Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Current Control System to PMSG in
Overmodulation Region
Thiago Bernardes
Humberto Pinheiro
Vinı́cius F. Montagner
Federal University of Santa Maria
Power Electronics and Control Research Group
4th Power Electronics and Control Seminar, 2010
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Summary
1
Introduction
Exemplification
Objective
2
Review in the Overmodulation
Operation Modes
Description of the overmodulation mode I
Description of the overmodulation mode II
Results
3
Control System
PMSG and Current controller
Harmonics of Compensation
Control System
4
Simulation results
Parameters of the simulation
Harmonics compensation
Comparing between the saturation functions
5
Conclusion
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Exemplification
Objective
Introduction
Important features in wind energy conversion systems: wide
range of speed operation, reduced torque pulsation and high efficiency.
To augment the range of speed operation and to maintain the generator voltage limited by DC link voltage, the operation of the PWM
rectifier in the overmodulation region will become required.
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Exemplification
Objective
Introduction
1.5
PshO
PshL
Potência (p.u.)
Pm
1
0.5
8
m
s
10
m
s
12
m
s
14
m
s
16
m
s
0
0
0.5
1
1.5
2
2.5
3
ωm (p.u.)
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Exemplification
Objective
Introduction
In this paper, a review of the space vector modulation in overmodulation region is presented and a control system with anti-windup action,
and harmonics compensation is proposed to guarantee a good performance of wind energy conversion systems.
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Operation Modes
Description of the overmodulation mode I
Description of the overmodulation mode II
Results
Space vector modulation
1
Linear mode: Full circular trajectory
2
Overmodulation mode I: Partially circular trajectory
3
Overmodulation mode II: Hexagonal trajectory
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Operation Modes
Description of the overmodulation mode I
Description of the overmodulation mode II
Results
Overmodulation mode I
vβ
v2
umod
c1
uαβ
v1
v0
c2
vα
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Operation Modes
Description of the overmodulation mode I
Description of the overmodulation mode II
Results
Overmodulation mode I
Modified vector
vβ
c1
v2
umod
kumod k =
uαβ
umod =
p
v0
v1
αc
c2
1
√
3 cos
π
− αc
6
!
1
umod
√
3
[ 3 1] • uTmod
2
vα
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Operation Modes
Description of the overmodulation mode I
Description of the overmodulation mode II
Results
Overmodulation mode II
vα
v2
uαβ
v0
αh
umod
v1
vβ
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Operation Modes
Description of the overmodulation mode I
Description of the overmodulation mode II
Results
Overmodulation mode II
vα
v2
uαβ
v0
αh
umod
v1
vβ
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Operation Modes
Description of the overmodulation mode I
Description of the overmodulation mode II
Results
Overmodulation mode II
vα
v2
uαβ
v0
αh
umod
v1
vβ
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Operation Modes
Description of the overmodulation mode I
Description of the overmodulation mode II
Results
Overmodulation mode II
vα
v2
uαβ
umod
v0
αh
v1
vβ
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Operation Modes
Description of the overmodulation mode I
Description of the overmodulation mode II
Results
Overmodulation mode II
vα
v2
uαβ
umod
v0
αh
v1
vβ
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Operation Modes
Description of the overmodulation mode I
Description of the overmodulation mode II
Results
Overmodulation mode II
vα
v2
umod
v0
αh
uαβ
v1
vβ
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Operation Modes
Description of the overmodulation mode I
Description of the overmodulation mode II
Results
Overmodulation mode II
vα
v2
umod
v0
αh
uαβ
v1
vβ
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Operation Modes
Description of the overmodulation mode I
Description of the overmodulation mode II
Results
Overmodulation mode II
vα
v2
umod
v0
αh
uαβ
v1
vβ
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Operation Modes
Description of the overmodulation mode I
Description of the overmodulation mode II
Results
Overmodulation mode II
vα
v2
umod
v0
αh
uαβ
v1
vβ
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Operation Modes
Description of the overmodulation mode I
Description of the overmodulation mode II
Results
Overmodulation mode II
vα
v2
umod
uαβ
v0
αh
v1
vβ
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Operation Modes
Description of the overmodulation mode I
Description of the overmodulation mode II
Results
Overmodulation mode II
Angular relationship
vα
v2
umod
uαβ
θm
θm
θ
v0
αh
v1

