Technical Articles
Detuned reactors / inductors are installed in series connection with power factor correction capacitors to avoid harmonic amplification and resonance. They are rated in kVAr along with tuning factor (7% or 14%). They are typically designed with high linearity to avoid saturation & withstand harmonics, along with safety features such as auto-thermal cut-off, higher insulation class for windings.
In addition to the above-mentioned parameters of detuned reactors, it is equally important to consider Quality Factor of the reactor, popularly referred as Q-factor. This article explains about the same, along with the importance of Q-factor and recommended values.
Q-factor:
Theoretically, an inductor would have pure inductance only, whereas in reality they have some resistance. This resistance causes energy loss and acts as performance limiting factors for the inductor.
Quality Factor, also called Q-factor is a dimensionless number and helps in defining that performance of the inductor. The Q-Factor is the ratio of Inductive impedance to DC Resistance of detuned reactor.
Q factor = 2ΟfL/R
Where,
f = Frequency
L = Inductance
R = Resistance
Effects of Q-factor on filter performance:
1. Losses:
Reactor with high Q-factor has lower power losses. Higher Q-factor implies lower DC resistance value which results in lower i2R losses (conductor loss). It can also be explained by below formula:
πππ€ππ πΏππ π = πππ‘ππ πππ€ππ (πππ΄) / π ππππ‘ππ
Let us compare the performance of two detuned reactors with different Q-factors based on tested values:
2. Impedance offered by reactors:
To understand this, we shall first understand the functioning of a detuned circuit:
Detuned circuit sets a resonant frequency and offers higher inductive impedance to the frequencies above the resonant frequency. A 7% detuned reactor sets a resonant frequency of 189 Hz and thus restricts harmonic amplification of 5th order (250 Hz) and above frequencies, while 14% detuned reactor sets a resonant frequency 133Hz and thus restricts harmonic amplification of 3th order (150 Hz) and above frequencies.
A detuned reactor with higher Q-factor has sharper impedance curve. Hence it offers more impedance to higher harmonic frequencies. Let us study the same based on tested values:
As can be seen in the graph, reactor with higher Q-factor offers almost double impedance than the reactor with lower Q-factor for higher order harmonics. All other parameters of both the reactors like the inductance, linearity, etc are same, except the Q-factor. The higher impedance results in better reduction of harmonic amplification & resonance.
How to achieve a high Q-factor?
To achieve good Quality factor, the detuned reactor should have minimum DC resistance as possible.
π ππ ππ π‘ππππ = ππ/A
Where,
Ο = Resistivity
l = Length
A = Area of cross-section
In this study, we have seen the Q-factor of two 50 kVAr 7% reactors one with Q-factor of 32 and other with Q- factor of 58. Practically, Q-factor as high as 58 is easily achievable (refer the above table). But considering smaller ratings & other practical factors, any Q-factor value above 35 is preferable.
Conclusion:
It is always challenging to select right electrical components for harmonic environments in industries. Detuned reactor-capacitors in APFC panels along with Active Harmonic filters are doing their part in controlling harmonics of the system. Choosing the detuned reactors with high Q-factor (Quality factor) can help to control harmonic amplification even more effectively. In addition to this, reactors with high linearity limit (>180%) and proper thermal design of panels will help in bringing the best out of the detuned reactors. While selecting detuned reactors, along with other specification / parameters like Linearity, Power Loss, Insulation class, etc., it is understood from this article that Q-factor should also be given equal importance.
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