Post on 04-Jun-2018
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November 1999 1Simone Buso - University of Padova - Lesson 5
Lesson 5Lesson 5
Digital Control of Three-Phase DC/ACDigital Control of Three-Phase DC/AC
Converters: Current Control TechniquesConverters: Current Control Techniques
DigitalDigitalHysteresisHysteresisControlControl
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November 1999 2Simone Buso - University of Padova - Lesson 5
DigitalDigitalHysteresis ControlHysteresis Control
Thank to itsThank to its inherent non-linearity,inherent non-linearity,thethehysteresishysteresiscurrent control is capable of providingcurrent control is capable of providing the fastestthe fastest
possible dynamic response.possible dynamic response.
Using this technique, it is possible to achieve theUsing this technique, it is possible to achieve the
maximum exploitation of the power converter.maximum exploitation of the power converter.TheThe limitlimit to current regulation capability, in fact,to current regulation capability, in fact,
is only given by the poweris only given by the power converter design.converter design.
TheThehysteresishysteresiscurrent controlcurrent controlis inherentlyis inherently stablestable
and robustand robustto load variations or any other type ofto load variations or any other type ofdynamic perturbations.dynamic perturbations.
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November 1999 3Simone Buso - University of Padova - Lesson 5
DigitalDigitalHysteresis ControlHysteresis Control
The generation ofThe generation of non-dcnon-dccurrent waveformscurrent waveforms
implies theimplies the variation of the instantaneousvariation of the instantaneous
switching frequency.switching frequency.
This isThis is not desirablenot desirablebecause:because:
thethe design of converters output filtersdesign of converters output filtersisis
more complicated and less effective;more complicated and less effective;
in case ofin case of motor drive applications,motor drive applications,acousticacoustic
noise due tonoise due to mechanicmechanicresonancesresonancesmay bemay be
generated.generated.
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November 1999 4Simone Buso - University of Padova - Lesson 5
DigitalDigitalHysteresis ControlHysteresis Control
Single-phase schematicSingle-phase schematicof theof thehysteresishysteresiscurrentcurrent
control. Thecontrol. ThehysteresishysteresisbandsbandsBBpp,,BBnnare supposedare supposedto beto be fixed.fixed.
LL RRi*i*LL
++--
11
00
iiLL
ii
ee++
--VVdcdc/2/2
++VVdcdc/2/2-B-B nn
BBpp iiLL
uuu
!!!
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November 1999 5Simone Buso - University of Padova - Lesson 5
DigitalDigitalHysteresis ControlHysteresis Control
edt
diLiRu LL ++++== edtdiLiRu LL ++++== Load equationLoad equationLoad equation
*LLi ii ==*LLi ii == Current errorCurrent errorCurrent error
edt
diLiRu
*L*
L* ++++== e
dtdi
LiRu*L*
L* ++++== Reference voltageReference voltageReference voltage
dtdLRuuii* ++== dtdLRuu ii* ++== Current errordynamic equationCurrent errorCurrent errordynamic equationdynamic equation
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November 1999 6Simone Buso - University of Padova - Lesson 5
DigitalDigitalHysteresis ControlHysteresis Control
dtdLRuu ii
* ++==dt
dLRuu ii* ++==
NormallyNormallythethe resistive termresistive termcan becan be neglectedneglectedandand
thethe reference voltage ureference voltage u**can be consideredcan be consideredconstantconstantduring a modulation period.during a modulation period.
Therefore,Therefore, the current errorthe current errorhas ahas a triangulartriangular
shapeshape(right-hand side is constant) and the(right-hand side is constant) and the
average of uaverage of uover a modulation period isover a modulation period is equalequalto u*to u*(total current variation is 0).(total current variation is 0).
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November 1999 7Simone Buso - University of Padova - Lesson 5
DigitalDigitalHysteresis ControlHysteresis Control
Current errorand hysteresis
band.
CurrentCurrent errorerrorandandhysteresishysteresis
band.band.
Inverter voltage
pulses.
InverterInverter voltagevoltage
pulses.pulses.
