Receiving End Angle Using Losses (STL) Calculator

Formula Used:

\[ \Phi_r = \cos^{-1}\left(\frac{(3 \times V_s \times I_s \times \cos(\Phi_s)) - P_{loss}}{3 \times V_r \times I_r}\right) \]

Sending End Voltage (Vs):

Volt

Sending End Current (Is):

Ampere

Sending End Phase Angle (Φs):

Radian

Power Loss (Ploss):

Watt

Receiving End Voltage (Vr):

Volt

Receiving End Current (Ir):

Ampere

Receiving End Phase Angle (Φr):

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1. What is Receiving End Angle Using Losses (STL)?

The Receiving End Phase Angle calculation determines the phase difference between current and voltage at the receiving end of a short transmission line, accounting for power losses in the system. This is crucial for analyzing power system stability and efficiency.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \Phi_r = \cos^{-1}\left(\frac{(3 \times V_s \times I_s \times \cos(\Phi_s)) - P_{loss}}{3 \times V_r \times I_r}\right) \]

Where:

\( \Phi_r \) — Receiving End Phase Angle (Radian)
\( V_s \) — Sending End Voltage (Volt)
\( I_s \) — Sending End Current (Ampere)
\( \Phi_s \) — Sending End Phase Angle (Radian)
\( P_{loss} \) — Power Loss (Watt)
\( V_r \) — Receiving End Voltage (Volt)
\( I_r \) — Receiving End Current (Ampere)

Explanation: The formula calculates the phase angle at the receiving end by considering the power balance between sending and receiving ends, accounting for system losses.

3. Importance of Receiving End Phase Angle Calculation

Details: Accurate calculation of receiving end phase angle is essential for power system analysis, voltage stability assessment, and determining the efficiency of power transmission in short transmission lines.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure that sending and receiving voltages and currents are positive values. The sending end phase angle should be in radians. All values must be valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: Why is the receiving end phase angle important?
A: It helps in analyzing the power flow, stability, and efficiency of the transmission system, particularly in short transmission lines.

Q2: What are typical values for receiving end phase angle?
A: The phase angle typically ranges between -π and π radians, depending on the system load and generation conditions.

Q3: What causes phase angle differences in transmission lines?
A: Phase angle differences are caused by the impedance of the transmission line, load characteristics, and power flow direction.

Q4: How does power loss affect the phase angle calculation?
A: Power loss accounts for the energy dissipated in the transmission line, which affects the power balance and consequently the phase angle at the receiving end.

Q5: Can this calculator be used for long transmission lines?
A: This specific formula is designed for short transmission lines. Long transmission lines require additional parameters and more complex calculations due to distributed parameters.