Sending End Voltage (LTL) Calculator

✖Receiving end voltage is the voltage developed at the receiving end of a long transmission line.ⓘ Receiving End Voltage [V_r]			+10% -10%
✖Propagation Constant is defined as the measure of the change in amplitude and phase per unit distance in a transmission line.ⓘ Propagation Constant [γ]			+10% -10%
✖Length is defined as the end to end distance of the conductor used in a long transmission line.ⓘ Length [L]			+10% -10%
✖Characteristic Impedanceis defined as the ratio of the amplitudes of voltage and current of a single wave propagating along the transmission line.ⓘ Characteristic Impedance [Z₀]			+10% -10%
✖Receiving End Current is defined as the magnitude and phase angle of current received at the load end of a long transmission line.ⓘ Receiving End Current [I_r]			+10% -10%

✖Sending end voltage is the voltage at the sending end of a long transmission line.ⓘ Sending End Voltage (LTL) [V_s]

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Formula

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Sending End Voltage (LTL)

Formula

V s = V r \cdot \cosh (γ \cdot L) + Z 0 \cdot I r \cdot \sinh (γ \cdot L)

Example

189.5744 kV = 8.88 kV \cdot \cosh (1.24 \cdot 3 m) + 48.989 Ω \cdot 6.19 A \cdot \sinh (1.24 \cdot 3 m)

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Sending End Voltage (LTL) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sending End Voltage = Receiving End Voltage*cosh(Propagation Constant*Length)+Characteristic Impedance*Receiving End Current*sinh(Propagation Constant*Length)
V_s = V_r*cosh(γ*L)+Z₀*I_r*sinh(γ*L)
This formula uses 2 Functions, 6 Variables

Functions Used

sinh - The hyperbolic sine function, also known as the sinh function, is a mathematical function that is defined as the hyperbolic analogue of the sine function., sinh(Number)
cosh - The hyperbolic cosine function is a mathematical function that is defined as the ratio of the sum of the exponential functions of x and negative x to 2., cosh(Number)

Variables Used

Sending End Voltage - (Measured in Volt) - Sending end voltage is the voltage at the sending end of a long transmission line.
Receiving End Voltage - (Measured in Volt) - Receiving end voltage is the voltage developed at the receiving end of a long transmission line.
Propagation Constant - Propagation Constant is defined as the measure of the change in amplitude and phase per unit distance in a transmission line.
Length - (Measured in Meter) - Length is defined as the end to end distance of the conductor used in a long transmission line.
Characteristic Impedance - (Measured in Ohm) - Characteristic Impedanceis defined as the ratio of the amplitudes of voltage and current of a single wave propagating along the transmission line.
Receiving End Current - (Measured in Ampere) - Receiving End Current is defined as the magnitude and phase angle of current received at the load end of a long transmission line.

STEP 1: Convert Input(s) to Base Unit

Receiving End Voltage: 8.88 Kilovolt --> 8880 Volt (Check conversion here)
Propagation Constant: 1.24 --> No Conversion Required
Length: 3 Meter --> 3 Meter No Conversion Required
Characteristic Impedance: 48.989 Ohm --> 48.989 Ohm No Conversion Required
Receiving End Current: 6.19 Ampere --> 6.19 Ampere No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_s = V_r*cosh(γ*L)+Z₀*I_r*sinh(γ*L) --> 8880*cosh(1.24*3)+48.989*6.19*sinh(1.24*3)

Evaluating ... ...

