Long Transmission Line: Ferranti Effect, SIL, and Voltage Profile Explained

Introduction to Long Transmission Lines

Power transmission lines can stretch over 1500 km, especially when connecting hydro-electric plants to distant cities. Lines longer than about 200 km require special compensation to control voltage and ensure stability. Without compensation, the voltage along the line deviates from the ideal flat profile, depending on load and line length. This tutorial explores the Ferranti effect, surge impedance loading (SIL), and the impact of line length using a lumped-parameter model.

Understanding the Ferranti Effect

The Ferranti effect describes the voltage rise along a lightly loaded or open-circuited transmission line. At the receiving end, voltage can exceed the sending-end voltage by a factor of 1/cos(θ), where θ is the electrical length. For example, if θ = 30°, the receiving-end voltage is 15% higher than the sending-end voltage. This phenomenon is critical for power system engineers to manage.

Surge Impedance and Natural Load

The surge impedance Z₀ is given by Z₀ = √(L/C), where L is total line inductance and C is total line capacitance. Despite L and C being reactive, Z₀ is real (resistive). When a line is terminated with a load equal to Z₀, it operates at its natural load or surge impedance load (SIL). At SIL, the voltage profile is flat (constant voltage along the line), and reactive power at both ends is zero.

Electrical Length and Its Significance

Electrical length θ = ω√(LC) (in radians), where ω = 2πf. For a 50 Hz system, a line length of one wavelength corresponds to θ = 2π, but practical lines rarely exceed θ = π/6 (30°). The electrical length determines the phase shift and voltage variation along the line.

Lumped-Parameter Model

A long transmission line can be approximated by a ladder network of LC sections. In this tutorial, we use a model with ten sections, each with L = 7.29 mH and C = 0.020 µF, operating at 700 Hz. The total line inductance L_total = 10 × 7.29 mH = 72.9 mH, and total capacitance C_total = 10 × 0.020 µF = 0.20 µF.

Calculating Surge Impedance and Electrical Length

Using the given values: Z₀ = √(72.9e-3 / 0.20e-6) = √(364500) ≈ 603.7 Ω. Electrical length θ = ω√(L_total C_total) = 4398 × √(72.9e-3 × 0.20e-6) = 4398 × √(1.458e-8) = 4398 × 0.0001207 ≈ 0.531 rad = 30.4°.

Experiment 1: Open-Circuit Test (Ferranti Effect)

With the receiving end open, measure voltages at each of the 10 points using a DVM. The voltage ratio V/VS should follow V(x)/VS = cos(θ x/a) / cos(θ), where a is the line length. At the receiving end (x=a), Vr/VS = 1/cos(θ). For θ=30.4°, Vr/VS ≈ 1.16, confirming the Ferranti effect. Use an oscilloscope to measure phase angles at mid-point and receiving end relative to VS. The phase shift increases linearly with distance.

Experiment 2: Surge Impedance Load (SIL) Test

Connect a resistive load of 604 Ω (≈ Z₀). Adjust sending-end voltage to the same value as in the open-circuit test. Measure voltages along the line; they should be nearly constant (flat profile). The phase shift between VS and Vr should equal the electrical length θ (≈30.4°). The mid-point voltage phase should be half of that. Any deviations from flatness may be due to component tolerances or frequency variations.

Experiment 3: Load Above SIL

Connect a load of 302 Ω (half of Z₀). This represents a load above SIL. The voltage profile will sag (decrease toward the receiving end) because the line absorbs reactive power. Measure voltages and phase angles; the receiving-end voltage will be lower than the sending-end voltage. Compare with the open-circuit and SIL cases to understand how loading affects voltage regulation.

Practical Implications and Modern Trends

Understanding transmission line behavior is essential for integrating renewable energy sources like large solar farms or wind parks, which are often located far from load centers. For example, the 2026 expansion of the North Sea Wind Power Hub involves long submarine cables where Ferranti effect and SIL must be managed using shunt reactors or series compensation. Similarly, long-distance HVDC lines for intercontinental power exchange rely on similar principles. Mastering these concepts helps engineers design efficient and stable power systems.

Conclusion

Long transmission lines exhibit voltage rise under light load (Ferranti effect) and voltage sag under heavy load. The surge impedance load provides a flat voltage profile and zero reactive power exchange. Using a lumped-parameter model, we demonstrated these effects experimentally. These fundamentals are crucial for power system engineers working on modern grid challenges.