Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model...
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Model Predictive Control in
Medium‐Voltage Drives
Tobias Geyer
Department of Electrical and Computer Engineering
The University of Auckland
New Zealand
In collaboration with
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Outline
Introduction•
Control problem
•
Performance trade‐off•
Control and modulation schemes
Model Predictive Control•
1‐step predictive control
•
Model predictive direct current/torque control•
Computational efficiency
Summary and Outlook
Control Problem
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
M
(Active) RectifierInverterElectrical
Machine Grid
Controller
Control Problem
Low current distortions => low thermal losses
Low torque distortions => no excitation of mech.
resonances
Low switching
losses
=> high efficiency, low thermal
losses
Fast
torque response => high dynamic
performance
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Control and Modulation
(Active) Rectifier
Inverter
Electrical Machine
Grid
Dc-Link
u
M
is
Modulator*
Currentcontroller
Speedcontroller
u*is*Te*
Fundamental trade‐off between switching losses (frequency) and the current / torque distortion
levels
•
Cascaded
control loops:–
Speed control loop
–
Current control loop
•
Current
control problem=> split into current controller
and modulator
Performance Trade‐Off
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Trade‐Off (High
Switching Frequency)
u* u
is
T
fsw
=700HzPsw
=16.7kW,Pcon
=2.7kWTHDI
=2.31%THDT
=1.93%
Inverter:
3‐level NPC with IGCTsInduction machine:
3.3kV, 2MVA
Operation point:
we
=1pu, Te
=1pu
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Trade‐Off (Low
Switching Frequency)
u* u
is
T
fsw
=150HzPsw
=3.9kW, Pcon
=2.8kWTHDI
=6.9%THDT
=6.0%
Inverter:
3‐level NPC with IGCTsInduction machine:
3.3kV, 2MVA
Operation point:
we
=1pu, Te
=1pu
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Trade‐Off for PWM / SVM
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
2
4
6
8
10
12
14
16
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
1
2
3
4
5
6
7
Current THD vs
switching losses Torque THD vs
switching losses
Switching losses [%] Switching losses [%]
THD [%
]
THD [%
]
? ?
Control and Modulation Schemes
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Torque response time(controller bandwidth)slowfast
small
largeField Oriented Control with PWM/SVM
Control and Modulation
Switching lossesper distortions
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Torque response time(controller bandwidth)slowfast
small
largeField Oriented Control with PWM/SVM
Control and Modulation
Model Predictive Control with PWM/SVM
Switching lossesper distortions
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Torque response time(controller bandwidth)slowfast
small
largeField Oriented Control with PWM/SVM
Control and Modulation
V/f Control with Optimized Pulse Patterns
Model Predictive Control with PWM/SVM
Switching lossesper distortions
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Torque response time(controller bandwidth)slowfast
small
largeField Oriented Control with PWM/SVM
Control and Modulation
V/f Control with Optimized Pulse Patterns
Controller and modulator
Model Predictive Control with PWM/SVM
Direct Torque Control
Switching lossesper distortions
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Switching lossesper distortions
Torque response time(controller bandwidth)slowfast
small
largeField Oriented Control with PWM/SVM
Control and Modulation
V/f Control with Optimized Pulse Patterns
Controller and modulator
Model Predictive Control with PWM/SVM
Direct Torque Control
One‐step Predictive Control
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Torque response time(controller bandwidth)slowfast
small
large
Control and Modulation: Goal
V/f Control with Optimized Pulse Patterns
?
?
