Loading documentation...

Fault Classification

Fault type identification using sequence component ratios, FIDS angle-based phase selection, and multi-window temporal analysis.

In Detego

See the Fault Analysis Guide for how to interpret these results in the app. This page covers the mathematical theory.

Overview

Fault classification determines which type of short circuit has occurred on the power system and identifies the specific phases involved. The classification proceeds through a layered analysis: sequence component ratios determine the fault category (balanced, unbalanced, grounded), FIDS angle analysis identifies the faulted phases, and I₀/I₂ ratio discrimination distinguishes single-phase from double-phase ground faults. These methods draw on Fortescue's symmetrical component theory, with the angular relationships first formalised for protective relaying by SEL (Costello & Zimmerman, 2015).

Accurate fault classification drives relay coordination decisions, informs maintenance priorities, and helps identify recurring fault patterns. Different fault types stress equipment differently and require different protection responses.

Sequence Component Analysis

Fortescue's theorem decomposes any unbalanced three-phase system into three balanced sets: positive sequence (normal rotation), negative sequence (reversed rotation), and zero sequence (in-phase). The ratios between these components directly indicate the type of fault.

Positive Sequence (V₁)

Negative Sequence (V₂)

Zero Sequence (V₀)

Fortescue sequence components. Positive sequence: balanced ABC rotation. Negative sequence: reversed ACB rotation (indicates unbalance). Zero sequence: all phasors in-phase (indicates ground path).

Negative/Positive Sequence Ratio

Unbalance Detection

\frac{I_2}{I_1} > \text{threshold} \implies \text{Unbalanced fault}

Where

$I_2$ Negative-sequence current magnitude
$I_1$ Positive-sequence current magnitude

A balanced three-phase fault produces negligible negative sequence. Any significant I2 indicates an asymmetric (unbalanced) fault.

The $I_2 / I_1$ ratio is the primary discriminator between balanced and unbalanced faults. Three-phase faults produce $I_2 \approx 0$ because the fault is symmetric. Single line-to-ground, line-to-line, and double line-to-ground faults all produce significant negative-sequence current because the fault is asymmetric.

Zero/Positive Sequence Ratio

Ground Fault Detection

\frac{I_0}{I_1} > \text{threshold} \implies \text{Ground fault involvement}

Where

$I_0$ Zero-sequence current magnitude
$I_1$ Positive-sequence current magnitude

Zero-sequence current requires a ground return path. Its presence confirms that the fault involves one or more phases connected to ground.

Zero-sequence current can only flow when there is a ground path -- through the fault arc to earth and back through the system neutral grounding. Phase-to-phase faults (without ground involvement) produce no zero-sequence current because the three phase currents still sum to zero.

Phase Magnitude Analysis

Phase magnitude comparison provides a simple, intuitive check of which phases are involved in the fault. Individual phase magnitudes are compared against a baseline to detect voltage dips and current rises characteristic of faulted phases.

Voltage Dip Detection

Faulted Phase (Voltage)

|V_{\phi}| < k_V \times \overline{V} \implies \text{Faulted phase (voltage dip)}

Where

$V_\phi$ Individual phase voltage RMS magnitude
$\overline{V}$ Average of all three phase voltage magnitudes
$k_V$ Configurable voltage dip threshold (e.g., 0.70)

A voltage drop below the threshold fraction of the three-phase average indicates the faulted phase.

Current Rise Detection

Faulted Phase (Current)

|I_{\phi}| > k_I \times \min(I_A, I_B, I_C) \implies \text{Faulted phase (current rise)}

Where

$I_\phi$ Individual phase current RMS magnitude
$\min(I_A, I_B, I_C)$ Minimum of the three phase current magnitudes
$k_I$ Configurable current rise threshold (e.g., 1.50)

Current rise is measured against the minimum phase current, which represents the healthy-phase baseline. Using the average would be inflated by the fault current itself, reducing sensitivity.

Both voltage and current criteria are evaluated together. A phase is confirmed as faulted when it shows a voltage dip, a current rise, or both. Phase magnitude analysis serves as a supporting method alongside the angle-based FIDS technique described below.

FIDS Phase Identification

The Fault Identification using Directional Sequence components (FIDS) method identifies faulted phases by examining the angular relationship between the negative-sequence current ( $I_2$ ) and the zero-sequence current ( $I_0$ ). This approach was formalised for protective relaying by Costello and Zimmerman (SEL, 2015) and is widely used in modern phase-selection relays.

FIDS Angle

\alpha = \angle I_2 - \angle I_0

Where

$\alpha$ Angle difference between negative-sequence and zero-sequence current
$\angle I_2$ Angle of the negative-sequence current phasor
$\angle I_0$ Angle of the zero-sequence current phasor

The angle alpha falls into distinct 120-degree sectors, each corresponding to a specific phase.

