Receiving End Angle using Losses (STL) Calculator

✖Sending end voltage is the voltage at the sending end of a transmission line.ⓘ Sending End Voltage [V_s]			+10% -10%
✖Sending End Current is defined as the amount of current injected into a short transmission line from the source or injectors.ⓘ Sending End Current [I_s]			+10% -10%
✖Sending End Phase Angle is the difference between the phasors of current and voltage at thee sending end of a short transmission line.ⓘ Sending End Phase Angle [Φ_s]			+10% -10%
✖Power Loss is defined as the deviation in the power transferred from sending end to receiving end of a short transmission line.ⓘ Power Loss [P_loss]			+10% -10%
✖Receiving end voltage is the voltage developed at the receiving end of a transmission line.ⓘ Receiving End Voltage [V_r]			+10% -10%
✖Receiving End Current is defined as the magnitude and phase angle of current received at the load end of a short transmission line.ⓘ Receiving End Current [I_r]			+10% -10%

✖Receiving End Phase Angle is the difference between the phasor of the current and voltage at the receiving end of a short transmission line.ⓘ Receiving End Angle using Losses (STL) [Φ_r]

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Formula

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Receiving End Angle using Losses (STL)

Formula

`"Φ"_{"r"} = acos(((3*"V"_{"s"}*"I"_{"s"}*cos("Φ"_{"s"}))-"P"_{"loss"})/(3*"V"_{"r"}*"I"_{"r"}))`

Example

`"75.19433°"=acos(((3*"400V"*"3.98A"*cos("30°"))-"3000W")/(3*"380V"*"3.9A"))`

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Receiving End Angle using Losses (STL) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Receiving End Phase Angle = acos(((3*Sending End Voltage*Sending End Current*cos(Sending End Phase Angle))-Power Loss)/(3*Receiving End Voltage*Receiving End Current))
Φ_r = acos(((3*V_s*I_s*cos(Φ_s))-P_loss)/(3*V_r*I_r))
This formula uses 2 Functions, 7 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)

Variables Used

Receiving End Phase Angle - (Measured in Radian) - Receiving End Phase Angle is the difference between the phasor of the current and voltage at the receiving end of a short transmission line.
Sending End Voltage - (Measured in Volt) - Sending end voltage is the voltage at the sending end of a transmission line.
Sending End Current - (Measured in Ampere) - Sending End Current is defined as the amount of current injected into a short transmission line from the source or injectors.
Sending End Phase Angle - (Measured in Radian) - Sending End Phase Angle is the difference between the phasors of current and voltage at thee sending end of a short transmission line.
Power Loss - (Measured in Watt) - Power Loss is defined as the deviation in the power transferred from sending end to receiving end of a short transmission line.
Receiving End Voltage - (Measured in Volt) - Receiving end voltage is the voltage developed at the receiving end of a 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 short transmission line.

STEP 1: Convert Input(s) to Base Unit

Sending End Voltage: 400 Volt --> 400 Volt No Conversion Required
Sending End Current: 3.98 Ampere --> 3.98 Ampere No Conversion Required
Sending End Phase Angle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Power Loss: 3000 Watt --> 3000 Watt No Conversion Required
Receiving End Voltage: 380 Volt --> 380 Volt No Conversion Required
Receiving End Current: 3.9 Ampere --> 3.9 Ampere No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ_r = acos(((3*V_s*I_s*cos(Φ_s))-P_loss)/(3*V_r*I_r)) --> acos(((3*400*3.98*cos(0.5235987755982))-3000)/(3*380*3.9))

Evaluating ... ...

Φ_r = 1.31238861074275

STEP 3: Convert Result to Output's Unit

1.31238861074275 Radian -->75.1943284766114 Degree (Check conversion here)

FINAL ANSWER

75.1943284766114 ≈ 75.19433 Degree <-- Receiving End Phase Angle

(Calculation completed in 00.020 seconds)

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Home » Engineering » Electrical » Power System » Transmission Lines » Short Line » Power & Phase Difference » Receiving End Angle using Losses (STL)

Credits

Created by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has created this Calculator and 1500+ more calculators!

