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August 2001 Lesson 4 1
Lesson 4
Implementation of Synchronous Frame
Harmonic Control for High-Performance ACPower Supplies
Lesson 4
Implementation of Synchronous Frame
Harmonic Control for High-Performance ACPower Supplies
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August 2001 Lesson 4 2
Goal of the workGoal of the work
Investigation of selective control on output
voltage harmonics.
Motivations:
• reduction of voltage distortion in AC Power
Supplies (even with limited voltage loopbandwidth);
•
refinements aimed at an efficientimplementation in fixed-point DSP’s (here
tested on ADMC401 by Analog Devices).
Investigation of selective control on output
voltage harmonics.
Motivations:
• reduction of voltage distortion in AC Power
Supplies (even with limited voltage loopbandwidth);
•
refinements aimed at an efficientimplementation in fixed-point DSP’s (here
tested on ADMC401 by Analog Devices).
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August 2001 Lesson 4 3
Presentation outlinePresentation outline
• Review of synchronous reference frame
harmonic regulation
• Decomposition in three-layer control
scheme
• A modified solution based on DiscreteFourier Transform
•Design guidelines for regulator parameters
• DSP implementation using ADMC401
•Experimental results
• Review of synchronous reference frame
harmonic regulation
• Decomposition in three-layer control
scheme
• A modified solution based on DiscreteFourier Transform
•Design guidelines for regulator parameters
• DSP implementation using ADMC401
•Experimental results
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August 2001 Lesson 4 4
Current
Controller
Space
Vector Modulator
Space
Vector Modulator
Current control(optional) Current control(optional)
udc
+
_
L
C
Fi Li
+
+Ouput voltagefeed-forwardOuput voltagefeed-forward
Fi
Load
ou+
_
+
+
+
+
KsKs
conventional regulator conventional regulator
iFαααα
+
+
abc
αβαβαβαβ
+
+
Transformer
αααα
ββββ
εεεε
εεεε+
abc
αβαβαβαβ
ou*αααα
ou*ββββ
Closed-loopcontrol ofselectedharmonics
ou
+
*
iF*ββββ
Synchronous frame harmonic controlSynchronous frame harmonic control
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August 2001 Lesson 4 5
Basic schemeBasic scheme
Outputvoltageerrors
Outputvoltageerrors
Referencecurrents
Referencecurrents
Leadingangle φ φφ φ k
Leadingangle φ φφ φ k
εεεεααααεεεε ββββ
αβαβαβαβ
αβαβαβαβ
αβαβαβαβ
αβαβαβαβ
dqk+
dqk+
dqk-
dqk-
Reg k
iFαααα∗∗∗∗+
+ +
+
θθθθk + φ+ φ+ φ+ φk
iFββββ∗∗∗∗
Reg k
Reg k
Reg k
θθθθk + φ+ φ+ φ+ φk
θθθθk
θθθθk
Regulation of positive sequence k-th harmonicRegulation of positive sequence k-th harmonic
Regulation of negative sequence k-th harmonicRegulation of negative sequence k-th harmonic
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August 2001 Lesson 4 6
εεεε
εεεε
ωωωωωωωω−−−−
ωωωωωωωω====
εεεε
εεεε
ββββ
αααα
++++
++++
)tkcos()tk(sin
)tk(sin)tkcos(
SS
SS
qk
dk
εεεε
εεεε
ωωωωωωωω−−−−
ωωωωωωωω====
εεεε
εεεε
ββββ
αααα
++++
++++
)tkcos()tk(sin
)tk(sin)tkcos(
SS
SS
qk
dk
φφφφ++++ωωωωφφφφ++++ωωωω
