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Home / AC Circuits / Harmonics


HARMONICS

Harmonics are unwanted higher frequencies which superimposed on the fundamental
waveform creating a distorted wave pattern



Harmonics and harmonic distortion is the difference between the ideal sinusoidal
waveform the supply voltage or the load current waveform should look like, and
what it really is as a result of a non-linear load.

In an AC circuit, a resistance behaves in exactly the same way as it does in a
DC circuit. That is, the current flowing through the resistance is proportional
to the voltage across it. This is because a resistor is a linear device and if
the voltage applied to it is a sine wave, the current flowing through it is also
a sine wave so the phase difference between the two sinusoids is zero.

Generally when dealing with alternating voltages and currents in electrical
circuits it is assumed that they are pure and sinusoidal in shape with only one
frequency value, called the “fundamental frequency” being present, but this is
not always the case.

In an electrical or electronic device or circuit that has a voltage-current
characteristic which is not linear, that is, the current flowing through it is
not proportional to the applied voltage. The alternating waveforms associated
with the device will be different to a greater or lesser extent to those of an
ideal sinusoidal waveform. These types of waveforms are commonly referred to as
non-sinusoidal or complex waveforms.



Complex waveforms are generated by common electrical devices such as iron-cored
inductors, switching transformers, electronic ballasts in fluorescent lights and
other such heavily inductive loads as well as the output voltage and current
waveforms of AC alternators, generators and other such electrical machines. The
result is that the current waveform may not be sinusoidal even though the
voltage waveform is.

Also most electronic power supply switching circuits such as rectifiers, silicon
controlled rectifier (SCR’s), power transistors, power converters and other such
solid state switches which cut and chop the power supplies sinusoidal waveform
to control motor power, or to convert the sinusoidal AC supply to DC. Theses
switching circuits tend to draw current only at the peak values of the AC supply
and since the switching current waveform is non-sinusoidal the resulting load
current is said to contain Harmonics.

Non-sinusoidal complex waveforms are constructed by “adding” together a series
of sine wave frequencies known as “Harmonics”. Harmonics is the generalised term
used to describe the distortion of a sinusoidal waveform by waveforms of
different frequencies.

Then whatever its shape, a complex waveform can be split up mathematically into
its individual components called the fundamental frequency and a number of
“harmonic frequencies”. But what do we mean by a “fundamental frequency”.




FUNDAMENTAL FREQUENCY

A Fundamental Waveform (or first harmonic) is the sinusoidal waveform that has
the supply frequency. The fundamental is the lowest or base frequency, ƒ on
which the complex waveform is built and as such the periodic time, Τ of the
resulting complex waveform will be equal to the periodic time of the fundamental
frequency.

Let’s consider the basic fundamental or 1st harmonic AC waveform as shown.





Where: Vmax is the peak value in volts and ƒ is the waveforms frequency in Hertz
(Hz).

We can see that a sinusoidal waveform is an alternating voltage (or current),
which varies as a sine function of angle, 2πƒ. The waveforms frequency, ƒ is
determined by the number of cycles per second. In the United Kingdom this
fundamental frequency is set at 50Hz while in the United States it is 60Hz.

Harmonics are voltages or currents that operate at a frequency that is an
integer (whole-number) multiple of the fundamental frequency. So given a 50Hz
fundamental waveform, this means a 2nd harmonic frequency would be 100Hz (2 x
50Hz), a 3rd harmonic would be 150Hz (3 x 50Hz), a 5th at 250Hz, a 7th at 350Hz
and so on. Likewise, given a 60Hz fundamental waveform, the 2nd, 3rd, 4th and
5th harmonic frequencies would be at 120Hz, 180Hz, 240Hz and 300Hz respectively.

So in other words, we can say that “harmonics” are multiples of the fundamental
frequency and can therefore be expressed as: 2ƒ, 3ƒ, 4ƒ, etc. as shown.


COMPLEX WAVEFORMS DUE TO HARMONICS






Note that the red waveforms above, are the actual shapes of the waveforms as
seen by a load due to the harmonic content being added to the fundamental
frequency.

