Phase Academy · Symmetrical Components & Fault Visualizer

Fault Type

Balanced

Severity

None

Zero Sequence?

Grounding

Solidly Grounded

S Base

100 MVA

I Base

4184 A

Z Base

1.904 Ω

⚠ Ampere values are illustrative per-unit conversions on the selected MVA base (System Type) — not equipment fault duty. Conceptual teaching model only.

Phase Phasor Diagram

ABC

Sequence Magnitudes

Positive

1.00

Negative

0.00

Zero

0.00

Phase Current Waveforms

Grounding Effect

Solidly Grounded

Zero-sequence current has a clear return path through the grounded neutral.

Assumptions

Default assumptions shown here after computation.

Live Insights

System Status: Nominal

Everything is balanced. All three phases carry equal magnitude, 120° apart.

Educational disclaimer: conceptual per-unit teaching tool using simplified sequence-network models. Not for power system design, protection coordination, arc-flash studies, or safety-critical engineering calculations.

Sequence Sandbox

Independent explorer — all components at a 0° reference angle, not synced to the fault solver

Use the Sequence Sandbox sliders in the sidebar to dial in the three sequence magnitudes and watch them combine into phase quantities. By construction every component here is entered at 0°, so this tab answers “what do in-phase sequence sets add up to?” Real faults give each sequence its own phase angle — see the Fault Explorer tab for solved fault values. Symmetrical components: turning one messy problem into three tidy ones since 1918.

Phases +Seq −Seq 0Seq

Layered Phasor Diagram

ABC+−0

Phase Composition

Fortescue Transform Matrix

Ia	=	1	1	1	×	I₀
Ib	=	1	a²	a	×	I₁
Ic	=	1	a	a²	×	I₂

where a = 1∠120° = −0.5 + j0.866

What to notice

When only positive sequence is present, phases are balanced at 120° separation. Add negative sequence and watch the symmetry break.

Fault Type Comparison

Three-phase faults are balanced. Everything else gets more interesting.

Fault	Symmetry	+Seq	−Seq	0Seq	Severity	Ground
Three-Phase	Balanced	Yes	No	No	Equipment duty basis	No
SLG	Unbalanced	Yes	Yes	Yes	System dependent	Yes
Line-to-Line	Unbalanced	Yes	Yes	No	~87% of 3φ (Z₁≈Z₂)	No
DLG	Unbalanced	Yes	Yes	Yes	High	Yes

Phase Current Phasors

IaIbIc

Magnitude Comparison

Phase Current Waveforms

Voltage Triangle (Phase-to-Ground)

Solid arrows: phase-to-ground voltages at the fault point (from the solver). Dashed: pre-fault 1.0 pu reference. In an ungrounded ground fault the neutral shifts to the faulted phase and the healthy phases rise to the line-to-line value √3 ≈ 1.73 pu, 60° apart.

Fault Behavior

Select a fault type to see how it changes phase currents and sequence components.

Conceptual Sequence Network Connection

Each sequence has its own network. The fault type determines how they connect. This is the core trick: solve simple networks, combine results.

Positive

⊕

Source + Z₁
Always present

―

Negative

⊖

Z₂ only
No source

―

Zero

⊙

Z₀ + 3Zn
Needs ground path

Network Connection Rule

No Fault

Only positive-sequence network is active. System is balanced.

Current Flow Visualization

Grounding Influence

Solidly Grounded

Zero sequence tends to show up only when the system gives it somewhere to go.

Interactive Scenario Lab

Drag the phasor endpoints to set phase currents manually — sequence components computed in real time via the inverse Fortescue transform. This is your sandbox: break things intentionally.

Interactive Phase Phasors

Click & drag phasor tips to change magnitude and angle (fixed 1.5 pu axis scale)

IaIbIc

Computed Sequence Components

I₁ (Positive)

1.00

I₂ (Negative)

0.00

I₀ (Zero)

0.00

Phase Values

1.00

∠0°

1.00

∠-120°

1.00

∠120°

Waveform

Lab Summary

Interactive Mode

Drag the phasors above, or use the sidebar controls. Both update in real-time.

