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Model Predictive Control in MediumVoltage Drives Tobias Geyer Department of Electrical and Computer Engineering The University of Auckland New Zealand In collaboration with

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Page 1: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

Model Predictive Control in

Medium‐Voltage Drives

Tobias Geyer

Department of Electrical and Computer Engineering 

The University of Auckland

New Zealand

In collaboration with

Page 2: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Outline

Introduction•

Control problem

Performance trade‐off•

Control and modulation schemes

Model Predictive Control•

1‐step predictive control

Model predictive direct current/torque control•

Computational efficiency

Summary and Outlook

Page 3: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

Control Problem

Page 4: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

M

(Active) RectifierInverterElectrical

Machine Grid

Controller

Control Problem

Low current distortions                    => low thermal losses

Low torque distortions => no  excitation of mech.

resonances

Low switching

losses

=> high  efficiency, low thermal

losses

Fast

torque response => high  dynamic

performance

Page 5: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Control and Modulation

(Active) Rectifier

Inverter

Electrical Machine

Grid

Dc-Link

u

M

is

Modulator*

Currentcontroller

Speedcontroller

u*is*Te*

Fundamental trade‐off between switching losses (frequency) and the current / torque distortion

levels

Cascaded

control loops:–

Speed control loop

Current control loop

Current

control problem=> split into current controller

and modulator

Page 6: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

Performance Trade‐Off

Page 7: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Trade‐Off (High

Switching Frequency)

u* u

is

T

fsw

=700HzPsw

=16.7kW,Pcon

=2.7kWTHDI

=2.31%THDT

=1.93%

Inverter:

3‐level NPC with IGCTsInduction machine:

3.3kV, 2MVA 

Operation point:

we

=1pu, Te

=1pu

Page 8: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Trade‐Off (Low

Switching Frequency)

u* u

is

T

fsw

=150HzPsw

=3.9kW, Pcon

=2.8kWTHDI

=6.9%THDT

=6.0%

Inverter:

3‐level NPC with IGCTsInduction machine:

3.3kV, 2MVA 

Operation point:

we

=1pu, Te

=1pu

Page 9: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Trade‐Off for PWM / SVM

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

2

4

6

8

10

12

14

16

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

1

2

3

4

5

6

7

Current THD vs

switching losses Torque THD vs

switching losses

Switching losses [%] Switching losses [%]

THD [%

]

THD [%

]

? ?

Page 10: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

Control and Modulation Schemes

Page 11: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Torque response time(controller bandwidth)slowfast

small

largeField Oriented Control with PWM/SVM

Control and Modulation

Switching lossesper distortions

Page 12: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Torque response time(controller bandwidth)slowfast

small

largeField Oriented Control with PWM/SVM

Control and Modulation

Model Predictive Control with PWM/SVM

Switching lossesper distortions

Page 13: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Torque response time(controller bandwidth)slowfast

small

largeField Oriented Control with PWM/SVM

Control and Modulation

V/f Control with Optimized Pulse Patterns

Model Predictive Control with PWM/SVM

Switching lossesper distortions

Page 14: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Torque response time(controller bandwidth)slowfast

small

largeField Oriented Control with PWM/SVM

Control and Modulation

V/f Control with Optimized Pulse Patterns

Controller and modulator

Model Predictive Control with PWM/SVM

Direct Torque Control

Switching lossesper distortions

Page 15: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Switching lossesper distortions

Torque response time(controller bandwidth)slowfast

small

largeField Oriented Control with PWM/SVM

Control and Modulation

V/f Control with Optimized Pulse Patterns

Controller and modulator

Model Predictive Control with PWM/SVM

Direct Torque Control

One‐step Predictive Control

Page 16: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Torque response time(controller bandwidth)slowfast

small

large

Control and Modulation: Goal

V/f Control with Optimized Pulse Patterns

?

?

