This article introduces you to the Ferranti Effect and its impact on voltage regulation in long-distance high-voltage AC transmission lines, highlighting the physical causes.
In long high-voltage AC transmission lines, especially those exceeding 250 km, the combination of distributed capacitance and inductance can cause the receiving-end voltage to exceed the sending-end voltage under light or no-load conditions—a phenomenon known as the Ferranti Effect.
This occurs because the line capacitance draws a leading charging current that flows through the inductive impedance, creating a voltage rise. The effect becomes more pronounced with longer lines, higher voltages, and lower loads, potentially stressing insulation and equipment.
In this article—Part 3 of our Transmission Line Losses and Efficiency Optimization series—, we’ll introduce you to the concepts of the Ferranti Effect. In the next article (Part 4) in this series, we’ll discuss the key mitigation techniques.
Long-Distance Power Transmission Overview
Modern electric power systems rely on long-distance transmission lines to transfer bulk electrical energy from generation stations—often located far from load centers—to substations where the power is distributed. These transmission systems, operating at high voltages (typically ranging from 110 kV to 765 kV AC and beyond), minimize I²R losses and improve overall system efficiency by reducing the current for a given power transfer.
The modeling of these lines becomes increasingly complex as their physical length increases. Short lines (under 80 km) can be modeled with lumped parameters, while medium-length lines (80–250 km) require more accurate models including the effect of distributed capacitance.
For long transmission lines (typically >250 km), the distributed nature of line parameters—resistance (R), inductance (L), capacitance (C), and conductance (G)—must be fully accounted for using transmission line theory. The transmission line equations are derived from Maxwell’s equations and lead to hyperbolic solutions describing voltage and current along the line:
$$V(x) = V_+e^{-gamma x} + V_-e^{gamma x}$$
and
$$I(x) = big(frac{V_+}{Z_0} big) e^{-gamma x} – big(frac{V_-}{Z_0} big) e^{gamma x} $$
where the complex propagation constant is given by:
$$gamma = sqrt{(R~+~j omega L) + (G~+~j omega C)}$$
and the characteristic impedance is defined as:
$$Z_0 = sqrt{ frac{R~+~j omega L}{G~+~j omega C}}$$
Importance of Voltage Control in Transmission Systems
Voltage stability is a core objective in the design and operation of power transmission networks. Voltage magnitudes must be maintained within strict tolerances (typically ±5% of nominal values) to ensure proper functioning of equipment, protection systems, and customer loads. In long transmission lines, maintaining this voltage balance is particularly challenging due to line charging currents caused by the line’s inherent capacitance.
At high voltages and long distances, capacitive effects dominate, and reactive power flows become a major consideration in voltage regulation. Overvoltage conditions can stress insulation, damage equipment, and compromise system reliability. This challenge becomes acute under light load or open-circuit conditions, where traditional load-induced voltage drops are absent.
Ferranti Effect
The Ferranti Effect is a classic voltage phenomenon observed in long AC transmission lines, where the voltage at the receiving end exceeds the sending end voltage when the line is lightly loaded or open-circuited. This counterintuitive voltage rise is primarily due to the interaction of line inductance and capacitance. Specifically, the capacitive charging current leads the voltage and, when interacting with the series inductance, produces a voltage gain along the line length.
The Ferranti Effect becomes increasingly pronounced with:
- Longer line lengths
- Higher operating voltages
- Lower receiving-end load currents
This phenomenon can be analytically described using the long line model. Assuming a no-load condition and lossless line for simplicity:
$$V_R = V_S cosh(gamma l)$$
where:
- VR is the receiving-end voltage
- VS is the sending-end voltage
- γ is the propagation constant
- l is the line length
For practical cases, the Ferranti effect can cause receiving-end voltages to rise by several percent, requiring the use of voltage regulation equipment such as shunt reactors, synchronous condensers, or transformer tap changers.
This effect is named after Sebastian Ziani de Ferranti, who first observed and documented it in the late 19th century during early experimentation with AC power systems.
