# Power Factor Correction Capacitors: Part 2

We covered some of the reasons for installing power-factor capacitors, along with some of the harmonics issues that can arise in such projects, in the first installment of this two-part article. Here we cover strategies for identifying and addressing potential problems.

Engineers need to consider an electrical system's harmonic content when using power-factor correction capacitors. These devices won't produce harmonics, but they can magnify existing harmonics under certain conditions. Harmonics are produced when non-linear loads drawing power in a non-linear fashion anywhere in a power-distribution system. The more any connected equipment's current waveform differs from the sine wave, the more total harmonic distortion (THD) the waveform contains. Non-linear loads can include:

%%POINT%%Adjustable speed drives, variable frequency drives

%%POINT%%Induction furnaces

%%POINT%%Uninterruptible power supplies

%%POINT%%Switch mode power supplies

%%POINT%%Programmable logic controllers

%%POINT%%Computers

Power-factor correction capacitors can be used effectively with non-linear loads when harmonic-resonant conditions in the system are avoided. However, minimizing these conditions requires engineers to first identify the distribution system's resonant harmonic %%MDASSML%% factoring in contributions from both the power-factor correction capacitor and any inductive loads. The resonant frequency can be calculated by the following formula:

h =

kVA sc / kVAR

H = The calculated system harmonic

kVAR = The rating of the capacitor

kVA sc = The short circuit power of the system

In addition to the 5thand 7thharmonics noted above, the 3rdharmonic should be avoided because it is the same harmonic level produced by switch-mode power supplies and other devices in a typical office environment. Also, harmonic values of 11 and 13 should be avoided because they match up to the characteristic harmonics of other non-linear loads that are commonly found in electrical-distribution systems.

The following is an example of the resonant frequency calculation:

Utility transformer 12.47 kV to 480 V, 3 phase:2,000 kVA @ 5.467% impedance

Fault current at the main electrical service: 2000 kVA / .831 / 0.05467 = **44,023 A**

Fault current in kVA at 480 V, 3 phase: 44,023 * .48 kV * sqrt (3) = **36,583 kVA**

Size of power factor correction capacitor: **300 kVAR**

**System harmonic calculation:** h =

36,583 / 300 = **11.04 (11thharmonic)**

**This calculation indicates that the system harmonic is at the 11thharmonic. As a result, a resonant circuit could develop if the distribution system contains the 11thharmonic in any significant amount, causing the capacitor to overheat and, possibly, explode. In this case, if the capacitor size was changed, the harmonic value that produced the resonant circuit also would change.**

In the next example, the capacitor is increased to a 350 kVAR.

Utility transformer 12.47 kV to 480 V, 3 phase:2,000 kVA @ 5.467% impedance

Fault current at the main electrical service: 2000 kVA / .831 / 0.05467 = **44,023 A**

Fault current in kVA at 480 V, 3 phase:44,023 * .48 kV * sqrt (3) = **36,583 kVA**

Size of power factor correction capacitor: **350 kVAR**

**System harmonic calculation:** h =

36,583 / 350 = **10.2 (10thharmonic)**

This calculation indicates that the system harmonic is approximately at the 10thharmonic. The 10thharmonic is not a commonly produced multiple of the fundamental frequency in switch-mode power supplies or other harmonics-producing loads found in commercial or industrial facilities. By reducing the size of the capacitor, the potential of producing a resonant frequency from system harmonics has been reduced.

Remember, however, that when decreasing the size of the capacitor to avoid a resonant frequency, it's important to ensure that the resized unit still raises the system power factor enough to avoid low power-factor penalties. Engineers taking the opposite tack by increasing the capacitor to avoid a resonant frequency must ensure the capacitor does not over-correct or cause a leading power factor at the point of utility connection.

Also, capacitor resizing does not always remove the resonant frequency because normally some portion of the applied kVAR is switched on and off as load profile changes. To eliminate a resonant frequency for all potential levels of kVAR power-factor correction, the calculation of system harmonics performed above should be duplicated for each level of potential capacitive correction.

Other tactics

Resizing capacitors isn't the only option for addressing potential resonance points. A number of alternatives exist for protecting installed capacitors in these situations.

**Provide harmonic filters.** Tuned harmonic filters can be used to filter harmonics at a specific location in the electrical system. With a harmonic filter, a capacitor is connected in series with an inductive load so that the resonant frequency of the filter is equal to the harmonic frequency the system designer is intending to eliminate. Tuned filters should not be added to the electrical system without a thorough analysis of the entire electrical system's harmonic content. Because the exact amount and frequency of harmonic current in the electrical system and the amount ofkVAR capacitance can change as loads switch on and off, it may be difficult to determine the correct harmonic filter for all of the system dynamics.

**Provide blocking inductors.** Inserted line inductors on the conductors feeding the power-factor correction capacitor can be sized to block certain harmonic currents in the electrical system. This mitigation method only protects the capacitor from the damaging effects of harmonics, but does not remove the harmonics from the electrical distribution system. As with the other methods of mitigation, an electrical-system study is required to determine the correct ratings for the capacitor and inductors.

Understanding the economics

It has been my experience with the low-power-factor penalties in Seattle that when the power factor readings are below a range of 0.85 %%MDASSML%% 0.90 and a single capacitor is used and no stepping or harmonic filtering is required, normally a capacitor bank would provide a return on investment of 2-4 years. If capacitor stepping and/or a harmonic filter are required, return on investment can be significantly longer. A rough order-of-magnitude cost of a fixed capacitor is $25 per kVAR and about $40 per kVAR for a stepped capacitor.

The calculation below (Diagram #3) illustrates how a 200-kVAR capacitor improved the power factor at the building from a range of 84% to 88%, to a power factor in the range of 98% to almost unity (1.0). The existing power factor as illustrated over a one-year period has remained in a narrow window. In this case a static capacitor can work to improve the power factor to a level above 97% and below a leading power factor. In Seattle, the building is only penalized if the power factor drops below 97%. The reduction in penalty charge from the utility is $2,513. This yearly savings can be utilized with the total cost of installation to determine a time for the return on the investment. After the investment is returned, all additional savings go right back to the owner.

Placement issues to remember

Capacitors placed in the electrical distribution system will increase the power factor of the system and will also reduce the amperes and kVA in the system. However, it's important to note that the current reduction will take place from the capacitor installation point back to the utility point of connection, not forward within the distribution system, itself. Therefore capacitors placed at the main service will improve the power factor and reduce the utility charges for low power factor, but will not reduce the extra current flowing in your system caused by low power factor.

By placing a switched capacitor near each large motor, the electrical distribution system will experience less I squared R losses, and more electrical capacity can be made available as well as improving the power factor at the utility interface point.