Angle of PF using Area of X-Section(3-Phase 3-Wire OS) Calculator

✖Resistivity is the measure of how strongly a material opposes the flow of current through them.ⓘ Resistivity [ρ]			+10% -10%
✖Power Transmitted is defined as the product of current and voltage phasor in a overhead ac line at the receiving end.ⓘ Power Transmitted [P]			+10% -10%
✖Length of Overhead AC Wire is the total length of the wire from one end to other end.ⓘ Length of Overhead AC Wire [L]			+10% -10%
✖Area of Overhead AC Wire is defined as the cross-sectional area of the wire of an AC supply system.ⓘ Area of Overhead AC Wire [A]			+10% -10%
✖Line Losses is defined as the total losses occurring in an Overhead AC line when in use.ⓘ Line Losses [P_loss]			+10% -10%
✖Maximum Voltage Overhead AC is defined as the peak amplitude of the AC voltage supplied to the line or wire.ⓘ Maximum Voltage Overhead AC [V_m]			+10% -10%

✖Phase Difference is defined as the difference between the phasor of apparent and real power (in degrees) or between voltage and current in an ac circuit.ⓘ Angle of PF using Area of X-Section(3-Phase 3-Wire OS) [Φ]

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Angle of PF using Area of X-Section(3-Phase 3-Wire OS) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Phase Difference = acos(sqrt(2*Resistivity*(Power Transmitted^2*Length of Overhead AC Wire^2)/(3*Area of Overhead AC Wire*Line Losses*(Maximum Voltage Overhead AC^2))))
Φ = acos(sqrt(2*ρ*(P^2*L^2)/(3*A*P_loss*(V_m^2))))
This formula uses 3 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)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Phase Difference - (Measured in Radian) - Phase Difference is defined as the difference between the phasor of apparent and real power (in degrees) or between voltage and current in an ac circuit.
Resistivity - (Measured in Ohm Meter) - Resistivity is the measure of how strongly a material opposes the flow of current through them.
Power Transmitted - (Measured in Watt) - Power Transmitted is defined as the product of current and voltage phasor in a overhead ac line at the receiving end.
Length of Overhead AC Wire - (Measured in Meter) - Length of Overhead AC Wire is the total length of the wire from one end to other end.
Area of Overhead AC Wire - (Measured in Square Meter) - Area of Overhead AC Wire is defined as the cross-sectional area of the wire of an AC supply system.
Line Losses - (Measured in Watt) - Line Losses is defined as the total losses occurring in an Overhead AC line when in use.
Maximum Voltage Overhead AC - (Measured in Volt) - Maximum Voltage Overhead AC is defined as the peak amplitude of the AC voltage supplied to the line or wire.

STEP 1: Convert Input(s) to Base Unit

Resistivity: 1.7E-05 Ohm Meter --> 1.7E-05 Ohm Meter No Conversion Required
Power Transmitted: 890 Watt --> 890 Watt No Conversion Required
Length of Overhead AC Wire: 10.63 Meter --> 10.63 Meter No Conversion Required
Area of Overhead AC Wire: 0.79 Square Meter --> 0.79 Square Meter No Conversion Required
Line Losses: 8.23 Watt --> 8.23 Watt No Conversion Required
Maximum Voltage Overhead AC: 62 Volt --> 62 Volt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ = acos(sqrt(2*ρ*(P^2*L^2)/(3*A*P_loss*(V_m^2)))) --> acos(sqrt(2*1.7E-05*(890^2*10.63^2)/(3*0.79*8.23*(62^2))))

Evaluating ... ...

Φ = 1.36794422694041

STEP 3: Convert Result to Output's Unit

1.36794422694041 Radian -->78.3774308129865 Degree (Check conversion here)

FINAL ANSWER

78.3774308129865 ≈ 78.37743 Degree <-- Phase Difference

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electrical » Power System » Overhead AC Supply » 3 3 Wire System » Power and Power Factor » Angle of PF using Area of X-Section(3-Phase 3-Wire OS)

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< Power and Power Factor Calculators

Power Transmitted using Area of X-Section(3-Phase 3-Wire OS)

LaTeX Go Power Transmitted = sqrt((3*Area of Overhead AC Wire*(Maximum Voltage Overhead AC^2)*Line Losses*((cos(Phase Difference))^2))/(Resistivity*2*Length of Overhead AC Wire))

Transmitted Power using Load Current(3-Phase 3-Wire OS)

LaTeX Go Power Transmitted = Current Overhead AC*Maximum Voltage Overhead AC*(cos(Phase Difference))/(sqrt(2))

Power Factor using Load Current(3-Phase 3-Wire OS)

LaTeX Go Power Factor = sqrt(2)*Power Transmitted/(3*Current Overhead AC*Maximum Voltage Overhead AC)

Power Transmitted(3-Phase 3-Wire OS)

LaTeX Go Power Transmitted = (1/3)*Power Transmitted per Phase

Angle of PF using Area of X-Section(3-Phase 3-Wire OS) Formula

LaTeX Go

How is a three-wire three-phase system is better than a two-wire single-phase system?

