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Evgenii Konkin
Evgenii Konkin

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Harmonic Distortion: The THD Number That Can Hide a Power Quality Problem

Harmonic distortion is one of those power quality numbers that looks simple until someone uses it as a diagnosis.

A power analyzer gives a THD percentage.

The number looks clean.

Maybe it says:

Voltage THD = 4.8%
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or:

Current THD = 13%
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Then the mistake begins.

Someone treats that one number as the whole power quality story.

But THD is not the whole story.

It is a ratio. It tells you how much harmonic RMS content exists compared with the fundamental RMS component. It does not tell you every harmonic order, resonance risk, neutral loading, transformer heating, capacitor bank stress, or whether the site complies with every applicable limit.

The formula is useful.

The interpretation needs care.

The basic THD formula

Total Harmonic Distortion compares the RMS value of harmonic components with the RMS value of the fundamental component.

For voltage THD:

THD (%) = [sqrt(H2² + H3² + H4² + ... + H13²) / V1] × 100
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For current THD:

THD (%) = [sqrt(I2² + I3² + I4² + ... + I13²) / I1] × 100
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Where:

V1 or I1 = fundamental RMS value
H2...H13 = harmonic RMS values above the fundamental
THD = total harmonic distortion, percent
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The same RMS structure applies to voltage and current.

But the values must not be mixed.

For voltage THD, use volts RMS for the fundamental and all harmonic components.

For current THD, use amps RMS for the fundamental and all harmonic components.

Do not mix volts and amps.

Do not mix peak values and RMS values.

Do not enter harmonic percentages when the calculator expects RMS magnitudes.

That sounds obvious, but it is one of the most common ways to get a wrong THD result.

THD is an RMS calculation, not an arithmetic sum

A common mistake is adding the harmonic values directly.

That is not how THD is calculated.

Harmonic components are combined as root-sum-square:

Harmonic_RMS = sqrt(H2² + H3² + H4² + ... + H13²)
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Then that combined harmonic RMS value is compared with the fundamental.

Example:

Fundamental voltage V1 = 230 V RMS
3rd harmonic H3 = 6 V RMS
5th harmonic H5 = 9 V RMS
7th harmonic H7 = 4 V RMS
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Wrong approach:

6 + 9 + 4 = 19 V
THD = 19 / 230 × 100
THD = 8.26%
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Correct RMS approach:

Harmonic_RMS = sqrt(6² + 9² + 4²)
Harmonic_RMS = sqrt(36 + 81 + 16)
Harmonic_RMS = sqrt(133)
Harmonic_RMS ≈ 11.53 V
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Now calculate THD:

THD = 11.53 / 230 × 100
THD ≈ 5.01%
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The wrong arithmetic-sum method gave 8.26%.

The correct RMS method gives about 5.01%.

That is a big difference.

The harmonic values were the same.

The calculation method changed the conclusion.

Worked example: current THD from a nonlinear load

Suppose a power quality check on a panel with VFDs and switching power supplies shows:

Fundamental current I1 = 120 A RMS
3rd harmonic I3 = 8 A RMS
5th harmonic I5 = 12 A RMS
7th harmonic I7 = 5 A RMS
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Use the current THD formula:

THD (%) = [sqrt(I3² + I5² + I7²) / I1] × 100
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Square the harmonic currents:

I3² = 8² = 64
I5² = 12² = 144
I7² = 5² = 25
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Add them:

64 + 144 + 25 = 233
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Take the square root:

sqrt(233) ≈ 15.26 A
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Divide by the fundamental current:

THD = 15.26 / 120 × 100
THD ≈ 12.72%
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So the current THD is about:

Current THD ≈ 12.7%
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That is not a clean sinusoidal current waveform.

It does not automatically prove equipment failure, but it is high enough to justify a closer review of nonlinear loads, transformer loading, neutral currents, cable heating, harmonic filters, and possible resonance conditions.

Voltage THD and current THD are not the same problem

Voltage THD and current THD both use the same mathematical structure.

But they do not mean the same thing.

Voltage THD describes distortion in the voltage waveform.

Current THD describes distortion in the load current waveform.

A site can have high current THD but acceptable voltage THD if the upstream system is stiff enough.

For example:

Current THD = high
Voltage THD = moderate or low
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That may mean the nonlinear loads are drawing distorted current, but the source impedance is low enough that the voltage waveform is not heavily distorted.

On the other hand, if current harmonics flow through system impedance, they can create voltage distortion:

Harmonic current × system impedance = harmonic voltage distortion
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That distorted voltage can then affect other equipment connected to the same system.

So the mistake is saying:

Current THD is high, therefore voltage quality is definitely bad.
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Or the opposite:

Voltage THD is low, therefore harmonics are not a problem.
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Both can be wrong.

You need to understand which waveform was measured and where.

The common mistake: confusing THD with TDD

THD and TDD are not the same.

THD compares harmonic RMS content with the fundamental RMS component:

THD = harmonic RMS content / fundamental RMS component
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TDD compares current harmonic content with maximum demand load current:

TDD = harmonic current content / maximum demand load current
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That difference matters in electrical power systems.

Current THD can look high at light load because the fundamental current is small.

Example:

Harmonic current RMS = 10 A
Fundamental current = 40 A
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Then:

Current THD = 10 / 40 × 100
Current THD = 25%
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Now suppose the same harmonic current exists when the fundamental current is higher:

Harmonic current RMS = 10 A
Fundamental current = 200 A
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Then:

Current THD = 10 / 200 × 100
Current THD = 5%
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The harmonic current stayed the same.

The THD percentage changed because the fundamental current changed.

