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Receiving End Current Using Sending End Voltage (LTL) Calculator

Formula Used:

\[ I_r = \frac{V_s - (V_r \times \cosh(\gamma \times L))}{Z_0 \times \sinh(\gamma \times L)} \]

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1. What is Receiving End Current?

Receiving End Current is defined as the magnitude and phase angle of current received at the load end of a long transmission line. It is a critical parameter in power system analysis for determining the performance and efficiency of transmission lines.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ I_r = \frac{V_s - (V_r \times \cosh(\gamma \times L))}{Z_0 \times \sinh(\gamma \times L)} \]

Where:

Explanation: This formula calculates the current at the receiving end of a long transmission line using hyperbolic functions to account for distributed parameters.

3. Importance of Receiving End Current Calculation

Details: Accurate calculation of receiving end current is essential for power system stability analysis, voltage regulation, load flow studies, and determining the efficiency of power transmission over long distances.

4. Using the Calculator

Tips: Enter all values in appropriate units. Sending and receiving end voltages in volts, propagation constant (dimensionless), length in meters, and characteristic impedance in ohms. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why are hyperbolic functions used in this calculation?
A: Hyperbolic functions (sinh and cosh) are used to model the distributed nature of parameters in long transmission lines, providing more accurate results than simplified lumped parameter models.

Q2: What is the significance of propagation constant?
A: The propagation constant (γ) represents the rate of change of amplitude and phase of a wave as it propagates along the transmission line, accounting for both attenuation and phase shift.

Q3: How does characteristic impedance affect the calculation?
A: Characteristic impedance determines how voltage and current waves propagate along the transmission line and affects the relationship between sending and receiving end parameters.

Q4: When is this formula most applicable?
A: This formula is specifically designed for long transmission lines (typically longer than 250 km) where distributed parameter analysis is necessary for accurate results.

Q5: What are the limitations of this calculation?
A: The calculation assumes uniform transmission line parameters along the entire length and may not account for non-linear effects, frequency dependencies, or transient conditions.

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