harmonic generation

7/30/2019 Harmonic Generation

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HARMONICGENERATION

Generation of harmonics

Effects of harmonics Harmonic modeling, and

analysis

Mitigation of harmonics bypassive filter

Measurements of harmonics


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TYPES OF LOADS

1. Linear time-invariant loads

These loads display constant steady

state impedance during the appliedSinusoidal voltage.

Incandescent lighting

Rotating machines

Harmonics due to non-uniform air gap

and tooth ripples.

TransformersSaturation in a transformer and its

Inrush current contains odd and even

Harmonics, including a dc component.

2. Non-linear loads

They draw a current that is discontinuous

for a part of the sinusoidal voltage cycle. Adjustable drive systems

Cycloconverters

Arc furnaces

Switching mode power supplies

Static VAR compensators (SVCs)

HVDC transmission Electric traction

Wind and solar power generation

Slip recovery schemes of inductionmotors

Fluorescent lighting and electronic

ballasts


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INTEGRAL AND NON-INTEGRAL

HARMONICS

INTEGRAL HARMONICS

A distorted waveform having a Fourier series with fundamental frequency equal to power

system frequency, and its periodic steady state exist.

NON-INTEGRAL HARMONICS

A distorted waveform having sub multiples of power system frequency. For them a

trigonometric Fourier series expansion is used.

Such Non-Integral harmonic generators include:

Arcing devices Arc furnaces

Fluorescent, mercury, and sodium vapor lighting

They cause phase unbalance, flicker, impact loading, harmonics, and resonance, and may give

rise to torsion vibrations in rotating equipment.


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LINEAR TIME-INVARIANT LOADS

Rotating machinesVariable flux path

Tooth Ripple

Transformers

Shunt Capacitors


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VARIABLE FLUX PATH IN

ELECTRICAL MACHINES

Reluctance of the air gap to carry a

certain flux across, is not applicable

and the flux density in the air gap is notsinusoidal

The harmonic flux components are

affected by:

1. Phase spread

2. Fractional slotting

3. Coil span.

Figure: Armature reaction of a three-phase winding spanning a polepitch.


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TOOTH RIPPLES IN ELECTRICAL

MACHINES

Tooth ripples in electrical machinery

are produced by slotting as these affect

air-gap permeance.

The frequency of flux pulsations is

given by 2gf,

g is the number of slots per pole

f is the system frequency

This pulsation may be regarded as twowaves rotating at angular velocity 2g in

forward and backward directions.

The component fields will generate

harmonic emf of frequencies 2g cycles

per second.


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TRANSFORMERS

Harmonics in transformers originate due to:

1. Magnetic saturation

2. Continuous high speed switching

3. High-magnetic flux densities

4. Winding connections

Transformers are operated close to the knee

point of its saturation characteristics.

A sinusoidal flux wave demands a

magnetizing current with a harmonic content.

The third harmonic flux produce a third

harmonic emf and current, which when

summed give a total peaky current.


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Continued..

In wye-wye connected transformers all the third harmonics cancel between the lines,no third harmonic currents flow, and the flux wave in the transformer is flat topped.

Tertiary delta-connected windings are included in wye-wye connected transformersfor neutral stabilization or else as shown in the figure the neutral shifts if flux is flat

topped.

The spectrum of magnetizing inrush current resembles a rectified current. Its peakvalue may reach 8-15 times the transformer full-load current. However the inrushcurrent lasts for a very short duration (0.1 sec).

Over excitation of transformers in steady-state operation can also produce

harmonics. The V/f factor measures the over excitation.


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SHUNT CAPACITORS

High inrush frequencies on switching

of shunt capacitors are given by

F inrush = 1 / 2 pi sqrt (Leq * Ceq)

Series filter reactors and switching

inrush current limiting reactors reduce

these frequencies

The power capacitors do not generate

harmonics by themselves, but are themain cause of amplification of the

harmonics due to resonance .

They can also reduce harmonic

distortion, when applied as filters.


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NON-LINEAR TIME-INVARIANT LOADS

STATIC POWER CONVERTERS

ADJUSTABLE SPEED DRIVES

INVERTERS AND ELECTRIC TRACTION ARC FURNACES

CYCLOCONVERTERS

THYRISTOR-CONTROLLED REACTOR

THYRISTOR-SWITCHED CAPACITORS

PULSE WIDTH MODULATION

CHOPPER CIRCUITS

SLIP FREQUENCY RECOVERY SCHEMES

LIGHTING BALLASTS


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STATIC POWER CONVERTERS

The primary source of harmonics are:

1. Power converters

2. Rectifiers3. Inverters ( VFDs )

4. Adjustable speed drives

Non-characteristic harmonics are produced by sources other than

power electronic. These are at frequencies other than the integer

multiple of the fundamental power frequency.

