What happens to active power as the power angle increases up to 90 degrees?

As the power angle increases up to 90 degrees, active power increases until it reaches a maximum transfer limit. This relationship is governed by the power flow equations in alternating current (AC) systems, particularly in the context of synchronous generators and transmission lines.

The active power transfer can be represented by the equation:

[ P = \frac{V_1 V_2}{X} \sin(\delta) ]

where ( P ) is the active power, ( V_1 ) and ( V_2 ) are the voltage magnitudes at the sending and receiving ends, ( X ) is the reactance of the transmission line, and ( \delta ) is the power angle between the two voltage sources.

As the power angle (( \delta )) increases from 0 to 90 degrees, the sine function increases from 0 to 1. Consequently, the active power being transferred increases linearly as the power angle approaches 90 degrees. This concept is fundamental in power system analysis, demonstrating how robust power transfer occurs under certain angle conditions. At 90 degrees, the maximum power transfer condition is achieved, beyond which the system may begin to experience stability issues, potentially leading to voltage collapse.

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