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This
quantity is called real (active) power and is measured in watts (symbol: W):
Real Power(W)=average{p(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 usually 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, 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
source. Reactive power is measured in Volt-Amps-Reactive (VAR).
Contrary to real power which is an average value, numerically
VAR represents an amplitude of the instantaneous reactive power.
Besides reactances, practical electrical systems 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 (active) power, distortion power and reactive
power makes up apparent (or
total) power, measured in Volt-Amps
(VA):
VA= V×I,
where V and I are root-mean-square (RMS) values of voltage and current.
WHAT IS POWER FACTOR?
The ratio of real power to apparent power is called power factor (PF):
PF=W / VA
Sometimes people are asking how to convert volt-amps (VA) to watts. Well, you need to know the value of PF to do the calculation: Watt=VA×PF, where PF is in decimal. Likewise, you can convert watt to VA: VA=Watt / PF.
Old computers have PF=0.6-0.65. Modern computers normally use a power supply 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 power factor of your device (which is practically never stated in its spec sheet), you can assume in your calculations the worse case PF=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 power 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. This is not true
however for non-sinusoidal currents, which is neglected in many
tutorials on electricity (for detailed analysis see Mathematics of Electric Power and Power Factor).
Power factor measures how effectively electricity is being utilized. 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 lines, 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 real power transfers when
they are in phase. If sinusoidal voltage and current have 90o
phase shift, the real power is zero. Note that so far residential meters
measure only real power (watts), and PF of your appliances does not
affect your cost of electricity. So, in residential applications power
factor correcting (PFC) devices will not reduce your electric bills.
However, 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 power supply).
Also, low 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 home use 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 just need to multiply this current value by nominal AC voltage (120V in US) to get the VA amount. For example, if your single-phase appliance is rated for 10 A maximum current, it consumes up to 120×10=1200 VA. This value should be used in sizing your backup generator or UPS to power 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 watt 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) equal to one thousand
watts, is frequently used as a measure of residential electricity
usage, rating of generators as well as the power 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
physics. 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 power flow over certain period of time. One kilowatt-hour is the amount of energy equivalent to a
steady flow of 1 kW for 1 hour. For example, a 100-watt bulb in 10 hours will use 1 kWh energy.
Note that 1 kWh=3,600,000 J. |