Chapter 4 - Inverters

7/22/2019 Chapter 4 - Inverters

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Si l


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Full bridge (single phase) is built from two half -bridge leg. The switching in the second leg is delayed by 180 degreesfrom the first leg.

Single-phase,

Full-bridge

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Three-Phase Inverter

Each leg(Red, Yellow,Blue) is delayedby 120degrees.

A three -phaseinverter withstar connected

load is shownon the right

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Three phase


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Three phaseinverter

waveforms

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Three Phase


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Three PhaseInverter

Waveforms(6 steps output

VL-N)

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3-phase Inverter - Analysis

R total = R + R/2 = 3R/2

iTotal = V s /R total = 2V s /3R

Van = V cn = i Total .R/2 = V s /3

Vbn

= - iTotal

.R = - 2Vs/3

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3-phase Inverter - Harmonics

THD i is load dependent.The output voltage magnitude can only be controlled by V DC ,and switching frequency controls the output frequency.Harmonics of order three and multiples of three are absent

Example:

VDC = 100 V,Output fundamentalfrequency = 60 Hz,Load R-L series

Y- connected withR = 10 ohm andL = 20 mH,determine the THD i .

Answer : THDi = 7 %

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Pulse Width Modulation (PWM)

Objective PWM

- Control of inverter output voltage- Reduction of harmonics

Disadvantages of PWM - Increase of switching losses due to high PWM frequency- Reduction of available voltage- EMI problems due to high-order harmonics

Control of Inverter Output Voltage

- PWM frequency is the same as the frequency of V triangular

- Amplitude is controlled by the peak value of V control (Ma)

- Fundamental frequency is controlled by the frequency of V control

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Triangulation Method(Natural Sampling)

Amplitudes of the triangular wave(carrier) and sine wave (modulating)

are compared to obtain PWMwaveform. Simple analoguecomparator can be used.(Introducedby Scnohung & Stemmler)

Basically an analogue method. Itsdigital version, known as REGULARsampling is widely used inindustry.(Introduced by Bowes)


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PWM Types

Natural (sinusoidal) sampling (as shown on previous slide)

Problems with analogue circuitry, e.g. Drift, sensitivity,temperature, interference, etc . Regular sampling simplified version of natural sampling that results in simple digitalimplementation

Optimized PWM PWM waveform are constructed based on certain performancecriteria, e.g . THD. Harmonic elimination/minimisation PWM PWM waveforms are constructed to eliminate some undesirable

harmonics from the output waveform spectra. Highly mathematical in nature Space-Vector Modulation (SVM) A simple technique based on volt-second that is normally usedwith three-phase inverter motor drive

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Modulation


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ModulationIndex, Ratio

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Modulation Index determines the output voltage fundamental

component

Modulation ratio determines the incident (location) ofharmonics in the spectra.

Modulation Index, Ratio

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Regular Sampling (Asymmetric)

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Asymmetric and


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Asymmetric andsymmetric

regular sampling

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Bipolar


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BipolarSwitching

Output voltage alternatesbetween plus and minusthe DC supply, i.e

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Unipolar


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pSwitching

Extra Reading

http://sureshks.netfirms.com/article/apfc2/apfc2.htm#31

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Unipolar switching
http://sureshks.netfirms.com/article/apfc2/apfc2.htmhttp://sureshks.netfirms.com/article/apfc2/apfc2.htmhttp://sureshks.netfirms.com/article/apfc2/apfc2.htmhttp://sureshks.netfirms.com/article/apfc2/apfc2.htmhttp://sureshks.netfirms.com/article/apfc2/apfc2.htmhttp://sureshks.netfirms.com/article/apfc2/apfc2.htmhttp://sureshks.netfirms.com/article/apfc2/apfc2.htmhttp://sureshks.netfirms.com/article/apfc2/apfc2.htm


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Unipolar switching

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H i f bi l PWM


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Harmonics of bipolar PWM

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Harmonics of


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bipolar PWM

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PWM Spectra


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PWM Spectra

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PWM Spectra Observations


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PWM Spectra Observations

The harmonics appear in clusters at multiple of the carrierfrequencies . Main harmonics located at :

f = k.p.( f m) where k = 1, 2, 3....where f m is the frequency of the modulation (sine) waveform.

There also exist side-bands around the main harmonic frequencies. Amplitude of the fundamental is proportional to the modulation index.

The relation ship is given as:

V1= M IVin The amplitude of the harmonic changes with M I. Its incidence (location onspectra) is not. When p >10, or so, the harmonics can be normalized. For lower valuesof p, the side-bands clusters overlap-normalized results no longer apply.

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Tabulated


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BipolarPWM

Harmonics

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Three phase Harmonics


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Three-phase Harmonics

For three -phase inverters, there is significant advantage if M R

is chosen to be: Odd: All even harmonic will be eliminated from the

pole-switching waveform. triplens (multiple of three ( e.g . 3, 9, 15, 21, 27...):

All triplens harmonics will be eliminated from theline-to-line output voltage.

By observing the waveform, it can be seen that with odd M R,the line-to- line voltage shape looks more sinusoidal. As can be noted from the spectra, the phase voltage amplitudeis 0.8 (normalized). This is because the modulation index is 0.8.The line voltage amplitude is square root three of phase voltagedue to the three-phase relationship

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Effect of Odd


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and Triplens

P = 8 not a multiple of 3

VRY high harmonics

P = 9 Multiple of 3

VRY Low harmonicsMore Sinusoidal

p = 8, M = 0.6

p = 9, M = 0.6

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Spectra: Effect of Triplens


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Spectra: Effect of Triplens

A

B

0.83 (Line to line voltage)

Fundamental

p = 21, M = 0.8

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Comments on PWM scheme


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Comments on PWM scheme

It is desirable to have M R as large as possible.

This will push the harmonic at higher frequencies on thespectrum. Thus filtering requirement is reduced.

Although the voltage THD improvement is not significant,

but the current THD will improve greatly because the load

normally has some current filtering effect.

However, higher M R has side effects:

Higher switching frequency: More losses.

Pulse width may be too small to be constructed.

Pulse dropping may be required.

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Example :


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Example :

Q. A single-phase full-bridge inverter supplies a load of 10 W in series with aninductance of 31.8 mH. The inverter is supplied by a 380 VDC source.

(a) Sketch the inverter circuit as described above. (5 marks)(b) Calculate the rms value of the fundamental (n = 1) of the inverteroutput voltage assuming it is a square-wave. (3 marks)(c) Assuming a quasi square-wave output voltage waveform with a delayangle of 45, calculate the rms value of the fundamental and the twolowest order harmonics of the inverter output voltage. (5 marks)(d) Explain how the 7th harmonic of the inverter output voltage can beeliminated while maintaining the same rms value of the fundamental asobtained from (c). Then, plot the frequency spectrum of the inverter outputvoltage up to the 11th order (consider magnitude only). Label the

important parameters clearly. (7 marks)(e) Suggest and then describe a switching strategy for the inverter powerdevices that can shift the lower order harmonics in the inverter outputvoltage to the higher order side. Provide diagrams if necessary to supportyour suggestion. (5 marks)

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Chapter 4 - Inverters

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