Technical Articles
Many industries may not generate high harmonics. Sometimes harmonic resonance occurring between power capacitors and transformers causes very high magnification of harmonics. This causes increased rate of failures and over-heating of electrical equipments. This article briefs about the basics of harmonic resonance, a practical case study and solution to avoid resonance.
In a system with inductive (XL) and capacitive (XC) impedances, resonance can happen at one particular frequency (resonant frequency, FR). At this point XL will be equal to XC and the net impedance will be very low. Hence, at resonance point, the magnitude of the current (with frequency FR) will be maximum and only inherent resistance in the network would limit the current.
In practical network, the resonance is possible because of one of the following reasons:
Typically, the inductance (L, of the transformer) in the system will remain almost constant, but the capacitance(C) is varied (in steps) as per the requirement to maintain higher power factor. So, when the capacitance increases the resonant frequency (FR) drops, as FR is inversely proportional to square root of capacitance.
Resonant frequency,
The lower resonant frequency is dangerous, as it may match with any of the predominant harmonics and causes more damage. Let us see a practical case study of resonance happening between variable PFC capacitors (C) and transformer.
Consider an industry with 1000 kVA transformer of %Z = 5.67% and 750 kVAr APFC panel. The resonant frequency can be calculated from the below formula:
Where,
FS is the System frequency = 50 Hz
kVASC is the short circuit power of the transformer
kVAr is the power rating of the capacitor connected under the transformer for power factor correction.
Case 1: When 145 kVAr is connected to the system,
This frequency exactly matches with 11th harmonic (550 Hz) and results in resonance. Following is the harmonics measurement that depicts the 11th harmonic resonance, where it increases from less than 5% to 25%. This huge amplification will damage the capacitor and other equipments.
Once again, this frequency perfectly matches with 5th harmonic. Typically 5th harmonic is the least order harmonic with higher magnitude (6 pulse drives). Resonance at this harmonic order would result in even worse damage than the case 1.
From the above cases it is evident that any peculiar problems like frequent failure of capacitors (worst case THD may not be revealed during measurement), nuisance tripping of MCCBs, frequent blowing of fuses and over-heating of busbars are may be because of harmonic resonance. The failure happens only at a certain moment and during troubleshooting the issue, the network may not reveal harmonic resonance. Hence at times, finding the root cause of any such failures would be very difficult.
Solution for harmonic resonance is to detune, by using a reactor in series with each capacitor. This detuned filter will forcefully create one resonant frequency, so that the combination offers higher impedance for high frequency harmonics. For example, installation of 7% reactor with each capacitor in APFC panel, will create tuning frequency at 189 Hz. Hence, resonance at harmonic frequencies (5th harmonics and above) can be avoided. Moreover, all the harmonics having frequency above 189 Hz (i.e., from 5th harmonics onwards) will lie in inductive region, where the impedance increases when the frequency increases (XL =2Ï€FL One important point to note is that all the capacitors in the industry must have similar series inductor; else the overall tuning frequency may not be at 189 Hz.
Abhinav L Purkar,
Manager Product Management & Marketing (PMM)Abhinav Purkar is a Product Management, Marketing, and Application Engineering professional with over 10 years of experience in the Power Quality domain. He has extensive expertise in power quality analysis, harmonic mitigation, reactive power compensation, energy efficiency, and electrical system optimization, helping customers improve system reliability and operational performance. With proven experience in product lifecycle management, market development, portfolio growth, and go-to-market strategy, Abhinav has successfully driven initiatives that enhance customer value and strengthen market presence. His strong technical foundation, combined with strategic business acumen, enables him to bridge the gap between customer requirements and innovative product offerings.
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