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Predictive Control - A Simple and Powerful Method
to Control Power Converters and Drives Ralph M. Kennel, Technische Universitaet Muenchen,Germany
Marian Kazmierkowski, Technical University of Warsaw, Poland
José Rodríguez, Universidad Técnica Federico Santa María, Valparaiso, Chile
Outline
Introduction
Predictive Control - Why
Predictive Control Principles
Predictive Control Methods
Different Way of Thinking
Review of classical PWM
The principle of MPC in Power Electronics
Review of converter topologies controlled using MPC
Some applications of converters controlled using MPC
Predictive Control – where’s the future ?
Conclusions/Discussion
State of the Art : Field Oriented Control
model
PWM
mainsstator coordinatesfield coordinates
currentcontrollers
fluxcontroller
speedcontroller
encoder
M3~
r
r
is
is
us
ej
e-j
us
6
in cascaded control structures
speed control must be much faster than position control
and current control must be much faster than speed control
current control must be very fast
to achieve position control with reasonable cycle times
in the controlled system (drive, converter, …)
however, there is no time constant justifying cycle times
of 100 µs or less
Problems
of Linear Algorithms
Outline
Introduction
Predictive Control - Why
Predictive Control Principles
Predictive Control Methods
Different Way of Thinking
Review of classical PWM
The principle of MPC in Power Electronics
Review of converter topologies controlled using MPC
Some applications of converters controlled using MPC
Predictive Control – where’s the future ?
Conclusions/Discussion
… it is not better performance !
• more power
• more dynamics
• etc.
… we already operate our systems at the physical limits !!!
Predictive Control
Why ?
… you do not need a Ph.D.
to do the set-up
Predictive Control
Why ?
… the real reason is …
simpler handling !
General Structure
of a Predictive Controller
inertia gear etc.
switchingstate
actual
machine state
I
prediction andcalculation
machine andpower electronics
model
motorwindings
powerelectronics
reminds slightly to state control
state control, however, is basically a linear control
predictive control is not !!!
Usual Structure of Drive Control
DC link
PI controller
why PWM ?
• linearization of the inverter
consequences ?
• very high switching frequency
Structure of a Direct Control
DC link
direct controller
Outline
Introduction
Predictive Control - Why
Predictive Control Principles
Predictive Control Methods
Different Way of Thinking
Review of classical PWM
The principle of MPC in Power Electronics
Review of converter topologies controlled using MPC
Some applications of converters controlled using MPC
Predictive Control – where’s the future ?
Conclusions/Discussion
Principle of Predictive Control
inverter
definite number of
switching elements
definite number of
switching states
definite number of
equivalent circuits
without switching
elements
precalculation of the
behaviour for each of
the switching states
next switching state
or switching time
can be fixed
comparison between
precalculation and
reference commands
reference
commands
direct control of IM currents (Mayer/Pfaff)
direct digital predictive current controller (Holmes/Martin)
digital current controller
(Betz/Cook/Henriksen)
current control (Choi/Sul)
direct torque control (DTC) (Takahashi/Nogushi)
(Tiitinen/Lalu)
multilevel hysteresis DTC
(Purcell/Acarnley)
direct torque control (DTC)
(Chapuis, et.al.)
DTC with ORS (Moucary et.al.)
DTC-PPWC (Nillesen et.al.)
direct mean torque control (DMTC) (Flach, et.al.)
new direct torque control
(Kang/Sul)
torque pulsation reduced DTC (Vas, et.al.)
DTC + dithering (Noguchi, et.al.)
DTC with reduction of torque ripple (La/Shin/Hyun)
DTDTC (Maes/Melkebeek)
DTC-SVM (Lascu et.al.)
DTC-DSVM (Casadei et.al)
adaptive switching pattern (ASP)
(Nagy)
direct current control
(Pfaff/Wick)
current control method
(Salama et.al)
adaptive and optimized regulator
(Ackva, et.al.)
“space vector” control
(Wuest/Jenni)
“space vector” control
(Kazmierkowski, et.al.)
direct self control (DSC) (Depenbrock)
direct speed control (DSPC)
(Mutschler)
integral space-vector PWM
(Trzynadlowski, et.al.)
direct self control (DSC)
(Bonanno, et.al.)
predictive control (Kennel/Schröder)
fast-response current control (Holtz, et.al)
improved predictive control (Warmer et.al.)
new predictive current control
(Hecht)
Family tree of predictive control algorithms
optimal on-line-tuning current regulator
(du Toit Mouton/Enslin)
predictive current control for resonant link inverter
(Oh/Jung/Youn)
vectorial torque control (Attaianese, et.al.)
trajectory tracking control (Holtz/Beyer)
sliding mode control (Emeljanov)
trajectory based strategies
predictive current control
(Holtz/Stadtfeld)
hysteresis control (bang bang)
PROMC voltage control
(Hintze)
PROMC current control
(Kohlmeier et.al.)
hysteresis based strategieshysteresis based strategies trajectory based strategies
Family tree of predictive control algorithms
Part 2 MPC
Continuous-Set-Model based strategies Finite-Set-Model based strategies
DMC
(Cutler/Ramaker)
GPC
(Clarke)
Modular multilevel converter
(Perez/Rodriguez)
Direct matrix converter
(Vargas/Rodriguez)
Indirect matrix converter
(Correa/Rodriguez/Espinoza)
Fast online optimization
Fast gradient method for converter
control
(Richter/Morari)
LP solution for quadratic cost
(Stumper/Kennel)
Explicit MPC
(Bemporad)
MPC with MPT
(Kvasnica)
MPC for PMSM
(Kuehl/Bolognani/Kennel)
Dead beat control
(Lee)
dc-dc converter
(Geyer/Morari)
MPTC
(Rodriguez)
Predictive current control
(Rodriguez)
Predictive speed control
(Fuentes/Rodriguez/Kennel)
Heuristic direct MPC
(Stolze/Kennel)
Sensorless MPC
(Wojciechowski/Strzelecki)
Saliency based encoderless
PTC
(Landsmann/Kennel)
Observer-based sensorless
PTC
(Davari/Wang/Kennel)
Weighting factors design
(Cortes/Rodriguez)
Weighting factor optimization
(Davari/Kennel)
2-steps MPC of 3 phase UPS
inverter
(Cortes/Rodriguez)
FPGA-based PCC
(Naouar/Monmasson)
ac-ac converter
CRHPC
(Clarke/Scattolini)
GPC--PID
(Nakano)
GPC for motor control
(Linder/Kennel) dc-ac converter
2L-VSI
(Cortes/Rodriguez)
3L-NPC
(Geyer/Rodriguez)
CHB
(Perez/Rodriguez/Cortes)
Flying capacitor converter
(Lezana/Aguilera/Quevedo)
Current source rectifier
(Correa/Rodriguez)
ac-dc converter
Outline
Introduction
Predictive Control - Why
Predictive Control Principles
Predictive Control Methods
Different Way of Thinking
Review of classical PWM
The principle of MPC in Power Electronics
Review of converter topologies controlled using MPC
Some applications of converters controlled using MPC
Predictive Control – where’s the future ?
