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