Relevance in Modern Power Systems
In today’s grid, with increasing reliance on long-distance power corridors (especially those integrating renewables from remote areas), the Ferranti Effect poses real-world operational concerns. Understanding this effect is crucial not only for planning but also for real-time control of transmission systems, especially under dynamic loading conditions or post-contingency states where certain lines may temporarily go underutilized.
Ferranti Effect Explained
The Ferranti Effect refers to the condition in which the receiving-end voltage (VR) of a long AC transmission line exceeds the sending-end voltage (VS), even though there is no load connected at the receiving end (open-circuit condition), or under very light load. While this may appear to contradict intuitive expectations—where voltage typically drops along a resistive or inductive line due to losses—the effect is a direct consequence of distributed capacitance and inductive reactance intrinsic to long transmission lines.
This phenomenon is particularly noticeable in high-voltage AC lines longer than approximately 200–250 km and is amplified with increasing line length and voltage level.
Phasor diagram illustrating the Ferranti effect. Image used courtesy of ijisae.org
Physical Basis of the Ferranti Effect
The underlying mechanism is the charging of line capacitance. A transmission line, even under no-load conditions, supports a voltage profile along its length, and the line capacitance draws a leading charging current from the sending end to maintain the voltage on the conductors. This current flows through the series inductive reactance of the line, which introduces a voltage rise in the direction of normal load flow, due to the leading nature of the capacitive current.
This can be understood through the series impedance (jωL) and shunt admittance (jωC) of the line: the capacitive current leads the sending-end voltage, and when this leading current flows through the series inductance, it creates an in-phase component that adds to the receiving-end voltage. This cumulative effect results in a voltage magnification toward the receiving end in the absence of sufficient load current to counterbalance it.
Mathematical Analysis Using Distributed Parameter Model
The Ferranti Effect is best analyzed using the long transmission line model, where parameters are distributed along the length rather than lumped. The voltage and current at any point x on the line (assuming a sinusoidal steady-state) can be described using the telegrapher’s equations:
$$frac{dV(x)}{dx} = -(R~+~j omega L)I(x)$$
$$frac{dI(x)}{dx} = -(G~+~j omega C)V(x)$$
For a lossless line (R = 0, G = 0), these reduce to:
$$frac{d^2V(x)}{dx^2} = omega^2 LCV(x)$$
The solution is harmonic:
$$V(x) = V_+e^{-jbeta x} + V_-e^{jbeta x}$$
Where $$beta = omega sqrt{LC}$$ is the phase constant. The sending-end and receiving-end voltages are related by:
$$V_S = V_R cosh(gamma l) + I_R Z_C sinh(gamma l)$$
$$I_S = frac{V_R}{Z_C} sinh(gamma l) + I_R cosh(gamma l)$$
Where:
- $$Z_C = sqrt{L/C}$$ is the characteristic impedance of the line,
- γ = jꞵ for a lossless line,
- l is the line length,
- IR = 0 under no-load condition.
Under no-load (IR = 0):
$$V_S = V_R cosh(gamma l) Rightarrow V_R = frac{V_S}{cosh(gamma l)}$$
However, since cosh(γl) < 1 for imaginary γ, VR > VS .
This equation quantitatively captures the voltage rise due to the Ferranti Effect. The increase is exponential with line length and is more pronounced for lines operating at higher frequencies and voltages.
Magnitude of the Voltage Rise
The percent overvoltage at the receiving end due to the Ferranti Effect can be roughly approximated for lightly loaded lines using:
$$% text{Overvoltage} approx frac{1}{2} omega^2 LCV^2I^2$$
Where L and C are per-unit-length values, l is the length of the line, and V is the nominal system voltage.
This approximation clearly shows that the voltage rise increases:
- Proportionally to the square of the line length l2
- Proportionally to the square of the voltage V2
- Directly with line inductance L and capacitance C
Thus, systems operating at EHV (for example., 400–765 kV) and long distances are especially susceptible.
Coming soon, Part 4 of this article series, “Implications of the Ferranti Effect Under No-Load and Light-Load Conditions” will examine Ferranti effect mitigation techniques, including OLTCs, shunt reactors, and synchronous condensers.
Featured image used courtesy of Adobe Stock (licensed)
