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Impact of Q-factor On Performance of Detuned Reactors

Impact of Q-factor On Performance of Detuned Reactors
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The quality factor or Q-Factor is a dimensionless parameter that characterizes a resonator's bandwidth relative to its center frequency. It also describes the damping nature of a resonant circuit. Higher Q indicates a lower rate of energy loss relative to the stored energy of the oscillator; i.e., the oscillations die out more slowly. For example, a pendulum suspended from a high-quality bearing, oscillating in air, has a high Q, while a pendulum immersed in oil has a low one. Oscillators with high quality factors have low damping making them ring longer.


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 helps in defining that performance of the inductor. The Q-Factor is the ratio of Inductive impedance to DC Resistance of detuned reactor.

Harmonic frequencies

Where,


f = Frequency; L = Inductance; R = Resistance


Thus, we can calculate the Q-Factor, just by knowing the power factor of the circuit.

or just the tangent of the phase angle


Q factor = | tanØ l

Harmonic frequencies

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:


Power Loss = Total Power (kVA) 

Q factor


Let us compare the performance of two detuned reactors with different Q-factors based on tested values:


<table component>

Thus, by choosing the detuned reactor with high Q-factor we can minimise the power loss (conductor loss). The reduction in reactor loss can be as high as 1.5 W/kVAr. Consequently, heat generation (temperature rise) in Power Factor correction panels will also come down.

2. Impedance offered by reactors:


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:

Q Factor

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.


Resistance = ρI/A


Where, r = Resistivity, I = Length, A = Area of cross-section

  1. Resistance is directly proportional to resistivity. Conductor with lower resistivity (copper coil) can be chosen for winding of detuned reactors to get low DC resistance, thereby high Q-factor.
  2. For a relatively higher resistivity materials like Aluminium, the cross-sectional area of the windings to be increased to decrease the effective resistance.

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 other practical factors, any Q-factor value above 35 is preferable. 

Conclusion:


Choosing the detuned reactors with good Q-factor (Quality factor) can help to control harmonic amplification even more effectively. In addition to this, reactors with good linearity limit 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 section that Q-factor should also be given equal importance.