# Power Factor Explanation

## Disadvantages of Low Power Factor:

Lower power factor on a line means that higher current is flowing through it. The following are a few disadvantages to that:

• Higher current results in a greater voltage drop on the line, especially if the line is marginally sized or very long.
• It’s like trying to push too much water flow through a pipe; the pressure drops as you move down the pipe.

In the cable, this results in an energy loss due to heat dissipation. Also, higher current can push equipment closer to their rated capacities. Cables are rated based on their current carrying capacity. Transformers and generators are rated by VA (Volt-Amps) which is current carrying capacity at a certain voltage.

Another disadvantage to excess current flow, and it can be a big one, is the Reactive Demand Charge. The Utility that delivers the power to you will likely charge you if your Power Factor is too low. There are many different ways to determine this charge but the rational is this. If the Utility line that delivers your power (remember all lines have a current carrying capacity) is carrying your magnetizing current (current that could be supplied locally by you), then you are eating into the capacity of that line and taking away the ability for them to sell power to other customers with that line. The result... Surprise! You Pay!!

## Capacitors, VARS and the Power Triangle

The Power Factor explanation is not over.

We need to discuss the Power Factor Triangle, also called the Power Triangle, but first I'd like to explain how a capacitor is used in Power Factor Correction and then explain some Power Factor Terminology.

The Power Factor Correction Capacitor - What it Does, Now I'll explain why we would connect a Power Factor Correction Capacitor to the motor's circuit. This gets sort of fun... not too complicated! Motor current is composed of 2 parts: "Load Current" and "Magnetizing Current". They add together inside the motor to make the total current delivered to the motor. Magnetizing Current, establishes the magnetic field so the motor will spin, its current is constant and does not vary with load, it uses no energy and its sine wave lags the voltage's sine wave by 90 degrees. Load Current is zero if the motor is spinning with no load (theoretically, meaning no friction losses, wind losses, etc.) and increases with increased resistance to spinning. Load Current delivers energy to do the work (i.e. drives the pump) and the Load Current's sine wave is in-phase with the voltage's sine wave. On the flip side, when the magnetic field is collapsing and kicking current back into the system, the capacitor is demanding current and building a charge. A Match made in Heaven!... a perfectly compatible couple. What does this mean? If we connect a Power Factor Correction Capacitor near the motor, the capacitor and the motor can take turns feeding each other the current associated with the magnetic field. Now, the cable that connects the motor to its source of power needs only to deliver load current.

## Power Factor Terminology:

Power Factor Terminology, because now you understand the concept of Power Factor and a Power Factor Correcting Capacitor, is something that you are ready for (exciting!). After that... "The Power Triangle".

Load Current is also referred to as Real Current because it’s the component of current that’s really doing the work. (Remember? The magnetizing current only builds a magnetic field, the load current is associated with driving the load.)

If the current peaks before the applied voltage, it is said to be Leading Current. If the current peaks after the voltage, it is referred to as Lagging Current.

Capacitor Current and Magnetizing Current, which leads and lags (respectively) the voltage by 90 degrees, is also called Reactive Current or Imaginary Current (I wish they wouldn't call it "Imaginary" because it really does happen).

The Total Motor Current (or total current delivered to a set of loads, like a building) which is the instantaneous sum of the Real Current and Reactive Current, is also called the Apparent Current (remember, 1 amp + 1 amp = 2 amps of RMS current ONLY IF THEY ARE IN PHASE WITH EACH OTHER).

Power Factor Terminology often focuses on load and power. If we multiply the Real Current (the current that drives the load) by the system voltage we get the Real Load or Real Power. The units of Real Load, or Real Power, are Watts (i.e. kW, MW, etc.)

If we multiply the Reactive Current (the current that’s associated with storing and releasing energy for magnetic fields) by the system voltage we get the Reactive Load or Reactive Power, which is also called Imaginary Load. Its called Imaginary Load because its really not a load....it consumes no energy, but rather swaps it during every cycle from one storage device (magnetic field) to another (capacitor or generator), similar to how a pendulum continuously changes from potential to kinetic energy and back. The units of Reactive Load or Reactive Power are VARs, which stands for Volts-Amps-Reactive (i.e. kVAR, MVARs, etc.)

If we multiply the Apparent Current (the total current delivered to the load) by the system voltage we get the Apparent Load or Apparent Power. The units of Apparent Load are VA, for Volt-Amps (i.e. kVA, MVA, etc.). Apparent Power is a combination of work-related current and non-work related current. Many devices, including transformers, are rated in VA, which is really their current carrying ability at the system voltage (regardless of how much of the current is driving a load vs. building a magnetic field).

