elec 6411 - project final final
TRANSCRIPT
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ELEC-6411 Final Project Report
Bi-directional Cascaded Buck-Boost ConverterDesign and simulation
Submitted to:
Dr Luiz A. C. Lopes
Submitted by:
Andrew Jensson !"""##$%
&a'endra ()ike *+$+#,%#
Date o Submission: December *% *"%
(erm: /all *"%
ABS(&AC(
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Power electronic converters are efficient in supplying power at a regulated voltage or regulated current.
Buck converters can supply power at a voltage level lower than the source while boost converters can
supply power at higher voltage level than the supply. Besides these converters, there are converters
which can source or sink the power depending on the requirement. In general, these are bi-directional
converters either with current reversal capability or voltage reversal capability.
In this project, a cascade type bi-directional buck-boost converter has been analyed and designed for
supplying power to charge an ultracapacitor or use the power stored in the ultracapacitor. !he
converter is capable of changing the direction of the current and incrementing the voltage level either
lower or higher compared to the source voltage. "nalytical design of each component#s parameters
including inductor, $%&'(! rating, and harmonic filter for safe operation of the selected )*+ '
ultracapacitor from $awell. !he converter was simulated in P&I$ for four of its operating conditions,
vi. buck charging of ultracapacitor, boost charging of the ultracapacitor, buck discharge of
ultracapacitor and boost discharge of ultracapacitor. !he harmonics from the simulation for each case
was analyed and a second order filter was designed for the supply and load accordingly. !he
resulting current ripple waveforms were found to have less harmonic magnitude as calculated.
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(ABL0 1/ C12(02(S
Abstract i
(able o contents ii
List o /i3ures iii
List o (ables iv
C)apter % %
1. Introduction 1
2. cope 2
C)apter * ,
1. Con!erter components "
2. Con!erter #nal$sis %
". Con!erter &peration %
C)apter , 4
1. peci'cation o( t)e ultracapacitor *
2. election o( t)e s+itc) *
". +itc)ing (re,uenc$ *
4. Inductor design
%. atter$
C)apter ! %"
1. PI/ simulation 102. uc - C)arge mode 11
". oost - C)arge /ode 12
4. uc Disc)arge /ode 1"
%. oost - Disc)arge /ode 14
C)apter %
1. 3armonic anal$sis 1%
2. umerical Fourier anal$sis 1%
". Filter design 16
4. Filter implementation 15
%. imulation 15
C)apter $ *"
1. Results 20
2. Conclusions 21
Appendi5
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Datas)eets
&eerences
L6S( 1/ /6Figure 1. 1
Conceptual Bi-directional Cascaded Buck-Boost Converter topology______________1YFigure 2. 1 MOSFE sc!e"atic diagra"____________________________________________________#
Figure 2. 2 $nductor sc!e"atic diagra"_____________________________________________________%
Figure 2. # Sc!e"atic diagra" o& a 'attery_________________________________________________%
Figure 2. % Basic structure o& a capacitor____________________________________________________(
Figure 2. ( Sc!e"atic diagra" o& t!e converter_____________________________________________)
YFigure %. 1 Converter sc!e"atic in *S$M__________________________________________________1+
Figure %. 2 Buck - C!arge ,ave&or"s______________________________________________________11
Figure %. # Boost - C!arge ,ave&or"s_____________________________________________________12
Figure %. % Buck - isc!arge ,ave&or"s___________________________________________________1#
Figure %. ( Boost - isc!arge ,ave&or"s___________________________________________________1%
YFigure (. 1 $deal rectangular current ,ave&or"___________________________________________1(Figure (. 2 Current !ar"onic content ,it!out lter________________________________________1)
Figure (. # /ar"onic lter i"ple"entation in si"ulation___________________________________10
Figure (. % Current ,ave&or"s &or Buck - C!arge "ode ,it! lter__________________________1
Figure (. ( Current ,ave&or"s &or Boost - C!arge "ode ,it! lter_________________________1
Figure (. ) Current ,ave&or"s &or Buck - isc!arge "ode ,it! lter_______________________1
Figure (. 0 Current ,ave&or"s &or Boost - isc!arge "ode ,it! lter______________________1
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L6S( 1/ (ABLa'le 2. 1 Converter "odes o& operation____________________________________________________)
a'le 2. 2 3elation o& drive-"ode and s,itc!ing state______________________________________)Y
a'le #. 1 4ltracapacitor para"eters________________________________________________________
a'le #. 2 MOSFE para"eters______________________________________________________________
a7le ". " Inductor parameters
a'le ). 1 esign and si"ulated converter results_________________________________________2+
a'le ). 2 esign and si"ulated lter results______________________________________________2+
C7A8(0& %
1. Introduction
Power electronics converters have a wide range of applications. %ne of particular interest is the
regulated dc supply. In many applications, the output voltage may be required to be higher or
lower compare to the source. Buck-Boost converters can be used to achieve this requirement.
