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:

7.2 Detuning ratios for 60 Hz systems

7.2 Detuning ratios for 60 Hz systems

Using 50 Hz tuning frequencies in a US design is a common and costly error. A designer who looks up "7% equals 189 Hz" and compares it with 300 Hz for the 5th harmonic gets the right conclusion for the wrong reason; one who applies a 50 Hz table to select a ratio for a target frequency gets the wrong reactor.

7.3 Capacitor voltage rise

The series reactor raises the fundamental voltage across the capacitor:

For a 480 V bus with 7% detuning, VC = 480 ÷ 0.93 = 516 V. Harmonic voltages add to this. Capacitors in detuned banks must therefore be rated above system voltage — typically 525 V or 600 V units on a 480 V system, and correspondingly higher ratings at medium voltage.

7.4 Effective kvar output



The output of a detuned step depends on the capacitor's rated voltage and the detuning ratio:

A 600 kvar, 525 V capacitor step with 7% detuning on a 480 V bus delivers about 600 × (480 ÷ 525)² ÷ 0.93 ≈ 539 kvar. Designers who specify detuned banks by nameplate capacitor kvar without this correction will under- or over-compensate.

7.5 The resonance that detuning creates

A detuned bank does not eliminate parallel resonance. It moves the combined network resonance below the branch tuning frequency. In Keentel's 13.8 kV model, the 7% detuned 9 Mvar bank produces a parallel resonance near the 3.1st harmonic. That is harmless if 3rd harmonic current is negligible — usually true on a balanced three-wire 13.8 kV bus with six-pulse drives. It can be harmful at 480 V or 208 V buses with large single-phase loads or unbalance, where 3rd harmonic current flows. In those cases a 14% ratio, tuning at 160 Hz, keeps the resonance below the 3rd.

7.6 What detuned reactors are not

Detuned reactors protect the capacitor bank and prevent it from creating a resonance at characteristic harmonics. They are not harmonic filters. A 7% detuned bank absorbs only a modest share of 5th harmonic current. If a facility must reduce harmonic current to meet IEEE 519 at the point of common coupling, a tuned filter or active harmonic filter is usually needed.

8. Tuned passive filters

8.1 Single-tuned filters

A single-tuned filter deliberately creates a low-impedance series path at a specific harmonic, slightly below it to allow for capacitor tolerance, temperature drift and aging. For the 5th harmonic, tuning near 4.7th is typical. The reactor ratio is:

8.2 Worked example: 9 Mvar, 13.8 kV 5th harmonic filter

The filter still forms a parallel resonance with the source, now below 4.7th. The design must confirm that this resonance does not coincide with any harmonic present, including non-characteristic harmonics from unbalance and transformer inrush.

8.3 Filter duty and absorption

A tuned filter absorbs harmonic current not only from the plant's drives but from the entire utility system. A filter designed only for the plant's own harmonic load can be overloaded by background distortion. IEEE 1531 describes the design process, including background distortion, detuning, unbalance protection and ratings of each component.

8.4 Damped and high-pass filters

Second-order high-pass and C-type filters provide damping across a band rather than a single sharp notch. They are common at transmission and collector levels, where the resonant frequency may move with network configuration and a sharp notch could create new resonances. C-type filters avoid fundamental-frequency losses in the damping resistor by tuning an auxiliary branch to fundamental frequency.

9. Active harmonic filters and network impedance

Active harmonic filters (AHFs) inject harmonic currents in opposition to load harmonics, measured through current transformers. They are effective for variable loads and for multiple harmonic orders. However, they are not a substitute for understanding network impedance:

An AHF should be specified after a frequency scan of the network, with its rating, CT location and control settings selected for the actual resonance conditions.