Synchronizationclock.SynchronizationSynchronizationclock.clock.
iii
-Vdc/2--VVdcdc/2/2
Vdc/2VVdcdc/2/2
TTT
uuu
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November 1999 8Simone Buso - University of Padova - Lesson 5
DigitalDigitalHysteresis ControlHysteresis Control
==2
Vuu dc*
n
==2
Vuu dc*
n
It is possible to derive the followingIt is possible to derive the following periodperiodequation:equation:
(( ))2ndc u1V
L4T
==
(( ))2ndc u1V
L4T
==
where:where:
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November 1999 9Simone Buso - University of Padova - Lesson 5
DigitalDigitalHysteresis ControlHysteresis Control
TheThe period equationperiod equationshows that:shows that:
ifif isisconstantconstantandanduunnvariesvariesthe periodthe period T alsoT alsovaries;varies;
toto
get a constant switching frequency (1/Tget a constant switching frequency (1/T
dd))
thethehysteresishysteresisbandband has to behas to be dynamicallydynamicallymodified,modified, according to this equation:according to this equation:
(( )2nddc u1L4 TV == (( 2nddc u1L4TV
==
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November 1999 10Simone Buso - University of Padova - Lesson 5
DigitalDigitalHysteresis ControlHysteresis Control
The application of theThe application of thehysteresishysteresiscurrentcurrentcontrol tocontrol tothree phase systemsthree phase systemswith insulatedwith insulated
neutralneutralis made a little more complicated byis made a little more complicated by
the unavoidablethe unavoidable interference among the phaseinterference among the phase
currents.currents. It is anywayIt is anyway possible to strongly reducepossible to strongly reduce thethe
interference by suitablyinterference by suitably manipulating themanipulating the
current error.current error.
This only requires aThis only requires a simplesimpleadditional analogadditional analogcircuit.circuit.
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November 1999 11Simone Buso - University of Padova - Lesson 5
In aIn a three-phase system with insulated neutralthree-phase system with insulated neutral
the load equation must be modified to takethe load equation must be modified to take
into accountinto account the load midpoint voltage (neutralthe load midpoint voltage (neutral
voltage).voltage).
DigitalDigitalHysteresis ControlHysteresis Control
1uedt
idLiRu oLL ++++++== 1uedt
idLiRu oLL ++++++==
wherewhereuuoois the load midpoint voltageis the load midpoint voltage(neutral(neutral
voltage) andvoltage) and 11is theis the unity vector.unity vector.
(( ))
3
uuuu 321o
++++==
(( ))
3
uuuu 321o
++++==
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November 1999 12Simone Buso - University of Padova - Lesson 5
DigitalDigitalHysteresis ControlHysteresis Control
WithWith the same definitionsthe same definitionsand procedure of theand procedure of the
single phase case, the followingsingle phase case, the following dynamicdynamic
equationequationcan be derived for thecan be derived for the current error:current error:
dt
dLR1uuu i
io
* ++==dt
dLR1uuu i
io
* ++==
Because of theBecause of the presence ofpresence ofuuoo,,the currentthe current
error in a switching perioderror in a switching periodis not triangular andis not triangular and
its slopeits slope(on each phase)(on each phase) depends on the statedepends on the state
of all phasesof all phases(through(throughuuoo). This phenomenon is). This phenomenon is
known asknown as phase-interference.phase-interference.
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November 1999 13Simone Buso - University of Padova - Lesson 5
DigitalDigitalHysteresis ControlHysteresis Control
ToTo eliminate the phase interference,eliminate the phase interference,whichwhich
negatively affectsnegatively affectsthethehysteresishysteresiscontrolcontrol
behavior, abehavior, adecouplingdecouplingtermtermiican be definedcan be definedas follows:as follows:
1udtdLR oii ==
++ 1udtdLR oii ==
++
which can bewhich can be easily implementedeasily implementedbyby filteringfilteringthethe
instantaneous voltageinstantaneous voltageuuoowith an analogwith an analog lowlow
pass filterpass filterhaving thehaving the same time constantsame time constantof theof theloadload (L/R).(L/R).Tuning is normally required.Tuning is normally required.
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November 1999 14Simone Buso - University of Padova - Lesson 5
Re-writingRe-writingthe error dynamic equation as athe error dynamic equation as a
function of thefunction of thedecoupleddecoupledcurrent errorcurrent errorii::
DigitalDigitalHysteresis ControlHysteresis Control
iii == iii ==
it is possible to derive theit is possible to derive thedecoupleddecouplederrorerroriidynamic equation:dynamic equation:
dt
dLRuu ii
* ++==dt
dLRuu ii
* ++==
whichwhich no longer dependsno longer dependson the load midpointon the load midpoint
voltagevoltageuuoo..
