Receiving End Angle using Transmission Efficiency in Nominal Pi Method Calculator

✖Transmission Efficiency in PI is the total sideband power by the total transmitted power.ⓘ Transmission Efficiency in PI [η_pi]			+10% -10%
✖Sending End Power in PI is defined as the power at receiving end of a medium transmission line.ⓘ Sending End Power in PI [P_s(pi)]			+10% -10%
✖Receiving End Current in PI is defined as the magnitude and phase angle of current received at the load end of a medium transmission line.ⓘ Receiving End Current in PI [I_r(pi)]			+10% -10%
✖Receiving End Voltage in PI is the voltage developed at the receiving end of a transmission line.ⓘ Receiving End Voltage in PI [V_r(pi)]			+10% -10%

✖Receiving End Phase Angle in PI is the difference between the phasors of current and voltage at the receiving end of a transmission line.ⓘ Receiving End Angle using Transmission Efficiency in Nominal Pi Method [Φ_r(pi)]

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Formula

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Receiving End Angle using Transmission Efficiency in Nominal Pi Method

Formula

`"Φ"_{"r(pi)"} = acos(("η"_{"pi"}*"P"_{"s(pi)"})/(3*"I"_{"r(pi)"}*"V"_{"r(pi)"}))`

Example

`"87.99815°"=acos(("0.745"*"335W")/(3*"7.44A"*"320.1V"))`

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Receiving End Angle using Transmission Efficiency in Nominal Pi Method Solution

STEP 0: Pre-Calculation Summary

Formula Used

Receiving End Phase Angle in PI = acos((Transmission Efficiency in PI*Sending End Power in PI)/(3*Receiving End Current in PI*Receiving End Voltage in PI))
Φ_r(pi) = acos((η_pi*P_s(pi))/(3*I_r(pi)*V_r(pi)))
This formula uses 2 Functions, 5 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 in PI - (Measured in Radian) - Receiving End Phase Angle in PI is the difference between the phasors of current and voltage at the receiving end of a transmission line.
Transmission Efficiency in PI - Transmission Efficiency in PI is the total sideband power by the total transmitted power.
Sending End Power in PI - (Measured in Watt) - Sending End Power in PI is defined as the power at receiving end of a medium transmission line.
Receiving End Current in PI - (Measured in Ampere) - Receiving End Current in PI is defined as the magnitude and phase angle of current received at the load end of a medium transmission line.
Receiving End Voltage in PI - (Measured in Volt) - Receiving End Voltage in PI is the voltage developed at the receiving end of a transmission line.

STEP 1: Convert Input(s) to Base Unit

Transmission Efficiency in PI: 0.745 --> No Conversion Required
Sending End Power in PI: 335 Watt --> 335 Watt No Conversion Required
Receiving End Current in PI: 7.44 Ampere --> 7.44 Ampere No Conversion Required
Receiving End Voltage in PI: 320.1 Volt --> 320.1 Volt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ_r(pi) = acos((η_pi*P_s(pi))/(3*I_r(pi)*V_r(pi))) --> acos((0.745*335)/(3*7.44*320.1))

Evaluating ... ...

Φ_r(pi) = 1.53585739859534

STEP 3: Convert Result to Output's Unit

1.53585739859534 Radian -->87.9981468734714 Degree (Check conversion here)

FINAL ANSWER

87.9981468734714 ≈ 87.99815 Degree <-- Receiving End Phase Angle in PI

(Calculation completed in 00.020 seconds)

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Home » Engineering » Electrical » Power System » Transmission Lines » Medium Line » Nominal Pi-Method in Medium Line » Receiving End Angle using Transmission Efficiency in Nominal Pi Method

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< 20 Nominal Pi-Method in Medium Line Calculators

Receiving End Current using Transmission Efficiency in Nominal Pi Method

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

Receiving End Angle using Transmission Efficiency in Nominal Pi Method

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

Sending End Voltage using Transmission Efficiency in Nominal Pi Method

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

Sending End Current using Transmission Efficiency in Nominal Pi Method

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

Receiving End Voltage using Sending End Power in Nominal Pi Method

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

Load Current using Transmission Efficiency in Nominal Pi Method

Go Load Current in PI = sqrt(((Receiving End Power in PI/Transmission Efficiency in PI)-Receiving End Power in PI)/Resistance in PI*3)

Voltage Regulation (Nominal Pi Method)

Go Voltage Regulation in PI = (Sending End Voltage in PI-Receiving End Voltage in PI)/Receiving End Voltage in PI

Losses using Transmission Efficiency in Nominal Pi Method

Go Power Loss in PI = (Receiving End Power in PI/Transmission Efficiency in PI)-Receiving End Power in PI

B Parameter for Reciprocal Network in Nominal Pi Method

Go B Parameter in PI = ((A Parameter in PI*D Parameter in PI)-1)/C Parameter in PI

