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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

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Page 1: Predictive Control - A Simple and Powerful Method to ...rpsonline.com.sg/peds/Tutorial-1.pdf · Predictive Control - A Simple and Powerful Method to Control Power Converters and Drives

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

Page 2: Predictive Control - A Simple and Powerful Method to ...rpsonline.com.sg/peds/Tutorial-1.pdf · Predictive Control - A Simple and Powerful Method to Control Power Converters and Drives
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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

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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

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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

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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

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… it is not better performance !

• more power

• more dynamics

• etc.

… we already operate our systems at the physical limits !!!

Predictive Control

Why ?

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… you do not need a Ph.D.

to do the set-up

Predictive Control

Why ?

… the real reason is …

simpler handling !

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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 !!!

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Usual Structure of Drive Control

DC link

PI controller

why PWM ?

• linearization of the inverter

consequences ?

• very high switching frequency

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Structure of a Direct Control

DC link

direct controller

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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

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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

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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

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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

Page 18: Predictive Control - A Simple and Powerful Method to ...rpsonline.com.sg/peds/Tutorial-1.pdf · Predictive Control - A Simple and Powerful Method to Control Power Converters and Drives

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

Page 19: Predictive Control - A Simple and Powerful Method to ...rpsonline.com.sg/peds/Tutorial-1.pdf · Predictive Control - A Simple and Powerful Method to Control Power Converters and Drives

Outline

Introduction

Predictive Control Methods

Trajectory Based Predictive Control

Hysteresis Based Predictive Control

Long-Range Predictive Control

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Example : Trajectory Based Predictive Control

Predictive Current Control acc. to Kennel

DC drive supplied by a line commutated thyristor inverter

+ + +

grid

U0 ≈

- - -

=

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Example : Trajectory Based Predictive Control

Predictive Current Control acc. to Kennel

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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

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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

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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

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Example : Trajectory Based Predictive Control Direct Self Control (DSC) acc. to Depenbrock

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Example : Hysteresis Based Predictive Control Direct Self Control acc. to Takahashi

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Outline

Introduction

Predictive Control Methods

Trajectory Based Predictive Control

Hysteresis Based Predictive Control

Long-Range Predictive Control

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Hysteresis Based Predictive Control Strategies

switching of inverter takes place

at the (multi-dimensional) border(s)

of a hysteresis area

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Example : Hysteresis Based Predictive Control Predictive Current Control acc. to Holtz

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Example : Hysteresis Based Predictive Control Predictive Current Control acc. to Holtz

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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

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Example : Hysteresis Based Predictive Control Predictive Current Control acc. to Holtz

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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

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Example : Hysteresis Based Predictive Control Predictive Current Control acc. to Holtz

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Comparison

of different

predictive control

schemes

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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:

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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:

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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:

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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

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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

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Outline

Introduction

Predictive Control Methods

Trajectory Based Predictive Control

Hysteresis Based Predictive Control

Long-Range Predictive Control

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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

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• 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

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Page 44

Model Predictive Control

History Future

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Model Predictive Control

Overview

Page 45

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Page 46

Direct Model Predictive Control System Model / Cost Function

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Direct Model Predictive Control

System Model / Cost Function

Page 47

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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

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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

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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

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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 ?

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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 ?

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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

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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.

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-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

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-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

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-4- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013

Introduction

Converter control methods

IEEE Energy Conversion Congress and Exposition, ECCE 2014

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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)

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-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

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-28- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013

Review of converter topologies controlled using MPC

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-29- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013

Review of converter topologies controlled using MPC

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-30- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013

Review of converter topologies controlled using MPC

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-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

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-32- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013

Review of converter topologies controlled using MPC

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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).

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-85- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013

Comparison of operating principle

IEEE Energy Conversion Congress and Exposition, ECCE 2014

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-86- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013

Comparison of operating principle

IEEE Energy Conversion Congress and Exposition, ECCE 2014

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-87- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013

Comparison of operating principle

IEEE Energy Conversion Congress and Exposition, ECCE 2014

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-88- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013

Comparison of operating principle

IEEE Energy Conversion Congress and Exposition, ECCE 2014

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-89- Symposium on Predictive Control of Electrical Drives and Power Electronics - 2013

Comparison of operating principle

IEEE Energy Conversion Congress and Exposition, ECCE 2014

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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-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

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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

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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

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Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - [email protected]

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

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Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - [email protected]

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

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Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - [email protected]

Saliency

Tracking

Predictive

Torque

Control

Simulation

Results

Conclusion

Overview

Measure-

ments

Predictive Torque Control

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Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - [email protected]

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

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Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - [email protected]

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

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Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - [email protected]

Saliency

Tracking

Predictive

Torque

Control

Simulation

Results

Conclusion

Overview

Measure-

ments

Predicted current progression

Real current progression

Prediction error

Saliency Tracking Approach

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Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - [email protected]

Saliency

Tracking

Predictive

Torque

Control

Simulation

Results

Conclusion

Overview

Measure-

ments

Measured prediction error

Reconstructed prediction error

PLL controller input

Saliency Tracking Approach

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Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - [email protected]

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

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Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - [email protected]

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

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Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - [email protected]

Saliency

Tracking

Predictive

Torque

Control

Simulation

Results

Conclusion

Overview

Measure-

ments

Measurements with Reluctance Machine

Data of transverse laminated RM

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Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - [email protected]

Saliency

Tracking

Predictive

Torque

Control

Simulation

Results

Conclusion

Overview

Measure-

ments

Speed controlled step response to 160% rated speed

Measurements with Reluctance Machine

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Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - [email protected]

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

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Institute for Electrical Drive Systems & Power Electronics – Technische Universität München Arcisstr. 21, D-80333 Munich - [email protected]

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

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„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“

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„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 !!!

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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 !!

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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

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Experimental Results (DMPC) current control

comparison : PI control model predictive control

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Experimental Results (DMPC) current control

a change of the cost function (nothing else !!!)

results in different behaviour !

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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

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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

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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

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There is definitely a strong demand

for reducing the calculation power

necessary for predictive control

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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

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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

• …

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Control task

Current control of a three-phase resistive-inductive-active load

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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

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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

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Simulation Results Three-Level Inverter with Capacitor Voltage Balancing

Sinusoidal references Flying capacitor voltages

R = 10Ω, L = 10mH, Vdc = 540V, T = 100μs, C = 480μF

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Peter Stolze

Finite-Set Model Predictive Control of a

Flying Capacitor Converter with Heuristic

Voltage Vector Preselection

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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

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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

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Simulation Results

Sinusoidal references Flying capacitor voltages

R = 10Ω, L = 10mH, Vdc = 540V, T = 100μs, C = 480μF

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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

• …

Page 205: Predictive Control - A Simple and Powerful Method to ...rpsonline.com.sg/peds/Tutorial-1.pdf · Predictive Control - A Simple and Powerful Method to Control Power Converters and Drives

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

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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 ???

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… 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

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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

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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

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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

Page 211: Predictive Control - A Simple and Powerful Method to ...rpsonline.com.sg/peds/Tutorial-1.pdf · Predictive Control - A Simple and Powerful Method to Control Power Converters and Drives

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

Page 212: Predictive Control - A Simple and Powerful Method to ...rpsonline.com.sg/peds/Tutorial-1.pdf · Predictive Control - A Simple and Powerful Method to Control Power Converters and Drives

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

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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

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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

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What do you think ?

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Thank you !