Power Factor Terminology is important because EEs are always trying to squeeze these words into a conversation. This might be a good page to print and read every night before bed (like EEs do).

## PF Correction Location Considerations for Choosing the Correct Location:

Your PF correction location is a fundamental part of the correction.

Poor power factor is most commonly corrected with the insertion of a capacitor or a capacitor bank (a grouping of capacitors) at the desired location to perform the correction. If you don't correct for power factor, your source will carry the excess current associated with the building and collapsing of magnetizing fields. This limits the capacity of all the components along the transmission path.

The capacitor provides current that Leads the voltage. This combines with the current associated with the magnetic fields that Lags the voltage and cancels it out, if sized correctly. Synchronous machines (either motors or generators) can also supply leading current, similar to a capacitor, by over-exciting their rotating field. Also, solid state devices are now available for supplying leading current, but for this discussion the capacitor will be used for correction.

Regarding PF correction location, as stated at the end of the Power Factor Capacitor section, if we connect a capacitor at the motor, the capacitor and the magnetizing field of the motor take turns feeding each other electric current. This is reactive load being supplied by the capacitor. When the capacitor discharges into the motor it builds the magnetic field. When the magnetic field collapses as a result of the voltage changing directions, the current is pushed out of the motor and into the capacitor and builds the charge.

Putting in too much capacitance can cause conditions of voltage spiking and instability. As a result, a common practice is to limit the capacitor's reactive load to 90%, or less, of the magnetizing load.

Because the capacitor supplies the magnetizing current (the Reactive Load), the cable coming from the source of power need only supply the load current (Real Load). The cable and other components upstream of the point where the capacitor ties in, deliver only load current to that motor, or the "corrected current" and therefore don't need to be sized to also handle the magnetizing current of that motor. "Corrected Current" has been emphasized because the current flow to the load has only been corrected upstream of the point in the system where you tie in the capacitor. There is no change to the current flow downstream of the tie-in point, which is still carrying the magnetizing current. Thus the PF correction location is key to accomplishing your goal.

Note: Choosing a PF correction location at a motor merely corrects the amperage demands on upstream equipment imposed by that motor. An upstream transformer may still be delivering disproportionately large amount of magnetizing current to other motors.

The real and reactive loads at an MCC, at a substation transformer or a feeder cable are simply the sum of all the real and reactive loads that it supplies. So if an MCC supplies 3 motors that each draw 2 kW and 0.3 KVARs, the feed to the MCC is delivering:
2 + 2 + 2 = 6 kW and 0.3 + 0.3 + 0.3 + 0.9 KVARs

A system will have several power factors. Every location in the system where the current changes, which is every branch, will have a different power factor.
*this means that the load that the transformer is supplying is:
2MVA x 0.7 = 1.4 MWatts
*correcting to a power factor of 0.9 would mean that the 1.4MW load would now only draw:
1.4 MW / 0.9 = 1.56 MVA
(that freed up 22% of the transformers capacity!)

## Reactive Demand & Reactive Demand Charges

#### What is a Reactive Demand Charge?

The Reactive Demand Charge on an electric bill can be one of the largest justifications of improving a plant's power factor. It is not an energy related savings, but rather a penalty avoidance savings. The charge exists to deter a utility customer from drawing excessive current flow to his plant due to poor power factor.

(If you are unclear about this concept, finish reading this section. If you then feel that you need a better understanding of Power Factor, go to our Homepage... that’s what this site is all about!)

Many electric bills don't have a Reactive Demand charge. Usually only the rate structures for larger customers contain this charge.

The reason for the Reactive Demand Charge is twofold and both are related to equipment capacities. The first is related to the generation of power, and the second has to do with delivering that power to the end-user.

#### Power Plant Generators

Power Plant Generators are capable of supplying a fixed amount of current (amperage). It doesn't matter if the generator's current is used to supply the power requirements of customers or just the magnetic fields of the customer's equipment. If the Utility invests in a generator and the customer is pulling in excess current due to a low power factor, the customer is eating into the generator's capacity and thus cuts down the Utility's ability to make money by selling power to other customers with that generator. (You know that's not going to happen.) The utility will often install the capacitors themselves, to supply the magnetizing current being demanded by the customer, thus freeing up the generator's current carrying capacity to deliver power.

#### Transmission Lines and Transformer Capacities

Transmission lines and transformers are also capable of carrying a fixed amount of current. Beyond that amount, they begin to heat and can potentially fail, thus the limit. So if the Utility invests in a transmission line or a transformer and the customer is pulling in current to supply his power requirements plus the excess current associated with a low power factor (current that could be supplied locally by the customer with capacitors), the customer is eating into the capacity of the utility's transmission equipment and thus restricts their ability to sell power to other customers with those investments.

