Modulation Techniques for Low Voltage Drives and their ... fileModulation Techniques for Low Voltage...

Slide 1

Modulation Techniques for Low Voltage Drives and

their System Aspects

Ioannis Tsoumas

Senior Scientist

ABB Corporate Research

Baden-Dättwil Switzerland

Slide 2

Variable Speed Drives

Converter Topologies

Modulation Techniques

Evaluation Criteria and Important Drive System Aspects

Conclusion

Outline

Slide 3





Conclusion

Outline

Slide 4

Variable speed drives – What are they ?

+

Transformer

Reduction of the grid

voltage

Power Electronics

+

Motor

Decoupling of the

machine from the grid

Electro-mechanical power

conversion

+

Controller

Control of the motor

currents (fluxes)

+

Auxiliaries

Cooling, breakers,

fuses, etc.

[Source of pictures: ABB]

Slide 5

Variable speed drives – Role of the converter

• Decoupling of the motor from the grid => variable speed operation

• Control of the motor currents (fluxes) => fast torque and speed response

Electric Motor

Mechanical

load

Mechanical

Coupling

Non-Drive End

(NDE)

Grid

~

~

~

~

~ −

−

Rectifier InverterDC-link

Converter

Slide 6

Variable speed drives - Applications

[Source: ABB Website]

Slide 7




Evaluation Criteria and Important System Aspects

Conclusion

Outline

Slide 8

Two level converter (2LC)

Starting from the buck converter …

Vdc

+

−

output filter load

Vdc

+

−

output filter load

Vdc

+

−

output filter load

Vdc

+

−

output filter load

practical

implementation

of the switches

active switch on

active switch off

Slide 9


DC to 3xAC inverter by differential connection of 3-phase load

A

B

C

+− Vdc

N

+

−

+

−

+

−

+ −

O

Slide 10



A

B

C

+− Vdc

N

+

−

+

−

+

−

+ −

O

𝑉𝐴𝑁 = 𝑉𝐴𝑂-𝑉𝑁𝑂

𝑉𝐵𝑁 = 𝑉𝐵𝑂-𝑉𝑁𝑂

𝑉𝐶𝑁 = 𝑉𝐶𝑂-𝑉𝑁0

𝑉𝑁𝑂 =𝑉𝐴𝑂 + 𝑉𝐵𝑂 + 𝑉𝐶𝑂

3

Slide 11



A

B

C

+− Vdc N





3

Slide 12



3~ M

oA

BC

Vdc

N

Vdc

* Vdc is from now on defined as the half of the dc link voltage

Implementation of the switches with IGBTS and antiparallel diodes

Blocking Voltage : 2Vdc





3

Slide 13




3~ M

oA

BC

N

Vdc

Vdc





3

Upper IGBT on

Slide 14

3~ M

oA

BC

N

Vdc

Vdc








3

Lower IGBT on

Slide 15







3

+Vdc

-Vdc

Output voltage AO Output phase voltage AN Output line to line voltage AB+2Vdc

-2VdcPhase current for an

inductive load

+4Vdc/3

+2Vdc/3

-4Vdc/3

-2Vdc/3

Reference voltage

5 levels 3 levels

3~ M

oA

BC

Vdc

N

Vdc

Slide 16

3-Level Neutral Point Clamped Converter (3LNPC2)

Vdc

Vdc

+

−

+

−

clamping

diodes

Slide 17


Vdc

Vdc

+

−

+

−

+

−

+

−

Vdc

Vdc

AO

AO

Connection of the phase to the positive rail of the dc-link

Slide 18

+

−

+

−

Vdc

Vdc


Vdc

Vdc

+

−

+

−

AO

AO

Connection of the phase to the neutral point through the clamping diodes

Slide 19


The clamping diodes limit the necessary

blocking voltage to Vdc

Over proportionally decreased switching

losses compared to 2LC, due to decreased

commutation voltage and decreased

blocking voltage of the semiconductors

Increased conduction losses compared to

2LC (2 devices in series)

Half output voltage steps compared to 2LC

Vdc

Vdc

+

−

+

−

Blocking Voltage : Vdc

AO

+Vdc

− Vdc

Output Voltage VAO

Slide 20

3-Level Active Neutral Point Clamped Converter (3LANPC2)

Vdc

Vdc

+

−

+

−

active

switches

Slide 21

Vdc

Vdc

+

−

+

−

Vdc

Vdc

+

−

+

−

3-Level Active Neutral Point Clamped Converter (3LANPC2)

Additional switching states compared to 3LNPC2 give the possibility of active loss balancing

switching losses

switching losses

Losses can be distributed evenly

Increased semiconductor utilization

Vdc

Vdc

+

−

+

−

3LNPC option to

switch to O

Additional 3LANPC

option to switch to O

O A

OA

OA

Slide 22

3-Level T-type Converter (3LT2C)

+

−

+

−

Vdc

Vdc

Slide 23

+

−

+

−

Vdc

Vdc

+

−

+

−

Vdc

Vdc


AO

Connection of the phase to the positive rail of the dc-link

AO

Slide 24


Connection of the phase to the neutral point

+

−

+

−

Vdc

Vdc

AO

+

−

+

−

Vdc

Vdc

AO

Slide 25


The conventional 2LC topology is extended

with an active bidirectional switch to the dc-

link neutral point

Due to the reduced blocking voltage the

middle switch has low switching losses and

acceptable conduction losses

Contrary to 3LNPC2 there is no series

connection of devices that have to block the

whole dc-link voltage lower conduction

losses


+Vdc

− Vdc

Output Voltage VAO

+

−

+

−

Vdc

Vdc


Blocking Voltage : Vdc

AO

Slide 26

3-Level Flying Capacitor Converter (3LFC2)