φφφφ++++ωωωω−−−−φφφφ++++ωωωω====
++++
++++
++++ββββ
++++αααα
qk
dk
kSkS
kSkS
k
k
y
y
)tkcos()tk(sin
)tk(sin)tkcos(
y
y
φφφφ++++ωωωωφφφφ++++ωωωω
φφφφ++++ωωωω−−−−φφφφ++++ωωωω====
++++
++++
++++ββββ
++++αααα
qk
dk
kSkS
kSkS
k
k
y
y
)tkcos()tk(sin
)tk(sin)tkcos(
y
y
φφφφ++++ωωωωφφφφ++++ωωωω−−−−
φφφφ++++ωωωωφφφφ++++ωωωω====
−−−−
−−−−
−−−−ββββ
−−−−αααα
qk
dk
kSkS
kSkS
k
k
y
y
)tkcos()tk(sin
)tk(sin)tkcos(
y
y
φφφφ++++ωωωωφφφφ++++ωωωω−−−−
φφφφ++++ωωωωφφφφ++++ωωωω====
−−−−
−−−−
−−−−ββββ
−−−−αααα
qk
dk
kSkS
kSkS
k
k
y
y
)tkcos()tk(sin
)tk(sin)tkcos(
y
y
εεεε
εεεε
ωωωωωωωω
ωωωω−−−−ωωωω====
εεεε
εεεε
ββββ
αααα
−−−−
−−−−
)tkcos()tk(sin
)tk(sin)tkcos(
SS
SS
qk
dk
εεεε
εεεε
ωωωωωωωω
ωωωω−−−−ωωωω====
εεεε
εεεε
ββββ
αααα
−−−−
−−−−
)tkcos()tk(sin
)tk(sin)tkcos(
SS
SS
qk
dk
Basic scheme equationsBasic scheme equations
αβαβαβαβ
dqk+
αβαβαβαβ
dqk-
αβαβαβαβ
dqk+
αβαβαβαβ
dqk-
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August 2001 Lesson 4 7
Equivalence with stationary frame controlEquivalence with stationary frame control
Reg kAC
Reg kAC
[[[[ ]]]]
[[[[ ]]]])k js(gRe)k js(gResin j
)k js(gRe)k js(gRecos)s(gRe
skskk
skskkkAC
ωωωω++++−−−−ωωωω−−−−φφφφ++++
++++ωωωω++++++++ωωωω−−−−φφφφ==== [[[[ ]]]]
[[[[ ]]]])k js(gRe)k js(gResin j
)k js(gRe)k js(gRecos)s(gRe
skskk
skskkkAC
ωωωω++++−−−−ωωωω−−−−φφφφ++++
++++ωωωω++++++++ωωωω−−−−φφφφ====
εεεεααααεεεεββββ
αβαβαβαβ
αβαβαβαβ
αβαβαβαβ
αβαβαβαβ
dqk+
dqk+
dqk-
dqk-
Reg k
iFαααα
∗∗∗∗++
+
+
θθθθ k θθθθk + φ+ φ+ φ+ φ k
iFββββ∗∗∗∗
EquivalenceEquivalence
iFαααα∗∗∗∗
iFββββ∗∗∗∗
εεεεαααα
εεεε ββββ
Reg k
Reg k
Reg k
θθθθ θθθθ k + φ+ φ+ φ+ φ k k
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August 2001 Lesson 4 8
• If Regk(s) is a integral regulator, the previous
equivalence implies that RegkAC(s) is a band-
pass filter centered on the kth
harmonicfrequency.
• This is true if and only if both direct and reverse
sequence controllers are implemented.
• It is possible to implement synchronous
regulators either in the dq rotating frame or in
the αβαβαβαβ stationary frame, with perfectly equivalent
performance.
• If Regk(s) is a integral regulator, the previous
equivalence implies that RegkAC(s) is a band-
pass filter centered on the kth
harmonicfrequency.
• This is true if and only if both direct and reverse
sequence controllers are implemented.
• It is possible to implement synchronous
regulators either in the dq rotating frame or in
the αβαβαβαβ stationary frame, with perfectly equivalent
performance.
Equivalence with stationary frame controlEquivalence with stationary frame control
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August 2001 Lesson 4 9
Equivalence with stationary frame controlEquivalence with stationary frame control
• The leading angle φφφφk can be used to
compensate for internal delays, such as that of
the current controller.
• In practice, the current reference is phase
shifted to compensate for the currentcontroller delay.
• In the stationary frame implementation, based
on band-pass filters, this may or may not have
a possible equivalent (depending on the
regulator structure).