Model Predictive Control with PWM/SVM
One‐step Predictive Control
Switching lossesper distortions
Field Oriented Control with PWM/SVM
Direct Torque Control
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Torque response time(controller bandwidth)slowfast
small
large
Control and Modulation: New Methods
V/f Control with Optimized Pulse Patterns
Model Predictive Direct Torque /
Current Control
Model Predictive Control with PWM/SVM
One‐step Predictive Control
Field Oriented Control with PWM/SVM
Direct Torque Control
Switching lossesper distortions
Controller and modulator
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Torque response time(controller bandwidth)slowfast
small
large
Control and Modulation: New Methods
V/f Control with Optimized Pulse Patterns
Model Predictive Direct Torque /
Current ControlFast Control ofOptimized
Pulse Patterns
Model Predictive Control with PWM/SVM
One‐step Predictive Control
Field Oriented Control with PWM/SVM
Direct Torque Control
Switching lossesper distortions
Controller and modulator
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
(Active) Rectifier
Inverter
Electrical Machine
Grid
Dc-Link
u
M
is
Modulator*
Currentcontroller
Speedcontroller
u*is*Te*
Control and Modulation: New Methods
Goal: Fully utilize capability of drive hardware•
Minimize switching losses
per distortions
•
Achieve very fast
torque and current response
Approach:•
Treat control and modulation problem in one stage
•
Work in the time‐domain•
Adopt model predictive control
Current controller and modulator
Model Predictive Control
for MV Electrical Drives
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Classification of MPC Schemes for Electrical Drives
Hysteresis boundsReference tracking
Model Predictive Control: Direct methods (without a modulator)
Current control
Torque / flux ctrl.
Trajectory control
Current control
Torque / flux ctrl.
Current trajectoryFlux
trajectory
Very short prediction
horizons (typically one step)
Medium to long prediction
horizons (20 to 150 steps)
Closed‐loop control of pre‐
computed pulse patterns
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Classification of MPC Schemes for Electrical Drives
Hysteresis boundsReference tracking
Model Predictive Control: Direct methods (without a modulator)
Current control
Torque / flux ctrl.
Trajectory control
Current control
Torque / flux ctrl.
Current trajectoryFlux
trajectory
Very short prediction
horizons (typically one step)
Medium to long prediction
horizons (20 to 150 steps)
Closed‐loop control of pre‐
computed pulse patterns
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
One‐Step Predictive Current
Control
timek k+1
isα
isα,refisα
(k)
isα
(k+1)
timek k+1
isβ
isβ,refisβ
(k)
isβ
(k+1)
Algorithm•
Enumerate all 27 switch
transitions•
Predict currents at k+1
•
Choose switch transition with minimal current
error at k+1
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Performance Index:
Constraints
• prediction horizon
is one• machine model•minimization of switching effort (e.g. frequency)• λn
=> trade‐off between tracking accuracy and switching • conceptually and computationally very simple
Main features:
Discrete‐valued switch positions
Deviation from
current reference
Model of machine
One‐Step Predictive Current
Control
Restrictions on switch transitions
Penalty on
switching effort
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
One‐step Predictive Current
Control
Current TDD vs
switching losses Torque TDD vs
switching losses
Switching losses [%] Switching losses [%]
TDD [%
]
TDD [%
]
•
Current THD similar to PWM•
Torque THD significantly worse than PWM
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
1
2
3
4
5
6
7PWM
OPP
1-step pred. current ctrl.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
2
4
6
8
10
12
14
16OPP
PWM1-step pred. current ctrl.
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Classification of MPC Schemes for Electrical Drives
Hysteresis boundsReference tracking
Model Predictive Control: Direct methods (without a modulator)
Current control
Torque / flux ctrl.
Trajectory control
Current control
Torque / flux ctrl.
Current trajectoryFlux
trajectory
Very short prediction
horizons (typically one step)
Medium to long prediction
horizons (20 to 150 steps)
Closed‐loop control of pre‐
computed pulse patterns
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
One‐step Predictive Torque
Control
Current TDD vs
switching losses Torque TDD vs
switching losses
Switching losses [%] Switching losses [%]
TDD [%
]
TDD [%
]
•
Torque THD similar to PWM•
Current THD significantly worse than PWM
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
1
2
3
4
5
6
7PWM
OPP
1-step pred. torque ctrl.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
2
4
6
8
10
12
14
16OPP
PWM
1-step pred. torque ctrl.
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Classification of MPC Schemes for Electrical Drives
Hysteresis
boundsReference tracking
Model Predictive Control: Direct methods (without a modulator)
Current control
Torque / flux ctrl.
Trajectory control
Current control
Torque / flux ctrl.
