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Power Factor, Capacitors, Harmonic Filters, and Resonance — Part 1

Feb 1, 2009 12:00 PM, By Tom Shaughnessy, PowerCET Corp.

IEEE 519 provides a way to estimate harmonic resonance for a facility before capacitors are installed. You can use the following equations to estimate harmonic frequency:

h_r = √(MVA_sc 4 Mvar_cap) = √(X_c 4X_sc)

Where,

h_r = Resonant frequency as a multiple of the fundamental frequency

MVA_sc = Short circuit value for the service

Mvar_cap = Capacitor rating at the system voltage

X_c = Capacitive reactance of the capacitor bank at the fundamental frequency

X_sc = Short-circuit reactance at the substation.

The main determinant of short-circuit current for a facility is the inductance of the electric utility transformer serving it. The electric utility may be able to provide you with the transformer inductance as well as the short circuit current. If this is the case, then calculating potential resonance is much easier. However, if the transformer inductance is not available, then you can approximate the leakage inductance by using the transformer impedance along with the rated voltage and current values:

Find the full load capacity: Transformer VA ÷ 3 = single-phase VA

Find the single-phase circuit capacity (A): Single-phase VA ÷ L-N voltage rating

Find short circuit capacity (base impedance in ohms): Single-phase current divided by rated transformer impedance

Find the inductance (L): base impedance (ohms) ÷ (2 × ϖ × 60)

If the above estimation processes indicate that the use of a capacitor bank poses a resonance risk, you can tune a simple bank to a nonharmonic frequency by adding series inductance (Fig. 7).

In reality, the aforementioned estimation processes are the basic building blocks for many passive harmonic filters. As noted earlier, the selection of the L and C components determines the frequency to which the filter is tuned (see Equation 1 on page 14), but you must be careful because the upstream circuit inductance is present, and the combination of upstream inductance interacting with the filter inductance creates a secondary filter response point, as described by the following equation:

h_r = 1 ÷ 2ϖ√[(L_upstream + L_filter) × C]

Although this secondary response can further serve to reduce the filter response to upstream harmonics, it can also create an unwanted resonant response characteristic.

In Part 2 of this article, we'll discuss filter design and various system parameters that affect filter performance.

Shaughnessy is vice president, PowerCET Corp., Santa Clara, Calif. He can be reached at TomS@powercet.com.

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© 2012 Penton Business Media, Inc.

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