/owever, in some applications, the direction of power flow should also be reversible. 'or such
conditions, bi-directional converters are used. !here are many different topologies for the bi-
directional converters with each topology having certain advantages over others.
!he Bi-directional ascaded Buck-Boost onverter, which for simplicity will be referred to as
0converter1 from herein, is one topology of dc-dc converters that has unique features andfunctions that make it an attractive option for certain applications. 2hen variable power must
be sent and returned to a dc source 3hence bi-directional4, a dc-dc converter may be selected5
even providing a more stable operating dc source for critical loads, a Bi-directional ascaded
Buck-Boost onverter may be utilied. !he 0cascaded1 component stems from the series
connection of both types of converters. !he converter presented in this project has application
in many systems.
(lectric 6ehicle 7rive and 8egenerative Brakingi
Back-up Power &upplyii
Photo-voltaic &ystems
(nergy 8ecovery &ystems
Back-to-back 2ind Power &ystems
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'or the purpose of this project, the converter will be modeled in an electric vehicle inspired
application, with the load of the converter being an ultracapacitor. 7epending on the status of
the ultracapacitor, it will be charged or discharged using a Buck or Boost configuration. !he
topology for this converter is shown in figure ).) iii.
Figure 1. 1Conceptual Bi-directional Cascaded Buck-Boost Converter topology
2. Scope
!his project is limited to the design of the inductor between the two legs, selection of the
switching devices and the rating of the switches based on the load. "dditionally, a second order
filter is designed and component are selected for the battery side and the ultracapacitor side.
7esign of the controller is out of the scope of this course project, so it is not discussed in this
report. !he designed converter is simulated in P&I$ software for validation.
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C7A8(0& *
1. Converter components
Before designing a functional converter, one must understand the fundamentals of operation of
the circuit, as well as fundamental components and concepts individually.
i. $%&'(!
Based on the characteristics of different available power electronic switches, the $%&'(!
was selected5 the criteria which will be discussed in a later chapter of this report. 'or the
purpose of design and analysis of the converter, the $%&'(! operates as an idealied
switch. !his means that the $%&'(! will not have a voltage drop across it when closed and
no current will leak through it when opened. !he idealied $%&'(! will also have an
instantaneous turn-on and turn-off time and is capable of operating under all voltage and
current conditions present in the converter. !o operate the $%&'(!, a gate signal will be
applied to the 091 node when a closed switch is desired5 under all other conditions, the gate
signal will be grounded with : v.
Figure 2. 1 MOSFE sc!e"atic diagra"iv
ii. Inductor
!he inductor plays a vital role in the converter circuit5 namely to act as the energy storage
medium while the $%&'(!s are switching to provide the desired output voltage. !he basic
inductor is a simple component in that it has a magnetic or air core with a wire coiled
around. !here are many other types of inductors, but the scope of this project will not
eplore these configurations, rather the inductance is the only parameter considered. 2hen
current passes through the coil of wire, the inductor presents 0inertia1, or resists the changeof current, depending upon the current applied and the inductance, measured in henries.
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Figure 2. 2 $nductor sc!e"atic diagra"v
iii. Battery
Batteries are the portable source of power which can store and generate electrical power as a
result of a chemical reaction. 'or electrical vehicle and other applications where power is
bi-directional, rechargeable batteries are used. !hese batteries can go through many charge
and discharge cycles, however there is some limit on the continuous current and the current
should have low ripple to maintain epected life of the battery.