For standard ABC phase rotation, the FIDS angle maps to three sectors:

FIDS Angle Sector	Identified Phase	Description
$\alpha \approx 0°$	Phase A	$I_2$ approximately in phase with $I_0$
$\alpha \approx -120°$	Phase B	$I_2$ lags $I_0$ by 120°
$\alpha \approx +120°$	Phase C	$I_2$ leads $I_0$ by 120°

The FIDS angle identifies the phase that is “different” from the other two. Its interpretation depends on the fault type:

For SLG faults: the identified phase IS the faulted phase. In an A-G fault, phase A is the only phase carrying fault current to ground, so $I_2$ aligns with $I_0$ .
For DLG faults: the FIDS-identified phase is theoretically the HEALTHY one. However, fault resistance can rotate the $I_2/I_0$ angle significantly (documented shifts exceeding 50 degrees at moderate fault resistance), pushing it into the wrong sector. For this reason, DLG phase identification uses current magnitude ranking as the primary method: the phase with the lowest current is the healthy phase, and the other two are faulted. When pre-fault data is available, the comparison uses the change in current (delta) rather than absolute magnitude, which eliminates the effect of pre-fault load current.

FIDS Applicability

The FIDS angle method is highly reliable for SLG faults where the angle is determined by network topology. For DLG faults, fault resistance causes the angle to rotate away from the ideal sector boundary. Current magnitude ranking is immune to this effect because it measures fault current flow directly, rather than computing an angle from sequence component relationships.

SLG vs DLG Discrimination

When the classifier determines that a ground fault is present (both unbalance and ground indicators exceed their thresholds), a key question remains: is this a single line-to-ground (SLG) or double line-to-ground (DLG) fault? The $I_0 / I_2$ ratio provides the answer, based on how the sequence networks interconnect for each fault type.

SLG: Series Connection

For a single line-to-ground fault, the positive, negative, and zero sequence networks are connected in series (NPAG Chapter A3, Eq. A3.12). This means the same current flows through all three networks:

SLG Sequence Currents

I_1 = I_2 = I_0 = \frac{V_{\text{pre}}}{Z_1 + Z_2 + Z_0 + 3Z_f}

Where

$I_1, I_2, I_0$ Positive, negative, and zero sequence fault currents
$V_{\text{pre}}$ Pre-fault voltage at the fault point
$Z_1, Z_2, Z_0$ Sequence impedances of the network
$Z_f$ Fault impedance

Because all three sequence currents are equal, the I0/I2 ratio at the fault point is exactly 1.0.

DLG: Parallel Connection

For a double line-to-ground fault, the negative and zero sequence networks are connected in parallel with each other, and this parallel combination is in series with the positive sequence network (NPAG Chapter A3, Eq. A3.18-20). The zero-sequence current is determined by the current divider between the negative and zero sequence branches:

DLG Zero-Sequence Current

I_0 = -I_1 \times \frac{Z_2}{Z_0 + Z_2 + 3Z_f}

Where

$I_0$ Zero-sequence current (at the fault point)
$I_1$ Positive-sequence current
$Z_2, Z_0$ Negative and zero sequence impedances

Because the zero and negative sequence networks share the fault current, I0 is typically much less than I2.

For overhead transmission lines where $Z_0 \gg Z_2$ (zero-sequence impedance is typically 2-4 times the positive/negative-sequence impedance), the $I_0 / I_2$ ratio for DLG faults is well below 1.0. This creates clear separation from the SLG case where the ratio is near unity.

Effect of Relay Location

At the relay location (as opposed to the fault point), the sequence current distribution factors $C_0$ and $C_1$ shift the measured $I_0 / I_2$ ratio away from the ideal values. The distribution factors depend on the source impedance behind the relay and the line impedance to the fault. Despite this shift, the SLG and DLG populations remain well separated: SLG ratios cluster near 1.0 while DLG ratios are substantially lower. A configurable threshold band between the two populations provides reliable discrimination.

LL Pair Identification (Beta Method)

For line-to-line faults without ground involvement, zero-sequence current is absent ( $I_0 \approx 0$ ), so the FIDS angle $\alpha = \angle I_2 - \angle I_0$ is undefined. Instead, the faulted phase pair is identified using the angle between the negative-sequence and positive-sequence currents:

Beta Angle

\beta = \angle I_2 - \angle I_1

Where

$\beta$ Angle difference between negative-sequence and positive-sequence current
$\angle I_2$ Angle of the negative-sequence current phasor
$\angle I_1$ Angle of the positive-sequence current phasor

The beta angle falls into 60-degree sectors, each identifying a specific line-to-line fault pair.

Each of the three possible line-to-line fault pairs (AB, BC, CA) maps to a distinct 60-degree sector in the beta angle space. This method is also applicable to DLG faults as a cross-check, since the phase pair identified by the beta angle should be consistent with the phases identified by FIDS.

When Beta is Used

The beta method is the primary phase pair identifier whenever unbalance is present but ground is absent. When ground IS present, FIDS (alpha angle) is preferred because the I₂/I₀ relationship is more directly tied to the faulted phase through the zero-sequence network path.

Fault Types

Type	Designation	I2/I1	I0/I1	Characteristics
Single Line-to-Ground	SLG (A-G, B-G, C-G)	High	High	One phase voltage dips, one phase current rises. Both negative and zero sequence present. I0/I2 near unity.
Line-to-Line	LL (AB, BC, CA)	High	Low	Two phases affected, no ground path. Negative sequence present, zero sequence absent. Phase pair identified via beta angle.
Double Line-to-Ground	DLG (AB-G, BC-G, CA-G)	High	High	Two phases affected with ground involvement. Both negative and zero sequence present. I0/I2 well below unity.
Three-Phase	3P (ABC)	Low	Low	Balanced fault. All three phases affected equally. Negligible negative and zero sequence.
Three-Phase-to-Ground	3P-G (ABC-G)	Low	Moderate	Balanced fault with ground current. I2 negligible but I0 may be present depending on grounding.

