Harmonics

Harmonics

Introduction

Harmonics are produced in sine wave due to distortion and continuous use of nonlinear devices. In industrial and residential buildings, it affects power quality that causes severe conditions like; fault, malfunctioning of devices.

Therefore, these conditions are responsible for other problems like; reduced efficiency, overheating, and reliability of the equipment. Generally, harmonic currents flow back from the load to source. And it causing them to propagate as the voltage harmonics that wrench the source waveform.

In power system networks, the frequent sources of harmonics are adjustable speed drives (ASDs) and switching loads.

The Load employs SCRs, diodes, power transistors, and other power electronics switches. ASDs include pumps and chillers. The most common harmonics are third and fifth harmonics. Harmonics in the power system network can causes the below listed severe problems;

  • Make relay malfunction
  • Increase losses in capacitors, transformers
  • Increase noise in machine
  • Give rise to telephone interference
  • They are responsible for resonance

What are Harmonics?

While playing a musical instrument, we hear is the pitch. By the instrument, the pitch played is a combination of several frequencies that is heard as the single tone. Similarly, harmonics are defined as those frequencies that the integral multiple of frequency.

Harmonics of a waveform of voltage or current that are integral multiple of original frequency. Due to device frequency other than the standard frequency, harmonics are the distortions of the sine wave.

The pure sinusoidal waveform of voltage and current is considered as;

    \[ Voltage, \* v(t) = V \sin{\omega t} \]

    \[ Current, \* i(t) = I \sin{(\omega t \pm \phi)} \]

Where, ω = 2πf and that is known as angular frequency.

Ф = Phase angle difference between voltage and current. If this angle is negative current lags voltage and if this angle is positive voltage lags current.

Below figure shows, the example of pure sine waveform of voltage and current. And in this condition current lags voltage.

voltage and current waveform
voltage and current waveform

The voltage for the periodic waveform. Hence, the instantaneous value of voltage and current is changing with respect to time. So, general expression of voltage can be written as;

    \[ V = V_0 sin{(\omega t)} + V_1 \sin{(2 \omega t)} + V_2 \sin{(3 \omega t)} + ........ + V_{(n-1)} \sin{(n \omega t)} \]

Where,

Vo = DC constant,

VI, V2, V3 are the harmonics of the fundamental waveform.

Therefore, the Vo has the original frequency of f. and number of harmonics is multiplied by fundamental frequency. For example, 2nd harmonics is twice as that of fundamental frequency (2f), the 3rd harmonics has the frequency of 3f, and so on.

different harmonics waveforms
different harmonics waveforms

From the above waveform, it is clear that the second harmonic completes two full cycles as compared to fundamental waveform. Similarly, the third harmonics waveform complete three cycles when the fundamental waveform complete one cycle.

For the non-sinusoidal waveform, the harmonics of individual sinusoidal waveforms found individually. Then sum up all signals waveforms to find the net harmonics.

non-linear waveform with harmonics
non-linear waveform with harmonics

In simple terms, harmonics the diverse frequencies beside the original frequency summed in the current and voltage waveforms.

Harmonic Number (h)

Harmonic number is the separate frequency components that form the fundamental waveform. For example, if h = 3, it denotes to the third harmonic factor that is three times of the fundamental frequency.

If suppose the base frequency equals to 50Hz, eventually the third harmonic frequency is 3 multiplied by 50, (3X50=150Hz). So, our interest is which number of harmonic is present in the fundamental waveform.

Harmonic number is a sum of the reciprocal of the integers, making the harmonic series.

Odd and Even Harmonics Multiple

As the name suggest, odd harmonics contains odd times of fundamental harmonic like (3f, 5f, 7f,….) and even harmonic contain even times of fundamental harmonic like (2f, 4f, 6f, 8t…).

The first value of harmonic number (h=1) is allotted for the fundamental frequency and zero number of harmonics (h=0) allotted for the DC constant of the fundamental waveform.

The addition of positive and negative half cycle of one complete waveform known as DC Component. It produces undesirable effects in transformers core.

When the magnetising field is above the knee of the curve, saturation in the transformer occurs. The transformer should designed less than the knee of the curve for proper operation of transformer.

Transformer Characteristic
Transformer Characteristic

Huge magnetic field set up in the transformer, when DC voltage or current injected in the transformer winding. Hence, this additional DC voltage or current gets add up and moves the operation region of the transformer above or below the knee point.

Harmonics generally viewed as the integer number. In some cases, it is not an integer. Some examples are electric arc and arc welders. When current and voltage are out of phase, odd harmonics occur in the signal. These happens with the nonlinear load.

Transformer energizing core and arc furnaces produces even harmonics. The harmonics which has the frequencies below the fundamental frequencies known as sub harmonics.

The sub harmonic causes the resonance. It generated when there  large capacitor banks.

Causes of Harmonics

In the power system network, the harmonics causes by several reasons. Out of them, some reasons for causes the harmonics is as listed below;

Extensive use of non-linear loads causes the harmonics. The example of nonlinear loads includes diodes, rectifiers, transformers, and adjustable speed drives (ASD).

The diodes allow only positive cycle of the waveform. And in the transformer, current produced not sinusoidal. The waveforms of the nonlinear loads are different from that of the fundamental waveform.

The voltage distortion is inversely related to that of current distortion. Or in other words, current distortion increases with applied voltage.

During the time of generation, due to irregularities in of their own field, the waveform of current or the voltage has distortion in them due to irregularities in of their own field. The distortion produced at the initial state is very low, which is below 1%.

The produced voltage traverses many miles to reach the distribution system. The equipment installed at user side, produces harmonics currents with varying frequency.

The current distortion produced is the sum of voltage distortion and various powers available in the transmission line, distribution line and cables. Because, it transvers the power from load to source.

Voltage distortion
Voltage distortion

The above figure shows, the conversion of voltage deformation from current deformation. For example, based on their operation, UPS can generate voltage distortion. Inverter converts AC to DC.

Waveform shaping circuits used to get the original voltage from the distorted voltage waveform.

Voltage distortion tends to increase as they travel from the source to the load. When there distortion in source voltage itself, nonlinear currents also produced from linear loads.

Although same power line shared among the users, voltage distortion created as a result of current distortion may affect the other users as well.

The current distortions are due to out of phase voltage and currents, ASDs, lightning, rectifiers and arc furnaces.

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