Figure 2. # Sc!e"atic diagra" o& a 'attery
iv. apacitor
!he capacitor is another energy storing element in the converter to aid in reducing the
voltage ripple and is often applied on the supply and output of a converter. 'or the design of
the converter within the scope of this project, the capacitor will be considered ideal,
meaning that it contains no parasitic resistance. " capacitor acts as an energy storage device
and will oppose the change in voltage by drawing in the ripple currents, so the current that is
supplied to the capacitor is dependent on the rate of change of the voltage applied, and the
capacitance, measured in farads.
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Figure 2. % Basic structure o& a capacitorvi
v. ;ltracapacitor
"n ultracapacitor is an energy storage device that is utilied in applications where
frequent bursts of power is required for short duration. !he energy storage density for
ultracapacitor is very high compared to normal capacitors. ;ltracapacitors typically
store ): to ):: times more energy per unit volume or massthan electrolytic capacitors,
can accept and deliver chargemuch faster than batteries, and tolerate many more charge
and discharge cycles than rechargeable batteries.
2. Converter Analysis
i. &teady-state "nalysis
&teady-state analysis is an important tool used by designers and engineers to allow for
certain assumptions that simplify the design process. !he assumptions presume that all
analyses of the circuit will be done after any transient or sub-transient responses of the
components have been cleared. !his is done to allow designers to calculate parameters and
components while utiliing simplified equations and processes.
ii. ontinuous onduction $ode
"lso known as $, this describes the operation principle of the converter when the
inductor is not allowed to fully discharge its stored energy. 'orcing the converter to operate
in $ will simplify the design procedure and analysis of the circuit. !his is done by siing
the inductor so that the current flowing through the inductor never reaches a ero-value andthis allows for a designer to use common analysis and design equations to create a converter
that operates as epected.
iii. 7iscontinuous onduction $ode
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a'le 2. 1 Converter "odes o& operation
Mode Current Source Current Sink Description
Buck - Car!e Battery ;ltracapacitor Vbattery>Vsupercap
Boost - Car!e Battery ;ltracapacitor Vbattery Vsupercap
Buck - Discar!e ;ltracapacitor Battery Vbattery Vsupercap
Boost - Discar!e ;ltracapacitor Battery Vbattery>Vsupercap
!he relation of the drive-mode and switching states are shown in table =.=.
a'le 2. 2 3elation o& drive-"ode and s,itc!ing state
Mode "1 "2 "3 "# Description
Buck - Car!e P2$ %'' %'' %'' harging ;ltracapacitor
Boost - Car!e %> %'' %'' P2$ harging ;ltracapacitor
Buck - Discar!e %'' %'' P2$ %'' harging Battery
Boost - Discar!e %'' P2$ %> %'' harging Battery
"s table =.= has identified, the modulation of specific configurations of the switches will
result in measurable and distinct changes in the output voltage. !his converter requires
relatively more comple control and a larger quantity of switching devices, but is able to
operate in a wide range of applications and maintain suitable performance under all current
and voltage conditions presented in this arrangement. !he critical modes of converter
operation are discussed below.
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i.Buck - harge
In this mode the ultracapacitor voltage is less than the battery voltage. &witch ?) is
switched in pwm mode to charge the ultracapacitor in current controlled mode. !he
switching is based on the maimum current through the ultracapacitor.
ii. Boost - harge
2hen the ultracapacitor voltage is greater than the battery voltage, switch ?) is kept on and
switch ?@ will be switched on pwm mode to get higher output voltage than the battery
voltage. /ere again the control is done based on the current through the inductor.
iii. Buck - 7ischarge
!o discharge the ultracapacitor when its voltage is greater than the battery voltage, the
converter is operated in current controlled mode operating the switch ?A in pwm mode.
iv. Boost - 7ischarge
2hen the ultracapacitor voltage is lower than the battery voltage, the converter is operated
in this mode to supply power to the battery. !his is done by keeping ?A on all the time and
switching ?= in pwm mode with current through inductor being controlled.
