Ferranti Effect in Transmission Lines: Causes and Mitigation

Part A — The Ferranti Effect at a Glance

Energize a long extra-high-voltage transmission line from one end and leave the far end open, and the voltage at the open end is higher than the voltage at the source. Nothing has failed. No load is connected. The line itself, through its own distributed capacitance and series inductance, creates the rise. This is the Ferranti effect, first observed in the 1880s on a cable feeding London from the Deptford power station, and it remains one of the first constraints an engineer checks when energizing, restoring, or lightly loading a long 230 kV, 345 kV, 500 kV or 765 kV line.

The mechanism in one paragraph

A transmission line has capacitance distributed along its length. Under no load or light load, that capacitance draws charging current, which leads the voltage by 90°. The charging current flows through the line's series inductance, and the voltage drop across an inductance carrying a leading current is a voltage rise. The rise accumulates toward the open end, where all of the downstream charging has been supplied. The longer the line, and the higher the frequency, the larger the rise.

What Keentel's long-line model shows

Keentel Engineering modeled a representative 345 kV line with twin-bundled conductors (R = 0.030 Ω/km, X = 0.370 Ω/km and B = 4.5 µS/km at 60 Hz) using exact distributed-parameter equations, cascaded pi sections and an EMT traveling-wave model.

For the Keentel 345 kV model:

That is 0.074° per kilometer, or about 11.9° per 100 miles at 60 Hz. A full wavelength is about 4,870 km (3,020 miles) — close to the free-space value of 5,000 km at 60 Hz, because overhead line waves travel at about 97% of the speed of light.

2.3 Surge impedance loading

For the 345 kV model, SIL = 345² ÷ 287 ≈ 415 MW. At SIL, the line's reactive generation (charging) exactly balances its reactive consumption (I²X), and the voltage profile is flat. Below SIL, the line generates net reactive power and voltage rises toward the receiving end. The Ferranti effect is the limiting case at zero load.

3. The long-line equations

3.1 ABCD parameters



For a uniform line of length ℓ, sending-end and receiving-end quantities are related by:

3.2 Open-circuit receiving end



With the receiving end open, IR = 0, so:

The lossless approximation is excellent for EHV lines. The voltage at any point x measured from the receiving end follows a cosine profile:

so the voltage rises continuously from the sending end to the open end, as shown in the middle panel of Figure 1.



3.3 Worked example: 217-mile, 345 kV line

The open-end voltage exceeds the 362 kV maximum operating voltage by about 6%. Energizing this line from one end without compensation is not acceptable for continuous operation.



3.4 The quick approximation

Expanding the cosine for short electrical lengths:

For the 217-mile line, (0.452)² ÷ 2 = 10.2%, compared with the exact 11.1%. The approximation underestimates the rise and becomes increasingly inaccurate beyond roughly 150 miles at 60 Hz. It does, however, show the two key scaling laws: the rise grows with the square of length and with the square of frequency.

3.5 Why 60 Hz matters

The same physical line has 20% more electrical length at 60 Hz than at 50 Hz. Because the rise scales roughly with the square of electrical length, it is about 45% to 50% larger at 60 Hz.

This is the most important correction when applying international literature to US systems: 50 Hz results understate the Ferranti rise on US lines.

3.6 The quarter-wavelength limit

As βℓ approaches 90°, cos(βℓ) approaches zero and the open-end voltage tends toward infinity, limited only by losses and corona. At 60 Hz, a quarter wavelength is about 755 miles (1,215 km). No uncompensated line approaches this length in practice, but the rapid growth of the rise beyond 300 miles explains why very long EHV lines always require compensation.

3.7 Does voltage class matter?

A useful and often surprising result is that the per-unit Ferranti rise of an overhead line depends almost entirely on its length and frequency, not on its voltage class. The phase velocity of overhead lines is close to the speed of light for every voltage class, because √(lc) depends on geometry ratios that change little. What changes dramatically with voltage class is the amount of charging reactive power — and therefore the source-side rise and the size of the reactors needed.

For a 150-mile overhead line at 60 Hz:

The practical consequence is that Ferranti problems become severe at EHV not because the per-unit line rise is larger, but because EHV lines tend to be longer, carry far more charging, and connect to sources whose strength is small relative to that charging. At 765 kV, a single long line can draw as much charging as a large generator's entire reactive capability, which is why 765 kV lines are almost always built with line-connected reactors.

