Power Factor

Published On: May 22, 2023By Categories: Engineering Your Business, Pumps and Water Systems

Part 1. Low Power Factor and Correction Methods

By Ed Butts, PE, CPI

We have reviewed electrical circuit protection methods, primarily for electric motors, this year. We are now going to continue the topic but deviate somewhat and cover electrical system power factor, what causes a low power factor, and the methods used to increase it.

What Is Power Factor?

Figure 1. Illustration for power factor in Example 1.

In an alternating current (AC) power system, the power factor (PF), denoted by the Greek letter lambda (λ), is an important parameter that defines how efficiently electrical power is being utilized by the load. It is a rational number between –1 and 1 but has no actual unit. The typical power factor for an unconditioned water treatment plant and pumping station ranges between 75%–85% (0.75–0.85).

The PF of a system depends on the type of load present: whether resistive, inductive, or capacitive. The inductive and capacitive load has a negative impact on the PF of the system and results in an increase in current drained by the load.

Power factor can be defined as the ratio of the real power (i.e., active power) to the apparent power. The real and reactive power portions of an AC power circuit are based on trigonometric functions of phase angle (θ). In equation form, it is denoted as:

Equation 1: 1Φ & 3Φ Power Factor (PF) (λ) =
KW (Real Power)
KVA (Apparent Power)

Equation 2a:
1ɸ: Real Power (P in KW) = Volts × Current (amps)
× Cosine of Phase Angle θ
3ɸ: Real Power (P in KW) = Volts × Current (amps)
× 1.732 × Cosine of Phase Angle θ

Figure 2. Alternating current (AC) power relationships.

Equation 2b:
1ɸ: Apparent Power (S in KVA) = Volts × Current (amps)
3ɸ: Apparent Power (S in KVA) = Volts × Current (amps)
× 1.732

Equation 2c:
1ɸ: Reactive Power (Q in KVAR) = Volts × Current (amps)
× Sine of Phase Angle θ
3ɸ: Reactive Power (Q in KVAR) = Volts × Current (amps)
× 1.732 × Sine of Phase Angle θ

Example 1:
What is the power factor for the example shown in Figure 1?
Real Power = 80 KW
Apparent Power = 100 KVA
PF = 80 KW/100 KVA = 0.80 × 100 = 80%.

As shown in Figure 2, the true or real power (P), measured in thousands of watts or kilowatts (KW or kW) is the active power transmitted to the load for energy conversion and is measured as the cosine of phase angle θ.

Figure 3. Power triangle.

For example, a motor consumes the true power from the circuit and converts it into mechanical power for work, while a lighting fixture converts the same true power into illumination. Reactive power (Q), measured as kilovolt-amperereactive (KVAR or kVAR) power, is the power required to produce the magnetic field needed in motors and transformers and has a direct impact on the PF; it is measured as the sine of angle θ. Although the magnetizing current is necessary to produce rotation in an induction motor, the reactive power produces no real work and is therefore not a component of the true power.

Apparent power (S), measured in thousands of volts × amperes or kilovolt-amperes (KVA or kVA), also known as the demand, is the amount of power used to run machinery and equipment during a certain time period. It is the product of the voltage and current consumed by a load irrespective of its phase angle (θ). Thus, it is the combination of both real and reactive power.

The usual definition of power factor in terms of the phase relationship of voltage and current in a sine wave is intentionally avoided because it is abstract and difficult to translate into a simple and understandable physical concept.

Figure 4. Power factor by using the beer analogy.

The concept used here is there are two types of current in an AC circuit, which is particularly helpful in understanding the effect of power factor on system operation and understanding capacitor applications.

Power factor can also be defined as the power triangle which is the absolute value of the cosine (cos): kilowatts or kW of the phase shift angle (θ) between the voltage (V) and current (I) or kilovolts-amperes or kVA in an AC circuit (Figure 3).

A common method used to visualize the concept of power factor is performed by using a beer mug analogy.

Examining the mug of beer being shown in Figure 4, the thirst-quenching or actual liquid portion of the mug that satisfies the drinker is represented by kW (the true power) while the wasted or undrinkable upper part of the mug, the foam, is designated as the reactive power or kVAR. Finally, the total content of the mug represents the apparent power, in kVA (i.e., the summation of kW (the liquid beer) and kVAR (the foam).