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C7A8(0& ,
1. Speci$ication o$ te ultracapacitor
!o specify the individual components that make the converter, a circuit consisting of a battery
and an ultracapacitor was selected. !his type of load and source is an analogy to an electric
vehicle application. In this application, the current flowing is bi-directional and the magnitude
must be limited to a value within the tolerable levels of the components. !he $awell
BMOD%1&' (%#) B** ultracapacitor with the parametersviigiven in table A.) was selected as
an appropriate load for this study.
a'le #. 1 4ltracapacitor para"eters
Capacitanc
e
+ated ,olta!e Ma Continuous Current eaka!e Current /S+
)*+ ' @ 6 CC " +.= m" *.A mD
'rom the leakage current, the leakage resistance is calculated to be E,=A) D.
2. Selection o$ te s0itc
'rom the rating of the ultracapacitor and the level of the operating voltage, the switching device
should be selected. !he maimum voltage across each switch is @ 6 and the average current
through each of the switch is maimum continuous current through the ultracapacitor. Because
of the low voltage, high current, high switching frequency capability, a $%&'(! is selected as
the switching device. !he $%&'(! must be capable of handling the application demands
without damage5 therefore the &!$icroelectronics S1)'1%43-2 $%&'(!viiiwith )::F
safety margin was selected. !he parameters of the $%&'(! are listed in table A.=.
a'le #. 2 MOSFE para"eters
,olta!e5VDS ):: 6
Continuous current5ID ): "
ermal resistance 6unction-case5Rthjcase :.@ GH2
urn on delay time5td ,o n =+.* ns
+ise time5 tr EC.) ns
urn-o$$ delay5td,off EE.E ns
4all time5tf *.E ns
+esistance o$ drain-source5 +DS7on8ma @.+ mD
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3. S0itcin! $re9uency
!he $%&'(! must be able to dissipate the heat generated due to conduction and switching
losses. !he switching frequency,fS of the converter, is calculate by balancing the rate of
heat generation and the rate of heat loss.
!he conduction loss is given by Pcond 8ds3on4JI7=JdutyKcycle L3=.)4
'or the worst case, dutyKcycle is considered unity.
!he switching loss is given by Psw MJ67&JI7&J3td3on4N trNtd3off4Ntf4Jfsw L3=.=4
!he maimum allowable power loss can be calculated using equation 3=.A4
Pallowable T
R thjcase L3=.A4
!o limit the junction temperature to )::o, the maimum allowable power loss is calculated to
be )+*.=+ watts. "s per the datasheet, the drain to source resistance varies with temperature, at
)::o, it is given by equation 3=.@4.
87&3on4).+J87&3normal4L3=.@4
onsidering the non-perfect junction between the $%&'(! and the heat sink the switching
frequency is selected to be )H+ thof the switching frequency given by the calculations using
equations 3=.)4 to 3=.@4 which is +: k/.
#. Inductor desi!n
%nce the switching frequency is fied, the sie of the coupling inductor, , can be properly
designed. In order to maintain the continuous current mode operation of the converter, the
inductor can be sied according to the following equationiO
L= TSVbat
8ILB ,max
;sing a fair assumption of maintaining continuous conduction mode at +F of the safe
continuous current value, which is set at :F of the maimum continuous allowable current,the following values are obtained and are listed in table A.A.
a'le #. # $nductor para"eters
S0itcin! ime5
TS
Battery
,olta!e5
)%: Ma Continuous
Current5 Sa$e Operatin! (oint
Minimum Inductor
Current5ILB ,max
Induct
ance5
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Vbat
1
50kH=20!s 24V 8077"=61.6" 561.6"=3.08"
2% ;
'. Battery
'or this project, an ideal battery in the P&I$ software component library is selected. " small
resistance of + mD is added in series with the battery to represent the internal resistance of the
battery. %ther parasitic and intrinsic factors of the battery are not considered in this project.
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C7A8(0& !
1. (SIM simulation
" circuit shown in figure @.) is made in P&I$ for simulation realiation.
