Technical Article

An Introduction to Harmonics

May 06, 2021 by Alex Roderick

This article will provide a basic introduction of harmonics in power engineering.

A harmonic is a current or voltage component at a frequency that is an integer (whole number) multiple (2nd, 3rd, 4th, etc.) of the fundamental frequency. For example, when the power supply is 60 Hz AC, the first harmonic (60 Hz) is the fundamental frequency. Other multiples of the fundamental harmonic are the second harmonic (120 Hz), third harmonic (180 Hz), fourth harmonic (240 Hz), etc. When these harmonics are present in a circuit, the resulting waveform consists of the sum of the fundamental and the higher harmonics at every instant. See Figure 1. The result is a distorted waveform from the contribution of the harmonics.

Figure 1. Harmonics are multiples of the fundamental waveform. Image courtesy of SALICRU
Figure 1. Harmonics are multiples of the fundamental waveform. Image courtesy of SALICRU



High-frequency harmonics can shorten the operating life or cause the failure of electrical equipment.

The basic design of most electrical distribution equipment assumes that the current and voltage waveforms of the circuit will be sinusoidal. In power distribution systems, there are different types of nonlinear components that draw current disproportionately with respect to the source voltage. This causes non-sinusoidal current waveforms that contain harmonic components. For example, the equipment that draws current in pulses for only a portion of the cycle will cause harmonic components. 

Knowledge of harmonics present on a power line is important for working on any power distribution system. When evaluating power quality, the incoming power, types (linear and nonlinear) and the number of loads, and equipment used in the distribution system must all be tested. A power quality meter can be used to measure the amount of voltage and current harmonics on a line. The amount of each harmonic present on the line and related information are indicated by numeric data and the frequency spectrum on the graphic display of the power quality meter. See Figure 2.


Figure 2. A power quality meter can be used to indicate the presence and magnitude of harmonics.
Figure 2. A power quality meter can be used to indicate the presence and magnitude of harmonics.


Odd-and Even-Numbered Harmonics

Odd harmonics are odd multiples (3rd, 5th, 7th, etc.) of the fundamental. They add together and increase their effect. Loads that draw odd harmonics have increased resistance (I2R) losses and eddy current losses in transformers. If the harmonics are significant, a transformer must be derated to prevent overheating.

Even harmonics are even multiples (2nd, 4th, 6th, etc.) of the fundamental. Even harmonics are generally fairly small because most non-linear loads in power systems produce odd harmonics and even harmonics tend to cancel each other. If even harmonics are present, this fact may be used as a troubleshooting tool. They generally indicate that a DC current may be present in the secondary winding of the transformer. The DC offset is typically caused by half-wave rectification due to a failed rectifier.

On alternate half-cycles, a DC offset may cause a transformer to become saturated and draw exceedingly high currents, causing the primary to burn out. The transformer core can experience a strong vibration and a very loud noise as a result of these issues. Generally, a DC offset of more than 1% of the rated current can cause problems.


Triplen Harmonics

Triplen harmonics (triplens) are odd multiples of the third harmonic (3rd, 9th, 15th, etc.). Only single-phase loads generate triplen harmonics. Three-phase loads do not generate triplen harmonics. Triplen harmonics can cause problems such as overloading of neutral conductors, telephone interference, and transformer overheating. Special types of transformers are used to reduce triplen harmonics.

Single-phase electronic loads connected phase-to-neutral, such as 120V office circuits or 277V lighting circuits, generate third harmonics with decreasing amounts of the higher odd harmonics.

Three-phase electronic loads connected phase-to-phase, such as 208V power supplies or 480 V variable-speed motor drives, do not generate the triplen harmonics, but they do generate significant levels of the other higher-level harmonics. See Figure 3. 


Figure 3. Triplen harmonics are generated by circuits wired phase-to-neutral.
Figure 3. Triplen harmonics are generated by circuits wired phase-to-neutral.


Third Harmonic

Single-phase electronic loads generate third harmonics in addition to smaller amounts of higher odd harmonics. Only the triplen harmonics contribute to the high neutral currents problem. The 9th, 15th, and higher triplen harmonics have a relatively lower current level and distort the neutral current just marginally. Hence, they do not have a noticeable impact on the actual rms neutral current.

Since the higher harmonics are relatively smaller, the third harmonic, as a percentage of total rms current, multiplied by three, is a fairly good estimate of the percent neutral current that results from three identical non-linear single-phase loads. Thus, the neutral current is at about 100% of the fundamental phase current when the third harmonic is at 331⁄3% of the fundamental phase current.


Harmonic Sequence

The harmonic sequence is the phasor rotation of the harmonic with respect to the fundamental (60 Hz) frequency. The order in which waveforms from each phase (A, B, and C) cross zero is referred to as phasor rotation. Phasor rotation is simplified by using lines and arrows instead of waveforms to show phase relationships. See Figure 4. The harmonic phase sequence is critical because it determines how the harmonic affects the operation of loads and components like conductors in a power distribution system.


Figure 4. Phasor rotation of Positive, Negative, and Zero Sequence Harmonics
Figure 4. Phasor rotation of Positive, Negative, and Zero Sequence Harmonics

Positive Sequence

Positive sequence harmonics (1st, 4th, 7th, etc.) have the same phase sequence as the fundamental harmonic. Positive sequence harmonics cause additional heat in transformers, conductors, circuit breakers, and panels in a power distribution system. A positive sequence harmonic rotates in the same direction as the fundamental in an induction motor.


Negative Sequence

Negative sequence harmonics (2nd, 5th, 8th, etc.) have the opposite phase sequence compared to the fundamental harmonic. Like positive sequence harmonics, negative sequence harmonics cause additional heat in power distribution system components such as transformers, conductors, circuit breakers, and panels. A negative sequence harmonic rotates in the opposite direction from the fundamental in an induction motor. The reverse rotation is not enough to cause the motor to reverse direction, but it does reduce the forward torque of the motor. The reduced torque causes a higher motor current to be drawn and results in excessive heating.


Zero Sequence

Zero sequence harmonics (3rd, 6th, 9th, etc.) do not produce a rotating field in either direction. However, zero-sequence harmonics do cause component and system heating. Zero sequence harmonics do not cancel but can add together in the neutral conductor of 3-phase, 4-wire systems. Single-phase appliances that use rectifier power supplies, including computers, fluorescent lighting with electronic ballasts, and other common electronic devices, contribute significantly to current on neutral wires.

  • rcvkumar2000 July 04, 2022

    Great summary, Very helpful. Thank you.

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    alvrm November 09, 2022

    This is a very well written explanation, although I will point out that zero sequence does not mean “no rotation” as you show in your picture.  It means all phases are in-phase with each other (or without a sequence).  If there was no rotation it wouldn’t be a harmonic or a frequency.  Triplen harmonics create current on a neutral wire because of the lack of sequence (all phases will pull current at the same time) thus requiring the neutral to make up for that summation of current.  If you were to draw a wave form of three phases, and then draw a multiple of 3 frequency for each phase (like 3rd harmonic), you would see that the 3 separate harmonics perfectly overlap each other (All in-phase with a rotation speed of 3 x 60 Hz = 180 Hz).  That’s why we say zero-sequence.

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