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November 1999 15Simone Buso - University of Padova - Lesson 5
DigitalDigitalHysteresis ControlHysteresis Control
TheThe structurestructure of theof thedecoupleddecouplederror dynamicerror dynamic
equation isequation is exactly the sameexactly the sameof theof the single-phasesingle-phasecase.case.
Therefore, onceTherefore, once a suitablea suitabledecouplingdecouplingcircuit iscircuit is
implemented, theimplemented, the three-phase systemthree-phase systembehavesbehaves
exactly asexactly as three single phase ones,three single phase ones,withwithtriangulartriangulardecoupleddecoupledcurrent errors,current errors,whose slopewhose slope
depends onlydepends onlyon the state of theon the state of the correspondingcorresponding
inverter phase.inverter phase.
From now on,From now on, the explanationthe explanationof the digitalof the digitalcontrol system for thecontrol system for thehysteresishysteresiscontrollercontroller willwill
refer to the single phase case.refer to the single phase case.
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November 1999 16Simone Buso - University of Padova - Lesson 5
DigitalDigitalHysteresis ControlHysteresis Control
TheThe
controller maintains its analog structure,controller maintains its analog structure,
but abut a bandwidth digital controlbandwidth digital controlis added whichis added which
ensuresensures constant switching frequency.constant switching frequency.
LL RRi*i*LL
++-- 11
00
iiLL
ii
ee++
--VVdcdc/2/2
++VVdcdc/2/2
-B-B nn
BBpp iiLL
uu
DigitalDigital
ControlControl BBpp,,BBnn
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November 1999 17Simone Buso - University of Padova - Lesson 5
Bandwidth Control AlgorithmBandwidth Control Algorithm
T(k)T(k)T(k) T(k+1)T(k+1)T(k+1)
(k)(k)(k) (k+1)(k+1)(k+1)S+(k+1)SS++(k+1)(k+1)
S-(k+1)SS--(k+1)(k+1)
S+(k)SS++(k)(k)
S-(k)SS--(k)(k)
k:k:k:S+Ton= S-Toff= SS++TTonon= S= S--TToffoff==
Ton+ Toff= TTTonon++TToffoff= T= T
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November 1999 18Simone Buso - University of Padova - Lesson 5
Bandwidth Control AlgorithmBandwidth Control Algorithm
From theFrom the previous equationsprevious equationsit is possible toit is possible to
derive:derive:
)k(S
)k(S)k(S)k(
)k(S
)k(
)k(S
)k()k(T
p
++
++
++==
++
==
)k(S
)k(S)k(S)k(
)k(S
)k(
)k(S
)k()k(T
p
++
++
++==
++
==
and assuming:and assuming:
)k(
)k(T)1k()1k(T
++==++
)k(
)k(T)1k()1k(T
++==++
)k(S)1k(S ++++ ==++ )k(S)1k(S ++++ ==++ )k(S)1k(S ==++ )k(S)1k(S ==++
we can get:we can get:
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November 1999 19Simone Buso - University of Padova - Lesson 5
Bandwidth Control AlgorithmBandwidth Control Algorithm
From the previous equations, it is possible toFrom the previous equations, it is possible to
derive thederive the control equation:control equation:
)k(T
T)k()1k( d==++
)k(T
T)k()1k( d==++
where Twhere Tddis theis the desired switching period.desired switching period.
It is worth noting thatIt is worth noting that this reasoning leads tothis reasoning leads to
an algorithman algorithmwhich is equivalent to awhich is equivalent to a firstfirst
order dead-beat controlorder dead-beat controlof the switchingof the switchingperiod.period.
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November 1999 20Simone Buso - University of Padova - Lesson 5
Bandwidth Control AlgorithmBandwidth Control Algorithm
The control algorithm is very simple. It onlyThe control algorithm is very simple. It only
requiresrequires time measurements,time measurements,which can bewhich can be
easily implemented byeasily implemented by using the captureusing the capture
function of any micro-controller.function of any micro-controller.
The algorithm isThe algorithm is auto-tuning,auto-tuning,does not requiredoes not require
anyany knowledge of the load parameters.knowledge of the load parameters.They areThey are
implicitlyimplicitly estimated by measuring the switchingestimated by measuring the switching
period with a knownperiod with a known ..