Current trajectoryFlux
trajectory
Very short prediction
horizons (typically one step)
Medium to long prediction
horizons (20 to 150 steps)
Closed‐loop control of pre‐
computed pulse patterns
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Model Predictive Direct Current
Control: Step 1
Key ingredients:• Drive model• Extrapolation
a
b
c
k Np
iripβ
iripα
u
t
t
t
e EE SS
Predict current trajectories for (all)possible
switching sequences
Switching horizon, e.g. ‘eSESE’• S: consider all switch transitions• E: extrapolate/extend currents and NPP• e: optional ‘E’
Prediction horizon
NpTypically 50..150 time‐steps
NP potential not shown here
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Model Predictive Direct Current
Control: Step 1
a
b
c
k Npt
t
t
e EE SS
Key ingredients:• Drive model• Extrapolation
Switching horizon, e.g. ‘eSESE’• S: consider all switch transitions• E: extrapolate/extend currents and NPP• e: optional ‘E’
Prediction horizon
NpTypically 50..150 time‐steps
Predict current trajectories for (all)possible
switching sequences
iripβ
iripα
u
NP potential not shown here
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Model Predictive Direct Current
Control: Step 2
Evaluate and
minimize
=> Optimal
switching sequence U
Evaluate and
minimize sw. losses
a
b
c
k Npt
t
t
e EE SS
iripβ
iripα
u
NP potential not shown here
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Model Predictive Direct Current
Control: Steps 2 & 3
Evaluate and
minimize
=> Optimal
switching sequence U
Evaluate and
minimize sw. losses
a
b
c
k Npt
t
t
e EE SS
tPlanDo
tPlanDo
tPlanDo
k
k+1
k+2
Apply only
the first element of U
iripβ
iripα
u
NP potential not shown here
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Performance Index:
Constraints
• short switching
horizon but long prediction
horizon•models
of machine, inverter
and losses
•minimization of switching losses• receding horizon
policy
• tailored
online solution approach
Main features:
Bounds on currents and NP
Discrete‐valued switch positions
Short‐term avg. switching losses (power)
Model of machine and inverter
Outputs (currents and NP)
Model Predictive Direct Current
Control
Restrictions on switch transitions
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Performance during Transients
Speed:
we
=0.6 puTorque:
reference steps between T=1 and 0 pu
Torque Stator currents Switch positions
Torque (current) response time of 2 ms
3‐level NPC inverter with 2MVA
induction machine
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Performance at Steady‐State
FOC withPWM andfc
=270 Hz
MPDCC ‘e(SE)3’
3‐level NPC inverter with 2MVA ind. machinewe
=0.6 pu, Te
=1 pu
Current Current spectrum Switch positions
ITHD
= 7.69%
ITHD
= 4.56%
Psw
= 4.15kW
Psw
= 4.02kWNp
=70
Current
THD
reduced by 40%
(for the same switching losses)Similar to optimal pulse patterns
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
MPDCC outperforming OPP
•
OPPs: for a given switching frequency, minimize the current THD•
MPDCC: for a given current THD, minimize the switching losses
Optimized Pulse Pattern Model Pred. Direct Current Ctrl.
Time [ms] Time [ms]
ITHD
= 8.18 %
Psw
= 1.92 kW
ITHD
= 8.60 %
Psw
= 1.15 kW40% less
5% more
3‐level NPC inverter with 2MVA ind. machinewe
=0.6 pu, Te
=1 pu
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Model Predictive Direct Current
Control
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
2
4
6
8
10
12
14
16OPP
PWM
MPDCC e(SE)3MPDCC eSE
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
1
2
3
4
5
6
7PWM
MPDCC e(SE)3
MPDCC eSEOPP
Current TDD vs
switching losses Torque TDD vs
switching losses
Switching losses [%] Switching losses [%]
TDD [%
]
TDD [%
]
Long switching horizon eSESESE
(50‐150 steps): •
Current THD: better than with optimized pulse patterns
•
Torque THD: similar to PWM
‐50%
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Tuning
Current THDTorque THD
Switching losses
Switching frequency
Current bound width [*100]
3‐level NPC inverter with 2MVA IMwe
=0.6 pu, Te
=1 pu, MPDCC with ‘eSE’
In percent, n
ormalized to m
axim
um
•
Current and torque distortions: linear
function of bound width•
Switching frequency
(and losses): hyperbolic
function of bound width
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Classification of MPC Schemes for Electrical Drives
Hysteresis
boundsReference tracking
Model Predictive Control: Direct methods (without a modulator)
Current control
Torque / flux ctrl.