10. Equipment duty

10.1 Capacitor limits under IEEE 18

IEEE Std 18 specifies continuous operating limits for shunt power capacitors, including harmonic content:

Duty quantities are calculated by summing harmonic components:

10.2 Worked example: duty of the 9 Mvar bank in resonance



Using the harmonic voltages from Keentel's scan for the 9 Mvar case at nominal fundamental voltage:

This result is instructive. The capacitor bank itself is within its IEEE 18 ratings, yet the bus voltage THD of 7.7% exceeds the IEEE 519 limit of 5% for 13.8 kV buses. Equipment damage is not the only consequence of resonance; voltage quality for every load on the bus is. With operating voltage at 105% and a lighter load (less damping), the margins on peak voltage and current shrink rapidly. Capacitor fuses — sized with modest margin over fundamental current — and capacitor units with manufacturing tolerances or aging can fail long before the bank as a whole reaches its limits.

10.3 Transformers

Harmonic currents increase transformer eddy-current and stray losses, which rise roughly with the square of harmonic order. IEEE C57.110 provides the harmonic loss factor method for derating:

A transformer carrying amplified 5th and 7th harmonic currents in series resonance can overheat at a fundamental load well below nameplate.

10.4 Drives, UPS and electronic loads

Voltage distortion flattens or peaks the voltage waveform. Six-pulse drives charge their DC link from the voltage peaks; a peaked waveform raises DC bus voltage and can cause overvoltage trips, while a flattened waveform reduces it and can cause undervoltage trips under load. Distortion can also disturb zero-crossing detection in thyristor controls, synchronization of UPS and generator systems, and the operation of sensitive instrumentation.

10.5 Cables, motors and metering

Harmonic currents increase cable heating through skin and proximity effects. Negative-sequence harmonics (5th, 11th) create counter-rotating torque in motors, raising losses and vibration. Revenue meters and protective relays may respond differently to distorted waveforms, causing billing disputes or protection misoperation.

11. IEEE 519-2022 limits

IEEE 519-2022 sets harmonic limits at the point of common coupling (PCC) — the point where the utility serves multiple customers, or as agreed between the user and utility.

11.1 Voltage distortion limits

In US voltage classes: 480 V and 600 V buses fall in the first row; 4.16 kV, 13.8 kV, 34.5 kV and 69 kV in the second; 115 kV and 138 kV in the third; 230 kV, 345 kV, 500 kV and 765 kV in the fourth.

11.2 Current distortion limits (120 V through 69 kV)

Even harmonics are limited to 25% of the odd harmonic limits. The 2022 edition also allows defined percentages of time above the limits (for example, statistical evaluation using very-short-time and short-time values) and provides adjustments for low-order harmonics in certain conditions. The current limits apply to the user's emissions; the voltage limits are the shared responsibility of user and utility.

11.3 Why resonance complicates compliance

IEEE 519 compliance is assessed at the PCC, but resonance inside a facility can cause problems that never violate PCC limits, and a utility-side resonance can cause PCC voltage limits to be exceeded even when every customer meets its current limits. Compliance and reliability are related but not the same question.

12. Credible operating configurations

Resonance studies must consider every credible configuration, not just the design case.

13. A practical investigation and study workflow

1. Collect data: one-line diagrams, transformer nameplates, cable lengths and types, capacitor banks and controls, drive and converter inventory, utility short-circuit data (maximum and minimum) and utility capacitor banks near the PCC.
2. Measure: install power quality monitors at the PCC, main buses and suspected equipment, recording harmonic voltages and currents with phase angles over at least a week of representative operation. Use measurement methods consistent with IEEE 1159 and IEEE 519-2022.
3. Build the harmonic model: frequency-dependent models of sources, transformers, cables, capacitors, motors, loads and harmonic sources in a harmonic analysis program.
4. Run frequency scans: driving-point impedance at key buses and transfer impedances between buses for every credible configuration.
5. Run harmonic load flows: calculate harmonic voltages and currents for each configuration with realistic harmonic spectra.
6. Validate the model: compare calculated distortion with measurements for the configurations observed in the field. Adjust source impedance, load damping and harmonic spectra as needed.
7. Check equipment duty: capacitors (IEEE 18), filters (IEEE 1531), transformers (IEEE C57.110), cables, drives and protective devices.
8. Design mitigation: detuned or tuned banks, filters, AHFs, configuration limits or source changes.
9. Verify after installation: measure again and confirm that distortion and duty match predictions.

