What is the Power Angle in a Power Transmission Line?

The power angle, denoted by δ, is the phase angle difference between two voltage levels in a power transmission line. Specifically, it represents the angular discrepancy between the sending-end voltage phasor and the receiving-end voltage (or between voltages at two bus points). In simpler terms, it quantifies the phase shift between voltage and current waveforms in the transmission line.

Also referred to as the torque angle or load angle, this parameter is critical for two key reasons: it determines the amount of power transmitted between two points and influences the stability of the entire power system.

A larger power angle signifies the system approaching its stability limit, enabling higher power transmission. However, if the power angle exceeds 90 degrees, the system may lose synchronism, potentially causing blackouts. Thus, maintaining the power angle within safe thresholds is critical for stable power system operation.

During normal operation, the power angle is constrained within a defined range. Exceeding acceptable limits can trigger instability and system collapse. System operators continuously monitor and regulate the power angle to ensure grid stability and reliability.

Calculating Power Angle in Transmission Lines

The power angle can be computed using the following formula:

where:

• $\δ$ = the power angle,

• $P$ = the real power flowing through the transmission line,

• V_s = the magnitude of the sending-end voltage,

• V_r = the magnitude of the receiving-end voltage.