Conclusions/Discussion
Outline
Introduction
Predictive Control Methods
Trajectory Based Predictive Control
Hysteresis Based Predictive Control
Long-Range Predictive Control
Example : Trajectory Based Predictive Control
Predictive Current Control acc. to Kennel
DC drive supplied by a line commutated thyristor inverter
+ + +
grid
U0 ≈
- - -
=
Example : Trajectory Based Predictive Control
Predictive Current Control acc. to Kennel
Trajectory Based Predictive Control Strategies
system states are forced to follow
(pre-)defined natural reference trajectories
difference to sliding mode control
there the trajectories are not natural
Example : Trajectory Based Predictive Control
Direct Speed Control acc. to Mutschler
model andprediction
3~M
*
ud
uk
isus
=~
e
e = – ref
a =
e ak k/
e ak+3 k+3/
e ak+1 k+1/
e ak+2 k+2/
+Hy–Hy
Sk
Sk+1
Sk+2
Characteristics of Trajectory Based Predictive Control
• system states are forced to follow (pre-)defined reference trajectories
• switching takes place at intersections
between different system-trajectories or at (pre-)defined instants
• switching frequency of the inverter can be fixed to a constant value
• control behaviour comparable to feedforward control
• exact knowledge of system parameters is required
• appropriate for realisation by digital circuits or controllers
Example : Trajectory Based Predictive Control Direct Self Control (DSC) acc. to Depenbrock
Example : Hysteresis Based Predictive Control Direct Self Control acc. to Takahashi
Outline
Introduction
Predictive Control Methods
Trajectory Based Predictive Control
Hysteresis Based Predictive Control
Long-Range Predictive Control
Hysteresis Based Predictive Control Strategies
switching of inverter takes place
at the (multi-dimensional) border(s)
of a hysteresis area
Example : Hysteresis Based Predictive Control Predictive Current Control acc. to Holtz
Example : Hysteresis Based Predictive Control Predictive Current Control acc. to Holtz
Re
jIm
0
s
is
is*
din
dt
3~M
=predictis
model
uduk
usk
is
is
disk
is
*
dt us
~
Example : Hysteresis Based Predictive Control Predictive Current Control acc. to Holtz
Example : Hysteresis Based Predictive Control Predictive Current Control acc. to Holtz
Characteristics of Hysteresis Based Predictive Control
• switching takes place at borders of a hysteresis area
• a maximum error can be (pre-)defined
• switching frequency of the inverter is not constant
• control behaviour comparable to feedback control
• exact knowledge of system parameters is not required
• appropriate for realisation by analog circuits
Example : Hysteresis Based Predictive Control Predictive Current Control acc. to Holtz
Comparison
of different
predictive control
schemes
Flux Trajectories 10 Hz fundamental frequency
500 Hz switching frequency
standard PWM
DSC (Depenbrock)
bang-bang control
DSC (Takahashi)
7 % hysteresis
predictive control
(Holtz) DSC (Takahashi)
2 % hysteresis
source Andreas Haun, Vergleich von Steuerverfahren …, VDI-Fortschrittsbereichte, Reihe 21, Nr. 113, 1992:
Flux Trajectories 40 Hz fundamental frequency
500 Hz switching frequency
standard PWM
DSC (Depenbrock)
bang-bang control
DSC (Takahashi)
7 % hysteresis
predictive control
(Holtz) DSC (Takahashi)
2 % hysteresis
source Andreas Haun, Vergleich von Steuerverfahren …, VDI-Fortschrittsbereichte, Reihe 21, Nr. 113, 1992:
standard PWM
DSC (Depenbrock)
bang-bang control
DSC (Takahashi)
7 % hysteresis
predictive control
(Holtz) DSC (Takahashi)
2 % hysteresis
Stator Current Trajectories 40 Hz fundamental frequency
500 Hz switching frequency
source Andreas Haun, Vergleich von Steuerverfahren …, VDI-Fortschrittsbereichte, Reihe 21, Nr. 113, 1992:
source Andreas Haun, Vergleich von Steuerverfahren …, VDI-Fortschrittsbereichte, Reihe 21, Nr. 113, 1992:
Frequency Spectrum of Torque
a) 40 Hz fundamental frequency
250 Hz switching frequency
b) 45 Hz fundamental frequency
500 Hz switching frequency
1. standard PWM
2. bang-bang control
3. predictive control (Holtz)
4. DSC (Depenbrock)
5. DSC (Takahashi) with 7 % hysteresis
source Andreas Haun, Vergleich von Steuerverfahren …, VDI-Fortschrittsbereichte, Reihe 21, Nr. 113, 1992:
Additional Losses
under Inverter Supply
a) variable fundamental frequency
500 Hz switching frequency
b) 40 Hz fundamental frequency
variable switching frequency
1. standard PWM
2. bang-bang control
3. predictive control (Holtz)
4. DSC (Depenbrock)
5. DSC (Takahashi) with 7 % hysteresis
6. DSC (Takahashi) with 7 % hysteresis
Outline
Introduction
Predictive Control Methods
Trajectory Based Predictive Control
Hysteresis Based Predictive Control
Long-Range Predictive Control
switching control
SVM (space vector modulation)
directly
steps of
prediction
(prediction
horizon)
1
>1
• DTC
• DSC
• DSPC
• direct control of
IM currents
• DFC
• DMC
• GPC
• DMPC
predictive control categories another way of distinction
• the player calculates
in advance
all possible moves
until a „prediction horizon“
• the player chooses
the move with the best
expectations of success
• after each opponent‘s move
pre-calculation and
optimization is repeated DMPC is like playing chess
The „Human Behaviour“ of DMPC
Page 44
Model Predictive Control
History Future
Model Predictive Control
Overview
Page 45
Page 46
Direct Model Predictive Control System Model / Cost Function
Direct Model Predictive Control
System Model / Cost Function
Page 47
Characteristics of Model Based Predictive Control
• basic ideas are derived from state-space control
• the past is explicitely considered (mostly by the system state)
• future control values are pre-calculated and optimized
until a (pre-)defined „horizon“
• the first of the precalculated control values only
is transmitted to the controlled system
• model parameters can be estimated on-line
• extension to MIMO-control is possible with little additional effort
• use of non-linear model is possible for non-linear control systems
• a lot of calculation power is required
Features of
(Longe Range) Predictive Control
Advantages
• possibility to use foreknowledge about drive system (system model)
• inverter limitations and dynamic behaviours are taken into account
• improved representation of non-linear systems
• no need for time challenging cascade structure
• improved dynamic behaviour
Disadvantages
• high processing capability required
• for industrial use change in teaching engineers necessary
• stationary accuracy and dynamic behaviour
depend on accurracy of model parameters
Outline
Introduction
Predictive Control - Why
Predictive Control Principles
Predictive Control Methods
Different Way of Thinking
Review of classical PWM
The principle of MPC in Power Electronics
Review of converter topologies controlled using MPC
Some applications of converters controlled using MPC
Predictive Control – where’s the future ?
Conclusions/Discussion
Different Way of Thinking in Model Based Predictive Control
1. model of the controlled system
this is no difference to conventional control
the better the model, the better the prediction
Page 51
2. cost function
the engineer has to learn to describe
what he wants the controlled system really to do !!!
3. stability
… that‘s a really good question … next question ?
Different Way of Thinking in Model Based Predictive Control
1. model of the controlled system
this is no difference to conventional control
the better the model, the better the prediction
Page 52
2. cost function
the engineer has to learn to describe
what he wants the controlled system really to do !!!
3. stability
… that‘s a really good question … next question ?
Outline
Introduction
Predictive Control - Why
Predictive Control Principles
Predictive Control Methods
Different Way of Thinking
Review of classical PWM
The principle of MPC in Power Electronics
Review of converter topologies controlled using MPC
Some applications of converters controlled using MPC
Predictive Control – where’s the future ?
Conclusions/Discussion
Predictive Control: A new and Powerful Alternative for Power Electronics and Drives
IEEE Energy Conversion Congress and Exposition, ECCE 2014
Jose Rodriguez Fellow IEEE
Distinguished Lecturer IEEE Universidad Técnica Federico Santa María
Valparaíso, Chile.
-2- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Outline
Introduction
Review of classical PWM
The principle of MPC in Power Electronics
Review of converter topologies controlled using MPC
Some applications of converters controlled using MPC
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-3- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Outline
Introduction
Review of classical PWM
The principle of MPC in Power Electronics
Review of converter topologies controlled using MPC
Some applications of converters controlled using MPC
Comparison between MPC and classical solutions
– In current control
– In drives
Open questions and future work
Conclusions
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-4- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Introduction
Converter control methods
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-5- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Introduction
Converter control methods
Predictive control methods
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-6- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of Classical PWM
The control of power converters and of energy is based on the “mean
value principle”.
