# AC POWER BASICS

WATT, KILOWATT, VA, and POWER FACTOR

There is a common confusion about the difference between the watt and volt-amp (VA) measures for electric power, as well as about power factor. In this tutorial you will find a simple explanation of AC power calculation, the usage of these quantities in specifying backup energy sources, conversion formulas, and an online calculator.

## WATT and VA RELATIONSHIP

Energy in general is defined as the capacity for doing work. Power by definition is the rate of work or energy flow (which are numerically the same): P = Energy/Time.

It can be shown that in electrical circuits the instantaneous power is p(t)=v(t)×i(t). In this equation v(t) and i(t) are instantaneous voltage and current as functions of time t. In alternating current (AC) circuits all these quantities are continuously varying.

The value of the main interest in electrical industry is an average value of p(t) over a complete AC cycle. 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. 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 rms value of the reactive power. Besides reactances, practical electrical systems also contain non-linear components such as rectifiers, which distort electric current waveform and create harmonics. If voltage is a pure sinewave, all the current 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, obviously 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 by using this formula: VA=W/PF.
Unfortunately, PF value is practically never stated in appliance's spec sheet. For old computers it used to be 0.6-0.65. Modern computers normally have an SMPS PSU with PFC that assures near unity PF. For the motor-driven appliances (such as refrigerators and air conditioners) this value is typically 0.6-0.9. If you don't know the PF of your device, assume the worse case of 0.6.
Enter any two known values and press "Calculate" to find the remaining value.
Reset before each new calculation.
 VA Power Factor Watts
A "power triangle" in which active, reactive and total power are represented as vectors, is often used to visualize the relationship between W and VA in linear circuits with sinusoidal signals. When voltage and current are sine waves, 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. 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) energy is transferred by the components of voltage and current which have the same frequency. At given values of V and I, the maximum wattage transfers when they are in phase. If sinusoidal voltage and current have 90o phase shift, the net wattage is zero and likewise PF=0.

In some US regions the utilities already installed residential digital electric meters, which compute W, VAR, and PF. They may surcharge you for VAR. However, so far most residential meters in U.S. are still rotating-disc devices that measure only real watts, so PF of your appliances does not affect the cost of your electricity. Therefore, using power factor correcting (PFC) devices will not reduce your electric bills as some claim. Nevertheless, PF of the appliances should be taken into account when choosing the size of a backup system, such as a generator or UPS. Also, lower PF will cause larger current in utility lines and additional voltage drop in the wiring. In an extreme case, this can cause overheating and premature failure of a motor and other equipment. Unlike most residential users, for commercial and industrial customers, an electric utility company may assess a surcharge when power factor drops below 0.95 or so.

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

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