13.1 Digital twins and EMT simulation

For complex systems — large data centers, inverter-based plants, facilities with many converters — frequency-domain models can be supplemented by electromagnetic transient (EMT) simulations. EMT models capture capacitor switching transients, transformer inrush, converter control behavior and nonlinear interactions that frequency-domain methods simplify. A validated model, kept current as the facility changes, becomes a digital twin that can screen future additions before they are installed.

14. Resonance in inverter-based plants and data centers

14.1 Solar, wind and storage collector systems

Utility-scale plants use long 34.5 kV collector cables, inverter step-up transformers, a main power transformer to 115 kV, 138 kV, 230 kV or 345 kV, and sometimes shunt capacitor banks or harmonic filters. Cable capacitance resonating with transformer inductance typically produces resonances in the range of several hundred hertz to a few kilohertz. Background harmonic distortion from the transmission system can be amplified into the plant, and inverter emissions can be amplified out to the POI. Transmission providers increasingly require harmonic studies demonstrating IEEE 519 compliance at the POI.

14.2 Data centers

Data centers combine large UPS and server power supply loads, MV cable networks within the campus, power factor correction (sometimes integrated in UPS systems), on-site generators, and increasingly BESS and on-site generation. Modern UPS and power supplies with active front ends produce low low-order harmonics but emit near their switching frequencies. Generator operation raises source impedance dramatically compared with utility supply, moving resonances lower and increasing distortion during generator operation — a configuration that must be studied separately.

14.3 EV charging hubs

DC fast chargers aggregate tens of megawatts of converter load at a single service. Charger designs vary, and the combination of chargers from different vendors, service transformers and any site capacitors or storage converters creates resonances that must be studied as the hub grows.

14A. Capacitor switching, inrush and resonance

Resonance is a steady-state frequency-domain concept, but the same inductance and capacitance also govern switching transients. When a capacitor bank is energized, the network rings at its natural frequency — which is the same parallel resonant frequency identified in a frequency scan. Two effects deserve attention.

Magnification of switching transients

When a utility switches a large capacitor bank on its system, an oscillatory transient at a few hundred hertz propagates down the feeder. If a customer's low-voltage capacitor bank and service transformer form a series circuit tuned near that transient frequency, the transient voltage at the customer bus can be magnified to two to four times its normal peak. Drives with diode front ends are especially vulnerable: the DC link capacitor charges through the surge and trips the drive on DC overvoltage. The classic remedy is to add input reactance (line reactors or DC chokes) to drives, convert the customer bank to a detuned bank, or ask the utility to use synchronous closing or pre-insertion devices on its bank.

Back-to-back switching inrush

When one capacitor stage is energized next to stages already in service, the inrush current is limited only by the small inductance between them. The peak inrush current and frequency for back-to-back switching are approximately:

where Ceq is the series combination of the switched and energized capacitances and Leq is the inductance between them. Inrush frequencies of several kilohertz and peaks of many times rated current are common. IEEE C37.012 and IEEE 1036 provide guidance on limiting reactors and switching device capability. A detuned reactor in each step also limits back-to-back inrush — a secondary benefit that is often overlooked.

Transformer energization and the 2nd harmonic

Transformer inrush current is rich in the 2nd harmonic and also contains odd harmonics. If a network has a parallel resonance near the 2nd or 3rd harmonic — as happens with heavily detuned banks or very large capacitance relative to source strength — energizing a transformer can excite sustained resonant overvoltage that decays slowly. This temporary overvoltage can stress surge arresters and delay relay restraint. EMT studies are the appropriate tool when a resonance below the 4th harmonic is identified at a bus where large transformers are energized.

14B. Worked example: should the plant buy an active filter or a detuned bank?