Example;
Mean value of 𝑣𝐿
𝑣 𝐿 =𝑡𝑜𝑛
𝑇𝑠𝑉𝐵 = 𝐷𝑉𝐵 𝐷: duty cycle
Changing the duty cycle you can control the energy flow to the load.
This principle comes from analog electronics.
It is an old principle repeated today with microprocessors.
R C
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-7- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of Classical PWM
Subharmonic control
The same principle of “mean value” is used to control an inverter.
Example:
At every period of the carried, the mean value 𝑣𝐿 is generated.
This strategy comes from the analog electronics.
Using microprocessors we have replaced the oscillators by counters,
but the principle remains the same!
R C
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-8- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of Classical PWM
Subharmonic control
The same principle of “mean value” is used to control an inverter.
Example:
At every period of the carried, the mean value 𝑣𝐿 is generated.
This strategy comes from the analog electronics.
Using microprocessors we have replaced the oscillators by counters,
but the principle remains the same!
R C
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-9- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of Classical PWM
Subharmonic control
The same principle of “mean value” is used to control an inverter.
Example:
At every period of the carried, the mean value 𝑣𝐿 is generated.
This strategy comes from the analog electronics.
Using microprocessors we have replaced the oscillators by counters,
but the principle remains the same!
R C
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-10- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of Classical PWM
Subharmonic control
The same principle of “mean value” is used to control an inverter.
Example:
At every period of the carried, the mean value 𝑣𝐿 is generated.
This strategy comes from the analog electronics.
Using microprocessors we have replaced the oscillators by counters,
but the principle remains the same!
R C
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-11- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of Classical PWM
Subharmonic control
The same principle of “mean value” is used to control an inverter.
Example:
At every period of the carried, the mean value 𝑣𝐿 is generated.
This strategy comes from the analog electronics.
Using microprocessors we have replaced the oscillators by counters,
but the principle remains the same!
R C
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-12- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of Classical PWM
Subharmonic control
The same principle of “mean value” is used to control an inverter
Example:
At every period of the carried, the mean value 𝑣𝐿 is generated.
This strategy comes from the analog electronics.
Using microprocessors we have replaced the oscillators by counters,
but the principle remains the same!
R C
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-13- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of Classical PWM
Space Vector Modulation (SVM)
Modulation principle
Voltage vectors of a 2-level inverter
Calculate times 𝑡𝑎 and 𝑡𝑏 every period of the carried, so the mean value 𝑣 is
equal to the reference 𝑣∗.
We have learned that this is the only way to control energy.
𝑣∗ =1
𝑇𝑣𝑎𝑡𝑎 + 𝑣𝑏𝑡𝑏 + 𝑣𝑜𝑡𝑜
𝑡𝑎 + 𝑡𝑏 + 𝑡𝑜 = 𝑇
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-14- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of Classical PWM
Space Vector Modulation (SVM)
Predictive control offers a completely different and
powerful approach to control power converters
Modulation principle
Voltage vectors of a 2-level inverter
Calculate times 𝑡𝑎 and 𝑡𝑏 every period of the carried, so the mean value 𝑣 is
equal to the reference 𝑣∗.
We have learned that this is the only way to control energy.
𝑣∗ =1
𝑇𝑣𝑎𝑡𝑎 + 𝑣𝑏𝑡𝑏 + 𝑣𝑜𝑡𝑜
𝑡𝑎 + 𝑡𝑏 + 𝑡𝑜 = 𝑇
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-15- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
The principle of MPC in Power Electronics
Current control in a two-level voltage source inverter.
Power circuit of a 2L-VSI
Vectors generated by the 2L-VSI
𝑣 =2
3𝑣𝑎𝑁 + 𝑎 𝑣𝑏𝑁 + 𝑎2𝑣𝑐𝑁
𝑎 = 𝑒𝑗 2𝜋/3
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-16- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
The principle of MPC in Power Electronics
Mathematical model of the inverter
Using Euler’s discretization:
Equation for current prediction:
𝑖 =2
3𝑖𝑎 + 𝑎𝑖𝑏 + 𝑎2𝑖𝑐
𝑣 =2
3𝑣𝑎 + 𝑎𝑣𝑏 + 𝑎2𝑣𝑐
𝑣 = 𝑅𝑖 + 𝐿𝑑𝑖
𝑑𝑡+ 𝑒
𝑑𝑖
𝑑𝑡≈
𝑖 𝑘 + 1 − 𝑖(𝑘)
𝑇𝑠
𝑖𝑃 𝑘 + 1 = 1 −𝑅𝑇𝑠𝐿
𝑖 𝑘 +𝑇𝑠𝐿
𝑉 𝑘 − 𝑒 𝑘
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-17- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
The principle of MPC in Power Electronics
Current control in a two-level VSI: The algorithm
1) The load and reference currents are measured at sampling
interval k
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-18- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
The principle of MPC in Power Electronics
Current control in a two-level VSI: The algorithm
1) The load and reference currents are measured at sampling
interval k
2) Use the prediction equation to calculate the value of the current
in the next sampling interval (k+1) for each voltage vector
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-19- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
The principle of MPC in Power Electronics
Current control in a two-level VSI: The algorithm
1) The load and reference currents are measured at sampling
interval k
2) Use the prediction equation to calculate the value of the current
in the next sampling interval (k+1) for each voltage vector
3) For each voltage vector, calculate the cost function:
IEEE Energy Conversion Congress and Exposition, ECCE 2014
𝑔 = 𝑖𝛼∗ − 𝑖𝛼
𝑃 + 𝑖𝛽∗ − 𝑖𝛽
𝑃
-20- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
The principle of MPC in Power Electronics
Current control in a two-level VSI: The algorithm
1) The load and reference currents are measured at sampling
interval k
2) Use the prediction equation to calculate the value of the current
in the next sampling interval (k+1) for each voltage vector
3) For each voltage vector, calculate the cost function:
4) Select the switching state that minimizes the cost function
𝑔 = 𝑖𝛼∗ − 𝑖𝛼
𝑃 + 𝑖𝛽∗ − 𝑖𝛽
𝑃
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-21- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
The principle of MPC in Power Electronics
Current control in a two-level VSI: The algorithm
1) The load and reference currents are measured at sampling
interval k
2) Use the prediction equation to calculate the value of the current
in the next sampling interval (k+1) for each voltage vector
3) For each voltage vector, calculate the cost function:
4) Select the switching state that minimizes the cost function
5) Apply the new switching state
𝑔 = 𝑖𝛼∗ − 𝑖𝛼
𝑃 + 𝑖𝛽∗ − 𝑖𝛽
𝑃
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-22- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
The principle of MPC in Power Electronics
Current control in a two-level VSI: Block diagram
𝑔 = 𝑖𝛼∗ − 𝑖𝛼
𝑃 + 𝑖𝛽∗ − 𝑖𝛽
𝑃
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-23- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
The principle of MPC in Power Electronics
Current control in a two-level VSI: Algorithm flowchart
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-24- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
The principle of MPC in Power Electronics
Current control in a two-level VSI :
Voltage and current waveforms
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-25- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
The principle of MPC in Power Electronics
Some preliminary conclusions:
– MPC looks simple. Actually, it is simple and intuitive.
– It is a different approach from a conceptual point of view.
– Needs a deep and rigorous comparison with standard methods:
parameter variations, noise, robustness, model mismatches, etc.
– Good performance. It works!
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-26- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
The principle of MPC in Power Electronics
Some preliminary conclusions:
– MPC looks simple. Actually, it is simple and intuitive.
– It is a different approach from a conceptual point of view.
– Needs a deep and vigorous comparison with standard methods:
parameter variations, noise, robustness, model mismatches, etc.
– Good performance. It works!
J. Rodríguez, J. Pontt, C.A. Silva, P. Correa, P. Lezana, P. Cortés and U.
Ammann, “Predictive current control of a voltage source inverter”, Industrial
Electronics, IEEE Transactions on, vol. 54, no. 1, pp. 495-503, 2007
• Award: Best paper of year 2007!
