Capacitors: How They Work, Equations, Types, and Power-System Applications

Learn how capacitors store energy, behave in AC and DC circuits, produce reactive power, and are applied in power systems for voltage support, filtering, and capacitor-bank compensation—plus the harmonics, switching, protection, and discharge checks that prevent bad applications.

Direct Answer

A capacitor stores electrical energy in an electric field created by separated charge. Its basic relationship is \(Q=CV\): more capacitance or voltage means more stored charge. In AC circuits, capacitor current leads voltage and capacitive reactance decreases as frequency rises.

In power systems, capacitor banks are commonly connected in shunt to supply leading reactive power, support voltage, reduce upstream reactive current, and improve system capacity utilization. Their application must also account for voltage rise, harmonic resonance, switching transients, failed units, protection, discharge time, and changing load conditions.

How a Capacitor Stores Charge and Energy

A capacitor consists of conductive electrodes separated by a dielectric. Applying voltage moves charge onto the electrodes and establishes an electric field in the dielectric. Energy is stored in that field rather than as a continuous flow of current through the dielectric.

Capacitor electric-field diagram showing two conductive plates, dielectric, separated charge, voltage, capacitance, and stored energy
A capacitor stores energy in the electric field between conductive electrodes separated by a dielectric. Larger electrode area, smaller spacing, and higher dielectric permittivity generally increase capacitance.

What Determines Capacitance?

For an ideal parallel-plate capacitor, capacitance increases with plate area and dielectric permittivity and decreases as plate spacing increases:

C = ε A / d
Geometry terms
  • \(C\)Capacitance in farads.
  • \(\varepsilon\)Permittivity of the dielectric.
  • \(A\)Effective electrode area.
  • \(d\)Effective dielectric spacing.
Core concept

A capacitor stores separated charge and electric-field energy. It does not “store current,” and in AC power systems it does not create free real power.

Key Capacitor Equations

Charge

Q = C V

Stored Energy

E = 1/2 C V²

Current-Voltage Relationship

i(t) = C dv(t)/dt

Capacitive Reactance

X_C = 1 / (2πfC)

Capacitive reactance falls as frequency rises. This is why capacitors can behave very differently at harmonic frequencies than they do at the 50 or 60 Hz fundamental.

Series and Parallel Capacitors

C_parallel = C₁ + C₂ + …
1/C_series = 1/C₁ + 1/C₂ + …
High-voltage reality

Ideal series equations are not enough for high-voltage assemblies. Unit tolerances, internal discharge elements, voltage distribution, failed units, fusing, and bank connection all affect actual stress.

Capacitor Behavior in DC and AC Circuits

With steady DC, ideal capacitor current falls to zero after charging. With AC, changing voltage continuously moves charge, so alternating current flows.

Capacitor AC and DC behavior showing DC charging current decay and sinusoidal AC current leading voltage
After an ideal capacitor charges on DC, steady current falls to zero. Under sinusoidal AC, current continues to flow and leads voltage by 90 degrees in the ideal model.

DC Charging

An initially uncharged capacitor draws charging current when connected to a DC source. As capacitor voltage approaches source voltage, charging current decays. The charging rate is determined by the surrounding circuit resistance and capacitance.

AC Phase Relationship

For an ideal sinusoidal capacitor, current leads voltage by 90°. Real capacitors introduce losses and parasitic inductance, so the phase relationship is not perfectly ideal.

Real Capacitor Model

Practical capacitors have equivalent series resistance (ESR), equivalent series inductance (ESL), dielectric loss, leakage, tolerance, and temperature-dependent behavior. At sufficiently high frequency, ESL can dominate and the device can stop behaving capacitively.

Capacitor Types and Ratings

Capacitance value alone is never enough to select a capacitor. Voltage, current, dielectric technology, temperature, losses, duty cycle, frequency, and expected life must match the application.

Common capacitor technologies and applications
Type Common use Important limitation
CeramicDecoupling, filtering, RF, electronicsSome dielectric classes vary strongly with DC bias and temperature
Aluminum electrolyticBulk DC filtering and energy bufferingPolarity, ripple current, temperature, and lifetime are critical
FilmAC duty, pulse duty, power electronics, motor/run applicationsLarger physical size for a given capacitance than some alternatives
SupercapacitorShort-duration energy bufferingLow cell voltage, balancing, leakage, and energy-density tradeoffs
Shunt power capacitorPower factor / reactive support / voltage supportMust be applied for system voltage, frequency, harmonics, switching, protection, and discharge

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Ratings Engineers Actually Check

Capacitor rating checks
Rating / property Why it matters
Capacitance and toleranceSets reactance, stored charge, filter response, and reactive output
Voltage ratingControls dielectric stress and failure margin
RMS / ripple currentControls internal heating from AC current
ESR / loss tangentDetermines losses and temperature rise
Temperature rangeAffects capacitance, losses, and aging
FrequencyChanges reactance and harmonic-current stress
Duty / switching frequencyImportant for pulse, power-electronic, and switched-bank service
Life / reliability ratingImportant where capacitor aging is a maintenance driver

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Power-System Capacitor Banks

Power-system capacitors are commonly assembled into shunt banks connected to distribution feeders, substations, industrial buses, or individual loads. Their main function is to supply leading reactive power locally.