3.8 Physical intuition: the phasor picture

Consider the line as many short segments. At the open end, the last segment carries only its own small charging current. Moving toward the source, each segment carries the charging current of all segments downstream, so the current grows almost linearly toward the sending end. Each segment's inductance develops a voltage jωLI that, for a leading current, adds in phase with the local voltage. The rise accumulates from the source to the open end, and because the current is largest near the source, most of the rise happens in the first half of the line — which is exactly the shape of the uncompensated profile in Figure 1. Shunt reactors placed at the ends cancel part of the charging current where it accumulates most, which explains why end-located reactors are so effective and why the compensated profile peaks near the middle of the line.

4. The role of the source

4.1 Source impedance raises the sending end

Charging current drawn by the line flows through the source impedance, and because it is leading current, it raises the sending-end bus voltage. The rise is approximately:

For one 345 kV, 217-mile circuit drawing about 187 Mvar of charging from a 10,000 MVA source, the sending-end rise is about 1.9%. For both circuits of a double-circuit line, charging doubles to about 375 Mvar and the sending-end rise to about 3.8%.

4.2 Combined rise relative to source voltage

The open-end voltage relative to the source's internal voltage combines both effects:

Energizing a long line from the weaker end produces a markedly higher open-end voltage. Operating procedures therefore normally specify energization from the stronger terminal, with the sending-end voltage reduced before closing if necessary.

4.3 Generator self-excitation

When a long line is energized from a small generator — as in black-start restoration — the line's charging can exceed the generator's underexcited reactive capability. The generator's terminal voltage can then rise uncontrollably as the line's capacitive reactance resonates with the generator's synchronous reactance. A simplified check for self-excitation risk is:

where XC,line is the capacitive reactance of the energized line seen at the generator terminals and Xd is the generator's synchronous reactance (on a common base). Restoration plans must confirm that cranking paths stay well clear of this condition, typically by energizing with shunt reactors in service, limiting the length of line energized at once and picking up load early.

5. Line modeling approaches

5.1 Nominal and equivalent pi models

The nominal pi model lumps the series impedance zℓ in a single branch and splits the shunt admittance yℓ equally between two shunt branches. It is accurate for short lines and for steady-state calculations on medium-length lines. The equivalent pi model corrects the lumped values with hyperbolic factors so that it reproduces the exact long-line solution at one frequency:

Power flow programs use equivalent pi models, so steady-state Ferranti rise calculated in a load flow is exact at 60 Hz — provided the line data are correct.

Keentel's comparison for the 217-mile line shows how cascading nominal pi sections converges:

5.2 Pi models in time-domain simulation



In EMT simulation, a cascade of pi sections represents traveling waves only approximately. Each section acts as a low-pass filter with a cutoff frequency near:

where Δℓ is the section length. A practical guideline is that each section should be shorter than about one-tenth of the shortest wavelength of interest. For switching transients with content up to several kilohertz, a 200-mile line needs many short sections, and the model still introduces spurious oscillations. Pi models are therefore best reserved for short lines or for low-frequency studies.

5.3 Bergeron (constant-parameter distributed) model

The Bergeron model represents the line as lossless traveling waves with travel time τ = ℓ√(lc) and surge impedance Zc, with resistance lumped at the ends and middle. Parameters are calculated at one frequency, usually 60 Hz. It reproduces fundamental-frequency behavior and wave travel times accurately and is computationally efficient. Its limitation is that line resistance and inductance actually change with frequency, particularly in zero sequence because of ground-return effects, so damping and wave shape at high frequencies are approximate.



The traveling-wave relationship at each terminal k of a line between nodes k and m is:

5.4 Frequency-dependent models

Frequency-dependent (FD) models fit the line's characteristic admittance and propagation function over a wide frequency range, either in modal form or directly in the phase domain (the universal line model used in modern EMT programs). They capture:

• the strong frequency dependence of zero-sequence resistance and inductance due to earth return,
• skin effect in conductors and ground wires,
• untransposed geometry and mutual coupling between circuits on the same towers,
• realistic damping of switching transients.