Fault Frequency in Practice

Single line-to-ground faults are by far the most common fault type, accounting for approximately 70-80% of all faults on overhead transmission and distribution systems. Most SLG faults are caused by lightning strikes, tree contact, or insulator flashover -- all of which establish a single-phase path to ground. Line-to-line faults account for roughly 10-15%, double line-to-ground faults for 5-10%, and three-phase faults for only 2-5%.

Classification Decision Logic

The classification algorithm follows a layered decision process that evaluates the fault characteristics in order of decreasing generality:

Ground detection: Check whether $I_0 / I_1$ (or $V_0 / V_1$ as a voltage-based alternative) exceeds a configurable threshold. If so, the fault involves ground.
Unbalance detection: Check whether $I_2 / I_1$ (or $V_2 / V_1$ ) exceeds a configurable threshold. If so, the fault is asymmetric (unbalanced).
Fault type determination:
- Balanced (no significant unbalance): three-phase fault. Check ground indicator to distinguish 3P from 3P-G.
- Unbalanced + no ground: line-to-line fault. Identify the phase pair using the beta angle.
- Unbalanced + ground: SLG or DLG. Discriminate using the $I_0 / I_2$ ratio (near unity for SLG, well below unity for DLG).
Phase identification: Use the FIDS alpha angle as the primary method for ground faults and the beta angle for ungrounded faults. Phase magnitude comparison (voltage dip and current rise) serves as a supporting check.

Compensated System Fallback

On Petersen coil (compensated earthed) systems, the tuning coil is designed to suppress zero-sequence current at the fault location. Because the ground-fault current is compensated to near zero, both $I_0$ and $I_2$ measured at the relay are negligible -- the current-based methods described above lose sensitivity.

However, the voltages still clearly reveal the fault. On a compensated system during an SLG fault:

The faulted phase voltage collapses toward zero (for a solid fault).
The healthy phase voltages rise to line-to-line voltage ( $\sqrt{3}$ times nominal phase voltage).
The zero-sequence voltage $V_0$ becomes very large (full voltage displacement), even though $I_0$ is suppressed.

When current-based classification is inconclusive, the algorithm falls back to comparing each phase voltage against its pre-fault value. The phase with the largest voltage depression is identified as the faulted phase. This approach is consistent with standard Petersen coil theory and NPAG Section 6.3.1 on isolated/compensated neutral systems.

Fallback Behavior

When neither angle-based nor magnitude-based methods can clearly identify the faulted phases (e.g., evolving faults, CT saturation, or heavily loaded systems with significant pre-fault imbalance), the algorithm reports the fault type from sequence analysis without specifying the individual phases. In these cases, the classification will show the fault type (e.g., “SLG”) without the phase suffix (e.g., without “A-G”).

Superimposed (Delta) Sequence Components

Classical fault classification operates on the total phasors and sequence components measured during the fault. On a heavily loaded line this is problematic: load current produces its own positive-sequence component, and its natural unbalance adds a small negative-sequence component. Minor unbalanced faults are partially masked by this pre-fault baseline.

The superimposed (or delta, or pure-fault) quantities isolate the fault contribution by subtracting the pre-fault phasor from the during-fault phasor:

\Delta \bar{I}_\phi(t) = \bar{I}_\phi(t) - \bar{I}_\phi(t - T_{\text{pre}})

Where

$\Delta \bar{I}_\phi$ delta (superimposed) phase current phasor
$\bar{I}_\phi(t)$ phase current phasor during the fault
$\bar{I}_\phi(t - T_{\text{pre}})$ phase current phasor at a pre-fault reference time

The same subtraction is applied to voltages. Because the DFT is linear, taking the delta of phasors is equivalent to taking the phasor of the time-domain delta signal $\Delta i(t) = i(t) - i(t - T)$ . The sequence components of the delta quantities then reflect only the fault-induced change:

\Delta \bar{I}_1, \Delta \bar{I}_2, \Delta \bar{I}_0 \;\leftarrow\; \text{sym}(\Delta \bar{I}_A, \Delta \bar{I}_B, \Delta \bar{I}_C)

Where

$\Delta \bar{I}_1$ delta positive-sequence current (fault contribution to balanced current)
$\Delta \bar{I}_2$ delta negative-sequence current (asymmetry from the fault)
$\Delta \bar{I}_0$ delta zero-sequence current (ground involvement from the fault)

Using the ratios $|\Delta \bar{I}_2| / |\Delta \bar{I}_1|$ and $|\Delta \bar{I}_0| / |\Delta \bar{I}_1|$ for the unbalance and ground tests -- instead of the total-quantity ratios -- removes the load-current bias and makes the classifier more sensitive to minor faults on loaded systems. The superimposed approach is standard in transmission-line protection literature and is used by modern phase-selection relays.

Multi-Window Classification

A single classification point is a single snapshot of a fault that may actually evolve. Real-world examples include:

SLG to DLG evolution: a single phase-to-ground arc that flashes to a second phase as ionised air breaks down the second clearance.
Two-stage faults: cascading failures on adjacent equipment during a long-duration fault.
Auto-reclose sequences: a fault cleared by a breaker that then re-closes onto a persistent fault, producing distinct classification intervals.

