The Ferranti Effect: A Complete Technical Guide

Why sending-end voltage becomes higher than receiving-end voltage on long, lightly loaded AC transmission lines

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🔍 1. What Is the Ferranti Effect?

The Ferranti Effect is a phenomenon where the receiving-end voltage of a long AC transmission line becomes higher than the sending-end voltage, even though no mechanical tap-up or control action is applied.

This effect occurs when:

• The line is long (typically > 200 km for EHV AC)

• The line is lightly loaded or open-circuited

• The system voltage is high (≥ 220 kV)

In short:

👉 Light load + long AC line = voltage rise at the receiving end

Because the line’s distributed capacitance draws a leading charging current, causing voltage amplification toward the receiving end.

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⚙️ 2. Why the Ferranti Effect Happens

Long AC lines behave like distributed RLC circuits.
When there is little or no load:

1️⃣ The line capacitance draws a leading charging current

Transmission lines have inherent capacitive effects:

• Conductor-to-earth capacitance

• Conductor-to-conductor mutual capacitance

This causes charging current:

$$I_c = \omega C V$$

This charging current leads the voltage by 90°.

2️⃣ Line inductance creates reactive voltage drop

The line inductance (L) creates voltage rise when the current is leading:

$$V_L = I_c X_L$$

Thus:

• Capacitive reactive power is generated along the length

• Inductive voltage rise adds to the magnitude

• Voltage at the receiving end increases

3️⃣ Distributed parameters amplify the effect

In long lines, the effect compounds along each small segment.

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📏 3. Mathematical Explanation

For a lossless line:

$$V_R = V_S \cosh(\gamma l) - I_S Z_c \sinh(\gamma l)$$

Under open-circuit condition:

$$I_S = 0$$

Thus:

$$V_R = V_S \cosh(\gamma l)$$

Because:

$$\cosh(\gamma l) > 1$$

➡️ Receiving-end voltage > Sending-end voltage

Where:

• $\gamma = \sqrt{LC}$ = propagation constant

• $l$ = line length

• $Z_c = \sqrt{L/C}$ = surge impedance

The longer the line and the higher the voltage, the greater the voltage rise.

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🧮 4. Numerical Example (Realistic EHV Case)

500 kV AC line, length = 300 km
Typical line parameters per phase:

• Capacitance $C = 0.012 \, \mu F/km$

• Inductive reactance $X_L = 0.35\, \Omega/km$

• No load at receiving end

Step 1 — Compute charging current

$$I_c = \omega CV = 2\pi(60)(0.012e^{-6})(500e^3) = 2.26 \, A/km$$

Over 300 km:

$$I_{total} = 2.26 \times 300 = 678 \, A$$

Step 2 — Voltage rise

$$V_{rise} = I_{total} \cdot X_L = 678 \cdot (0.35 \cdot 300)$$ $$= 678 \cdot 105 = 71,190 \, V$$

Step 3 — Receiving-end voltage

$$V_R = 500 kV + 71 kV = 571 kV$$

➡️ Voltage rises by ~14%
This is a very typical Ferranti effect magnitude for long, lightly loaded AC lines.

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🚨 5. Why the Ferranti Effect Is Dangerous

⚠️ Overvoltage on equipment

Insulators, transformers, arresters, and breakers can exceed BIL.

⚠️ Resonance conditions

Line capacitance + system inductance → resonance risk.

⚠️ Reactive power imbalance

Uncontrolled reactive power generation leads to:

• Voltage instability

• Under/overvoltage trips

• Oscillations

⚠️ Parallel line interaction

Loaded and unloaded lines create:

• circulating reactive currents

• voltage imbalance

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🛠️ 6. How Utilities Mitigate the Ferranti Effect

✔ 1. Shunt Reactors

This is the most common solution.

Reactors are placed:

• at line ends

• at intermediate substations

• on tertiary windings

They absorb excessive reactive power:

$$Q_{absorbed} = \omega L I^2$$

✔ 2. Controlled Switching

Used on:

• 400 kV

• 500 kV

• 765 kV lines

Ensures the line is energized at the exact voltage minimum.

✔ 3. FACTS Devices

• STATCOM

• SVC

• TCSC

• MSC/MRC

Provide dynamic voltage control.

✔ 4. Line Shutoff / Reconfiguration

At night, some utilities:

• open long lines

• re-route load

• reduce no-load energization

✔ 5. Bundled Conductors

Larger diameters reduce reactance and modify capacitance.

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🔬 7. Systems Where Ferranti Effect Is Most Severe

• 500 kV, 735 kV, and 765 kV AC lines

• Lines > 200 km

• High-capacitance lines (closely spaced bundles)

• Light-load conditions (nighttime, low demand)

• Remote hydro → urban grid corridors

• Offshore AC links (wind farms)

• Mountain valley long-span lines