• The leading angle φφφφk can be used to
compensate for internal delays, such as that of
the current controller.
• In practice, the current reference is phase
shifted to compensate for the currentcontroller delay.
• In the stationary frame implementation, based
on band-pass filters, this may or may not have
a possible equivalent (depending on the
regulator structure).
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August 2001 Lesson 4 10
Three-layer decompositionThree-layer decomposition
AC Power Supplies requirements
•
Fast transient response with limitedovershoot under load changes;
• Possibly fast regulation of output voltage
fundamental harmonic component;
• For distorting loads with slowly-varying
harmonics, harmonic control in somefundamental cycles (decoupling between
different controllers is needed!).
AC Power Supplies requirements
•
Fast transient response with limitedovershoot under load changes;
• Possibly fast regulation of output voltage
fundamental harmonic component;
• For distorting loads with slowly-varying
harmonics, harmonic control in somefundamental cycles (decoupling between
different controllers is needed!).
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August 2001 Lesson 4 11
Three-layer decompositionThree-layer decomposition
• The previous requirements suggest a
decomposition of the control system in three
layers:• reference tracking control (for a quick
dynamic response) loop bandwidth;
• fundamental component control high loop
gain at the fundamental frequency, with low
selectivity;
• harmonics control high loop gain at each
harmonic frequency with high selectivity.
• The previous requirements suggest a
decomposition of the control system in three
layers:• reference tracking control (for a quick
dynamic response) loop bandwidth;
• fundamental component control high loop
gain at the fundamental frequency, with low
selectivity;
• harmonics control high loop gain at each
harmonic frequency with high selectivity.
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August 2001 Lesson 4 12
Three-Layer DecompositionThree-Layer Decomposition
x xz-1
e+jωωωω st e-j ωωωω st
x xz-1
z-Na
running DFTrunning DFT
+ ++
+
+
+
+
+
K P
proportional gainproportional gain
fundamental frequency controlfundamental frequency control
1
uoαβαβαβαβ
uoαβαβαβαβ
_
*
i Fαβαβαβαβ
currentreferences
*
K F
TswK I1
TswK I1
εεεεαβαβαβαβ
HarmonicsControl
HarmonicsControl
FundamentalComponentControl
FundamentalComponentControl
TrackingControl
TrackingControl
e-j ωωωω st e+jωωωω st
2
3
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August 2001 Lesson 4 14
• In principle, harmonics could be controlled by
integral, rotating frame regulators.
• This solution is cumbersome, requiring a largenumber of dq transformations.
•
The AC equivalent of the integral controller is ahigh selectivity band-pass filter. This is difficult
to implement because of fixed point arithmetic.
• Even if no stability problems can be generated,the selectivity is strongly limited by rounding
errors affecting the filter coefficients.
• In principle, harmonics could be controlled by
integral, rotating frame regulators.
• This solution is cumbersome, requiring a largenumber of dq transformations.
•
The AC equivalent of the integral controller is ahigh selectivity band-pass filter. This is difficult
to implement because of fixed point arithmetic.
• Even if no stability problems can be generated,the selectivity is strongly limited by rounding
errors affecting the filter coefficients.