Classifying at a single point reports whichever state happens to be present at the sample time -- typically the initial fault type -- and misses the evolution entirely. A multi-window scan walks across the fault window at fixed time steps, runs the full classifier at each step, and collects the results into a timeline.

Noise Filtering and Scan Boundaries

Short-lived classification changes that persist for fewer than multiple half-cycles are treated as transient noise and are absorbed into the surrounding segment. This prevents single-point glitches -- caused by spectral leakage, CT saturation, or measurement noise -- from appearing as spurious fault type transitions.

The scan window is bounded to stop before the fault clearance boundary. This avoids contamination from breaker transients: as each phase interrupts at a different zero-crossing, phasor filters produce spurious negative-sequence current that can be misclassified as an evolving fault (Kasztenny, SEL 2019). By excluding the clearance region, the classifier reports only genuine fault-period behaviour.

Segment Interpretation

Consecutive identical results are collapsed into segments. A segment is a contiguous run of scan points with the same fault type and faulted phases. The number of segments distinguishes three regimes:

Segments	Interpretation
1	Stable fault -- classification held throughout the fault window.
2-3	Evolving fault -- genuine transitions between fault types (e.g., SLG evolving to DLG).
Many	Usually classifier instability -- bouncing on noise, marginal thresholds, or post-fault transients rather than real fault evolution.

Classification Pipeline

The classification algorithm follows a layered pipeline where each layer narrows the fault type and identifies specific phases. The pipeline is designed so that later layers only run when earlier layers produce ambiguous or incomplete results.

Classification Pipeline — Multi-Layer Decision Flow

Layer 1 computes sequence component ratios to determine ground involvement and unbalance. Layer 2 combines these indicators to classify the fault type and uses the $I_0 / I_2$ band to discriminate SLG from DLG. Layer 3 identifies specific phases using FIDS alpha (for SLG), current magnitude ranking (for DLG), or beta angle (for LL faults and compensated systems). Layer 4 cross-validates the result using independent methods. Layer 5 computes a confidence score.

Beta Method for Compensated Systems

On systems with Petersen coil (resonance) earthing, high-impedance earthing, or isolated (ungrounded) neutrals, the tuning inductor or absent ground path suppresses zero-sequence current to near zero. The FIDS alpha angle ( $\alpha = \angle I_2 - \angle I_0$ ) becomes undefined or dominated by measurement noise.

The beta angle resolves this limitation by using only the positive and negative sequence currents, both of which remain substantial during any unbalanced fault regardless of grounding:

Beta Angle (extended use)

\beta = \angle I_2 - \angle I_1

Where

$\angle I_2$ Angle of the negative-sequence current phasor
$\angle I_1$ Angle of the positive-sequence current phasor

Unlike FIDS alpha, beta is independent of zero-sequence current and works on all earthing configurations.

The beta angle maps to six 60-degree sectors — three for single-phase faults and three for phase-pair faults — providing both SLG phase identification and LL pair identification from a single measurement:

FIDS Alpha vs Beta Angle — Sector Comparison

Beta Sector	Type	Identification
$\beta \approx 0°$	SLG	Phase A
$\beta \approx +60°$	LL / DLG	A-B pair
$\beta \approx +120°$	SLG	Phase B
$\beta \approx \pm180°$	LL / DLG	B-C pair
$\beta \approx -120°$	SLG	Phase C
$\beta \approx -60°$	LL / DLG	C-A pair

Modern relay designs combine both alpha and beta angles as cross-checks (Kariyawasam et al., PSE 2023). On standard grounded systems, the FIDS alpha method remains primary because it is more resistant to fault resistance rotation. On compensated or ungrounded systems, beta becomes the primary classification path because it does not depend on $I_0$ .

Grounding Type Inference

The classification algorithm needs to know the system earthing type to select the correct analysis path (FIDS alpha vs. beta). Rather than requiring the user to specify grounding manually, the algorithm infers it from the fault signatures themselves.

Healthy-Phase Voltage Rise

The primary indicator is the voltage behaviour on healthy (unfaulted) phases during a ground fault. On solidly-grounded systems, healthy-phase voltages remain approximately at their pre-fault levels. On ungrounded or compensated systems, the neutral point shifts, causing healthy-phase voltages to rise toward line-to-line values:

Healthy-Phase Voltage Ratio

\text{ratio} = \frac{\max(V_{\text{healthy,fault}})}{\overline{V}_{\text{pre-fault}}}

Where

$V_{\text{healthy,fault}}$ Maximum healthy-phase voltage during the fault
$\overline{V}_{\text{pre-fault}}$ Average phase voltage before the fault

A ratio above approximately 1.5 (i.e., healthy-phase voltage rising toward √3 × nominal) indicates a compensated or ungrounded system.

V0/I0 Angle Discrimination

When healthy-phase voltage rise is detected, the angle between zero-sequence voltage and zero-sequence current distinguishes between compensated and ungrounded systems:

Compensated (Petersen coil): $I_0$ is approximately in phase with $V_0$ . The coil's inductive current nearly cancels the capacitive ground fault current, leaving a small resistive residual that aligns with the voltage (ABB Protection Application Handbook, pp. 50–82).
Ungrounded (isolated neutral): $I_0$ leads $V_0$ by approximately 90°. The fault current is purely capacitive (flowing through the distributed phase-to-ground capacitance of the network), producing the characteristic 90° lead.

