Power Factor Angle for Single 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 Single Phase 3 Wire System [Φ]

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Formula

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Power Factor Angle for Single Phase 3 Wire System

Formula

`"Φ" = acos("P"/(2*"V"_{"ac"}*"I"))`

Example

`"82.01644°"=acos("300W"/(2*"120V"*"9A"))`

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Power Factor Angle for Single Phase 3 Wire System Solution

STEP 0: Pre-Calculation Summary

Formula Used

Phase Difference = acos(Power Transmitted/(2*Voltage Underground AC*Current Underground AC))
Φ = acos(P/(2*V_ac*I))
This formula uses 2 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)

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/(2*V_ac*I)) --> acos(300/(2*120*9))

Evaluating ... ...

Φ = 1.43145698603713

STEP 3: Convert Result to Output's Unit

1.43145698603713 Radian -->82.01644385446 Degree (Check conversion here)

FINAL ANSWER

82.01644385446 ≈ 82.01644 Degree <-- Phase Difference

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electrical » Power System » Underground AC Supply » 1-Φ 3-Wire System » Power & Power Factor » Power Factor Angle for Single Phase 3 Wire System

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< 9 Power & Power Factor Calculators

Power Transmitted using Area of X Section (1 Phase 3 Wire US)

Go Power Transmitted = sqrt(Area of Underground AC Wire*Line Losses*(Maximum Voltage Underground AC^2)*(cos(Phase Difference)^2)/(4*Resistivity*Length of Underground AC Wire))

Transmitted Power using Volume of Conductor Material(1 Phase 3 Wire US)

Go Power Transmitted = sqrt(Line Losses*Volume Of Conductor*(Maximum Voltage Underground AC*cos(Phase Difference))^2/(10*Resistivity*(Length of Underground AC Wire)^2))

Power Factor using Volume of Conductor Material(1 Phase 3 Wire US)

Go Power Factor = sqrt(10*Resistivity*((Power Transmitted*Length of Underground AC Wire)^2)/(Line Losses*Volume Of Conductor*((Maximum Voltage Underground AC)^2)))

Power Factor using Area of X Section (1 Phase 3 Wire US)

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

Power Transmitted using Line Losses (1 Phase 3 Wire US)

Go Power Transmitted = sqrt(Line Losses*(Maximum Voltage Underground AC^2)*(cos(Phase Difference)^2)/(4*Resistance Underground AC))

Power Factor using Line Losses (1 Phase 3 Wire US)

Go Power Factor = ((2*Power Transmitted/Maximum Voltage Underground AC)*sqrt(Resistance Underground AC/(Line Losses)))

Transmitted Power using Load Current (1 Phase 3 Wire US)

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

Power Factor using Load Current (1 Phase 3 Wire US)

Go Power Factor = sqrt(2)*Power Transmitted/(Maximum Voltage Underground AC*Current Underground AC)

Power Factor Angle for Single Phase 3 Wire System

Go Phase Difference = acos(Power Transmitted/(2*Voltage Underground AC*Current Underground AC))

Power Factor Angle for Single Phase 3 Wire System Formula

Phase Difference = acos(Power Transmitted/(2*Voltage Underground AC*Current Underground AC))
Φ = acos(P/(2*V_ac*I))

What is the value of maximum voltage and volume of conductor material in 1-phase 3-wire system?

The volume of conductor material required in this system is 2.5/cos²θ times that of 2-wire d.c.system with the one conductor earthed. The maximum voltage between conductors is v_m so that r.m.s. value of voltage between them is v_m/√2.

How to Calculate Power Factor Angle for Single Phase 3 Wire System?

Power Factor Angle for Single Phase 3 Wire System calculator uses Phase Difference = acos(Power Transmitted/(2*Voltage Underground AC*Current Underground AC)) to calculate the Phase Difference, Power factor angle for single phase 3 wire system formula is defined as the phase angle between reactive and active power. Phase Difference is denoted by Φ symbol.

How to calculate Power Factor Angle for Single Phase 3 Wire System using this online calculator? To use this online calculator for Power Factor Angle for Single 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 Single Phase 3 Wire System calculation can be explained with given input values -> 4699.196 = acos(300/(2*120*9)).

FAQ

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

Power factor angle for single phase 3 wire system formula is defined as the phase angle between reactive and active power and is represented as Φ = acos(P/(2*V_ac*I)) or Phase Difference = acos(Power Transmitted/(2*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 Single Phase 3 Wire System?

Power factor angle for single phase 3 wire system formula is defined as the phase angle between reactive and active power is calculated using Phase Difference = acos(Power Transmitted/(2*Voltage Underground AC*Current Underground AC)). To calculate Power Factor Angle for Single 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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