Load Voltage of Synchronous Motor given 3 Phase Mechanical Power Calculator

✖Three Phase Mechanical Power is defined as the power developed by a 3-Φ Synchronous Motor to rotate the shaft.ⓘ Three Phase Mechanical Power [P_me(3Φ)]			+10% -10%
✖Armature Current Motor is defined as the armature current developed in an synchronous motor due to the rotation of rotor.ⓘ Armature Current [I_a]			+10% -10%
✖The Armature Resistance is the ohmic resistance of the copper winding wires plus the brush resistance in an electrical motor.ⓘ Armature Resistance [R_a]			+10% -10%
✖Load current is defined as the magnitude of the current drawn from an electric circuit by the load (electrical machine) connected across it.ⓘ Load Current [I_L]			+10% -10%
✖Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor.ⓘ Phase Difference [Φ_s]			+10% -10%

✖The Load Voltage is defined as the voltage between two terminals of load.ⓘ Load Voltage of Synchronous Motor given 3 Phase Mechanical Power [V_L]

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Load Voltage of Synchronous Motor given 3 Phase Mechanical Power Solution

STEP 0: Pre-Calculation Summary

Formula Used

Load Voltage = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*cos(Phase Difference))
V_L = (P_me(3Φ)+3*I_a^2*R_a)/(sqrt(3)*I_L*cos(Φ_s))
This formula uses 2 Functions, 6 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)
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

Load Voltage - (Measured in Volt) - The Load Voltage is defined as the voltage between two terminals of load.
Three Phase Mechanical Power - (Measured in Watt) - Three Phase Mechanical Power is defined as the power developed by a 3-Φ Synchronous Motor to rotate the shaft.
Armature Current - (Measured in Ampere) - Armature Current Motor is defined as the armature current developed in an synchronous motor due to the rotation of rotor.
Armature Resistance - (Measured in Ohm) - The Armature Resistance is the ohmic resistance of the copper winding wires plus the brush resistance in an electrical motor.
Load Current - (Measured in Ampere) - Load current is defined as the magnitude of the current drawn from an electric circuit by the load (electrical machine) connected across it.
Phase Difference - (Measured in Radian) - Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor.

STEP 1: Convert Input(s) to Base Unit

Three Phase Mechanical Power: 1056.2505 Watt --> 1056.2505 Watt No Conversion Required
Armature Current: 3.7 Ampere --> 3.7 Ampere No Conversion Required
Armature Resistance: 12.85 Ohm --> 12.85 Ohm No Conversion Required
Load Current: 5.5 Ampere --> 5.5 Ampere No Conversion Required
Phase Difference: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_L = (P_me(3Φ)+3*I_a^2*R_a)/(sqrt(3)*I_L*cos(Φ_s)) --> (1056.2505+3*3.7^2*12.85)/(sqrt(3)*5.5*cos(0.5235987755982))

Evaluating ... ...

V_L = 192

STEP 3: Convert Result to Output's Unit

192 Volt --> No Conversion Required

FINAL ANSWER

192 Volt <-- Load Voltage

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electrical » Machine » AC Machines » Synchronous Motor » Voltage and EMF » Load Voltage of Synchronous Motor given 3 Phase Mechanical Power

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< Voltage and EMF Calculators

Load Voltage of Synchronous Motor given 3 Phase Mechanical Power

LaTeX Go Load Voltage = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*cos(Phase Difference))

Load Voltage of Synchronous Motor using 3 Phase Input Power

LaTeX Go Load Voltage = Three Phase Input Power/(sqrt(3)*Load Current*cos(Phase Difference))

Back EMF of Synchronous Motor using Mechanical Power

LaTeX Go Back EMF = Mechanical Power/(Armature Current*cos(Load Angle-Phase Difference))

Voltage of Synchronous Motor given Input Power

LaTeX Go Voltage = Input Power/(Armature Current*cos(Phase Difference))

< Synchronous Motor Circuit Calculators

Load Current of Synchronous Motor given 3 Phase Mechanical Power

LaTeX Go Load Current = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*cos(Phase Difference))