FD models are the preferred choice for switching overvoltage studies, transient recovery voltage, secondary arc and single-pole tripping studies, and resonance studies involving double-circuit coupling.

5.5 Model selection summary

The published 50 Hz comparison reviewed in Part A illustrates the first row: all models agreed within 0.13 percentage points on steady-state rise. That agreement should not be extrapolated to transient studies, where the models can differ substantially in peak overvoltage and damping.

6. From steady-state rise to switching overvoltage

6.1 Energization transients

When a breaker closes onto an open line, a voltage step travels down the line at nearly the speed of light, reflects at the open end and doubles. The reflected wave returns to the source, reflects again and continues to bounce, superimposed on the rising steady-state voltage. The peak transient voltage at the open end depends on:

In Keentel's single-phase-equivalent EMT model of the 217-mile line, closing at a voltage peak from a 10,000 MVA source produces a peak of about 2.2 pu at the open end. Closing at a voltage zero limits the peak to about 1.6 pu. Three-phase studies with realistic breaker pole scatter and statistical switching typically show 2% switching overvoltages of 2.0 to 2.8 pu for unmitigated EHV line energization, and higher for reclosing onto trapped charge.

6.2 Insulation coordination

IEEE 1313.1 and IEEE 1313.2 define the insulation coordination process. For EHV lines, switching surge performance often controls tower clearances and insulator string length. The steady-state Ferranti rise, the temporary overvoltages it creates and the switching surge distribution must be considered together:

6.3 Temporary overvoltage and surge arresters

The Ferranti rise appears as a temporary overvoltage (TOV) lasting until the line is loaded, compensated or switched. Metal-oxide surge arresters have finite TOV capability defined by their maximum continuous operating voltage (MCOV) and TOV curves under IEEE C62.11. An arrester selected for normal operating voltage may absorb excessive energy, overheat and fail if the line remains open-ended with a large Ferranti rise. Arrester selection must therefore use the maximum credible open-end voltage, including the source-side rise and any load-rejection overvoltage.

7. Mitigation

7.1 Shunt reactors



Shunt reactors absorb part of the line's charging and are the primary mitigation for the Ferranti effect. The degree of shunt compensation is:

With reactors at both ends, the open-end voltage ratio becomes approximately:

where Xr is the reactance of the reactor at the receiving end. Keentel's model results for the 217-mile line:

Typical EHV practice uses 50% to 80% shunt compensation on long lines. Very high compensation can create resonance with the line's capacitance in an open phase during single-pole tripping, sustaining the secondary arc or causing resonant overvoltage; four-reactor schemes with a neutral reactor are used to neutralize interphase capacitance where single-pole reclosing is required. Reactors are specified under IEEE C57.21.



7.2 Line-connected versus bus-connected reactors

7.3 Static var compensators, STATCOMs and synchronous condensers

Dynamic reactive devices can absorb reactive power under light load and supply it under heavy load. They complement fixed reactors but are rarely the sole mitigation for energization, because they must be in service and correctly controlled at the moment of energization.



7.4 Operating practices

7.5 Worked example: sizing reactors to meet a voltage limit



Goal: keep the open-end voltage of the 217-mile, 345 kV line at or below 362 kV when energized at 350 kV from a stiff source.

A practical design would select standard reactor ratings, then confirm the result with load flow, light-load voltage control studies and EMT energization studies.

8. Light-load operation and voltage control



The Ferranti effect is not only an energization problem. Any line loaded below SIL generates net reactive power. A 345 kV line loaded at 100 MW (about a quarter of SIL) on a mild night still generates most of its charging. Several lightly loaded EHV lines in one area can raise voltages throughout the region, forcing generators to absorb reactive power and pushing them toward underexcitation limits.

NERC VAR-001 and VAR-002 require transmission operators and generator operators to maintain voltage schedules and reactive capability. Planning studies under NERC TPL-001 must show acceptable voltages in light-load cases, including the outage of key reactive devices.

9. Cables: the Ferranti effect in its original form



Underground and submarine cables have capacitance per mile 20 to 50 times higher than overhead lines, and their waves travel at only about half the speed of light. Both effects lengthen their electrical length and increase charging.

