A nonlinear load can produce a strongly distorted current while the supply voltage remains comparatively close to a sine wave. The two distortion percentages share a mathematical pattern, but they describe different signals and system boundaries.
This guide follows a fictional fifth-and-seventh-harmonic case from load current through network impedance to bus voltage, then tests grouping, light load, resonance and measurement uncertainty.
The worked records are original teaching examples. Each keeps the observed value, reference condition, derived result and decision in separate fields so the reader can see where a conclusion begins and where it stops.
A changed-context check alters one consequential condition while leaving the other inputs fixed. This makes transfer visible and prevents the original numerical answer from becoming a rule without a scope.
Keep a compact evidence receipt: object, method, units, reference, conditions, transformation, result and nearest rival explanation. A future reader should be able to reproduce the narrow claim from that receipt.
The five reading routes move from definitions to mechanism, evidence, transfer and reporting. Readers may enter by task, but the examples remain connected so the explanation never becomes a list of detached tips.
The practical standard is an answer that can be checked. Preserve raw inputs, intermediate calculations, exclusions and versioned sources; then state one stronger claim that the evidence still cannot support.
Before choosing a formula or property, name the reader job in one sentence. A diagnostic question, a design choice, a compliance check and a teaching comparison may use the same observation differently.
Every worked case includes a counterexample with one familiar surface feature and a different mechanism underneath. The pair matters because a definition becomes useful only when the learner can reject a tempting near-match.
The evidence route treats missing information honestly. An unknown method, reference condition or boundary stays blank until a source supplies it; a plausible assumption may complete the arithmetic while weakening the conclusion.
The transfer route changes scale, location, timing or composition without silently changing every other field. Predict the direction first, then calculate or inspect the result.
The reporting route keeps measurement and judgement separate. State what was observed, what rule produced the derived value, what uncertainty remains and which action follows only under the declared conditions.
The final check is reader-facing: a person entering through the short answer should know the distinction, a person following the worked example should reproduce it, and a person using the sources should see where the example ends.
A useful misconception test asks the learner to construct two cases with the same headline number and different underlying records. If the interpretation changes, the omitted condition belongs in the result.
Where a standard leaves behaviour to the platform, method or competent decision-maker, the article says so directly. A boundary is useful evidence because it tells the reader which conclusion can travel.
The examples avoid hidden precision. Rounded display values remain linked to the unrounded calculation, and stipulated inputs are labelled as teaching data.
A complete explanation keeps three layers apart: the thing in the world, the method that turns it into a value, and the decision made from that value. When two labels sit in different layers, numerical agreement is evidence to investigate rather than permission to merge their meanings.
For each central example, sketch the boundary before calculating. Mark what crosses it, what stays outside, what the instrument or algorithm can observe, and what must be inferred. This small diagram prevents a later percentage, ratio or diagnostic label from silently changing its object.
This specialist guide belongs to the Utilities root. It also connects to The Gold Standard of Education | Learning That Transfers into Life and the How X Works hub. The worked cases are original teaching examples; their numbers are stipulated so that the reasoning can be checked.
eduKateSG · Utilities
Find your next learning step
Read the short answer first: calculate voltage THD from voltage harmonics and the fundamental voltage, and current THD from current harmonics and the fundamental current. Keep location, spectrum, denominator, interval and network impedance attached to both.
ROUTE 1 · CHAPTERS 1–4
Define the quantities
Name the quantities, reference conditions and reporting rules.
ROUTE 3 · CHAPTERS 9–12
Audit the evidence
Check instruments, algorithms, assumptions and rival explanations.
ROUTE 5 · CHAPTERS 17–20
Report and continue
Repair shortcuts, answer questions and follow verified routes.