+

−

+

−

Vdc

+−

Vdc

Vdc

Slide 27

+

−

+

−

Vdc

+−

Vdc

Vdc


AO

Connection for output voltage VAO equal to Vdc

Vdc

Vdc

+

−

+

−

Vdc

+− AO

Slide 28


Connection for output voltage VAO equal to zero

+

−

+

−

Vdc

+−

Vdc

Vdc

AO

Vdc

Vdc

+

−

+

−

Vdc

+− AO

Slide 29

+

−

+

−

Vdc

+−

Vdc

Vdc


Blocking Voltage : Vdc As in the 3L(A)NPC the blocking voltage of

the devices is Vdc

As in the 3L(A)NPC we have over

proportionally decreased switching losses

compared to 2LC, due to decreased

commutation voltage and decreased

blocking voltage of the semiconductors

As in the 3L(A)NPC there we have

increased conduction losses because of

two devices in series that are conducting


+Vdc

− Vdc

Output Voltage VAO

AO

Slide 30





Conclusion

Outline

Slide 31

Control Strategies Classification

Voltage Source Inverter

Electrical Motor

Controller

Torque, Speed, Current, Flux

Reference

Switching signals

Fundamental VoltageComponent

Modulator

Modulation-Based Controller

Voltage Source Inverter

Electrical Motor

Controller


Reference

Switching signals

Controller without Modulator

(e.g. Field Oriented Control)

(e.g. Direct Torque Control,

Direct Model Predictive Control)Voltage Source Inverter

Electrical Motor

Controller


Reference

Switching signals

Controller with Embedded Modulator(e.g. Model Predictive Pulse Pattern Control)

Slide 32

Modulation Techniques Classification

CB-PWM SVM

On-Line

Natural and Regular Sampling

Synchronous – Asynchronous

Continuous – Discontinuous

Off-Line

Pulse Width Modulation

Optimized Pulse Patterns

(OPPs)

(also known as synchronous

optimal modulation)

Slide 33

Modulation Techniques – Carrier Based PWM

Objectives

1) Generate the desired fundamental component

2) Minimize the side effects

How can a sinusoid with a specific amplitude be approximated by a switched waveform?

1st approach: Consider only the switching period and calculate the

fundamental component from the volt-second equality

�

𝑇𝑝

𝑣∗𝑑𝑡 = �

𝑡𝑜𝑛

𝑉𝑑𝑐𝑑𝑡 ⇒

𝑇𝑝 � 𝑣∗ 𝑡𝑠 = 𝑡𝑜𝑛 � 𝑉𝑑𝑐 ⇒

𝑣∗ 𝑡𝑠 =𝑡𝑜𝑛

𝑇𝑠� 𝑉𝑑𝑐

time instant of sampling

−𝑉𝑑𝑐

+𝑉𝑑𝑐

𝑣∗ 𝑡

𝑣∗ 𝑡

Slide 34


Objectives




+𝑉𝑑𝑐

−𝑉𝑑𝑐

𝑣∗ 𝑡

m=�𝑣∗

𝑉𝑑𝑐

𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑖𝑛𝑑𝑒𝑥:

Carrier Based Pulse Width Modulation (CB-PWM) for 2L Converters

natural sampling

Slide 35


Objectives





𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 (𝐻𝑧)

𝑎𝑚

𝑝𝑙𝑖

𝑡𝑢𝑑

𝑒(𝑛

𝑜𝑟𝑚

𝑎𝑙𝑖

𝑧𝑒𝑑

𝑡𝑜𝑉

𝑑𝑐)

𝑓𝑢𝑛𝑑𝑎𝑚𝑒𝑛𝑡𝑎𝑙ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐 1𝑥𝑓𝑐

1𝑥𝑓𝑐

𝑠𝑖𝑑𝑒𝑏𝑎𝑛𝑑ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐𝑠

2𝑥𝑓𝑐3𝑥𝑓𝑐 4𝑥𝑓𝑐 5𝑥𝑓𝑐

2𝑥𝑓𝑐

3𝑥𝑓𝑐 4𝑥𝑓𝑐 5𝑥𝑓𝑐

𝑓𝑢𝑛𝑑𝑎𝑚𝑒𝑛𝑡𝑎𝑙ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐

Harmonics at multiples of the

carrier frequency and their

sidebands

Common mode harmonics

included in the phase-to-neutral

point voltage

Only differential mode harmonics

in the phase-to-star point and

phase-to-phase voltage

natural sampling

Slide 36


Objectives





regular symmetric sampling (sampling once per carrier period)

Slide 37


Objectives





regular asymmetric sampling (sampling twice per carrier period)

Slide 38


Objectives





regular asymmetric sampling


𝑎𝑚

𝑝𝑙𝑖

𝑡𝑢𝑑

𝑒(𝑛

𝑜𝑟𝑚

𝑎𝑙𝑖

𝑧𝑒𝑑

𝑡𝑜𝑉

𝑑𝑐)