The fundamental waveform can also be called a 1st harmonics waveform. Therefore,
a second harmonic has a frequency twice that of the fundamental, the third
harmonic has a frequency three times the fundamental and a fourth harmonic has
one four times the fundamental as shown in the left hand side column.

The right hand side column shows the complex wave shape generated as a result of
the effect between the addition of the fundamental waveform and the harmonic
waveforms at different harmonic frequencies. Note that the shape of the
resulting complex waveform will depend not only on the number and amplitude of
the harmonic frequencies present, but also on the phase relationship between the
fundamental or base frequency and the individual harmonic frequencies.

We can see that a complex wave is made up of a fundamental waveform plus
harmonics, each with its own peak value and phase angle. For example, if the
fundamental frequency is given as; E = Vmax(2πƒt), the values of the harmonics
will be given as:

For a second harmonic:

E2 = V2(max)(2*2πƒt) = V2(max)(4πƒt), = V2(max)(2ωt)

For a third harmonic:

E3 = V3(max)(3*2πƒt) = V3(max)(6πƒt), = V3(max)(3ωt)

For a fourth harmonic:

E4 = V4(max)(4*2πƒt) = V4(max)(8πƒt), = V4(max)(4ωt)

and so on.

Then the equation given for the value of a complex waveform will be:





Harmonics are generally classified by their name and frequency, for example, a
2nd harmonic of the fundamental frequency at 100 Hz, and also by their sequence.
Harmonic sequence refers to the phasor rotation of the harmonic voltages and
currents with respect to the fundamental waveform in a balanced, 3-phase 4-wire
system.

A positive sequence harmonic ( 4th, 7th, 10th, …) would rotate in the same
direction (forward) as the fundamental frequency. Where as a negative sequence
harmonic ( 2nd, 5th, 8th, …) rotates in the opposite direction (reverse) of the
fundamental frequency.

Generally, positive sequence harmonics are undesirable because they are
responsible for overheating of conductors, power lines and transformers due to
the addition of the waveforms.

Negative sequence harmonics on the other hand circulate between the phases
creating additional problems with motors as the opposite phasor rotation weakens
the rotating magnetic field require by motors, and especially induction motors,
causing them to produce less mechanical torque.

Another set of special harmonics called “triplens” (multiple of three) have a
zero rotational sequence. Triplens are multiples of the third harmonic ( 3rd,
6th, 9th, …), etc, hence their name, and are therefore displaced by zero
degrees. Zero sequence harmonics circulate between the phase and neutral or
ground.

Unlike the positive and negative sequence harmonic currents that cancel each
other out, third order or triplen harmonics do not cancel out. Instead add up
arithmetically in the common neutral wire which is subjected to currents from
all three phases.

The result is that current amplitude in the neutral wire due to these triplen
harmonics could be up to 3 times the amplitude of the phase current at the
fundamental frequency causing it to become less efficient and overheat.

Then we can summarise the sequence effects as multiples of the fundamental
frequency of 50Hz as:


HARMONIC SEQUENCING

Name Fund. 2nd 3rd 4th 5th 6th 7th 8th 9th Frequency, Hz 50 100 150 200 250 300
350 400 450 Sequence + – 0 + – 0 + – 0

Note that the same harmonic sequence also applies to 60Hz fundamental waveforms.

Sequence Rotation Harmonic Effect + Forward Excessive Heating Effect – Reverse
Motor Torque Problems 0 None Adds Voltages and/or Currents in Neutral Wire
causing Heating


HARMONICS SUMMARY

Harmonics are higher frequency waveforms superimposed onto the fundamental
frequency, that is the frequency of the circuit, and which are sufficient to
distort its wave shape. The amount of distortion applied to the fundamental wave
will depend entirely on the type, quantity and shape of the harmonics present.

Harmonics have only been around in sufficient quantities over the last few
decades since the introduction of electronic drives for motors, fans and pumps,
power supply switching circuits such as rectifiers, power converters and
thyristor power controllers as well as most non-linear electronic phase
controlled loads and high frequency (energy saving) fluorescent lights. This is
due mainly to the fact that the controlled current drawn by the load does not
faithfully follow the sinusoidal supply waveforms as in the case of rectifiers
or power semiconductor switching circuits.