Chapter contents
Define the quantities · Chapters 1–4
1. Name voltage and current distortion separately
2. Attach each spectrum to a measurement point
Work the mechanism · Chapters 5–8
5. Work the central nonlinear-load case
6. Trace harmonic order instead of one headline
Audit the evidence · Chapters 9–12
9. Audit aggregation and subgrouping
10. Audit the observation interval
Transfer the reasoning · Chapters 13–16
13. Transfer to a lightly loaded feeder
14. Transfer to a capacitor bank
Report and continue · Chapters 17–20
17. Repair the higher percentage means worse shortcut
18. Repair THDv plus THDi as one score
CHAPTER 1 OF 20 · Define the quantities
1. Name voltage and current distortion separately
Voltage total harmonic distortion compares the RMS contribution of selected voltage harmonics with the fundamental voltage. Current total harmonic distortion applies an analogous construction to current. They use different signals, denominators and system roles.
Write the evidence in the order a reader can audit: the Utilities quantity, its reference object, the observation or browser rule, the transformation, and the decision being made. Keeping those fields visible prevents a familiar label from hiding a changed basis.
At one fictional point of common coupling, V1 is 230 V and the selected harmonic-voltage RSS is 9.2 V, so THDv is 4.0%. I1 is 80 A and the selected harmonic-current RSS is 24 A, so THDi is 30%.
First-principles test: ask what physical, observational or algorithmic operation produces each value in this chapter. Then ask whether the second value could change while the first stays fixed. If it can, the two labels are not substitutes. For Utilities, this counterfactual is often clearer than a definition learned in isolation.
Hold the current spectrum fixed and stiffen the source so harmonic voltage falls; predict THDv changes while THDi can remain similar.
Evidence check: another reader should be able to reproduce the narrow result from the stored definitions, inputs and intermediate steps, then identify the nearest stronger claim that the evidence does not support.
The included orders, grouping and observation window must follow the declared method.
CHAPTER 2 OF 20 · Define the quantities
2. Attach each spectrum to a measurement point
A harmonic percentage is incomplete without phase, conductor, meter location, interval and aggregation rule. A feeder current and a bus voltage may be causally related but they are not the same record.
Trace the mechanism before interpreting the result. For Utilities, mark which value belongs to the source, which belongs to the measurement or layout algorithm, and which is a reported summary. A calculation is useful only when those roles remain attached.
Label the bus-voltage channels V-A, V-B and V-C and the feeder-current channels I-A, I-B and I-C before calculating any ratio.
Practical transfer: build two records that share the headline number but differ in the condition discussed here. If the correct interpretation changes, the omitted condition is decision-relevant and belongs in the report. This test turns a vocabulary distinction into a reusable Utilities checking habit.
Move the current clamp to a different feeder while retaining the bus-voltage probe and identify which comparison is lost.
Practical check: keep one counterexample beside the worked case. If the wording fails when that one condition changes, narrow the sentence until it describes only the evidence actually in hand.
Real installations require safe, qualified measurement practice.
CHAPTER 3 OF 20 · Define the quantities
3. Keep the fundamental denominator visible
THD is a ratio to the fundamental component under a stated definition. A shrinking fundamental can raise the percentage even when the absolute harmonic RMS does not rise.
Use a compact decision table with columns for condition, input, operation, result and limit. This makes the comparison reproducible and exposes where a missing field would force an assumption instead of an observation.
If harmonic current stays 12 A but I1 falls from 80 A to 40 A, THDi rises from 15% to 30%.
Misconception check: a plausible output does not prove the right reference, denominator, ancestor, spectrum or observation rule was used. Reconstruct one intermediate step and one changed-context prediction. If either cannot be stated, keep the result provisional rather than strengthening its wording.
Double both the fundamental and every harmonic amplitude and show the ratio stays fixed.
Transfer check: repeat the reasoning with one consequential condition changed while holding the rest fixed. State what changes, what stays comparable and why the original label alone was insufficient.
Near-zero fundamentals can make the ratio unstable or unhelpful.
Total RMS combines the fundamental and harmonic components by root-sum-square when they are orthogonal components. It is not obtained by adding THD percent to the fundamental magnitude.
Preserve the raw inputs beside the derived result. If a later reader changes one condition, the original Utilities reasoning should still be recoverable without reverse-engineering a rounded headline or an unlabeled screenshot.
With I1=80 A and harmonic RSS=24 A, total RMS is sqrt(80²+24²)=83.5 A, not 104 A.
