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# Power System Resonance

Hot vibes can result when harmonics and capacitors get together

Is it possible to install “Power Factor Correction Capacitors” and have PF get worse? It certainly is, and a starting place to understanding this puzzle lies in the distinction between Displacement PF (DPF) and Total Power Factor (PF). The penalty for not understanding the difference can be blown capacitors and wasted investment. Total PF and Displacement PF are the same in one basic sense: they are the ratio of Real Power to Apparent Power, or Watts to VA. DPF is the classic concept of power factor. It can be considered as the power factor at the fundamental frequency. Total Power Factor, abbreviated to Power Factor (PF), now includes the effects of fundamental and of harmonic currents (it is also referred to as True PF or Distortion PF). It follows that with the presence of harmonics, PF is always lower than DPF and is also a more accurate description of total system efficiency than DPF alone.

Strictly speaking, the term “Power Factor” refers to Total PF, but in practice can also be used to refer to DPF. Needless to say, this introduces some confusion into discussions of power factor. You have to be clear which one you’re talking about.

Displacement Power Factor

Lower DPF is caused by motor loads which introduce the need for Reactive Power (Volt-Amp Reactive or VARs). The system has to have the capacity, measured in Volt-Amps (VA) to supply both VARs and Watts. The more VARs needed, the larger the VA requirement and the smaller the DPF. The cost of VARs is accounted for in a power factor penalty charge. Utilities often levy additional charges for DPF below a certain level; the actual number varies widely, but typical numbers are 0.90 to 0.95. To reduce VARs caused by motor loads, power factor correction capacitors are installed. Upstream system capacity, both in the plant and at the utility level, is released and available for other uses. Historically, this has been the gist of the PF story: a relatively well-known problem with a relatively straightforward solution.

Harmonics and Capacitors

Harmonics have had a dramatic impact on our approach to Power Factor correction. The motor and capacitor loads described above are all linear and for all practical purposes generate no harmonics. Non-linear loads such as ASDS, on the other hand, do generate harmonic currents. Take a plant which is step-by-step putting adjustable speed drives on its motor loads. ASDs generate significant harmonic currents (5th and 7th on six-pulse converter drives). Suddenly the fuses on existing PF correction caps start blowing. Since these are three-phase caps, only one of the three fuses might blow. Now you’ve got unbalanced currents, possibly unbalanced voltages. The electrician replaces the fuses. They blow again. He puts in larger fuses. Now the fuses survive, but the capacitor blows. He replaces the capacitor. Same thing happens. What’s going on? Harmonics are higher frequency currents. The higher the frequency, the lower the impedance of a cap (XC = 1/ 2pfC). The cap acts like a sink for harmonic currents.

Power System Resonance

In a worst-case scenario, the inductive reactance (XL) of the transformer and the capacitive reactance (XC) of the PF correction cap form a parallel resonant circuit: XL= XC at a resonant frequency which is the same as or close to a harmonic frequency. The harmonic current generated by the load excites the circuit into oscillation. Currents then circulate within this circuit which are many times greater than the exciting current. This so-called “tank circuit” can severely damage equipment, and it will also cause a drop in power factor. Perversely, this resonant condition often appears only when the system is lightly loaded, because the damping effect of resistive loads is removed. In other words, we have what the audio buffs call a “high Q” circuit.

Imagine coming to work on a Monday and seeing the insulation on your cables melted off. How can this happen over a weekend when there was hardly any load on the system? Has Ohm’s Law been overruled? Not quite. Your power system just spent the weekend tanked out on the Harmonics. It was quite a party, but now comes the clean-up.

The correct solution path starts with measuring and mitigating the harmonics generated by the drives. (One useful tool for measuring harmonics and capacitance is the Fluke 43B Power Quality Analyzer.) Harmonic trap filters would generally be called for. These trap filters are installed locally on the line side of the drive. Their effect is very much like the traditional PF correction cap, in two senses: they reduce DPF as well as PF, and also they localize the circulation of the problem harmonics (generally the 5th). Harmonics mitigation and traditional DPF correction should be addressed as one systems issue. In other words, manage Total PF, not just DPF.

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