• Second most cited paper of year 2007! (405 citations, Google Scholar Sept. 2013)
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-27- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of converter topologies
controlled using MPC
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-28- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of converter topologies controlled using MPC
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-29- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of converter topologies controlled using MPC
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-30- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of converter topologies controlled using MPC
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-31- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of converter topologies controlled using MPC
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-32- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of converter topologies controlled using MPC
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-33- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of converter topologies controlled using MPC
Some basic control objectives using MPC in
power electronics
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-34- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of converter topologies controlled using MPC
Current control in a three-level neutral point
clamped inverter
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-35- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of converter topologies controlled using MPC
Current control in a three-level neutral point
clamped inverter
From: (R. Vargas, et al, “Predictive Control of a Three-Phase Neutral-Point-Clamped
Inverter”, IEEE-TIE, vol. 54, no. 5, pp. 2697-2705, Oct. 2007).
𝑔 = 𝑖𝛼∗ − 𝑖𝛼
𝑃 + 𝑖𝛽∗ − 𝑖𝛽
𝑃 + 𝜆𝑛𝑛𝑐 + 𝜆𝑣 𝑣𝑐1𝑃 − 𝑣𝑐2
𝑃
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-36- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of converter topologies controlled using MPC
Current control in a cascaded H-bridge inverter
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-37- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of converter topologies controlled using MPC
Current control in a cascaded H-bridge inverter
Cost function to be minimized:
𝑔 = 𝑖𝛼∗ − 𝑖𝛼
𝑃 + 𝑖𝛽∗ − 𝑖𝛽
𝑃
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-38- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of converter topologies controlled using MPC
Current control in a cascaded H-bridge inverter
Cost function to be minimized:
Obtained with a dSPACE DS1104
A lot of calculations
Modified strategy to reduce the number of calculations has
been developed (use of adjacent vectors)
More complexity needed to cancel input current harmonics.
From: (P. Cortes, et al, “Model Predictive Control of Multilevel Cascaded H-Bridge Inverters”,
IEEE-TIE, vol. 57, no. 8, pp. 2691-2699, Aug. 2010).
𝑔 = 𝑖𝛼∗ − 𝑖𝛼
𝑃 + 𝑖𝛽∗ − 𝑖𝛽
𝑃
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-39- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of converter topologies controlled using MPC
Current control in a flying capacitor inverter
𝑔 = 𝑖𝛼∗ − 𝑖𝛼
𝑃 + 𝑖𝛽∗ − 𝑖𝛽
𝑃 + 𝜆𝑐1|𝑣𝑐1∗ − 𝑣𝑐1
𝑃 | + 𝜆𝑐2 𝑣𝑐2∗ − 𝑣𝑐2
𝑃
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-40- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of converter topologies controlled using MPC
Current control in a flying capacitor inverter
From: (E. I. Silva, et al, “Predictive Control of a Flying Capacitor Converter”, Proc. IEEE-
ACC, pp. 3763-3768, 2007).
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-41- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of converter topologies controlled using MPC
Application of MPC in matrix converters
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-42- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of converter topologies controlled using MPC
Continuous equations
- Load equations
- Input filter equations
- Instantaneous reactive power on the input
𝑣𝑜 = 𝑅𝑙𝑖𝑜 − 𝐿𝑙
𝑑𝑖𝑜𝑑𝑡
𝑣𝑠 = 𝑣𝑖 + 𝑅𝑓𝑖𝑠 + 𝐿𝑓
𝑑𝑖𝑠𝑑𝑡
𝑖𝑠 = 𝑖𝑖 + 𝐶𝑓
𝑑𝑣𝑖
𝑑𝑡
𝑞𝑠 = 𝑣𝑠𝛼𝑖𝑠𝛽 − 𝑣𝑠𝛽𝑖𝑠𝛼
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-43- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Review of converter topologies controlled using MPC
Prediction equations
- Current load prediction (Euler)
- Filter equations (State-space Model)
𝑖𝑜𝑘+1 = 1 −
𝑅𝑙𝑇𝑠𝐿𝑙
𝑖𝑜𝑘 +
𝑇𝑠𝐿𝑙
𝑣𝑜𝑘
𝑣𝑖𝑘+1 = 𝑐1𝑣𝑖
𝑘 + 𝑐2𝑖𝑠𝑘 + 𝑐5𝑣𝑠
𝑘 + 𝑐6𝑖𝑖𝑘
𝑖𝑠𝑘+1 = 𝑐3𝑣𝑖
𝑘 + 𝑐4𝑖𝑠𝑘 + 𝑐7𝑣𝑠
𝑘 + 𝑐8𝑖𝑖𝑘
𝑐5 𝑐6𝑐7 𝑐8
= 𝐴𝑐−1 𝑒𝐴𝑐𝑇𝑠 − 𝐼2𝑥2 𝐵𝑐
𝑐1 𝑐2𝑐3 𝑐4
= 𝑒𝐴𝑐𝑇𝑠
𝐴𝑐 =
01
𝐶𝑓
−1
𝐿𝑓−
𝑅𝑓
𝐿𝑓
, 𝐵𝑐 =
0 −1
𝐶𝑓
1
𝐿𝑓0
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-44- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Reminder: How the classical current control and
modulation of a Matrix Converter is done today?
Application times of the switching states
Review of converter topologies controlled using MPC
𝑑𝛼 =𝑇𝛼𝑇𝑠
𝑑𝛽 =𝑇𝛽
𝑇𝑠
𝑑0𝑣 =𝑇0𝑣
𝑇𝑠= 1 − 𝑑𝛼 − 𝑑𝛽
𝑑𝜇 =𝑇𝜇
𝑇𝑠
𝑑𝑣 =𝑇𝑣𝑇𝑠
𝑑0𝑐 =𝑇0𝑐
𝑇𝑠= 1 − 𝑑𝜇 − 𝑑𝑣
𝑑𝛼𝜇 = 𝑑𝛼𝑑𝜇 =𝑇𝛼𝜇
𝑇𝑠
𝑑𝛽𝜇 = 𝑑𝛽𝑑𝜇 =𝑇𝛽𝜇
𝑇𝑠
𝑑𝛼𝑣 = 𝑑𝛼 𝑑𝑣 =𝑇𝛼𝑣
𝑇𝑠
𝑑𝛽𝑣 = 𝑑𝛽𝑑𝑣 =𝑇𝛽𝑣
𝑇𝑠 𝑑0 = 1 − 𝑑𝛼𝜇 − 𝑑𝛽𝜇 − 𝑑𝛼𝑣 − 𝑑𝛽𝑣 =
𝑇0
𝑇𝑠
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-45- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Predictive current control of a Matrix Converter
Cost function
- Output current control
- Output current and input reactive power control
Review of converter topologies controlled using MPC
𝑔 = 𝑖0𝛼∗ − 𝑖0𝛼
𝑃 + 𝑖0𝛽∗ − 𝑖0𝛽
𝑃
𝑔 = 𝑖0𝛼∗ − 𝑖0𝛼
𝑃 + 𝑖0𝛽∗ − 𝑖0𝛽
𝑃 − 𝜆𝑞|0 − 𝑞𝑠|
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-46- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Predictive current control of a Matrix Converter
Only control of
load current
Review of converter topologies controlled using MPC
𝑔 = 𝑖𝑜𝛼∗ − 𝑖𝑜𝛼
𝑃 + 𝑖𝑜𝛽∗ − 𝑖𝑜𝛽
𝑃
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-47- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Predictive current control of a Matrix Converter
Only control of
load current
Control of load current
and reactive power
Review of converter topologies controlled using MPC
𝑔 = 𝑖𝑜𝛼∗ − 𝑖𝑜𝛼
𝑃 + 𝑖𝑜𝛽∗ − 𝑖𝑜𝛽
𝑃 𝑔 = 𝑖𝑜𝛼∗ − 𝑖𝑜𝛼
𝑃 + 𝑖𝑜𝛽∗ − 𝑖𝑜𝛽
𝑃 − 𝜆𝑞 0 − 𝑞𝑠
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-48- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Field oriented speed control of an induction machine
driven by a Matrix Converter using MPC for current control
Only control of
load current
Review of converter topologies controlled using MPC
𝑔 = 𝑖𝑜𝛼∗ − 𝑖𝑜𝛼
𝑃 + 𝑖𝑜𝛽∗ − 𝑖𝑜𝛽
𝑃
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-49- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Field oriented speed control of an induction machine
driven by a Matrix Converter using MPC for current control
Only control of
load current
Control of load current
and reactive power
Review of converter topologies controlled using MPC
From: (R. Vargas, et al, “Predictive Current Control of an Induction Machine Fed by a Matrix
Converter With Reactive Power Control”, IEEE-TIE, vol. 55, no. 12, pp. 4362-4371, Dec. 2008).