Evidence design: retain both a positive case and a near-miss. The positive case shows when the rule applies; the near-miss changes one consequential condition and shows when the conclusion fails. Together they teach the boundary of the Utilities mechanism better than another unlabelled example.
Set harmonic RSS to zero and recover total RMS equal to the fundamental.
Audit check: retain the source version, units, settings, exclusions and rounding rule. A future correction should be able to alter one field without rebuilding the entire explanation from memory.
Instrument bandwidth and non-harmonic components affect practical RMS readings.
A nonlinear load draws distorted current; source and network impedance convert harmonic current into harmonic voltage drops. The observed bus-voltage distortion therefore depends on both current emission and the network.
Ask what would have to stay fixed for the comparison to be fair. Record those controls explicitly, then name the first uncontrolled condition that could reverse the conclusion. This is the practical transfer step, not an optional footnote.
Use I5=20 A and I7=13.3 A, giving about 24 A harmonic RSS. With stipulated harmonic impedances, compute 6.0 V and 7.0 V drops, giving 9.2 V voltage RSS.
Communication test: replace any sentence that says two things are “the same” or “different” with a sentence naming the operation, reference condition and supported consequence. The extra words are useful when they let a future reader repeat the decision without access to the original author.
Reduce both harmonic impedances by half while holding current harmonics fixed; the voltage-harmonic RSS halves.
Decision check: end with an action or interpretation that follows from the stated conditions, followed by a boundary sentence explaining when a specialist rule, local procedure or additional measurement is needed.
The simplified two-order model omits phase angles and other sources.
CHAPTER 6 OF 20 · Work the mechanism
6. Trace harmonic order instead of one headline
The same THD can come from different harmonic-order distributions. Equipment heating, resonance and neutral current can depend on which orders dominate.
Write the evidence in the order a reader can audit: the Utilities quantity, its reference object, the observation or browser rule, the transformation, and the decision being made. Keeping those fields visible prevents a familiar label from hiding a changed basis.
Create two current spectra with 24 A RSS: one dominated by the fifth, another split among third, fifth and seventh.
First-principles test: ask what physical, observational or algorithmic operation produces each value in this chapter. Then ask whether the second value could change while the first stays fixed. If it can, the two labels are not substitutes. For Utilities, this counterfactual is often clearer than a definition learned in isolation.
Keep THDi equal and change the third-harmonic share; predict a different neutral-current concern in a four-wire system.
Evidence check: another reader should be able to reproduce the narrow result from the stored definitions, inputs and intermediate steps, then identify the nearest stronger claim that the evidence does not support.
A headline ratio cannot replace a full spectrum where order matters.
Harmonic voltage is a phasor result of multiple sources and impedances. Magnitudes from different sources cannot always be added arithmetically.
Trace the mechanism before interpreting the result. For Utilities, mark which value belongs to the source, which belongs to the measurement or layout algorithm, and which is a reported summary. A calculation is useful only when those roles remain attached.
Two 5th-harmonic voltage contributions of 4 V at opposite phase can partly cancel even though each source remains present.
Practical transfer: build two records that share the headline number but differ in the condition discussed here. If the correct interpretation changes, the omitted condition is decision-relevant and belongs in the report. This test turns a vocabulary distinction into a reusable Utilities checking habit.
Rotate one contribution by 180 degrees while preserving magnitudes and recompute the bus result.
Practical check: keep one counterexample beside the worked case. If the wording fails when that one condition changes, narrow the sentence until it describes only the evidence actually in hand.
A complete study needs complex impedances and source phases.
CHAPTER 8 OF 20 · Work the mechanism
8. Separate emission from compatibility at the PCC
Current distortion characterises a user current under a stated reference, while voltage distortion describes supply quality at the measurement point. Standards can set different steady-state limits because the responsibilities and denominators differ.
Use a compact decision table with columns for condition, input, operation, result and limit. This makes the comparison reproducible and exposes where a missing field would force an assumption instead of an observation.
Store THDi 30% for the feeder and THDv 4% for the bus rather than averaging them into 17%.
Misconception check: a plausible output does not prove the right reference, denominator, ancestor, spectrum or observation rule was used. Reconstruct one intermediate step and one changed-context prediction. If either cannot be stated, keep the result provisional rather than strengthening its wording.