Model Predictive Control with PWM/SVM

One‐step Predictive Control

Switching lossesper distortions

Field Oriented Control with PWM/SVM

Direct Torque Control

Page 17: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Torque response time(controller bandwidth)slowfast

small

large

Control and Modulation: New Methods

V/f Control with Optimized Pulse Patterns

Model Predictive Direct Torque / 

Current Control

Model Predictive Control with PWM/SVM

One‐step Predictive Control

Field Oriented Control with PWM/SVM

Direct Torque Control

Switching lossesper distortions

Controller and modulator

Page 18: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Torque response time(controller bandwidth)slowfast

small

large

Control and Modulation: New Methods

V/f Control with Optimized Pulse Patterns

Model Predictive Direct Torque / 

Current ControlFast Control ofOptimized

Pulse Patterns

Model Predictive Control with PWM/SVM

One‐step Predictive Control

Field Oriented Control with PWM/SVM

Direct Torque Control

Switching lossesper distortions

Controller and modulator

Page 19: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

(Active) Rectifier

Inverter

Electrical Machine

Grid

Dc-Link

u

M

is

Modulator*

Currentcontroller

Speedcontroller

u*is*Te*

Control and Modulation: New Methods

Goal: Fully utilize capability of drive hardware•

Minimize switching losses

per distortions

Achieve very fast

torque and current response

Approach:•

Treat control and modulation problem in one stage

Work in the time‐domain•

Adopt model predictive control

Current controller and modulator

Page 20: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

Model Predictive Control

for MV Electrical Drives

Page 21: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Classification of MPC Schemes for Electrical Drives

Hysteresis boundsReference tracking

Model Predictive Control: Direct methods (without a modulator)

Current  control

Torque /  flux ctrl.

Trajectory control

Current  control

Torque /  flux ctrl.

Current  trajectoryFlux 

trajectory

Very short prediction 

horizons (typically one step)

Medium to long prediction 

horizons (20 to 150 steps)

Closed‐loop control of pre‐

computed pulse patterns

Page 22: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Classification of MPC Schemes for Electrical Drives

Hysteresis boundsReference tracking

Model Predictive Control: Direct methods (without a modulator)

Current  control

Torque /  flux ctrl.

Trajectory control

Current  control

Torque /  flux ctrl.

Current  trajectoryFlux 

trajectory

Very short prediction 

horizons (typically one step)

Medium to long prediction 

horizons (20 to 150 steps)

Closed‐loop control of pre‐

computed pulse patterns

Page 23: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

One‐Step Predictive Current

Control

timek k+1

isα

isα,refisα

(k)

isα

(k+1)

timek k+1

isβ

isβ,refisβ

(k)

isβ

(k+1)

Algorithm•

Enumerate all 27 switch 

transitions•

Predict currents at k+1

Choose switch transition  with minimal current 

error at k+1

Page 24: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Performance Index:

Constraints

• prediction horizon

is one• machine model•minimization of switching effort (e.g. frequency)• λn

=> trade‐off between tracking accuracy and switching • conceptually and computationally very simple

Main features:

Discrete‐valued switch positions

Deviation from 

current reference

Model of machine

One‐Step Predictive Current

Control

Restrictions on switch transitions

Penalty on 

switching effort

Page 25: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

One‐step Predictive Current

Control

Current TDD vs

switching losses Torque TDD vs

switching losses

Switching losses [%] Switching losses [%]

TDD [%

]

TDD [%

]

Current THD similar to PWM•

Torque THD significantly worse than PWM

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

1

2

3

4

5

6

7PWM

OPP

1-step pred. current ctrl.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

2

4

6

8

10

12

14

16OPP

PWM1-step pred. current ctrl.

Page 26: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Classification of MPC Schemes for Electrical Drives

Hysteresis boundsReference tracking

Model Predictive Control: Direct methods (without a modulator)

Current  control

Torque /  flux ctrl.

Trajectory control

Current  control

Torque /  flux ctrl.

Current  trajectoryFlux 

trajectory

Very short prediction 

horizons (typically one step)

Medium to long prediction 

horizons (20 to 150 steps)

Closed‐loop control of pre‐

computed pulse patterns

Page 27: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

One‐step Predictive Torque

Control

Current TDD vs

switching losses Torque TDD vs

switching losses

Switching losses [%] Switching losses [%]

TDD [%

]

TDD [%

]

Torque THD similar to PWM•

Current THD significantly worse than PWM

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

1

2

3

4

5

6

7PWM

OPP

1-step pred. torque ctrl.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

2

4

6

8

10

12

14

16OPP

PWM

1-step pred. torque ctrl.

Page 28: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Classification of MPC Schemes for Electrical Drives

Hysteresis

boundsReference tracking

Model Predictive Control: Direct methods (without a modulator)

Current  control

Torque /  flux ctrl.

Trajectory control

Current control

Torque /  flux ctrl.

