Transmission Lines and Substations: Parameters, SIL, Sag and Layout
This domain covers line electrical and mechanical design plus substation arrangement - surge impedance loading, voltage regulation, corona, sag-tension, insulation coordination and busbar configurations.
Line performance
- Short lines (under about 80 km): regulation = (IR cos φ ± IX sin φ)/V_R, with the sign set by load power factor.
- Medium lines use nominal π or T; long lines need distributed (hyperbolic) ABCD parameters.
- Surge impedance Z_c = √(L/C), about 400 Ω for overhead lines; SIL = V_L²/Z_c. Loading near SIL gives flat voltage profile.
- Ferranti effect: at light load the receiving-end voltage exceeds the sending-end voltage because of line charging current.
- Corona is reduced by larger conductor diameter and bundled conductors; it worsens at high altitude and in rain.
Mechanical design
Sag S = wL²/(8T) for a level span with uniformly distributed weight; ice and wind add to effective weight. String efficiency = V_string/(n × V_unit nearest the conductor); grading rings and larger discs improve it.
Substations
400 kV switchyards commonly use one-and-a-half breaker or double main-plus-transfer bus schemes for reliability; earthing design checks step and touch potentials, and lightning protection uses shield wires and surge arresters.
Worked example
A 200 m span of conductor weighing 1 kg/m is strung at 1000 kg tension. Sag = wL²/(8T) = (1 × 200²)/(8 × 1000) = 40,000/8,000 = 5 m.
Traps
Confusing SIL with thermal rating, forgetting Ferranti raises receiving voltage, and computing string efficiency by dividing by total string voltage instead of n × unit voltage.