Volt-amperes reactive: Definition from Answers.com

In alternating current power transmission and distribution, volt-ampere reactive (var) is a unit used to measure reactive power in an AC electric power system. The correct symbol is var and not VAr,^[1] but the latter is widely used. The term var was proposed by the Romanian Professor Constantin Budeanu and introduced in 1930 by the IEC in Stockholm, which has adopted it as the unit for reactive power.^[1]

Vars may be considered as either the imaginary part of apparent power, or the peak power flowing into a reactive load, where voltage and current are specified in volts and amperes. The two definitions are equivalent.

Reactive power

Main article: Reactive power

A sinusoidally alternating voltage applied to a purely resistive load results in an alternating current that is fully in phase with the voltage. In many applications it is however common for there to be a reactive component to the system, that is, the system possess capacitance, inductance, or both. These electrical properties cause the current to change phase with respect to the voltage: capacitance tending the current to lead the voltage in phase, and inductance to lag it.

If we define the sinusoidal voltage as: $v(t) = V_0 sin ~\omega t$ , where $V 0$ is the peak voltage, the phase-shifted current may be similarly expressed: $i(t) = I_0 sin ~ (\omega t + \phi)$ , where $φ$ is the phase angle by which the current lags the voltage.

The instantaneous power $p (t)$ supplied to the load is the product of $v (t)$ and $i (t)$ :

$p(t) = v(t) \cdot i(t) = V_0 I_0 \left[ cos ~\phi - cos \left( \omega t\right) cos \left(\omega t + \phi \right) \right]$

An equivalent and more commonly-found form is:

$p(t) = (V_0 I_0/2) \cdot \left[ cos ~\phi - cos \left(2 \omega t + \phi \right) \right]$

Since AC power has a varying voltage, efficient power systems must therefore vary the current in synchronism with the voltage. Vars measure unsynchronized "leading" or "lagging" currents. These currents are usually caused by the side effects of powering equipment that behaves like coils (e.g. motors) or capacitors (e.g. arc welders).

Technically, vars are the product of the rms voltage and current, or the apparent power, multiplied by the sine of the phase angle between the voltage and the current. In mathematical terms, the reactive power $Q$ , (measured in units of volt-amperes reactive or var), is given by:

$Q = V_\mathrm{rms}I_\mathrm{rms}\sin \left(\phi \right)\,$

where $φ$ is the phase angle between the voltage and current.

for convert var to c : Depends on your source voltage and frequency.

VAR = reactive power = V*I (for a capacitor)

For a capacitor in a steady state AC circuit,
${ V=\frac{I}{j\omega C}=\frac{I}{2 \pi f C}}$
or
$I = 2π f C V$

Substituting, then

$VAR=C*(2\pi fV^2)\;\;kVAR=\frac{VAR}{1000}$
[1]

Note 1: The unit var represents the power consumed by a reactive load, i.e. when there is a phase difference between the applied voltage and the current.

Note 2: Only effective power, i.e. the actual power delivered to or consumed by the load, is expressed in watts. Imaginary power is properly expressed in volt-amperes reactive.

Note 3: To maximize transmission efficiency, vars must be minimized by balancing capacitive and inductive loads, or by the addition of an appropriate (off-setting) capacitive or inductive reactance to the load.

Note 4: Apparent power, or the product of the rms voltage and current, measured in volt-amperes (VA), graphically presented as the hypotenuse of the power triangle, is typically the power rating measure of transmission or distribution equipment. Except in purely resistive circuits, apparent power is always larger than effective power (watts), hence the use of VA as the power rating measure in alternating circuits.

Notes and references

^ ^a ^b SI units – Electricity and magnetism, IEC webpage.

This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C".

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