A 12-mile, 230 kV cable can draw roughly 50 Mvar of charging comparable to a 160-mile overhead line at the same voltage. The open-end Ferranti rise of a short cable is small, but its charging current raises the source-side voltage, loads the cable's own ampacity, and dominates reactive compensation design. Long AC cables require shunt reactors at one or both ends, and beyond a few tens of miles at EHV, the charging current consumes so much of the cable's ampacity that HVDC becomes the practical choice. Cable systems also have resonant frequencies far lower than equivalent overhead lines, so energization and harmonic studies require frequency-dependent cable models.

10. Study workflow for long lines and cables

1. Line constants: calculate positive-, negative- and zero-sequence parameters from conductor and tower geometry, including mutual coupling for double-circuit lines.
2. Steady-state screening: calculate open-end rise for each energization direction, source strength and reactor configuration.
3. Load flow and light-load studies: check voltages across the system under minimum load, outages of reactors and lines, and voltage schedules.
4. Reactor sizing: select compensation degree, arrangement and switching, and check transfer capability at heavy load.
5. EMT energization and reclosing studies: statistical switching studies with frequency-dependent line models, realistic sources, breaker pole scatter and trapped charge.
6. Insulation coordination and arrester selection: confirm clearances, insulators and arrester energy and TOV capability.
7. Special studies: single-pole tripping and secondary arc, resonance in open phases of compensated double-circuit lines, transient recovery voltage for line breakers.
8. Operating procedures: energization direction, voltage targets, reactor status and restoration sequences.

10A. Worked example: double-circuit energization from a moderate source

Consider both circuits of the 217-mile, 345 kV line energized together from a substation with 10,000 MVA of short-circuit capacity, receiving ends open, no reactors.

Energizing both circuits simultaneously from a 10,000 MVA bus produces about the same open-end voltage as energizing one circuit from a 5,000 MVA bus. The practical guidance is to energize one circuit at a time, from the stronger terminal, with line reactors in service, and to close the far-end breaker of the first circuit before energizing the second.

10B. Load rejection: the Ferranti effect in reverse

The Ferranti effect also appears suddenly when a heavily loaded long line loses its receiving-end load for example, when the receiving-end breaker opens during a fault elsewhere or a large load trips. The line instantly becomes open-ended. At the same time:

• generators at the sending end, previously supplying both load and line losses, are suddenly underloaded and accelerate, raising frequency and therefore electrical length;
• automatic voltage regulators, set to support a heavily loaded system, take time to reduce excitation;
• capacitor banks switched in for heavy load remain in service until they are switched out.

The combination can produce temporary overvoltages of 1.3 to 1.5 pu at the open end of long EHV lines for hundreds of milliseconds to seconds longer than switching transients and shorter than steady-state conditions. Surge arresters must withstand this TOV without thermal runaway, and line protection may need overvoltage elements (ANSI 59) with time delays coordinated with arrester capability. Load rejection studies combine EMT models for the first cycles with dynamic models for generator response over the following seconds.

10C. Single-pole switching and neutral reactors

Many long EHV lines use single-pole tripping and reclosing to maintain synchronism during single-line-to-ground faults, which are the large majority of EHV faults. When one phase is opened, it remains capacitively coupled to the two energized phases, which sustain a secondary arc at the fault location. On shunt-compensated lines, the phase reactors and the line's interphase capacitance can also form a resonant circuit in the open phase.

A four-reactor scheme three phase reactors plus a neutral reactor between the reactor neutral and ground neutralizes the interphase capacitance. Using positive-sequence susceptance B1 and zero-sequence susceptance B0 of the line (totals for the compensated section), the phase reactor reactance Xp is set by the compensation degree, and the zero-sequence reactance X0 of the bank is chosen so that:

Worked example

For the 217-mile, 345 kV line, assume B1 = 4.5 µS/km and B0 = 2.9 µS/km, giving totals of 1.575 mS and 1.015 mS. For 70% compensation with all reactors at one end (simplified):

The neutral reactor is about one-third of the phase reactor reactance, a typical ratio. Its continuous current is small, but it must be rated for the zero-sequence current during faults and open-phase conditions and insulated for the neutral voltage. In practice the neutral reactor is often detuned slightly from full neutralization to avoid exact resonance with variations in line parameters, and the final design is confirmed by EMT secondary arc studies with frequency-dependent line models.

