Sending End Current using Losses (STL) Calculator

Formula Used:

\[ I_s = \frac{3 \times V_r \times I_r \times \cos(\Phi_r) + P_{loss}}{3 \times V_s \times \cos(\Phi_s)} \]

Receiving End Voltage (Vr):

Receiving End Current (Ir):

Receiving End Phase Angle (Φr):

rad

Power Loss (Ploss):

Sending End Voltage (Vs):

Sending End Phase Angle (Φs):

rad

Sending End Current (Is):

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1. What is Sending End Current using Losses (STL)?

The Sending End Current using Losses (STL) formula calculates the current at the sending end of a short transmission line by considering the receiving end parameters, power losses, and phase angles at both ends. This calculation is essential for power system analysis and transmission line efficiency evaluation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ I_s = \frac{3 \times V_r \times I_r \times \cos(\Phi_r) + P_{loss}}{3 \times V_s \times \cos(\Phi_s)} \]

Where:

\( I_s \) — Sending End Current (A)
\( V_r \) — Receiving End Voltage (V)
\( I_r \) — Receiving End Current (A)
\( \Phi_r \) — Receiving End Phase Angle (rad)
\( P_{loss} \) — Power Loss (W)
\( V_s \) — Sending End Voltage (V)
\( \Phi_s \) — Sending End Phase Angle (rad)

Explanation: The formula accounts for the three-phase power system parameters and calculates the sending end current by considering both the power delivered to the receiving end and the losses in the transmission line.

3. Importance of Sending End Current Calculation

Details: Accurate calculation of sending end current is crucial for transmission line design, power system stability analysis, loss calculation, and determining the efficiency of power transmission systems.

4. Using the Calculator

Tips: Enter all values in appropriate units. Voltages and currents must be positive values. Phase angles should be entered in radians. Ensure sending end voltage is not zero to avoid division by zero.

5. Frequently Asked Questions (FAQ)

Q1: Why is the 3 multiplier used in the formula?
A: The multiplier 3 accounts for the three-phase nature of the power system, converting per-phase quantities to total three-phase quantities.

Q2: What are typical values for phase angles?
A: Phase angles typically range from -π to π radians (-180° to 180°), with positive values indicating lagging power factor and negative values indicating leading power factor.

Q3: How does power loss affect sending end current?
A: Higher power losses require more current to be injected at the sending end to deliver the same power to the receiving end, thus increasing the sending end current.

Q4: Can this formula be used for single-phase systems?
A: For single-phase systems, remove the 3 multipliers from both numerator and denominator, as the formula would then represent single-phase power calculations.

Q5: What are the limitations of this calculation?
A: This formula assumes balanced three-phase conditions and may not be accurate for unbalanced systems or very long transmission lines where distributed parameter effects become significant.