Shunt capacitor bank connected near an inductive load showing reduced upstream reactive power and improved power factor
A shunt capacitor bank supplies leading VARs locally, reducing the reactive current that must be supplied by upstream transformers, feeders, or the utility source.

Where Banks Are Installed

Common shunt capacitor bank locations
Location Primary objective Tradeoff
Individual motor / loadLocal VAR support and feeder-current reductionMust switch appropriately with the load
MCC / facility busGroup-load power-factor correctionAutomatic steps may be needed for variable load
Distribution feederVoltage support and loss reduction along feederPlacement and switching influence feeder voltage profile
Substation busBulk reactive support and voltage controlLess local current reduction downstream than distributed placement

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Fixed vs. Switched Banks

A fixed bank remains connected continuously. A switched bank is divided into steps that can be connected or disconnected based on voltage, VAR demand, power factor, time schedule, or other control logic. Switched banks reduce the risk of overcompensation when load changes significantly.

For detailed kVAR sizing and economic application, see Power Factor Correction. This page focuses on capacitor behavior and power-capacitor application.

Capacitor Reactive Power, kVAR/MVAR, and Voltage Dependence

Power capacitor banks are usually specified by reactive-power output rather than farads because the operational question is how many VARs the bank supplies at the actual system voltage and frequency.

Single-Phase Capacitor Reactive Power

Q_C = V² / X_C = 2πf C V²

Why Capacitor kVAR Changes With Voltage

At constant capacitance and frequency, reactive output varies approximately with the square of applied voltage:

Q₂ / Q₁ = (V₂ / V₁)²

Example: Bank Output at Lower Voltage

A 1,000 kVAR bank is rated at 13.8 kV. If the bus operates at 13.2 kV and frequency is unchanged:

Q₂ = 1000 × (13.2/13.8)² ≈ 915 kVAR
Answer: the bank supplies only about 915 kVAR at 13.2 kV, not its 1,000 kVAR nameplate output.
Voltage-control implication

A shunt capacitor produces less VAR support when voltage is already depressed. That characteristic is important in voltage-control and stability studies.

Capacitor Banks, Harmonics, and Resonance

This is one of the most important power-system capacitor topics. Because capacitive reactance falls with frequency, harmonic currents can be much larger than a simple 60 Hz calculation suggests.

Parallel Resonance

System inductance and shunt capacitance can form a parallel resonant circuit near a harmonic frequency. If that resonant frequency is close to a strong harmonic source, bus voltage distortion and capacitor current can increase substantially.

Series Resonance

Capacitors and reactors may also form series-resonant paths with low impedance at selected frequencies. This principle is used intentionally in passive filters but can be damaging when it occurs unintentionally.

Detuned Capacitor Banks

Detuned banks add series reactors so the capacitor-reactor combination is tuned below a dominant harmonic, reducing the chance that the bank will resonate directly at that harmonic. The exact tuning, reactor rating, capacitor voltage stress, and thermal duty must be engineered for the application.

Do not add capacitors blindly

Facilities with significant VFDs, rectifiers, UPS systems, EV chargers, inverters, or other nonlinear loads should evaluate harmonic spectrum and system resonance before adding conventional power-factor correction banks.

IEEE 519-2022 provides the current IEEE harmonic-control framework at the point of common coupling. See Power Quality for harmonic measurement and troubleshooting context.

Capacitor Switching, Protection, Failed Units, and Discharge

Capacitor banks can experience high transient current and voltage during energization, de-energization, restrike, back-to-back switching, and nearby fault events. Switching duty is therefore part of bank design—not an afterthought.

Switching Transients and Inrush

Energizing an uncharged bank can produce high-frequency inrush current. Switching one bank when another energized bank is nearby can create particularly severe back-to-back inrush. Breaker or contactor selection, pre-insertion components where used, reactor application, and switching sequence may all matter.