Figure %. 1 Converter sc!e"atic in *S$M
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2. Buck - Car!e mode
Figure %. 2 Buck - C!arge ,ave&or"s
In this mode ?) is operated in pwm mode with ?=, ?A and ?@ turned off. 'or simulation
purpose, the battery voltage is fied at =@ 6 and ultracapacitor voltage is set to =: 6. !he
inductor current is forced to maintain :F of rated ultracapacitor current i.e. *= ". !he
modulating triangular waveform, gate signal to transistor ?), battery voltage, ultracapacitor
voltage, capacitor current, inductor current and the battery current are plotted
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3. Boost - Car!e ModeFigure %. # Boost - C!arge ,ave&or"s
In this mode ?) is on all the time with ?@ operated in pwm mode while ?= and ?A are turned
off. 'or simulation purpose, the battery voltage is fied at =@ 6 and the ultracapacitor voltage is
set to @: 6. !he inductor current is forced to maintain an average value of *= ". !he waveforms
as in buck charge mode are plotted in figure @.@ and figure @.+. It shows that ultracapacitor
current has a pulsed waveform while inductor current and battery current has an average value
of current close to *+ ".
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#.
#.
#.
#.
#.#.
#.
#.
#.
#.
#.
#.
#.
#.
#.
#.
#.
#.
#.
#.
#.
#.
#.
#.#.
#.
#.
Buck < Discar!e Mode
Figure %. % Buck - isc!arge ,ave&or"s
!he ultracapacitor is discharging into the battery with current being maintained within a ripple
of approimately A " near an average value of *= ". !he voltage of the ultracapacitor in this
simulation is @: 6, and the battery voltage is =@ 65 this gives a duty cycle for the switching$%&'(! 3?A4 of :.*, which can be seen in the gate voltage waveform. !he current in the
ultracapacitor is pulsed waveform with a peak to peak ripple of around *+ ".
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'. Boost - Discar!e Mode
Figure %. ( Boost - isc!arge ,ave&or"s
!he voltage of the ultracapacitor is measured to be =: 6 and is slowly decreasing as it discharges into
the battery5 this eplains the negative values for current in figure @.+. !he duty cycle of the switching
$%&'(!, ?= is calculated as :.=, which can be seen in the gate voltage waveform. !he inductor
current is held within the A " ripple around C= ", while the battery current is a pulsed waveform with a
peak to peak ripple of nearly C+ ".
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C7A8(0&
1. armonic analysis
'rom the waveforms shown in figure @.= to @.+, the battery current is pulsed in buck charge
mode and boost discharge mode while the ultracapacitor current is pulsed in boost charge mode
and buck discharge mode. !his is due to the nature of the circuit and the switching operation
required to obtain the buck and boost modes. !o determine the harmonic content present in the
pulsed waveforms, the pulsed waveform is assumed to have an ideal rectangular shape as
shown in figure +.).
Figure (. 1 $deal rectangular current ,ave&or"
2ith the idealied rectangular waveform shown in figure +.), the 'ourier series analysis is
simplified and using equation +.), the amplitude of the harmonic currents is calculated.
ah=2"
h# (sinhd#)
L 3+.)4
2hen d is :.+, the amplitude of harmonics is largest. !he fundamental component,a1 , with a
frequency of +: k/, which is the same as the switching frequency,fS , has a peak to peak
amplitude of4"
# .
!his large amplitude is undesirable for the life of the battery and ultracapacitor, and a filter is
needed to limit this value.
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fres= fh
10
$a%n(dB)40dB /Dec L 3+.+4
;sing equations +.= to +.+, the resonant frequency of the filter,
fres
, is calculated to be E.E
k/. !he angular frequency becomes )res=2 # fres=62.25krad /sec .
!he resonant angular frequency of the second order harmonic filter can be written as equation
+.*.
)res= 1
L* L 3+.*4
!o limit the voltage ripple of the filter capacitor to +F of the battery voltage, the sie ofcapacitance for the worst-case of duty cycle equal to ), is calculated to be )::: ' using
equation +.C.
V=+
* =
I"V$t
* L 3+.C4
>ow the filter inductance is determined from equation +.* to be =*: n/.
