Multiphase Space Vector Control Modulation ...

Introduction

Multiphase SVC Technique

Multiphase SVC Simulation

Experimental Results

Conclusions

Multiphase Space Vector Control Modulation Technique for Voltage Source Converters ´ ´ Oscar López, Jacobo Alvarez, Jano Malvar, Alejandro G. Yepes, Ana Vidal, Pablo Fernández-Comesa˜ na, Francisco D. Freijedo, Jes´ us Doval-Gandoy Electronics Technology Department University of Vigo, Spain

IECON’12, 25–28 October ´ ETS, Montréal, Canada

IECON’12 - Multiphase Space Vector Control Modulation Technique for VSCs

1

Introduction




Conclusions

Outline

1

Introduction

2

Multiphase Space Vector Control Technique

3

Simulation of the Multiphase Space Vector Control Technique

4


5

Conclusions


2

Introduction




Conclusions

Multilevel Multiphase Modulation Techniques Modulation Techniques Classification Per-phase

Joint-phase

High switching frequency

SPWM

SVPWM

Low switching frequency

SHE

SVC

Multilevel Selective Harmonic Elimination (SHE) 4 Per-phase technique + Straightforward extension to multiphase inverters 6 Requires to solve non-linear equations (offline) 6 High number of levels + High number of equations • High number of levels + SVC is an alternative IECON’12 - Multiphase Space Vector Control Modulation Technique for VSCs

3

Introduction




Conclusions

Space Vector Control Technique Based on space vector theory Minimizes error between reference vector and switching vector: α-β plane

Low output voltage error + High space vector density IECON’12 - Multiphase Space Vector Control Modulation Technique for VSCs

4

Introduction




Conclusions

Space Vector Control in Multiphase Systems Multiphase systems are characterized by multiple planes The error in all planes must be taken into account: β (p.u.) 1.5

α-β plane

y (p.u.) 1.5

1.0

1.0

0.5

0.5

0

0

–0.5

–0.5

–1.0

–1.0

–1.5 –1.5 –1.0 –0.5

0

0.5

1.0 1.5 α (p.u.)

x-y plane

–1.5 –1.5 –1.0 –0.5

0

0.5

1.0 1.5 x (p.u.)

Three-phase SVC extension to multiphase is not possible IECON’12 - Multiphase Space Vector Control Modulation Technique for VSCs

5

Introduction




Conclusions

Outline

1

Introduction

2


3


4


5

Conclusions


6

Introduction




Conclusions

Multiphase Space Vector Control Technique Full search SVC Search the space vector with minimum error: qP p 2 ej = p ej Multiphase inverter + High number of space vectors: Phases Levels Number of space vectors 3 9 217 5 9 26 281 6 9 269 297 7 9 2 685 817 15 9 1.7070676×1014 Very high computational cost Very difficult to implement in real time IECON’12 - Multiphase Space Vector Control Modulation Technique for VSCs

7

Introduction




Conclusions

Multiphase Space Vector Control Technique SVPWM based SVC P -phase SVPWM + Obtains the P nearest vectors SVPWM modulation law: ωr =

P X

ω sj tj ,

j=1

P X

tj = 1

j=1

ω r is the weighted average of ω sj tj are the weighting factors

The most similar ω sj to the ω r is the one with highest tj Among the P nearest space vectors search the one with the maximum dwell time Low computational cost + Real-time implementation IECON’12 - Multiphase Space Vector Control Modulation Technique for VSCs

8

Introduction




Conclusions

Example I Reference vector vr = [1.43, 1.13, −0.73, −1.58, −0.25]T Multilevel multiphase SVPWM results: vs1 = [2, 1, −1, −2, 0]T

Ý

t1 = 0.01

(e1 = 0.81)

T

Ý

t2 = 0.15

(e2 = 0.78)

T

Ý

t3 = 0.14

(e3 = 0.69)

T

Ý

t4 = 0.38

(e4 = 0.46)

T

Ý

t5 = 0.32

(e5 = 0.56)

vs2 = [2, 1, −1, −1, 0] vs3 = [2, 1, 0, −1, 0] vs4 = [2, 2, 0, −1, 0] vs5 = [2, 2, 0, −1, 1]

