#### Power Factor Correction Solutions

Power factor - The power factor of an AC electric power system is defined as the ratio of the real power flowing to the load to the apparent power,[1][2] and is a dimensionless number between 0 and 1 (frequently expressed as a percentage, e.g. 0.5 pf = 50% pf).

Power Factory Theory and Additional Cost Incurred

An inefficient and costly path electricity takes from the source to a load can be described as a power factor. Increasing the power factor can impact a factory, facility, or home in many ways. A Low power factor requires an increase in the electric utility’s transmission and distribution capacity in order to handle the reactive power component caused by inductive loads. Having a power factor of anything below one essentially means that unwanted electricity is being fed back to the Electric Supply Company. Most utilities charge large customers with power factors less than about 0.95 an additional fee per kVAR. After interviewing Mrs. Welch from National Grid Electric Supply Company I learned that there is an additional charge per kVAR (Kilo Volt Amps Reactance) if the facility’s power factor is below .95. Let me make myself clear and that is “Only the Electric Supply Company” applies an additional charge per kVAR, which is derived from the power factor. The Electric Distribution Company does not apply an additional charge for a power factor below .95. A kVAR calculation is shown below.

KVAR = (0.746 x Bhp) / ((Eff. x PF) x 1 - (PF)squrared

Where kVAR = Reactive KVA

Bhp = Horsepower Output

Eff. = Operating Efficiency

PF = Power Factor Expressed as a decimal

Note that the reactive KVA may be either leading or lagging (Peerless Pump.com, July, 2006). The power factor is defined as the ratio of the real power flowing to the load to the apparent power.

Increasing your power factor will increase your internal electrical system’s capacity. An uncorrected power factor will cause increased losses in your electrical distribution system and limit capacity for future expansion. With low power factor loads, the current flowing through electrical components is higher than necessary to do the required work. This results in excess heating, which can damage or shorten the life of equipment. Increasing the power factor will minimize or decrease voltage drops at the point of use. Voltages below equipment specifications will cause a reduction in efficiency, an increase in current, and a reduced starting torque in motors. Under-voltage reduces the load motors can carry without overheating or stalling. To become electrically efficient or better your power factor we need to understand what a power factor is; how to measure and calculate it, and finally how to correct it.

What is a power factor? The power factor is defined as the ratio of true power or watts to apparent power or volt amps. The power factor is also said to be the measurement of how close the given load is to a purely resistive load. In order to explain a power factor a few terms must be defined.

kVA (kilo-Volt-Amperes): kVA is a term for rating electrical devices. A device's kVA rating is equal to its rated output in amperes multiplied by its rated operating voltage. In the case of three-phase generator sets, kVA is the kW output rating divided by 0.8, the rated power factor. kVA is the vector sum of the active power (kW) and the reactive power (kVAR) flowing in a circuit. (http://www.maxim-ic.com/glossary/definitions.mvp/term/kVA/gpk/574)

kVAR (kilo-Volt-Amperes Reactive) is the product of the voltage and the amperage required to excite inductive circuits. It is associated with the reactive power which flows between paralleled generator windings and between generators and load windings that supply the magnetizing currents necessary in the operation of transformers, motors and other electromagnetic loads. (http://www.sommersgen.com/basics/glossary.php) National Grid defines kVAR as the power used to magnetize the field of motors, transformers and ballasts for lighting fixtures.

Real power is the actual amount of present power, which is expressed in watts. Real power is the rate of supply of the actual power doing work.

Apparent power is the product of rms voltage and rms current. When the impedance is a pure resistance, the apparent power is the same as the true power or real power. Conversely, when reactance exists, the apparent power is greater than the true power. The vector difference between the apparent and true power is considered reactive power. To determine whether or not the apparent power is the same as the real power we need to observe the voltage and current within the circuit.