𝑔 = 𝑖𝑜𝛼∗ − 𝑖𝑜𝛼
𝑃 + 𝑖𝑜𝛽∗ − 𝑖𝑜𝛽
𝑃 𝑔 = 𝑖𝑜𝛼∗ − 𝑖𝑜𝛼
𝑃 + 𝑖𝑜𝛽∗ − 𝑖𝑜𝛽
𝑃 − 𝜆𝑞 0 − 𝑞𝑠
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-50- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters
controlled using MPC
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-51- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Distributed generation system
Drives:
- Predictive Torque Control
- Predictive Speed Control
Active filters
Uninterruptible power supplies
Multiphase converters
Non-conventional renewable energy
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-52- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Application of MPC in a distributed generation
system (NPC inverter)
1. Injected current control
2. Capacitor balance control
3. Commutations reduction
4. Internal resonance filter 1 2 3 4
MPC for LCL coupled
Inverter-based distributed
generation system
𝑔 = 𝜆𝑖 𝑖2∗ − 𝑖2
𝑃 + 𝜆𝑣 𝑣𝑐1𝑃 − 𝑣𝑐2
𝑃 + 𝜆𝑛 𝑛𝑠𝑤 + 𝜆𝑟 𝑊1𝑖1𝑃
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-53- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Application of MPC in a distributed generation
system
Converter Side
Current i1 [A]
Grid Current
i2 [A]
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-54- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Application of MPC in a distributed generation
system
Converter Side
Current i1 [A]
Grid Current
i2 [A]
Active Power
P [MW]
Reactive Power
Q [MVAr]
From: (H. Miranda, et al, “Model Predictive Current Control for High-Power Grid-Connected
Converters With Output LCL Filter”, Proc. IEEE-IECON, pp. 633-638, 2009).
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-55- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Drives
High Performance
Drives
High Performance
Drives
Field Oriented Control (FOC) Field Oriented Control (FOC)
Direct Torque Control (DTC) Direct Torque Control (DTC)
Model Predictive
Control (MPC)
Model Predictive
Control (MPC)
Predictive Field Oriented Control
Predictive Field Oriented Control
Predictive Torque Control
Predictive Torque Control
Predictive Speed Control
Predictive Speed Control
Direct Direct Cascaded Cascaded
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-56- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Predictive Torque Control (PTC)
- Induction machine equations
Stator voltage
Rotor voltage
Stator flux
Rotor flux
Electrical torque
𝑣 𝑠 = 𝑅𝑠𝑖 𝑠 +𝑑𝜓𝑠
𝑑𝑡
0 = 𝑅𝑟𝑖 𝑟 +𝑑𝜓𝑟
𝑑𝑡− 𝑗𝜔𝜓𝑟
𝜓𝑠 = 𝐿𝑠𝑖 𝑠 + 𝐿𝑚𝑖 𝑟
𝜓𝑟 = 𝐿𝑚𝑖 𝑠 + 𝐿𝑟𝑖 𝑟
𝑇 =3
2𝑝𝐼𝑚{𝜓𝑠
∗ ⋅ 𝑖 𝑠}
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-57- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Predictive Torque Control
- Prediction equations
Stator flux
Stator current
Electrical torque
𝜓𝑠𝑘+1 = 𝜓𝑠
𝑘 + 𝑇𝑠𝑣 𝑠𝑘 − 𝑅𝑠𝑇𝑠𝑖 𝑠
𝑘
𝑖𝑠𝑘+1 = 1 +
𝑇𝑠𝜏𝜎
𝑖 𝑠𝑘 +
𝑇𝑠𝜏𝜎 + 𝑇𝑠
1
𝑅𝜎
𝑘𝑟
𝜏𝑟− 𝑘𝑟𝑗𝜔 𝜓𝑟
𝑘 + 𝑣 𝑠𝑘
𝑇𝑘+1 =3
2𝑝𝐼𝑚 𝜓 𝑠
𝑘+1∗ ⋅ 𝑖 𝑠𝑘+1
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-58- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Block diagram of Predictive Torque Control (PTC)
𝑔 = 𝑇𝑟𝑒𝑓 − 𝑇𝑝𝑟𝑒𝑑 + 𝜆𝜓 𝜓𝑟𝑒𝑓 − 𝜓𝑝𝑟𝑒𝑑
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-59- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Speed control of an induction machine using PTC
From: (J. Rodriguez, et al, “High-Performance Control Strategies for Electrical Drives: An
Experimental Assessment”, IEEE-TIE, vol. 59, no. 2, pp. 812-820, Feb. 2012).
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-60- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
A key issue in PTC is the weighting factor selection
- Commonly, this factor is obtained by a heuristic procedure
- However, there are two alternatives to avoid the weighting
factor tuning:
1. Predictive field-oriented control (PFOC)
2. Ranking-based PTC
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-61- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
1) Predictive field-oriented control
- Equivalences between torque/flux with synchronous stator
currents
- Simplified cost function without any weighting factor
𝑔 = 𝑖𝑠𝑑∗ − 𝑖𝑠𝑑
𝑝+ 𝑖𝑠𝑞
∗ − 𝑖𝑠𝑞𝑝
𝑖𝑠𝑑∗ ≈
1
𝐿𝑠𝜓𝑠
∗ 𝑖𝑠𝑞∗ =
2𝐿𝑟
3𝐿𝑚𝑝𝜓𝑟𝑑𝑇∗
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-62- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
1) Predictive field-oriented control
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-63- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
1) Predictive field-oriented control
Speed
Torque
Stator Flux
Stator Current
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-64- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
2) Ranking-based PTC
- Each obtained error is evaluated separately and sorted
- A ranking value is assigned to each error value: voltage
vectors with lower error are assigned a lower ranking
- Finally, the voltage vector with the minimum average value
of its rankings is selected, resulting in an equal compromise
of tracking for both variables, torque, and flux.
𝑔1 = 𝑇∗ − 𝑇𝑝 2
𝑔2 = 𝜓𝑠∗ − 𝜓𝑠
𝑝 2
𝑔1 → 𝑟1
𝑔2 → 𝑟2
𝑣𝑠𝑜𝑝𝑡= arg 𝑣0,…,𝑣7
min𝑟1 + 𝑟2
2
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-65- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
2) Ranking-based PTC
Speed
Torque
Stator Flux
Stator Current
From: (C. A. Rojas, et al, “Predictive Torque and Flux Control Without Weighting Factors”, IEEE-
TIE, vol. 60, no. 2, pp. 681-690, Feb. 2013).
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-66- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
How to control the speed of a machine?
- without linear speed controller
- without PWM
- without linear current controllers
Direct or cascaded speed controller ?