TheThe calculationcalculation of the newof the new requires arequires adivision.division.This implies a certainThis implies a certain computationcomputationtime.time.
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November 1999 21Simone Buso - University of Padova - Lesson 5
Bandwidth Control AlgorithmBandwidth Control Algorithm
The control algorithm is able to guarantee aThe control algorithm is able to guarantee a
good frequency regulation.good frequency regulation.
Unfortunately, theUnfortunately, the switching pulsesswitching pulsesfor thefor the
three phases are not phase-controlled. Thisthree phases are not phase-controlled. This
means thatmeans that the allocation inside the modulationthe allocation inside the modulation
period of the switching pulses is random.period of the switching pulses is random.
ThisThis implies a slightly increased current rippleimplies a slightly increased current ripple
with respect with the optimum pulse allocationwith respect with the optimum pulse allocation
(centered pulses).(centered pulses).
Methods to improve the algorithm,Methods to improve the algorithm, includingincluding
pulses phase controlpulses phase controlare available.are available.
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November 1999 22Simone Buso - University of Padova - Lesson 5
Bandwidth Control AlgorithmBandwidth Control Algorithm
A feasible way toA feasible way to
regulate the phaseregulate the phase
shiftshift
between the pulsesbetween the pulsesis tois to lock them to alock them to a
synchronizing clock.synchronizing clock.
TheThe time differencetime difference between thebetween thesynchronizingsynchronizing
clock and the inverter pulsesclock and the inverter pulsescan be measuredcan be measured
and used to modify the bandwidth.and used to modify the bandwidth.
AA proper regulator must be designedproper regulator must be designedto stabilizeto stabilize
the system.the system.
ThisThis solutionsolution is equivalent tois equivalent tothe implementationthe implementationofofaadigital Phase Locked Loop (PLL).digital Phase Locked Loop (PLL).
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November 1999 23Simone Buso - University of Padova - Lesson 5
Bandwidth Control AlgorithmBandwidth Control Algorithm
Hysteresis
Comparator
HysteresisHysteresis
ComparatorComparator Switching PulsesSwitching PulsesSwitching Pulses
BandwidthCalculatorBandwidthBandwidthCalculatorCalculator
BandwidthCorrectorBandwidthBandwidthCorrectorCorrector ClockClock
Clock
iLiiLL
i*Lii**LL iii
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November 1999 24Simone Buso - University of Padova - Lesson 5
Bandwidth Control AlgorithmBandwidth Control Algorithm
The designThe designof the bandwidth corrector is normallyof the bandwidth corrector is normally
complicated by the open loop gain variability.complicated by the open loop gain variability.
Small signal analysis shows that theSmall signal analysis shows that thehysteresishysteresis
comparatorcomparatorgaingainis given by:is given by:
(( ))
==
==
== d2n2dc fu1
L4
V
d
dfHC (( ))
==
==
== d2n2dc fu1
L4
VddfHC
This gain, together with theThis gain, together with the phase-detectorphase-detector
(integrator)(integrator)and theand the regulatorregulator (which is normally a(which is normally aPI)PI)gainsgainsgives thegives the open loop gain.open loop gain.
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November 1999 25Simone Buso - University of Padova - Lesson 5
Bandwidth Control AlgorithmBandwidth Control Algorithm
[dB][dB][dB]
log10floglog1010ff
GGG
un= 0uunn= 0= 0
un= 0.8uunn= 0.8= 0.8
fzffzz
z2
z2n
2r
dc
p
Ts
sT1
u1
f
V
Lk8G
++
==
z2
z2n
2r
dc
p
Ts
sT1
u1
f
V
Lk8G
++
==
z
zp
sT
sT1k
d
dPI
++==
==
z
zp
sT
sT1k
d
dPI
++==
==
s2
dfdPhD ==== s
2dfdPhD ====
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November 1999 26Simone Buso - University of Padova - Lesson 5
Bandwidth Control AlgorithmBandwidth Control Algorithm
To avoidTo avoid instabilityinstabilitywhen thewhen the modulation indexmodulation index
is maximum,is maximum,the bandwidth of the regulationthe bandwidth of the regulation
must be reduced.must be reduced.
