📘 Distance Relay – Impedance, Reactance & Mho Relay (Worked Numerical Problems)
Distance relay operates based on impedance seen between relay location and fault. It is widely used for transmission line protection.
🔹 Basic Principle
Z_seen = V / I
Relay operates when:Z_seen ≤ Z_setting
🔹 Problem 1: Impedance Relay Operation
A 100 km transmission line has impedance 0.2 + j0.4 Ω/km. Relay setting is 80% of line impedance. Fault occurs at 60 km. Determine whether relay operates.
Step 1: Total Line Impedance
Z_line = (0.2 + j0.4) × 100 = 20 + j40 Ω
Step 2: Relay Setting (80%)
Z_setting = 0.8 × (20 + j40) = 16 + j32 Ω
Step 3: Impedance up to Fault (60 km)
Z_fault = (0.2 + j0.4) × 60 = 12 + j24 Ω
Magnitude: |Z_fault| = √(12² + 24²) = √(144 + 576) = √720 = 26.83 Ω Magnitude of setting: |Z_setting| = √(16² + 32²) = √(256 + 1024) = √1280 = 35.77 ΩSince 26.83 < 35.77 → Relay Operates
🔹 Problem 2: Reactance Relay
Line reactance = 0.5 Ω/km Length = 120 km Relay reactance setting = 70% Fault at 90 km Check operation.
Step 1: Total Reactance
X_total = 0.5 × 120 = 60 Ω
Step 2: Relay Setting
X_setting = 0.7 × 60 = 42 Ω
Step 3: Fault Reactance
X_fault = 0.5 × 90 = 45 Ω
Since 45 > 42 → Relay Does NOT Operate
🔹 Problem 3: Mho Relay Operation
Line impedance = 30∠60° Ω Relay characteristic circle radius = 25 Ω Fault impedance seen = 20∠55° Ω Check operation.
Concept
Mho relay operates if impedance point lies inside circle in R-X plane. Given: |Z_fault| = 20 Ω Relay reach = 25 ΩSince 20 < 25 → Fault lies inside characteristic circle → Relay Operates
🎯 Important Comparison
| Relay Type | Characteristic | Best For |
|---|---|---|
| Impedance | Circle centered at origin | Short lines |
| Reactance | Vertical line | High resistance faults |
| Mho | Circle passing through origin | Long transmission lines |
🎯 GATE Key Points
- Distance relay measures V/I
- Relay operates when impedance seen is less than setting
- Mho relay is inherently directional
- Reactance relay immune to fault resistance
Distance Protection = Fast & Selective Line Protection
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