Transmission

Moving bulk power over hundreds of kilometres at high voltage. Learn line parameters, short/medium/long line models, losses, voltage regulation, the power-transfer equation, surge impedance loading and HVDC.

Transmission lines connect power stations to load centres, often hundreds of kilometres apart, at 132–765 kV AC or ±320–1100 kV DC. The high voltage keeps current, and therefore I²R loss and voltage drop, small.

A line isn't just a wire: it has series resistance and inductance and shunt capacitance distributed along its length. Those parameters decide how much power it can carry, how much the voltage sags and how stable the system is.

An analogy

A transmission line is like a motorway: raising the voltage is like raising the speed limit — the same traffic (power) flows with fewer lanes (less current), and less energy is wasted to friction (resistance).

Why high voltage

For a fixed power, current ∝ 1/V and losses ∝ I², so doubling voltage cuts losses to a quarter. That is why transmission uses hundreds of kilovolts even though every consumer needs only 230/400 V.

Line construction

Overhead lines use aluminium conductors with steel reinforcement (ACSR), bundled conductors (2–4 per phase) at EHV to reduce corona and reactance, porcelain or composite insulators, and shield wires on top for lightning protection. Underground cables are used in cities and under water.

Line models

Short lines (< 80 km): series R + jX only. Medium lines (80–250 km): add shunt capacitance as a π or T network. Long lines (> 250 km): use distributed-parameter equations with hyperbolic functions (ABCD parameters). Lightly loaded long lines see a voltage rise at the receiving end — the Ferranti effect — caused by line capacitance.

Power transfer and stability limit

Real power flows from the leading to the lagging voltage angle: P = V_s·V_r·sin δ / X. Maximum transfer is at δ = 90°, but lines operate at 20–40° for stability margin. Reactive power flows from higher to lower voltage magnitude, which is why voltage control is local.

SIL, compensation and FACTS

At surge impedance loading, the reactive power generated by line capacitance equals that absorbed by line inductance, and the voltage profile is flat. Above SIL lines need reactive support; below SIL they may need shunt reactors. Series capacitors reduce X to raise transfer capability; FACTS devices (SVC, STATCOM, TCSC, UPFC) control flows and voltages dynamically.

HVDC

HVDC has no reactive current, no stability angle limit and no skin-effect or charging-current issues. It wins for very long overhead lines (> ~600 km), submarine and underground cables (> ~50 km) and for linking asynchronous grids. Converter stations (LCC thyristor or VSC IGBT) are expensive, so there's a break-even distance.

Formulas

• Line current (3-phase): I = P / (√3 · V_L · pf)
• Line losses: P_loss = 3 · I² · R
• Power transfer: P = V_s · V_r · sin δ / X
• Surge impedance loading: SIL = V_L² / Z_c
• Regulation: VR = (V_r,NL − V_r,FL) / V_r,FL × 100 %

Worked example: Losses at 132 kV vs 400 kV

Given: P = 50 MW, pf = 0.9; R = 8 Ω per phase (80 km)

Find: Line current and loss at 132 kV and at 400 kV.

• 132 kV: I = 50e6 / (√3 × 132e3 × 0.9) = 243 A → loss = 3 × 243² × 8 = 1.42 MW (2.8 %)
• 400 kV: I = 50e6 / (√3 × 400e3 × 0.9) = 80.2 A → loss = 3 × 80.2² × 8 = 0.154 MW (0.3 %)

Answer: 1.42 MW vs 0.15 MW — about 9× less at 400 kV

Worked example: Surge impedance loading and transfer

Given: V_L = 400 kV; Z_c = 300 Ω; X = 100 Ω, δ = 30°

Find: SIL and the power transferred.

• SIL = 400² / 300 = 533 MW
• P = 400 × 400 × sin 30° / 100 = 800 MW

Answer: SIL ≈ 533 MW; P = 800 MW at δ = 30°

Common mistakes

• Wrong: Assuming line voltage always drops toward the receiving end. — Right: Lightly loaded long lines can see a voltage rise (Ferranti effect) due to capacitive charging current.
• Wrong: Using single-phase formulas for three-phase line loss. — Right: Loss = 3·I²·R with phase current, or √3 in the current formula for line voltage.

Applications

• Interconnectors: HVDC links such as the North Sea Link (1400 MW, 720 km) trade power between countries and balance renewables.
• Renewable zones: New transmission corridors move wind and solar energy from remote areas to cities; transmission is often the bottleneck for decarbonisation.
• Dynamic line rating: Sensors measure conductor temperature and wind to raise line ratings in real time instead of using conservative static limits.

Key takeaways

• High voltage cuts current and losses (loss ∝ 1/V²).
• P = V_sV_r sin δ / X; operate well below δ = 90°.
• SIL marks where line reactive generation and absorption balance.
• HVDC wins for long distances, cables and asynchronous links.

Going further

• Corona and audible noise: When the conductor surface field exceeds ~30 kV/cm (peak), air ionises, causing corona loss, radio interference and hum. Bundled conductors increase the effective radius and reduce the surface field.
• Travelling waves: Lightning and switching surges propagate along lines at nearly the speed of light and reflect at impedance changes. Travelling-wave fault locators time these reflections to pinpoint faults to within a few hundred metres.
• N-1 security: Grids are operated so that losing any single element (line, transformer, generator) causes no overloads or voltage violations. Contingency analysis runs continuously in control rooms.