sources of harmonics

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SOURCES OF HARMONICS



OUTLINE

• Power System Harmonics?

• Nonlinear Loads Producing Harmonic

• Conclusions

• References



What are Power System Harmonics?

• Harmonic: a mathematical definition, generally

used when talking about Integral orders of

Fundamental frequencies.

• Power system harmonics:Currents or voltageswith frequencies that are integer multiples(h=0,1,2,…N) of the fundamental powerfrequency.

• Harmonics are integral multiples of somefundamental frequency that, when addedtogether, result in a distorted waveform.



f(x) = sin(x) f(x) = sin(5x) 5

+

The resulting wave shows a strong departure from the smooth

waves comprising it:

f(x) = sin(x) + sin(5x)

5 =



In fact, any function may be constructed from a

sine wave and some number of its harmonics:



Where do they come from?The power company typically supplies a reasonably

smooth sinusoidal waveform but nonlinear devices will draw distortedwaveforms which are comprised of harmonics of the source.

Nonlinear devices that do not follow the superposition rule.



Source of harmonics

• Converters,

• Devices which includes semi-conductor elements,

• Generators,

• Motors,

• Transformers,

• Lightening equipmentworking by gas dischargeprinciple,

• Photovoltaic systems,

• Computers,

• Electronic ballasts,

• Uninterruptable powersupplies,

• Switching power supplies,

• Welding machines,

• Control circuits,

• Frequency converters,

• Static VAr compensators,

• Arc furnaces,

•

HVDC transmission systems,• Electrical Communication

systems



Transformers

• The magnetization characteristic of a

transformer’s core is non-linear and will

produce harmonics as it is saturated.



Normal Excitation Characteristics

• At no-load the primary of a transformer is

practically balanced by the back e.m.f because

the effect of the winding resistance and

leakage reactance is negligible at low currents.



Determination of the Current Wave

shape

The magnetizing current harmonics often rise totheir maximum levels in the early hours of the

morning, in example, when the system is lightly

loaded and the voltage is high.



Symmetrical Overexcitation

• If a transformer running with this peak operatingmagnetic flux density is subjected to a magneticflux density of, 1.9-2.0 T, which will produceconsiderable saturation.

• The symmetrical magnetizing current associatedwith a single transformer core saturation isignored, and if it is assumed that all triplenharmonics are absorbed, then the harmonics

being generated are of orders5,7,11,13,17,19,……i.e. those of orders 6k , wherek is an integer.



Inrush Current Harmonics

• If a transformer is switched off it can be left with a residual

flux density in the core of

• magnitude + Br or – Br (or under some circumstances zero).

When the transformer is reenergized

• the flux density illustrated in figure can reach peak levels of 2

max B .



Arcing Devices

• The voltage-current

characteristics of electric arcs

are highly non-linear.

Following arc ignition the

voltage decreases due to theshort-circuit current, the value

of which is only limited by the

power system impedance.

• The main harmonic sources in

this category are the electricarc furnace and discharge type

lighting with magnetic ballasts.



Arc Furnaces

• Both odd and even harmonics are produced. Arcfurnace loads are harsh loads on the supply system,with attendant problems of phase unbalance, flicker,harmonics, impact loading, and possible resonance.

•Arc furnaces may range from small units of a few toncapacity, power rating 2 –3 MVA, to larger units having400-ton capacity and power requirement of 100 MVA.The harmonics produced by electric arc furnaces arenot definitely predicted due to variation of the arc feed

material. The arc current is highly nonlinear, andreveals a continuous spectrum of harmonic frequenciesof both integer and noninteger order.



Discharge-Type Lighting

• Discharge lighting is highly nonlinear and gives rise toconsiderable odd-ordered harmonic currents. This effect isillustrated in figures below, which shows the currentwaveform and harmonic spectrum of a high-efficiencylamp.

• This effect is particularly important in the case of fluorescent lamps, given the large concentration of thistype of lighting. Additional magnetic ballasts are needed tolimit the current to within the capability of the fluorescenttube and stabilize the arc.

• These type of lamps shows nonlinear voltage-currentcharacteristics because of their negative resistanceproperty.

Th f l h li



These type of lamps shows nonlinear

voltage-current characteristics because

of their negative resistance property.



Single-Phase Rectification

• Many commercial and domestic appliances require

direct current for their operation. The single phase

diode rectifier (as seen below) has become a popular

power source for these appliances because of itsreduced cost and relatively low sensitivity to supply

voltage variations under normal operating conditions.



• Modern appliances use the switch-mode power supply

concept, whereby the input rectifier is directly connected to the

a.c. source as in figure above; however, in this case the

rectified voltage is converted back to a.c. at a very high

frequency and then rectified again. This process provides a

very compact design and efficient operation, tolerating large

variations in input voltage. Personal computers and most office

appliances as well as electronic balast of modern fluorescent

lighting systems are now of this type.• Typical examples of single-phase

distorting appliances are tv

recievers, personal computers

and microwave ovens.



Rotating Machine Harmonics

• Rotating machines produce harmonic due to the field distributionof salient poles, the magnetic permeance is related with slots andthe saturation of the main circuit.

• As a result of small asymmetries on the machine stator or rotorslots or slight irregularities in the winding patterns of a three phase

winding of a rotating machine, harmonic currents can develop.These harmonics induce an electromotive force (emf) on the statorwindings at a frequency equal to the ratio of speed/wavelength.The resultant distribution of magneto motive forces (mmfs) in themachine produces harmonics that are a function of speed.Additional harmonic currents can be created upon magnetic core

saturation.• The harmonics produced by a synchronous generator will not be

taken into consideration if the generator’s power rating is smallerthan 1000 kVA



Voltage Harmonics Produced by

Synchronous Machines

• If the magnetic flux of the field system is distributedperfectly sinusoidal around the air gap, the e.m.f.generated in each full-pitched armature coil is sinvoltsper turn. Where is the total flux per pole and f is

frequency related to speed and pole pairs. Howeverthe flux is never exactly distributed in this way,particularly in salient pole machines.

• Figure below shows the mmf and the flux distribution

in one phase of a fully-pitched poly-phase winding withone slot per pole per phase on the assumption of aconstant air gap and in the absence of iron saturation

sources of harmonics

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