Left and right sideband harmonics not equal

Slide 39


Objectives





regular symmetric sampling


𝑎𝑚

𝑝𝑙𝑖

𝑡𝑢𝑑

𝑒(𝑛

𝑜𝑟𝑚

𝑎𝑙𝑖

𝑧𝑒𝑑

𝑡𝑜𝑉

𝑑𝑐)

Additional harmonic components appear:

- even sidebands at odd multiples of the carrier frequency

- odd sidebands at even multiples of the carrier frequency

Slide 40


Objectives


2) Minimize the side effects (harmonic current)

o

A

B

CN

~~~

LOAD

If the load star point impedance to the ground is considered

infinite, we have an additional degree of freedom for the

modulation : the Common Mode Voltage (CMV)

Advantages of adding a common mode component:

Increase of the overmodulation limit and thus the inverter

output voltage

Transfer of the harmonic energy to higher frequencies

and thus better filtering and more sinusoidal current for an

inductive load

Addition of a common mode voltage (CMV) to the reference signal

Slide 41


Objectives



𝑚 � 𝑠𝑖𝑛𝜔1𝑡

𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑠𝑖𝑔𝑛𝑎𝑙

1

6𝑚 � 𝑠𝑖𝑛𝜔1𝑡 or

1

4𝑚 � 𝑠𝑖𝑛𝜔1𝑡

𝑚=1.1

1/6 : max. output voltage

1/4 : optimal harmonic performance

𝑜𝑣𝑒𝑟𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑚𝑖𝑡

𝑎𝑚

𝑝𝑙𝑖

𝑡𝑢𝑑

𝑒(𝑛

𝑜𝑟𝑚

𝑎𝑙𝑖

𝑧𝑒𝑑

𝑡𝑜𝑉

𝑑𝑐)

𝑡𝑖𝑚𝑒 (𝑠)

Typical common mode voltages added to the sinusoidal reference

Slide 42


Objectives





𝑎𝑚

𝑝𝑙𝑖

𝑡𝑢𝑑

𝑒(𝑛

𝑜𝑟𝑚

𝑎𝑙𝑖

𝑧𝑒𝑑

𝑡𝑜𝑉

𝑑𝑐)

CMV

𝑚=0.9

𝑚=0.9 Transfer of harmonic energy

to higher frequencies

Slide 43


Objectives




𝑚 � 𝑠𝑖𝑛𝜔1𝑡

𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑠𝑖𝑔𝑛𝑎𝑙

𝐦𝐚𝐱[𝑚 � 𝑠𝑖𝑛𝜔1𝑡, 𝑚 � 𝑠𝑖𝑛(𝜔1𝑡 − 2𝜋/3), 𝑚 � 𝑠𝑖𝑛(𝜔1𝑡 + 2𝜋/3)] + 𝐦𝐢𝐧[𝑚 � 𝑠𝑖𝑛𝜔1𝑡, 𝑚 � 𝑠𝑖𝑛(𝜔1𝑡 − 2𝜋/3), 𝑚 � 𝑠𝑖𝑛(𝜔1𝑡 + 2𝜋/3)]

2

𝑚=1.1

𝑜𝑣𝑒𝑟𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑚𝑖𝑡

𝑎𝑚

𝑝𝑙𝑖

𝑡𝑢𝑑

𝑒(𝑛

𝑜𝑟𝑚

𝑎𝑙𝑖

𝑧𝑒𝑑

𝑡𝑜𝑉

𝑑𝑐)

𝑡𝑖𝑚𝑒 (𝑠)

𝑚 =2

3= 1.1547

Slide 44


Objectives




𝑎𝑚

𝑝𝑙𝑖

𝑡𝑢𝑑

𝑒(𝑛

𝑜𝑟𝑚

𝑎𝑙𝑖

𝑧𝑒𝑑

𝑡𝑜𝑈

𝑑𝑐)


CMV

𝑚=0.9

𝑚=0.9

Slide 45


Objectives




Increased utilization od dc-link voltage

Slide 46


Measurement of the phase current fundamental component

with appropriate sampling only the fundamental current harmonic is measured

fundamental

current harmonic

total current

Slide 47


Discontinuous modulation

PWM Reference Phase to neutral point waveform

Line-to-Line waveform

decrease of switching frequency to only 2/3 of

the continuous modulation sw. frequency

decrease of switching losses up to 50% for

cosφ=1

Slide 48


CB-PWM for three-level converters Phase Disposition (PD)

Phase Opposition Disposition (POD)

𝑆1

𝑆1

𝑆1

𝑆21

0

1

0

𝑆2

𝑆2

Ou

tpu

t V

olt

ag

e

No

rmali

zed

to

Vd

c

Refe

ren

ce a

nd

Carr

iers

Sw

itch

ing

Fu

nc

tio

ns

𝑆1

𝑆210

1

0

Ou

tpu

t V

olt

ag

e

No

rmali

zed

to

Vd

c

Refe

ren

ce a

nd

Carr

iers

Sw

itch

ing

Fu

nc

tio

ns

PD has superior harmonic performance

Slide 49


CB-PWM for three-level converters with flying capacitor

inherent balancing of the flying

capacitor

the switching frequency is twice the

carrier frequency because two

devices are switched within a

modulation period

The higher the switching frequency,

the lower the capacitor voltage

ripple

𝑆1

𝑆1

𝑆2

𝑆2

Phase Shifted Carrier PWM (PSCPWM)

Ou

tpu

t V

olt

ag

e

No

rmali

zed

to

Vd

c

Refe

ren

ce a

nd

Carr

iers

Sw

itch

ing

Fu

nc

tio

ns

𝑆1

𝑆2

+

−

+

−

Vdc

+−

Vdc

Vdc

1

0

1

0

+

−

Slide 50

Modulation Techniques – Optimized Pulse Patterns

Objectives




2nd approach: Consider the fundamental period and calculate the fundamental component from the

Fourier integral

-Vdc

+Vdc

V�𝑣∗ = 𝑉𝑑𝑐 �

2

𝜋�

0

𝜋

𝑓 𝜔𝑡 � sin𝜔1𝑡 � 𝑑𝜔𝑡 ⇒

�𝑣∗ = 𝑉𝑑𝑐 �4

𝜋�

𝑖=1

𝑁

Δu𝑖 � cos𝑎𝑖

N : number of switching angles in a quarter wave

Δu𝑖 : switching function step at switching angle 𝑎𝑖

e.g. for 3-level inverter and quarter wave symmetry

Slide 51


Calculation of the harmonic current

1) Frequency Domain