They are caused by:

1. Non uniform ignition delay angles

2. Un-balance supply voltages.


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RECTIFIERS

Rectified output comprises of a

number integral multiples of

fundamental frequency of input.

The efficiency of rectification is

Efficiency = Pdc/Pac

The form factor is a measure of the

shape of the output voltage or current

and is defined as;FF = Irms / Idc

The ripple factor, which is a measure

of the ripple content of the output

current or voltage

RF = Sqrt (FF2- 1)


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INVERTERS (VARIABLE SPEED

DRIVES)

In VFD systems, the inverter

frequency increases from 0Hz to 120

Hz with the motor acceleration.

Up to the motor base speed the

inverter switches many times per

cycle.

1. PWM switching has odd and even

harmonics, with positive and negative

sequence components mitigating;

leaving only zero & triple harmonics.

2. Torque band control switching, higher

6h & 3h harmonics are produced,

with some sub harmonics

3. In chopper inverter drive, the

harmonics due to chopper and

inverter combine.


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ADJUSTABLE SPEED DRIVES

Adjustable speed drives account forthe largest percentage of nonlinearloads in the industry.

Most systems require that theincoming ac power supply to berectified into dc. The dc power is theninverted back to ac.

Either the inverted back AC supply is

provided to the variable-frequencydrive at a regulated frequency.

Or the dc power is fed directly to dcdrive systems through powerconverters.

Adjustable-Speed Drive Systems

Drive Motor

Horse

power

Speed

range Converter type

DC Motor 110,000 50:1

Phase controlled, line

commutated

Squirrel-cage

induction

100

4000 10:1

Current link, force

commutated

Squirrel-cage

induction 11500 10:1

Voltage link, force

commutated

Wound rotor500

20000 3:1Current link, line

commutated

Synchronous

(brushless

excitation)

1000

60000 50:1

Current link, load

commutated

Synchronous/squirr

el cage

1000

60000 50:1

Phase controlled, line

commutated


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ARC FURNACES

The harmonics produced by electric

arc furnaces are not predictable

due to variation of the arc feed

material.

The arc current is highly nonlinear,

and reveals a continuous spectrum

of harmonic frequencies of both

integer and non-integer order.

Large erratic reactive current

swings generate voltage dropsacross the ac system, resulting in

irregular variation of the terminal

voltage.

Voltage variations cause the

incandescent lamps to flicker.

h Percent Of Fundamental

Harmonic Melting Refining Magnitude

2 7.7 0 0.54

3 5.8 2 0.81

4 2.5 0 0.60

5 4.2 2.1 0.37

7 3.1 2.5 0.157


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CYCLOCONVERTERS

If the delay angles of the

cycloconverter segments arevaried so that the average is

closely to the desired sinusoidal

output voltage, the harmonics

at the output are minimized.

Because of load unbalance andasymmetry between phase

voltages and firing angles, non

characteristic harmonics are

also generated.


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PULSE WIDTH MODULATION

The techniques of pulse widthmodulation (PWM) are:

1. Single-pulse width modulation

2. Multiple-pulse width modulation3. Sinusoidal pulse-width modulation

4. Modified sinusoidal pulse-widthmodulation

They reduce the rise time

Over the years the pulse switching

time of the power devices have beendrastically reduced by: SCR (fast thyristor) 4sec

GTO (gate turn off thyristor) 1sec

GTR (giant transistor) 0.8sec

IGBT (insulated gate bipolar) 0.2sec

IGBT (power plate type) 0.1sec

1. In a single-PWM, there is one pulseper half-cycle and the width of thepulse is varied to control the inverter

output voltage.

2. The harmonic content can be reducedby using several pulses in each half-cycle of the output voltage.

3. Sinusoidal PWM has pulse width

varied in proportion to the sine wave.The DF and the lower order harmonicmagnitudes are reduced.

4. Modified sinusoidal PWM eliminatesharmonics and generates a nearlysinusoidal voltage wave


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CHOPPER CIRCUITS

The dc traction supply from rectifier substations have harmonics injected into

the supply system as switching transients from commutation occur.

Thyristor choppers are operated at fixed frequency and the chopping frequency

is superimposed as the line harmonics.

An input low-pass filter is normally connected to filter out the chopper-

generated harmonics.


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SLIP FREQUENCY RECOVERY

SCHEMES

The slip frequency recovery

systems the rotor slip frequency

voltage is rectified, and the power

taken by the rotor is fed into thesupply system through a line

commutated inverter.

Such a system causes sub

harmonics in the ac system.

The ac harmonics for this type of

load cannot be reduced as dc

current ripple is independent of the

rectifier ripple.


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LIGHTING BALLASTS

Lighting ballasts produce large harmonic distortions and zerosequence third harmonic currents in the neutral.

The current harmonic limits for lighting ballasts show that the limits forthe newer ballasts are much lower as compared to earlier ballasts.

harmonic generation

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