Armature Current of Synchronous Motor given 3 Phase Mechanical Power

LaTeX Go Armature Current = sqrt((Three Phase Input Power-Three Phase Mechanical Power)/(3*Armature Resistance))

Armature Current of Synchronous Motor given Mechanical Power

LaTeX Go Armature Current = sqrt((Input Power-Mechanical Power)/Armature Resistance)

Armature Current of Synchronous Motor given Input Power

LaTeX Go Armature Current = Input Power/(cos(Phase Difference)*Voltage)

Load Voltage of Synchronous Motor given 3 Phase Mechanical Power Formula

LaTeX Go

Load Voltage = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*cos(Phase Difference))
V_L = (P_me(3Φ)+3*I_a^2*R_a)/(sqrt(3)*I_L*cos(Φ_s))

How does back EMF affects synchronous motor?

Back EMF (Electromotive Force) is an opposing voltage generated by the rotor of a synchronous motor when it rotates. In synchronous motors, the back EMF plays a crucial role in maintaining the synchronization between the rotor and the stator magnetic fields. If the rotor speed changes, the back EMF also changes, which causes a corresponding change in the current flowing through the DC excitation field.

How to Calculate Load Voltage of Synchronous Motor given 3 Phase Mechanical Power?

Load Voltage of Synchronous Motor given 3 Phase Mechanical Power calculator uses Load Voltage = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*cos(Phase Difference)) to calculate the Load Voltage, The Load Voltage of Synchronous Motor given 3 phase Mechanical Power formula is defined as the voltage generated at the load of the synchronous motor. Load Voltage is denoted by V_L symbol.

How to calculate Load Voltage of Synchronous Motor given 3 Phase Mechanical Power using this online calculator? To use this online calculator for Load Voltage of Synchronous Motor given 3 Phase Mechanical Power, enter Three Phase Mechanical Power (P_me(3Φ)), Armature Current (I_a), Armature Resistance (R_a), Load Current (I_L) & Phase Difference (Φ_s) and hit the calculate button. Here is how the Load Voltage of Synchronous Motor given 3 Phase Mechanical Power calculation can be explained with given input values -> 192 = (1056.2505+3*3.7^2*12.85)/(sqrt(3)*5.5*cos(0.5235987755982)).

FAQ

What is Load Voltage of Synchronous Motor given 3 Phase Mechanical Power?

The Load Voltage of Synchronous Motor given 3 phase Mechanical Power formula is defined as the voltage generated at the load of the synchronous motor and is represented as V_L = (P_me(3Φ)+3*I_a^2*R_a)/(sqrt(3)*I_L*cos(Φ_s)) or Load Voltage = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*cos(Phase Difference)). Three Phase Mechanical Power is defined as the power developed by a 3-Φ Synchronous Motor to rotate the shaft, Armature Current Motor is defined as the armature current developed in an synchronous motor due to the rotation of rotor, The Armature Resistance is the ohmic resistance of the copper winding wires plus the brush resistance in an electrical motor, Load current is defined as the magnitude of the current drawn from an electric circuit by the load (electrical machine) connected across it & Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor.

How to calculate Load Voltage of Synchronous Motor given 3 Phase Mechanical Power?

The Load Voltage of Synchronous Motor given 3 phase Mechanical Power formula is defined as the voltage generated at the load of the synchronous motor is calculated using Load Voltage = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*cos(Phase Difference)). To calculate Load Voltage of Synchronous Motor given 3 Phase Mechanical Power, you need Three Phase Mechanical Power (P_me(3Φ)), Armature Current (I_a), Armature Resistance (R_a), Load Current (I_L) & Phase Difference (Φ_s). With our tool, you need to enter the respective value for Three Phase Mechanical Power, Armature Current, Armature Resistance, Load Current & Phase Difference 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 Load Voltage?

In this formula, Load Voltage uses Three Phase Mechanical Power, Armature Current, Armature Resistance, Load Current & Phase Difference. We can use 2 other way(s) to calculate the same, which is/are as follows -

Load Voltage = Three Phase Input Power/(sqrt(3)*Load Current*cos(Phase Difference))
Load Voltage = Three Phase Input Power/(sqrt(3)*Load Current*cos(Phase Difference))

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