Voltage and current are supplied to a load at the same time from the source, but depending on the circuit or load depends on whether or not there is a lag or lead between the voltage and current when power is consumed. A power factor is usually stated as “leading” or “lagging”, which shows the sign of the phase angle. The power factor is one when the voltage and current are in phase. When the power factor is zero the current leads or lags the voltage by 90 degrees. The power factor calculation is:

PF = P(Real Power) / S(Apparent Power)

In a purely resistive circuit the power factor is 1; therefore, the phase angle between the current and voltage is 0. In a purely resistive circuit there is no lead or lag between voltage and current. Incandescent lights and heating elements are examples of a purely resistive component. Figure 1 shows the voltage to current relationship in a purely resistive circuit.

Figure 1 - Resistive Load

In a purely capacitive circuit the power factor is 0; therefore, the phase angle between the current and voltage is 90 degrees. In a purely capacitive circuit the current leads the voltage by 90 degrees. Figure 2 shows the voltage to current relationship in a purely capacitive circuit.

Figure 2 - Capacitive Load

In a purely inductive circuit the power factor is 0; therefore, the phase angle between the current and voltage is 90 degrees. In a purely inductive circuit the voltage leads the current by 90 degrees. Figure 3 shows the voltage to current relationship in a

purely inductive circuit.

Figure 3 - Inductive Load

After the reader has determined that there is a poor power factor, how do we correct it? Theoretically a capacitive circuit is 180 degrees or completely opposite to an inductive circuit; therefore, to combat a low power factor due to induction you would use capacitors. Applying capacitors or a capacitor bank within the inductive circuit will cancel out or minimize the reactance of the circuit. Solve low power factor problems by adding power factor correction capacitors to your electrical network or distribution. Power factor correction capacitors work as reactive current generators which will provide the needed reactive power (kVAR) to the power supply. Capacitors end up supplying their own source of reactive power; therefore, the total amount of apparent power (kVA) supplied by the utility will be less. Power factor correction capacitors reduce the total current drawn from the distribution system. A power vector triangle comparison (Figure 5) can better explain the effects capacitance will have on an inductive circuit a power. Before showing the vector comparison the investigator would like to explain and show how the calculations are derived (Figure 4).

Real power (P)

Reactive power (Q)

Apparent Power (|S|)

Phase of Current (φ)

The apparent power is the vector sum of real and reactive power.

PF = Real Power (kW) / Apparent Power(kVA)

|PF| = |S| |cosφ|

Figure 4 - Power Triangle

Figure 5 shows three power vectors and all three have the same apparent power of 1000KVA. Starting at the bottom vector with a real power of 700KW and a phase angle of 0.7 we can calculate a reactive power of 700KVAR. Increasing the power factor from 0.7 to 0.8 will take 100 KVAR of capacitors; therefore, the calculated KVAR will decrease to 600. Once again increasing the power factor from 0.8 to 0.9 will take 160 KVAR of capacitors, but will decrease the KVAR to 400. Finally to go from 0.9 to 1 will take 440 KVAR of capacitors, which will cancel out the reactance of the circuit.

One observation made from this exercise is that the greater the power factor the greater the increase in the capacitors needed to do so. In order to go from a power factor of 0.7 to a 0.8 it only took 100 KVAR of capacitors, but to go from a power factor of 0.9 to 1 it takes 440 KVAR of capacitors.

Figure 5 - Power Triangles

## Power Factor Correction and Cost Savings

The Electric Supply Company prefers a clean power going to the customer and no power back from the customer. Having a power factor of anything below a one essentially means that unwanted electricity is being fed back to the Electric Supply Company. The Electric Supply Company will then apply an extra charge per kVAR. For example, Company A was charged $1.02 per kVAR and used 1,203 kVAR for the month of March. Having a power factor below.95 tacked on an additional $1,227.06 for the month of March! The reader can completely avoid this additional fee by increasing your power factor to a 0.95 or greater. Saving money is not the only benefit to correcting the power factor. Correcting the power factor may be costly, but the pay back may exceed the initial investment over a period of time. As mentioned earlier, Company A was penalized $1,227.06 for the month of March for having a power factor below 0.95. Now multiply that monthly penalty by 12 to get an annual penalty, which equates to $14,724.72. Moreover, when the power factor is increased the loss or I^2 R is decreased; therefore, less power is consumed overall. With consuming less power the monthly bill will be less because, the kW/hr usage was less.