0,




 θ − αh π
,
π
=
− αh 6

6


π

,
3
0 ≤θ ≤ αh
π
− αh
3
π
π
− αh ≤θ ≤
3
3
αh <θ <
vβ
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Operation Modes
Description of the overmodulation mode I
Description of the overmodulation mode II
Results
Fundamental magnitude versus modulation index
Fundamental
Overmodulation mode II
Overmodulation mode I
Linear mode
Modulation index (m)
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Operation Modes
Description of the overmodulation mode I
Description of the overmodulation mode II
Results
Voltage harmonics
0.14
a
5 harmonic
0.12
a
V
Vcc
¶
7 harmonic
0.1
11 harmonic
0.08
13 harmonic
µ
a
a
0.06
0.04
0.02
0
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
Modulation index (m)
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
PMSG and Current controller
Harmonics of Compensation
Control System
PMSG Model
" Rs
− Ld
d id
=
e Ld
− ωL
dt iq
q
ωe Lq
Ld
s
−R
Lq
# "
1
id
+ Ld
0
iq
# "
#
0
vd
ωe
+
ψ
1
− Lpm
vq
Lq
q
0
MIMO controller
d xd
ed
1 0 udL
=
− kw
eq
0 1 uqL
dt xq
ud
1 0 xd
1
= ki
+ kp
uq
0 1 xq
0
− ud
− uq
0 ed
1 eq
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
PMSG and Current controller
Harmonics of Compensation
Control System
PI controller with anti-windup
Gc (s )
id*
kp
ud
ki
udL
G (s )
id
s
kw
Dud
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
PMSG and Current controller
Harmonics of Compensation
Control System
Saturation function of the actuator
in Euclidean norm
in magnitude
q
q
u0
u0
-u0
u0
O
-u0
d
-u0
sat(u) = u0
u0
O
d
-u0
u
kuk
sat(ui ) = sign(ui ) min (u0 , |ui |)
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
PMSG and Current controller
Harmonics of Compensation
Control System
Estimation of the current harmonics
SVM with
overmodulation
qe
udqL
Controller
ab
uab
u mod
dq
Command
signal
ab
udqL
u m od dq
qe
dq
u%dq
Feedback
signal
i%dq
idq - i%dq
Current
ripple model
PMSG
idq
we
Harmonics compensation
qe
dq
abc
iabc
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
PMSG and Current controller
Harmonics of Compensation
Control System
Implementation of the control system
PI Controller with anti-windup
qe
Actuator
*
idq
udq
udqL
ab
SVM with overmodulation
u mod
uab
PWM
Rectifier
PWM
PMSG
dq
wm
idq - i%dq
ab
qe
Du
kw
u%dq
i%dq
idq
qe
DSP
dq
u m od dq
Current
ripple model
PMSG
we
Harmonics compensation
dq
abc
iabc
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Parameters of the simulation
Harmonics compensation
Comparing between the saturation functions
Parameters of the simulation
Stator resistance
Direct inductance
Quadrature inductance
PM flux
Rs
Ld
Lq
ψpm
0.64
8.7
28.3
0.108
Proportional gain
Integral gain
Anti-windup gain
kp
ki
kw
114.9
145426.8
0.1375
Ω
mH
mH
Wb
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Parameters of the simulation
Harmonics compensation
Comparing between the saturation functions
Compensation of the current harmonics
Proposed
Convencional
0.2
0.2
i
i
d
i
0
q
Current (normalized)
Current (normalized)
0
-0.2
-0.4
-0.6
-0.8
-1
i
d
q
-0.2
-0.4
-0.6
-0.8
-1
-1.2
-1.2
0
50
100
time (ms)
150
200
0
50
100
time (ms)
150
200
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Parameters of the simulation
Harmonics compensation
Comparing between the saturation functions
Current generator
in magnitude
0
0
−0.2
−0.2
Current (normalized)
Current (normalized)
in Euclidean norm
−0.4
−0.6
−0.8
−1
id
−1.2
1000
−0.6
−0.8
−1
i
d
−1.2
iq
1500
−0.4
2000 2500 3000
ωm (rpm)
3500
1000
iq
1500
2000 2500 3000
ωm (rpm)
3500
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Parameters of the simulation
Harmonics compensation
Comparing between the saturation functions
Voltage generator axis-d
in Euclidean norm
in magnitude
0.8
0.6
0.4
usat
0.2
d
Voltage (normalized)
Voltage (normalized)
0.8
0.6
0.4
usat
d
0.2
ud
0
1000
1500
2000
2500 3000
ωm (rpm)
3500
ud
0
1000
1500
2000
2500 3000
ωm (rpm)
3500
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Conclusion
This paper presents a current control system in the overmodulation region, considering the saturation in Euclidean norm and in
magnitude with anti-windup method.
A good agreement is obtained between the theoretical analysis
and the simulations results that point out advantages in the use of
magnitude saturation.
The proposed control system indicate that is is possible to control
the currents in the overmodulation region as long as the current
references are compute to hold the magnitude of the vector of
control action smaller or equal that the fundamental of six-step.
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Introduction
Review in the Overmodulation
Control System
Simulation results
Conclusion
Thanks for your attention!
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