slides topic

VDM5000 Two-level VSI
Topic 5
Two-Level Voltage Source Inverter (VSI)
Source:
Alstom

Sinusoidal PWM
Space vector modulation
Lecture Topics
To control inverter output frequency (fundamental)
To control inverter output voltage (fundamental)
To minimize harmonic distortion
Why Use PWM Techniques?
Two Level Voltage Source Inverter

Inverter Configuration
Assumption:
dc capacitor very large → dc voltage ripple free
Sinusoidal PWM

Modulating and Carrier Waves
vcr – Carrier wave (triangle)
Amplitude modulation index
Frequency modulation index
vm – Modulating wave (sine)
Sinusoidal PWM

Gate Signal Generation
Vg1 and Vg4 are complementary
Sinusoidal PWM

Line-to-Line Voltage vAB
Sinusoidal PWM

Waveforms and FFT
ma = 0.8, mf = 15,
fm = 60Hz, fcr = 900Hz
Switching frequency
fsw = fcr = 900Hz
Sinusoidal PWM

Harmonic Content
Low order harmonics
n < (mf -2) are eliminated VAB1 versus ma is linear
VAB1,max = 0.612Vd
Sinusoidal PWM

Over-Modulation
Fundamental voltage ↑
Low-order harmonics ↑
Sinusoidal PWM

Third Harmonic Injection PWM
- Fundamental voltage increased
- No low order harmonics produced
3rd harmonic – zero sequence (to appear in vAN and vBN )
No triplen harmonics in vAB (vAB = vAN - vBN)
Sinusoidal PWM

Switching States
Space Vector Modulation

Switching States (Three-Phase)
Eight switching states
Space Vector Modulation

Space Vector Diagram
Active vectors: to
(stationary, not rotating)
Zero vector: Six sectors: I to VI
Space Vector Modulation

Space Vectors
Three-phase voltages
Two-phase voltages
Space vector representation
(2) → (3) where
(3)
(1)
(2)
(4)
Space Vector Modulation

Space Vectors (Example)
Switching state [POO] → S1, S6 and S2 ON
and
(5) → (4)
(7)
(5)
(6)
Similarly,
Space Vector Modulation

Active and Zero Vectors
Active Vector: 6
Zero Vector: 1
Redundant switching
states: [PPP] and [OOO]
Space Vector Modulation

(8)
Reference Vector Vref
Definition
Angular displacement
(9)
Rotating in space at ω
Space Vector Modulation

Relationship Between Vref and VAB
Vref is approximated by two active and a zero vectors
Vref rotates one revolution,
VAB completes one cycle
Length of Vref corresponds to
magnitude of VAB
Space Vector Modulation

Dwell Time Calculation
Volt-Second Balancing
(10)
Ta, Tb and T0 – dwell times for and
Ts – sampling period
Space vectors
, and
(11) → (10)
(11)
(12)
Space Vector Modulation

Dwell Times
Solve (12)
(13)
Space Vector Modulation

Vref Location versus Dwell Times
Space Vector Modulation

Modulation Index
(15)
(16)
Space Vector Modulation

Modulation Range
Vref,max
(17)
(17) → (16)
ma,max = 1 →
Modulation range: 0 ≤ ma ≤ 1
(18)
Space Vector Modulation

Switching Sequence Design
Basic Requirement:
Minimize the number of switchings per
sampling period Ts
Implementation:
Transition from one switching state to the next involves only two switches in the same inverter leg.
Space Vector Modulation

Seven-segment Switching Sequence
Total number of switchings: 6
Selected vectors:
V0, V1 and V2
Dwell times:
Ts = T0 + Ta + Tb
Space Vector Modulation

Undesirable Switching Sequence
Vectors V1 and V2 swapped
Total number of switchings: 10
Space Vector Modulation

Switching Sequence Summary (7–segments)
Note: The switching sequences for the odd and ever sectors are different.
Space Vector Modulation

Simulated Waveforms
f1 = 60Hz, fsw = 900Hz, ma = 0.696, Ts = 1.1ms
Space Vector Modulation

Waveforms and FFT
Space Vector Modulation

Waveforms and FFT (Measured)
Space Vector Modulation

Waveforms and FFT (Measured)
( and )
Space Vector Modulation

Even-Order Harmonic Elimination
Type-A sequence
(starts and ends with [OOO])
Type-B sequence
(starts and ends with [PPP])
Space Vector Modulation

Even-Order Harmonic Elimination
Space vector Diagram
Space Vector Modulation

Even-Order Harmonic Elimination
Measured waveforms and FFT
Space Vector Modulation

Even-Order Harmonic Elimination
( and )
Space Vector Modulation

Five-segment SVM
Space Vector Modulation

Switching Sequence ( 5-segment)
Space Vector Modulation

Simulated Waveforms ( 5-segment)
No switching for a 120° period per cycle.
Low switching frequency but high harmonic distortion
f1 = 60Hz, fsw = 600Hz, ma = 0.696, Ts = 1.1ms
Space Vector Modulation