Receiving End Voltage Using Sending End Current (LTL) Calculator

Formula Used:

\[ V_r = (I_s - I_r \times \cosh(\gamma \times L)) \times (Z_0 / \sinh(\gamma \times L)) \]

Sending End Current (Is):

Receiving End Current (Ir):

Propagation Constant (γ):

Length (L):

Characteristic Impedance (Z0):

Receiving End Voltage (Vr):

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1. What is Receiving End Voltage Using Sending End Current (LTL)?

The Receiving End Voltage calculation using Sending End Current is a method to determine the voltage at the receiving end of a long transmission line (LTL) based on the sending end current, receiving end current, propagation constant, line length, and characteristic impedance.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V_r = (I_s - I_r \times \cosh(\gamma \times L)) \times (Z_0 / \sinh(\gamma \times L)) \]

Where:

\( V_r \) — Receiving End Voltage (V)
\( I_s \) — Sending End Current (A)
\( I_r \) — Receiving End Current (A)
\( \gamma \) — Propagation Constant
\( L \) — Length (m)
\( Z_0 \) — Characteristic Impedance (Ω)

Explanation: This formula accounts for the hyperbolic relationship between sending and receiving end parameters in long transmission lines, considering the propagation characteristics and impedance matching.

3. Importance of Receiving End Voltage Calculation

Details: Accurate calculation of receiving end voltage is crucial for power system analysis, voltage regulation, stability assessment, and ensuring proper power delivery in long transmission lines.

4. Using the Calculator

Tips: Enter all values in appropriate units. Sending End Current and Receiving End Current in amperes, Propagation Constant as a dimensionless quantity, Length in meters, and Characteristic Impedance in ohms. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a long transmission line (LTL)?
A: A long transmission line is typically considered to be longer than 250 km, where distributed parameter analysis is necessary due to significant capacitive and inductive effects.

Q2: Why use hyperbolic functions in this calculation?
A: Hyperbolic functions (sinh and cosh) accurately model the wave propagation characteristics and impedance relationships in long transmission lines.

Q3: What is the significance of characteristic impedance?
A: Characteristic impedance represents the ratio of voltage to current for a wave propagating along the transmission line and is crucial for impedance matching and power transfer efficiency.

Q4: How does propagation constant affect the calculation?
A: The propagation constant determines how the voltage and current waves attenuate and change phase as they propagate along the transmission line.

Q5: What are typical values for these parameters in real transmission lines?
A: Characteristic impedance typically ranges from 200-400 Ω for overhead lines, while propagation constant depends on frequency and line parameters, usually between 0.001-0.01 per km.