# Power Factor

The Power Factor of your electrical system can cost you money. A low Power Factor will cause your utility company to add a penalty to your electric bill, and your increased system losses will turn electricity into wasted heat, shortening equipment life.

The Sales Engineering staff at Kele often receives calls concerning Power Factor. Some of the calls are for application assistance in choosing Power Factor monitoring equipment. Other calls come during start-up with questions about the validity of watt, current and voltage measurements that are affected by Power Factor.

**What Is Power Factor?**

Power Factor (pf) is the ratio of real power to total power. Real, or productive power, is the actual power used in a building, measured in kilowatts (kW). Reactive power generates the magnetic field for inductive loads such as motors, transformers, lighting ballasts, etc. Reactive power is measured in kilovars (kVAR). Total power (measured in kVA) is a combination of real power and reactive power.

The basic formula for Power Factor is the mathematical ratio of real power to total power. This ratio is an effective measure of system electrical efficiency and is represented as a percentage or decimal (e.g., 90% or 0.9).

**Other Power Factor Calculations**

Graphically, the Power Triangle on a system would look like this:

The relationship between kVA, kW, and kVAR is as follows:

***kVA ^{2}= kW^{2} + kVAR^{2} or VA^{2} = W^{2} + VAR^{2}**

Thus, with substitution, another formula for power factor could be derived:

On a single-phase circuit, the current will usually lag behind the voltage. The amount of the lag can be measured in degrees (360° for one complete cycle). The cosine of this phase angle also equals the power factor.

**Effects Of Power Factor**

System Capacity – Your kVA is the total power available. Your useful power kW = (kVA)(pf). The higher the system power factor, the more system capacity that is available. With more system capacity, voltage will remain more stable as loads are cycled on and off. Also more load can be added to the system as needed.

System Losses – With a higher Power Factor, less current flows through your system. There is less power lost (I2R losses) to heating of cables, bus bars, transformers, panels, etc. These devices will run cooler and last longer too.

Utility Charges – Electric utilities must maintain a high Power Factor on their distribution system for efficiency. They will typically bill customers for a low Power Factor or they may bill on kVA demand, which Power Factor will affect. Most utilities that bill a Power Factor penalty require a user to maintain a 95% Power Factor to avoid penalty.

**Power Factor And Motor Loading**

Power Factor is affected significantly by motor loading. Figure 1 represents a typical T-frame motor curve. It is evident that the highest Power Factor is at full loading. Since this Power Factor will affect the system Power Factor, proper sizing of motors is important. Over-sizing motors will lower the system Power Factor. Understanding motor efficiency and Power Factor is important in building automation. As you can see, your control scheme for the loading of chillers can affect your power usage.

Frequently we get calls on chiller applications using watt transducers. The installer believes the watt transducer is reading low, compared to voltage and current measurements. We usually find the chiller is only partially loaded and the Power Factor is low (e.g., 48% pf at 25% loading).

The addition of capacitors or the use of high efficiency motors will improve the Power Factor. Application of capacitors at the right locations and precautions involving electronic equipment need to be considered. High efficiency motors are more expensive but have a higher Power Factor.

**Power Factor Correction**

Capacitors are typically added to a system to increase system Power Factor. Some users install switched capacitor banks at the incoming service for utility bill savings only.

Since capacitors only improve a system from the capacitor back to the power source, many users will install capacitors at motor loads so they will be switched with the motor. With this method the benefits of lower *(I2R) losses improve their whole system. The addition of variable frequency drives will usually improve the Power Factor.

**Measuring Power Factor**

There are several methods to calculate Power Factor. The method is usually determined by the math capabilities of the automation system. If a watt transducer is used with a voltage and current transducer, the following formula is used:

If a VAR and Watt Transducer are used, the following formula would be used:

If a phase angle transducer is used to determine phase angle, then the following formula is used:

**pf = Cos Ø**

Kele offers a full line of Power Factor monitoring equipment, along with our other power monitoring products. Call our Sales Engineers for application assistance.

* This equation contains subscripts or superscripts which may not be supported by all web browsers. Contact your Kele Sales Representative if there are any questions about this formula.