10D. Interaction with series compensation

Long US lines are sometimes series compensated to increase transfer capability. Series capacitors reduce the effective series reactance of the line, which slightly reduces the Ferranti rise at no load, because the charging current flows through less net inductance. However, series compensation brings its own concerns: subsynchronous resonance with nearby turbine generators, subsynchronous control interaction with inverter-based resources, protection challenges and higher transient recovery voltage for line breakers. When a long line is both shunt- and series-compensated, the reactor sizing, series capacitor protection and switching sequence must be studied together.

10E. Field verification



Model predictions for long-line energization can and should be checked in the field.

Differences between measured and calculated values usually point to incorrect line constants (for example, conductor or ground wire data), unmodeled equipment (station capacitor banks, reactors) or different source strength than assumed. Correcting the model after the first energization improves every later study on the same corridor.



11. Common misconceptions corrected

12. Key takeaways

1. The Ferranti rise is a no-load, light-load phenomenon caused by line charging current flowing through series inductance.
2. At 60 Hz, the rise for a long line is roughly 45% higher than at 50 Hz.
3. Use the exact long-line equations: VR ÷ VS = 1 ÷ cos(βℓ). The (βℓ)² ÷ 2 approximation underestimates the rise.
4. Include the source. Weak sources and double circuits raise the sending end and the open-end voltage further.
5. Every model agrees in steady state; choose the model for the transients. Frequency-dependent models are preferred for switching and resonance studies.
6. Shunt reactors, energization practice and controlled switching are complementary mitigations.

13. How Keentel Engineering helps

Keentel Engineering performs transmission planning, EMT, insulation coordination and interconnection studies for utilities, transmission developers, renewable developers, data center owners and independent power producers, from 69 kV to 765 kV.

Why clients choose Keentel Engineering

• EHV transmission expertise: practical experience with 230 kV, 345 kV, 500 kV and 765 kV lines and substations.
• EMT depth: frequency-dependent line and cable modeling for energization, TRV and resonance studies.
• US standards and utility practice: IEEE, NERC and ISO/RTO requirements applied correctly to 60 Hz systems.
• Planning to operations: from line design and compensation to operating procedures and restoration plans.
• Licensed professional engineering: a Florida-registered firm with offices in Tampa, Austin, Sacramento and Baltimore, supporting projects nationwide.
  

Part C — Case Studies

The following are illustrative scenarios based on conditions typical of US transmission projects. They show how Keentel Engineering approaches Ferranti-effect and line-energization problems; site details are generalized and figures are rounded.

Case Study 1 — 345 kV renewable export line: energizing from the weak end

Situation

A transmission developer plans a 190-mile, 345 kV double-circuit line connecting a cluster of wind and solar plants to a load-center substation. The initial design includes 40% shunt compensation using bus-connected reactors at the load-center end. The renewable-end substation has a relatively weak source when the plants are offline.

Analysis

Keentel's study shows that energizing the line from the renewable end at night a likely operating scenario during restoration after an outage produces an open-end voltage of about 1.12 pu relative to the source voltage, because the bus-connected reactors at the far end are not connected to the open line, and the weak source adds a sending-end rise of about 4% when both circuits are energized. EMT studies show statistical switching overvoltages above the insulation design target for energization from that end.

Engineered solution

Keentel recommends converting the reactors to line-connected units split between both ends, raising total compensation to about 65%, and specifying controlled switching on the line breakers. Operating procedures are revised to require energization from the load-center end, with the renewable-end energization allowed only with a reduced sending-end voltage.

Outcome

Open-end voltages stay below 362 kV in all studied energization scenarios, switching overvoltages fall within the insulation design, and the transmission owner approves the revised design without changes to tower clearances.

Case Study 2 — Black-start restoration over a 230 kV cranking path

Situation

A utility's restoration plan uses a combustion turbine black-start unit to energize a 230 kV cranking path of about 110 miles of overhead line to reach a large steam unit's station service. A restoration drill simulation shows the black-start unit reaching its underexcitation limit as the line is energized.