That is one reason current distortion compliance work often needs more than a simple current THD number.

THD is useful.

But for standards review, utility requirements, and point-of-common-coupling studies, TDD and individual harmonic limits may be required.

A single THD number can hide the dominant harmonic

Another mistake is looking only at total THD and ignoring which harmonic order is causing it.

For example, two systems may both show:

THD = 8%
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But the harmonic spectrum may be very different.

System A:

Mostly 5th harmonic
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System B:

Mostly 3rd harmonic
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Those are not the same engineering problem.

A strong 5th harmonic may be associated with six-pulse rectifiers, VFDs, and certain power electronic loads.

A strong 3rd harmonic is a triplen harmonic and can be especially important in three-phase four-wire systems because triplen harmonics can add in the neutral conductor instead of cancelling like balanced fundamental currents.

So the total THD value is useful, but the spectrum matters.

A total number tells you distortion exists.

The individual harmonic orders help explain what kind of distortion you have.

Why harmonics matter

Harmonics are not just waveform aesthetics.

They can create real system effects:

Extra transformer heating
Extra conductor heating
Neutral conductor loading
Motor heating and torque pulsation
Capacitor bank stress
Nuisance trips
Generator voltage distortion
Poor power factor behavior
Control and sensor interference
Resonance risk with power factor correction capacitors
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A waveform can deliver power and still be distorted.

A panel can operate and still run hotter than expected.

A transformer can be within kVA rating and still be stressed by harmonic heating.

That is why THD is often used as an early warning indicator.

It does not complete the diagnosis, but it tells you whether the waveform is close to sinusoidal or noticeably distorted.

Example: why low voltage THD may not mean “no harmonic issue”

Suppose a facility has several VFDs.

Measured values:

Voltage THD = 3.5%
Current THD = 38%
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Someone may say:

Voltage THD is only 3.5%, so harmonics are fine.
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That may be too optimistic.

The voltage waveform may still be acceptable because the source is strong, but the current waveform is heavily distorted. That distorted current may still contribute to:

Transformer heating
Cable heating
Generator loading issues
Harmonic filter requirements
Neutral conductor concerns
Distorted voltage under weaker source conditions
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The correct conclusion is more careful:

Voltage distortion is currently moderate, but current distortion is high and should be reviewed at the load and distribution level.
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That is a better engineering interpretation.

Example: why high current THD at light load may be misleading

Now consider a UPS or VFD at very light load.

Measured values:

Fundamental current = 10 A
Combined harmonic RMS current = 5 A
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Then:

Current THD = 5 / 10 × 100
Current THD = 50%
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That looks terrible.

But the absolute harmonic current is only 5 A.

At higher load, the same equipment may show:

Fundamental current = 100 A
Combined harmonic RMS current = 10 A
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Then:

Current THD = 10 / 100 × 100
Current THD = 10%
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The THD percentage dropped a lot.

But the harmonic current doubled from 5 A to 10 A.

So current THD must be interpreted with load level.

High THD at light load can look dramatic because the denominator is small.

That does not mean it should be ignored, but it should not be interpreted without load context.

RMS values matter

The THD formula requires RMS values.

If someone enters peak values for harmonics but RMS for the fundamental, the result is wrong.

For a sine component:

Vpeak = Vrms × sqrt(2)
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If a harmonic component is accidentally entered as peak instead of RMS, it will be about 1.414 times too large.

That error propagates into the root-sum-square calculation and inflates the THD result.

The safest workflow is:

Confirm the analyzer reports RMS harmonic magnitudes.
Use the same unit for all components.
Do not mix voltage and current.
Do not mix RMS and peak.
Do not enter percentages as RMS values.
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The formula is only as good as the input definitions.

THD does not prove compliance by itself

THD is a screening metric.

It is not a full compliance report.

A final power quality review may require:

Measured harmonic spectrum
Individual harmonic order limits
Point of common coupling definition
Short-circuit ratio
Maximum demand load current
TDD calculation
Voltage distortion limits
Current distortion limits
Measurement duration
Operating scenarios
Utility interconnection requirements
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This is especially important for large facilities, industrial plants, data centers, solar inverters, generator systems, and sites with major nonlinear loads.

A calculator can give a consistent first-pass THD estimate.

It cannot replace a full power quality study when standards compliance or utility approval is involved.

Practical design takeaway

Use THD as a power quality screening number.

It helps answer:

How distorted is the waveform compared with the fundamental?
Which harmonic RMS values dominate the result?
Is the waveform close to sinusoidal or heavily distorted?
Is the distortion voltage THD or current THD?
Is a detailed harmonic review needed?
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But do not use THD as the only conclusion.

It does not show the full harmonic spectrum by itself.

It does not calculate TDD.

It does not check IEEE 519 compliance by itself.

It does not model resonance.

It does not calculate transformer derating.

It does not prove that neutral current, capacitor stress, or motor heating is acceptable.

It is a first-pass indicator.

A useful one.

But still only one part of the power quality picture.

Final thought

Total Harmonic Distortion is a compact number:

THD (%) = [sqrt(sum of harmonic RMS values squared) / fundamental RMS] × 100
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That compact number can be very useful.

It can show when a waveform is close to sinusoidal.

It can warn that nonlinear loads are producing significant distortion.

It can help compare voltage and current quality between systems.

But it can also mislead if the engineer forgets the context.

Current THD changes with load level.

Voltage THD and current THD describe different things.

A single THD value can hide the dominant harmonic order.

And THD is not the same as TDD or full standards compliance.

For quick THD checks from fundamental and harmonic RMS values, use the Harmonic Distortion Calculator on CalcEngineer.

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