Loading documentation...
Impedance measurement principles, zone characteristic equations, and fault loop mathematics.
In Detego
Distance protection determines whether a fault lies within a defined reach by measuring the apparent impedance at the relay location. The measured impedance is proportional to the electrical distance between the relay and the fault point -- hence the name "distance" protection.
The relay computes for each fault loop and compares the result against predefined zone boundaries on the R-X impedance plane. If the measured impedance falls inside a zone, the relay operates (trips) after the corresponding zone time delay.
The impedance measurement depends on the fault type. Different voltage and current combinations are used to compute the correct loop impedance for each fault scenario.
For faults between two phases, the delta voltage is divided by the delta current. This cancels the zero-sequence component and yields the positive-sequence impedance to the fault point.
Phase-phase loop impedance
Where
Similarly for Z_BC = (V_B - V_C)/(I_B - I_C) and Z_CA = (V_C - V_A)/(I_C - I_A).
For single-phase-to-ground faults, the phase voltage is divided by the phase current plus a zero-sequence compensation term. The compensation accounts for the difference between the zero-sequence and positive-sequence impedances of the line.
Phase-ground loop impedance
Where
Similarly for Z_BG (using V_B, I_B) and Z_CG (using V_C, I_C).
The zero-sequence compensation factor corrects for the difference between the zero-sequence impedance and the positive-sequence impedance of the transmission line. Without this correction, ground distance elements would overreach or underreach depending on the line construction.
Zero-sequence compensation factor
Where
K0 is a complex number. Typical values for overhead lines: magnitude 0.5-0.7, angle -10 deg to -30 deg.
For overhead lines, is typically 2.5-4 times due to the ground return path. For cables, the ratio is lower (1.5-2.5) because of the metallic sheath return. The K0 value is displayed in the settings panel below the Z0 inputs as magnitude and angle.
The Mho characteristic is a circular boundary on the R-X plane that passes through the origin. The circle diameter lies along the RCA (Relay Characteristic Angle), with the far edge at the zone reach impedance. Because the circle passes through the origin, the Mho element is inherently directional -- it only operates for forward faults.
Mho circle geometry
Where
The circle is tilted at the RCA, not the line angle. Typical RCA = Z1 angle minus 5 deg.
Mho characteristic: circles pass through the origin, tilted at the RCA (75°). The circle center is at Zr/2 along the RCA direction; radius = |Zr|/2. The Z₁ angle (80°, dotted gray) differs from the RCA (dotted amber) — this offset improves arc resistance coverage.
When to Use Mho
The polygonal characteristic is a rotated rectangle aligned with the line impedance angle (Z1 angle). It combines independent R-reach and X-reach settings, giving protection engineers precise control over fault coverage.
Each polygonal zone is the intersection of four boundary lines controlled by the per-zone alpha (resistance boundary tilt) and sigma (reactance boundary tilt) angles:
The corner points of the polygon are computed using the configured reach and angle parameters (alpha, sigma, R-reach, X-reach). When sigma is zero, the shape reduces to the classic parallelogram characteristic.
Polygonal characteristic (shown at α = 65°, σ = 0° for clarity). Each zone is a parallelogram: top/bottom boundaries are horizontal when σ = 0 (classic shape), while the side boundaries tilt at the per-zone α angle. Non-zero σ tilts the reactance boundaries (e.g. P437 σₙ = −15°). X-reach sets the top/bottom; R-reach (Rφ for phase, Rg for ground) sets the horizontal width. Points B and C mark the Zone 1 and Zone 2 reach along the Z₁ direction.
After constructing the base parallelogram, each zone is clipped against a directional boundary line through the origin. This boundary is perpendicular to the Z1 impedance angle and separates the forward and reverse half-planes. For a Z1 angle of 70 deg, the boundary runs from 110 deg to -70 deg.
Forward zones keep only the portion in the forward half-plane (toward the line impedance direction), and reverse zones keep the opposite side. This produces the asymmetric trapezoid shapes seen in relay software like the P437, where the left side of a forward zone follows the directional boundary rather than extending to -R-reach.
Note
Ground faults through tower footing resistance or arc resistance have higher resistive components than phase-phase faults. To account for this, each zone has two separate R-reach settings:
The zone width on the R-X chart changes dynamically based on which loops are active in the header toggle bar.
Minimum load impedance
Where
Zone 3 and Zone 4 reaches must be checked against this value to avoid load encroachment.
The following table summarises the voltage and current quantities used for each of the six measurement loops:
| Loop | Type | Voltage | Current |
|---|---|---|---|
| AB | Phase | ||
| BC | Phase | ||
| CA | Phase | ||
| AG | Ground | ||
| BG | Ground | ||
| CG | Ground |