Receiving End Current Using Sending End Angle (STL) Calculator

Formula Used:

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

Sending End Voltage (V_s):

Volt

Sending End Current (I_s):

Ampere

Sending End Phase Angle (Φ_s):

Radian

Power Loss (P_loss):

Watt

Receiving End Voltage (V_r):

Volt

Receiving End Phase Angle (Φ_r):

Radian

Receiving End Current (I_r):

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1. What is the Receiving End Current Formula?

The formula calculates the receiving end current in a short transmission line system based on sending end parameters, power loss, and receiving end voltage and phase angle. It's essential for analyzing power system performance and efficiency.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( I_r \) — Receiving End Current (Ampere)
\( V_s \) — 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)
\( \Phi_r \) — Receiving End Phase Angle (Radian)

Explanation: The formula accounts for the three-phase power system parameters and calculates the current at the receiving end considering power losses and phase angles.

3. Importance of Receiving End Current Calculation

Details: Accurate calculation of receiving end current is crucial for power system analysis, load flow studies, system protection design, and ensuring efficient power transmission with minimal losses.

4. Using the Calculator

Tips: Enter all values in appropriate units. Voltage and current values must be positive. Phase angles should be entered in radians. Ensure denominator (3×V_r×cos(Φ_r)) is not zero to avoid division by zero.

5. Frequently Asked Questions (FAQ)

Q1: Why is the cosine function used in this formula?
A: The cosine function represents the power factor component, which is essential for calculating the real power component in AC power systems.

Q2: What happens if the denominator becomes zero?
A: If 3×V_r×cos(Φ_r) equals zero, the formula becomes undefined due to division by zero. This typically occurs when the receiving end voltage is zero or when cos(Φ_r) equals zero (phase angle = π/2 or 3π/2 radians).

Q3: Can this formula be used for single-phase systems?
A: This specific formula is designed for three-phase systems. For single-phase systems, a modified version without the factor of 3 would be used.

Q4: What are typical units for these parameters?
A: Voltage in volts (V), current in amperes (A), power in watts (W), and phase angles in radians. Ensure all inputs use consistent units.

Q5: How accurate is this calculation for practical applications?
A: The formula provides a theoretical calculation based on ideal conditions. In practical applications, additional factors like line impedance, capacitance, and system harmonics may need to be considered for more accurate results.