Add a second harmonic-producing user and trace how the shared voltage result changes.
Transfer check: repeat the reasoning with one consequential condition changed while holding the rest fixed. State what changes, what stays comparable and why the original label alone was insufficient.
Compliance interpretation belongs to the applicable standard and agreement.
Standards define how spectral bins, harmonics and interharmonics are grouped. Different analyser settings can produce different reported values from the same waveform.
Preserve the raw inputs beside the derived result. If a later reader changes one condition, the original Utilities reasoning should still be recoverable without reverse-engineering a rounded headline or an unlabeled screenshot.
Compute one value from exact harmonic bins and another from stipulated harmonic subgroups; record the setting beside each.
Evidence design: retain both a positive case and a near-miss. The positive case shows when the rule applies; the near-miss changes one consequential condition and shows when the conclusion fails. Together they teach the boundary of the Utilities mechanism better than another unlabelled example.
Change only the window and grouping rule and identify why the results cease to be directly comparable.
Audit check: retain the source version, units, settings, exclusions and rounding rule. A future correction should be able to alter one field without rebuilding the entire explanation from memory.
Use the current edition and instrument class required for the task.
Loads cycle, converters change operating point and voltages vary over time. A ten-cycle snapshot and a weekly percentile describe different evidence.
Ask what would have to stay fixed for the comparison to be fair. Record those controls explicitly, then name the first uncontrolled condition that could reverse the conclusion. This is the practical transfer step, not an optional footnote.
Record THDv values every interval, then compare the maximum, median and 95th percentile without calling them one number.
Communication test: replace any sentence that says two things are “the same” or “different” with a sentence naming the operation, reference condition and supported consequence. The extra words are useful when they let a future reader repeat the decision without access to the original author.
Insert one short high-distortion event and show which summaries move.
Decision check: end with an action or interpretation that follows from the stated conditions, followed by a boundary sentence explaining when a specialist rule, local procedure or additional measurement is needed.
Event handling and statistical aggregation must be declared.
Network impedance varies with transformer size, conductor length and frequency. The same harmonic current can create different voltage distortion at two buses.
Write the evidence in the order a reader can audit: the Utilities quantity, its reference object, the observation or browser rule, the transformation, and the decision being made. Keeping those fields visible prevents a familiar label from hiding a changed basis.
Use 24 A harmonic RSS at a stiff 0.2-ohm equivalent and a weak 0.5-ohm equivalent as a controlled comparison.
First-principles test: ask what physical, observational or algorithmic operation produces each value in this chapter. Then ask whether the second value could change while the first stays fixed. If it can, the two labels are not substitutes. For Utilities, this counterfactual is often clearer than a definition learned in isolation.
Move the load closer to the transformer and predict the direction of voltage distortion.
Evidence check: another reader should be able to reproduce the narrow result from the stored definitions, inputs and intermediate steps, then identify the nearest stronger claim that the evidence does not support.
Scalar impedances are teaching simplifications.
Voltage probes, current transformers and analysers have bandwidth, range, phase and saturation limits. A clipped current channel can understate harmonic magnitudes while appearing tidy.
Trace the mechanism before interpreting the result. For Utilities, mark which value belongs to the source, which belongs to the measurement or layout algorithm, and which is a reported summary. A calculation is useful only when those roles remain attached.
Compare a 100 A clamp that clips a 140 A peak with a correctly ranged channel; preserve both raw waveforms.
Practical transfer: build two records that share the headline number but differ in the condition discussed here. If the correct interpretation changes, the omitted condition is decision-relevant and belongs in the report. This test turns a vocabulary distinction into a reusable Utilities checking habit.
Increase the range and verify whether the high-order spectrum changes.
Practical check: keep one counterexample beside the worked case. If the wording fails when that one condition changes, narrow the sentence until it describes only the evidence actually in hand.
Measurement uncertainty and calibration require documented procedures.
When the fundamental current falls faster than its harmonic current, THDi can rise even though absolute harmonic amperes fall. The network voltage response may also fall if harmonic current falls.
Use a compact decision table with columns for condition, input, operation, result and limit. This makes the comparison reproducible and exposes where a missing field would force an assumption instead of an observation.
