Models and Performance of Transmission Lines and Cables
GATE Electrical Engineering – Complete Notes
1. Transmission Line Parameters
Transmission line has four important parameters:
- Resistance (R)
- Inductance (L)
- Capacitance (C)
- Conductance (G)
Series Impedance: Z = R + jωL
Shunt Admittance: Y = G + jωC
2. Classification of Transmission Lines
| Type | Length | Voltage | Model |
|---|---|---|---|
| Short Line | < 80 km | < 20 kV | Series impedance only |
| Medium Line | 80–250 km | 20–100 kV | Nominal Ï€ model |
| Long Line | > 250 km | > 100 kV | Distributed model |
3. Short Transmission Line Model
VS = VR + IZ
A = 1, B = Z, C = 0, D = 1
4. Medium Transmission Line Model
Nominal π Model
A = D = 1 + YZ/2
B = Z
C = Y(1 + YZ/4)
5. Long Transmission Line Model
A = D = cosh(γl)
B = Zc sinh(γl)
C = (1/Zc) sinh(γl)
6. Voltage Regulation
Voltage Regulation =
(VR no-load − VR full-load) / VR full-load × 100
7. Transmission Efficiency
Efficiency = Receiving Power / Sending Power × 100
Loss = I²R
8. Characteristic Impedance
Zc = √(Z/Y)
For lossless line: Zc = √(L/C)
9. Surge Impedance Loading (SIL)
SIL = V² / Zc
10. Power Transfer Equation
P = (VS × VR / X) × sinδ
Maximum Power: Pmax = VS × VR / X
11. Underground Cable Characteristics
- High capacitance
- Low inductance
- No corona loss
- High reliability
12. Important GATE Exam Points
Short line → capacitance neglected
Medium line → Nominal Ï€ model
Long line → distributed model
ABCD parameters very important
Surge impedance loading important
Voltage regulation important
Medium line → Nominal Ï€ model
Long line → distributed model
ABCD parameters very important
Surge impedance loading important
Voltage regulation important