Trajectory control
Current control
Torque / flux ctrl.
Current trajectoryFlux
trajectory
Very short prediction
horizons (typically one step)
Medium to long prediction
horizons (20 to 150 steps)
Closed‐loop control of pre‐
computed pulse patterns
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Direct Torque Control
Control objectives:•
Keep torque, stator flux
and neutral point
potential within given bounds•
Minimize the switching losses
Control variable:•
Discrete inverter switch positions
0 2 4 6 8 10 12 14 16 18 200.2
0.4
0.6
0.8
Torque
T e [pu]
0 2 4 6 8 10 12 14 16 18 20
0.95
1
1.05
Stator flux magnitude
Psi
s [pu]
0 2 4 6 8 10 12 14 16 18 20
-0.05
0
0.05
Neutral point potential
NP
[pu]
0 2 4 6 8 10 12 14 16 18 20
-101
-101
-101
Switch positions
u abc
Time [ms]
DTC look-up table
u
M
is
Dc-link
Observer
s*
Te*
sTe
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Model Predictive Direct Torque
Control
Challenging control problem:•
Nonlinear
•
Hybrid•
MIMO
•
Sampling interval Ts
= 25us
0 2 4 6 8 10 12 14 16 18 200.2
0.4
0.6
0.8
Torque
T e [pu]
0 2 4 6 8 10 12 14 16 18 20
0.95
1
1.05
Stator flux magnitude
Psi
s [pu]
0 2 4 6 8 10 12 14 16 18 20
-0.05
0
0.05
Neutral point potential
NP
[pu]
0 2 4 6 8 10 12 14 16 18 20
-101
-101
-101
Switch positions
u abc
Time [ms]
DTC look-up table
u
M
is
Dc-link
Observer
s*
Te*
sTe
replace by Model Predictive DTC
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Model Predictive Direct Torque
Control
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
2
4
6
8
10
12
14
16OPP
PWM
MPDTC e(SE)3
MPDTC eSE
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
1
2
3
4
5
6
7PWM
OPP
MPDTC eSEMPDTC e(SE)3
Current TDD vs
switching losses Torque TDD vs
switching losses
Switching losses [%] Switching losses [%]
TDD [%
]
TDD [%
]
Long switching horizon eSESESE
(50‐150 steps): •
Current THD: similar to optimized pulse patterns (OPP)
•
Torque THD: significantly better than OPP, but at the expense of current THD –
points on curves do not
correspond to each other!
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Classification of MPC Schemes for Electrical Drives
Hysteresis
boundsReference tracking
Model Predictive Control: Direct methods (without a modulator)
Current control
Torque / flux ctrl.
Trajectory control
Current control
Torque / flux ctrl.
Current trajectoryFlux
trajectory
Very short prediction
horizons (typically one step)
Medium to long prediction
horizons (20 to 150 steps)
Closed‐loop control of pre‐
computed pulse patterns
+
Computational efficiency
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Search Tree
Search tree
induced by optimization problem
Computational burden ≈ number of nodes
So far: full enumeration
time
Not
candidates
Candidateswitching
sequence Optimal
switching
sequence
E
SS
S
E
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Search Tree
time
Not
candidates
Candidateswitching
sequence Optimal
switching
sequence
E
SS
S
E
Search tree
induced by optimization problem
Computational burden ≈ number of nodes
So far:
full enumeration
•
More efficient implementation
of algorithm
•
More efficient extension
/ extrapolation step
•
Reduce number of nodes explored in search tree by using Branch & Bound
Approaches to reducecomputation time?
