INVERTERS(DC-AC Converters)

INVERTERS for SEE 4433

• Square wave inverters (1-phase)• Amplitude and harmonic control (quasi

square wave)• Total Harmonic Distortion

3-phase inverters• Square wave (six-step)• PWM

Pulse Width Modulation (PWM) (1-phase)• Bipolar and unipolar• Harmonics

INVERTERS

A. Full-bridge inverter

• Upper and lower switches cannot be ON simultaneously

• Depending on the switches positions, there can be 3 possible output voltage:

(Vdc), (-Vdc) and 0Vdc

Q1

Q2

Q3

Q4

+ vo −

D1 D3

D2D4

io

In SEE 4433, regardless of the control method, the circuit topology of single-phase inverter are of two types: Full-bridge and half-bridge

INVERTERS

B. half-bridge inverter

• The capacitors equally devide the voltage Vdc

• Depending on the switches positions, the output voltage can be either (Vdc/2) or (−Vdc/2)

Vdc

C1

Q2

Q1

C2

+ vo −

In SEE 4433, regardless of the control method, the circuit topology of single-phase inverter are of two types: Full-bridge and half-bridge

+Vdc/2−

+Vdc/2−

D1

D2

INVERTERS

Square-wave inverter (with full-bridge)

• Can also be implemented using half-bridge inverters

S1, S2 S3, S4 S1, S2

• It can be shown that:

INVERTERS

Square-wave inverter (with full-bridge)

Vdc

Q1

Q2

Q3

Q4

+ vo −

D1 D3

D2D4

io

Current path for inductive load:

SEE EXAMPLE 8-2

INVERTERS

TOTAL HARMONIC DISTORTION

• THD is used to measure the quality of the AC voltage or current

• The closer the waveform to sinusoidal, the smaller is the THD

• Can be applied to voltage or current

SEE EXAMPLE 8-3

INVERTERS

Quasi-square wave inverter – Amplitude and harmonic control

• Amplitude of the fundamental component can be controlled (by controlling α)

• Certain harmonic contents can be eliminated (also by controlling α !)

Duration of ZERO output voltage is introduced and it can be shown that:

Amplitude and harmonics cannot be controlled independentlyCannot be implemented using the half-bridge inverter.

INVERTERS

Quasi-square wave inverter – Amplitude and harmonic control

Fourier series of the output voltage is given by:

where

INVERTERS

Quasi-square wave inverter – Amplitude and harmonic control

Amplitude control

Amplitude of fundamental component:

By changing α the amplitude of the fundamental will change

Harmonic control

The nth harmanic can be eliminated if its amplitude made zero

For example, the amplitude of the third harmonic (n=3) is zero when α = 30o

INVERTERS

Quasi-square wave inverter – Amplitude and harmonic control

Simultaneous control of amplitude and harmonic

In order to be able to control amplitude and harmonic simultaneously, variable Vdc has to be added

Controlled via DC link

Fixed DC voltage Variable DC

LoadInverterDC-DCconverter

INVERTERS

Quasi-square wave inverter – Amplitude and harmonic controlSwitching signals (full-bridge inverter)

S1

S2

S3

S4

S1

S2

S3

S4

20 20

INVERTERSPulse Width Modulation

Is a method used to control the output voltage (amplitude and frequency) of an inverter by modulating the width of the pulses of the output waveform

Main advantages of PWM control:• Filter requirement is reduced• Amplitude and frequency can be control independently• Significant reduction in THD of load current (inductive load)

Disadvantages of PWM control:• More complex control circuit• Higher switching losses

In SEE4433, two switching scheme for single-phase inverter will be discussed:• Bipolar switching scheme• Unipolar switching scheme

INVERTERSPulse Width Modulation

Bipolar switching scheme

(vsine > vtri) : Q1 and Q2 ON; vo=Vdc

(vsine < vtri) : Q3 and Q4 ON; vo=-Vdc

INVERTERSPulse Width Modulation

Bipolar switching scheme

ftri

fsine

Vm,sineVm,tri

Frequency modulation index

Amplitude modulation index

The amplitude of the fundamental component of vo is proportional to ma:

V1=maVdc

INVERTERSHarmonics in PWM single-phase inverter

INVERTERSHarmonics in PWM single-phase inverter : Bipolar switching scheme

• If mf is chosen as odd integer with the triangular wave synchronize with the modulating signal, then the PWM output is an odd quarter-wave symmetry.

• an = 0 and bn exist only for odd

1n

ono tnVtv )sin()(

Graphically, this can be represented using frequency spectrum diagram :

OR using a normalized Fourier coefficients table:

INVERTERSPulse Width Modulation

Unipolar switching scheme

(vsine > vtri) : Q1 ON, Q4 OFF; va= Vdc

Vab = va - vb

(vsine < vtri) : Q1 OFF, Q4 ON; va= 0

(-vsine > vtri) : Q3 ON, Q2 OFF; vb= Vdc

(-vsine < vtri) : Q3 OFF, Q2 ON; vb= 0

INVERTERSHarmonics in PWM single-phase inverter : Unipolar switching scheme

• The frequency of the output voltage is doubled.• If mf is chosen as even integer then the first cluster of harmonics

appear around 2mf (the harmonic at 2mf itself is zero)

Graphically, this can be represented using frequency spectrum diagram :

Or using a normalized Fourier coefficients table:

INVERTERS

• Contains harmonics at relatively low frequency: 3rd, 5th, 7th, 9th, etc. • In order to improve the THDV , a low pass filter can be employed filter

will be bulky since cutoff frequency is low difficult to remove harmonics since at the same time must ensure fundamental component is not attenuated.

Harmonics in PWM single-phase inverter : Comparison between square wave

and PWM

SQUARE-WAVE

PWM

• Harmonics appear around mf which is further away from fundamental.• To improve THDV, filter with higher cutoff can be used smaller in size

easier to filter out harmonics.

PWMmf = 21

1 3 5 7 9 11 13 n 1 3 5 7 9 11 13 15 17 19 21 23 25

Square wave

INVERTERS

Three-phase invertersSix-step inverter

S1

S2

S3

S4

S5

S6

vAo

vBo

vCo

vAB

vAn

A

S2

Vdc

S4

S5

S6

C

Bn

S3S1

o

• THDV of line-line and line-n are both 31%• THDI of line current depends on load,

however it will be smaller than the single phase

Vdc

INVERTERS

Three-phase invertersPWM inverter

mf is chosen to be multiple of 3 so that the harmonic at multiple of 3, including mf (and its multiple) are suppressed (or canceled out) in the line-line voltage