Change I1 from 80 A to 30 A and harmonic RSS from 24 A to 15 A: THDi rises from 30% to 50% while harmonic amperes fall.
Misconception check: a plausible output does not prove the right reference, denominator, ancestor, spectrum or observation rule was used. Reconstruct one intermediate step and one changed-context prediction. If either cannot be stated, keep the result provisional rather than strengthening its wording.
Keep source impedance fixed and compute the lower voltage-harmonic drop.
Transfer check: repeat the reasoning with one consequential condition changed while holding the rest fixed. State what changes, what stays comparable and why the original label alone was insufficient.
Percentages alone can mislead maintenance priorities.
A capacitor bank can change harmonic impedance and create or shift resonance. Current distortion at a load can stay similar while bus voltage distortion changes sharply.
Preserve the raw inputs beside the derived result. If a later reader changes one condition, the original Utilities reasoning should still be recoverable without reverse-engineering a rounded headline or an unlabeled screenshot.
Add a stipulated parallel resonance near the fifth harmonic and triple only the fifth-harmonic bus impedance.
Evidence design: retain both a positive case and a near-miss. The positive case shows when the rule applies; the near-miss changes one consequential condition and shows when the conclusion fails. Together they teach the boundary of the Utilities mechanism better than another unlabelled example.
Detune the bank in the model and trace the changed voltage spectrum.
Audit check: retain the source version, units, settings, exclusions and rounding rule. A future correction should be able to alter one field without rebuilding the entire explanation from memory.
Real resonance assessment needs a validated network model.
Harmonic sequence and transformer connection affect which components pass, circulate or appear on another side. Do not copy a percentage across the transformer without the connection and measurement basis.
Ask what would have to stay fixed for the comparison to be fair. Record those controls explicitly, then name the first uncontrolled condition that could reverse the conclusion. This is the practical transfer step, not an optional footnote.
Track a triplen component in a delta-wye teaching network separately from fifth and seventh harmonics.
Communication test: replace any sentence that says two things are “the same” or “different” with a sentence naming the operation, reference condition and supported consequence. The extra words are useful when they let a future reader repeat the decision without access to the original author.
Change the connection in the schematic and state which prediction must be redone.
Decision check: end with an action or interpretation that follows from the stated conditions, followed by a boundary sentence explaining when a specialist rule, local procedure or additional measurement is needed.
Transformer design details and loading determine actual behaviour.
An inverter can regulate current tightly while the grid voltage already contains distortion, or its control can interact with grid impedance. Direction of causation cannot be read from two percentages alone.
Write the evidence in the order a reader can audit: the Utilities quantity, its reference object, the observation or browser rule, the transformation, and the decision being made. Keeping those fields visible prevents a familiar label from hiding a changed basis.
Compare the inverter current spectrum before and after connecting to a weaker grid while keeping commanded power fixed.
First-principles test: ask what physical, observational or algorithmic operation produces each value in this chapter. Then ask whether the second value could change while the first stays fixed. If it can, the two labels are not substitutes. For Utilities, this counterfactual is often clearer than a definition learned in isolation.
Add a background fifth-harmonic voltage and check whether current changes.
Evidence check: another reader should be able to reproduce the narrow result from the stored definitions, inputs and intermediate steps, then identify the nearest stronger claim that the evidence does not support.
Attribution requires synchronized data and system tests.
CHAPTER 17 OF 20 · Report and continue
17. Repair the higher percentage means worse shortcut
A higher THDi does not automatically mean the bus voltage is more distorted, and a lower THDi does not prove harmless interaction. The absolute spectrum, impedance and decision criterion matter.
Trace the mechanism before interpreting the result. For Utilities, mark which value belongs to the source, which belongs to the measurement or layout algorithm, and which is a reported summary. A calculation is useful only when those roles remain attached.
Contrast the lightly loaded 50% THDi case with the 30% full-load case and compare absolute harmonic amperes.
Practical transfer: build two records that share the headline number but differ in the condition discussed here. If the correct interpretation changes, the omitted condition is decision-relevant and belongs in the report. This test turns a vocabulary distinction into a reusable Utilities checking habit.
