A three-phase supply can have a small voltage-unbalance ratio while one branch carries strongly unbalanced currents. The numbers interact through impedances and equipment, but they belong to different objects and boundaries.
This guide follows synchronized voltage and current phasors through sequence ratios, branch location, source impedance, harmonics, aggregation and changed loads.
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. Keeping the job visible prevents a technically correct number from being asked to settle a different decision.
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, explain which evidence changed and carry that distinction into an unfamiliar example.
The evidence route treats missing information honestly. An unknown method, reference condition or sample boundary stays blank until a source supplies it. Filling the gap with a plausible assumption may make the arithmetic complete while making the conclusion less trustworthy.
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. A correct prediction with an explicit reason demonstrates more understanding than repeating the original procedure after seeing the answer.
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. This structure makes later review easier and prevents caveats from being detached from the claim they qualify.
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 and the authoritative definition begins.
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 is part of the result. This exercise turns a vocabulary distinction into a practical habit for checking claims.
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 to the changed case and which conclusion must wait for a new measurement or rule.
The examples avoid hidden precision. Rounded display values remain linked to the unrounded calculation, and stipulated inputs are labelled as teaching data. This lets the reader inspect the reasoning without mistaking a clean result for a measured property of an unnamed real system.
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.
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Read the short answer first: calculate voltage unbalance at the declared bus and current unbalance in the declared branch with the stated method and interval. Relate them only through a network and equipment model; one percentage cannot replace the other.
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 unbalance
2. Keep the measurement point attached
Work the mechanism · Chapters 5–8
5. Work the unbalanced-load counterexample
Audit the evidence · Chapters 9–12
9. Audit RMS magnitude screens
Transfer the reasoning · Chapters 13–16
13. Transfer to a single-phase load change
14. Transfer to a rotating machine
Report and continue · Chapters 17–20
17. Repair equal percentages means same severity
18. Repair current unbalance proves supply fault
Voltage unbalance describes asymmetry in a three-phase voltage set; current unbalance describes asymmetry in the load currents. They interact through the network and equipment but are not interchangeable percentages.
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 point of common coupling, the negative-to-positive sequence voltage ratio is 1.2% while a downstream motor current ratio is 6.8%. Record both objects and locations.
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.
Disconnect the motor while preserving the upstream voltage set; current evidence disappears while the voltage observation can remain.
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.
Real equipment decisions require qualified power-quality assessment.
Voltage is observed at a node; current is observed in a branch or load. Comparing values from different boundaries without labels can invent a relationship.
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.
Voltage phasors are measured at bus B; currents are measured on feeder F2. A second feeder cannot be assigned F2 current unbalance.
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 clamps to the bus incomer and explain why the population of loads 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.
Instrument installation on live systems is outside this educational guide.
For fundamental phasors, voltage unbalance factor can be |V2|/|V1| and current unbalance factor |I2|/|I1| when that method is declared. Positive and negative sequences must not be mixed across quantities.
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.
Use stipulated V1=230 V and V2=2.3 V for 1.0%; use I1=40 A and I2=3.2 A for 8.0%.
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 only I2 and predict that current unbalance doubles while voltage ratio need not.
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.
Magnitude-only screens and sequence ratios are different methods.
CHAPTER 4 OF 20 · Define the quantities
4. Work the balanced-current counterexample
A supply can have some voltage unbalance while an actively controlled load draws nearly balanced currents, depending on its design and operating state.
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.
Stipulate 1.5% voltage unbalance and three 20 A fundamental currents with ideal 120-degree separation, giving zero negative-sequence current in the teaching case.
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.
Add a single-phase branch on phase A and recompute the current sequence.
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.
The idealised controller behaviour is not a product guarantee.
A balanced source can feed unequal single-phase loads and therefore carry current unbalance even when the bus voltage is nearly symmetric at light loading.
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.
Currents are 30 A, 20 A and 10 A at 120-degree phase positions from an ideal balanced 230 V source. The current sequence is nonzero.
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.
Increase source impedance and predict that the same load currents can now contribute more voltage unbalance.
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.
Actual currents also depend on load voltage sensitivity and harmonics.
Negative-sequence current flowing through network negative-sequence impedance contributes a negative-sequence voltage. The relationship needs both the disturbance current and the network seen from the point.
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.
With a stipulated I2=4 A and Z2=0.15 ohm, the simple drop magnitude is 0.6 V; the associated ratio depends on V1.
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.
Halve Z2 while holding the current model fixed and predict half the negative-sequence drop.
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 scalar magnitude omits phase angle and the rest of the network solution.
Two feeders share a bus. F1 has balanced currents; F2 carries most negative-sequence current. Bus voltage unbalance is common to both, but current unbalance remains branch-specific.
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.
V1=400 V and V2=4 V gives 1%. F1 has I2/I1=0.5%; F2 has 7%. Report three rows, not one site score.
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.
Open F2 and predict the change in bus voltage using a declared source impedance.
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.
Protection and operating changes require authorised engineering.
Four-wire systems can carry zero-sequence current from phase-to-neutral load imbalance. Negative-sequence voltage coordination and neutral-current questions are related but distinct.
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.
Three in-phase third-harmonic current components add in the neutral even when the fundamental negative-sequence ratio is modest.
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.
Remove harmonic content but preserve unequal fundamental loads; the neutral and negative-sequence results change differently.
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.
A single current-unbalance percentage cannot describe all sequence components.
A maximum deviation from average current uses phase magnitudes only. It can be useful as a screen but cannot recover sequence components without angle information.
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.
Magnitudes 44, 40 and 36 A average 40; maximum magnitude deviation is 10%. A synchronized phasor calculation may give a different sequence ratio.
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.
Keep magnitudes fixed and perturb one phase angle; the magnitude screen stays fixed while I2 changes.
