Instataneous Power and Average Power

INSTANTANEOUS POWER AND AVERAGE POWER

Power is the most important quantity in electric utilities, electronics . . . because such system involve transmission of power from one point to another.

Instantaneous power is the power at any instant of time. In Ac circuit the instantaneous electric power is given by 

P= VI

but these quantities are continuously varying. Instantaneous Power p(t) is the power, p(t)= u(t)*i(t). It is the product of the time functions of the voltage and current. This definition of instantaneous  power is valid for signals of any waveform. The unit for instantaneous power is VA.

REAL and ACTIVE POWER

P can be define in two ways: as the real part of the complex power or as the simple average of the instantaneous power. The second definition is more general because with it we can define the instantaneous power for any signal waveform, not just sinusoids.

The instantaneous power at any time t can be expressed as:

Pinstantaneous= VmImsinωtsin(ωt-ɸ)

Average power is more convenient to measure. It is the average of the instantaneous power over one period. And it is given by:

Pave= VIcosɸ

where ɸ is the phase angle between the current and the voltage and where V and I are understood to be the effective or rms of the voltage and current. The term cos ɸ is called the power factor for the circuit.