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Receiving End Angle using Losses (STL) Formula

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GoReceiving End Angle using Receiving End Power (STL) Formula

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Receiving End Phase Angle is the difference between the phasor of the current and voltage at the receiving end of a short transmission line. Check FAQs

Φ r = a \cos (\frac{(3 \cdot V s \cdot I s \cdot \cos (Φ s)) - P loss}{3 \cdot V r \cdot I r})

Φ_r - Receiving End Phase Angle?V_s - Sending End Voltage?I_s - Sending End Current?Φ_s - Sending End Phase Angle?P_loss - Power Loss?V_r - Receiving End Voltage?I_r - Receiving End Current?

Receiving End Angle using Losses (STL) Example

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Here is how the Receiving End Angle using Losses (STL) equation looks like with Values.

Here is how the Receiving End Angle using Losses (STL) equation looks like with Units.

Here is how the Receiving End Angle using Losses (STL) equation looks like.

75.1943 = a \cos (\frac{(3 \cdot 400 \cdot 3.98 \cdot \cos (30)) - 3000}{3 \cdot 380 \cdot 3.9})

75.1943° = a \cos (\frac{(3 \cdot 400V \cdot 3.98A \cdot \cos (30°)) - 3000W}{3 \cdot 380V \cdot 3.9A})

75.1943 = a \cos (\frac{(3 \cdot 400 \cdot 3.98 \cdot \cos (30)) - 3000}{3 \cdot 380 \cdot 3.9})

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Receiving End Angle using Losses (STL) Solution

Follow our step by step solution on how to calculate Receiving End Angle using Losses (STL)?

FIRST Step Consider the formula

Φ r = a \cos (\frac{(3 \cdot V s \cdot I s \cdot \cos (Φ s)) - P loss}{3 \cdot V r \cdot I r})

Next Step Substitute values of Variables

∴

Φ r = a \cos (\frac{(3 \cdot 400V \cdot 3.98A \cdot \cos (30°)) - 3000W}{3 \cdot 380V \cdot 3.9A})

Next Step Convert Units

∴

Φ r = a \cos (\frac{(3 \cdot 400V \cdot 3.98A \cdot \cos (0.5236rad)) - 3000W}{3 \cdot 380V \cdot 3.9A})

Next Step Prepare to Evaluate

∴

Φ r = a \cos (\frac{(3 \cdot 400 \cdot 3.98 \cdot \cos (0.5236)) - 3000}{3 \cdot 380 \cdot 3.9})

Next Step Evaluate

∴

Φ r = 1.31238861074275rad

Next Step Convert to Output's Unit

∴

Φ r = 75.1943284766114°

LAST Step Rounding Answer

∴

Φ r = 75.1943°

Receiving End Angle using Losses (STL) Formula Elements

Variables

Functions

Receiving End Phase Angle

Receiving End Phase Angle is the difference between the phasor of the current and voltage at the receiving end of a short transmission line.

Symbol: Φ_r

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Receiving End Phase Angle

Sending End Voltage

Sending End Voltage is the voltage at the sending end of a short transmission line.

Symbol: V_s

Measurement: Electric PotentialUnit: V

Note: Value can be positive or negative.

Formulas to find Sending End Voltage

Sending End Current

Sending End Current is defined as the amount of current injected into a short transmission line from the source or injectors.

Symbol: I_s

Measurement: Electric CurrentUnit: A

Note: Value can be positive or negative.

Formulas to find Sending End Current

Sending End Phase Angle

Sending End Phase Angle is the difference between the phasors of current and voltage at thee sending end of a short transmission line.

Symbol: Φ_s

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Sending End Phase Angle

Power Loss

Power Loss is defined as the deviation in the power transferred from sending end to receiving end of a short transmission line.

Symbol: P_loss

Measurement: PowerUnit: W

Note: Value should be greater than 0.

Formulas to find Power Loss

Receiving End Voltage

Receiving End Voltage is the voltage developed at the receiving end of a short transmission line.

Symbol: V_r

Measurement: Electric PotentialUnit: V

Note: Value can be positive or negative.

Formulas to find Receiving End Voltage

Receiving End Current

Receiving End Current is defined as the magnitude and phase angle of current received at the load end of a short transmission line.

Symbol: I_r

Measurement: Electric CurrentUnit: A

Note: Value can be positive or negative.

Formulas to find Receiving End Current

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: acos(Number)

Other Formulas to find Receiving End Phase Angle

Go Receiving End Angle using Transmission Efficiency (STL)

Φ r = a \cos (η \cdot V s \cdot I s \cdot \frac{\cos (Φ s)}{I r \cdot V r})

Go Receiving End Angle using Receiving End Power (STL)

Φ r = a \cos (\frac{P r}{3 \cdot V r \cdot I r})

Other formulas in Power and Phase Difference category

Go Transmitted Current (SC Line)

I t = \frac{V t}{Z 0}

Go Receiving End Power (STL)

P r = 3 \cdot V r \cdot I r \cdot \cos (Φ r)

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

Receiving End Angle using Losses (STL) evaluator 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 evaluate the Receiving End Phase Angle, The Receiving End Angle using Losses (STL) is the phase angle of the voltage at the load end relative to the source voltage. In short lines, this angle is typically small due to negligible reactive components, indicating minimal phase shift and efficient power transfer from the source to the load. Receiving End Phase Angle is denoted by Φ_r symbol.

How to evaluate Receiving End Angle using Losses (STL) using this online evaluator? To use this online evaluator 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.

FAQs on Receiving End Angle using Losses (STL)

What is the formula to find Receiving End Angle using Losses (STL)?

The formula of Receiving End Angle using Losses (STL) is expressed as 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)). Here is an example- 2586.298 = acos(((3*400*3.98*cos(0.5235987755982))-3000)/(3*380*3.9)).

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

With 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) we can find Receiving End Angle using Losses (STL) using the formula - 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)). This formula also uses Cosine (cos), Inverse Cosine (acos) function(s).

What are the other ways to Calculate Receiving End Phase Angle?

Here are the different ways to Calculate Receiving End Phase Angle-

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))

Can the Receiving End Angle using Losses (STL) be negative?

Yes, the Receiving End Angle using Losses (STL), measured in Angle can be negative.

Which unit is used to measure Receiving End Angle using Losses (STL)?

Receiving End Angle using Losses (STL) is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Receiving End Angle using Losses (STL) can be measured.

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Receiving End Angle using Losses (STL) Formula

​GoReceiving End Angle using Transmission Efficiency (STL) Formula

​GoReceiving End Angle using Receiving End Power (STL) Formula

Receiving End Angle using Losses (STL) Example

Receiving End Angle using Losses (STL) Solution

Receiving End Angle using Losses (STL) Formula Elements

Other Formulas to find Receiving End Phase Angle

Other formulas in Power and Phase Difference category

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

FAQs on Receiving End Angle using Losses (STL)

Variable Name

GoReceiving End Angle using Transmission Efficiency (STL) Formula

GoReceiving End Angle using Receiving End Power (STL) Formula