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Tech Tip 07

Avoiding Steady-State Harmonic Resonances When Installing Capacitors


  • Installing capacitors
  • Capacitor fuse blowing
  • High levels of harmonic distortion
  • More than 20% of load is static power converters


  • Capacitors resonate with system inductance


  • Install capacitors as harmonic filter
  • Relocate capacitor bank
  • Install capacitors as harmonic filter
  • Size capacitor, capacitor step sizes to avoid characteristic harmonic load currents


To operate power systems more efficiently, utilities and their customers are installing numerous capacitor banks. Many of the capacitor banks are being installed within customer's premises. This Tech Tip will review the analysis necessary to prevent steady-state harmonic resonances when installing capacitors on a utility system or inside a customer facility. Note that further investigation is required to prevent other potential problems such as capacitor transient amplification.


Calculating the resonant frequency created with a capacitor and system inductance is surprisingly simple. As shown in Equation 1, simply calculating the square root of the three phase short circuit MVA divided by the capacitor MVAR will provide the resonant harmonic, hf, for the system under study.

 Calculate the resonant frequency


Consider a case where a 1200 KVAR capacitor is to be installed on a 12.47 kV system at a location where the three phase short circuit current is 2800 amps.

 Distribution line example

Resonant conditions near the 3rd, 5th, 7th, 11th, and 13th harmonic are often the most troublesome since these are common load currents found on the distribution system. Installing a 900 KVAR capacitor at this location would move the resonance to the 8.2nd harmonic, farther away from the characteristic harmonic load currents.


Consider a case where installing 600 KVAR capacitors in a customer facility is necessary to improve the customer's power factor to 95%. The capacitor will be switched in four steps of 150 KVAR each. The three phase short circuit current is 18000 amps at 480 volts.

Resonance calculation steps (600 KVAR energized):

Customer facility example 

Installing these capacitors could cause resonance problems if the customer has six pulse rectifier loads (adjustable speed drives, arc furnaces, etc.) These loads require significant 5th, 7th, 11th, and 13th harmonic currents. With 600 KVAR energized, the 5th harmonic load current would resonate with the system inductance and 480 volt capacitor. With two steps on-line (300 KVAR), the 7th harmonic current would resonate with the system inductance and 480 volt capacitor. Installing these capacitors as a harmonic filter or altering the amount of capacitance would be viable alternatives.

The information and diagrams presented herein are for general educational purposes only, and should not be relied upon as instructions for customer self-wiring. Customers should at all times seek the assistance of qualified electricians or utility personnel for all wiring projects.