Current  trajectoryFlux 

trajectory

Very short prediction 

horizons (typically one step)

Medium to long prediction 

horizons (20 to 150 steps)

Closed‐loop control of pre‐

computed pulse patterns

Page 29: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Model Predictive Direct Current

Control: Step 1

Key ingredients:• Drive model• Extrapolation

a

b

c

k Np

iripβ

iripα

u

t

t

t

e EE SS

Predict current trajectories for (all)possible

switching sequences

Switching horizon, e.g. ‘eSESE’• S: consider all switch transitions• E: extrapolate/extend currents and NPP• e: optional ‘E’

Prediction horizon

NpTypically 50..150 time‐steps

NP potential not shown here

Page 30: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Model Predictive Direct Current

Control: Step 1

a

b

c

k Npt

t

t

e EE SS

Key ingredients:• Drive model• Extrapolation

Switching horizon, e.g. ‘eSESE’• S: consider all switch transitions• E: extrapolate/extend currents and NPP• e: optional ‘E’

Prediction horizon

NpTypically 50..150 time‐steps

Predict current trajectories for (all)possible

switching sequences

iripβ

iripα

u

NP potential not shown here

Page 31: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Model Predictive Direct Current

Control: Step 2

Evaluate and

minimize

=> Optimal

switching sequence U

Evaluate and

minimize sw. losses

a

b

c

k Npt

t

t

e EE SS

iripβ

iripα

u

NP potential not shown here

Page 32: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Model Predictive Direct Current

Control: Steps 2 & 3

Evaluate and

minimize

=> Optimal

switching sequence U

Evaluate and

minimize sw. losses

a

b

c

k Npt

t

t

e EE SS

tPlanDo

tPlanDo

tPlanDo

k

k+1

k+2

Apply only

the first element of U

iripβ

iripα

u

NP potential not shown here

Page 33: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Performance Index:

Constraints

• short switching

horizon but long prediction

horizon•models

of machine, inverter

and losses

•minimization of switching losses• receding horizon

policy

• tailored

online solution approach

Main features:

Bounds on currents and NP

Discrete‐valued switch positions

Short‐term avg. switching losses (power)

Model of machine and inverter

Outputs (currents and NP)

Model Predictive Direct Current

Control

Restrictions on switch transitions

Page 34: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Performance during Transients

Speed:

we

=0.6 puTorque:

reference steps between T=1 and 0 pu

Torque Stator currents Switch positions

Torque (current) response time of 2 ms

3‐level NPC inverter with 2MVA 

induction machine

Page 35: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Performance at Steady‐State 

FOC withPWM andfc

=270 Hz

MPDCC ‘e(SE)3’

3‐level NPC inverter with 2MVA ind. machinewe

=0.6 pu, Te

=1 pu

Current Current spectrum Switch positions

ITHD

= 7.69%

ITHD

= 4.56%

Psw

= 4.15kW

Psw

= 4.02kWNp

=70

Current

THD

reduced by 40%

(for the same switching losses)Similar to optimal pulse patterns

Page 36: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

MPDCC outperforming OPP

OPPs: for a given switching frequency, minimize the current THD•

MPDCC: for a given current THD, minimize the switching losses

Optimized Pulse Pattern Model Pred. Direct Current Ctrl.

Time [ms] Time [ms]

ITHD

= 8.18 %

Psw

= 1.92 kW

ITHD

= 8.60 %

Psw

= 1.15 kW40% less

5% more

3‐level NPC inverter with 2MVA ind. machinewe

=0.6 pu, Te

=1 pu

Page 37: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Model Predictive Direct Current

Control

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

2

4

6

8

10

12

14

16OPP

PWM

MPDCC e(SE)3MPDCC eSE

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

1

2

3

4

5

6

7PWM

MPDCC e(SE)3

MPDCC eSEOPP

Current TDD vs

switching losses Torque TDD vs

switching losses

Switching losses [%] Switching losses [%]

TDD [%

]

TDD [%

]

Long switching horizon eSESESE

(50‐150 steps): •

Current THD: better than with optimized pulse patterns

Torque THD: similar to PWM

‐50%

Page 38: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Tuning

Current THDTorque THD

Switching losses

Switching frequency

Current bound width [*100]

3‐level NPC inverter with 2MVA IMwe

=0.6 pu, Te

=1 pu, MPDCC with ‘eSE’

In percent, n

ormalized to m

axim

um

Current and torque distortions: linear

function of bound width•

Switching frequency

(and losses): hyperbolic

function of bound width

Page 39: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Classification of MPC Schemes for Electrical Drives

Hysteresis

boundsReference tracking

Model Predictive Control: Direct methods (without a modulator)

Current  control

Torque /  flux ctrl.