Both SVC techniques provide the same result: vs = [2, 2, 0, −1, 0]T IECON’12 - Multiphase Space Vector Control Modulation Technique for VSCs

9

Introduction




Conclusions


Ý

t1 = 0.01

(e1 = 0.81)

T

Ý

t2 = 0.15

(e2 = 0.78)

T

Ý

t3 = 0.14

(e3 = 0.69)

T

Ý

t4 = 0.38

(e4 = 0.46)

T

Ý

t5 = 0.32

(e5 = 0.56)

vs2 = [2, 1, −1, −1, 0] vs3 = [2, 1, 0, −1, 0] vs4 = [2, 2, 0, −1, 0] vs5 = [2, 2, 0, −1, 1]


10

Introduction




Conclusions


Ý

t1 = 0.01 (e1 = 0.81)

T

Ý

t2 = 0.15 (e2 = 0.78)

T

Ý

t3 = 0.14 (e3 = 0.69)

T

Ý

t4 = 0.38 (e4 = 0.46)

T

Ý

t5 = 0.32 (e5 = 0.56)

vs2 = [2, 1, −1, −1, 0] vs3 = [2, 1, 0, −1, 0] vs4 = [2, 2, 0, −1, 0] vs5 = [2, 2, 0, −1, 1]


11

Introduction




Conclusions

Example II Reference vector vr = [0.98, 0.32, 1.02, 0.62, −0.98]T Multilevel multiphase SVPWM results: vs1 = [−1, 0, 1, 0, −1]T

Ý

t1 = 0.40

(e1 = 0.5367)

vs2 = [−1, 0, 1, 1, −1]T

Ý

t2 = 0.30

(e2 = 0.4980)

T

vs3 = [−1, 1, 1, 1, −1]

Ý

t3 = 0.30

(e3 = 0.6387)

vs4 = [ 0, 1, 1, 1, −1]T

Ý

t4 = 0.00

(e4 = 0.8764)

T

Ý

t4 = 0.00

(e5 = 0.8532)

vs5 = [ 0, 1, 2, 1, −1]

Both techniques provide different results! IECON’12 - Multiphase Space Vector Control Modulation Technique for VSCs

12

Introduction




Conclusions

Outline

1

Introduction

2


3


4


5

Conclusions


13

Introduction




Conclusions

Plane Mapping of Reference and Switching Vectors β (p.u.) 6

y (p.u.) 6

4

4

2

2

0

0

–2

–2

–4

–4

–6 –6

–4

–2

0

2

4

6 α (p.u.)

–6 –6

–4

–2

0

2

4

6 x (p.u.)

Inverter: 9 levels, 5-phases (26 281 space vectors) Voltage reference: A = 4.3 p.u., f1 = 50 Hz Sampling frequency: fs = 10 kHz IECON’12 - Multiphase Space Vector Control Modulation Technique for VSCs

14

Introduction




Conclusions

Reference voltage and phase-to-neutral output voltage

Voltage (p.u.)

4

e

a

b

c

d

2 0 –2 –4 0

5

10 Time (ms)

15

20

4 SVC: 80 switchings per fundamental cycle 6 SVPWM: ≈2 000 switchings per fundamental cycle


15

Introduction




Conclusions

Total Harmonic Distortion (THD) 30% 25%

1

2

3

4

5

6

7

Output levels 8 9 10 11

13 14 15 16

SVPWM based SVC

20% THD

12

15% 10% 5% 0% 0

1

2

3

5 4 Modulation index

6

7

8

• Modulation index: m = Vfund /Vdc 6 Low modulation index + High THD • THD < 5% + m ≥ 5.83 and N ≥ 12 4 Similar THD as full search SVC! IECON’12 - Multiphase Space Vector Control Modulation Technique for VSCs

16

Introduction




Conclusions

Total Harmonic Distortion (THD) 30% 25%

1

2

3

4

5

6

7


13 14 15 16

SVPWM based SVC

20% THD

12

Full search SVC

15% 10% 5% 0% 0

1

2

3


6

7

8

• Modulation index: m = Vfund /Vdc 6 Low modulation index + High THD • THD < 5% + m ≥ 5.83 and N ≥ 12 4 Similar THD as full search SVC! IECON’12 - Multiphase Space Vector Control Modulation Technique for VSCs