Analysis

Keentel models the cranking path in steady state and EMT. The line charging of about 33 Mvar, plus the step-up transformer magnetizing behavior and the generator's limited underexcited capability, leaves little margin. The open-end Ferranti rise is modest at this length, but the generator is near self-excitation conditions, and energizing the step-up transformer at the far end produces harmonic-rich inrush with a temporary overvoltage risk.

Engineered solution

Keentel recommends a revised energization sequence: energize the line in two segments, place a 230 kV station reactor in service before the second segment, pick up a block of station service load at an intermediate substation, and lower the generator terminal voltage before closing. EMT studies confirm acceptable transformer energization overvoltages with the revised sequence.

Outcome

The restoration plan is updated for NERC EOP-005 compliance, the next drill succeeds within generator limits, and operators gain a clear, studied energization sequence.

Case Study 3 — 230 kV underground cable for a hyperscale data center campus



Situation

A data center developer plans a 12-mile, 230 kV underground XLPE cable from a utility substation to its campus substation. The utility's interconnection study flags high voltages at the utility substation under light load and asks the developer to address reactive compensation.

Analysis

Keentel calculates cable charging of about 50 Mvar. The open-end Ferranti rise along the cable is small, but the charging raises the utility substation voltage by about 1.5% at minimum load, and the campus's light-load periods — commissioning, partial build-out — leave the cable largely uncompensated. Frequency-dependent cable models show a low-order parallel resonance near the 6th harmonic with the utility source, relevant to the campus's power electronics.

Engineered solution

Keentel specifies a 40 Mvar switched shunt reactor at the campus substation, with a control scheme that keeps it in service at light load and removes it as campus load grows. Harmonic and energization studies confirm acceptable resonance and transient performance with the reactor in either state.

Outcome

The utility accepts the compensation design, the campus energizes without voltage violations, and the reactor control adapts to load growth across the build-out.

Part D — Technical FAQ: The Ferranti Effect

References and Further Reading

Links were current at publication (October 2026).

• IEEE Std 1313.1, Standard for Insulation Coordination — Definitions, Principles, and Rules. IEEE.
• IEEE Std 1313.2, Guide for the Application of Insulation Coordination. IEEE.
• IEEE Std C62.11, Standard for Metal-Oxide Surge Arresters for AC Power Circuits (>1 kV). IEEE.
• IEEE Std C57.21, Standard Requirements, Terminology, and Test Code for Shunt Reactors Rated Over 500 kVA. IEEE.
• IEEE Std C37.06 and C37.09, AC High-Voltage Circuit Breakers: Preferred Ratings and Test Procedures. IEEE.
• NERC Reliability Standards TPL-001, VAR-001, VAR-002 and EOP-005. North American Electric Reliability Corporation.
• EPRI, Transmission Line Reference Book: 345 kV and Above (the "Red Book"). Electric Power Research Institute.
• J. D. Glover, T. J. Overbye and M. S. Sarma, Power System Analysis and Design. Cengage.
• H. W. Dommel, EMTP Theory Book. Bonneville Power Administration and Microtran Power System Analysis Corporation.
• A. Morched, B. Gustavsen and M. Tartibi, "A Universal Model for Accurate Calculation of Electromagnetic Transients on Overhead Lines and Underground Cables," IEEE Transactions on Power Delivery, 1999.
• J. R. Martí, "Accurate Modelling of Frequency-Dependent Transmission Lines in Electromagnetic Transient Simulations," IEEE Transactions on Power Apparatus and Systems, 1982.
  

Disclaimer

This article is general technical information for educational purposes. It is not engineering advice for any specific project and does not create a professional relationship. The results presented come from Keentel Engineering's simplified models with typical line parameters; actual voltage rise, switching overvoltages and compensation requirements depend on project-specific line geometry, conductors, sources, equipment and operating conditions and must be verified by detailed study. Designs must follow current IEEE standards, the NESC, NERC requirements, utility and transmission provider criteria and project-specific engineering analysis, sealed by a licensed professional engineer where required.



Case studies are illustrative scenarios based on typical project conditions, not records of specific client projects. Figures are rounded and indicative.

IEEE, NERC, EPRI and other names are the property of their respective owners. Keentel Engineering is not affiliated with or endorsed by these organizations or any software or equipment vendor.