Power is defined as the rate of flow of energy past a given point. In alternating current circuits, energy storage elements such as inductance and capacitance may result in periodic reversals of the direction of energy flow. The portion of power flow that, averaged over a complete cycle of the AC waveform, results in net transfer of energy in one direction is known as real power. On the other hand, the portion of power flow due to stored energy, which returns to the source in each cycle, is known as reactive power.

AC power flow has the three components:

The unit for all forms of power is the watt (symbol: W). In practice, however, this is generally reserved for the real power component. Apparent power is conventionally expressed in volt-amperes (VA) since it is the simple product of rms voltage and current. The unit for reactive power is given the special name "VAR", which stands for volt-amperes-reactive.

The mathematical relationship among them can be represented by vectors and is typically expressed using complex numbers:

In the case of a perfectly sinusoidal waveform, P, Q and S can be expressed as vectors that form a vector triangle with phase angle φ such that:

where

Consider an ideal alternating current (AC) circuit consisting of a source and a generalized load, where both the current and voltage are sinusoidal,using trigonometric identities, the instantaneous power may be expressed as the sum of two sinusoids of twice the frequency.

If the load is purely resistive, the two quantities reverse their polarity at the same time; the direction of energy flow does not reverse; and only real power flows.

If the load is purely inductive or capacitive, then the voltage and current are 90 degrees out of phase (for a capacitor, current leads voltage; for an inductor, current lags voltage) and there is no net power flow. This energy flowing backwards and forwards is known as reactive power.

If a capacitor and an inductor are placed in parallel, then the currents caused by the inductor and the capacitor are in antiphase with each other and therefore partially cancel out rather than adding to each other. Conventionally, capacitors are considered to generate reactive power and inductors to consume it. In reality, the load is likely to have resistive, inductive, and capacitive parts; and so both real and reactive power will flow to the load. The apparent power is the result of a naive calculation of power from the voltage and current in which the RMS voltage is simply multiplied by the rms current. Apparent power is handy for rough sizing of generators or wiring, especially when the power factor is close to 1. However, adding the apparent power for two loads will not give the total apparent power unless the two loads have the same phase difference between voltage and current.

The above graph shows the instantaneous and average power calculated from AC voltage and current with a lagging power factor (φ=45, cosφ=0.71).Average power is the real power and instantaneous power is the apparent power.

For more details on this topic see the following links :http://hyperphysics.phy-astr.gsu.edu/hbase/electric/powerac.html#c2 http://www.phptr.com/articles/article.asp?p=101617&seqNum=3&rl=1 http://www.ibiblio.org/kuphaldt/electricCircuits/AC/AC_11.html -- Explanation with examples http://www.circuit-magic.com/acpower.htm --- Voltage,Current and Power waveforms for different types of circuits

http://en.wikipedia.org/wiki/Ac_power

AC power flow has the three components:

- Real power (P), measured in watts (W)
- Reactive power (Q), measured in reactive volt-amperes (VAr).
- Complex power (S), measured in volt-amperes (VA).S, the modulus of complex power, is referred to as apparent power

The unit for all forms of power is the watt (symbol: W). In practice, however, this is generally reserved for the real power component. Apparent power is conventionally expressed in volt-amperes (VA) since it is the simple product of rms voltage and current. The unit for reactive power is given the special name "VAR", which stands for volt-amperes-reactive.

The mathematical relationship among them can be represented by vectors and is typically expressed using complex numbers:

*S = P + jQ*(where j is the imaginary unit)In the case of a perfectly sinusoidal waveform, P, Q and S can be expressed as vectors that form a vector triangle with phase angle φ such that:

where

*S = VI**P = VI cosφ = S cosφ**Q =VI sinφ = S sinφ*Consider an ideal alternating current (AC) circuit consisting of a source and a generalized load, where both the current and voltage are sinusoidal,using trigonometric identities, the instantaneous power may be expressed as the sum of two sinusoids of twice the frequency.

If the load is purely resistive, the two quantities reverse their polarity at the same time; the direction of energy flow does not reverse; and only real power flows.

If the load is purely inductive or capacitive, then the voltage and current are 90 degrees out of phase (for a capacitor, current leads voltage; for an inductor, current lags voltage) and there is no net power flow. This energy flowing backwards and forwards is known as reactive power.

If a capacitor and an inductor are placed in parallel, then the currents caused by the inductor and the capacitor are in antiphase with each other and therefore partially cancel out rather than adding to each other. Conventionally, capacitors are considered to generate reactive power and inductors to consume it. In reality, the load is likely to have resistive, inductive, and capacitive parts; and so both real and reactive power will flow to the load. The apparent power is the result of a naive calculation of power from the voltage and current in which the RMS voltage is simply multiplied by the rms current. Apparent power is handy for rough sizing of generators or wiring, especially when the power factor is close to 1. However, adding the apparent power for two loads will not give the total apparent power unless the two loads have the same phase difference between voltage and current.

The above graph shows the instantaneous and average power calculated from AC voltage and current with a lagging power factor (φ=45, cosφ=0.71).Average power is the real power and instantaneous power is the apparent power.

For more details on this topic see the following links :http://hyperphysics.phy-astr.gsu.edu/hbase/electric/powerac.html#c2 http://www.phptr.com/articles/article.asp?p=101617&seqNum=3&rl=1 http://www.ibiblio.org/kuphaldt/electricCircuits/AC/AC_11.html -- Explanation with examples http://www.circuit-magic.com/acpower.htm --- Voltage,Current and Power waveforms for different types of circuits

http://en.wikipedia.org/wiki/Ac_power

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