A 480 V plant has 900 kW of six-pulse drive load and a 2,000 kVA, 5.75% transformer. It wants both power factor correction (about 600 kvar) and compliance with an IEEE 519 TDD limit of 8% at its 13.8 kV PCC, where ISC/IL is about 35.

The engineering point is that the decision depends on the resonance analysis. A plain bank — the cheapest line in the table — is the one most likely to create the problem the plant is trying to avoid. Keentel's practice is to select the option by modeling all four alternatives in every credible configuration, then confirming the chosen option with measurements after installation.

15. Common misconceptions corrected

16. Key takeaways

1. The network matters as much as the harmonic source. Vh = Ih × Zh, and Zh is set by the network.
2. Parallel resonance amplifies voltage; series resonance amplifies current. Both can occur in the same facility.
3. Estimate first, then scan. hr = √(MVAsc ÷ Mvar) gives a fast warning; frequency scans and harmonic load flows confirm.
4. Study every credible configuration. Capacitor stages, transformer paralleling, source changes and load levels all move the resonance.
5. Use 60 Hz numbers. ft = 60 ÷ √p for detuned and tuned banks in the US.
6. Check equipment duty and voltage quality. IEEE 18, IEEE 1531, IEEE C57.110 and IEEE 519-2022 each address a different part of the problem.
7. Verify in the field. Measurement before and after mitigation closes the loop.

17. How Keentel Engineering helps



Keentel Engineering performs power quality and harmonic studies for industrial plants, data centers, water and wastewater utilities, EV charging hubs, solar, wind and storage plants and electric utilities, from 480 V to 765 kV.

Why clients choose Keentel Engineering

• System-level thinking: we study the network, not only the equipment.
• From measurement to design: field data, models and engineered solutions under one team.
• Utility and industrial experience: practical knowledge of utility requirements and facility operations.
• Inverter-based resource expertise: harmonic and EMT studies for solar, wind and storage interconnections.
• Licensed professional engineering: a Florida-registered firm with offices in Tampa, Austin, Sacramento and Baltimore, supporting projects nationwide.

Capacitor fuses operating, transformers running hot or drives tripping without explanation? Talk to Keentel Engineering at (813) 389-7871, contact@keentelengineering.com, or book a 15-minute scoping call at calendly.com/keentel-engineering/15min.

Part C — Case Studies

The following are illustrative scenarios based on conditions typical of US facilities and interconnections. They show how Keentel Engineering approaches harmonic resonance problems; site details are generalized and figures are rounded.

Case Study 1 — 480 V food processing plant: capacitor fuses and drive trips

Situation. A food processing plant supplied by a 2,000 kVA, 13.8 kV to 480 V transformer installs a 1,200 kvar automatic power factor correction bank in four 300 kvar steps. Within weeks, capacitor fuses operate repeatedly, the transformer runs hot, and several conveyor and pump drives trip on DC bus overvoltage, usually during evening shifts when process heating is off.

Analysis. Keentel installs power quality monitors on the main bus and the capacitor bank. With all four steps in service, 5th harmonic voltage reaches 9% and capacitor current reaches 140% of rated during light-load periods. Hand calculation and a frequency scan show the parallel resonance moving from the 10.8th harmonic with one step to about the 5.4th with four steps — and closer still when the utility source impedance is included. Evening loss of resistive heating load reduces damping and sharpens the peak.

Engineered solution. Keentel specifies replacement of the bank with a 7% detuned automatic bank using 525 V capacitors, sized for an effective 1,100 kvar after accounting for voltage rise and detuning. The design confirms that the new network resonance near the 3rd harmonic does not coincide with significant 3rd harmonic current, which measurements show to be small on the three-wire 480 V system.

Outcome. Voltage THD falls below 4%, capacitor fuse operations stop, drive trips cease, and the plant retains its power factor improvement.