A three-wire, three-phase system can then transmit 73% more power than a two-wire, single-phase system by just the addition of one wire. A three-phase system also has some major advantages in the generation and use of electricity by rotating machines as will be explained later.

How to Calculate Angle of PF using Area of X-Section(3-Phase 3-Wire OS)?

Angle of PF using Area of X-Section(3-Phase 3-Wire OS) calculator uses Phase Difference = acos(sqrt(2*Resistivity*(Power Transmitted^2*Length of Overhead AC Wire^2)/(3*Area of Overhead AC Wire*Line Losses*(Maximum Voltage Overhead AC^2)))) to calculate the Phase Difference, The Angle of PF using Area of X-section(3-phase 3-wire OS) formula is defined as the phase angle between reactive and active power. Phase Difference is denoted by Φ symbol.

How to calculate Angle of PF using Area of X-Section(3-Phase 3-Wire OS) using this online calculator? To use this online calculator for Angle of PF using Area of X-Section(3-Phase 3-Wire OS), enter Resistivity (ρ), Power Transmitted (P), Length of Overhead AC Wire (L), Area of Overhead AC Wire (A), Line Losses (P_loss) & Maximum Voltage Overhead AC (V_m) and hit the calculate button. Here is how the Angle of PF using Area of X-Section(3-Phase 3-Wire OS) calculation can be explained with given input values -> 4490.696 = acos(sqrt(2*1.7E-05*(890^2*10.63^2)/(3*0.79*8.23*(62^2)))).

FAQ

What is Angle of PF using Area of X-Section(3-Phase 3-Wire OS)?

The Angle of PF using Area of X-section(3-phase 3-wire OS) formula is defined as the phase angle between reactive and active power and is represented as Φ = acos(sqrt(2*ρ*(P^2*L^2)/(3*A*P_loss*(V_m^2)))) or Phase Difference = acos(sqrt(2*Resistivity*(Power Transmitted^2*Length of Overhead AC Wire^2)/(3*Area of Overhead AC Wire*Line Losses*(Maximum Voltage Overhead AC^2)))). Resistivity is the measure of how strongly a material opposes the flow of current through them, Power Transmitted is defined as the product of current and voltage phasor in a overhead ac line at the receiving end, Length of Overhead AC Wire is the total length of the wire from one end to other end, Area of Overhead AC Wire is defined as the cross-sectional area of the wire of an AC supply system, Line Losses is defined as the total losses occurring in an Overhead AC line when in use & Maximum Voltage Overhead AC is defined as the peak amplitude of the AC voltage supplied to the line or wire.

How to calculate Angle of PF using Area of X-Section(3-Phase 3-Wire OS)?

The Angle of PF using Area of X-section(3-phase 3-wire OS) formula is defined as the phase angle between reactive and active power is calculated using Phase Difference = acos(sqrt(2*Resistivity*(Power Transmitted^2*Length of Overhead AC Wire^2)/(3*Area of Overhead AC Wire*Line Losses*(Maximum Voltage Overhead AC^2)))). To calculate Angle of PF using Area of X-Section(3-Phase 3-Wire OS), you need Resistivity (ρ), Power Transmitted (P), Length of Overhead AC Wire (L), Area of Overhead AC Wire (A), Line Losses (P_loss) & Maximum Voltage Overhead AC (V_m). With our tool, you need to enter the respective value for Resistivity, Power Transmitted, Length of Overhead AC Wire, Area of Overhead AC Wire, Line Losses & Maximum Voltage Overhead AC 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 Phase Difference?

In this formula, Phase Difference uses Resistivity, Power Transmitted, Length of Overhead AC Wire, Area of Overhead AC Wire, Line Losses & Maximum Voltage Overhead AC. We can use 1 other way(s) to calculate the same, which is/are as follows -

Phase Difference = acos(sqrt(2)*Power Transmitted/(3*Maximum Voltage Overhead AC*Current Overhead AC))

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