Therefore,Therefore, the quality of thethe quality of theswitching pulsesswitching pulses
phase regulationphase regulationisis notnot very high.very high.
In case ofIn case of transients,transients,the regulator of the pulsethe regulator of the pulse
phase inducesphase induces oscillations,oscillations,which furtherwhich further
decrease the effectiveness of the control.decrease the effectiveness of the control.
AlternativeAlternativemethods to achieve the pulsesmethods to achieve the pulsesphase lockphase lock can be identified.can be identified.
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November 1999 27Simone Buso - University of Padova - Lesson 5
Bandwidth Control AlgorithmBandwidth Control Algorithm
kk k+1k+1 k+2k+2
T*T*
ClockClock
tk+3k+3k-1k-1
BBpp(k)(k)
BB**
TTspsp(k)(k)
ttee(k)(k)
BBpp(k+2)(k+2)
TTclockclock
iiiiii
--BBnn(k)(k)
-B-B**
ttee(k+1)(k+1)
TTspsp(k+1)(k+1)
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November 1999 28Simone Buso - University of Padova - Lesson 5
2
T)1k(T)k(t)1k(t
*
spee ++++==++2
T)1k(T)k(t)1k(t
*
spee ++++==++
Bandwidth Control AlgorithmBandwidth Control Algorithm
The algorithmThe algorithm modifies the twomodifies the twohysteresishysteresis
thresholdsthresholdsindependentlyindependentlyfrom each other.from each other.
TheThe input is the timing errorinput is the timing errorttee(k)(k)between thebetween the
current errorcurrent error zero crossingzero crossingand the externaland the external
synchronization clock.synchronization clock.
At any zero-crossingAt any zero-crossingttee(k) is measured(k) is measuredand theand the
followingfollowingttee(k+1) is estimated(k+1) is estimatedaccording to theaccording to the
following equation, wherefollowing equation, where T* is the desiredT* is the desired
period (= 2Tperiod (= 2Tclkclk):):
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November 1999 29Simone Buso - University of Padova - Lesson 5
Bandwidth Control AlgorithmBandwidth Control Algorithm
TheThe half periodhalf periodTTspsp(k)(k)also needs to bealso needs to be
estimatedestimatedaccording to the following equation:according to the following equation:
)k(T)k(B
)k(B)1k(T sp
p
nsp ==++ )k(T
)k(B
)k(B)1k(T sp
p
nsp ==++
Note thatNote that at instant kat instant kthethe thresholdsthresholdsBBpp(k) and(k) and
BBnn(k) are known(k) are knownto the algorithm. The algorithmto the algorithm. The algorithm
modifies the threshold the current error is notmodifies the threshold the current error is not
going to.going to.In this caseIn this caseBBppwill be modifiedwill be modified to getto getthe timing error to zero.the timing error to zero.
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November 1999 30Simone Buso - University of Padova - Lesson 5
Bandwidth Control AlgorithmBandwidth Control Algorithm
First,First, the correct threshold amplitudethe correct threshold amplitudemust bemust be
identified, according to the following equation:identified, according to the following equation:
)k(T
)k(B
2
T)k(B
sp
p*
* ==)k(T
)k(B
2
T)k(B
sp
p*
* ==
Then, the new value ofThen, the new value of thresholdthresholdBBpp(k+2),(k+2),whichwhicheliminates the timing error,eliminates the timing error,can be computed:can be computed:
2
T
)1k(t2
T
)k(B
)2k(B
*
e
*
*
p++
==
++
2
T
)1k(t2
T
)k(B
)2k(B
*
e
*
*
p++
==
++
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November 1999 31Simone Buso - University of Padova - Lesson 5
Bandwidth Control AlgorithmBandwidth Control Algorithm
)k(T
)k(B)k(B)k(T)k(tT
)k(B)2k(Bsp
p
nspe
*
pp
==++)k(T
)k(B)k(B)k(T)k(tT
)k(B)2k(Bsp
p
nspe
*
pp
==++
Substituting all theSubstituting all the known quantitiesknown quantitiesin thein the
previous equationprevious equation the final equation,the final equation,basedbasedonon measured data,measured data,whichwhich updates theupdates the
thresholdthresholdand,and, theoretically,theoretically,eliminates theeliminates the
error, is obtained:error, is obtained:
A totallyA totally symmetrical equationsymmetrical equationcan be derivedcan be derived
forforBBnn..
