What is power angle in transmission line system?

The power angle in a transmission line system is the angle between the voltages at two different points (or buses) of the system.

It is also called the load angle or the torque angle. The power angle affects the amount of power that can be transferred between the two points.

The higher the power angle, the more power is transferred, up to a certain limit. Beyond that limit, the system becomes unstable and may lose synchronism.

The power angle can be calculated using the following formula:$$\\delta = \\cos^{-1}\\left(\\frac{V_1 V_2 \\cos\\theta – P}{V_1 V_2}\\right)$$where $\\delta$ is the power angle, $V_1$ and $V_2$ are the magnitudes of the voltages at the two points, $\\theta$ is the phase difference between the voltages, and $P$ is the real power transferred.

For example, if $V_1 = 100 \\text{ kV}$, $V_2 = 90 \\text{ kV}$, $\\theta = 30^\\circ$, and $P = 50 \\text{ MW}$, then the power angle is:$$\\delta = \\cos^{-1}\\left(\\frac{100 \\times 90 \\times \\cos30^\\circ – 50 \\times 10^3}{100 \\times 90}\\right)$$$$\\delta = 18.4^\\circ$$.