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-67- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Predictive Speed Control of a PMSM
- Direct alternative
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-68- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Predictive Speed Control of a PMSM
1. rotor speed tracking
2. Maximization of the torque per ampere ratio
1 2
𝑔1 = 𝜆𝜔𝑟 𝜔𝑟∗ − 𝜔𝑟
𝑝 2+ 𝜆𝑖𝑑 0 − 𝑖𝑑
𝑝 2+ 𝜆𝑖𝑞𝑓 0 − 𝑖𝑞𝑓
𝑝2+ 𝑔𝑐 𝑖𝑑 , 𝑖𝑞
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-69- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Predictive Speed Control of a PMSM
1. rotor speed tracking
2. Maximization of the torque per ampere ratio
3. Minimization of high-frequency torque components
4. Stator current limitations
1 2 3 4
𝑔 = 𝜆𝜔𝑟 𝜔𝑟∗ − 𝜔𝑟
𝑝 2+ 𝜆𝑖𝑑 0 − 𝑖𝑑
𝑝 2+ 𝜆𝑖𝑞𝑓 0 − 𝑖𝑞𝑓
𝑝2+ 𝑔𝑐 𝑖𝑑 , 𝑖𝑞
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-70- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Predictive Speed Control of a PMSM
1. rotor speed tracking
2. Maximization of the torque per ampere ratio
3. Minimization of high-frequency torque components
4. Stator current limitations
How to limit the current?
1 2 3 4
𝑔 = 𝜆𝜔𝑟 𝜔𝑟∗ − 𝜔𝑟
𝑝 2+ 𝜆𝑖𝑑 0 − 𝑖𝑑
𝑝 2+ 𝜆𝑖𝑞𝑓 0 − 𝑖𝑞𝑓
𝑝2+ 𝑔𝑐 𝑖𝑑 , 𝑖𝑞
𝑔𝑐 = ∞ 𝑖𝑓 𝑖𝑞
𝑝> 𝑖𝑞
𝑚𝑎𝑥 𝑜𝑟 𝑖𝑑𝑝
> 𝑖𝑑𝑚𝑎𝑥
0 𝑖𝑓 𝑖𝑞𝑝
≤ 𝑖𝑞𝑚𝑖𝑛 𝑜𝑟 𝑖𝑑
𝑝≤ 𝑖𝑑
𝑚𝑖𝑛
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-71- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Predictive Speed Control of a PMSM
From: (Fuentes, et al, “Predictive Speed Control of a Synchronous Permanent Magnet
Motor”, IEEE-ICIT 2010).
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-72- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Non-conventional renewable energy
Diagram of the overall grid
connected PV system
configuration implementing
MPPT through the MPC
technique
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-73- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Non-conventional renewable energy
1. dc-link voltage control
2. Input current control
1 2
Diagram of the overall grid
connected PV system
configuration implementing
MPPT through the MPC
technique
From: (P. E. Kakosimos, et al, “Implementation of Photovoltaic Array MPPT Through Fixed
Step Predictive Control Technique”, Renewable Energy, pp. 2508-2514, 2011).
𝑔 = 𝜆𝑣 𝑣𝑑𝑐∗ − 𝑣𝑑𝑐
𝑝+ 𝜆𝑖 𝑖𝑝𝑣
∗ − 𝑖𝑝𝑣𝑝
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-74- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Uninterruptible power supplies
𝑔 = 𝑣𝑜𝑟𝑒𝑓
− 𝑣𝑜𝑝𝑟𝑒𝑑
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-75- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Uninterruptible power supplies
Output voltages and currents for a passive load step
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-76- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Uninterruptible power supplies
Output voltages and currents in steady state for a nonlinear load
From: (P. Cortes, et al, “Model Predictive Control of an Inverter With Output LC Filter for UPS
Applications”, IEEE-TIE, vol. 56, no. 6, pp. 1875-1883, June 2009).
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-77- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
Multiphase converters
Conventional
modulation
3D-SVM
- Four-leg two level voltage source inverter
Predictive current control
𝑔1 𝑘 + 1 = ||𝑖𝑜∗ 𝑘 + 1 − 𝑖𝑜 𝑘 + 1 ||
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-78- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
- Four-leg two level voltage source inverter
From: (J. Rodriguez, et al, “Predictive Current Control of Three-Phase Two-Level Four-
Leg Inverter”, IEEE-EPE-PEMC, pp. T3.106-110, 2010).
Balanced load Unbalanced load
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-79- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
PTC of an induction machine driven by a matrix
converter
Without control of qs
With control of qs
𝑔 = 𝑇𝑟𝑒𝑓 − 𝑇𝑝𝑟𝑒𝑑 + 𝜆𝜓 𝜓𝑟𝑒𝑓 − 𝜓𝑝𝑟𝑒𝑑
𝑔 = 𝑇𝑟𝑒𝑓 − 𝑇𝑝𝑟𝑒𝑑 + 𝜆𝜓 𝜓𝑟𝑒𝑓 − 𝜓𝑝𝑟𝑒𝑑 − 𝜆𝑞 0 − 𝑞𝑠
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-80- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
PTC in a matrix converter
Without control of qs
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-81- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
PTC in a matrix converter
Without control of qs With control of qs
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-82- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
PTC in a matrix converter: Speed reversal
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-83- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Some applications of converters controlled using MPC
PTC in a matrix converter: Speed reversal
Best paper award 2010 of the Industrial Power Electronics
From: (R. Vargas, U. Ammann, B. Hudoffsky, J. Rodriguez, and P. Wheeler, “Predictive torque
control of an induction machine fed by a matrix converter with reactive input power control,”
IEEE-TIE, vol. 25, no. 6, pp. 1426-1438, June 2010).
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-84- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison between MPC and
classical solutions
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-85- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison of operating principle
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-86- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison of operating principle
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-87- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison of operating principle
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-88- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison of operating principle
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-89- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison of operating principle
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-90- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison between MPC and classical solutions
Performance criteria used for comparison:
– Total harmonic distortion
– Root mean square error
– Integral average error
– Settling time
𝑇𝐻𝐷 =𝑋𝑅𝑀𝑆
𝑋1,𝑅𝑀𝑆
2
− 1
𝑅𝑀𝑆𝐸 =1
𝑇 𝜀𝛼
2 + 𝜀𝛽2 𝑑𝑡
12
𝐼𝐴𝐸 =1
𝑇 𝜀𝛼
2 + 𝜀𝛽2
12𝑑𝑡
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-91- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison between MPC and classical solutions
Conditions for the comparison
– Similar average switching frequency
• PI+SVM
• MPC
– PI controller in synchronous rotating coordinates for avoiding
steady-state error.
𝑓 𝑠 =1
3𝑇(𝑁𝑎 + 𝑁𝑏 + 𝑁𝑐)
𝑓 𝑠 ≈ 4.0[𝑘𝐻𝑧]
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-92- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison between MPC and classical solutions
PI controller
𝑇𝑠𝑒𝑡𝑡𝑙𝑖𝑛𝑔 = 12.5[𝑚𝑠]
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-93- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison between MPC and classical solutions
PI controller Predictive controller
𝑇𝑠𝑒𝑡𝑡𝑙𝑖𝑛𝑔 = 12.5[𝑚𝑠] 𝑇𝑠𝑒𝑡𝑡𝑙𝑖𝑛𝑔 = 1.5[𝑚𝑠]
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-94- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison between MPC and classical solutions
Steady-state performance:
Index MPC PI+SVM
RMSE 0.1928 0.1466
IAE 0.1772 0.1322
THDv [%] 86.20 76.50
THDi [%] 2.16 1.94
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-95- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison between MPC and classical solutions
High Performance Speed Control of an AC-Machine:
- Field Oriented Control (FOC)
- Direct Torque Control (DTC)
- Predictive Torque Control (PTC)
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-96- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison between MPC and classical solutions
High Performance Speed Control of an AC-Machine:
- Field Oriented Control (FOC)
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-97- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison between MPC and classical solutions
High Performance Speed Control of an AC-Machine:
- Direct Torque Control (DTC)
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-98- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison between MPC and classical solutions
High Performance Speed Control of an AC-Machine:
- Predictive Torque Control (PTC)
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-99- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison between MPC and classical solutions
High Performance Speed Control of an AC-Machine:
- Field Oriented Control (FOC)
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-100- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison between MPC and classical solutions
High Performance Speed Control of an AC-Machine:
- Direct Torque Control (DTC)
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-101- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison between MPC and classical solutions
High Performance Speed Control of an AC-Machine:
- Predictive Torque Control (PTC)
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-102- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Comparison between MPC and classical solutions
Torque response comparison
FOC (black) and DTC (gray)
PTC (black) and DTC (gray)
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-103- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Open questions and future work
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-104- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Open questions and future work
Long prediction horizon FCS-MPC?
