Relay Protection Academy Module 05 of 25
05
Module 05 Intermediate

Power System
Plant Parameters

⌛ ~2 hours 📚 IEC 60076 / IEC 60034 📑 10 slides

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5.1

Synchronous Machine Reactances

A synchronous machine does not present a fixed impedance during a fault. Three time-frame reactances apply, corresponding to the decay of flux in successive winding layers:

Sub-transient X″d
First ~50 ms. Damper winding flux still frozen. Smallest reactance, therefore highest initial fault current. Sets switchgear break rating and peak mechanical stress.
Transient X′d
50 ms to ~3 s. Damper winding current has decayed; field winding flux still maintained. Governs primary protection operating period and transient stability studies.
Synchronous Xd
Steady state. All induced field currents have decayed. Armature reaction fully establishes. Fault current falls below rated in some designs: relevant for back-up relay settings.
Critical mistake: using Xd for switchgear ratings Using synchronous reactance Xd to calculate fault current for switchgear selection gives a value 10x too low (typical Xd/X″d ratio). This leads to selection of equipment with insufficient breaking capacity, a potentially catastrophic failure mode. Always use X″d for instantaneous ratings.
5.2

DC Asymmetry

When a fault occurs at an instant other than the voltage peak, the physical constraint that current cannot change instantaneously forces a DC offset onto the AC fault current waveform.

Worst case: fault at voltage zero-crossing If the voltage is at zero when the fault strikes, the AC current should be at its peak at that instant. Because it must start from zero, a full DC offset equal in magnitude to the AC peak is superimposed. The total peak current is then at the worst point.
CT saturation risk The DC offset causes asymmetric current peaks significantly higher than the rated AC current. If CT cores are not sized for this peak (using the transient dimensioning factor TF = 1 + X/R), they will saturate in the first half-cycle of the fault and distort the relay input. This is covered in detail in Module 06.
Saturation correction factor In practice, a factor of approximately 0.9 accounts for the effect of magnetic saturation on the unsaturated sub-transient reactance: . This 10% correction keeps fault calculations conservative without requiring complex saturation modelling.
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Illustration prompt

AC waveform showing a fault current that starts at zero and decays from a high asymmetrical peak. Three envelopes labeled: I'' (sub-transient, red), I' (transient, yellow), I (steady state, grey). A decaying DC offset dashed line is shown below the waveform. Time axis with markers at 50ms, 200ms, 1s. Dark background, engineering style.

5.3

Transformer Positive Sequence Equivalent

For fault studies, the transformer is modelled as a series leakage impedance (resistance + reactance). The magnetising branch is neglected because it is typically 2000% of rated impedance versus 10% for the leakage.

Two-winding transformer Single series impedance , referred to one winding using the turns ratio. Quoted as a percentage on the equipment MVA base. Convert to system base using the Module 03 formula before use.
IEC 60076 reference values Standard transformer impedances range from 4% (small distribution) to 20% (large GSP autotransformers). For early-stage studies without nameplate data, IEC 60076 tables provide conservative estimates within a standard tolerance of ±7.5% (2-winding) or ±10% (3-winding).
Three-winding and autotransformers Three-winding transformers have three leakage impedances: primary (p), secondary (s), and tertiary (t). All three are referred to a common MVA base and connected in a T-circuit. One of the three referred impedances may be negative on the standard test base, which is normal and does not indicate an error. Autotransformers are handled similarly but with the series/common winding split accounted for.
5.4

Transformer Zero-Sequence Equivalent

Zero-sequence current requires an earth return path. The transformer winding configuration determines whether zero-sequence current can flow on each side.

