## Question:

I am looking for the following information regarding power factor correction for a utility distribution system:

- How to compute apparent power (kVA) from measured power (kW) and power factor (PF) data
- Means of applying PF compensation capacitors and how to size them

## Answer:

In addition to the information you requested, I have included some additional information about the precautions that should be taken with respect to installing power factor correction equipment and the methodology in where to place it.

### How to Compute kVA

The concept for power factor can be described by the "power triangle," which is defined by three measurable parameters: apparent power (kVA), measured working power (kW), and reactive power (kVAR). Typically some if not all of these values are available on a facility’s utility bill. However, if some values are not present, they can be back calculated through trigonometry if at least two are available. Furthermore the power factor value in percent or decimal format offers additional ease in calculating unknown values.

It should be noted that when power factor is corrected and results in savings from power factor penalties, it does not save significant amounts of energy. Correction at the switchyard or plant service entrance does reduce the amount of current delivered, and if the working power (kW) remains constant, there are no energy savings (which would be measured in kWh). In some cases where a utility bills based on monthly kVA demand, power factor correction can reduce demand charges; thus the facility consumes the same amount of energy, but pays a lower monthly bill.

The defining equations for power factor can be rearranged such that, if the power factor (PF) and measured working power (kW) are available, the apparent power (kVA) can be calculated:

PF = cos θ = kW/kVAand

tan θ = kVAR/kWWhere,

PF = Power Factorand when rearranged, the apparent power can be evaluated:

θ = Power Factor Angle (leading or lagging)

kW = Measured Power or Demand (can be calculated)

kVA = Apparent Power

kVAR = Reactive Power

NOTE: The calculator being used for the calculations must be set on degrees or DEG, and not radians or RAD.

kVA = kW/PF

For instance if a facility has a 2.5 MW load with a power factor of 72%, the apparent power can be calculated as shown below:

Apparent Power(MVA) = MW/PF = 2.5 MW/0.72 = 3.47 MVA

Although having a working power of 2.5 MW, due to inductive motor loads, the facility has an apparent power of 3.47 MVA. If the inductive loads were corrected to 95% with power factor compensation devices such as a capacitor bank, the new MVA would be significantly reduced:

Apparent Power(MVA) = MW/PF = 2.5 MW/0.95 = 2.63 MVA

When comparing the original with the corrected power factor scenarios, the improved case would require much less current to perform the same facility operations (at the same voltage and working power):

Reduced Current Draw (%) = (MVA_existing/MVA_improved - 1) × 100% Reduced Current Draw (%) = (3.47 MVA/2.63 MVA - 1) × 100% = 31.9%

### Sizing and Installing Capacitors for Power Factor Correction

To size and install a capacitor for power factor correction, additional information needs to be known, such as the reactive power rating of the capacitors, the loads that they will be compensating, and if those loads have a constant or variable duty.

From the above, if the facility demand is 2.5 MW, and if the power factor is going to be corrected from 72% to 95%, a certain amount of capacitance is needed to generate the required amount of reactive current such that it reduces the amount supplied by the utility. From the original equations for power factor, the amount of capacitor kVAR needed can be calculated:

tan θ = kVAR/kWand when rearranged, the reactive power can be evaluated:

kVAR = tan θ × kW

NOTE: To find the power factor angle θ, the inverse cosine function must be applied to the power factor number:

θ = cos^(-1) PF

Below is the calculation to determine the existing and improved power factor angles and their respective reactive power values:

θ_existing = cos^(-1)(0.72) = 43.9455 θ_improved = cos^(-1)(0.95) = 18.1949

and

kVAR_existing = tan(43.9455) × 2,500 kW = 2,410 kVAR

kVAR_improved = tan(18.1949) × 2,500 kW = 822 kVAR

The difference of the existing and improved kVAR cases results in an installed capacitor bank that has a value of 1,588 kVAR. To find the appropriate ratings for individual inductive loads, the individual equipment manufacturers or distributors of the equipment should be consulted for precautions, ratings, and design specifications.

In the guide *Design It Right, Power Factor Correction: A Guide for the Plant Engineer* you can find power factor correction tables for different motor types (for PF correction and individual motors) and a general table that can be used to generate the numbers to calculate kVAR values for a larger circuit. These tables between pages 10-15 streamline the above calculations. By knowing the existing and the desired power factors, you can find multipliers that can be multiplied by the plant kW to find the kVAR needed to achieve the desired power factor value. For the example shown above, tables show a multiplier is 0.635, which when multiplied by the plant demand of 2,500 kW yields a value of 1,587.5 kVAR, which when rounded up is 1,588 kVAR, the same value calculated using the defining formulas.

Before sizing a capacitor bank the following items must be accounted for to avoid operational problems and/or damage to equipment and/or personal injury to personnel:

- Type of Load and Location

Power factor is reduced by inductive loads. These loads require a magnetic field to operate, which includes equipment such as transformers, gaseous tube lighting ballasts, induction furnaces/melters, and induction motors. The equipment manufacturer specifications should be consulted to see if damage can occur if power factor compensation is installed. For instance when power factor correction capacitors are installed, there may be peripheral effects on the surrounding system, with the potential of surges and transients that can damage sensitive electronics and equipment.

If power factor compensation is to be installed at individual motors, capacitors can be installed and switched with the motor; however if there are multiple motors on a single circuit, they should be installed on the bus.

Regardless of the type of power factor correction capacitors, to achieve utility bill cost reductions the capacitors must be installed between the inductive load and the utility meter. If the utility is concerned about the low power factor, instead of installing on the high voltage side of the transformer, it would be reasonable for them to invest in correction on the plant side.

- Motor Loads

If the inductive loads are induction motors, power factor correction capacitors should not be installed directly onto the motor circuits of the following conditions:

- Solid-state starters
- Open-transition starting
- Multi-speed motors
- Motor reversing
- High-inertia loads
- Operations such as: repetitive switching, jogging, inching, or plugging
- Variable frequency drives (as capacitors tend to surge and can damage the sensitive power electronics used in those devices). Furthermore, voltage transients become more prominent when capacitors are switched on and off, thus switched resistors are deployed to protect the equipment during variable loading conditions.

- Load Consistency

Before choosing the type of capacitor system to install, the load of the facility should be base-lined to determine how consistent it is. If the load is relatively constant, a non-switching capacitor bank can be installed; however, if the load varies, a switching capacitor bank would be recommended.

- Circuit Protection

When installing the capacitors, the manufacturers and/or distributors of the capacitors and the existing equipment should be consulted for any precautions pertaining to interactions between the equipment and to see if any additional safety measures need to be considered for the installation.

Once the above precautions are taken, then a capacitive load can be sized and installed to the system.

For motors it should be noted that the horsepower, nominal RPM, voltage, efficiency class, and enclosure ratings are values that dictate the suggested maximum capacitor ratings for kVAR compensation.

For electrical infrastructure and protection equipment, capacitors are also sized according to their respective kVAR ratings. Also, when any power factor correction is implemented, because the ampacity will be increased (capacity for the circuit to draw additional current with respect to the current draw prior to the correction), ratings and settings of protective equipment on the same circuit should be analyzed to ensure that they are sized properly to protect the components and the system from voltage surges.

Below I’ve listed some additional resources that discuss capacitor sizing and illustrate ways to correct power factor:

- Eaton
*Power Factor Correction Calculator* - National Institute for Building Sciences:
*Capacitors for Power Factor Correction* *Design It Right, Power Factor Correction: A Guide for the Plant Engineer*

Topic: Electrical Systems--General

Topic: Electrical Systems--Distribution

Topic: Electrical Systems--Power Factor