Case Study 2 — 13.8 kV water treatment plant: the second transformer

Situation. A water treatment plant has two 13.8 kV buses, each fed by a 115 kV to 13.8 kV transformer, with a normally open tie breaker. Large pump drives and a 6 Mvar capacitor bank are on Bus A. During a planned maintenance outage, operators close the tie and run both buses from one transformer, then later parallel both transformers. Pump drives on Bus B begin tripping, and power quality alarms report high 7th harmonic distortion.

Analysis. Keentel builds a harmonic model for every credible configuration: buses split, tie closed with one transformer, and tie closed with both transformers paralleled. With buses split, Bus A resonance is near the 6.5th harmonic — high distortion but within limits because of load damping. Paralleling the transformers lowers source impedance and moves the resonance to about the 7.4th, while the tie adds Bus B's drives as additional 7th harmonic sources. Measured 7th harmonic voltage exceeds 5%.

Engineered solution. Keentel recommends converting the 6 Mvar bank to a 5th harmonic tuned filter at the 4.7th harmonic, with a reactor and capacitors rated for background distortion and both configurations, and develops an operating procedure for tie operation until the filter is installed.

Outcome. Distortion remains below IEEE 519 limits in all configurations, the plant can use its tie breaker flexibly, and maintenance outages no longer cause drive trips.

Case Study 3 — 200 MW solar plant at 138 kV: amplified background distortion

Situation. A 200 MW solar plant with a 34.5 kV collector system connects to a 138 kV substation. After the utility installs a new 138 kV capacitor bank at a nearby substation, the plant's POI meter shows 13th harmonic voltage above the IEEE 519 individual limit of 1.5% for that voltage class, and the transmission provider asks the plant to investigate.

Analysis. Keentel's measurements show 13th harmonic current flowing into the plant from the 138 kV system, not out of it. A frequency scan of the plant and surrounding network reveals a parallel resonance near the 13th harmonic formed by the collector cable capacitance, the main power transformer and the new utility capacitor bank's effect on the system impedance. The plant's inverters are minor 13th harmonic sources; the resonance is amplifying existing background distortion.



Engineered solution. Keentel presents the analysis to the transmission provider with measured harmonic power flow direction and the frequency scan. The solution combines a damped high-pass filter at the plant's 34.5 kV bus, sized for background distortion, and an adjustment to the inverters' harmonic damping settings recommended by the inverter vendor.

Outcome. 13th harmonic voltage at the POI falls below 1%, the transmission provider accepts the study, and the plant avoids curtailment while the utility updates its own capacitor bank switching practice.

Part D — Technical FAQ: Harmonic Resonance

References and Further Reading

Links were current at publication (October 2026).



• IEEE Std 519-2022, Standard for Harmonic Control in Electric Power Systems. IEEE.
• IEEE Std 18-2012, Standard for Shunt Power Capacitors. IEEE.
• IEEE Std 1531-2020, Guide for the Application and Specification of Harmonic Filters. IEEE.
• IEEE Std 1036-2020, Guide for the Application of Shunt Power Capacitors. IEEE.
• IEEE Std C57.110-2018, Recommended Practice for Establishing Liquid-Immersed and Dry-Type Power and Distribution Transformer Capability When Supplying Nonsinusoidal Load Currents. IEEE.
• IEEE Std 1159-2019, Recommended Practice for Monitoring Electric Power Quality. IEEE.
• IEEE Std 399, Recommended Practice for Industrial and Commercial Power Systems Analysis (Brown Book), harmonic analysis chapter. IEEE.
• R. C. Dugan, M. F. McGranaghan, S. Santoso and H. W. Beaty, Electrical Power Systems Quality, McGraw-Hill.
• J. Arrillaga and N. R. Watson, Power System Harmonics, Wiley.
  

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 frequency scan results come from Keentel Engineering's simplified illustrative model; actual resonances and distortion depend on site-specific source impedance, equipment, loads and operating configurations and must be verified by project-specific study and measurement. Designs must follow current IEEE standards, the NEC, utility and transmission provider requirements 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 and other names are the property of their respective owners. Keentel Engineering is not affiliated with or endorsed by these organizations or any equipment vendor.