Verified by Payal Priya

Birsa Institute of Technology (BIT), Sindri

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< 8 Power & Phase Difference Calculators

Receiving End Angle using Transmission Efficiency (STL)

Go Receiving End Phase Angle = acos(Transmission Efficiency*Sending End Voltage*Sending End Current*cos(Sending End Phase Angle)/(Receiving End Current*Receiving End Voltage))

Receiving End Angle using Losses (STL)

Go Receiving End Phase Angle = acos(((3*Sending End Voltage*Sending End Current*cos(Sending End Phase Angle))-Power Loss)/(3*Receiving End Voltage*Receiving End Current))

Sending End Angle using Receiving End Parameters (STL)

Go Sending End Phase Angle = acos((Receiving End Voltage*cos(Receiving End Phase Angle)+(Receiving End Current*Resistance))/Sending End Voltage)

Receiving End Angle using Receiving End Power (STL)

Go Receiving End Phase Angle = acos(Receiving End Power/(3*Receiving End Voltage*Receiving End Current))

Receiving End Power (STL)

Go Receiving End Power = 3*Receiving End Voltage*Receiving End Current*(cos(Receiving End Phase Angle))

Sending End Angle using Sending End Power (STL)

Go Sending End Phase Angle = acos(Sending End Power/(Sending End Voltage*Sending End Current*3))

Sending End Power (STL)

Go Sending End Power = 3*Sending End Current*Sending End Voltage*cos(Sending End Phase Angle)

Transmitted Current (SC Line)

Go Transmitted Current = Transmitted Voltage/Characteristic Impedance

Receiving End Angle using Losses (STL) Formula

What are losses of short transmission lines?

Short transmission lines incur losses primarily due to conductor resistance, dielectric losses in insulation, and leakage losses. Conductor resistance leads to I²R losses, while dielectric losses occur from the insulating materials. Leakage losses stem from the electric field extending beyond the line, dissipating energy.

How to Calculate Receiving End Angle using Losses (STL)?

Receiving End Angle using Losses (STL) calculator uses Receiving End Phase Angle = acos(((3*Sending End Voltage*Sending End Current*cos(Sending End Phase Angle))-Power Loss)/(3*Receiving End Voltage*Receiving End Current)) to calculate the Receiving End Phase Angle, The Receiving End Angle using Losses (STL) formula is defined as the angle between receiving end voltage and receiving end current. Receiving End Phase Angle is denoted by Φ_r symbol.

How to calculate Receiving End Angle using Losses (STL) using this online calculator? To use this online calculator for Receiving End Angle using Losses (STL), enter Sending End Voltage (V_s), Sending End Current (I_s), Sending End Phase Angle (Φ_s), Power Loss (P_loss), Receiving End Voltage (V_r) & Receiving End Current (I_r) and hit the calculate button. Here is how the Receiving End Angle using Losses (STL) calculation can be explained with given input values -> 2586.298 = acos(((3*400*3.98*cos(0.5235987755982))-3000)/(3*380*3.9)).

FAQ

What is Receiving End Angle using Losses (STL)?

The Receiving End Angle using Losses (STL) formula is defined as the angle between receiving end voltage and receiving end current and is represented as Φ_r = acos(((3*V_s*I_s*cos(Φ_s))-P_loss)/(3*V_r*I_r)) or Receiving End Phase Angle = acos(((3*Sending End Voltage*Sending End Current*cos(Sending End Phase Angle))-Power Loss)/(3*Receiving End Voltage*Receiving End Current)). Sending end voltage is the voltage at the sending end of a transmission line, Sending End Current is defined as the amount of current injected into a short transmission line from the source or injectors, Sending End Phase Angle is the difference between the phasors of current and voltage at thee sending end of a short transmission line, Power Loss is defined as the deviation in the power transferred from sending end to receiving end of a short transmission line, Receiving end voltage is the voltage developed at the receiving end of a transmission line & Receiving End Current is defined as the magnitude and phase angle of current received at the load end of a short transmission line.

How to calculate Receiving End Angle using Losses (STL)?

The Receiving End Angle using Losses (STL) formula is defined as the angle between receiving end voltage and receiving end current is calculated using Receiving End Phase Angle = acos(((3*Sending End Voltage*Sending End Current*cos(Sending End Phase Angle))-Power Loss)/(3*Receiving End Voltage*Receiving End Current)). To calculate Receiving End Angle using Losses (STL), you need Sending End Voltage (V_s), Sending End Current (I_s), Sending End Phase Angle (Φ_s), Power Loss (P_loss), Receiving End Voltage (V_r) & Receiving End Current (I_r). With our tool, you need to enter the respective value for Sending End Voltage, Sending End Current, Sending End Phase Angle, Power Loss, Receiving End Voltage & Receiving End Current and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Receiving End Phase Angle?

In this formula, Receiving End Phase Angle uses Sending End Voltage, Sending End Current, Sending End Phase Angle, Power Loss, Receiving End Voltage & Receiving End Current. We can use 2 other way(s) to calculate the same, which is/are as follows -

Receiving End Phase Angle = acos(Transmission Efficiency*Sending End Voltage*Sending End Current*cos(Sending End Phase Angle)/(Receiving End Current*Receiving End Voltage))
Receiving End Phase Angle = acos(Receiving End Power/(3*Receiving End Voltage*Receiving End Current))

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