Zero-Sequence Current Magnitude

When healthy-phase voltages do not rise (grounded systems), the $I_0 / I_1$ ratio discriminates between solidly grounded systems (high zero-sequence current, typically $I_0 / I_1 > 30\%$ ) and low-impedance grounded systems (moderate zero-sequence current). This classification follows the earthing factor definitions in IEC 60071-2 and the NPAG (Schneider) Section 6.3.

SLG/DLG Cross-Validation

The $I_0 / I_2$ ratio alone can be unreliable for distinguishing SLG from DLG faults, particularly at low $Z_0 / Z_1$ ratios or with significant fault resistance. Multiple independent cross-validation methods improve reliability:

Phase Comparison

Compares the change in current magnitude from pre-fault to during-fault on each phase. For a genuine SLG fault, only the faulted phase should carry significantly elevated current. If two phases show similar current elevation, the fault is likely DLG. This method is robust because it uses direct physical measurements rather than derived angles, and is immune to fault resistance effects.

Fault Resistance Comparison

Computes the apparent fault resistance under two competing hypotheses: “this is an SLG fault on the FIDS-identified phase” vs. “this is an LL fault between the other two phases.” The hypothesis that produces a physically reasonable (positive, finite) fault resistance is more likely correct (Costello & Zimmerman, SEL 6386).

Competing Fault Resistance

R_f = \frac{\text{Im}[V \cdot (Z_{1L} \cdot I_{\text{comp}})^*]}{\text{Im}[I_f \cdot (Z_{1L} \cdot I_{\text{comp}})^*]}

Where

$V$ Faulted-phase voltage (SLG hypothesis) or voltage difference (LL hypothesis)
$I_{\text{comp}}$ Compensated fault current (includes k₀ correction for zero-sequence)
$Z_{1L}$ Positive-sequence line impedance (angle only, magnitude cancels)
$I_f$ Estimated total fault current

This formula is evaluated for both the ground (SLG) and phase (LL) hypotheses. A negative result invalidates that hypothesis.

Beta Cross-Check

When the $I_0 / I_2$ ratio places the fault outside the SLG band (suggesting DLG), a beta angle check can confirm or contradict. If beta points to an SLG sector and the corresponding phase carries significantly more current than the other two phases, the classification is corrected to SLG. This catches cases where the $I_0 / I_2$ band is shifted by network topology while the beta angle, being independent of $I_0$ , remains correct.

Line-to-Line Voltage Derivation

Some recordings provide only line-to-line voltages ( $V_{AB}, V_{BC}, V_{CA}$ ) rather than phase-to-neutral voltages. Phase-to-neutral voltages are needed for sequence component calculation, so the classifier derives them using the zero-sequence voltage assumption:

Phase-Neutral Derivation

V_A = \frac{2V_{AB} + V_{BC}}{3}, \quad V_B = \frac{2V_{BC} + V_{CA}}{3}, \quad V_C = \frac{2V_{CA} + V_{AB}}{3}

Where

$V_{AB}, V_{BC}, V_{CA}$ Measured line-to-line voltages
$V_A, V_B, V_C$ Derived phase-to-neutral voltages

This derivation assumes V₀ = 0. On solidly-grounded systems this is a good approximation. On compensated or ungrounded systems, V₀ can be substantial during ground faults, introducing error into the derived voltages.

Limitation on Compensated Systems

When the recording has only line-to-line voltages AND the system is compensated or ungrounded, the zero-sequence voltage during a ground fault can approach full phase voltage. The derived phase-neutral voltages will contain errors proportional to

V_0

, which may affect voltage-based classification indicators. In these cases, the current-based classification (sequence ratios and beta angle) is more reliable.

Confidence Assessment

Each classification decision (ground detection, unbalance detection, $I_0 / I_2$ band placement, FIDS/beta angle sector identification) involves comparing a measured quantity against a threshold boundary. The confidence score measures how far each decision is from its threshold — the further from the boundary, the more confident the result.

The overall confidence is the weakest-link margin: the minimum confidence across all decisions in the classification chain. This reflects the principle that a classification is only as reliable as its least certain step. For example, if the ground detection is very strong (high $I_0 / I_1$ ) but the FIDS angle falls near a sector boundary, the overall confidence will be low — driven by the uncertain angle measurement.

Interpreting Confidence

High confidence (>70%) means all decision steps had clear margins. Low confidence (<30%) means at least one step was very close to a threshold boundary and the classification could change with small measurement variations. The confidence label in the Fault ID tab verdict banner identifies which specific step is limiting.

Pre-fault Quality Validation

The superimposed (delta) approach subtracts pre-fault phasors from fault phasors to isolate the fault contribution. This works well when the pre-fault system is reasonably balanced. However, if the pre-fault system already has significant negative-sequence current (due to untransposed lines, unbalanced loads, or a previous fault), the delta quantities will inherit this unbalance and produce distorted ratios.