C Parameter in Nominal Pi Method

Go C Parameter in PI = Admittance in PI*(1+(Admittance in PI*Impedance in PI/4))

Load Current using Losses in Nominal Pi Method

Go Load Current in PI = sqrt(Power Loss in PI/Resistance in PI)

Receiving End Voltage using Voltage Regulation in Nominal Pi Method

Go Receiving End Voltage in PI = Sending End Voltage in PI/(Voltage Regulation in PI+1)

Sending End Voltage using Voltage Regulation in Nominal Pi Method

Go Sending End Voltage in PI = Receiving End Voltage in PI*(Voltage Regulation in PI+1)

Sending End Power using Transmission Efficiency in Nominal Pi Method

Go Sending End Power in PI = Receiving End Power in PI/Transmission Efficiency in PI

Transmission Efficiency (Nominal Pi Method)

Go Transmission Efficiency in PI = Receiving End Power in PI/Sending End Power in PI

Impedance using A Parameter in Nominal Pi Method

Go Impedance in PI = 2*(A Parameter in PI-1)/Admittance in PI

A-Parameter in Nominal Pi Method

Go A Parameter in PI = 1+(Admittance in PI*Impedance in PI/2)

D Parameter in Nominal Pi Method

Go D Parameter in PI = 1+(Impedance in PI*Admittance in PI/2)

Losses in Nominal Pi Method

Go Power Loss in PI = (Load Current in PI^2)*Resistance in PI

Resistance using Losses in Nominal Pi Method

Go Resistance in PI = Power Loss in PI/Load Current in PI^2

Receiving End Angle using Transmission Efficiency in Nominal Pi Method Formula

Which of the following transmission line can be considered as a medium transmission line?

The transmission lines having a length of more than 80 Km and less than 200 Km are considered medium transmission lines. Their operating voltage is more than short transmission lines but less than long transmission lines.

How to Calculate Receiving End Angle using Transmission Efficiency in Nominal Pi Method?

Receiving End Angle using Transmission Efficiency in Nominal Pi Method calculator uses Receiving End Phase Angle in PI = acos((Transmission Efficiency in PI*Sending End Power in PI)/(3*Receiving End Current in PI*Receiving End Voltage in PI)) to calculate the Receiving End Phase Angle in PI, The Receiving End Angle using Transmission Efficiency in Nominal Pi method formula is defined as the angle between receiving end voltage and receiving end current. Receiving End Phase Angle in PI is denoted by Φ_r(pi) symbol.

How to calculate Receiving End Angle using Transmission Efficiency in Nominal Pi Method using this online calculator? To use this online calculator for Receiving End Angle using Transmission Efficiency in Nominal Pi Method, enter Transmission Efficiency in PI (η_pi), Sending End Power in PI (P_s(pi)), Receiving End Current in PI (I_r(pi)) & Receiving End Voltage in PI (V_r(pi)) and hit the calculate button. Here is how the Receiving End Angle using Transmission Efficiency in Nominal Pi Method calculation can be explained with given input values -> 5041.922 = acos((0.745*335)/(3*7.44*320.1)).

FAQ

What is Receiving End Angle using Transmission Efficiency in Nominal Pi Method?

The Receiving End Angle using Transmission Efficiency in Nominal Pi method formula is defined as the angle between receiving end voltage and receiving end current and is represented as Φ_r(pi) = acos((η_pi*P_s(pi))/(3*I_r(pi)*V_r(pi))) or Receiving End Phase Angle in PI = acos((Transmission Efficiency in PI*Sending End Power in PI)/(3*Receiving End Current in PI*Receiving End Voltage in PI)). Transmission Efficiency in PI is the total sideband power by the total transmitted power, Sending End Power in PI is defined as the power at receiving end of a medium transmission line, Receiving End Current in PI is defined as the magnitude and phase angle of current received at the load end of a medium transmission line & Receiving End Voltage in PI is the voltage developed at the receiving end of a transmission line.

How to calculate Receiving End Angle using Transmission Efficiency in Nominal Pi Method?

The Receiving End Angle using Transmission Efficiency in Nominal Pi method formula is defined as the angle between receiving end voltage and receiving end current is calculated using Receiving End Phase Angle in PI = acos((Transmission Efficiency in PI*Sending End Power in PI)/(3*Receiving End Current in PI*Receiving End Voltage in PI)). To calculate Receiving End Angle using Transmission Efficiency in Nominal Pi Method, you need Transmission Efficiency in PI (η_pi), Sending End Power in PI (P_s(pi)), Receiving End Current in PI (I_r(pi)) & Receiving End Voltage in PI (V_r(pi)). With our tool, you need to enter the respective value for Transmission Efficiency in PI, Sending End Power in PI, Receiving End Current in PI & Receiving End Voltage in PI 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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