Harmonics

INTRODUCTION

• A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency i.e., if fundamental frequency is f, the harmonics will have frequencies 2f, 3f, 4f etc.
• The harmonics have property that they are all periodic at fundamental frequency, hence sum of harmonics is also periodic at that frequency.
• Harmonic frequencies are equally spaced by the width of the fundamental frequency and can be found by repeatedly adding that frequency. Eg: if fund freq is Hz then the freq of harmonics will be 50hz, 75hz, 100hz etc.

HARMONICS (ELECTRIC POWER)

• Harmonics are a mathematical way of describing distortion to a voltage or current wave form.
• Harmonic refers to a component of wave form that occurs at an integer multiple of fundamental frequency.
• Harmonics are electric voltages and currents that appear on electric power system due to certain kinds of electric loads.
• Harmonic frequencies in power grid are frequent cause of power quality problems.
• Harmonics can be analyzed by using Fourier series. Fourier theory tells that any repetitive wave form can be defined in terms of summing sinusoidal waveforms which are integer multiples of the fundamental frequency.
• Harmonics should not be confused with spikes, dips, impulses, oscillations or other form of transients.
• A common term that is used in relation to harmonics is THD i.e., Total Harmonic Distortion. THD can be used to describe voltage or current distortion and is calculated as follows:

THD (%) = √ (ID₁² + ID₂²+ ….. + ID_n²)

Where, ID_n is the magnitude of n^th harmonic as a percentage of the fundamental freq.

CAUSES

• In a normal alternating current power system, the voltage varies sinusoidally at a specific frequency, usually at 50 or 60 Hz. When a linear electric load is connected to the system, it draws a sinusoidal current at same frequency as the voltage is usually not in phase.

• When a non linear load such as a rectifier is connected to a system, it draws a current that is not sinusoidal. The current waveform can become quite complex, depending upon the type of load and its interaction with other components of the system.
• However complex the waveform may be, it is possible to decompose it into a series of simple sinusoids which start at the power system fundamental frequency and occur at multiple fundamental frequency.
• Some e.g. of non linear loads are – electric arc furnaces, static VAR compensators, inverters, DC converters, switch mode power supplies and AC or DC motor drives.
• If we say 5^th harmonic it means that it is 1/5^thof the fundamental current.

EFFECTS

• One of the major effects of harmonics in a power system is to increase the current in the system. This is particularly in case of 3^rd harmonic, which causes a sharp increase in the zero sequence current and therefore increases the current in the neutral conductor.
• In addition to the increased line current, different pieces of electrical equipment can suffer from effects from harmonics on the power systems. E.g. electric motors experience hysteresis loss caused by eddy currents set up in the iron core of the motor. 5^th harmonic can cause counter electromotive force (CEMF).
• High levels of harmonic distortion can cause effects such as increased transformer, capacitor, motor or generator heating, mis-operation of electronic equipments, incorrect readings on meters, mis-operation of protective relays, interference with telephone circuits etc.
• Resonance occurs when a harmonic frequency produced by a non linear load closely coincides with a power system natural frequency.
• There are two types of resonance- series and parallel.
• Series resonance is a result of series combination of inductance and capacitance. It presents a low impedance path for harmonic currents at natural freq. The effect of series resonance can be a high voltage distortion level between the inductance and capacitance.

• Parallel resonance occurs when a natural frequency of the parallel combination of capacitor banks and system inductance falls at or near harmonic freq. This can cause substantial amplification of the harmonic current that flows between the capacitors and the system inductance. This may lead to the blowing of the capacitor fuse or its failure or over heating of the capacitor.