Visualise the "Ferranti effect" that appears on long, lightly-loaded AC transmission lines. Adjust the line length, sending-end voltage and line constants to see the receiving-end voltage rise, surge impedance and the voltage profile along the line update in real time, and grasp intuitively why the far end can sit at a higher voltage.
Parameters
Line length l
km
Length of the line from sending to receiving end
Sending-end voltage V_s
kV
Line inductance L
mH/km
Series inductance per kilometre
Line capacitance C
nF/km
Shunt (line-to-ground) capacitance per kilometre
Frequency f
Hz
System frequency (50 or 60 Hz)
Results
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Electrical length βl (°)
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Receiving/sending voltage ratio
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Receiving-end voltage V_r (kV)
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Voltage rise ΔV (kV)
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Voltage rise (%)
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Surge impedance Z_c (Ω)
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Transmission line & voltage profile — charging-current animation
Left is the sending-end source, right is the open (unloaded) receiving end. The curve below is the voltage along the line, rising toward the open end. The small arrows are the leading current that charges the shunt capacitance.
Receiving-to-sending voltage ratio for a lossless, open-circuited (unloaded) line. β: phase constant [rad/km], ℓ: line length [km], ω = 2πf. An open or lightly-loaded line raises the receiving-end voltage, and the effect is worse for longer lines.
Electrical length βℓ [rad] and surge (characteristic) impedance Z_c [Ω]. L is the series inductance per km and C the shunt capacitance per km. As βℓ approaches π/2, cos(βℓ) approaches 0 and the voltage ratio diverges.
Voltage rise ΔV [kV] and voltage rise percentage [%]. The rise scales roughly with (βℓ)²/2, so it grows approximately with the square of the line length.
What is the Ferranti Effect?
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I've never heard of the "Ferranti effect". I always thought the voltage on a transmission line drops as you move away from the source.
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That's the natural assumption. A line has resistance and inductance, so when current flows there is an I·Z voltage drop, and normally the far end sits at a lower voltage. But the Ferranti effect is the opposite: on a long, high-voltage AC line that is open-circuited or only lightly loaded, the receiving end — the far end — ends up at a higher voltage than the sending end. It is counter-intuitive, which is why it surprises so many people learning power systems.
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Wait — the voltage rises even though no current is flowing? That seems impossible.
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The key is that "no current to the load" does not mean "no current in the line". A transmission line is two long parallel conductors, so it behaves like a huge capacitor — it has distributed shunt capacitance. With AC, a "charging current" keeps flowing to charge that capacitance even with no load. That current leads the voltage by 90°. As this leading charging current passes through the line's series inductance, it keeps adding voltage toward the open end. Increase the line length in the left panel above and you will see the receiving-end voltage V_r climb past the sending end.
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I see — so a longer line gives a bigger effect. The chart shows that doubling the line length increases the rise by even more.
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Good catch. The voltage ratio is 1/cos(βℓ), and βℓ — the electrical length — is proportional to the line length ℓ. For small βℓ, cos(βℓ) ≈ 1 − (βℓ)²/2, so the rise is about (βℓ)²/2 — it grows roughly with the square of the line length. That is why at 300 km the rise might be only 5%, but at 500 or 700 km it shoots up. Underground cables have shunt capacitance several times larger than overhead lines, so they hit the same problem over much shorter distances.
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If the voltage rises too far, does something actually go wrong?
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Yes — leave it unchecked and it gets serious. If the receiving-end voltage exceeds equipment ratings, transformers go into over-excitation, the core saturates, and you get humming and overheating. Insulation degrades faster at higher voltage too. The Ferranti effect is strongest when demand is low — light-load hours such as overnight. A classic field problem is "the system voltage rises too high overnight and trips an alarm". So in operation you switch in shunt reactors during light-load periods.
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How does a shunt reactor actually hold the voltage rise down?
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Roughly speaking, it cancels it with an "opposite current". The culprit behind the Ferranti effect is the line's leading charging current. A shunt reactor is a coil, so connecting it at the receiving end draws a "lagging current". Leading and lagging currents point in opposite directions, so they cancel each other, and the net charging current in the line shrinks. With less charging current there is less voltage build-up, so the rise is suppressed. The usual practice is to switch reactors in during low-demand nights and switch them out as load picks up during the day. For continuous compensation you use an SVC or STATCOM.
Frequently Asked Questions
The Ferranti effect is the phenomenon where the receiving-end (load-side) voltage of a long, high-voltage AC transmission line becomes higher than the sending-end (source-side) voltage when the line is open-circuited or only lightly loaded. A line has distributed series inductance and shunt capacitance; with little load, a leading "charging current" flows to charge the line's own capacitance. This charging current passing through the series inductance raises the voltage toward the open far end. The effect is named after the engineer S.Z. de Ferranti, who observed it in 1890.
For a lossless, open-circuited (unloaded) line, the ratio of receiving-end voltage V_r to sending-end voltage V_s is V_r/V_s = 1/cos(βl). Here β is the phase constant per km, β = ω√(LC), l is the line length and βl is the electrical length in radians. L is the series inductance per km and C is the shunt capacitance per km. When βl is small, cos(βl) is slightly less than 1, so the ratio is greater than 1 and the receiving-end voltage rises.