NotesNotes
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August 2001 Lesson 4 15
F h- pass-band filter with unity gain and zero phase at harmonic h, with good selectivity F h- pass-band filter with unity gain and zero phase at harmonic h, with good selectivity
(((( ))))
∈∈∈∈
∈∈∈∈
∈∈∈∈∈∈∈∈ −−−−≈≈≈≈
−−−−====
ωωωω++++====
h
h
hh
Nh
h
Nh h
F
Nh h
hF
Nh2
s2
Ih
hACF1
F
KF1
FKhs
sK2)s(gRe(((( ))))
∈∈∈∈
∈∈∈∈
∈∈∈∈∈∈∈∈ −−−−≈≈≈≈
−−−−====
ωωωω++++====
h
h
hh
Nh
h
Nh h
F
Nh h
hF
Nh2
s2
Ih
hACF1
F
KF1
FKhs
sK2)s(gRe
Harmonic controlHarmonic control
sh
IhF
h
KK
ωωωωξξξξ
====sh
IhF
h
KK
ωωωωξξξξ
====
KF is defined as follows:KF is defined as follows:
KF is constant provided KIh are equal to h·KIKF is constant provided KIh are equal to h·KI
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August 2001 Lesson 4 16
−−−−
====
−−−−
ππππ====
1N
0i
idh zih
N
2cos
N
2)z(F
−−−−
====
−−−−
ππππ====
1N
0i
idh zih
N
2cos
N
2)z(F
The above approximation is well verified by
several types of band-pass filters. A good choice,
which offers significant implementationadvantages, is represented by FIR filters based on
DFT such as:
The above approximation is well verified by
several types of band-pass filters. A good choice,
which offers significant implementationadvantages, is represented by FIR filters based on
DFT such as:
For a single harmonic frequencyFor a single harmonic frequency
Harmonic controlHarmonic control
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August 2001 Lesson 4 17
Harmonic controlHarmonic control
−−−−
====
−−−−
ππππ====
1N
0i
idh zih
N
2cos
N
2)z(F
−−−−
====
−−−−
ππππ====
1N
0i
idh zih
N
2cos
N
2)z(F
• This equation is based on the expression of
the h-th harmonic component of a given input
signal’s DFT to derive a filter (running DFT).• The structure is that of a typical FIR filter
(linear combination of delays).
•From this standpoint N·Ts (Ts is the samplingperiod) does not necessarily represent the
period of the input signal, which can be even
non-periodic.
• This equation is based on the expression of
the h-th harmonic component of a given input
signal’s DFT to derive a filter (running DFT).• The structure is that of a typical FIR filter
(linear combination of delays).
•From this standpoint N·Ts (Ts is the samplingperiod) does not necessarily represent the
period of the input signal, which can be even
non-periodic.
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August 2001 Lesson 4 18
−−−−
====
−−−−
ππππ====
1N
0i
idh zih
N
2cos
N
2)z(F
−−−−
====
−−−−
ππππ====
1N
0i
idh zih
N
2cos
N
2)z(F
Computing this equation in the time-domain gives:Computing this equation in the time-domain gives:
Harmonic controlHarmonic control
FIR filter transfer function
−−−−
====
−−−−
ππππ====1N
0i
h )ik(xihN2cos
N2)k(y
−−−−
====
−−−−
ππππ====1N
0i
h )ik(xihN2cos
N2)k(y
yh(k) is a sinusoidal signal that represents theprojection of the input signal x(k) upon the cosine
base function of order h.
yh(k) is a sinusoidal signal that represents theprojection of the input signal x(k) upon the cosine
base function of order h.
coefficients are nottime dependent!
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August 2001 Lesson 4 19
Harmonic controlHarmonic control
Comparison with DFT:Comparison with DFT:
−−−−
====
ππππ====
1N
0k
N )k(xkhN
2cos)h(X
−−−−
====
ππππ====
1N
0k
N )k(xkhN
2cos)h(X
−−−−
====
−−−−
ππππ====
1N
0ih)ik(xih
N
2cos
N
2)k(y
−−−−
====
−−−−
ππππ====
1N
0ih)ik(xih
N
2cos
N
2)k(y FIR filter
hth order cosine
component in theDFT of signal x(k)
k is the time index, so in the DFT coefficients are
time dependent. The structure of the two algorithms
is exactly the same.
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August 2001 Lesson 4 20
0 2 4 6 8 10 12 14 16 18 200
1
Harmonic orderHarmonic order
Harmonic controlHarmonic control
Sampledfrequency
response, asseen by signalswith periodN·T
s /h.
Sampledfrequency
response, asseen by signalswith periodN·T
s /h.
Frequency response of function Fdh
(z) for h = 3.Frequency response of function Fdh
(z) for h = 3.
