a neutral point voltage control for an NPC power
converter,” in Proc. IEEE PCC-Nagaoka’97, pp. 225-230.
[41] G. Hilpert and T. Zullig, “Integrated power module in IGBT
technology for modular power traction converters,” in Proc. EPE’97,
1997, pp. 1.106-1.111.
[42] S. Inarida, W. Miyake, N. Mizuguchi, T. Haryama and K. Hoshi,
“Development of three-level power converter system using IGBTs for
Shinkansen trains,” in Proc. EPE’97, 1997, pp. 1.216-1.220.
[43] P. Oom, I. Gehrke, C. Endrikat and E. D. Lettner, “MITRAC drive
control unit for IGBT converters,” in Proc. EPE’97, 1997, pp. 1.2211.226.
[44] L. Fratelli and G. Giannini, “Power traction converter with 3.3 kV
IGBT modules,” in Proc. EPE’97, 1997, pp. 1.232-1.237.
[45] J. B. Saada, P. Colignon, P. Thomas, F. Avaux, L. Delporte and P.
Mathys, “High power factor, high efficiency bi-directional GTO
rectifiers for locomotive application,” in Proc. EPE’97, 1997, pp.
4.298-4.304.
[46] J. Shen and N. Butterworth, “Analysis and design of a three-level
PWM converter system for railway-traction applications,” IEE Proc.Electric Power Applications, vol. 144, no. 5, pp. 357-371, Sept. 1997.
[47] J. G. Mayordomo, M. Lopez, R. Asensi, L. F. Beites, J. M. Rodriguez
and J. Bueno, “A general treatment of traction PWM converters for
load flow and harmonic penetration studies,” in Proc. IEEE
ICHQPP’98, 1998, pp. 685-692.
[48] M. Madrigal, O. Anaya, E. Acha, J. G. Mayordomo and R. Asensi,
“Single-phase PWM converters array for three-phase reactive power
compensation. Part I: time domain studies,” in Proc. IEEE
ICHQPP’00, 2000, pp. 541-547.
[49] B. R. Lin, Y. L. Hou and H. K. Chiang, “Implementation of a threelevel rectifier for power factor correction,” IEEE Trans. Power
Electron., vol. 15, pp.891-900, September 2000.
NATIONAL POWER SYSTEMS CONFERENCE, NPSC 2002
[50] B. R. Lin, H. H. Lu and H. C. Tsay, “Control technique for high power
factor multilevel rectifier,” IEEE Trans. Aerospace and Electronic
Systems, vol. 37, pp. 226-241, January 2001.
[51] B. R. Lin and Y. L. Hou, “High-power-factor single-phase capacitor
clamped rectifier,” IEE Proc.-Electric Power Applications, vol. 148,
pp. 214-224, March 2001.
i dc
is
vs
Ls
C1
Cd
v dc
Load
C2
Fig1a Half Bridge Bidirectional Boost Converter.
i dc
is
vs
Ls
Cd
Load
v dc
Fig1b VSC H-Bridge Bidirectional Boost Converter.
idc
vs
is
Cs1 Ls
Cd
Cs2
vdc
Load
Fig.1c Bridge Bidirectional Boost Converter with DC
Ripple Compensation using AC Mid Point Capacitors and
Third Leg.
idc
vs
is
Ls
Lr
Cd
vdc
Load
Fig.1d Bridge Bidirectional Boost Converter with DC
Ripple Compensation using an Inductor and Third Leg.
idc
vs
is L
s
Cd1
vdc
Load
Cd2
Fig. 2a Bidirectional Three Level Converter using Two
Bidirectional Switches.
INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR 721302, DECEMBER 27-29, 2002
715
idc
Cd1
vs
is
Ls
Load
v dc
Cd2
Fig. 2b Bi-directional Diode Clamped Three Level
Converter.
idc
vs
is
Ls
Cd
Load
vdc
Fig. 4 Harmonic Spectrum of Input Current Drawn by HBridge Converter (neglecting fundamental
harmonic)
20
0
Fig.2c Bi-directional Flying Capacitor Clamped Three
Level Converter.
-20
Input Current
0
500
0.1
0.2
0.3
0.4
0.5
0.1
0.2
0.3
0.4
0.5
0.1
0.2
0.3
0.4
0.5
0
idc
C d1
is
-500
Input Voltage
0
410
400
390
0
Output Voltage
vs
vdc
Load
Time
Fig. 5 Dynamic Performance of H-Bridge Converter.
C d2
Fig. 2d Bidirectional Cascaded Five Level Converter.
SWITCHING
SIGNAL
vdc*
ve
*
PI
Controller
*
Is
is
m
vdc*
? iL
PWM
u(t)
vdc
c
Vd
iL
Current
Estimation
Fig3 Control Block of AC-DC Converter System