Rank the cases once by THDi and once by harmonic current; explain the reversal.
Practical check: keep one counterexample beside the worked case. If the wording fails when that one condition changes, narrow the sentence until it describes only the evidence actually in hand.
The correct ranking depends on the stated engineering question.
Voltage and current distortion cannot be added or averaged into a physically meaningful universal score. They refer to different quantities and denominators.
Use a compact decision table with columns for condition, input, operation, result and limit. This makes the comparison reproducible and exposes where a missing field would force an assumption instead of an observation.
Reject a dashboard score of (4%+30%)/2=17%; display two labelled panels and their spectra.
Misconception check: a plausible output does not prove the right reference, denominator, ancestor, spectrum or observation rule was used. Reconstruct one intermediate step and one changed-context prediction. If either cannot be stated, keep the result provisional rather than strengthening its wording.
Change only the voltage fundamental and show the invented score changes without a coherent interpretation.
Transfer check: repeat the reasoning with one consequential condition changed while holding the rest fixed. State what changes, what stays comparable and why the original label alone was insufficient.
Composite indices need a defined model and purpose.
Record one-line diagram, PCC, channels, instrument class, firmware, sampling, grouping, harmonic range, fundamental, spectra, interval aggregation and uncertainty.
Preserve the raw inputs beside the derived result. If a later reader changes one condition, the original Utilities reasoning should still be recoverable without reverse-engineering a rounded headline or an unlabeled screenshot.
Package the 230 V/80 A central case with the fifth and seventh components and both RSS calculations.
Evidence design: retain both a positive case and a near-miss. The positive case shows when the rule applies; the near-miss changes one consequential condition and shows when the conclusion fails. Together they teach the boundary of the Utilities mechanism better than another unlabelled example.
Remove the meter location and ask another reader whether the result still supports a PCC conclusion.
Audit check: retain the source version, units, settings, exclusions and rounding rule. A future correction should be able to alter one field without rebuilding the entire explanation from memory.
Site data and standards access remain operational responsibilities.
A defensible report states THDv and THDi separately with location, interval, method, denominators and spectra, then describes the network relationship without claiming unique causation.
Ask what would have to stay fixed for the comparison to be fair. Record those controls explicitly, then name the first uncontrolled condition that could reverse the conclusion. This is the practical transfer step, not an optional footnote.
Write: “At bus B during interval T, THDv was 4.0% and feeder F THDi was 30% under the declared grouping; the values are not interchangeable.”
Communication test: replace any sentence that says two things are “the same” or “different” with a sentence naming the operation, reference condition and supported consequence. The extra words are useful when they let a future reader repeat the decision without access to the original author.
Ask which changed-context test best distinguishes a current-source change from an impedance change.
Decision check: end with an action or interpretation that follows from the stated conditions, followed by a boundary sentence explaining when a specialist rule, local procedure or additional measurement is needed.
The worked case is not a compliance certificate.
Continue through the verified reading route
Voltage unbalance and current unbalance
Voltage unbalance and current unbalance. Use this for negative-sequence ratios rather than harmonic spectra.
Real and reactive power
Real and reactive power. Use this for power components and power factor in AC loads.
Voltage sags and supply interruptions
Voltage sags and supply interruptions. Use this for time-domain RMS events rather than steady-state distortion.
Frequently asked questions
Can high THDi coexist with low THDv?
Yes. A stiff, low-impedance supply can limit harmonic voltage even while a load draws distorted current.
Can I average THDv and THDi?
No. They describe different signals and denominators.
Does lower THDi always mean fewer harmonic amperes?
No. A large fundamental can lower the percentage while absolute harmonic current rises.
Authoritative sources and further reading
IEC 61000-4-7:2002+A1:2008. Defines instrumentation and grouping for harmonics and interharmonics in supply systems and equipment.
IEC 61000-4-30:2025. Defines repeatable power-quality measurement methods including voltage and current harmonics.
IEEE 519-2022. Applies separate steady-state voltage and current distortion limits at the user point of common coupling.
Return to the Utilities subject guide, The Gold Standard of Education, or the How X Works hub.