#### How is a Reactive Demand Charge Calculated?

There are many versions of imposing this charge to customers; however, the concept usually goes as follows. Use the Terminology information following as a reference, if required.

A kW is a rate of power consumption. A KVAr is a rate of exchanging energy with magnetic fields. If the customer pulls a certain amount of current into his plant, even for a short time, the utility must assume, and allow for that amount to be pulled in at any time. This helps determine the capacity available on that transmission line. Hence, the highest rate of KVAr (usually the highest 1 hour average rate for the month), less an allowance of KVAr (which is usually a percentage of the kW for that same hour), is the value that is used to calculate the charge.

#### Terminology

A power factor definition is stated many ways, but it's the same phenomena explained from differing viewpoints. Often missing are some simple power factor theory fundamentals, thus causing it to seem like 'electrical voodoo'.

From an energy supplier's perspective: The power factor formula represents the fraction of power used by a customer compared to the total apparent power supplied, expressed as a percentage. Also stated as the ratio of 'real power' to 'apparent power', or as 'Watts' to 'KVA'.

PF = avg Watts / (rms Volts x rms Amps)

From a transmission and distribution perspective: A power factor represents how far the electrical equipment causes its current flow to be out of phase with the voltage in the transmission line.

Power Factor Definition from a Textbook: (which meant nothing to me for sooo long) Power Factor is the cosine of the phase angle between the voltage and the current.

From an Industrial Engineer's perspective: Power factor describes how much of the current is attributable to delivering real power. A power factor of one (unity or 1.0) means that all the current is delivering real power and a power factor of zero indicates that none of the current is delivering real power.

## Electrical Definitions:

#### Alternating Current (AC):

This is the type of current found in homes, businesses, etc. AC means the electricity can flow back and forth, reversing in direction. The speed or number of times per second it changes its direction is known as its "frequency". If the change is made at the rate of 60 times a second, it is said to have 60 "cycles" per second.

#### Ampere (Amp):

This is the term given to measure the rate at which an electric current flows through the wire at a resistance of 1 ohm when a potential of 1 volt is applied across the resistance.

#### Breaker or Circuit Breaker:

This term implies an electrical device located on an electric circuit that can "break" the circuit or open it at that particular location. Breakers are found on the Coop's lines as well as in the member home, only a substantial difference in sizing and construction differs. The Coop's breakers are found along the lines or in the substations, and the members are generally found in the main fuse box or occasionally in sub-fuse boxes that are inline somewhere along a given circuit. Breakers have the ability to be "reset" and used again. Breakers come in all sizes, depending upon the load and equipment. See "Fuses" below.

#### Direct Current (DC):

This is the type of current generally found in batteries and is no longer common for home use. As opposed to AC, DC flows continuously in one direction.

#### Demand:

In electricity, this refers to the amount of kilowatts a particular member or "load" requires. There are several types of demands, such as peak, coincident, non-coincident, off-peak, etc...

#### Coincident Demand:

Refers to the combined demand or load upon the system when it peaks, often referred to as "System Peak". When the system peaks out, everyone's load at that time makes up its coincident demand.

#### Non-coincident Demand:

Is the demand on the system at times other than coincidence or "peak". A customers non-coincidence demand is their demand at a time other than coincidence.

#### Peak Demand:

Is the load a customer puts upon the system at his highest usage or demand for electricity. Peak demand is often used in conjunction with "Coincident" demand, but may also be referred to as his "peak" during any given period.

#### Off-peak Demand:

Is the term used to describe a load's demand on the system at times other than "peak".

#### Fuses:

This is the devices installed on the Coops lines when there is a need to be able to isolate a line in the event a fault should appear on the line - we want to be able to isolate it but still keep the rest of the customers not on that particular line in service. The Coop often uses "fuses" on taps across private right of way or up a long lane to a few customers. Fuses in the home are found in many older homes, usually in the "fuse box" itself, and are activated when a fault appears on a circuit in the home. All fuses are good for one time only. Once blown, they must be replaced with a new fuse. Fuses come in all different sizes, depending upon the rating of the load and the equipment.

#### Horsepower (Hp):

Like the term "kilowatt" defined below, the term "horsepower" also denotes a unit of power. Hp indicates the rate at which energy is used or delivered - one horsepower is the equivalent of .746 kilowatts, i.e., a 10 horsepower rating has an equivalent rating of 7.46 kilowatts (10 x .746), meaning that this motor will use 7.46 kilowatt-hours per hour at full load.

#### House Current:

This refers to the common voltage level found in our member's homes. Nearly all houses and buildings are wired to allow 220/240 Volt service in them. This voltage is delivered to the member's home after it goes through our transformer. Once in the member's fuse box, the load will be distributed over the individual circuits within the home. Most of those circuits will be at 110/120 Volts, such as for lighting, receptacles, etc... Some loads, such as electric stoves, window air conditioners, electric furnaces, electric water heaters, etc. require 240 Volt service.