Before using delta quantities, the classifier evaluates the pre-fault $I_2 / I_1$ ratio. If the pre-fault unbalance exceeds a rejection threshold, the algorithm switches to classifying from total (absolute) phasors instead of delta phasors, at the cost of load current sensitivity. A moderate pre-fault unbalance triggers a warning but still uses the delta approach, as the benefits of load-current rejection typically outweigh the unbalance error.

Current-Collapse Scan Termination

As the fault is cleared by the circuit breaker, current decays rapidly. If the classification scan continues into this decay region, the DFT phasor estimates become unreliable — the decaying waveform is not periodic, producing spectral leakage artifacts that can be misinterpreted as fault type transitions. The classifier monitors the maximum fault current and terminates the scan early if the current falls to a small fraction of its peak for consecutive half-cycle windows. This prevents spurious segment creation from post-clearance transients (Kasztenny, SEL 2019).

Engineering Applications

Fault classification informs several protection engineering decisions:

Protection element selection: SLG faults should operate ground overcurrent (51N/50N) and ground distance (21N) elements. Phase faults should operate phase overcurrent (51/50) and phase distance (21) elements. Incorrect classification from the relay may indicate a coordination issue.
Fault current calculation verification: The measured fault currents can be compared against short-circuit study values for the classified fault type. Significant discrepancies may indicate modeling errors in the study.
Recurrence analysis: Repeated SLG faults on the same phase often indicate a specific physical cause (broken insulator, tree growth) that can be targeted for maintenance.
Auto-reclosing strategy: SLG faults on overhead lines are typically transient and suitable for auto-reclosing. Multi-phase faults are more likely to be permanent and may require different reclosing strategies or lockout.

Cross-Reference with AI Analysis

The Compute tab's fault classification provides raw sequence ratios and phase magnitudes. The AI Analysis engine uses these same quantities but adds engineering context, compares against typical thresholds, and provides a narrative explanation of the fault type determination. Use both together for the most complete assessment.

PreviousFault Detection NextFault Location

Loading documentation...

Fault Classification

Fault type identification using sequence component ratios, FIDS angle-based phase selection, and multi-window temporal analysis.

In Detego

See the Fault Analysis Guide for how to interpret these results in the app. This page covers the mathematical theory.

Overview

Sequence Component Analysis

Positive Sequence (V₁)

Negative Sequence (V₂)

Zero Sequence (V₀)

Fortescue sequence components. Positive sequence: balanced ABC rotation. Negative sequence: reversed ACB rotation (indicates unbalance). Zero sequence: all phasors in-phase (indicates ground path).

Negative/Positive Sequence Ratio

Unbalance Detection

\frac{I_2}{I_1} > \text{threshold} \implies \text{Unbalanced fault}

Where

$I_2$ Negative-sequence current magnitude
$I_1$ Positive-sequence current magnitude

A balanced three-phase fault produces negligible negative sequence. Any significant I2 indicates an asymmetric (unbalanced) fault.

Zero/Positive Sequence Ratio

Ground Fault Detection

\frac{I_0}{I_1} > \text{threshold} \implies \text{Ground fault involvement}

Where

$I_0$ Zero-sequence current magnitude
$I_1$ Positive-sequence current magnitude

Zero-sequence current requires a ground return path. Its presence confirms that the fault involves one or more phases connected to ground.

Phase Magnitude Analysis

Voltage Dip Detection

Faulted Phase (Voltage)

|V_{\phi}| < k_V \times \overline{V} \implies \text{Faulted phase (voltage dip)}

Where

$V_\phi$ Individual phase voltage RMS magnitude
$\overline{V}$ Average of all three phase voltage magnitudes
$k_V$ Configurable voltage dip threshold (e.g., 0.70)

A voltage drop below the threshold fraction of the three-phase average indicates the faulted phase.

Current Rise Detection

Faulted Phase (Current)

|I_{\phi}| > k_I \times \min(I_A, I_B, I_C) \implies \text{Faulted phase (current rise)}

Where

$I_\phi$ Individual phase current RMS magnitude
$\min(I_A, I_B, I_C)$ Minimum of the three phase current magnitudes
$k_I$ Configurable current rise threshold (e.g., 1.50)

Current rise is measured against the minimum phase current, which represents the healthy-phase baseline. Using the average would be inflated by the fault current itself, reducing sensitivity.

FIDS Phase Identification

FIDS Angle

\alpha = \angle I_2 - \angle I_0

Where

$\alpha$ Angle difference between negative-sequence and zero-sequence current
$\angle I_2$ Angle of the negative-sequence current phasor
$\angle I_0$ Angle of the zero-sequence current phasor

The angle alpha falls into distinct 120-degree sectors, each corresponding to a specific phase.

For standard ABC phase rotation, the FIDS angle maps to three sectors:

FIDS Angle Sector	Identified Phase	Description
$\alpha \approx 0°$	Phase A	$I_2$ approximately in phase with $I_0$
$\alpha \approx -120°$	Phase B	$I_2$ lags $I_0$ by 120°
$\alpha \approx +120°$	Phase C	$I_2$ leads $I_0$ by 120°

The FIDS angle identifies the phase that is “different” from the other two. Its interpretation depends on the fault type:

For SLG faults: the identified phase IS the faulted phase. In an A-G fault, phase A is the only phase carrying fault current to ground, so $I_2$ aligns with $I_0$ .
For DLG faults: the FIDS-identified phase is theoretically the HEALTHY one. However, fault resistance can rotate the $I_2/I_0$ angle significantly (documented shifts exceeding 50 degrees at moderate fault resistance), pushing it into the wrong sector. For this reason, DLG phase identification uses current magnitude ranking as the primary method: the phase with the lowest current is the healthy phase, and the other two are faulted. When pre-fault data is available, the comparison uses the change in current (delta) rather than absolute magnitude, which eliminates the effect of pre-fault load current.

