# Power Factor Correction Capacitors: Part 1

Incorporating power-factor correction capacitors into a building’s electrical system can mean life-cycle cost savings and increased system capacity for owners. These devices also may help developers achieve Leadership in Energy and Environmental Design (LEED) certification. However, successful installation depends on identifying potential problem, such as over correction (leading power factor) and harmonic currents that could cause capacitor failure.

Power factor defined

Mathematically, power factor is the ratio between kW and kVA (PF = kW / kVA). kW is the “real power” that actually does the work, kVA is the apparent power and kVAR is the reactive power. In an inductive load, such as a motor, active power performs the work, and reactive power creates the electromagnetic field. kVA is the vector sum of both the reactive and the active power. Power factor measures how efficiently the current is being converted into useful “real” work—with a low power factor, more electrical current will be required to provide the same amount of real power.

Consider the following induction motor example:

If a motor draws **150 kW** of real power and **187.5 kVA** of apparent power, the power factor is **80%.** 150 kW / 187.5 kVA = **80%.**

*The reactive power is equal to the square root of 187.5 kVA (squared) minus 150kW (squared)* *Ö* *(187.5 112.5 kVAR (reactive power)*

What size of capacitor is required to improve the power factor to **97%.** The kW (real power) will remain the same. The apparent power is equal to 150 kW / 0.97 = 154.64 kVA

*The reactive power is equal to the square root of 154.64 kVA (squared) minus 150kW (squared)* *Ö* *(154.64 37.6 kVAR (reactive power)*

The required kVAR of the capacitor is equal to the difference between the kVAR at 80% power factor and the kVAR at 97% power factor. **112.5 — 37.6 = 74.9.** The closest common size capacitor is a **75 kVAR.**

A **75 kVAR** capacitor will improve the system power factor from **80% to 97%.** Assuming that the motors is operating at 480 volt, 3 phase, the total current in the system would drop from 226 amps (187.5 kVA / .831) to 186 amps (154.6 kVA / 0.831), a total reduction of approximately 40 amps. This reduction in system current will reduce the I squared R losses and will allow more capacity for future loads in the electrical system.

**Diagram #1**

** In Diagram #1 above, a purely resistive load, like an incandescent light source or a resistive heater, the current is in phase with the voltage. The power is always positive. Power is always being dissipated by the resistive load. **

**Diagram #2**

** In Diagram #2, a purely inductive load, the current lags the voltage by 90 degrees. Power alternates equally between cycles of positive and negative. This means that the power is being alternately absorbed and returned to the source. If the power source is a mechanical generator, it would take almost no net mechanical energy to turn the shaft because no power would be utilized by the load. **

Many electric utilities charge building owners a penalty for a low power factor. In the city of Seattle for instance, Seattle City Light will begin charging the building owner $0.14 per kVAR Hours (kVA of reactive power x hours) for each month that the power factor drops below 0.97. In addition, the utility can stop serving the building owner if the power factor drops below 0.85% power factor.

Stepping capacitors are required to correct large swings in power factor. Determining the size and type of capacitor needed begins with utility-bill review, to understand both the total kW and power factor. In the example of Seattle City Light, a power factor of between 0.97 and 1.0 (unity) is the goal. The utility will not allow any leading power factor. In addition, the Seattle City Light requirements indicate that “The customers corrective equipment shall be switched with the load so that at no time will it supply leading reactive kVA’s to the department’s distribution system”.

Leading power factor is caused by over correction or too much capacitance in the electrical distribution system. Over correction can occur if there are large power factor swings in the electrical distribution system and if a static capacitor is utilized. Stepping capacitors are the only solution for maintaining near-unity power factor in facilities that would otherwise experience large power-factor swings.

Staying out of harmonics’ way

Harmonics can damage power-factor correction capacitors, so a successful capacitor installation may require harmonic filtering—either active harmonic filters, passive harmonic filters, flux shifting transformers or other mitigating tactics. Without such protection, a tuned resonant circuit could cause the capacitor to fail, or even explode. However, the added expense can drive overall costs up significantly.

Capacitor failure can, in many cases, be directly linked to harmonic content in the electrical-distribution system. Capacitors are low-impedance devices susceptible to harmonics, and large harmonic currents in the electrical system can over heat the units, causing untimely failure.

A capacitor bank, itself, can contribute to harmonics problems. Parallel resonance between the capacitor bank and the source impedance can cause electrical-system resonance, resulting in higher-than-typical voltages and currents within the overall distribution system. Inductive and capacitive reactance vary directly, and in an opposite manners, with changing frequency: At higher frequencies, inductive reactance increases and capacitive reactance is reduced.

Formulas for inductive and capacitive reactance:

XL (inductive reactance) = 2π f L

XC (capacitive reactance) =

[Note: f= frequency]

Most problems in industrial facilities with large motors and variable-frequency drives occur when the resonant frequency approaches the 5th or 7th harmonic. These harmonics are common distribution systems incorporating 6-pulse IGBT adjustable speed drives. In these cases, capacitor banks should be resized to shift the resonant point to another frequency.

Examining the distribution system’s harmonic content and sizing the capacitor so the resonant point is not at common harmonic levels will ensure that the correct capacitor system will be specified and installed. However, determining the power system’s resonant frequency requires analysis and modeling based on equivalent electrical circuits.

In the second part of the story, we’ll cover strategies for identifying potential harmonics problems and how to address them.

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