𝐼ℎ,𝑟𝑚𝑠 = �

ν=5,7,11,13…

∞𝚤ν2

2

-Vdc

+Vdc

V �𝑣v = 𝑉𝑑𝑐 �1

𝑣

4

𝜋�

𝑖=1

𝑁

𝛥𝑢𝑖 � cosν𝑎𝑖 ,

ν: ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐 𝑜𝑟𝑑𝑒𝑟

Harmonics calculation example for a three-level waveform

𝚤ν =�𝑣ν

ν= 𝑉𝑑𝑐 �

1

ν2

4

𝜋�

𝑖=1

𝑁

𝛥𝑢𝑖 � cosν𝑎𝑖

Slide 52


Calculation of the harmonic current

2) Time Domain𝐼ℎ,𝑟𝑚𝑠 = 𝐼𝑟𝑚𝑠

2 −𝚤ν=12

2

Example for a three-level waveform

𝐼𝑗 =1

𝜔1𝐿𝑘�

𝑖=𝑁+1,𝑁,…

𝑗+1

�𝑣𝐴𝐵[𝑎𝑖,𝑎𝑖−1]

� (𝑎𝑖 − 𝑎𝑖−1)

𝐼 𝑟𝑚𝑠 =2

𝜋�

𝑗=𝑁+1,𝑁,…

1𝐼𝑗

2 + 𝐼𝑗𝐼𝑗−1 + 𝐼𝑗−12

3(𝑎𝑗 − 𝑎𝑗−1)

𝑣𝐴𝐵

Slide 53


Objectives



Different optimization criteria (cost functions) can be considered:

- harmonic current

- harmonic motor losses

- motor noise

- common mode voltage

- converter switching losses

Multi-objective optimization also possible

f(α)

α2(0)

α1(0)0 10 20 30 40 50 60 70 80 90

0

9080

7060

5040

30

10

0

2

4

6

10

8

x10-4

20

non-convex cost functions with many local minima!

Slide 54


Example: 2L waveform when having only 2 switching angles in the range 0-π/2

π/2 π 3π/2 2π

α1 α2 π-α2 π-α1 π+α1 2π-α1 π+α2

ω1t

-Vdc

+Vdc

V

2π-α2

� 𝒊𝝂𝟐

�𝑢𝑣 = 𝑈𝑑𝑐 �1

𝑣

4

𝜋1 + 2 �

𝑖=1

2

𝛥𝑢𝑖 � 𝑐𝑜𝑠𝑣𝑎𝑖 ,

𝑣: ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐 𝑜𝑟𝑑𝑒𝑟

��𝑣 =�𝑢𝑣

𝑣= 𝑈𝑑𝑐 �

1

𝑣2

4

𝜋1 + 2 �

𝑖=1

2

𝛥𝑢𝑖 � 𝑐𝑜𝑠𝑣𝑎𝑖

Slide 55


Example: 2L waveform when having only 2 switching angles in the range 0-π/2

π/2 π 3π/2 2π

α1 α2 π-α2 π-α1 π+α1 2π-α1 π+α2

ω1t

-Vdc

+Vdc

V

2π-α2

red path shows the

global minima for each

modulation index

Lines of constant modulation index:

Slide 56


Calculation of the harmonic current in induction motors

��S = 𝑅S𝚤S +d

d𝑡𝛹S + 𝑗𝜔k𝛹S (1)

��R = 𝑅R𝚤R +d

d𝑡𝛹R + 𝑗 𝜔k − 𝜔 𝛹R (2)

𝛹S = 𝐿S𝚤S + 𝐿m𝚤R (3)

𝛹R = 𝐿m𝚤S + 𝐿R𝚤R (4)

𝑰𝒏𝒅𝒖𝒄𝒕𝒊𝒐𝒏 𝒎𝒐𝒕𝒐𝒓 𝒆𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝒄𝒊𝒓𝒄𝒖𝒊𝒕 𝒊𝒏 𝒕𝒉𝒆 𝒂𝒓𝒃𝒊𝒕𝒓𝒂𝒓𝒚 𝒓𝒆𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒇𝒓𝒂𝒎𝒆

𝐿S= 𝐿S𝑙 + 𝐿m (5)𝐿R= 𝐿R𝑙 + 𝐿m (6)

𝚤S =𝛹S − 𝑘R𝛹R

𝐿S′

𝐿𝑆′ = 𝐿S𝑙 + 𝐿𝑚||𝐿R𝑙

(3)

(4)𝚤R =

𝛹R − 𝑘S𝛹S

𝐿R′

𝐿𝑅′ = 𝐿R𝑙 + 𝐿𝑚||𝐿S𝑙

𝑘𝑆 =𝐿m

𝐿𝑆

𝑘𝑅 =𝐿m

𝐿𝑅

𝒕𝒓𝒂𝒏𝒔𝒊𝒆𝒏𝒕𝒊𝒏𝒅𝒖𝒄𝒕𝒂𝒏𝒄𝒆

𝜔k = 0

��R = 0


d𝑡𝛹S (7)

0 = 𝑅R𝚤R +d

d𝑡𝛹R − 𝑗𝜔𝛹R (8)

+ ─+

─

+

−

+ ─

Slide 57


Calculation of the harmonic current in induction motors


d𝑡𝛹S

𝛹S = 𝐿S𝚤S + 𝐿m𝚤R

𝚤R =𝛹R − 𝐿m𝚤S

𝐿R

𝑺𝒒𝒖𝒊𝒓𝒆𝒍𝒍 − 𝒄𝒂𝒈𝒆 𝒊𝒏𝒅𝒖𝒄𝒕𝒊𝒐𝒏 𝒎𝒐𝒕𝒐𝒓 𝒆𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝒄𝒊𝒓𝒄𝒖𝒊𝒕 𝒊𝒏 𝒕𝒉𝒆 𝒔𝒕𝒂𝒕𝒊𝒐𝒏𝒂𝒓𝒚 𝒓𝒆𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒇𝒓𝒂𝒎𝒆

��S = 𝑅S𝚤S + (𝐿S −𝐿𝑚

2

𝐿R)

d

d𝑡𝚤S+

𝐿𝑚

𝐿R

d

d𝑡𝛹R

𝐿𝑆′

≈ 𝑗𝜔S 𝛹R 𝑒𝑗𝜔S𝑡𝐿𝑆

′ : 𝑡𝑟𝑎𝑛𝑠𝑖𝑒𝑛𝑡 𝑖𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 (𝑎𝑙𝑠𝑜 𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑 𝑡𝑜 𝑎𝑠 𝑡𝑜𝑡𝑎𝑙 𝑙𝑒𝑎𝑘𝑎𝑔𝑒 𝑖𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒)

𝛹R 𝑖𝑠 𝑣𝑒𝑟𝑦 𝑐𝑙𝑜𝑠𝑒 𝑡𝑜 𝑎 𝑠𝑖𝑛𝑢𝑠𝑜𝑖𝑑𝑎𝑙 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑏𝑒𝑐𝑎𝑢𝑠𝑒 𝑖𝑠 𝑓𝑖𝑙𝑡𝑒𝑟𝑒𝑑 𝑏𝑦 𝑡ℎ𝑒 𝑙𝑎𝑟𝑔𝑒 𝑟𝑜𝑡𝑜𝑟 𝑡𝑖𝑚𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝐿R/𝑅R

The voltage source is considered zero for

the higher harmonics

The stator resistance is usually neglected

and only the transient reactance is

considered for the calculation of the current

harmonics

++

─−

Similar equivalent circuit considered for a synchronous motor (with total stator inductance)

Slide 58


Switching are angles

computed off-line and stored

e.g. in a Compact Flash Card

The controller

selects different

switching angles of

different OPPs

depending on the

output voltage and

the output

frequency of the

converter

102,3 %

116

100

SVM

OPP 1

Modulation index (%)

Output frequency (Hz)

OPP 2

OPP 3

OPP 4

OPP 5

100

CB-PWM

The design of the voltage-frequency table is also an optimization problem!

Slide 59

Modulation Techniques – Space Vector Modulation

Space Vector Modulation (SVM) for two level converters

Space Vector Transformation

𝑣𝑑

𝑣𝑞

𝑣0

=2

3

1 −1

2−

1

2

03

