# What is the Power Angle in a Power Transmission Line?

**What Is the Power Angle in Transmission Lines, and How Do You Calculate It?**

The power angle (denoted by δ) is the phase angle difference between two voltage levels in a power transmission line. In other words, It is the angle difference between the voltage phasor at sending end and receiving end voltage or voltage at two points i.e. buses). In very simple words, it is the phase angle difference between the voltage and current waveforms in a power transmission line.

The power angle (also known as torque angle or load angle) is an important parameter which defines the amount of transmitted power between two points as well as the stability of overall power system.

A larger power angle indicates that the system is closer to its stability limit and can transmit more power. If the power angle exceeds 90 degrees, the system can lose synchronism, leading to a blackout. Therefore, maintaining the power angle within safe limits is crucial for the stable operation of power systems.

During normal operation, the power angle is kept within a certain range. If the power angle exceeds the acceptable limits, it can lead to instability and potential system collapse. System operators closely monitor and control the power angle to maintain a stable and reliable power grid.

**How to Calculate Power Angle in Transmission Lines?**

The power angle can be calculated using the following formula:

where:

*$δ$*= the power angle,*$P$*= the real power flowing through the transmission line,*$V$*= the magnitude of the sending-end voltage,*$V$*= the magnitude of the receiving-end voltage.

**Example:**

Find the power angle in a 100 MW power transmission line system where the sending end voltage and receiving end voltage are 230 kV and 220 kV respectively.

**Solution:**

Real power ($P$) = 100 MW

Sending-end voltage ($V$) = 230 kV

Receiving-end voltage ($V$) = 220 kV

Using the formula:

*$δ$*= arccos (100 MW ÷ 50,600 MV) ≈ 0.001976

Now, take the arccosine (inverse cosine) of this value:

$δ$

δ ≈ 89.66°

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