Harmonics in the electrical power distribution system combine with the
fundamental frequency (50Hz or 60Hz) supply to create distortion of the voltage
and/or current waveforms. This distortion creates a complex waveform made up
from a number of harmonic frequencies which can have an adverse effect on
electrical equipment and power lines.

The amount of waveform distortion present giving a complex waveform its
distinctive shape is directly related to the frequencies and magnitudes of the
most dominant harmonic components whose harmonic frequency is multiples (whole
integers) of the fundamental frequency. The most dominant harmonic components
are the low order harmonics from 2nd to the 19th with the triplens being the
worst.


Previous
Reactive Power
Next
Passive Components in AC Circuits


READ MORE TUTORIALS INAC CIRCUITS

 * 1. AC Waveform and AC Circuit Theory
 * 2. Sinusoidal Waveforms
 * 3. Phase Difference and Phase Shift
 * 4. Phasor Diagrams and Phasor Algebra
 * 5. Complex Numbers and Phasors
 * 6. AC Resistance and Impedance
 * 7. AC Inductance and Inductive Reactance
 * 8. AC Capacitance and Capacitive Reactance
 * 9. Series RLC Circuit Analysis
 * 10. Parallel RLC Circuit Analysis
 * 11. Series Resonance Circuit
 * 12. Parallel Resonance Circuit
 * 13. RMS Voltage Tutorial
 * 14. Average Voltage Tutorial
 * 15. Reactive Power
 * 16. Harmonics
 * 17. Passive Components in AC Circuits
 * 18. Power in AC Circuits
 * 19. Power Triangle and Power Factor
 * 20. Power Factor Correction
 * 21. Impedance and Complex Impedance


118 COMMENTS




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 * Gary Harstvedt
   
   I wanted an antenna which could accept multiple harmonic sequences by a
   master / slave cable ready tuner receptor and find the variable for changing
   reception along with the remote control unit.
   
   Posted on March 17th 2023 | 10:38 pm
   Reply
   
 * Philip
   
   Just purchased a EcoFlow Delta 2 a weeks ago on Amazon. Has from 1800 watts
   to 2200 watt output. User manual describes consistent ac 119.7 volts 50/60HZ
   output from 6 receptacles. Notice when plugged into 1 – 3 prong receptacle
   and running my 1550 watt microwave. I noticed a sound that my microwave
   seemed to be bogging down and straining to operate to warm a cup of coffee. I
   became concerned so I meter tested the receptical it was plugged into on the
   solar generator it showed a 119.3V at 50Hz consistant output. I checked the
   other 5 remaining receptical on the solar generator. Yet my house recepticals
   any one I tested put out 120.3 volts at 60Hz consistently. Im concerned that
   the 50Hz 119.3 this solar generator puts out may be detrimental to my major
   appliances Fridg, microwave, large Toaster and even my Furnace Blower motor
   and other appliances and electronics and may cause some of them to fail I I
   keep this EcoFlow Delta3 solar generator. I just don’t know. Should I bee
   concerned or is this much to do about nothing. Your expert opinion would be
   greatly appreciated. Thanks. Philip of 73 yrs. Thanks
   
