Power Factor Angle for 3 Phase 3 Wire System Calculator

✖Power Transmitted is the amount of power that is transferred from its place of generation to a location where it is applied to perform useful work.ⓘ Power Transmitted [P]			+10% -10%
✖Voltage Underground AC is defined as the amount of work or force required to start the conduction of current within a line.ⓘ Voltage Underground AC [V_ac]			+10% -10%
✖Current Underground AC is defined as the current flowing through the overhead ac supply wire.ⓘ Current Underground AC [I]			+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.ⓘ Power Factor Angle for 3 Phase 3 Wire System [Φ]

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Formula

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Power Factor Angle for 3 Phase 3 Wire System

Formula

`"Φ" = acos("P"/(sqrt(3)*"V"_{"ac"}*"I"))`

Example

`"80.77133°"=acos("300W"/(sqrt(3)*"120V"*"9A"))`

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Power Factor Angle for 3 Phase 3 Wire System Solution

STEP 0: Pre-Calculation Summary

Formula Used

Phase Difference = acos(Power Transmitted/(sqrt(3)*Voltage Underground AC*Current Underground AC))
Φ = acos(P/(sqrt(3)*V_ac*I))
This formula uses 3 Functions, 4 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.
Power Transmitted - (Measured in Watt) - Power Transmitted is the amount of power that is transferred from its place of generation to a location where it is applied to perform useful work.
Voltage Underground AC - (Measured in Volt) - Voltage Underground AC is defined as the amount of work or force required to start the conduction of current within a line.
Current Underground AC - (Measured in Ampere) - Current Underground AC is defined as the current flowing through the overhead ac supply wire.

STEP 1: Convert Input(s) to Base Unit

Power Transmitted: 300 Watt --> 300 Watt No Conversion Required
Voltage Underground AC: 120 Volt --> 120 Volt No Conversion Required
Current Underground AC: 9 Ampere --> 9 Ampere No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ = acos(P/(sqrt(3)*V_ac*I)) --> acos(300/(sqrt(3)*120*9))

Evaluating ... ...

Φ = 1.40972569221026

STEP 3: Convert Result to Output's Unit

1.40972569221026 Radian -->80.7713324348213 Degree (Check conversion here)

FINAL ANSWER

80.7713324348213 ≈ 80.77133 Degree <-- Phase Difference

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electrical » Power System » Underground AC Supply » 3-Φ 3-Wire System » Power & Power Factor » Power Factor Angle for 3 Phase 3 Wire System

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< 8 Power & Power Factor Calculators

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

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

Power Transmitted using Volume of Conductor Material (3 Phase 3 Wire US)

Go Power Transmitted = sqrt(Line Losses*Volume Of Conductor*(Maximum Voltage Underground AC*cos(Phase Difference))^2/(6*Resistivity*(Length of Underground AC Wire)^2))

Power Factor using Area of X-Section (3 Phase 3 Wire US)

Go Power Factor = (Power Transmitted/Maximum Voltage Underground AC)*sqrt(2*Resistivity*Length of Underground AC Wire/(Area of Underground AC Wire))

Power Transmitted using Load Current Per Phase (3 Phase 3 Wire US)

Go Power Transmitted = Current Underground AC*3*Maximum Voltage Underground AC*cos(Phase Difference)/sqrt(6)

Power Factor Angle for 3 Phase 3 Wire System

Go Phase Difference = acos(Power Transmitted/(sqrt(3)*Voltage Underground AC*Current Underground AC))

Power Factor using Load Current Per Phase (3 Phase 3 Wire US)

Go Power Factor = sqrt(6)*Power Transmitted/(Current Underground AC*Maximum Voltage Underground AC*3)

Power Factor using Volume of Conductor Material (3 Phase 3 Wire US)

Go Power Factor = sqrt((1.5)*Constant Underground AC/Volume Of Conductor)

Power Transmitted Per Phase (3 Phase 3 Wire US)

Go Power Transmitted per Phase = Power Transmitted/3

Power Factor Angle for 3 Phase 3 Wire System Formula

Phase Difference = acos(Power Transmitted/(sqrt(3)*Voltage Underground AC*Current Underground AC))
Φ = acos(P/(sqrt(3)*V_ac*I))

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 Power Factor Angle for 3 Phase 3 Wire System?

Power Factor Angle for 3 Phase 3 Wire System calculator uses Phase Difference = acos(Power Transmitted/(sqrt(3)*Voltage Underground AC*Current Underground AC)) to calculate the Phase Difference, Power factor angle for 3 phase 3 wire system formula is defined as the phase angle between reactive and active power for a three phase and three wire system. Phase Difference is denoted by Φ symbol.

How to calculate Power Factor Angle for 3 Phase 3 Wire System using this online calculator? To use this online calculator for Power Factor Angle for 3 Phase 3 Wire System, enter Power Transmitted (P), Voltage Underground AC (V_ac) & Current Underground AC (I) and hit the calculate button. Here is how the Power Factor Angle for 3 Phase 3 Wire System calculation can be explained with given input values -> 4627.856 = acos(300/(sqrt(3)*120*9)).

FAQ

What is Power Factor Angle for 3 Phase 3 Wire System?

Power factor angle for 3 phase 3 wire system formula is defined as the phase angle between reactive and active power for a three phase and three wire system and is represented as Φ = acos(P/(sqrt(3)*V_ac*I)) or Phase Difference = acos(Power Transmitted/(sqrt(3)*Voltage Underground AC*Current Underground AC)). Power Transmitted is the amount of power that is transferred from its place of generation to a location where it is applied to perform useful work, Voltage Underground AC is defined as the amount of work or force required to start the conduction of current within a line & Current Underground AC is defined as the current flowing through the overhead ac supply wire.

How to calculate Power Factor Angle for 3 Phase 3 Wire System?

Power factor angle for 3 phase 3 wire system formula is defined as the phase angle between reactive and active power for a three phase and three wire system is calculated using Phase Difference = acos(Power Transmitted/(sqrt(3)*Voltage Underground AC*Current Underground AC)). To calculate Power Factor Angle for 3 Phase 3 Wire System, you need Power Transmitted (P), Voltage Underground AC (V_ac) & Current Underground AC (I). With our tool, you need to enter the respective value for Power Transmitted, Voltage Underground AC & Current Underground AC 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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