Although this analogy is somewhat simplistic, in actuality it is often helpful in understanding the basic concepts of power factor.

Optimum Power Factor and Causes of Low Power Factor

Simply stated, power factor in an AC circuit is a measure of how efficiently the load current is being converted into useful output for the purposes of work, and more particularly, is a good indicator of the effect of the load current on the efficiency of the power supply.

Figure 5a. AC power sine wave for a pure resistive or “tuned” circuit.

Mechanically, it can be equated with the power needed to pull a load inline and straight with a tractor as opposed to the required power when pulling the same load at an angle.

Power factor is a component of all AC electrical systems, single and three-phase, but is particularly important for systems with numerous induction loads, such as motors and transformers or capacitive loads including fluorescent lighting, synchronous motors, and computers. The power factor is determined from the offsetting impacts of the reactive power (i.e., the combined impacts from the inductive and/or capacitive reactance in a circuit).

Reactance is defined as the opposition of the flow of current in a circuit component because of that component’s inherent inductance or capacitance properties. For a purely resistive load (Figure 5a) such as a simple incandescent light, the two power factors for real and apparent power are identical or tuned.

However, systems with inductive or capacitive reactance will incur different power factors. Reactive power, displayed in units of volt-amperes-reactive (VAR), or more commonly, expressed in thousands (kilos) of VARs, kilo-volt-amperesreactive (KVAR or kVAR), is the power consumed or stored and discharged by the inductive and capacitive components of the system.

Figure 5b. AC power sine wave for an inductive “lagging” circuit.

Inductive reactance is the result from the operation of induction motors, transformers, welders, and high intensity lighting while capacitive reactance is caused from synchronous motors, capacitor banks, computers, and other energy storing devices.

Excessive inductance causes the load current in the power supply to lag the supply voltage or what is called a lagging power factor (Figures 5b and 6a) that generates a low power factor. Excessive capacitance creates a counter reactance condition where the load current now leads the supply voltage to create a leading power factor (Figures 5c and 6b).

Note the positions of the apparent power line as opposed to the real power line in Figures 6a and 6b. Power factor is often described strictly as an energy cost reduction measure, but it is not a true energy savings measure.

In the real world of industrial power use, a power factor of 100% (1 or unity) is not generally functionally or economically obtainable. Typically, the highest obtainable practical power factor is generally between 95%–98% (0.95–0.98) while a low power factor, typically 80% (0.80) or lower, reduces the load handling capability of an electrical system as well as the same capabilities of the power utility’s generators, transmission lines, and transformers.

The effects of a low operating power factor may be the result from any or all the following conditions:

  • Overloaded cables
  • Partially loaded induction motors or transformers
  • Increased copper losses
  • Reduced voltage level resulting in sluggish motor operation
  • Reduced illumination from lighting, especially where old incandescent lamps are used
  • Increased power costs where a power factor penalty or its equivalent is part of the utility rate structure and is enforced.

Figure 5c. AC power sine wave for a capacitive “leading” circuit.

Frequently, power factor losses occur with variable frequency drives (VFDs) that are designed to be overpowered relative to the load. That is, the motor is selected to handle the largest load condition but usually operates at less than fully loaded conditions.

There are also other factors contributing to a lower power factor, such as replacement of incandescent lamps with fluorescent or high intensity lamps; use of rectifiers instead of synchronous motor-generator sets for DC power supply; and increased installation of various induction devices, electronic equipment, or air-conditioning units.

Although most of these changes or replacements are initially implemented in the interest of efficiency, lower operating cost, and technological advances, they may result in a power factor reduction even though the fact that they contribute to a reduced power factor is generally of secondary importance to the gained advantages.

As water treatment and pumping plants become more and more complex and sophisticated, it can be expected that the plant’s power factor will progressively drop unless appropriate corrective measures are taken.

Power Factor Goals and Correction Methods

Figure 6a. Lagging power factor.

Improvement of power factor can reduce overall power costs; release and improve the electrical capacity of the power distribution system; increase the voltage level and reduce system losses. It is not usually necessary or even practical to achieve a power factor of 1 (i.e., unity) since most power utilities define their own desirable or required power factor.