Common Capacitor-Bank Protection

Common capacitor-bank protection and monitoring functions
Function What it detects / limits Why it matters
Unit / group fusesFailed capacitor units or elements depending on bank designIsolates failed portions and limits damage
Unbalance protectionCapacitance loss or failed elements/unitsDetects internal bank deterioration before excessive stress develops
OvercurrentMajor faults and abnormal bank currentBackup / fault protection
OvervoltageExcessive bus or unit voltageLimits dielectric stress
Neutral / residual measurementBank imbalance depending on connectionSensitive indication of failed units/elements
Temperature / enclosure monitoringAbnormal heating where providedSupports condition assessment

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Why a Failed Unit Can Overstress the Remaining Units

In some series-group bank arrangements, loss of capacitance in one unit or group changes voltage distribution. Remaining healthy units can experience increased voltage stress even though the overall bank remains connected. Unbalance protection is designed around the actual bank connection and failure mode.

Stored Charge and Discharge Safety

Capacitors can remain charged after disconnection. Power-capacitor installations therefore use discharge devices and operating procedures to reduce residual voltage. Personnel should never assume a disconnected bank is discharged without following the applicable procedure and verifying the condition.

Power-Capacitor Design and Field Review Checklist

A capacitor-bank application should begin with the electrical objective and end with verification under multiple operating conditions.

Power capacitor application checklist
Review item Verify Risk if missed
ObjectivePF correction, feeder voltage, substation VAR support, filter dutyBank solves the wrong problem
Voltage / frequencyActual normal and abnormal rangeWrong kVAR output or dielectric overstress
Load profilePeak, normal, light load, seasonal operationOvercorrection and voltage rise
HarmonicsSpectrum, nonlinear load, resonance scan where neededExcess current / voltage distortion / failure
Switching dutySingle-bank and back-to-back inrush, switching frequencyBreaker/contact damage or transient overvoltage
Bank connectionGrounded/ungrounded wye, delta, series groups, fuse schemeProtection and failure behavior misunderstood
ProtectionFuse, unbalance, overcurrent, overvoltage, alarmsFailed units remain undetected
DischargeDischarge devices, wait time, grounding procedureResidual-voltage hazard
Field conditionBulging, leaks, blown fuses, hot joints, corrosion, contaminationProgressive failure or outage

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Field Warning Signs

  • Repeated fuse operation or unbalance alarms
  • Bulging, leaking, cracked, or discolored capacitor units
  • Abnormal noise or vibration in reactors/contactors
  • Hot terminals or bus connections
  • Higher-than-expected harmonic current
  • Voltage rise or leading PF at light load
  • Frequent switching or controller hunting

Capacitor Engineering References

Frequently Asked Questions

What does a capacitor do?

A capacitor stores energy in an electric field and exchanges charge when its voltage changes. In power systems, capacitor banks are used primarily to supply leading reactive power and support voltage.

Why do capacitors block DC but pass AC?

After an ideal capacitor charges to a steady DC voltage, its current falls to zero. With AC, voltage keeps changing, so charge continually moves on and off the electrodes and alternating current flows.

Why are power capacitor banks rated in kVAR instead of microfarads?

For power-system operation, the useful quantity is reactive-power output at a specified voltage and frequency. Capacitance still determines that output, but kVAR or MVAR directly describes the VAR support the bank provides to the system.

Does a capacitor bank always improve voltage?

A shunt capacitor often raises local voltage by supplying reactive power, but the amount depends on system impedance, load, bank size, and operating condition. Too much capacitance can cause excessive voltage at light load.

Can capacitor banks cause harmonics or resonance?

Yes. Capacitors can resonate with system inductance and amplify harmonic current or voltage. Harmonic-rich systems may require detuned banks, filters, or a dedicated harmonic/resonance study.

Why is capacitor-bank switching difficult?

Capacitor energization can create high-frequency inrush current and switching transients. Back-to-back switching can be especially severe when another energized bank is already connected nearby.

Can a capacitor remain dangerous after it is disconnected?

Yes. Capacitors can retain stored charge after disconnection. Power capacitor installations use discharge devices and procedures, but maintenance still requires the applicable wait, grounding, and verification steps.

What happens when one capacitor unit fails in a bank?

The effect depends on the bank connection and fuse arrangement. In some series-group designs, failed capacitance changes voltage distribution and can overstress remaining units, which is why unbalance protection is important.

Summary and Next Step

Capacitors store electric-field energy, oppose rapid voltage change, and draw leading current in AC systems. Those fundamentals explain their role in electronics, power electronics, motors, filters, and utility capacitor banks.

For power-system work, the most important practical concepts are reactive-power output, voltage-squared behavior, bank location, harmonics and resonance, switching duty, protection, failed-unit voltage stress, discharge safety, and load variation. A correct kVAR number is only the start of a complete capacitor-bank application.

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