2−

3

21

2

1

2

1

2

𝑣𝑎

𝑣𝑏

𝑣𝑐

𝑣𝑑 corresponds to the phase-to-star point voltage

𝑣𝑞 corresponds to the phase-to-phase voltage

𝑣0 corresponds to the common mode voltage

Inverter switching states as space vectors

q-axis

d-axis

Note:

The symbol “P” is used in the space vector three-letter sequence

when the corresponding phase is connected to the positive dc-link rail.

The symbol “N” is used when the corresponding phase connected to

the negative dc-link rail.

Slide 60



Inverter switching states

Sequence of voltage vectors in the 1st sector:

Every converter leg can be switched at a certain

frequency and according to a certain pattern.

8 possible switching states.

Space Vector Modulation (SVM): “online”

technique the switching angles are computed

“on the run”.

Objective: control the amplitude of the

fundamental and minimize the harmonics.

Reference vector is approximated by a

combination of neighboring “active” vectors and

“zero vectors”.

Equivalent CB-PWM Reference

(known as Min-Max)

��𝑟𝑒𝑓 � 𝑇𝑠𝑤 =𝑡1

2𝑉1 +

𝑡2

2𝑉2

volt-second equality From the equality of the real and the imaginary part t1 and t2 can be computed

The rest of the sw. period is distributed equally between the two zero vectors

𝑉0 → 𝑉1 → 𝑉2 → 𝑉7 → 𝑉2 → 𝑉1 → 𝑉0

SVM is an intrinsically regular sampled process !

Slide 61



Overmodulation Limit

vector length : 4

3𝑉𝑑𝑐

4

3𝑉𝑑𝑐𝑐𝑜𝑠300 =

4

3𝑉𝑑𝑐

3

2=

2 3

3𝑉𝑑𝑐 =

2

3𝑉𝑑𝑐 ≈ 1.1547 � 𝑉𝑑𝑐

𝑻𝒉𝒆 𝒐𝒗𝒆𝒓𝒎𝒐𝒅𝒖𝒍𝒂𝒕𝒊𝒐𝒏 𝒍𝒊𝒎𝒊𝒕 𝒊𝒔 𝒅𝒆𝒇𝒊𝒏𝒆𝒅 𝒃𝒚 𝒕𝒉𝒆 𝒓𝒂𝒅𝒊𝒖𝒔𝒐𝒇 𝒕𝒉𝒆 𝒄𝒊𝒓𝒄𝒍𝒆 𝒕𝒉𝒂𝒕 𝒕𝒐𝒖𝒄𝒉𝒆𝒔 𝒕𝒉𝒆 𝒉𝒆𝒙𝒂𝒈𝒐𝒏:

Slide 62


Discontinuous Space Vector Modulation (SVM) for 2L Converters

01277210 >>>>>>> VVVVVVVV

DPWM1 (600 disc.) DPWM3 (300 disc.) Generalized Discontinuous SVM

PWM Reference PWM Reference

Only one zero vector is applied per

switching period

Slide 63

Modulation Techniques – Comparison of CB-PWM

Weighted THD for different reference signals (two level)

Same switching frequencySwitching frequency of discontinuous

modulation increased by 3/2

𝑊𝑇𝐻𝐷 =∑𝜈=2

∞ 𝑉𝜈𝜈

2

𝑉1, where ν is the harmonic order

Slide 64


Space Vector Modulation (SVM) for three level converters

Three categories of vectors:

small, large, medium

Redundant small vectors

Typically sequences of the

three nearest vectors are

employed

large

vector

medium

vector

small

vector

Slide 65


Space Vector Modulation (SVM) for three level converters

Same voltage vector but different zero sequence

voltage and direction of neutral point current

[Source: Ogasawara & Akagi, Analysis of variation of neutral point potential in

neutral-point-clamped voltage source PWM inverters, IEEE 1993]

Redundancy of small vectors can be

utilized for neutral point balancing:

Slide 66

Modulation Techniques – Summary

Characteristics of the CB-PWM/SVM

Constant switching frequency (can be varied if necessary, e.g. wobbling, but it

is not an inherent characteristic)

Asynchronous modulation

Higher harmonics with frequencies k·fc ± l·f1 , where k, l positive integers

Change of the switching frequency during operation can be easily made

Simple computation of the fundamental harmonic for control purposes

Fast dynamic response with classic PI controllers

Overmodulation is possible at the expense of higher harmonic content, non-

linearity of the output voltage, higher complexity in the calculation of the

fundamental harmonic

Slide 67


Characteristics of the discontinuous CB-PWM/SVM

Similar characteristics to continuous SVM

There is no switching in one phase for 60° (or 120°in some versions)

The average switching frequency reduces to 2/3 compared to normal SVM

For certain combinations of reference signals and cosφ the switching losses

reduce to only 50% (e.g. DPWM1 and cosφ=1)

Increase of the harmonic content, motor losses, motor temperature rise for the

same carrier frequency

