For example, in the figure below, the sum of the fundamental frequency and signals with frequencies 5, 7, 11 and 13 times the fundamental results in a near square waveform. The signal with a frequency 5 times the fundamental is called the 5th harmonic.

Thus, for a non-sinusoidal current, such as the input current of a typical Variable Frequency Drive (VFD), a harmonic analysis refers to the dissection of the current into the fundamental current (60Hz) and currents with frequencies equal to an integer multiple of the fundamental frequency. This breakdown is called a Fourier analysis, and can be seen in the diagrams below, where the current of a VFD (only half a period is shown) is subdivided into its harmonic currents.

Note here that the harmonic current caused by the rectifier part of the variable frequency drive, typically a 6-pulse diode bridge rectifier, has no even or 3rd order harmonics. If the signal is symmetrical to the time/x-axis, as the current of a 6-pulse diode rectifier normally is, no even harmonics will exist. Hence, only under severe unbalance of the supply voltage or different voltage drops of the upper diodes and lower diodes of a rectifier bridge (i.e. half controlled rectifiers or half wave rectifiers) would even harmonics appear. Third order harmonics are said to be zero-sequence currents (3rd order harmonics have the same phase-angle in all three phases and can therefore not be summed to zero in a star-connection as the fundamental is displaced by 120°) and can therefore not appear in a three-phase load with no neutral connection; which would work as a return path. If, however, 3rd order harmonics appear in a three-phase load without a neutral conductor, the cause is then voltage unbalance. This is because the 3rd order harmonics are no longer zero-sequence. Third order harmonics may also be caused by single-phase equipment connected between one phase and the neutral, in which case the 3rd order harmonics can cause severe overheating of the neutral conductor even though the equipment is balanced over the three phases. The 3rd order harmonics would sum up arithmetically and the neutral would then conduct up to three times the 3rd order of one phase.

The effects of harmonics
In variable frequency drive applications, both the harmonic current distortion and voltage distortion are of interest. The harmonic current and voltage distortion have different effects on the power system, and it is therefore important to distinguish between them when discussing the effects of ”harmonics.”

The harmonic currents can be described as reactive currents adding to the active current. Consequently, the harmonic current distortion increases the RMS current and, if not taken into account, can result in overheating of components such as the supply transformer or cables. The amount of harmonic current distortion is often described as a percentage of the fundamental current, also known as the total harmonic current distortion (THiD).

Harmonic current normally flows from the harmonic current generator (the VFD) to the main power. The voltage drop caused by the harmonic currents over the supply impedance then causes harmonic voltage distortion. The harmonic voltage distortion is the product of harmonic current distortion and the supply impedance. A grid with greater impedance (in other words, a weaker grid) therefore yields higher voltage distortion.

Harmonic voltage distortion can interfere with motors or electronic equipment connected to the same line and can eventually cause them to fail or operate erratically. The amount of harmonic voltage distortion is often described as a percentage of the fundamental voltage, also known as the total harmonic voltage distortion (THvD).

Harmonic limiting standards and recommendations
Several national and international standards and recommendations exist to prevent potential harmonic problems. One theme common among these standards is the objective of keeping the harmonic voltage distortion below a certain level. In the US, the IEEE recommendation, IEEE 519-1992, specifies a planning level of THvD of 5% on general systems. As a result, numerous methods of limiting harmonic current distortion have been developed or are under development.

Harmonic reduction techniques
To avoid potential harmonic problems or to comply with standards and recommendations such as IEEE 519-1992, several different harmonic reduction techniques for variable frequency drives exist.

The best-known solutions are:
- AC coils
- Built-in DC-coils
- Multi-pulse (12- and 18-pulse) front ends
- Active filters
- Passive filters

The most common and easiest harmonic reduction technique is the use of AC-line reactors in front of the VFD. The line reactor smoothes the line current drawn by the VFD and provides significantly reduced current distortion that cannot be achieved by a standard 6 pulse VFD without line reactors. Similar effects can be obtained with DC-coils built into the VFD, which offer some advantages over AC-line reactors. DC-coils are smaller in size than AC-coils, have higher efficiency, and result in no reduction of the DC-link voltage.

Twelve- and eighteen-pulse input bridge rectifiers are another solution. In theory, the 5th and 7th harmonic currents (and for 18-pulse, the 11th and 13th, as well) are cancelled by phase-shifting transformers coupled with the use of two (or three) six-pulse diode rectifiers. However, a significant disadvantage of the multi-pulse harmonic reduction technique is the susceptibility to non-ideal supply voltage. In reality, some voltage unbalance and/or harmonic background distortion is present, and complete cancellation of the 5th and 7th (11th and 13th) is rarely achieved. Additionally, transformer losses increase heating and reduce the efficiency of the entire VFD system.

Active filtration is an emerging technology with the potential to reduce the harmonic distortion to almost zero. However, for the active filter to be a successful harmonic reduction technique in the future, some significant challenges need to be addressed. For example, the active filter switches high voltages directly on the main power, resulting in the introduction of high frequency noise. For the time being, there are no guidelines to regulate the amount of the switching frequency noise (2kHz – 150 kHz) allowed onto the main power, thus a major task for the future is to determine a reasonable level of high frequency noise to ensure that no damage occurs on other equipment.

The Low Pass Filter solution
The following are two different levels of harmonic reduction techniques:

1. Some VFDs are equipped with built-in DC-link inductors, typically reducing harmonics by 50% as compared to VFDs without DC-link inductors. The built-in DC-link inductance not only ensures compliance with harmonic limits in most applications, but also ensures a longer lifetime for the DC-link capacitors.

2. New generation passive filters, called advanced harmonic filters, can be placed in front of one or several drives, reducing total harmonic current to less than 5%.
Advanced harmonic filters are passive filters and are not to be confused with traditional harmonic trap filters. They offer improved harmonic reduction performance over other known solutions:

Performance at non-ideal supply voltage
Recognizing that the ideal three-phase supply voltage is nearly non-existent, the new advanced harmonic filters are developed in such a way that they ensure values close to or better than 5% THiD even if the pre-existing total harmonic voltage distortion of the supply voltage is 2% or the voltage unbalance is 2%.

Comparing this performance with traditional solutions such as a 12-pulse or 18-pulse rectifier as in the figures below, it becomes clear that advanced harmonic filters provide superior performance under real-world conditions.

Current and Distortion Spectrum at Full Load

THiD of advanced harmonic filter vs. 18-pulse rectifier with up to 3% line unbalance

THiD of advanced harmonic filter vs. 18-pulse rectifier with background voltage distortion

Conclusion
In the vast majority of drive applications, the supply voltage conditions cannot be expected to be ideal. Under real-world conditions, advanced harmonic filters provide better performance than any previously known harmonic reduction technique for variable speed drives.

Furthermore, advanced harmonic filters provide greater versatility and ease of use than other harmonic reduction solutions. The installation and start-up of advanced harmonic filters are far simpler than complicated 12- and 18-pulse systems, especially in retrofit applications. And because a single filter can serve multiple drives, advanced harmonic filters make economic sense, too.