what are harmonics

8/19/2019 What Are Harmonics

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What are harmonics?

The harmonics allow to represent any periodic waveform. In fact, according to Fourier’s

theorem, any periodic function of a period T may be represented as a summation of:

• A sinusoid with the same period T;

• Some sinusoids with the same freuency as whole multiples of the fundamental;

• A possible continuous component, if the function has an a!erage !alue not null in

the period.

The harmonic with frequency corresponding to the period of the original waveform is

called fundamental and the harmonic with frequency equal to “n” times that of the

fundamental is called harmonic component of order “n”.

A perfectly sinusoidal wa!eform complying with Fourier’s theorem does not present

harmonic components of order di"erent from the fundamental one.

Therefore, it is understandable how there are no harmonics in an electrical system when

the wa!eforms of current and !oltage are sinusoidal. #n the contrary, the presence of

harmonics in an electrical system is an inde$ of the distortion of the !oltage or current

wa!eform and this implies such a distribution of the electric power that malfunctioning of

euipment and protecti!e de!ices can be caused.

To summarize: the harmonics are nothing less than the components of a distorted

wa!eform and their use allows us to analyse any periodic nonsinusoidal wa!eform through

di"erent sinusoidal wa!eform components.

Figure 1 below shows a graphical representation of this concept.

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Figure 1 – Graphical representation of harmonics

How harmonics are generated?

%armonics are generated by nonlinear loads. &hen we apply a sinusoidal !oltage to a

load of this type, we shall obtain a current with non'sinusoidal wa!eform. The diagram of

Figure ( illustrates an e$ample of nonsinusoidal current wa!eform due to a nonlinear load:


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Figure 2 – Left: Linear load waveform; Right: Non-linear load waveform

This nonsinusoidal wa!eform can be deconstructed into harmonics. If the networ)

impedances are !ery low, the !oltage distortion resulting from a harmonic current is low

too and rarely it is abo!e the pollution le!el already present in the networ). As a

conseuence, the !oltage can remain practically sinusoidal also in the presence of current

harmonics.

To function properly, many electronic de!ices need a denite current waveform and

thus they ha!e to ’cut’ the sinusoidal wa!eform so as to change its rms !alue or to get a

direct current from an alternate !alue. In these cases the current on the line has a

nonsinusoidal cur!e.

The main equipment generating harmonics are:

• *ersonal computer

• Fluorescent lamps

• Static con!erters

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• +ontinuity groups

• ariable speed dri!es

• &elders

In general, waveform distortion is due to the presence of bridge rectiers (inside of

these equipment, whose semiconductor devices carry the current only for a fraction of

the whole period, thus originating discontinuous curves with the consequent introduction

of numerous harmonics.

Also transformers can be cause of harmonic pollution. In fact, by applying a perfectly

sinusoidal !oltage to a transformer, it results into a sinusoidal magneti-ing u$, but, due to

the phenomenon of the magnetic saturation of iron, the magneti-ing current shall not be

sinusoidal.

Figure – !henomenon of the magnetic saturation of transformer iron

The resultant wa!eform of the magneti-ing current contains numerous harmonics, the

greatest of which is the third one. %owe!er, it should be noted that the magneti-ing


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current is generally a little percentage of the rated current of the transformer and the

distortion e"ect becomes more and more negligible the most loaded the transformer

results to be.

The main problems caused by harmonic currents are //

1. verloading of neutrals

!. "ncrease of losses in the transformers

#. "ncrease of s$in e%ect

The main e%ects of the harmonics voltages are //

&. 'oltage distortion

(. )isturbances in the torque of induction motors

/. #!erloading of neutrals

In a three phase symmetric and balanced system with neutral, the wa!eforms between the

phases are shifted by a 1!*+ phase angle so that, when the phases are eually loaded,

the current in the neutral is -ero.

