Harmonic THD formulas
Formula chart for total harmonic distortion from fundamental and harmonic RMS magnitudes.
THD measurements from one analyser record
Use these row summaries to read the calculation relationship before checking the value table.
Same-record harmonic set
Keep harmonic RMS inputs from one voltage or current measurement record.
H2, H3, H5, H7, H11, H13 and H_other come from the same analyser recordHarmonic RMS sum
Combine entered harmonic magnitudes.
Hsum = sqrt(H2^2 + H3^2 + H5^2 + H7^2 + H11^2 + H13^2 + H_other^2)THD percent
Display distortion relative to the fundamental.
THD = Hsum / H1 x 100Threshold margin
Compare with an optional user-entered review threshold.
margin = threshold - THD
- THD arithmetic using harmonic RMS magnitudes relative to the fundamental.
- Show THD formulas without diagnosing equipment or network power-quality conditions by itself.
- Power-quality measurement context, AS/NZS 61000, National Electricity Rules context, DNSP, equipment, analyser setup and project requirements govern interpretation.
- Record H1, H2, H3, H5, H7, H11, H13 and H_other as same-record analyser values; AS/NZS 61000 and National Electricity Rules context may matter.
Harmonic RMS rows for THD records
Show THD formulas without diagnosing equipment or network power-quality conditions by itself.
| Relationship | Formula | Use | Boundary |
|---|---|---|---|
| Same-record harmonic set | H2, H3, H5, H7, H11, H13 and H_other come from the same analyser record | Keep harmonic RMS inputs from one voltage or current measurement record. | Analyser setup, instrument measurement type and time window must be recorded. |
| Harmonic RMS sum | Hsum = sqrt(H2^2 + H3^2 + H5^2 + H7^2 + H11^2 + H13^2 + H_other^2) | Combine entered harmonic magnitudes. | Use consistent RMS units and do not mix voltage and current instrument measurements. |
| THD percent | THD = Hsum / H1 x 100 | Display distortion relative to the fundamental. | H1 must be valid, non-zero and from the same analyser record source. |
| Threshold margin | margin = threshold - THD | Compare with an optional user-entered review threshold. | AS/NZS 61000, National Electricity Rules, DNSP, equipment or project context may govern the threshold. |
- Use the calculator for entered harmonic rows.
- Power-quality interpretation needs analyser and project context.
Formula variables
Use these symbols and units when reading the chart rows.
| Variable | Meaning | Unit | Use |
|---|---|---|---|
| H1 | Fundamental RMS magnitude. | V or A | |
| H2 | Second harmonic RMS magnitude. | V or A | |
| H3 | Third harmonic RMS magnitude. | V or A | |
| H5 | Fifth harmonic RMS magnitude. | V or A | |
| H7 | Seventh harmonic RMS magnitude. | V or A | |
| H11 | Eleventh harmonic RMS magnitude. | V or A | |
| H13 | Thirteenth harmonic RMS magnitude. | V or A | |
| H_other | Other same-record harmonic RMS values. | V or A | |
| Hsum | RMS sum of harmonic magnitudes above the fundamental. | V or A | |
| THD | Total harmonic distortion. | % | Specify voltage THD or current THD. |
| threshold | Optional entered review threshold. | % | Threshold margin depends on the selected source, not this chart. |
| margin | Optional difference between threshold and THD. | % | A review aid, not a universal pass/fail result. |
Worked relationship example
This example shows how one set of entered values reads through the relationship.
Voltage THD relationship reading
Fundamental and harmonic RMS magnitudes from the same analyser record are used to read the THD formula.
- H1
- 230 Vfundamental RMS
- H5
- 9 V
- H7
- 6 V
- H11 + H13 + other
- 3 V, 2 V, 4 V
- Sum harmonic RMS valuesHsum = sqrt(9^2 + 6^2 + 3^2 + 2^2 + 4^2) = 12.1 V.
- Compare with fundamentalTHD% = 12.1 / 230 x 100 = 5.3%.
The comparison needs the same-record analyser setup and any selected review threshold.
Use this as formula reading only; power-quality interpretation depends on analyser setup, standards context and project review.
- Harmonic values are RMS magnitudes from the same analyser record.
- Voltage THD and current THD are not mixed.
Where the harmonic THD chart belongs
Use the chart to understand the formula basis; calculators handle project-specific inputs, warnings and results.
| Item | Value |
|---|---|
| Purpose | Show THD formulas without diagnosing equipment or network power-quality conditions by itself. |
| How to use the source | THD arithmetic using harmonic RMS magnitudes relative to the fundamental. |
| Standards and project context | Power-quality measurement context, AS/NZS 61000, National Electricity Rules context, DNSP, equipment, analyser setup and project requirements govern interpretation. |
| Where judgement is still needed | Use this chart to understand the relationship behind a calculation; do not treat it as a substitute for entered project values. |
| Before relying on it | Confirm current standards, local authority requirements, DNSP conditions, project documents and manufacturer data before relying on a decision. |
| Context | Applies to | Public boundary |
|---|---|---|
| Analyser setup | H1 and harmonic RMS values from H2, H3, H5, H7, H11, H13 and H_other | Use same-record analyser values and do not mix voltage THD with current THD. |
| AS/NZS 61000 and National Electricity Rules context | Threshold margin and power-quality interpretation | The chart does not set universal limits or diagnose equipment and network conditions by itself. |
| Project review boundary | Harmonic THD formulas chart | Confirm current Australian standards, local authority requirements, DNSP conditions, project documents and manufacturer data before relying on a decision. |
Measurement basis for harmonic THD
Review the cited calculator source, analyser setup, harmonic record basis and Australian power-quality boundary before using these THD formulas.
| Item | Value |
|---|---|
| Source | AUWiring harmonic THD calculator formula notes. |
| Source type | Measurement record with standards context |
| Derivation basis | Derived from AUWiring calculator logic and user-entered harmonic RMS values. |
| Last checked | 2026-07-13 |
| Review interval | Annual or when THD calculator formulas or measurement wording changes. |
| Review trigger | Formula change, measurement-record change, analyser context change or project feedback. |
| Version used | R40-2026-07-13 |
| Australian application | Australia; instrument setup, DNSP, equipment and project requirements govern formal interpretation. |
Use a calculator for project values
Use the chart to read the formula relationship, then open a calculator when you need entered project values, warnings and result context.