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.
Always name the method before comparing limits.
CHAPTER 10 OF 20 · Audit the evidence
10. Audit harmonics and fundamental extraction
Sequence unbalance usually concerns fundamental-frequency phasors, while total RMS currents can include harmonics. Mixing them can attribute harmonic distortion to fundamental unbalance.
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.
A phase has 40 A fundamental plus harmonic current; total RMS rises to 44 A although the fundamental phasor set remains balanced.
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.
Filter to the fundamental and compare both reports.
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.
Windowing and aggregation settings belong in the record.
Current transformers and voltage channels have ratio, phase and polarity errors. One reversed current channel can create a false negative-sequence result.
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.
A balanced 25 A set is recorded with phase B polarity reversed. The computed sequence result becomes implausible.
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.
Correct the polarity in the wiring model and verify the balanced baseline.
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.
Never alter real instrument wiring without authorised safe procedures.
A ten-minute voltage-unbalance statistic and a one-cycle motor-start current statistic do not describe the same interval. Align timestamps and aggregation before relating them.
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.
Voltage ratio is reported as a 10-minute 95th percentile; current ratio is a 200 ms maximum. Their numerical comparison is not causal evidence.
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.
Recompute both over synchronized one-cycle windows around the event.
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.
Long-term compatibility and event diagnosis can require different summaries.
CHAPTER 13 OF 20 · Transfer the reasoning
13. Transfer to a single-phase load change
Adding a phase-to-neutral load can increase current unbalance locally and may increase voltage unbalance depending on impedance and phase allocation.
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.
Add 12 A on phase A of F2. Recalculate branch sequences, then estimate the bus effect using the stated network model.
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.
Move the load to phase B and predict a rotated negative-sequence phasor rather than only a changed magnitude.
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.
Load rephasing is an engineering action, not a classroom instruction.
Negative-sequence voltage can drive negative-sequence current in a rotating machine and increase losses. The current response depends on machine impedance and load, so voltage and current percentages need not match.
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.
Two fictional motors see the same 1% V2/V1; motor M has 5% I2/I1 and motor N 8% because their stipulated sequence impedances differ.
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.
Hold supply fixed and change the machine model.
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.
Thermal acceptability needs the manufacturer and applicable standard.
A converter may regulate input currents or create switching harmonics. Its current-unbalance response cannot be inferred from a motor rule.
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.
A fictional active rectifier keeps fundamental currents within 1% while its total harmonic distortion changes under one low-voltage phase.
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.
Disable the ideal control in the model and compare current sequences.
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.
Use product-specific evidence for real equipment.
Voltage unbalance can differ between buses because source stiffness, transformers and connected loads differ. Current unbalance can differ between branches at the same bus.
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.
Measure bus A and bus B plus three feeders. Store a topology diagram before comparing ratios.
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 disturbance load from F2 to F3 and predict which branch record changes directly.
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.
Correlation across meters does not by itself identify the source.
CHAPTER 17 OF 20 · Report and continue
17. Repair equal percentages means same severity
A 2% voltage ratio and 2% current ratio use different numerators, denominators and physical objects. Equal numbers do not make them equivalent disturbances.
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.
Write two equations beside the reported 2% values and identify the missing equipment response.
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.
Change positive-sequence current while holding I2 fixed; current percentage changes without a voltage change.
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.
Severity depends on equipment, duration and applicable criteria.
CHAPTER 18 OF 20 · Report and continue
18. Repair current unbalance proves supply fault
Unequal currents can arise from load allocation, equipment behaviour, measurement error or supply asymmetry. A current result alone does not assign responsibility.
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.
A balanced-source model with unequal phase loads reproduces the observation. Keep supply and load hypotheses open until voltage and topology evidence are added.
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.
Swap the load among phases and predict the current change.
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.
Fault diagnosis belongs to qualified personnel.
A defensible package includes one-line diagram, meter locations, voltage and current fundamental phasors, sequence results, harmonics, aggregation and operating state.
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.
Save a table for bus B and feeder F2 over the same 10-cycle interval, with calibration and channel checks.
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.
Repeat after the suspected load is off and compare like with like.
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.
Operational confidentiality and safety constraints may limit available data.
State voltage unbalance at its bus and current unbalance in its branch, then describe only the supported relationship.
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: “Bus B V2/V1 was 1.1%; feeder F2 I2/I1 was 6.4% in the same interval. The data show asymmetric load current and do not alone apportion the bus voltage result.”
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 additional measurement would separate source and load contributions.
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.
Do not convert the teaching example into a compliance judgement.
Continue through the verified reading route
Voltage unbalance and phase deviation
Voltage unbalance and phase deviation. Use this for nominal-reference deviation versus three-phase symmetry.
Voltage sags and interruptions
Voltage sags and interruptions. Use this for magnitude-duration event classification.
Real and reactive power
Real and reactive power. Use this when the reader job concerns AC power flow rather than sequence asymmetry.
Frequently asked questions
Can current unbalance exceed voltage unbalance?
Yes. Equipment and load sequence impedances can make the current ratio much larger.
Does current unbalance prove a supply fault?
No. Load allocation, equipment behaviour, measurement error and supply asymmetry remain competing explanations.
Can magnitude-only phase readings replace sequence phasors?
No. They omit phase-angle information and must be labelled as a separate screening method.
Authoritative sources and further reading
IEC TR 61000-3-13:2008. Explains negative-sequence currents from unbalanced installations and their contribution to voltage unbalance.
IEC 61000-4-30:2025. Defines repeatable power-quality measurement methods including supply-voltage unbalance.
IEEE 1159-2019. Provides official power-quality monitoring context and reporting practice.
Return to the Utilities subject guide, The Gold Standard of Education, or the How X Works hub.