Trajectory control

Current  control

Torque /  flux ctrl.

Current  trajectoryFlux 

trajectory

Very short prediction 

horizons (typically one step)

Medium to long prediction 

horizons (20 to 150 steps)

Closed‐loop control of pre‐

computed pulse patterns

Page 40: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Direct Torque Control

Control objectives:•

Keep torque, stator flux

and neutral point

potential within given bounds•

Minimize the switching losses

Control variable:•

Discrete inverter switch positions

0 2 4 6 8 10 12 14 16 18 200.2

0.4

0.6

0.8

Torque

T e [pu]

0 2 4 6 8 10 12 14 16 18 20

0.95

1

1.05

Stator flux magnitude

Psi

s [pu]

0 2 4 6 8 10 12 14 16 18 20

-0.05

0

0.05

Neutral point potential

NP

[pu]

0 2 4 6 8 10 12 14 16 18 20

-101

-101

-101

Switch positions

u abc

Time [ms]

DTC look-up table

u

M

is

Dc-link

Observer

s*

Te*

sTe

Page 41: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Model Predictive Direct Torque

Control

Challenging control problem:•

Nonlinear

Hybrid•

MIMO

Sampling interval Ts

= 25us

0 2 4 6 8 10 12 14 16 18 200.2

0.4

0.6

0.8

Torque

T e [pu]

0 2 4 6 8 10 12 14 16 18 20

0.95

1

1.05

Stator flux magnitude

Psi

s [pu]

0 2 4 6 8 10 12 14 16 18 20

-0.05

0

0.05

Neutral point potential

NP

[pu]

0 2 4 6 8 10 12 14 16 18 20

-101

-101

-101

Switch positions

u abc

Time [ms]

DTC look-up table

u

M

is

Dc-link

Observer

s*

Te*

sTe

replace by Model Predictive DTC

Page 42: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Model Predictive Direct Torque

Control

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

2

4

6

8

10

12

14

16OPP

PWM

MPDTC e(SE)3

MPDTC eSE

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

1

2

3

4

5

6

7PWM

OPP

MPDTC eSEMPDTC e(SE)3

Current TDD vs

switching losses Torque TDD vs

switching losses

Switching losses [%] Switching losses [%]

TDD [%

]

TDD [%

]

Long switching horizon eSESESE

(50‐150 steps): •

Current THD: similar to optimized pulse patterns (OPP)

Torque THD: significantly better than OPP, but at the expense of current THD –

points on curves do not

correspond to each other!

Page 43: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Classification of MPC Schemes for Electrical Drives

Hysteresis

boundsReference tracking

Model Predictive Control: Direct methods (without a modulator)

Current  control

Torque /  flux ctrl.

Trajectory control

Current  control

Torque /  flux ctrl.

Current  trajectoryFlux 

trajectory

Very short prediction 

horizons (typically one step)

Medium to long prediction 

horizons (20 to 150 steps)

Closed‐loop control of pre‐

computed pulse patterns

+

Computational efficiency

Page 44: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Search Tree

Search tree

induced by  optimization problem

Computational burden ≈ number of nodes

So far: full enumeration

time

Not 

candidates

Candidateswitching 

sequence Optimal 

switching 

sequence

E

SS

S

E

Page 45: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Search Tree

time

Not 

candidates

Candidateswitching 

sequence Optimal 

switching 

sequence

E

SS

S

E

Search tree

induced by  optimization problem

Computational burden ≈ number of nodes

So far:

full enumeration

More efficient   implementation

of algorithm

More efficient extension

/  extrapolation step

Reduce number of nodes  explored in search tree by  using Branch & Bound

Approaches to reducecomputation time?