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November 1999 32Simone Buso - University of Padova - Lesson 5
Bandwidth Control AlgorithmBandwidth Control Algorithm
Based on this algorithm aBased on this algorithm a second order dead-second order dead-
beat control of the pulses timing errorbeat control of the pulses timing errorisisachieved.achieved.
In principle,In principle, the control eliminates any errorthe control eliminates any errorinin
frequency and phase with a modulation periodfrequency and phase with a modulation period
delaydelay (two clock cycles).(two clock cycles). BeingBeing the current zero-crossings synchronizedthe current zero-crossings synchronized
with the modulation period,with the modulation period,the pulses arethe pulses are
automatically centered.automatically centered.
Dead-times compensationDead-times compensationcan also be includedcan also be includedin the algorithm.in the algorithm.
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November 1999 33Simone Buso - University of Padova - Lesson 5
0us 100us 200us 300us 400us 500us
1.5
1.0
0.5
0.3
-0.3
0
Bandwidth Control AlgorithmBandwidth Control Algorithm
Controls dynamic
response to a
bandwidth error.
Controls dynamicControls dynamic
response to aresponse to a
bandwidth error.bandwidth error.
Solid: normalized
switching frequency.
Dashed: instantaneousphase error.
Solid:Solid:normalizednormalized
switching frequency.switching frequency.
Dashed:Dashed:instantaneousinstantaneousphase error.phase error.
i
B*
Bp
-Bn
0us 100us 200us 300us 400us 500us
2.0
1.0
0.0
-1.0
-2.0
-B*
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November 1999 34Simone Buso - University of Padova - Lesson 5
0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms 1.8ms 2.0ms
1.0
0.5
0.0
-0.5
-1.0
Bp
-Bn
i
0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms 1.8ms 2.0ms
1.5
1.0
0.5
Bandwidth Control AlgorithmBandwidth Control Algorithm
Control operation in
saturation mode.
Control operation inControl operation in
saturation mode.saturation mode.
Normalized switching
frequency.
Normalized switchingNormalized switching
frequency.frequency.
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November 1999 35Simone Buso - University of Padova - Lesson 5
Bp
n-B
i
e
Bandwidth Control AlgorithmBandwidth Control Algorithm
Experimentalmeasurement.
Control operation in
saturation mode.
ExperimentalExperimentalmeasurement.measurement.
Control operation inControl operation in
saturation mode.saturation mode.
Converter ParametersConverter Parameters
DC Link VoltageDC Link Voltage 300 V300 V
Output InductorOutput Inductor 1.81.8mHmHSwitching FrequencySwitching Frequency 20 kHz20 kHz
Nominal Output PowerNominal Output Power 5 kW5 kW
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November 1999 36Simone Buso - University of Padova - Lesson 5
Bandwidth Control AlgorithmBandwidth Control Algorithm
Experimental measurementsExperimental measurementsExperimental measurements
Phase current errorsPhasePhase current errorscurrent errors Phase voltage pulsesPhasePhase voltage pulsesvoltage pulses
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November 1999 37Simone Buso - University of Padova - Lesson 5
Bandwidth Control AlgorithmBandwidth Control Algorithm
00
2020
4040
6060
8080
100100
120120
140140
5050 100100 200200 300300 400400 500500 700700 10001000
Frequency [Hz]Frequency [Hz]
Phase
Error[
Phase
Error[deg
deg]]
experimentalexperimental
simulation 1simulation 1
simulation 2simulation 2
Phase error in degrees between clock and
phase voltage pulses. All plotted data refer
to the generation of a sinusoidal current (6 A
peak value) with a 0.8 modulation index.
Phase error in degreesPhase error in degrees between clock andbetween clock and
phase voltage pulses. All plotted data referphase voltage pulses. All plotted data refer
to the generation of ato the generation of a sinusoidal current (6 Asinusoidal current (6 A
peak value) with a 0.8 modulation index.peak value) with a 0.8 modulation index.
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November 1999 38Simone Buso - University of Padova - Lesson 5
ReferencesReferences
[1][1] L.L.MalesaniMalesaniand P.and P.TentiTenti: "A novel: "A novelhysteresishysteresiscontrol methodcontrol methodforfor
current controlled VSI PWM inverterscurrent controlled VSI PWM inverters with constant modulationwith constant modulation
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