AC POWER and ENERGY BASICS

This quantity is called real (active) power and is measured in watts (symbol: W):

Watts=average{v(t)×i(t)}

It represents that actual work done by an electric current or an actual energy consumed by a load to create for example heat, light or motion.
Electrical systems normally have inductors and capacitors, which are referred to as reactive components. Ideal reactive components do not dissipate any energy, but they draw currents and create voltage drops, which makes the impression that they actually do. This "imaginary power" is called reactive power. Its average value over a complete AC cycle is zero because of the phase shift between voltage and current. It doesn't contribute to net transfer of energy, but circulates back and force between the source and the load and places a heavier load on the utility. Reactive power is measured in Volt-Amps-Reactive (VAR). Contrary to wattage which represents an average value, numerically VAR represents an amplitude of the instantaneous reactive power. Besides reactances, practical electrical systems also contain non-linear components such as rectifiers, which distort current waveform and create current harmonics.
All these harmonics except for the fundamental one, do not contribute to the net energy transfer.
The combination of real, distortion and reactive power makes up apparent (or total) power, measured in Volt-Amps (VA):

VA= V×I

In this formula V and I are root-mean-square (RMS) values of voltage and current.

WHAT IS POWER FACTOR (PF)?

PF by definition is the ratio of real to apparent power: PF=W / VA .

People are often looking for a calculator to convert volt-amps (VA) to watts. Well, you need to know the value of PF to do the calculation: W=VA×PF, where PF is in decimal. Likewise, you can convert watt to VA power by using this formula: VA=W/PF.
Unfortunately, PF value is practically never stated in appliance's spec sheet. Old computers used to have PF=0.6-0.65. Modern computers normally have an SMPS PSU with PFC that assures near unity PF. The motor-driven appliances (such as refrigerators and air conditioners) typically have PF=0.6-0.8. If you don't know the PF of your device, assume the worse case of 0.6. A "power triangle" in which active, reactive and total power are represented as vectors, is often used to visualize the relationship between watts and VA in linear circuits with sinusoidal signals. When voltage and current are sinusoidal, it can be shown that PF=cosφ, where φ- angle between voltage and current phasors. For non-sinusoidal currents this triangle is invalid due to the presence of another component called "distortion power", This fact is neglected in many tutorials on electricity (for detailed math analysis see mathematics of AC power). PF value measures how effectively electricity is being utilized. Here is a simple mechanical analogy. We know from physics that when an object is moved by a force, mechanical work is done only by the component of the force in the direction of the motion. At a given force, maximum work is done when the force and the motion are in the same direction. If the force is perpendicular to the direction of motion, no energy is transferred by this force. Similarly, in electrical circuits, the real (working) power is transferred by the components of voltage and current which have the same frequency. At given voltage and current values, the maximum wattage transfers when they are in phase. If sinusoidal voltage and current have 90^o phase shift, the net wattage is zero and likewise PF=0. In some US regions electric utilities already installed digital power meters ("smart meters") at the residential level, which compute W, VAR, and PF. They may surcharge you for VAR. However, so far most US residential meters are still rotating-disc devices that measure only real watts, so PF of your appliances does not affect your cost of electricity. In this case, using power factor correcting (PFC) devices will not reduce your electric bills. Nevertheless, PF of the appliances should be taken into account when sizing a backup energy system, such as a home generator or an UPS (see: selecting an uninterruptible (UPS) power supply). Also, lower PF will cause larger current in utility lines and additional voltage drop in the wiring. In an extreme case, reduced voltage in the electrical system can cause overheating and premature failure of motors and other inductive equipment. Unlike residential customers, for commercial and industrial electrical customers, an electric utility company may assess a penalty for low power factor and collect additional charge when PF drops below 0.95.

Note that single-phase generators for homes are usually rated for loads with PF=1, so their wattage and VA ratings are the same. Since typical appliances have PF=0.6-0.8, their VA power consumption is 25-60% greater than their wattage. This has to be taken into account when sizing a backup generator: its output rating should be much greater than the net wattage of such motor-driven loads. For example, for 700 W device with PF=0.7 you need at least a 700/0.7=1000 watt generator. Nowadays an appliance's nameplate usually states its maximum current rather than wattage, so you don't need to know its PF: you just need to multiply this current value by nominal AC voltage (120V in US) to get the VA. For example, if your single-phase appliance is rated for 10 A maximum current, it may consume up to 120×10=1200 VA. This value should be used in sizing your backup generator or UPS to feed this appliance.

POWER AND ENERGY UNITS

The watt is the basic unit of real power. It is used as a derived unit in The International System of Units (SI). By definition, 1 W equals to one joule of energy per second. In electrical terms, it can be shown that power is produced or consumed at a rate of one watt when one ampere flows through a potential difference of one volt: 1 W = 1 V × 1 A. Since for the electrical industry this unit is small, larger units are frequently used. For example, the kilowatt (kW) which is equal to one thousand watts, is frequently used as a measure of residential electricity usage, rating of generators as well as the consumption of large tools and appliances: 1 kW=1000 W. Likewise 1 kVA=1000VA. Other derivative units are also frequently used (see power and energy unit conversion calculator).

The SI unit for energy is joule (J). Joule is used primarily in science. It is the amount of energy exerted by a force of one newton (1 N) to move an object through a distance of 1 m in the direction of the force. Joule is a relatively small unit. The energy unit commonly used for electricity consumption, particularly for utility bills, is the kilowatt-hour (kWh), which is a measurement of a net electricty flow over given period of time, such as a month. One kilowatt-hour is the amount of energy equivalent to a steady flow of 1 kW for 1 hour. For example, a 100-W bulb in 10 hours will use 1 kWh energy.
Note that 1 kWh=3,600,000 J.