Most are content to realize an upper power factor of 0.96 to 0.97, although electrical systems with a power factor less than almost 90% (0.90) should investigate the technical and economic feasibility of installing power factor correction. Typically, a reasonable goal for a facility with multiple motor loads is to obtain a 95% (0.95) power factor.

Improving the power factor, through power factor correction (PFC) measures, can reduce energy costs if the end-user is subject to low power factor penalties, including system performance and additional costs.

Figure 6b. Leading power factor.

Users with electric utility rates based on energy use only and without demand charges or low power factor penalties, such as residential and most small commercial users, will typically not directly benefit from PFC measures. PFC is primarily applied to a system to avoid additional electric utility charges for low power factor and to reduce demand on motors, transformers, and generators to increase system capacity.

Capacitive power factor correction is often applied to electric induction motor circuits as a means of minimizing or offsetting the inductive component of current, and thereby, reducing the losses in the power supply system. The introduction of PFC capacitors is a widely recognized, low cost, and frequently used method of reducing an electrical load, thus minimizing wasted energy and improving the efficiency of an electrical system while also reducing the electrical bill.

PFC capacitors generally consist of metal-encased oval or round oil-filled run types of capacitors designed for continuous duty. Connections are usually made at the top of the capacitor. Refer to Figure 7a for an example of a typical 20 MFD run capacitor.

If necessary, smaller capacitors can be grouped or connected in parallel to create a bank as the total capacitance of a set of parallel capacitors is simply the sum of the capacitance values of the individual capacitors. Figure 7b illustrates the symbols for a delta and wye connected, three-phase capacitor bank. For example, a group of 20 MFD capacitors wired in parallel will provide 120 MFD of total capacitance.

Figure 7a. “Run” capacitor.

The most common sizes of run capacitors range from 2 MFD up to 100 MFD with typical voltage ratings of 240, 370, and 440 VAC. Many manufacturers provide capacitors with dual voltage ratings, such as 370/440 VAC. The voltage across all capacitors connected in parallel is identical. Thus, capacitors wired in parallel possess a common connected voltage across the terminals.

However, the voltage rating of each capacitor must be equivalent to the other capacitors and equal to or greater than the operating voltage. This means a 240 VAC rated run capacitor must not be used on a 480 VAC circuit. Electrolytic start capacitors can never be used for this application and will immediately fail if used.

In extreme instances with multiple full voltage start motors or where the use of capacitor banks may be inadequate to increase the power factor to the desired level, the replacement of some of the induction motors with synchronous motors is often implemented. Synchronous motors apply capacitance to the line, offsetting much of the inductive reactance applied to the electrical system by the induction motors.

Low power factor increases the utility’s cost of supplying actual power because more current must be generated and transmitted than is consumed to perform useful work. This additional current increases the costs incurred by the power utility and is often passed on to and directly billed to the industrial or municipal consumer by means of a low power factor penalty or surcharge in their rate schedule.

Figure 7b. Capacitor bank symbols.

Induction motors require both real and reactive power to operate. Real power essentially produces work while the reactive power establishes the magnetic field in the motor that enables it to rotate. When this demand is multiplied by several motors or large motors, the penalty in power factor can be dramatic.

The power factor of a motor is lower when the motor is underloaded and is significantly reduced when the motor load is less than 70% of full load conditions. Real and reactive currents generate heat in the wires or conductors and reactive current is always present in inductive load devices. Although reactive current is part of the total current indicated by an ammeter reading, the reactive power does not register on a typical kilowatt-hour (kW-hr) meter but will record on a parallel KVAR meter when used.


This concludes part one of this discussion on power factor. Next month, we will continue the discussion with application and sizing of power factor correction capacitors.

Until then, work safe and smart.

Learn How to Engineer Success for Your Business
 Engineering Your Business: A series of articles serving as a guide to the groundwater business is a compilation of works from long-time Water Well Journal columnist Ed Butts, PE, CPI. Click here for more information.

Ed Butts, PE, CPI, is the chief engineer at 4B Engineering & Consulting, Salem, Oregon. He has more than 40 years of experience in the water well business, specializing in engineering and business management. He can be reached at epbpe@juno.com.

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