Design Challenge Mode

Select a challenge below, then use the sidebar controls to configure the system. When you think you have a valid design, hit Evaluate.

Challenge 1: Ground Fault Detection

Configure the system so a single line-to-ground fault produces detectable zero-sequence current (I₀ > 0.1 pu) while keeping maximum phase current moderate.

Challenge 2: Current Limiting

Set up a system where three-phase fault current stays below 5 pu. Think about source strength and fault location.

Challenge 3: Ungrounded Awareness

Demonstrate why an ungrounded system fails to produce zero-sequence current during a ground fault. Set grounding to ungrounded and apply an SLG fault.

Challenge 4: Maximum Asymmetry

Create the most asymmetric fault condition possible: maximize the ratio of negative-sequence to positive-sequence current.

Active Challenge

Goal: Ground Fault Detection

Fault type must be SLG or DLG
Zero-sequence current I₀ must be > 0.1 pu
Maximum phase current must be < 10 pu

Your Current Configuration

Fault Type

Balanced

I₁

1.00

I₂

0.00

I₀

0.00

Why Symmetrical Components Matter

Power systems are designed for balanced three-phase operation. But faults are unbalanced events. Analyzing them directly in three phases is painful—the math couples together and the physics gets tangled.

Symmetrical components (Fortescue, 1918) decompose any unbalanced three-phase set into three balanced sets:

Positive sequence: Equal magnitude, 120° apart, ABC rotation. Normal operating condition.
Negative sequence: Equal magnitude, 120° apart, ACB rotation. Appears during unbalanced faults.
Zero sequence: Equal magnitude, in phase. Related to ground current flow.

Key insight: Each sequence sees a different impedance. Solve three simple independent networks, combine results. That is the entire point.

How They Simplify Faults

Three-phase: Only positive sequence. Balanced.
Line-to-line: Positive and negative in parallel at fault point.
SLG: All three networks in series. I₁ = I₂ = I₀ when a zero-sequence return path exists and the model includes it.
DLG: Positive in series with negative ∥ zero. Current divides between negative- and zero-sequence branches based on their impedances.
Fault impedance Zf: enters as a series phase impedance for 3φ and LL faults, and as 3Zf in the zero-sequence (ground-return) branch for SLG and DLG. A DLG fault with no ground path degenerates to a line-to-line fault with Zf still in series.

Common Mistakes

Mistake: “Zero sequence means ground fault.”
Reality: Zero sequence is involved in ground faults, but only if there is a path for it. Ungrounded systems have ground faults without zero-sequence current. Idealized zero-sequence current is zero if capacitive charging is ignored.

Mistake: “Three-phase faults always produce the highest current.”
Reality: Three-phase faults are commonly used for equipment-duty calculations. However, the maximum fault current depends on transformer connection, grounding, location, and sequence impedances. DLG can exceed 3φ in certain configurations.

Mistake: “Negative sequence should never exist.”
Reality: It exists whenever the system is unbalanced—including normal small imbalances. High levels cause heating in machines.

What to Notice

Watch phasor shape change as you switch fault types
SLG and DLG have zero-sequence; LL does not
Switch to “ungrounded” and watch I₀ disappear—even during a ground fault
Three-phase fault is purely positive sequence
Try the interactive phasors in Scenario Lab

Pro tip: Use the Design Challenge tab to test your understanding with real goals.

Knowledge Check

Test your understanding. Select an answer for each question, then click Check Answers.

Educational Disclaimer: This is a conceptual learning tool using simplified per-unit models. It uses purely reactive sequence impedances and assumes standard sequence-network connections. Not for power system design, protection coordination, arc flash studies, or safety-critical engineering calculations.