- increased calculation time
- different alternatives:
short, long prediction horizon
fixed or variable prediction horizon
- different optimizations: branch and bound, dynamic
programming
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-105- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Open questions and future work
Calculation procedure of weighting factors
- offline, real-time, heuristic values, optimal value...
Steady-state error issues
- multi-sampling, integrative effects, adaptive models…
Fixed or variable switching frequency?
- losses, resonances, EMI, application dependency…
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-106- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Remark
Why is MPC so suitable for Power Electronics?
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-107- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Remark
Why is MPC so suitable for Power Electronics?
1. The Power Converters (the plant) has a discrete nature.
(Finite number of switching states).
2. The controller has a discrete nature (the microprocessor).
3. MPC adapts in a very natural and direct form the plant
with the controller, because both are discrete.
4. It is not necessary to linearize the system.
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-108- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Remark
Why is MPC so suitable for Power Electronics?
1. The Power Converters (the plant) has a discrete nature.
Finite number of switching states.
2. The controller has a discrete nature (the microprocessor).
3. MPC adapts in a very natural and direct form the plant
with the controller, because both are discrete.
4. It is not necessary to linearize the system.
My students: Why to study PWM if we have MPC?
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-109- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Conclusions
MPC presents a new approach to the control of
electrical energy using power semiconductors.
The research work developed so far has demonstrated
that, in principle, MPC works!
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-110- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Conclusions
MPC presents a new approach to the control of
electrical energy using power semiconductors.
The research work developed so far has demonstrated
that, in principle, MPC works!
MPC can be successfully implemented with existing
microprocessors.
Usually, MPC introduces a simplification in the control
algorithm (not always!).
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-111- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Conclusions
The performance of converters using MPC is
comparable with that of existing methods.
To find industrial use, the future research work must
demonstrate that MPC can introduce advantages in
terms of simplicity and performance (what is not easy!)
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-112- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Conclusions
The performance of converters using MPC is
comparable with that of existing methods.
To find industrial use, the future research work must
demonstrate that MPC can introduce advantages in
terms of simplicity and performance (what is not easy!)
This is a very attractive and emerging research area!
IEEE Energy Conversion Congress and Exposition, ECCE 2014
-113- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Conclusions
The performance of converters using MPC is
comparable with that of existing methods.
To find industrial use, the future research work must
demonstrate that MPC can introduce advantages in
terms of simplicity and performance (what is not easy!)
This is a very attractive and emerging research area!
With the potential to replace PWM!
IEEE Energy Conversion Congress and Exposition, ECCE 2014
Thanks for your attention
Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013
Predictive Control: A new and Powerful Alternative for Power Electronics and Drives
J. Rodríguez, Fellow IEEE
Universidad Técnica Federico Santa María
Valparaíso, Chile.
IEEE Energy Conversion Congress and Exposition, ECCE 2014
Outline
Introduction
Predictive Control - Why
Predictive Control Principles
Predictive Control Methods
Different Way of Thinking
Review of classical PWM
The principle of MPC in Power Electronics
Review of converter topologies controlled using MPC
Some more applications
Predictive Control – where’s the future ?
Conclusions/Discussion
Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - peter.landsmann@tum.de
Saliency
Tracking
Predictive
Torque
Control
Simulation
Results
Conclusion
Overview
Measure-
ments
Saliency based
Encoderless Predictive Torque Control
without Signal Injection
P. Landsmann, D. Paulus, P. Stolze and R. Kennel
Technische Universitaet Muenchen
Munich Germany
Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - peter.landsmann@tum.de
Saliency
Tracking
Predictive
Torque
Control
Simulation
Results
Conclusion
Overview
Measure-
ments
Basic Idea:
A Predictive Torque Controller
neglecting the saliency in the model
causes a prediction error
which contains the angle information
Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - peter.landsmann@tum.de
Saliency
Tracking
Predictive
Torque
Control
Simulation
Results
Conclusion
Overview
Measure-
ments
Predictive Torque Control
Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - peter.landsmann@tum.de
Saliency
Tracking
Predictive
Torque
Control
Simulation
Results
Conclusion
Overview
Measure-
ments
Current and PM flux linkage from
measurements
7 voltages vectors from inverter
prediction of current and
respective torque
Selecting optimum of cost function
Predictive Torque Control
Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - peter.landsmann@tum.de
Saliency
Tracking
Predictive
Torque
Control
Simulation
Results
Conclusion
Overview
Measure-
ments Discrete model of the machine
Current prediction based on
mean inverse inductance
Predictive Torque Control
Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - peter.landsmann@tum.de
Saliency
Tracking
Predictive
Torque
Control
Simulation
Results
Conclusion
Overview
Measure-
ments
Predicted current progression
Real current progression
Prediction error
Saliency Tracking Approach
Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - peter.landsmann@tum.de
Saliency
Tracking
Predictive
Torque
Control
Simulation
Results
Conclusion
Overview
Measure-
ments
Measured prediction error
Reconstructed prediction error
PLL controller input
Saliency Tracking Approach
Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - peter.landsmann@tum.de
Saliency
Tracking
Predictive
Torque
Control
Simulation
Results
Conclusion
Overview
Measure-
ments
Simulation Results for PMSM
Speed controlled encoderless predictive torque control
Simulation parameter of PMSM
Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - peter.landsmann@tum.de
Saliency
Tracking
Predictive
Torque
Control
Simulation
Results
Conclusion
Overview
Measure-
ments
Speed controlled step response to rated speed
very good dynamics
in simulation
dependency on
torque gradients
Simulation Results for PMSM
Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - peter.landsmann@tum.de
Saliency
Tracking
Predictive
Torque
Control
Simulation
Results
Conclusion
Overview
Measure-
ments
Measurements with Reluctance Machine
Data of transverse laminated RM
Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - peter.landsmann@tum.de
Saliency
Tracking
Predictive
Torque
Control
Simulation
Results
Conclusion
Overview
Measure-
ments
Speed controlled step response to 160% rated speed
Measurements with Reluctance Machine
Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - peter.landsmann@tum.de
Saliency
Tracking
Predictive
Torque
Control
Simulation
Results
Conclusion
Overview
Measure-
ments
Response to 66% rated torque load step at speed controlled standstill
Measurements with Reluctance Machine
Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - peter.landsmann@tum.de
Saliency
Tracking
Predictive
Torque
Control
Simulation
Results
Conclusion
Overview
Measure-
ments
Summary
Proposed Scheme:
Neglect the saliency in PTC equations
Prediction error contains angle information
Reconstruct Prediction Error using PLL angle
Vectorproduct of both is PLL input
Benefits:
Saliency based:
permanent operation at standstill
No signal injection:
operation at high speed as well as at standstill
„Limitations“ of HF Injection Methods
- HF injection voltage margin limitation to medium and low speed
- No physical necessity for injection shape
- Basically any current ripple contains the saliency angle information
- Finding a way to exploit this provides additional degrees of freedom
- Restriction to rotating or alternating shape due to algorithmic reasons
Encoderless Control with Arbitrary Injection
Meaning of „Arbitrary“
„Limitations“ of HF Injection Methods
- Basically any current ripple contains the saliency angle information
Encoderless Control with Arbitrary Injection
Meaning of „Arbitrary“
… usually the current ripple caused by the inverter switchings
are sufficient to exploit the rorot position …
… if not … any current ripple can eben be music !!!