FIDS Applicability

SLG vs DLG Discrimination

SLG: Series Connection

SLG Sequence Currents

I_1 = I_2 = I_0 = \frac{V_{\text{pre}}}{Z_1 + Z_2 + Z_0 + 3Z_f}

Where

$I_1, I_2, I_0$ Positive, negative, and zero sequence fault currents
$V_{\text{pre}}$ Pre-fault voltage at the fault point
$Z_1, Z_2, Z_0$ Sequence impedances of the network
$Z_f$ Fault impedance

Because all three sequence currents are equal, the I0/I2 ratio at the fault point is exactly 1.0.

DLG: Parallel Connection

DLG Zero-Sequence Current

I_0 = -I_1 \times \frac{Z_2}{Z_0 + Z_2 + 3Z_f}

Where

$I_0$ Zero-sequence current (at the fault point)
$I_1$ Positive-sequence current
$Z_2, Z_0$ Negative and zero sequence impedances

Because the zero and negative sequence networks share the fault current, I0 is typically much less than I2.

Effect of Relay Location

LL Pair Identification (Beta Method)

Beta Angle

\beta = \angle I_2 - \angle I_1

Where

$\beta$ Angle difference between negative-sequence and positive-sequence current
$\angle I_2$ Angle of the negative-sequence current phasor
$\angle I_1$ Angle of the positive-sequence current phasor

The beta angle falls into 60-degree sectors, each identifying a specific line-to-line fault pair.

When Beta is Used

Fault Types

Type	Designation	I2/I1	I0/I1	Characteristics
Single Line-to-Ground	SLG (A-G, B-G, C-G)	High	High	One phase voltage dips, one phase current rises. Both negative and zero sequence present. I0/I2 near unity.
Line-to-Line	LL (AB, BC, CA)	High	Low	Two phases affected, no ground path. Negative sequence present, zero sequence absent. Phase pair identified via beta angle.
Double Line-to-Ground	DLG (AB-G, BC-G, CA-G)	High	High	Two phases affected with ground involvement. Both negative and zero sequence present. I0/I2 well below unity.
Three-Phase	3P (ABC)	Low	Low	Balanced fault. All three phases affected equally. Negligible negative and zero sequence.
Three-Phase-to-Ground	3P-G (ABC-G)	Low	Moderate	Balanced fault with ground current. I2 negligible but I0 may be present depending on grounding.

Fault Frequency in Practice

Classification Decision Logic

The classification algorithm follows a layered decision process that evaluates the fault characteristics in order of decreasing generality:

Ground detection: Check whether $I_0 / I_1$ (or $V_0 / V_1$ as a voltage-based alternative) exceeds a configurable threshold. If so, the fault involves ground.
Unbalance detection: Check whether $I_2 / I_1$ (or $V_2 / V_1$ ) exceeds a configurable threshold. If so, the fault is asymmetric (unbalanced).
Fault type determination:
- Balanced (no significant unbalance): three-phase fault. Check ground indicator to distinguish 3P from 3P-G.
- Unbalanced + no ground: line-to-line fault. Identify the phase pair using the beta angle.
- Unbalanced + ground: SLG or DLG. Discriminate using the $I_0 / I_2$ ratio (near unity for SLG, well below unity for DLG).
Phase identification: Use the FIDS alpha angle as the primary method for ground faults and the beta angle for ungrounded faults. Phase magnitude comparison (voltage dip and current rise) serves as a supporting check.

Compensated System Fallback

However, the voltages still clearly reveal the fault. On a compensated system during an SLG fault:

The faulted phase voltage collapses toward zero (for a solid fault).
The healthy phase voltages rise to line-to-line voltage ( $\sqrt{3}$ times nominal phase voltage).
The zero-sequence voltage $V_0$ becomes very large (full voltage displacement), even though $I_0$ is suppressed.

Fallback Behavior

Superimposed (Delta) Sequence Components

The superimposed (or delta, or pure-fault) quantities isolate the fault contribution by subtracting the pre-fault phasor from the during-fault phasor:

\Delta \bar{I}_\phi(t) = \bar{I}_\phi(t) - \bar{I}_\phi(t - T_{\text{pre}})

Where

$\Delta \bar{I}_\phi$ delta (superimposed) phase current phasor
$\bar{I}_\phi(t)$ phase current phasor during the fault
$\bar{I}_\phi(t - T_{\text{pre}})$ phase current phasor at a pre-fault reference time

\Delta \bar{I}_1, \Delta \bar{I}_2, \Delta \bar{I}_0 \;\leftarrow\; \text{sym}(\Delta \bar{I}_A, \Delta \bar{I}_B, \Delta \bar{I}_C)

Where

$\Delta \bar{I}_1$ delta positive-sequence current (fault contribution to balanced current)
$\Delta \bar{I}_2$ delta negative-sequence current (asymmetry from the fault)
$\Delta \bar{I}_0$ delta zero-sequence current (ground involvement from the fault)

Multi-Window Classification

A single classification point is a single snapshot of a fault that may actually evolve. Real-world examples include:

SLG to DLG evolution: a single phase-to-ground arc that flashes to a second phase as ionised air breaks down the second clearance.
Two-stage faults: cascading failures on adjacent equipment during a long-duration fault.
Auto-reclose sequences: a fault cleared by a breaker that then re-closes onto a persistent fault, producing distinct classification intervals.

