Technical Articles
It's a known fact that harmonics cause over loading of power capacitors and consequently reduce the life of power capacitors. Normally lot of emphasis is given only to %THD for assessing the harmonics level while the frequency spectrum (5th, 7th, 11th, 13th and so on) of the harmonics are not given due importance. The over-current (and hence the stress on the capacitors) will not only depend on the %THD value but also on the magnitude of individual harmonics, which can be clearly seen in the frequency spectrum. Following calculations prove the above statement.
Case 1:
Assumptions:
Important Formulae:
where XC is the capacitive reactance, f is the frequency, C is the capacitance IC=VC / XC, where IC is the capacitive current, VC is the voltage across the capacitor and XC is the capacitive reactance
VTHD = √Σ(Vi)2 / V1), where i=3 to 99
Calculations:
Using the superposition theorem, we can calculate the current contribution of individual harmonic voltages.
Case:
Assumptions:
Net current, I =2 I1 > (2)
Thus, in the above two cases, even the THD value remains same (25%), the net rms current (ref. Eq 1 and Eq 2) value is different depending upon the spectral values.
Hence THD value and detailed information of the frequency spectrum are necessary to predict the capacitor over-current. Harmonics study is the best way to get the frequency spectrum details and hence the exact over current value can be calculated.
Detuned Filters are a combination of series inductors and power factor correction capacitors that are meant to:
Typically a detuned filter has a series connected capacitor and reactor. The capacitor terminal voltage varies with respect to the tuning factor (%p) of the reactor. Tuning factor (%p) is the ratio of inductive impedance to the capacitive impedance (XL / XC). Common tuning factors of detuned filters are 7% and 14%.
Every series LC combination behaves capacitive below its tuning frequency [fres = 1/ (√2πLC)] and inductive above. The inductive element of the detuned filter is selected such that the tuning frequency of the filter is significantly lower than the lowest order harmonic frequency present in the system. The filter is thus ‘detuned'. The ratio of inductive reactance (XL) and capacitive reactance (XC) is known as the tuning factor.
A tuning factor of 7% implies XL / XC = 0.07.
The tuning frequency using tuning factor can be calculated as:
Where,
fs = Supply Frequency = 50 Hz
For tuning factor of 7%,
ft = 189 Hz.
As can be seen from the above graph, for all frequencies above the tuning frequency (ft), the combination will provide increasing impedance. The combination will not provide a low impedance path for harmonics that the capacitor did earlier, thus preventing harmonic amplification. Further as the tuning frequency of the combination is lower than the lowest order harmonic in the system, there is no question of resonance. At 50 Hz the combination behaves capacitive and power factor correction is achieved.
Can i add de-tuned filters in my existing panel?
The voltage that appears across the terminals of a capacitor increases the moment you connect an inductor in series with it. This can be illustrated by the below phasor:
VS :System Voltage; VC :Voltage across the capacitor; VL :Voltage across the inductor; I :current.
As can be seen VC > VS by an amount VL. Thus if reactors are to be added to an existing APFC panel, the capacitors will V have to be replaced with those capable of withstanding higher voltages. More over, the output of the capacitors will have to compensate for the reactive power that will be consumed by the reactor.
As can be seen from the above graph, for all frequencies above the tuning frequency (ft), the combination will provide increasing impedance. The combination will not provide a low impedance path for harmonics that the capacitor did earlier, thus preventing harmonic amplification. Further as the tuning frequency of the combination is lower than the lowest order harmonic in the system, there is no question of resonance. At 50 Hz the combination behaves capacitive and power factor correction is achieved.
Reactors are a major source of heat and existing panel may not have sufficient space or cooling arrangement to handle the heat generated by the newly installed reactors.
For these reasons, it is not advisable to add de-tuned reactors to existing APFC panels.
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