#. 4ilter implementation
!he converter with the battery and load second order filters implemented is shown in figure +.A.
Figure (. # /ar"onic lter i"ple"entation in si"ulation
'. Simulation
'or the same cases in chapter @ sections = to +, P&I$ simulation with filter results the
waveforms shown in figure +.@ to figure +.C. !he waveforms shows that the peak to peak ripple
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of the fundamental harmonics were reduced. /owever, harmonics at the resonant frequency of
the filter were introduced.
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Figure(. %
Current ,ave&or"s &or Buck - C!arge "ode,it!lter
Figure (. ( Current ,ave&or"s &or Boost - C!arge "ode ,it! lter
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Figure (. ) Current ,ave&or"s &or Buck - isc!arge "ode ,it! lter
Figure (. 0 Current ,ave&or"s &or Boost - isc!arge "ode,it! lter
omparing the results in figure @.= to figure @.+ with figure +.@ to figure
+.C respectively, the current waveforms have lost their pulsed rectangular shape and are now much
closer to an ideal dc voltage. !here is still a ripple due to the siing of the filter, which was necessary to
maintain designed operation characteristics after implementation, while removing as much of the
harmonic current content as possible. !here is a possible resonance effect shown in the waveform
shape, but this impact on the components is much less than the large pulsed current waveform that was
present prior to filter implementation.
C7A8(0& $
1. +esults
!he average inductor current was designed to sustain :F of the maimum continuous current
rating of the ultracapacitor with a maimum ripple of +F at a switching frequency of +: k/.
!he second order filters were designed to limit the current ripple in the battery and
ultracapacitor to +F of the battery voltage and +F peak-to-peak of the current amplitude. "
summary of the results are listed in table *.) and table *.=.
a'le ). 1 esign and si"ulated converter results
Mode o$
Operation
Inductor Avera!e
Current5IL
Inductor +ipple
Current5IL Comments
Desi!ned Simulate Desi!ned Simulate
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d d
Buck - Car!e *).* " *= " A.: " =.= " &imulation as designed
Boost - Car!e *).* " *@ " A.: " C.: " IL higher than
designed
Buck - Discar!e *).* " *: " A.: " E.: " ILhigher than
designed
Boost - Discar!e *).* " C= " A.: " @.: "I,design
IL
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2. Conclusions
!he Bi-directional ascaded Buck-Boost onverter topology was analyed and designed for a
specific application supplying power to charge the ultracapacitor or use the power in the
ultracapacitor. !he sie of the switches, inductor and filter were determined using analytical
equations. !he converter was simulated in P&I$ to verify its operation. !he harmonics in
current was analyed using both 'ourier series method and numerical 'ourier transform in
software. 7esigning a second order filter, the dominant harmonic current was limited to
with +F of the peak amplitude which was verified in simulation.
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A8802D69
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DA(AS700(S
&0/0&02C0S
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i tud$ o( i-Directional uc-oost Con!erter opologies (or #pplication in Electrical
8e)icle /otor Dri!es F. Caricc)i9 F. Crescim7ini9 F. :iulii Capponi9 L. olero.
ii /odelling and Control (or a idirectional uc-oost Cascade In!erter 3onglin ;)ou9
)uai ??+ps.pren)all.com?c)et@pa$nter@introduct@6?6?1664?4261**.c+?indeA.)tml
! )ttps>??en.+iipedia.org?+ii?InductorB?media?File>InductorignalFilter1.png
!i )ttp>??+++.electronics-tutorials.+s?capacitor?cap@1.)tml
!ii )ttps>??+++.maA+ell.com?images?documents?),@4*!@ds1016201".pd(
!iii )ttp>??+++.st.com?st-+e7-
ui?static?acti!e?en?resource?tec)nical?document?datas)eet?D/001"""20.pd(
iAiAPo+er Electronics> Con!erters9 #pplications9 and Design - ed /o)an9 ore /.
ndeland9 illiam P. Ro77ins
A eamless Controlled Parallel i-directional DC-DC Con!erter (or Energ$ torage $stem
- aa$ui &uc)i9 #i)io anouda9 ao$a aa)as)i and /inoru /otei