Noise Filtering and Scan Boundaries

Segment Interpretation

Segments	Interpretation
1	Stable fault -- classification held throughout the fault window.
2-3	Evolving fault -- genuine transitions between fault types (e.g., SLG evolving to DLG).
Many	Usually classifier instability -- bouncing on noise, marginal thresholds, or post-fault transients rather than real fault evolution.

Classification Pipeline

Classification Pipeline — Multi-Layer Decision Flow

Beta Method for Compensated Systems

The beta angle resolves this limitation by using only the positive and negative sequence currents, both of which remain substantial during any unbalanced fault regardless of grounding:

Beta Angle (extended use)

\beta = \angle I_2 - \angle I_1

Where

$\angle I_2$ Angle of the negative-sequence current phasor
$\angle I_1$ Angle of the positive-sequence current phasor

Unlike FIDS alpha, beta is independent of zero-sequence current and works on all earthing configurations.

FIDS Alpha vs Beta Angle — Sector Comparison

Beta Sector	Type	Identification
$\beta \approx 0°$	SLG	Phase A
$\beta \approx +60°$	LL / DLG	A-B pair
$\beta \approx +120°$	SLG	Phase B
$\beta \approx \pm180°$	LL / DLG	B-C pair
$\beta \approx -120°$	SLG	Phase C
$\beta \approx -60°$	LL / DLG	C-A pair

Grounding Type Inference

Healthy-Phase Voltage Rise

Healthy-Phase Voltage Ratio

\text{ratio} = \frac{\max(V_{\text{healthy,fault}})}{\overline{V}_{\text{pre-fault}}}

Where

$V_{\text{healthy,fault}}$ Maximum healthy-phase voltage during the fault
$\overline{V}_{\text{pre-fault}}$ Average phase voltage before the fault

A ratio above approximately 1.5 (i.e., healthy-phase voltage rising toward √3 × nominal) indicates a compensated or ungrounded system.

V0/I0 Angle Discrimination

When healthy-phase voltage rise is detected, the angle between zero-sequence voltage and zero-sequence current distinguishes between compensated and ungrounded systems:

Compensated (Petersen coil): $I_0$ is approximately in phase with $V_0$ . The coil's inductive current nearly cancels the capacitive ground fault current, leaving a small resistive residual that aligns with the voltage (ABB Protection Application Handbook, pp. 50–82).
Ungrounded (isolated neutral): $I_0$ leads $V_0$ by approximately 90°. The fault current is purely capacitive (flowing through the distributed phase-to-ground capacitance of the network), producing the characteristic 90° lead.

Zero-Sequence Current Magnitude

SLG/DLG Cross-Validation

Phase Comparison

Fault Resistance Comparison

Competing Fault Resistance

R_f = \frac{\text{Im}[V \cdot (Z_{1L} \cdot I_{\text{comp}})^*]}{\text{Im}[I_f \cdot (Z_{1L} \cdot I_{\text{comp}})^*]}

Where

$V$ Faulted-phase voltage (SLG hypothesis) or voltage difference (LL hypothesis)
$I_{\text{comp}}$ Compensated fault current (includes k₀ correction for zero-sequence)
$Z_{1L}$ Positive-sequence line impedance (angle only, magnitude cancels)
$I_f$ Estimated total fault current

This formula is evaluated for both the ground (SLG) and phase (LL) hypotheses. A negative result invalidates that hypothesis.

Beta Cross-Check

Line-to-Line Voltage Derivation

Phase-Neutral Derivation

V_A = \frac{2V_{AB} + V_{BC}}{3}, \quad V_B = \frac{2V_{BC} + V_{CA}}{3}, \quad V_C = \frac{2V_{CA} + V_{AB}}{3}

Where

$V_{AB}, V_{BC}, V_{CA}$ Measured line-to-line voltages
$V_A, V_B, V_C$ Derived phase-to-neutral voltages

Limitation on Compensated Systems

V_0

, which may affect voltage-based classification indicators. In these cases, the current-based classification (sequence ratios and beta angle) is more reliable.

Protection element selection: SLG faults should operate ground overcurrent (51N/50N) and ground distance (21N) elements. Phase faults should operate phase overcurrent (51/50) and phase distance (21) elements. Incorrect classification from the relay may indicate a coordination issue.
Fault current calculation verification: The measured fault currents can be compared against short-circuit study values for the classified fault type. Significant discrepancies may indicate modeling errors in the study.
Recurrence analysis: Repeated SLG faults on the same phase often indicate a specific physical cause (broken insulator, tree growth) that can be targeted for maintenance.
Auto-reclosing strategy: SLG faults on overhead lines are typically transient and suitable for auto-reclosing. Multi-phase faults are more likely to be permanent and may require different reclosing strategies or lockout.

Cross-Reference with AI Analysis

PreviousFault Detection NextFault Location