The presence of unbalanced loads 0phase'to'phase, phase'to'neutral etc.1 allows theowing of an unbalanced current in the neutral.

Figure " – #n$alanced s%stem of currents

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Figure 2 shows an unbalanced system of currents 0phase 3 with a load 345 higher

than the other two phases1, and the current resultant in the neutral is highlighted in red.

6nder these circumstances, the Standards allow the neutral conductor to be dimensioned

with a cross section smaller than the phase conductors.

In the presence of distortion loads it is necessary to evaluate correctly the e%ects of

harmonics.

In fact, although the currents at fundamental freuency in the three phases cancel each

other out, the components of the third harmonic, ha!ing a period eual to a third of the

fundamental, that is eual to the phase shift between the phases 0see Figure 7 below1, are

reciprocally in phase and conseuently they sum in the neutral conductor adding

themsel!es to the normal unbalance currents.

The same is true also for the harmonics multiple of three 0e!en and odd, although

actually the odd ones are more common1.


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Figure & – Fundamental harmonic and rd harmonic


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2. Increase of losses in the transformers

The effects of harmonics inside the transformers involve mainly three aspects //

1. Increase of iron losses (or no-load losses)

. Increase of copper losses

!. "resence of harmonics circ#lating in the windings

The iron losses are d#e to the hysteresis phenomenon and to the losses ca#sed $y eddy c#rrents.

The losses d#e to hysteresis are proportional to the fre%#ency& whereas the losses d#e to eddy

c#rrents depend on the s%#are of the fre%#ency.

The copper losses correspond to the power dissipated $y 'o#le effect in the transformer windings. s

the fre%#ency rises (starting from !* H+) the c#rrent tends to thic,en on the s#rface of the cond#ctors

(s,in effect). nder these circ#mstances& the cond#ctors offer a smaller cross section to the c#rrent

flow& since the losses $y 'o#le effect increase.

These two first aspects affect the overheating which sometimes causes a derating of the transformer .

The third aspect is relevant to the effects of the triple-N harmonics (homopolar harmonics) on the

transformer windings. In case of delta windings& the harmonics flow thro#gh the windings and do not

propagate #pstream towards the networ, since they are all in phase.

The delta windings therefore represent a $arrier for triple- harmonics& $#t it is necessary to pay

partic#lar attention to this type of harmonic components for a correct dimensioning of the transformer.

3. Increase of skin effect

When the fre%#ency rises& the c#rrent tends to flow on the o#ter s#rface of a cond#ctor. This

phenomenon is ,nown as skin effect and is more prono#nced at high frequencies.

t * H+ power s#pply fre%#ency& s,in effect is negligi$le& $#t a$ove !* H+& which corresponds to the

th harmonic& the cross section for the c#rrent flow red#ces& th#s increasing the resistance and ca#sing

additional losses and heating.

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In the presence of high-order harmonics, it is necessary to take skin effect into account, because it

affects the life of cables. In order to overcome this problem, it is possible to use multiple conductor

cables or busbar systems formed by more elementary isolated conductors.

4. Voltage distortion

The distorted load c#rrent drawn $y the nonlinear load ca#ses a distorted voltage drop in the ca$le

impedance. The res#ltant distorted voltage waveform is applied to all other loads connected to the

same circ#it& ca#sing harmonic c#rrents to flow in them& even if they are linear loads.

The sol#tion consists in separating the circuits which s#pply harmonic generating loads from those

s#pplying loads sensitive to harmonics.

. !istur"ances in the torque of induction motors

Harmonic voltage distortion ca#ses increased edd# current losses in the motors& in the same way

as seen for transformers. The additional losses are d#e to the generation of harmonic fields in the

stator& each of which is trying to rotate the motor at a different speed& $oth forwards (1st& 0th& th& )

as well as $ac,wards (nd& th& 2th& ).

High fre%#ency c#rrents ind#ced in the rotor f#rther increase losses.
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what are harmonics

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