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August 2001 Lesson 4 21
Harmonic controlHarmonic control
−−−−
====
−−−−
ππππ====
1N
0i
i
dhzih
N
2cos
N
2)z(F
−−−−
====
−−−−
ππππ====
1N
0i
i
dhzih
N
2cos
N
2)z(F
−−−−
====
−−−−
∈∈∈∈∈∈∈∈
ππππ====
1N
0i
i
NhNh
dh zihN
2cos
N
2)z(F
kh
−−−−
====
−−−−
∈∈∈∈∈∈∈∈
ππππ====
1N
0i
i
NhNh
dh zihN
2cos
N
2)z(F
kh
For a single harmonicFor a single harmonic
No additional calculations
for more harmonics
No additional calculations
for more harmonics
For multiple frequenciesFor multiple frequencies
0 2 4 6 8 10 12 14 16 18 200
1
Harmonic order
0 2 4 6 8 10 12 14 16 18 200
1
Example: 3rdExample: 3rd
Example: 3rd, 5thExample: 3rd, 5th
Harmonic order
H i lH i l
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August 2001 Lesson 4 22
Harmonic controlHarmonic control
−−−−
====
−−−−
∈∈∈∈∈∈∈∈
ππππ====
1N
0i
i
NhNh
dh zihN
2cos
N
2)z(F
kh
−−−−
====
−−−−
∈∈∈∈∈∈∈∈
ππππ====
1N
0i
i
NhNh
dh zihN
2cos
N
2)z(F
kh
• The coefficient for the i-th term can be
computed off-line according to:
• The control complexity does not depend on
the number of harmonic components taken
into account.
• The coefficient for the i-th term can be
computed off-line according to:
• The control complexity does not depend on
the number of harmonic components taken
into account.
∈∈∈∈
ππππ
kNh
ihN
2cos
∈∈∈∈
ππππ
kNh
ihN
2cos
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August 2001 Lesson 4 23
Design CriteriaDesign Criteria
Proportional terms and fundamental frequency
control are based on specified bandwidth andphase margin:
Proportional terms and fundamental frequency
control are based on specified bandwidth andphase margin:
2c
2
s
2
cIc1I
2KK
ωωωωωωωω−−−−ωωωω====2c
2
s
2
cIc1I
2KK
ωωωωωωωω−−−−ωωωω====Equivalence with PI Equivalence with PI
Fundamental frequency controlFundamental frequency control
KIc is the integral gain of a conventionally
designed PI regulator.
KIc is the integral gain of a conventionally
designed PI regulator.
H i t lH i t l
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August 2001 Lesson 4 24
Harmonic controlHarmonic control
• Amplification of frequencies close to the
harmonics is an undesired effect of the filter
superposition.
• Introduction of the leading angle φφφφk is possible
by means of positive feedback, provided that
the angle is proportional to the harmonicfrequency.
• Internal delays can be compensated.
• Amplification of frequencies close to the
harmonics is an undesired effect of the filter
superposition.
• Introduction of the leading angle φφφφk is possible
by means of positive feedback, provided that
the angle is proportional to the harmonicfrequency.
• Internal delays can be compensated.
−−−−
====
−−−−
∈∈∈∈∈∈∈∈
++++
ππππ====
1N
0i
i
Nk
a
Nh
dh z)Ni(kN
2cos
N
2)z(F
kh
−−−−
====
−−−−
∈∈∈∈∈∈∈∈
++++
ππππ====
1N
0i
i
Nk
a
Nh
dh z)Ni(kN
2cos
N
2)z(F
kh
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August 2001 Lesson 4 25
Design CriteriaDesign Criteria
Specification
on the response time (npk )
Specification
on the response time (npk )Spk
Ik Tn
2.2
K ====
Harmonic controlHarmonic control
npk is the desired number of fundamental cyclesfor the dynamic response. It must be high enough
to provide de-coupling with the fundamental
frequency control. The equation is derived byapproximated relations between gain and settling
time of 2nd order band-pass filters.
npk is the desired number of fundamental cyclesfor the dynamic response. It must be high enough
to provide de-coupling with the fundamental
frequency control. The equation is derived byapproximated relations between gain and settling
time of 2nd order band-pass filters.
