📘 Transmission Line Models – Short, Medium & Long Lines
Transmission lines are classified based on length. Different models are used for different lengths. Very important for GATE.
🔹 1️⃣ Classification of Transmission Lines
- Short Line → Length < 80 km
- Medium Line → 80 – 250 km
- Long Line → > 250 km
🔹 2️⃣ Short Transmission Line
Assumptions:- Capacitance neglected
- Only series impedance considered
A = D = 1 B = Z C = 0
Very simple model.🔹 3️⃣ Medium Transmission Line
Capacitance considered. Two models used:- Nominal π Model
- Nominal T Model
A = D = 1 + (YZ/2) B = Z C = Y (1 + YZ/4)
Where: Z = series impedance Y = shunt admittance🔹 4️⃣ Long Transmission Line
Parameters distributed along line. Exact solution using: Hyperbolic functions. Propagation constant:γ = √(ZY)
Characteristic impedance:Zc = √(Z/Y)
ABCD parameters:A = D = cosh(γl) B = Zc sinh(γl) C = (1/Zc) sinh(γl)
Very important formulas.🔹 5️⃣ Example – Short Line Voltage Drop
Given: Z = 5 + j10 Ω Load current = 100 A Voltage drop: Vdrop = IZ = 100 (5 + j10) = 500 + j1000 Magnitude: = √(500² + 1000²) = √(250000 + 1000000) = √1250000Vdrop ≈ 1118 V
🔹 6️⃣ Important Observations
- Short line ignores capacitance
- Medium line uses lumped capacitance
- Long line uses distributed model
- ABCD parameters very important
🎯 GATE Important Points
- Know ABCD for short line
- Nominal π model most common
- Characteristic impedance formula important
- Long line uses hyperbolic functions
Transmission Line Models = Core of Power System Numericals
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