17

Introduction




Conclusions

Fundamental amplitude error

Fundamental Amplitude Error 30% 20%

1

2

3

4

5

6

7


12

13 14 15 16

10% 0% –10% SVPWM based SVC

–20% –30% 0

1

2

3


6

7

8

• Modulation index: m = Vfund /Vdc 6 Low modulation index + High error • Error < 2% + m ≥ 5.5 and N ≥ 12 4 Similar error as full search SVC! IECON’12 - Multiphase Space Vector Control Modulation Technique for VSCs

18

Introduction




Conclusions

Fundamental amplitude error

Fundamental Amplitude Error 30% 20%

1

2

3

4

5

6

7


12

13 14 15 16

10% 0% –10% SVPWM based SVC

–20% –30% 0

Full search SVC 1

2

3


6

7

8

• Modulation index: m = Vfund /Vdc 6 Low modulation index + High error • Error < 2% + m ≥ 5.5 and N ≥ 12 4 Similar error as full search SVC! IECON’12 - Multiphase Space Vector Control Modulation Technique for VSCs

19

Introduction




Conclusions

Outline

1

Introduction

2


3


4


5

Conclusions


20

Introduction




Conclusions

Experimental Setup dSPACE

FPGA

Control

SVC

dc link

Trigger signals

Optical link

Inverter

Motor

dSPACE DS1103 PPC Controller Board Xilinx XC3S200 FPGA Nine-level five-phase asymmetric cascaded full-bridge inverter 220/380 V, 1.420 r/min, 1.35 kW induction motor


21

Introduction




Conclusions

Experimental Setup

Inverter

Optical link dSPACE FPGA dc link

dc generator IECON’12 - Multiphase Space Vector Control Modulation Technique for VSCs

Motor 22

Introduction




Conclusions

Experimental Measurements Output Voltage and Current CH1: Vs a − Vn CH2: Vr a CH3: Ia MATH: (Vs a − Vn ) − Vr a

Reference voltage amplitude: 4.3 p.u. = 167.2 VRMS Reference voltage frequency: 50 Hz Sampling frequency: 10 kHz IECON’12 - Multiphase Space Vector Control Modulation Technique for VSCs

23

Introduction




Conclusions

Experimental Measurements Voltage and Current Low-Order Harmonics

Low-order voltage harmonics:

Low-order current harmonics:

CH1: Output voltage (Vs a − Vn )


CH3: Motor current (Ia )

24

Introduction




Conclusions

Experimental Measurements Trajectories of the voltage and current vectors 300

300

200

200

100

100 y [V]

β [V]

Voltage:

0

0

–100

–100

–200

–200

–300 –300 –200 –100

–300 –300 –200 –100

2

2

1

1 y [A]

β [A]

Current:

0 100 200 300 α [V]

0

–1

–2 –2

0 100 200 300 x [V]

0

–1

–2 0 –2 1 2 α [A] IECON’12 - Multiphase Space Vector Control Modulation Technique for VSCs –1

–1

0 x [A]

1

2 25

Introduction




Conclusions

Conclusions New multiphase space vector control technique: Based on a multilevel multiphase SVPWM Valid for standard multilevel topologies Any number of levels and phases Low computational complexity + Real-time implementation

Compared with the full search SVC: Similar THD Similar amplitude error Less computational cost

Experimentally tested: Implemented in low-cost FPGA Nine-level asymmetrical cascaded full-bridge inverter Five-phase induction motor


26

Introduction




Conclusions

Multiphase Space Vector Control Modulation Technique for Voltage Source Converters ´ ´ Oscar López, Jacobo Alvarez, Jano Malvar, Alejandro G. Yepes, Ana Vidal, Pablo Fernández-Comesa˜ na, Francisco D. Freijedo, Jes´ us Doval-Gandoy Electronics Technology Department University of Vigo, Spain

IECON’12, 25–28 October ´ ETS, Montréal, Canada


27