CC
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August 2001 Lesson 4 26
Design CriteriaDesign Criteria
Harmonic controlHarmonic control
gain of DFT filtersgain of DFT filters s
Ik
F 32.0
K
K ωωωω≈≈≈≈ s
Ik
F 32.0
K
K ωωωω≈≈≈≈
This relation is based on the approximation of thesingle DFT filter with a conventional second order
band-pass filter.
By trial and errors the 0.32 coefficient can bedetermined as the one minimizing the “distance”
between the two frequency responses.
This relation is based on the approximation of thesingle DFT filter with a conventional second order
band-pass filter.
By trial and errors the 0.32 coefficient can bedetermined as the one minimizing the “distance”
between the two frequency responses.
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DSP I l iDSP I l i
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August 2001 Lesson 4 28
DSP ImplementationDSP Implementation
Main features of DSP-based controller ADMC401:
• 16-bit fixed point DSP based on ADSP 2171 core.
• Fast arithmetic unit (38.5ns cycle).
• High-performance peripherals (double-update
PWM modulators, flash A/D 12 bit converters,
etc..).
• Suited for single-chip high-performance motion
control applications.
Main features of DSP-based controller ADMC401:
• 16-bit fixed point DSP based on ADSP 2171 core.
• Fast arithmetic unit (38.5ns cycle).
• High-performance peripherals (double-update
PWM modulators, flash A/D 12 bit converters,
etc..).
• Suited for single-chip high-performance motion
control applications.
C t l PC t l PInitialization
Routines
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August 2001 Lesson 4 29
Control Program
Flow-Chart
Control Program
Flow-Chart
Routines
Wait
Interrupt?
No
Yes
Reference Generation
[ s ]µµµµ
0
transformationsαβαβαβαβerrors calculations
Voltage control:proportional +
fundamental frequency
Harmonic control
deadbeat currentcontrol
SVM
Dead-time compensation
PWMSYNC
Timing starting
from ADC conversion
2 µµµµs
~3 µµµµs
~3 µµµµs
~18.4 µµµµsN=200
~ 6.4 µµµµsN=50
~2.7 µµµµs
~5 µµµµs
~36 µµµµs ~24 µµµµs
• Implementation on
ADMC401
• The control program
is written in assembly
language.• The use of DFT based
filters greatly
simplifies theimplementation.
• Execution times are
short.
• Implementation on
ADMC401
• The control program
is written in assembly
language.• The use of DFT based
filters greatly
simplifies theimplementation.
• Execution times are
short.
DSP ImplementationDSP Implementation
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August 2001 Lesson 4 30
.MODULE/RAM/SEG=USER_PM1 DFT_FILTER200;
.CONST ORD_N=200;
.VAR/RAM/PM/CIRC Filt_Coef[ORD_N];
#include "dft.dat” /* coefficients
initialization */
.ENTRY DFT200;
DFT200:
i5=^Filt_Coef; /* use dedicated */l5=%Filt_Coef; /* circular registers */
m5=1; /* i,l,m (0-7) */
l0=%Filt_Coef; /* i0 data pointer (same lenght) */
.MODULE/RAM/SEG=USER_PM1 DFT_FILTER200;
.CONST ORD_N=200;
.VAR/RAM/PM/CIRC Filt_Coef[ORD_N];
#include "dft.dat” /* coefficients
initialization */
.ENTRY DFT200;
DFT200:
i5=^Filt_Coef; /* use dedicated */l5=%Filt_Coef; /* circular registers */
m5=1; /* i,l,m (0-7) */
l0=%Filt_Coef; /* i0 data pointer (same lenght) */
DSP ImplementationProgram sample
DSP ImplementationProgram sample
DSP ImplementationDSP Implementation
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August 2001 Lesson 4 31
m1=1;
mr = 0, mx0 = dm(i0,m1), my0 = pm(i5,m5);
cntr=%Filt_coef-1;
do calc0 until ce;
