Detuned Reactor Calculation for Capacitor Banks

A detuned reactor calculation starts with the required fundamental-frequency kvar, system voltage and frequency, capacitor connection, selected detuning factor, and measured harmonic environment. The detuning factor is the ratio of reactor reactance to capacitor reactance at the fundamental frequency. From it, the ideal series-resonance frequency is approximately the system frequency divided by the square root of that ratio. This calculation is only the first design screen. The capacitor voltage rises when a reactor is added, component tolerances move the actual tuning point, and the network can contain parallel resonances. Verify the result with manufacturer data, a harmonic study, thermal and fault-duty checks, and the applicable project standards before ordering equipment.

İçindekiler

What detuning is intended to do
Define the detuning factor
Calculate branch current and reactor reactance
Account for capacitor voltage rise
Use measured harmonics and network impedance
Check tolerances and aging
Coordinate switching and protection
Calculation workflow and deliverables
Worked screening example and limits
Verify the installed branch after energization
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What detuning is intended to do

A series reactor changes the impedance of a capacitor branch so its series-resonance frequency lies below a troublesome harmonic order. Above that frequency, the branch behaves inductively rather than as an attractive low-impedance path for higher-order harmonic current. Detuning is primarily a protection and resonance-control strategy for power factor correction banks; it is not automatically a tuned harmonic filter with a guaranteed current-absorption target. The design objective, harmonic spectrum, bus impedance, and acceptance criteria must be stated before selecting a percentage.

Define the detuning factor

Three-phase series reactor for a detuned capacitor bank — Series reactor used with power-factor-correction capacitors

Let p equal XL divided by XC at the fundamental frequency, expressed as a decimal. XL is the reactor reactance and XC is the magnitude of capacitor reactance in the series branch. The ideal resonance frequency is fr = f1 / sqrt(p), where f1 is the system frequency. For example, p = 0.07 on a 50 Hz system gives an ideal value near 189 Hz. That arithmetic does not authorize a 7 percent reactor for every plant. It only shows the nominal relationship. Actual reactors and capacitors have tolerance, temperature dependence, and manufacturing limits, while the network has its own frequency-dependent impedance.

Calculate branch current and reactor reactance

For a balanced three-phase branch, begin from the capacitor bank's required kvar at the bus and identify whether the quoted rating refers to the capacitor alone or the complete reactor-capacitor assembly. The fundamental branch impedance is the net capacitive reactance after subtracting reactor reactance. If the assembly kvar and line voltage are known, calculate line current using I = Q / (sqrt(3) × VLL) for a balanced three-phase load. Derive the net per-phase impedance using the actual delta or wye connection, then separate XL and XC using the selected p. Because rating conventions differ, reconcile the hand calculation with the supplier's complete assembly tables.

Account for capacitor voltage rise

The reactor causes the capacitor terminal voltage to exceed the bus contribution under fundamental-frequency operation. A simplified ideal relationship indicates that capacitor voltage increases as the detuning factor grows. The capacitor must therefore be selected for the actual continuous voltage and current stress, including system voltage tolerance, harmonic current, temperature, and manufacturing tolerance. Do not pair a reactor with a capacitor based only on nominal bus voltage and kvar. Request the approved reactor-capacitor combination and its declared assembly output.