AC Power Analysis

AC Power Analysis =)

Instantaneous and Average Power

The instantaneously power, p(t) 

Instantaneous power is the power of a any object at an instant. if you differentiate work done w.r.t time it will be the instantaneous power. If the given velocity is instantaneous the power=F*v

Average Power

The average power is the average of the instantaneous power over one period.

Maximum Average Power Transfer

We have already seen that an AC circuit can (at one frequency) be replaced by a Thévenin or Norton equivalent circuit. Based on this technique, and with the Maximum Power Transfer Theorem for DC circuits, we can determine the conditions for an AC load to absorb maximum power in an AC circuit. For an AC circuit, both the Thévenin impedance and the load can have a reactive component. Although these reactances do not absorb any average power, they will limit the circuit current unless the load reactance cancels the reactance of the Thévenin impedance. Consequently, for maximum power transfer, the Thévenin and load reactances must be equal in magnitude but opposite in sign; furthermore, the resistive parts -according to the DC maximum power theorem- must be equal. In another words the load impedance must be the conjugate of the equivalent Thévenin impedance. The same rule applies for the load and Norton admittances.

RL= Re{ZTh} and XL = - Im{ZTh}

The maximum power in this case:

Where V2Th and I2N represent the square of the sinusoidal peak values.

For maximum average power transfer, the load impedance ZL must be equal to the complex conjugate ofthe Thevenin impedance ZTh.

Overview and Insights

              Power analysis is another chapter and view of understanding in our class since it has lesser circuit analysis. Power is the most important quantity in electric utilities, electronic, and communication systems, because such systems involve transmission of power from one point to another.