calc0: mr = mr + mx0 * my0 (ss),mx0 = dm(i0,m1), my0 = pm(i5,m5);
mr = mr + mx0 * my0 (rnd);
if mv sat mr;
rts;
.ENDMOD;
m1=1;
mr = 0, mx0 = dm(i0,m1), my0 = pm(i5,m5);
cntr=%Filt_coef-1;
do calc0 until ce;
calc0: mr = mr + mx0 * my0 (ss),mx0 = dm(i0,m1), my0 = pm(i5,m5);
mr = mr + mx0 * my0 (rnd);
if mv sat mr;
rts;
.ENDMOD;
DSP ImplementationProgram sample
DSP ImplementationProgram sample
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August 2001 Lesson 4 33
Experimental SetupExperimental Setup
Prototype ratings:
•DC-link voltage 300V
• Filter Inductance 1 mH
•Output Filter Capacitor 120µµµµF
• Switching frequency 10kHz
•Selected frequencies: 3rd, 5th,7th,9th,11th
Experimental ResultsExperimental Results
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August 2001 Lesson 4 34
Experimental ResultsThree-phase diode rectifiers - Proposed solution
Experimental ResultsThree-phase diode rectifiers - Proposed solution
(a) Ouput Voltage (40V/div)(a) Ouput Voltage (40V/div)
time (5ms/div)time (5ms/div) frequency (50Hz/div)frequency (50Hz/div)
(a)
(b) Ouput current (10A/div)(b) Ouput current (10A/div)
c) Output voltage
spectrum (10dB/div)
c) Output voltage
spectrum (10dB/div)
(c)(c)(b)
22
33 44 55 9966
77 88
Experimental ResultsExperimental Results
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August 2001 Lesson 4 35
(a) Ouput Voltage (40V/div)(a) Ouput Voltage (40V/div)
time (5ms/div)time (5ms/div) frequency (50Hz/div)frequency (50Hz/div)
(a)(a)
(b) Ouput current (10A/div)(b) Ouput current (10A/div)
(c)(c)
(b)(b)
22
33 44
55
9966
77
88
Experimental ResultsThree-phase diode rectifiers - PI controller
Experimental ResultsThree-phase diode rectifiers - PI controller
c) Output voltage
spectrum (10dB/div)
c) Output voltage
spectrum (10dB/div)
Experimental ResultsExperimental Results
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August 2001 Lesson 4 36
pSingle-phase diode rectifier
pSingle-phase diode rectifier
(a) Ouput Voltage (40V/div)(a) Ouput Voltage (40V/div)
time (5ms/div)time (5ms/div)
(a)(a)
(b) Ouput current (5A/div)(b) Ouput current (5A/div)
(b)(b)
(a)(a)
(b)(b)
Proposed solutionProposed solution Conventional PIConventional PI
time (5ms/div)time (5ms/div)
Experimental ResultsExperimental Results
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August 2001 Lesson 4 37
pDistorting Load Turn-on
pDistorting Load Turn-on
time (10ms/div)time (10ms/div)
(a)(a)
(b)(b)(b)
(a) Ouput Voltage (40V/div)(a) Ouput Voltage (40V/div) (b) Ouput current (10A/div)(b) Ouput current (10A/div)
Experimental ResultsExperimental Results
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August 2001 Lesson 4 38
pLinear Load Step-Changes
pLinear Load Step-Changes
Turn-off Turn-off Turn-onTurn-on
time (5ms/div)time (5ms/div) time (5ms/div)time (5ms/div)
(a) Ouput Voltage and its reference (40V/div)(a) Ouput Voltage and its reference (40V/div)
(b) Ouput current (5A/div)(b) Ouput current (5A/div)
(a)(a)
(b)(b)
(a)(a)
(b)(b)
R fR f
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August 2001 Lesson 4 39
ReferenceReference
P. Mattavelli, S. Fasolo: “Implementation of Synchronous
Frame Harmonic Control for High-Performance AC Power
Supplies”, IEEE IAS Annual Meeting 2000, Rome, Italy, 8-12 October, 2000, pp. 1988-1995.
P. Mattavelli, S. Fasolo: “Implementation of Synchronous
Frame Harmonic Control for High-Performance AC Power
Supplies”, IEEE IAS Annual Meeting 2000, Rome, Italy, 8-12 October, 2000, pp. 1988-1995.