#### KV (Kilovolts):

This term is usually used as opposed to expressing the number of Volts in the thousands. A 138,000 volt line is usually referred to as a "138KV" line as kilovolt is the equivalent of 1,000 Volts.

#### KVA (Kilovolt-Amperes):

KVA is the result of the kilovolts being multiplied by the amperes, which is also equal to the kilowatts, i.e., kilowatts = kilovolts x amperes at "Unity" (see Power Factor below). Most line transformers are rated in "kva", such as a "10 kva" transformer.

#### KW (Kilowatt):

This term is used to measure the ordinary unit of electric power - it is the rate at which "kilowatt-hours" are delivered or used per hour. If an electric generator has the power capacity of 25,000 kilowatts, this means the generator has the capacity to deliver energy at the maximum rate of "25,000 kilowatt-hours per hour". As "kilo" means 1,000, the kilowatt is the equivalent of 1,000 Watts. It should also be noted that 1 KW is the equivalent of 1.34 horsepower.

#### KWHr (Kilowatt-hours):

This term should not be confused with KW above as KWHr is merely a unit of measurement of electric energy transmitted through the electric wires. The KWHr is often compared to the "gallon of water" measurement for measuring your water usage. Although "hour" is included in its name, KWHr is a unit of quantity that really involves no time element, which tends to be misleading.

This term refers to the month's load on a system as compared to its maximum or peak load for that same period. When a customer creates his maximum demand on the system, he will probably not continue to use electricity at that same level for the whole month, but will use it at different levels throughout the month. The extent of his use for the month as compared to his maximum use for that same month is called his "load factor". Load Factor is computed by dividing his KWHr usage for the month by the product of the month's "peak" or maximum demand for him times the hours for the same period (730 for a month and 8,760 for a year). Shown more algebraically:

Load Factor = Month's KWHr Usage / (Peak Demand or KW x 730 or 8,760)

#### Ohm:

This is a unit of resistance, representing the amount of resistance which will permit 1 ampere to flow at a potential difference of 1 volt.

#### Power Factor (PF):

This term is used to express the relationship between "useless current" and "useful power". It is very confusing to explain and understand. Certain types of electrical devises are 100% useful power, such as an electric stove, a light bulb, toaster, etc. - when it's on, all power is being used to heat or light and none is being wasted. Some other devices, especially induction motors as commonly used today, are not being used at capacity and result in a demand on the system greater than actually being used or put to good use. The actual work being done by the motor results in a certain kilowatt (kw) demand that is measured by the ordinary meters for measuring such demands. This motor, however, when "partially" loaded, makes an additional demand on the electric system which is not measured by the ordinary meter, but such additional demand requires capacity in the electric system just the same as the useful demand requires capacity. When there is no useless current in evidence, the power factor is said to be in "Unity". Power Factor is normally used in calculating kilowatts by the expression KW = KVA x PF. To compute power factor, the expression would be:

PF = KW/KVA or (W/(E x I))

If an electric motor requires 100 kilowatts of useful power and is operating at 50% power factor, the above formula would yield as follows:

100 kw = kva x .50 pf. To solve for KVA, kva =100 / .5 = 200

In other words, this motor requires 200 kilovolt-amperes (kva) of capacity in the electric system although it only uses 100 kw of useful power. The electric system is still having to provide 200 units of capacity in transformers, lines, etc. to serve that motor. If power factor for that motor could be increased to "unity", the motor would do no more useful work, it would take no more energy to perform this work, but would make a demand of 100 kw on the electric system, and only 100 kw in capacity in the electric system would be required to serve the motor. If that same 100 kw motor is now working at 70% power factor, the KVA required would be 143, or 100 / .7. An improvement over the 200 previously required. The higher the power factor of a load, the better it is to serve.

#### Volt:

This is the unit of electrical pressure, that potential which will cause a current of 1 ampere to flow through a resistance of 1 ohm.

#### Watt:

This is a term used to represent a unit of power. It is used to rate appliances, etc. that usually use a relatively small amount of electricity. A watt is equal to 1/1,000 of a kilowatt, or it takes 1,000 watts to equal 1 kilowatt. A light bulb rated at 100 watts is the equivalent to 100/1,000 kilowatts or 1/10 of a kilowatt, meaning this bulb will use electric energy at the rate of 1/10 of a kilowatt-hours per hour. If this bulb is burned steadily for 60 hours, it will have used 6 KWHrs or (60 x 1/10) or (100 x 60) / 1000.