Better harmonic performance than continuous CB-PWM for high modulation

indices if the carrier frequency is increased in order to have the same average

switching frequency

Closer to linearity than normal SVM in the overmodulation region

Slide 68


Characteristics of the OPPs

Synchronous modulation

Harmonics with frequencies n·f1

Switching frequency proportional to output frequency

Change of the switching frequency during operation requires storage of

additional OPPs

Calculation of the optimal switching angles becomes very time consuming for

high pulse number (ratio of switching to fundamental frequency)

Slide 69


Characteristics of the OPPs

The computation of the fundamental harmonic is not an easy task as in

SVM/CB-PWM

Transition between OPPs is not trivial

Slow dynamic response compared to SVM when classic PI controllers are

employed

Fast dynamic response only when non-linear controllers are employed (e.g.

MP3C)

Linear relationship of modulation index and output voltage in the

overmodulation region

Increased converter output voltage and low harmonic content at the same time

possible

Slide 70





Conclusion

Outline

Slide 71

Modulation Techniques – Evaluation criteria

Typical evaluation criteria

Dynamic performance of closed-loop control

Converter switching losses versus harmonic current

Overmodulation characteristics

Neutral point / flying capacitor voltage ripple for 3LNPC (and T-Type) / 3LFC converters

Complexity of dynamic balancing for neutral point or flying capacitor voltage

Additional important drive system aspects

Converter and motor losses

Motor electromagnetic noise

Common mode voltage

Slide 72

Drive System Losses

EN 50598-2 : Losses distribution for a 400 kW reference Power Drive System (PDS)

The motor harmonic losses and the converter switching losses are directly influenced by the modulation

Slide 73

Motor Electromagnetic Noise

[Source: Tsoumas et al., International Conference on Electrical Machines, Berlin 2014]

Direction and spatial order of the radial force waves

𝑝𝑚 𝑡, 𝜑𝑥 =𝐵2(𝑡, 𝜑𝑥)

2𝜇0

Magnetic pressure

��1

��ℎ1 ��ℎ2

��1

Slide 74


[Source: Tsoumas et al., International Conference on Electrical Machines, 2014]

Frequencies of the dominating voltage harmonics in SVM

and of the corresponding radial force waves

𝑝𝑚 𝑡, 𝜑𝑥 =𝐵2(𝑡, 𝜑𝑥)

2𝜇0

Magnetic pressure

𝑉(f)

𝑃(f)

Slide 75

Motor Electromagnetic NoiseMeasured Sound Pressure Level

[Source: Tsoumas et al., IEEE Transactions on Industry Applications, 2014]

Randomized SVM does not reduce the noise level even if it sounds better!

Increase of the switching frequency doesn’t always decrease the noise

level, because additional strong vibration modes may be excited

Slide 76


[Source: Tsoumas et al., IEEE Transactions on Industry Applications, 2014]

The sound pressure level evolution follows the same pattern with the

corresponding current harmonics

Characteristic pattern in the case of SVM

Slide 77

Common mode voltage

The neutral-to-ground impedance is not infinite

The ground leakage current that will flow through

this impedance depends on the common mode

voltage and the system grounding

The common mode voltage (or part of it) will

appear through a capacitive voltage divider on the

bearings and cause electric discharges.

Slide 78

Common mode voltage

Voltage between converter neutral point and load star point

2L Inverter with load

𝑣AO = 𝑣A𝑁 + 𝑣NO = 𝐿A

𝑑𝑖𝐴

𝑑𝑡+ 𝑒A + 𝑣NO

𝑣BO = 𝑣BN + 𝑣NO = 𝐿B

𝑑𝑖𝐵

𝑑𝑡+ 𝑒B + 𝑣NO

𝑣CO = 𝑣CN + 𝑣NO = 𝐿C

𝑑𝑖𝐶

𝑑𝑡+ 𝑒C + 𝑣NO

𝑣N𝑂 =1

3(𝑣AO + 𝑣BO+𝑣CO)

−1

3(𝑒A+𝑒B+𝑒C) −

1

3(𝐿A

𝑑𝑖𝐴

𝑑𝑡+ 𝐿B

𝑑𝑖𝐵

𝑑𝑡+ 𝐿C

𝑑𝑖𝐶

𝑑𝑡)

For a symmetrical 3-phase load with sources that do not contain

any common mode components the above equation becomes

𝑣N𝑂 =1

3(𝑣A𝑂 + 𝑣B𝑂+𝑣C𝑂)

Equivalent circuit

--> The voltage 𝑣N𝑂 equals the common mode voltage

o

A

B

CN