The electrical length βl is proportional to the line length l, and the voltage rise is 1/cos(βl) − 1. For small βl, cos(βl) ≈ 1 − (βl)²/2, so the rise is approximately (βl)²/2. Since βl scales with l, the voltage rise grows roughly with the square of the line length. The effect is also stronger at higher frequency (larger β) and with larger shunt capacitance C, as in underground cables. That is why it matters most for long EHV overhead lines and long underground transmission cables.
The most common countermeasure is to connect a shunt reactor at the receiving end. A shunt reactor draws a lagging current that cancels the line's leading charging current, absorbing the excess reactive power and limiting the voltage rise. Operators switch shunt reactors in during light-load periods such as overnight and switch them out as the load increases. Without mitigation, the receiving-end voltage can exceed equipment ratings, causing transformer over-excitation and insulation degradation. Static var compensators (SVC) and STATCOM provide continuous compensation.
Real-World Applications
Extra-high-voltage (EHV) long transmission lines: On long 500 kV and 765 kV overhead lines, the Ferranti effect is a key design constraint. During power-system planning, engineers calculate the receiving-end voltage at no-load and light-load conditions and size the shunt reactors so the equipment rated voltage is not exceeded. On large grids in North America and China, and on long interconnectors, it is common to distribute several shunt reactors along the line.
Underground transmission cables: Underground cables have closely-spaced conductors surrounded by dielectric, so their shunt capacitance is 20 to 40 times that of overhead lines. As a result the Ferranti effect is very strong, and even a cable of only a few tens of kilometres shows a non-negligible no-load voltage rise. Long underground and submarine cables routinely include shunt reactors at both ends or at intermediate points, and this is one reason the practical distance of AC cable transmission is limited.
System operation and voltage management: System operators manage voltage against the daily load cycle. During low-demand nights and holidays the lines are lightly loaded and the Ferranti effect pushes voltages up, so operators balance reactive power by switching in shunt reactors, adjusting var equipment and running generators in leading mode. At peak demand they switch in capacitors to offset the voltage drop instead. Quantifying the Ferranti effect underpins this daily voltage-scheduling work.
Line energisation and system restoration: During system restoration after a blackout, or when energising a new line, the first step is to apply voltage to a long, unloaded line. The Ferranti effect can then raise the receiving-end voltage higher than expected, tripping protection relays or stressing equipment. Restoration procedures therefore calculate the no-load voltage rise in advance and plan countermeasures such as connecting shunt reactors first or energising in steps from a lower voltage.
Common Misconceptions and Pitfalls
The biggest misconception is confusing voltage drop with voltage rise. When people think of transmission-line voltage, they tend to picture only the I·Z voltage drop — but that applies when the load current is large. When a line is unloaded or lightly loaded, the line's charging current dominates over the load current, and the result is a voltage rise. A real line can show either a drop or a rise depending on its loading, and the dividing line is the relative size of the load current and the charging current. This tool models the extreme case of zero load (fully open), so it always shows a voltage rise.
Next, assuming the Ferranti effect is caused by losses or resistance. It is the opposite: the Ferranti effect arises purely from the lossless elements — the series inductance and the shunt capacitance. The formula V_r/V_s = 1/cos(βl) used here is a lossless model that ignores resistance. A real line does have resistance, and it slightly mitigates the rise, but the essence of the effect is the resonant-like behaviour of the distributed-parameter circuit formed by L and C. The Ferranti effect appears clearly even on an ideal zero-resistance line.
Finally, assuming the formula 1/cos(βl) can be used as-is for large electrical lengths. As βl approaches π/2 (90°), cos(βl) approaches 0 and the voltage ratio diverges to unrealistic values. Real power systems are designed so βl stays modest (one wavelength is several thousand km, so for normal line lengths βl is at most a few tens of degrees). For extremely long lines, or systems involving series and shunt compensation, you need a more rigorous distributed-parameter or four-terminal (ABCD) model. This tool is a quick estimate under the no-load, lossless simplification; detailed design should use a model that includes losses, load and compensation equipment.
How to Use
Enter transmission line length (50–300 km) using lenNum or lenRange slider to establish electrical length βl in degrees
Set sending-end voltage Vs (115–765 kV) via vsNum or vsRange; typical values for long lines are 230 kV or 345 kV
Input series inductance (0.8–1.2 mH/km) and shunt capacitance (10–14 nF/km) per unit length using indNum/indRange and capNum/capRange
Read receiving-end voltage Vr (kV), voltage rise ΔV (kV), rise percentage, surge impedance Zc (Ω), and Vr/Vs ratio instantly
Worked Example
A 275 km, 345 kV transmission line with L = 0.95 mH/km and C = 12 nF/km exhibits Ferranti effect. Sending-end voltage is 345 kV. Electrical length βl ≈ 68°. Surge impedance Zc ≈ 281 Ω. Under light load (near open-circuit), receiving-end voltage rises to approximately 367 kV, producing ΔV ≈ +22 kV (6.4% rise). This overvoltage occurs because the line's capacitive charging current creates a voltage rise across series inductance.
Practical Notes
Ferranti effect dominates on lines longer than 200 km with loading below ~30% of surge impedance current; 500 kV networks in Australia and Canada experience 8–12% rises
Use series reactors or shunt reactors (switched at low-load hours) to suppress overvoltage; typical reactor rating is 50–100 MVAR for 345 kV lines
βl near 90° (quarter-wave resonance) amplifies the effect; avoid operating near this point during light-load conditions
Verify results against IEC 60076 transformer insulation levels: a 10% rise on a 345 kV line approaches the 420 kV BIL threshold