RMS Output Voltage for Phase Controller Calculator

✖Peak Voltage is the peak or maximum voltage of a circuit/ rectifier.ⓘ Peak Voltage [V_m]			+10% -10%
✖Firing Angle of Thyristor Converter refers to the Angle at which the Thyristor is triggered to start Conducting Current in an AC (alternating current) Circuit.ⓘ Firing Angle of Thyristor Converter [α_f(thy)]			+10% -10%

✖RMS Output Voltage Full Converter is defined as the root mean square value of the voltage at output terminal of a full converter circuit.ⓘ RMS Output Voltage for Phase Controller [V_rms(full)]

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Formula

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RMS Output Voltage for Phase Controller

Formula

`"V"_{"rms(full)"} = sqrt((("V"_{"m"})^2/pi)*int((sin(x))^2,x,(60+"α"_{"f(thy)"}),(120+"α"_{"f(thy)"})))`

Example

`"30.9265V"=sqrt((("10V")^2/pi)*int((sin(x))^2,x,(60+"27.5°"),(120+"27.5°")))`

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RMS Output Voltage for Phase Controller Solution

STEP 0: Pre-Calculation Summary

Formula Used

RMS Output Voltage Full Converter = sqrt(((Peak Voltage)^2/pi)*int((sin(x))^2,x,(60+Firing Angle of Thyristor Converter),(120+Firing Angle of Thyristor Converter)))
V_rms(full) = sqrt(((V_m)^2/pi)*int((sin(x))^2,x,(60+α_f(thy)),(120+α_f(thy))))
This formula uses 1 Constants, 3 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(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)
int - The definite integral can be used to calculate net signed area, which is the area above the x -axis minus the area below the x -axis., int(expr, arg, from, to)

Variables Used

RMS Output Voltage Full Converter - (Measured in Volt) - RMS Output Voltage Full Converter is defined as the root mean square value of the voltage at output terminal of a full converter circuit.
Peak Voltage - (Measured in Volt) - Peak Voltage is the peak or maximum voltage of a circuit/ rectifier.
Firing Angle of Thyristor Converter - (Measured in Radian) - Firing Angle of Thyristor Converter refers to the Angle at which the Thyristor is triggered to start Conducting Current in an AC (alternating current) Circuit.

STEP 1: Convert Input(s) to Base Unit

Peak Voltage: 10 Volt --> 10 Volt No Conversion Required
Firing Angle of Thyristor Converter: 27.5 Degree --> 0.47996554429835 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_rms(full) = sqrt(((V_m)^2/pi)*int((sin(x))^2,x,(60+α_f(thy)),(120+α_f(thy)))) --> sqrt(((10)^2/pi)*int((sin(x))^2,x,(60+0.47996554429835),(120+0.47996554429835)))

Evaluating ... ...

V_rms(full) = 30.926495059665

STEP 3: Convert Result to Output's Unit

30.926495059665 Volt --> No Conversion Required

FINAL ANSWER

30.926495059665 ≈ 30.9265 Volt <-- RMS Output Voltage Full Converter

(Calculation completed in 00.020 seconds)

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Home » Engineering » Electrical » Power Electronics » Converters » Three Phase Full Converter » RMS Output Voltage for Phase Controller

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Created by Siddharth Raj

Heritage Institute of Technology ( HITK), Kolkata

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< 5 Three Phase Full Converter Calculators

RMS Output Voltage for Phase Controller

Go RMS Output Voltage Full Converter = sqrt(((Peak Voltage)^2/pi)*int((sin(x))^2,x,(60+Firing Angle of Thyristor Converter),(120+Firing Angle of Thyristor Converter)))

RMS Output Voltage of Three-Phase Full Converter

Go RMS Output Voltage 3 Phase Full Converter = ((6)^0.5)*Peak Input Voltage 3 Phase Full Converter*((0.25+0.65*(cos(2*Delay Angle of 3 Phase Full Converter))/pi)^0.5)

Average Output Voltage for Three-Phase Converter

Go Average Voltage 3 Phase Full Converter = (2*Peak Phase Voltage Full Converter*cos(Delay Angle of 3 Phase Full Converter/2))/pi

Peak Average Output Voltage of Three-Phase Full Converters

Go Peak Output Voltage 3 Phase Full Converter = (5.2*Peak Input Voltage 3 Phase Full Converter)/pi

Normalized Average Output Voltage in Three-Phase Full-Converter

Go Normalized Output Voltage 3 Phase Full Converter = (cos(Delay Angle of 3 Phase Full Converter))

RMS Output Voltage for Phase Controller Formula

What is the Significance of Integral Form of RMS Output voltage of 3-phase Full Converter?

The integral form expresses the RMS output voltage as a mathematical integral, which represents the area under the curve of the output voltage waveform. This representation allows for precise mathematical analysis and facilitates the understanding of how the output voltage is affected by variations in parameters such as input voltage and firing angle.

What is the Meaning of Root Mean Square?

The root mean square value of a quantity is the square root of the mean value of the squared values of the quantity taken over an interval. AC voltages are always given as RMS values because this allows a sensible comparison to be made with steady DC voltages.

How to Calculate RMS Output Voltage for Phase Controller?

RMS Output Voltage for Phase Controller calculator uses RMS Output Voltage Full Converter = sqrt(((Peak Voltage)^2/pi)*int((sin(x))^2,x,(60+Firing Angle of Thyristor Converter),(120+Firing Angle of Thyristor Converter))) to calculate the RMS Output Voltage Full Converter, RMS Output Voltage for Phase Controller is defined as the root mean square value of the voltage at output terminal of a full converter circuit. RMS Output Voltage Full Converter is denoted by V_rms(full) symbol.

How to calculate RMS Output Voltage for Phase Controller using this online calculator? To use this online calculator for RMS Output Voltage for Phase Controller, enter Peak Voltage (V_m) & Firing Angle of Thyristor Converter (α_f(thy)) and hit the calculate button. Here is how the RMS Output Voltage for Phase Controller calculation can be explained with given input values -> 30.9265 = sqrt(((10)^2/pi)*int((sin(x))^2,x,(60+0.47996554429835),(120+0.47996554429835))).

FAQ

What is RMS Output Voltage for Phase Controller?

RMS Output Voltage for Phase Controller is defined as the root mean square value of the voltage at output terminal of a full converter circuit and is represented as V_rms(full) = sqrt(((V_m)^2/pi)*int((sin(x))^2,x,(60+α_f(thy)),(120+α_f(thy)))) or RMS Output Voltage Full Converter = sqrt(((Peak Voltage)^2/pi)*int((sin(x))^2,x,(60+Firing Angle of Thyristor Converter),(120+Firing Angle of Thyristor Converter))). Peak Voltage is the peak or maximum voltage of a circuit/ rectifier & Firing Angle of Thyristor Converter refers to the Angle at which the Thyristor is triggered to start Conducting Current in an AC (alternating current) Circuit.

How to calculate RMS Output Voltage for Phase Controller?

RMS Output Voltage for Phase Controller is defined as the root mean square value of the voltage at output terminal of a full converter circuit is calculated using RMS Output Voltage Full Converter = sqrt(((Peak Voltage)^2/pi)*int((sin(x))^2,x,(60+Firing Angle of Thyristor Converter),(120+Firing Angle of Thyristor Converter))). To calculate RMS Output Voltage for Phase Controller, you need Peak Voltage (V_m) & Firing Angle of Thyristor Converter (α_f(thy)). With our tool, you need to enter the respective value for Peak Voltage & Firing Angle of Thyristor Converter 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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