~~~

LOAD

N

~

~

~

~

~

~

O

vNO

vAO

vBO

vCO

iA

iB

iC

vAN

vBN

vCN

eA

eB

eC

LA

LB

LC

Slide 79

Common mode voltage

Two level converter

1

1/3

-1/3

-1

Slide 80

Common mode voltage

[Source of the waveform: Tischmacher, Tsoumas et al., EPE 2015]

Diode Rectifier + 2L converter

Inverter CMV and the voltages of the positive and the negative DC rail to ground

Oscillation of the DC-link rails at three times the fundamental is superimposed to the inverter CMV !

Slide 81

Common mode voltage

Three level converter

2/31/3

-1/3

-2/3

Slide 82

Common mode voltage


Optimized pulse pattern with only two switching angles

• Red path corresponds to the global minima for

each modulation index between 0 and π/4

• Grey path shows the switching angle values for

zero CMV

Slide 83

Common mode voltage


Optimized pulse pattern with only two switching angles

Significant increase of harmonic current

Decrease of maximum possible modulation index

𝑇𝐷𝐷 =∑𝜈=2

∞ 𝐼𝜈2

𝐼1𝑁,

where ν is the harmonic order

Slide 84

Common mode voltage

Motor high frequency equivalent circuit

Bearing Voltage Ratio (BVR) :𝑈𝑏

𝑈𝑁0=

𝐶𝑤𝑟

𝐶𝑤𝑟+𝐶𝑟𝑓+2𝐶𝑏

BVR ≈ 0.03 …0.1

HF circuit diagramm of an electric motor

Cwr

Cwf

Cb Crf Cb

UN0 Cwf : winding-to-frame capacitance

Cwr : winding-to-rotor capacitance

Crf : rotor-to-frame capacitance

Cb : bearing capacitance

UN0 : Common Mode Voltage (CMV)

Ub

Ub : Bearing Voltage

Slide 85

Common mode voltage

Motor high frequency equivalent circuit

Bearing Voltage Ratio (BVR) :𝑈𝑏

𝑈𝑁0=

𝐶𝑤𝑟

𝐶𝑤𝑟+𝐶𝑟𝑓+2𝐶𝑏

BVR ≈ 0.03 …0.1

HF circuit diagramm of an electric motor

Cwr

Cwf

Cb Crf Cb

UN0 Cwf : winding-to-frame capacitance

Cwr : winding-to-rotor capacitance

Crf : rotor-to-frame capacitance

Cb : bearing capacitance

UN0 : Common Mode Voltage (CMV)

Ub

Ub : Bearing Voltage

Motor Power (kW) BVR

11 kW SH 160mm 2.5%

11 kW SH 160mm 7.5%

110 kW SH 280mm 3.5%

110kW SH 280mm 2.5%

500 kW SH 400mm 7.5%

[Source: A. Mütze, Dissertation, TU Darmstadt 2004]

(the motors with the same power levels

come from different manufacturers)