Star (earthed neutral) winding
Terminal connects to the external zero-sequence network. Zero-sequence current can flow into or out of this winding. The neutral impedance (if any) appears as 3Zn in the equivalent circuit.
Delta winding
No connection to earth. Zero-sequence current cannot pass between delta and external circuit. However, zero-sequence circulates inside the delta loop, maintaining ampere-turn balance. This is modelled as a closed short-circuit within the winding, with no terminal connection to the system zero-potential bus.
Star (isolated neutral) winding
Behaves like a delta for zero-sequence purposes. The open-circuit neutral means no earth return path; zero-sequence current is blocked from the terminal, same as a delta.
3-phase core type units
Zero-sequence flux finds a high reluctance path outside the core limbs. The effect reduces to approximately , unlike shell-type or bank-of-three-single-phase units where .
Practical impact on earth fault protection On a delta-star (earthed) transformer, earth fault current on the secondary is circulated in the delta primary winding and does not appear as zero-sequence current on the primary busbars. Earth fault relays on the primary circuit therefore cannot detect faults on the secondary; dedicated earth fault protection on the secondary neutral or a core-balance CT is required.
5.5

Overhead Line Sequence Impedances

Line impedances are calculated using Carson's equations, which account for conductor geometry and the earth return path. The positive-sequence impedance depends on conductor self-impedance and mutual coupling between phase conductors.

Carson's series self-impedance (per km)
= conductor AC resistance; = frequency (Hz); = equivalent earth return depth; = geometric mean radius (GMR).
Zero sequence is significantly higher than positive sequence
The mutual impedance between phases (via the earth return) adds twice to the self impedance to give . For a typical 132 kV line, with a different phase angle. Using in place of for earth fault calculations causes severe under-reach of distance relays.
GMR: geometric mean radius GMR replaces the physical conductor radius in inductance calculations by treating the conductor as an equivalent thin-walled hollow cylinder. For a solid round conductor, . Always use GMR (not physical radius) when applying Carson's equations or vendor inductance data in relay setting calculations.
5.6

Earth Return Compensation for Distance Relays

During a phase-to-earth fault, the fault loop impedance includes the line positive-sequence path to the fault plus the earth return path from fault back to source. A distance relay calibrated only for will over-read (under-reach) unless the earth path contribution is subtracted.

Earth return compensation factor
The relay algorithm adds (where is the residual current) to the denominator to reconstruct the correct loop impedance.
Vendor input conventions vary Different relay manufacturers express the same compensation differently. Common forms include: the complex ratio (dimensionless), or separated real and imaginary components and . Always identify the relay's specific input convention before entering settings.
Only applies to earth faults The compensation applies only when a residual (earth) current component is present: single phase-to-earth and double phase-to-earth faults. For phase-to-phase faults with no earth return, and no compensation is applied. Incorrectly applying the factor to phase faults causes measurement errors.
5.7

Plant Parameter Workflow

  1. Classify each plant item as static (transformer, line, cable) or rotating (generator, motor).
  2. For generators: select the appropriate reactance for the time frame. Use for switchgear ratings and peak current; for primary protection studies; for steady-state back-up relay settings.
  3. For transformers: read the positive-sequence leakage impedance from the nameplate or IEC 60076. Trace the winding configuration to build the zero-sequence equivalent circuit.
  4. For overhead lines and cables: extract conductor geometry and earth resistivity; apply Carson's equations to derive and per unit length.
  5. Convert all values to per-unit on a common system MVA and kV base (Module 03 base-change formula).
  6. Derive earth compensation: calculate for each line and enter it into the distance relay settings in the manufacturer's required format.
Worked Example

Earth Return Compensation: 132 kV Line

Given: 132 kV single-circuit overhead line, 100 km. . .

Step 1: Total line impedances (multiply by 100 km)
Step 2: Apply earth compensation formula
Key observation: Z0 is nearly 3x Z1 For this 132 kV line . An engineer who assumes would set the earth compensation to zero, causing the distance relay to severely under-reach on earth faults: a fault at 100 km could appear to the relay as a fault at 37 km beyond the line end, meaning it would not trip without a significant grading margin adjustment.
Module 05

Knowledge Check