   Posted on January 31st 2023 | 5:11 am
   Reply
   * William P Albright
     
     Philip, if your power source is providing 50hz and your appliances are
     North American 60hz, they won’t run as efficiently as they were designed.
     Transformers are wound a particular way to make the best inductive
     conversion at a given frequency. Same with motor windings. It will cause
     excessive heat and a low power effect, such as with the microwave. The high
     voltage transformer is whats taking the brunt of the effect from lower
     frequency. In turn its output voltage which gets rectified to close to 3000
     vdc in a doubler circuit using a high voltage capacitor and rectifier off
     the secondary of that transformer. So your supply to the magnetron will be
     less than what it needs. This will be the result of taking longer to cook.
     Also running low frequency AC can make a noise like its “laboring”, the
     normal inductive hum will be more prominent can even cause physical
     vibration of inductive components. A good example of problems with AC not
     being on frequency or sinusoidal in wave shape, is the output of
     inexpensive power inverters. Basically they are alternating a DC voltage 60
     times a second by swapping polarity with the use of power transistors. That
     type of power doesn’t have the linear gradual ramp as its cycle runs. True
     AC climbs up to its peak in a linear fashion and comes back down in that
     same linear fashion. Switching DC goes peak to peak instantaneously and
     there’s no gradual ramp up or down. For transformer action to take effect
     most efficiently it needs that sine wave and at the frequency it was
     designed for.
     You said the user manual states 50/60hz. Is it selectable? It should be if
     they’re referring to an inverter output. That kind of nomenclature usually
     means a product is capable of operating at 50 or 60 hz and generally will
     also state 120/240 vac most computer power supplies for laptops and
     cellphone chargers will automatically detect the input voltage and set
     itself to run on either without user selection. If you are running an
     inverter for your power, the base frequency or the “fundamental” frequency
     should be 60hz. As a matter of fact the frequency of AC coming from the
     utility company to residential homes is ‘always’ dead on 60hz all the time.
     The voltage may swing up/down especially during peak use periods, but that
     60hz will always be 60hz. Kinda gives an idea of its importance in AC
     power. Its probably directly dependent on the RPM of the megawatt
     generators/alternators the power companies use to make the electric current
     for our homes. Some old school electric clocks like you find on a stove,
     use that 60 hz for the time base in the design of those clocks that had a
     basic induction motor in them. Being 60 min in hour and 60 seconds in a
     minute, this simplified designing them. If your inverter cannot be set to
     put out 60hz you may want to see if you can return that one and get a 60hz
     inverter. You’ll have less possible problems, some equipment it will ruin
     it. Some plug in wall transformers like ones that take 120vac and have a
     9vdc output for a radio, or a Wi-Fi router, etc. They will run hot, and
     that just takes life off the unit and possibly complete failure. Dremel
     tool motors and the speed control circuit doesn’t like non-standard AC at
     all. Low speed, gets hot. With those problems of inefficiency going on,
     this means your using up more of your battery runtime because you’re having
     to run a microwave for longer times, probably is pulling a bit more current
     than normal also, so thats dragging your battery source down. Best thing
     get 60hz AC !!! Hope that explains whats going on when the frequency isn’t
     correct. I wouldn’t put my appliances or electronics on it. Lamps
     incandescent no problem, electric heater without digital thermostat no
     problem, although I wouldn’t use electric heat with battery/inverter.
     There’s way better ways for heat. Gas! Fireplace! B4 using electric.
     
     Posted on April 24th 2023 | 8:40 am
     Reply
     
   
 * Pathmanaban Deenadayalan
   
   Very informative.
   
   Posted on June 20th 2022 | 2:37 am
   Reply
   
 * Sunil Bhatt
   
   I interest in power quality improvement .
   
   Posted on June 09th 2022 | 8:32 am
   Reply
   
 * Ashwini Pandey
   
   Very informative content
   
   Posted on June 05th 2022 | 1:51 pm
   Reply
   
 * Vidhusharani R
   
   Nill
   
   Posted on May 26th 2022 | 4:05 am
   Reply
   
 * Abdulkadir A. Ohiare
   
   The reading is very educative and informative.
   
   Posted on April 23rd 2022 | 5:32 pm
   Reply
   
 * Marlene
   
   My neighbors AC vibration is making me crazy and they don’t care. The
   vibration stretches the entire length of my house on the side where their AC
   is located. I bought MLV soundproofing for outside use and would like to know
   how best to apply it to the fence (overlap, height, Lee, thickness, etc) .
   
   I need a lot of MLV material to cover my fence and it is exspensive. Can you
   please recommend what thickness, height and length, overlap, etc I should use
   and the most important thing to consider when soundproofing. Thank you for
   your help!
   
   Posted on April 22nd 2022 | 3:26 pm
   Reply
   * William P Albright
     
     Marlene, I know you said your neighbors don’t care, but your dilemma sounds
     like they need their AC unit serviced. It could be a bearing in the
     condenser fan motor or simply the metal grill is loose and vibrating. Both
     can cause an annoying sound. Neighbors probably don’t hear it from where
     they’re located inside or it’s on the side of a garage. What I am getting
     at is, try to solve the problem from the source. Do you think the neighbor
     would object to you having an AC tech look at it? Maybe go halves on the
     cost. I think it would be cheaper going this route. The insulating the
     problem doesn’t have any guarantee that it will block it satisfactorily.
     While fixing the problem would eliminate it. I’m not familiar with MLV
     material, it may be unpleasant to look at lining your fence? I don’t know
     but something to take into consideration.
     