Slide 86

Common mode voltage

Electric discharge bearing currents

[Source of the waveforms: A. Binder, ICEM 2016 Tutorial]

Cb

Rb

Breakdown of lubricant

Slide 87

Common mode voltage


[Source: Mütze, Binder et al., What can bearings bear, IEEE Industry Applications Magazine 2006]

fluting gray trace

Slide 88

Common mode voltage


[Source: Tischmacher, Bearing Wear Condition Identification on Converter-Fed Motors, SPEEDAM 2018]

Different grades of bearing damages

Slide 89

Common mode voltage

Circulating HF bearing currents

The common mode components of

the three phases do not add to zero

The net current creates a net flux

linkage ΦC surrounding the motor

shaft

𝑅𝑖𝑛𝑔 𝑓𝑙𝑢𝑥: 𝛷𝐶 = 𝜇𝐹𝑒 � 𝐻(𝑡) � 𝐴𝐹𝑒

𝐴𝑚𝑝𝑒𝑟𝑒′𝑠 𝑙𝑎𝑤: �𝐻𝑑𝑠 = 𝑁𝑠 � 𝛴𝐼

𝛴𝐼 = 2 � 𝛥𝐼𝑎 + 2 � 𝛥𝐼𝑏 + 2 � 𝛥𝐼𝑐

For a more detailed analysis see for example Chan and Lipo, «Circulating type motor bearing current in inverter

drives », IEEE Industry Applications Magazine,1998

Ia + ΔIaIa - ΔIa

ring flux ΦC

Slide 90

Common mode voltage


HF common mode ring flux ΦC induces according to Faraday’s law a shaft voltage ush

in the loop Ce of stator housing, bearings and rotor shaft

A circulating HF parasitic current is driven by the shaft voltage ush via the bearings

𝐹𝑎𝑟𝑎𝑑𝑎𝑦′𝑠 𝑙𝑎𝑤 𝑎𝑙𝑜𝑛𝑔 𝑙𝑜𝑜𝑝 𝐶𝑒:

𝑢𝑠ℎ = �𝐸𝑠ℎ𝑑𝑠 = −𝑑 ⁄𝛷𝐶 𝑑 𝑡

Stator winding

Stator

Stator

Rotor

ShaftShaft

bearing

bearing

Electric loop Ce

shaft voltage ush

ring flux ΦC

ring flux ΦC

bearing

bearing

Slide 91

Common mode voltage


[Source of the waveforms: A. Binder, ICEM 2016 Tutorial]

The shape of the circulating bearing current waveform resembles to the waveform of the

stator ground current

Slide 92

A further converter-motor system aspect

Motor Insulation Voltage Stress 𝒖𝒔𝒕𝒆𝒑,𝒎𝒐𝒕 =

𝒖𝒔𝒕𝒆𝒑,𝒊𝒏𝒗 + 𝒓𝒎𝒐𝒕 � 𝒖𝒔𝒕𝒆𝒑,𝒊𝒏𝒗

Slide 93

A further converter-motor system aspect Motor Insulation Voltage Stress

Oscillation of voltage at motor side due to wave reflection at

both ends of loss-free cable

The maximum possible voltage step at

the motor will appear if tr < 2 · tp,

where tr is the voltage rise time and

tp the propagation time

Critical length calculation:

𝒕𝒓 = 𝟐 � 𝒕𝒑= 𝟐𝒍𝒄𝒂𝒃𝒍𝒆

𝒗𝒑=> 𝒍𝒄𝒂𝒃𝒍𝒆 =

𝒗 � 𝒕𝒓

𝟐

𝒗𝒑 is approx. equal to half the

speed of light in vacuum, i.e.

150m/μs

For a rise time of 1μs the critical

length is approx. 75m

𝒗𝒐𝒍𝒕𝒂𝒈𝒆 𝒂𝒕𝒙 = 𝟎

𝒗𝒐𝒍𝒕𝒂𝒈𝒆 𝒂𝒕𝒙 = 𝒍𝒄𝒂𝒃𝒍𝒆

𝑽𝒅𝒄

𝑽𝒅𝒄

Slide 94


[Source of the waveforms: Hentschel et al., «Beanspruchung der Wicklungsisolierung

von Drehstrommaschinen», Elektrotechnische Zeitschrift, 1993]

Slide 95


Measures to reduce dv/dt and common mode voltage

These filters do not suppress the common mode voltage

dv/dt filter

Steep dv/dt slope reduced

Current ripple (harmonics) still present

Nearly sinusoidal line-to-line voltage

Current ripple (harmonics) removed

Much bigger and more expensive

than dv/dt filter

sine filter

Slide 96


Measures to reduce dv/dt and common mode voltage

L-C low pass filter with direct connection to the DC link to suppress the common mode

harmonics

Usually available only for small power ratings

This type of filter reduces all paracitic HF current effects in the motor,

because the common mode voltage is reduced

Slide 97





Conclusion

Outline

Slide 98

Conclusion

The modulation is an important system parameter which influences significantly

the drive system performance

The selection of the appropriate modulation techniques for a specific drive

system and their distribution in a voltage-frequency table is a “system

optimization” issue

Drive system efficiency, motor noise and common mode voltage are important

system aspects that must be considered

The “converter-motor-load” entity must be considered as a whole in order to

optimize the distribution of the modulation techniques in the voltage-frequency

plane

Different voltage-frequency tables for different applications are necessary

System Optimization

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