Angle of PF using Line Losses (Two-Phase Three-Wire OS) Calculator

✖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%
✖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%
✖Resistivity is the measure of how strongly a material opposes the flow of current through them.ⓘ Resistivity [ρ]			+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%
✖Line Losses is defined as the total losses occurring in an Overhead AC line when in use.ⓘ Line Losses [P_loss]			+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%

✖The power factor of an AC electrical power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit.ⓘ Angle of PF using Line Losses (Two-Phase Three-Wire OS) [PF]

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Formula

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Angle of PF using Line Losses (Two-Phase Three-Wire OS)

Formula

`"PF" = acos(("P"/"V"_{"m"})*sqrt((2+sqrt(2))*"ρ"*"L"/(2*"P"_{"loss"}*"A")))`

Example

`"1.471755"=acos(("890W"/"62V")*sqrt((2+sqrt(2))*"0.000017Ω*m"*"10.63m"/(2*"8.23W"*"0.79m²")))`

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Angle of PF using Line Losses (Two-Phase Three-Wire OS) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Power Factor = acos((Power Transmitted/Maximum Voltage Overhead AC)*sqrt((2+sqrt(2))*Resistivity*Length of Overhead AC Wire/(2*Line Losses*Area of Overhead AC Wire)))
PF = acos((P/V_m)*sqrt((2+sqrt(2))*ρ*L/(2*P_loss*A)))
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

Power Factor - The power factor of an AC electrical power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit.
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.
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.
Resistivity - (Measured in Ohm Meter) - Resistivity is the measure of how strongly a material opposes the flow of current through them.
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.
Line Losses - (Measured in Watt) - Line Losses is defined as the total losses occurring in an Overhead AC line when in use.
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.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

PF = 1.47175498040219

STEP 3: Convert Result to Output's Unit

1.47175498040219 --> No Conversion Required

FINAL ANSWER

1.47175498040219 ≈ 1.471755 <-- Power Factor

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electrical » Power System » Overhead AC Supply » 2-Φ 3-Wire System » Power & Power Factor » Angle of PF using Line Losses (Two-Phase Three-Wire OS)

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< 10+ Power & Power Factor Calculators

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

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

Transmitted Power using Line Losses (Two-Phase Three-Wire OS)

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

Power Transmitted using Volume of Conductor Material (Two-Phase Three-Wire OS)

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

Angle of PF using Line Losses (Two-Phase Three-Wire OS)

Go Power Factor = acos((Power Transmitted/Maximum Voltage Overhead AC)*sqrt((2+sqrt(2))*Resistivity*Length of Overhead AC Wire/(2*Line Losses*Area of Overhead AC Wire)))

Power Factor using Area of X-section(Two-Phase Three-Wire OS)

Go Power Factor = sqrt(((Power Transmitted^2)*Resistivity*Length of Overhead AC Wire*(2+sqrt(2)))/((2)*Area of Overhead AC Wire*Line Losses*(Maximum Voltage Overhead AC^2)))

Power Factor using Line Losses (Two-Phase Three-Wire OS)

Go Power Factor = (Power Transmitted/Maximum Voltage Overhead AC)*sqrt((2+sqrt(2))*Resistivity*Length of Overhead AC Wire/2*Line Losses*Area of Overhead AC Wire)

Power Transmitted using Load Current (Two-Phase Three-Wire OS)

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

Angle of PF using Volume of Conductor Material (Two-Phase Three-Wire OS)

Go Phase Difference = acos(sqrt((1.457)*Constant Overhead AC/Volume of Conductor))

Power Factor using Volume of Conductor Material (Two-Phase Three-Wire OS)

Go Power Factor = sqrt((1.457)*Constant Overhead AC/Volume of Conductor)

Power Transmitted(Two-Phase Three-Wire OS)

Go Power Transmitted = (1/2)*Power Transmitted per Phase

Angle of PF using Line Losses (Two-Phase Three-Wire OS) Formula

How are power factor and power angle related?

Power angles are generally caused due to voltage drop due to impedance in the transmission line. The power factor is caused due to phase angle between reactive and active power.

How to Calculate Angle of PF using Line Losses (Two-Phase Three-Wire OS)?

Angle of PF using Line Losses (Two-Phase Three-Wire OS) calculator uses Power Factor = acos((Power Transmitted/Maximum Voltage Overhead AC)*sqrt((2+sqrt(2))*Resistivity*Length of Overhead AC Wire/(2*Line Losses*Area of Overhead AC Wire))) to calculate the Power Factor, The Angle of PF using Line Losses (two-phase three-wire OS) formula is defined as the phase angle between reactive and active power. Power Factor is denoted by PF symbol.

How to calculate Angle of PF using Line Losses (Two-Phase Three-Wire OS) using this online calculator? To use this online calculator for Angle of PF using Line Losses (Two-Phase Three-Wire OS), enter Power Transmitted (P), Maximum Voltage Overhead AC (V_m), Resistivity (ρ), Length of Overhead AC Wire (L), Line Losses (P_loss) & Area of Overhead AC Wire (A) and hit the calculate button. Here is how the Angle of PF using Line Losses (Two-Phase Three-Wire OS) calculation can be explained with given input values -> 1.471755 = acos((890/62)*sqrt((2+sqrt(2))*1.7E-05*10.63/(2*8.23*0.79))).

FAQ

What is Angle of PF using Line Losses (Two-Phase Three-Wire OS)?

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

How to calculate Angle of PF using Line Losses (Two-Phase Three-Wire OS)?

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

In this formula, Power Factor uses Power Transmitted, Maximum Voltage Overhead AC, Resistivity, Length of Overhead AC Wire, Line Losses & Area of Overhead AC Wire. We can use 3 other way(s) to calculate the same, which is/are as follows -

Power Factor = sqrt(((Power Transmitted^2)*Resistivity*Length of Overhead AC Wire*(2+sqrt(2)))/((2)*Area of Overhead AC Wire*Line Losses*(Maximum Voltage Overhead AC^2)))
Power Factor = sqrt((1.457)*Constant Overhead AC/Volume of Conductor)
Power Factor = (Power Transmitted/Maximum Voltage Overhead AC)*sqrt((2+sqrt(2))*Resistivity*Length of Overhead AC Wire/2*Line Losses*Area of Overhead AC Wire)

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