     Posted on April 24th 2023 | 9:05 am
     Reply
     
   
 * Afonso Pereira
   
   you just save my college essay, thanks a lot
   
   Posted on February 14th 2022 | 11:05 pm
   Reply
   
 * Mohamed Salim Abdalla
   
   Thank you very much.
   The way you have written is very clear and understandable.
   
   Posted on February 10th 2022 | 2:14 pm
   Reply
   
 * Stanley
   
   Someone should kindly help out with
   
   A complex voltage wave is given by
   200Sin(((5)/(9))fPi^(2))+80Sin(((5)/(3))fPi^(2))+40Sin(((25)/(9))fPi^(2))
   
   Determine
   A. Which harmonics are present
   B. The RMS value of the fundamental
   C. The frequency of the fundamental
   D. The periodic time of the fundamental
   E. The frequency of the harmonics
   
   Posted on November 30th 2021 | 10:31 am
   Reply
   
 * Ryan
   
   Can you make a detail about harmonic sequence?
   Thanks
   
   Posted on May 30th 2021 | 11:54 am
   Reply
   
 * Abdirisak Abdukadir
   
   thanks.
   could you make a lesson of calculations?
   
   Posted on May 15th 2021 | 4:32 pm
   Reply
   
 * Shahid Lateef
   
   I am really confused that for the real power to flow in harmonics frequences
   must be same but is the same true for reactive power also ( i.e for the
   reactive power to flow frequences must be same)
   
   Posted on March 25th 2021 | 7:03 am
   Reply
   
 * Dada oluwagbenga
   
   Very knowledgeable lectures, but please do guys have any ideas how to model a
   nonlinear load with Matlab using an equivalent resistor and set of current
   sources.
   
   Posted on March 10th 2021 | 7:47 am
   Reply
   
 * Heramb Mayadeo
   
   First of all, thank you for posting this fundamental article. I wish to know
   if we take the ratio of the magnitude of nth order harmonic to the magnitude
   of the fundamental harmonic, what that ratio is called? Is there any such
   quantity defined? For example V2max/V1max and V3max/V1max.
   
   Posted on February 17th 2021 | 12:44 am
   Reply
   
 * Ajoy Ghosh
   
   Nice
   
   Posted on February 08th 2021 | 2:24 pm
   Reply
   
 * Manish Shukla
   
   Nice and informative article.
   
   Posted on December 08th 2020 | 3:44 pm
   Reply
   
 * Harish Chandra Barai
   
   Good
   
   Posted on December 07th 2020 | 7:41 am
   Reply
   
 * Mpke
   
   Thanks. Is the ω in this equation a typo?
   For a third harmonic: E3 = V3max(3*2πƒt) = V3max(6πƒt), = V3max(3ωπt)
   
   Posted on November 28th 2020 | 3:56 pm
   Reply
   * Wayne Storr
     
     Thanks
     
     Posted on November 29th 2020 | 7:34 am
     Reply
     
   * More
   

View More



READ MORE TUTORIALS INAC CIRCUITS

 * 1. AC Waveform and AC Circuit Theory
 * 2. Sinusoidal Waveforms
 * 3. Phase Difference and Phase Shift
 * 4. Phasor Diagrams and Phasor Algebra
 * 5. Complex Numbers and Phasors
 * 6. AC Resistance and Impedance
 * 7. AC Inductance and Inductive Reactance
 * 8. AC Capacitance and Capacitive Reactance
 * 9. Series RLC Circuit Analysis
 * 10. Parallel RLC Circuit Analysis
 * 11. Series Resonance Circuit
 * 12. Parallel Resonance Circuit
 * 13. RMS Voltage Tutorial
 * 14. Average Voltage Tutorial
 * 15. Reactive Power
 * 16. Harmonics
 * 17. Passive Components in AC Circuits
 * 18. Power in AC Circuits
 * 19. Power Triangle and Power Factor
 * 20. Power Factor Correction
 * 21. Impedance and Complex Impedance

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