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Evolution of the Optimal Cost during Optimization
Iteration step (number of nodes visited)
Cost (kW
)WithoutBranch & Bound
c*
u*
found
Certificate of optimality found
c
Search tree fully explored
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Evolution of the Optimal Cost during Optimization
Iteration step (number of nodes visited)
Cost (kW
)
c
cc*
u*
found u*
found
Certificate of optimality found
Certificate of optimality found
c
Search tree fully exploredUpper and lower bound converged
WithBranch & Bound
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Computational Effort
Example:
MPDTC with the switching horizon ’eSSESESE’
Probability distributions:Number of nodes
required to be
explored to obtain the optimal cost c*
Full enumeration
B&B
B&B with upper bound onnumber of computations
50% percentile
95% percentile
99% percentile
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Performance vs
Computational Burden
Short switching horizon (eSSE): •
B&B => computational burden reduced by factor 5.5
•
Switching losses and THDs
merely affected
Benefit:
simplify
implementation for short
switching horizons
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Performance vs
Computational Burden
Short switching horizon (eSSE): •
B&B => computational burden reduced by factor 5.5
•
Switching losses and THDs
merely affected
Benefit:
simplify
implementation for short
switching horizons
Benefit:
enable
implementation for long
switching horizons
Long switching horizon (eSSESESE):• B&B => computational burden reduced by factor 13• Switching losses and THDs
merely affected
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Performance Results
StandardDTC
MPDTC ‘eSSE’
MPDTC ‘eSSE(SE)2’
ACS 6000, we
=0.6 pu, Te
=1 pu; Same torque bounds, flux bounds relaxed by +/‐
0.01puABB’s simulation environment
Torque Stator flux Switch positions
TTHD
= 100%
TTHD
= 103%
TTHD
= 94%
ITHD
= 100%
ITHD
= 104%
ITHD
= 97%
Psw
= 100%
Psw
= 58%
Psw
= 39%Np
=88
Np
=22
Summary and Conclusions
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Commercial Benefits
•
Higher rating
of inverter possible–
40%
higher power capability
(e.g. from 5 MVA to 7 MVA)–
Hardware remains the same
•
Standard machines
can be used–
No derating
of machine required
•
For ‘complicated’
topologies–
MPC is enabling
technology
Fully utilize the drive
hardware
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Summary and Conclusions
Goal:
Fully utilize capability
of drive hardware•
Minimize switching losses
per distortions
•
Achieve very fast
torque and current response
Approach:•
Treat control and modulation problem in one stage
•
Work in the time‐domain•
Adopt model predictive control
Results:•
MPDxC
family
•
MP3C
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
For More Information
www.ece.auckland.ac.nz/tgey001
May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer
Selected Literature
•
T. Geyer: ʺLow complexity model predictive control in power electronics and
power
systemsʺ, PhD thesis, Automatic Control Laboratory, ETH Zurich, Switzerland, Mar. 2005.•
P. Cortés, M. P. Kazmierkowski, R. M. Kennel, D. E. Quevedo, and J. Rodríguez: ʺPredictive
Control in Power Electronics and Drivesʺ, IEEE Trans. on Industrial Electronics, vol. 55, no.
12, pp. 4312‐4324, Dec. 2008.•
T. Geyer, G. Papafotiou, and M. Morari: ʺModel predictive direct torque control ‐
part I:
concept, algorithm and analysisʺ, IEEE Trans. on Industrial Electronics, vol. 56, no. 6, pp.
1894‐1905, June 2009.•
G. Papafotiou, J. Kley, K. Papadopoulos, P. Bohren, M. Morari: ʺModel predictive direct
torque control ‐
part II: implementation and experimental evaluationʺ, IEEE Trans. on
Industrial Electronics, vol. 56, no. 6, pp. 1906‐1915, June 2009.•
T. Geyer: ʺGeneralized model predictive direct torque control: long prediction horizons and
minimization of switching lossesʺ, Proc. of the 48rd IEEE Conference on Decision and
Control, Shanghai, China, Dec. 2009.•
T. Geyer: ʺA comparison of control and modulation schemes for medium‐voltage drives:
emerging predictive control concepts versus field oriented controlʺ, Proc. of the Energy
Conversion Congress and Exposition, Atlanta, GA, Sep. 2010.•
T. Geyer: ʺModel predictive direct current control for multi‐level convertersʺ, Proc. of the
Energy Conversion Congress and Exposition, Atlanta, GA, Sep. 2010.