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))
VL = (Pme(3Φ)+3*Ia^2*Ra)/(sqrt(3)*IL*cos(Φs))
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
VL = (Pme(3Φ)+3*Ia^2*Ra)/(sqrt(3)*IL*cos(Φs)) --> (1056.2505+3*3.7^2*12.85)/(sqrt(3)*5.5*cos(0.5235987755982))
Evaluating ... ...
VL = 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)

Credits

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Vishwakarma Government Engineering College (VGEC), Ahmedabad
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6 Voltage & EMF Calculators

Load Voltage of Synchronous Motor given 3 Phase Mechanical Power
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
Go Load Voltage = Three Phase Input Power/(sqrt(3)*Load Current*cos(Phase Difference))
Back EMF of Synchronous Motor using Mechanical Power
Go Back EMF = Mechanical Power/(Armature Current*cos(Load Angle-Phase Difference))
Voltage of Synchronous Motor given Input Power
Go Voltage = Input Power/(Armature Current*cos(Phase Difference))
Back EMF of Synchronous Motor given Armature Winding Constant
Go Back EMF = Armature Winding Constant*Magnetic Flux*Synchronous Speed
Voltage Equation of Synchronous Motor
Go Voltage = Back EMF+Armature Current*Synchronous Impedance

25 Synchronous Motor Circuit Calculators

Load Current of Synchronous Motor given 3 Phase Mechanical Power
Go Load Current = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*cos(Phase Difference))
Power Factor of Synchronous Motor given 3 Phase Mechanical Power
Go Power Factor = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*Load Current)
Distribution Factor in Synchronous Motor
Go Distribution Factor = (sin((Number of Slots*Angular Slot Pitch)/2))/(Number of Slots*sin(Angular Slot Pitch/2))
Load Current of Synchronous Motor using 3 Phase Input Power
Go Load Current = Three Phase Input Power/(sqrt(3)*Load Voltage*cos(Phase Difference))
3 Phase Input Power of Synchronous Motor
Go Three Phase Input Power = sqrt(3)*Load Voltage*Load Current*cos(Phase Difference)
Mechanical Power of Synchronous Motor
Go Mechanical Power = Back EMF*Armature Current*cos(Load Angle-Phase Difference)
Armature Current of Synchronous Motor given 3 Phase Mechanical Power
Go Armature Current = sqrt((Three Phase Input Power-Three Phase Mechanical Power)/(3*Armature Resistance))
Armature Current of Synchronous Motor given Mechanical Power
Go Armature Current = sqrt((Input Power-Mechanical Power)/Armature Resistance)
Power Factor of Synchronous Motor using 3 Phase Input Power
Go Power Factor = Three Phase Input Power/(sqrt(3)*Load Voltage*Load Current)
Armature Resistance of Synchronous Motor given 3 Phase Mechanical Power
Go Armature Resistance = (Three Phase Input Power-Three Phase Mechanical Power)/(3*Armature Current^2)
3 Phase Mechanical Power of Synchronous Motor
Go Three Phase Mechanical Power = Three Phase Input Power-3*Armature Current^2*Armature Resistance
Phase Angle between Voltage and Armature Current given Input Power
Go Phase Difference = acos(Input Power/(Voltage*Armature Current))
Armature Current of Synchronous Motor given Input Power
Go Armature Current = Input Power/(cos(Phase Difference)*Voltage)
Input Power of Synchronous Motor
Go Input Power = Armature Current*Voltage*cos(Phase Difference)
Armature Resistance of Synchronous Motor given Input Power
Go Armature Resistance = (Input Power-Mechanical Power)/(Armature Current^2)
Magnetic Flux of Synchronous Motor given Back EMF
Go Magnetic Flux = Back EMF/(Armature Winding Constant*Synchronous Speed)
Armature Winding Constant of Synchronous Motor
Go Armature Winding Constant = Back EMF/(Magnetic Flux*Synchronous Speed)
Mechanical Power of Synchronous Motor given Input Power
Go Mechanical Power = Input Power-Armature Current^2*Armature Resistance
Power Factor of Synchronous Motor given Input Power
Go Power Factor = Input Power/(Voltage*Armature Current)
Angular Slot Pitch in Synchronous Motor
Go Angular Slot Pitch = (Number of Poles*180)/(Number of Slots*2)
Output Power for Synchronous Motor
Go Output Power = Armature Current^2*Armature Resistance
Number of Poles given Synchronous Speed in Synchronous Motor
Go Number of Poles = (Frequency*120)/Synchronous Speed
Synchronous Speed of Synchronous Motor
Go Synchronous Speed = (120*Frequency)/Number of Poles
Synchronous Speed of Synchronous Motor given Mechanical Power
Go Synchronous Speed = Mechanical Power/Gross Torque
Mechanical Power of Synchronous Motor given Gross Torque
Go Mechanical Power = Gross Torque*Synchronous Speed

Load Voltage of Synchronous Motor given 3 Phase Mechanical Power Formula

Load Voltage = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Current*cos(Phase Difference))
VL = (Pme(3Φ)+3*Ia^2*Ra)/(sqrt(3)*IL*cos(Φs))

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 VL 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 (Pme(3Φ)), Armature Current (Ia), Armature Resistance (Ra), Load Current (IL) & Phase Difference 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 VL = (Pme(3Φ)+3*Ia^2*Ra)/(sqrt(3)*IL*cos(Φs)) 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 (Pme(3Φ)), Armature Current (Ia), Armature Resistance (Ra), Load Current (IL) & Phase Difference 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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