Page 46: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Evolution of the Optimal Cost during Optimization

Iteration step (number of nodes visited)

Cost (kW

)WithoutBranch & Bound

c*

u*

found

Certificate of optimality found

c

Search tree fully explored

Page 47: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Evolution of the Optimal Cost during Optimization

Iteration step (number of nodes visited)

Cost (kW

)

c

cc*

u*

found u*

found

Certificate of optimality found

Certificate of optimality found

c

Search tree fully exploredUpper and lower bound converged

WithBranch & Bound

Page 48: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Computational Effort

Example:

MPDTC with the  switching horizon ’eSSESESE’

Probability distributions:Number of nodes

required to be 

explored to obtain the optimal  cost c*

Full enumeration

B&B

B&B with upper bound onnumber of computations

50% percentile

95% percentile

99% percentile

Page 49: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Performance vs

Computational Burden

Short switching horizon (eSSE): •

B&B => computational burden reduced by factor 5.5

Switching losses and THDs

merely affected

Benefit:

simplify

implementation for short

switching horizons

Page 50: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Performance vs

Computational Burden

Short switching horizon (eSSE): •

B&B => computational burden reduced by factor 5.5

Switching losses and THDs

merely affected

Benefit:

simplify

implementation for short

switching horizons

Benefit:

enable

implementation for long

switching horizons

Long switching horizon (eSSESESE):• B&B => computational burden reduced by factor 13• Switching losses and THDs

merely affected

Page 51: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Performance Results

StandardDTC

MPDTC ‘eSSE’

MPDTC ‘eSSE(SE)2’

ACS 6000, we

=0.6 pu, Te

=1 pu; Same torque bounds, flux bounds relaxed by +/‐

0.01puABB’s simulation environment

Torque Stator flux Switch positions

TTHD

= 100%

TTHD

= 103%

TTHD

= 94%

ITHD

= 100%

ITHD

= 104%

ITHD

= 97%

Psw

= 100%

Psw

= 58%

Psw

= 39%Np

=88

Np

=22

Page 52: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

Summary and Conclusions

Page 53: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Commercial Benefits

Higher rating

of inverter possible–

40%

higher power capability      

(e.g. from 5 MVA to 7 MVA)–

Hardware remains the same 

Standard machines

can be used–

No derating

of machine required

For ‘complicated’

topologies–

MPC is enabling

technology

Fully utilize the drive

hardware

Page 54: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Summary and Conclusions

Goal:

Fully utilize capability

of drive hardware•

Minimize switching losses

per distortions

Achieve very fast

torque and current response

Approach:•

Treat control and modulation problem in one stage

Work in the time‐domain•

Adopt model predictive control

Results:•

MPDxC

family

MP3C

Page 55: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

For More Information

www.ece.auckland.ac.nz/tgey001

Page 56: Model Predictive Control in Medium Voltage Drives · Medium ‐Voltage Drives ... Geyer Model predictive control in medium‐voltage drives May 9, 2011. M (Active) Rectifier Inverter

May 9, 2011Model predictive control in medium‐voltage drivesTobias Geyer

Selected Literature

T. Geyer: ʺLow complexity model predictive control in power electronics and

power 

systemsʺ, PhD thesis, Automatic Control Laboratory, ETH Zurich, Switzerland, Mar. 2005.•

P. Cortés, M. P. Kazmierkowski, R. M. Kennel, D. E. Quevedo, and J. Rodríguez: ʺPredictive 

Control in Power Electronics and Drivesʺ, IEEE Trans. on Industrial Electronics, vol. 55, no. 

12, pp. 4312‐4324, Dec. 2008.•

T. Geyer, G. Papafotiou, and M. Morari: ʺModel predictive direct torque control ‐

part I: 

concept, algorithm and analysisʺ, IEEE Trans. on Industrial Electronics, vol. 56, no. 6, pp. 

1894‐1905, June 2009.•

G. Papafotiou, J. Kley, K. Papadopoulos, P. Bohren, M. Morari: ʺModel predictive direct 

torque control ‐

part II: implementation and experimental evaluationʺ, IEEE Trans. on 

Industrial Electronics, vol. 56, no. 6, pp. 1906‐1915, June 2009.•

T. Geyer: ʺGeneralized model predictive direct torque control: long prediction horizons and 

minimization of switching lossesʺ, Proc. of the 48rd IEEE Conference on Decision and 

Control, Shanghai, China, Dec. 2009.•

T. Geyer: ʺA comparison of control and modulation schemes for medium‐voltage drives: 

emerging predictive control concepts versus field oriented controlʺ, Proc. of the Energy 

Conversion Congress and Exposition, Atlanta, GA, Sep. 2010.•

T. Geyer: ʺModel predictive direct current control for multi‐level convertersʺ, Proc. of the 

Energy Conversion Congress and Exposition, Atlanta, GA, Sep. 2010.