by **Simran Nanda, Keysight Technologies**

Harmonic analysis helps design electronics that will behave well on the power grid.

Electronics that include switch-mode power supplies (SMPSs) and VFDs depend on non-linear components to minimize size and cost. This approach, however, forces designers to note the impact non-linear current flows have on the signal integrity of the input mains power

SMPSs, for example, typically draw non-linear current and are therefore significant sources of harmonics on the power network. The same applies to VFDs, used with ac motors as often found in HVAC equipment and industrial fans. Even LED lamps, despite their low power consumption, can produce significant harmonics when a multitude of LED lamps are installed in a building or house.

The negative effects of harmonics are well-known. They can include overheating of cabling and transformers, current flowing through neutral ac conductors, nuisance tripping of circuit breakers, high electromagnetic emissions and reduced life of motors and transformers. In addition, the presence of these harmonics forces transformers and cables to have a higher rated capacity than would otherwise be necessary. To alleviate such problems, designers begin by assessing the actual harmonic levels. Unfortunately, getting a handle on the amplitude and character of harmonics present can be a challenging task.

Measuring the Total Harmonic Distortion (THD), power factor, and harmonic levels of the input mains provides a good indicator of how a device-under-test impacts power quality.

IEEE and IEC guidelines describe how measurements must take place and also specify maximum harmonic levels for power electronics connected to the power network (IEEE 519, IEC 61000-3-2). Many standards related to power quality are written in reference to harmonics, because this provides a rational way to specify testable limits on distortion.

If a power supply meets the limits specified in standards, it will be a minimal burden to power quality. Harmonic analysis provides an excellent tool to help identify the source of signal integrity issues and meet the specifications that standards require.

**Basics of harmonic analysis**

Harmonic analysis uses a Fourier series to decompose a complicated periodic waveform into a set of simple sinusoids. The original waveform may be arbitrarily complex and most likely doesn’t have an analytical equation. The waveform can be digitized, however, and run through a harmonic analysis to generate a set of sinusoids (harmonics) that, when added together, approximate the original waveform.

Readers may recall that harmonics are organized by frequency. The lowest non-zero-frequency harmonic is the fundamental (or first harmonic). All other harmonics have frequencies that are integer multiples of the fundamental. The second harmonic is twice the fundamental frequency, the third is three times, and so on.

Now consider a simple system of an ac source and a load. The average power delivered to the load from the source over one power line cycle is given by:

where T is the period of the power line cycle, v(t) is the voltage across the load, and i(t) is the current through the load. Substituting the harmonics formulation for the v(t) and i(t) waveforms gives:

This is a more useful form. Decomposing P_{avg} into sums of harmonics now lets you compute the power being delivered by a particular harmonic frequency. For example, if you want to know how much power the ninth harmonic delivers, you can compute it directly by multiplying the amplitudes of the ninth harmonic voltage and current times the cosine of the angle difference between them:

An interesting prediction from the above decomposition is that both voltage and current must have corresponding harmonics present. Otherwise there will be no average power transfer from that particular harmonic. For example, if the voltage contains just the fundamental, and the current contains just the third harmonic, the average power will be zero.

If the voltage is a clean sine wave and the current waveform is non-sinusoidal, only the fundamental will transfer power. All the higher harmonics in the current waveform will be unproductive.

One goal of power system design is to maximize the power factor, PF, defined as:

But the harmonics that don’t transfer power work against this goal. They don’t contribute to P_{avg}, but they boost the V_{rms}I_{rms}. The extra harmonic voltage and/or current is not used, but the power system still must carry the extra harmonic voltage and/or current and incur the associated losses. To maximize power transfer efficiency, it’s therefore beneficial to minimize higher harmonics.

A sensible first step before harmonic analysis is to measure the THD, especially if the purpose is to troubleshoot power quality problems. This measurement can be done with a true-RMS digital multimeter with a bandwidth and sampling rate high enough to capture the higher harmonic frequencies. If the THD level is low (less than 3 to 5% depending on amplitude), there are no harmonics issues. However, if either THD is too high or you want to characterize the performance of your device, the THD measurement is not enough. You need the full breakdown of harmonic amplitudes.

You may also want to conduct multiple runs, evaluating the device in different operating modes and varying load conditions. With general-purpose instruments (digital multimeters, spectrum analyzers or scopes), you may find the data collection and post-processing for harmonics analysis extremely time-consuming. In addition, the process of comparing the harmonic levels to published standards can be tedious.

The modern power analyzer simplifies and speeds up such procedures with features specifically intended for harmonic analysis. Data collection, frequency domain processing, and harmonics analysis are built-in. Power analyzers typically have high sample rates and a graphical display that permits viewing the waveform in a manner analogous to that of a scope. This visualization is invaluable because you can quickly verify what you are measuring and that cabling or misconnections aren’t causing issues.

The power analyzer can simultaneously display other relevant information such as THD, frequency, amplitude, phase of the voltage, current, and power waveforms. Once the measurement setup is verified, you can simply turn on the harmonic analysis and the power analyzer will display the harmonics in a table and/or visual bar graph format.

Many power analyzers also have built-in pass/fail limits based on widely used standards. This makes for quick, convenient and immediate feedback on how the harmonics of the device under test stack up against the compliance limits.

All in all, use of a power analyzer to minimize higher harmonics and maximize power transfer permits a quick investigation of harmonic content. Harmonic analysis can provide actionable guidance to address signal integrity issues in power systems with periodic switching waveforms. Using a modern power analyzer simplifies measurements and lets you model complicated interacting voltage and current waveforms in a way that is easy to understand.

**References**

**Keysight Technologies**

www.keysight.com

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