V_s = 189574.381124362

STEP 3: Convert Result to Output's Unit

189574.381124362 Volt -->189.574381124363 Kilovolt (Check conversion here)

FINAL ANSWER

189.574381124363 ≈ 189.5744 Kilovolt <-- Sending End Voltage

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electrical » Power System » Transmission Lines » Long Transmission Line » Current and Voltage » Sending End Voltage (LTL)

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Created by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

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Osmania University (OU), Hyderabad

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< Current and Voltage Calculators

Receiving End Current using Sending End Voltage (LTL)

Go Receiving End Current = (Sending End Voltage-(Receiving End Voltage*cosh(Propagation Constant*Length)))/(Characteristic Impedance*sinh(Propagation Constant*Length))

Receiving End Current using Sending End Current (LTL)

Go Receiving End Current = (Sending End Current-(Receiving End Voltage*(sinh(Propagation Constant*Length))/Characteristic Impedance))/cosh(Propagation Constant*Length)

Sending End Current (LTL)

Go Sending End Current = Receiving End Current*cosh(Propagation Constant*Length)+((Receiving End Voltage*sinh(Propagation Constant*Length))/Characteristic Impedance)

Sending End Voltage (LTL)

Go Sending End Voltage = Receiving End Voltage*cosh(Propagation Constant*Length)+Characteristic Impedance*Receiving End Current*sinh(Propagation Constant*Length)

Sending End Voltage (LTL) Formula

Sending End Voltage = Receiving End Voltage*cosh(Propagation Constant*Length)+Characteristic Impedance*Receiving End Current*sinh(Propagation Constant*Length)
V_s = V_r*cosh(γ*L)+Z₀*I_r*sinh(γ*L)

Which is the type of long transmission line?

A power transmission line with its effective length of around 250 Kms or above is referred to as a long transmission line. The line constants are uniformly distributed over the entire length of the line.

How to Calculate Sending End Voltage (LTL)?

Sending End Voltage (LTL) calculator uses Sending End Voltage = Receiving End Voltage*cosh(Propagation Constant*Length)+Characteristic Impedance*Receiving End Current*sinh(Propagation Constant*Length) to calculate the Sending End Voltage, The Sending End Voltage (LTL) formula is defined as the voltage at the sending end of the long transmission lines. Sending End Voltage is denoted by V_s symbol.

How to calculate Sending End Voltage (LTL) using this online calculator? To use this online calculator for Sending End Voltage (LTL), enter Receiving End Voltage (V_r), Propagation Constant (γ), Length (L), Characteristic Impedance (Z₀) & Receiving End Current (I_r) and hit the calculate button. Here is how the Sending End Voltage (LTL) calculation can be explained with given input values -> 0.189574 = 8880*cosh(1.24*3)+48.989*6.19*sinh(1.24*3).

FAQ

What is Sending End Voltage (LTL)?

The Sending End Voltage (LTL) formula is defined as the voltage at the sending end of the long transmission lines and is represented as V_s = V_r*cosh(γ*L)+Z₀*I_r*sinh(γ*L) or Sending End Voltage = Receiving End Voltage*cosh(Propagation Constant*Length)+Characteristic Impedance*Receiving End Current*sinh(Propagation Constant*Length). Receiving end voltage is the voltage developed at the receiving end of a long transmission line, Propagation Constant is defined as the measure of the change in amplitude and phase per unit distance in a transmission line, Length is defined as the end to end distance of the conductor used in a long transmission line, Characteristic Impedanceis defined as the ratio of the amplitudes of voltage and current of a single wave propagating along the transmission line & Receiving End Current is defined as the magnitude and phase angle of current received at the load end of a long transmission line.

How to calculate Sending End Voltage (LTL)?

The Sending End Voltage (LTL) formula is defined as the voltage at the sending end of the long transmission lines is calculated using Sending End Voltage = Receiving End Voltage*cosh(Propagation Constant*Length)+Characteristic Impedance*Receiving End Current*sinh(Propagation Constant*Length). To calculate Sending End Voltage (LTL), you need Receiving End Voltage (V_r), Propagation Constant (γ), Length (L), Characteristic Impedance (Z₀) & Receiving End Current (I_r). With our tool, you need to enter the respective value for Receiving End Voltage, Propagation Constant, Length, Characteristic Impedance & Receiving End Current and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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