Page
72
Industrial Needs
• The sensorless control scheme presented here
does not need additional voltage measurement devices
- neither on the machine/motor side nor on the line side
single scheme for wide speed range (no phase over)
no additional noise (except usual noise by inverter supply)
? insensitivity with respect to parameter variations
• The proposed PTC (Predictive Torque Control) method
works from standstill to maximum speed
• As long as there is a detectable saliency
PTC is very robust to variations of the motor parameters
further research to be done !!
Outline
Introduction
Predictive Control - Why
Predictive Control Principles
Predictive Control Methods
Different Way of Thinking
Review of classical PWM
The principle of MPC in Power Electronics
Review of converter topologies controlled using MPC
Some applications of converters controlled using MPC
Predictive Control – where’s the future ?
Conclusions/Discussion
Experimental Results (DMPC) current control
comparison : PI control model predictive control
Experimental Results (DMPC) current control
a change of the cost function (nothing else !!!)
results in different behaviour !
Features of (Longe Range) Predictive Control
Advantages
• possibility to use foreknowledge about drive system (system model)
• inverter limitations and dynamic behaviours are taken into account
• improved representation of non-linear systems
• no need for time challenging cascade structure
• improved dynamic behaviour
Disadvantages
• high processing capability required
• for industrial use change in teaching engineers necessary
• stationary accuracy and dynamic behaviour
depend on accurracy of model parameters
Discussion
• predictive control strategies
offer the possibility to use foreknowledge about the drive system
• physical limitations and dynamic behaviour of power electronics
are taken into account
• non-linear systems are represented better (by non-linear models)
• no need for time challenging cascaded structures
• the way of thinking is different
model of the controlled system cost function
Page 77
Outline
Introduction
Predictive Control - Why
Predictive Control Principles
Predictive Control Methods
Different Way of Thinking
Review of classical PWM
The principle of MPC in Power Electronics
Review of converter topologies controlled using MPC
Some applications of converters controlled using MPC
Predictive Control – where’s the future ?
Conclusions/Discussion
There is definitely a strong demand
for reducing the calculation power
necessary for predictive control
strategy Np max. calculation time cases
complete enumeration 2 35 µs 64
online-optimization is not applicable for drive control
Calculation Times DMPC - control, implicite solution
complete enumeration 3 > 500 µs 512
branch and bound 2 27 µs 64
branch and bound 3 186 µs 512
processor:
900 MHz AMD Duron, 128 MB RAM
Linux 2.2.14 with RTAI 1.3
There is definitely a strong demand
for reducing the calculation power
necessary for predictive control
• Relying on Moore‘s Law is not sufficient !
• Heuristic Preselection
• Extrapolation instead of Exact calculation
• …
Control task
Current control of a three-phase resistive-inductive-active load
Heuristic method
• Calculation effort rises exponentially with the prediction horizon
• Three or four prediction steps impossible in real-time
(online as well as offline)
• Cost function to describe the performance to be obtained
• Basic idea of Heuristic Method :
• Optimum integer solution of a linear program
is close to the continuous-valued solution of the integer problem
=> Important: Optimum integer solution is not necessarily
the integer solution which is closest to the continuous-valued optimum
=> Not all integer points have to be examined,
only the ones closest to the continuous-valued optimum
Peter Stolze
Heuristic method
• Continuous-valued “switching states“ in the range [0; 1]
• Determination of the sector in which the
continuous-valued optimum lies (I to VI)
• For the first two prediction steps the three
closest integer solutions are used for
an exhaustive search
(corners of the triangle)
• For the 3rd and 4th prediction step only the
2 closest integer solutions are used
• 3 prediction steps: 18 possible combinations
4 prediction steps: 36 possible combinations
• In more than 95% of the cases the “real“ optimum is still found
Simulation Results Three-Level Inverter with Capacitor Voltage Balancing
Sinusoidal references Flying capacitor voltages
R = 10Ω, L = 10mH, Vdc = 540V, T = 100μs, C = 480μF
Peter Stolze
Finite-Set Model Predictive Control of a
Flying Capacitor Converter with Heuristic
Voltage Vector Preselection
Control task • Current control of a three-phase resistive-inductive-active load
• Hysteresis controller for voltage balancing
C1
i1
S11
S12
S13
S14
C2
i2
S21
S22
S23
S24
C3
i3
S31
S32
S33
S34
0.5Vdc
0.5Vdc
R
L
R
L
R
L
E1
E2
E3
General remarks
• Heuristic voltage vector
selection algorithm basically
the same as for two-level
inverters but now the
continuous-valued “switching
states“ can be
in the range [-1; 1]
• 24 possible sectors
Re
Im
++-
+0-
+--
+-0
+-+0-+--+
-0+
-++
-+0
-+- 0+-
0+0
-0-
++0
00-
+00
0--
+0+
0-0
00+
--0
0++
-00
+++
000
---
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Simulation Results
Sinusoidal references Flying capacitor voltages
R = 10Ω, L = 10mH, Vdc = 540V, T = 100μs, C = 480μF
There is definitely a strong demand
for reducing the calculation power
necessary for predictive control
• Relying on Moore‘s Law is not sufficient !
• Heuristic Preselection
• Extrapolation instead of Exact calculation
• …
Model Based Predictive Current Control
there are
7 (or 8) possiblities
for “the following
switching state”
the respective
system behaviour (current)
can be calculated
in advance
complete enumeration extensive processing power needed
a chess player, however, does not really consider each possibility
further prediction, however,
is only considered for
the candidate sequences
staying within
the permitted limits
Model Based Predictive Current Control
… so why should we do that in predictive control ???
… determine those switching possibilities only
that are either feasible or point in the proper direction
these are candidate sequences
feasible pointing in the proper direction
Model Based Predictive Current Control
not feasible not pointing in the proper direction
Model Based Predictive Current Control
… determine those switching possibilities only
that are either feasible or point in the proper direction
these are candidate sequences
Model Based Predictive Current Control
… for the candidate sequences, further prediction (e. g. by a reduced system model) is performed
example : the number of steps after which the first of the two variables the isa and iisb
leaves the feasible region
is the number h
h1 = 4 h2 = 10
Model Based Predictive Current Control
… for the candidate sequences, further prediction (e. g. by a reduced system model) is performed
example : the number of steps after which the first of the two variables the isa and iisb
leaves the feasible region
is the number h
Outline
Introduction
Predictive Control - Why
Predictive Control Principles
Predictive Control Methods
Different Way of Thinking
Review of classical PWM
The principle of MPC in Power Electronics
Review of converter topologies controlled using MPC
Some applications of converters controlled using MPC
Predictive Control – where’s the future ?
Conclusions/Discussion
Features of (Longe Range) Predictive Control
Advantages
• possibility to use foreknowledge about drive system (system model)
• inverter limitations and dynamic behaviours are taken into account
• improved representation of non-linear systems
• no need for time challenging cascade structure
• improved dynamic behaviour
Disadvantages
• high processing capability required
• for industrial use change in teaching engineers necessary
• stationary accuracy and dynamic behaviour
depend on accurracy of model parameters
Actual Situation
in cascaded control structures
speed control must be much faster than position control
and current control must be much faster than speed control
current control must be extremely fast
to achieve position control with reasonable cycle times
at the time most requirements in industrial applications are satisfied sufficiently
there is no strong need for improvement in industry
however – at a certain time there will be a demand for improvement
with respect to a future increase of requirements
more investigations should be done
Page 99
Discussion
• predictive control strategies
offer the possibility to use foreknowledge about the drive system
• physical limitations and dynamic behaviour of power electronics
are taken into account
• non-linear systems are represented better (by non-linear models)
• no need for time challenging cascaded structures
• the way of thinking is different
model of the controlled system cost function
with respect to a future increase of requirements
more investigations should be done
Page
100
What do you think ?
Thank you !
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