Average Thyristor Current under AC Regulator Solution

STEP 0: Pre-Calculation Summary
Formula Used
Average Thyristor Current Under AC Regulator = ((sqrt(2)*Supply Voltage)/(2*pi*Impedance))*int(sin(x-Phase Angle)-sin(Firing Angle-Phase Angle)*exp((Resistance/Inductance)*((Firing Angle/Angular Frequency)-Time)),x,Firing Angle,Extinction Angle of Thyristor)
Iav = ((sqrt(2)*Es)/(2*pi*Z))*int(sin(x-φ)-sin(α-φ)*exp((R/L)*((α/ω)-t)),x,α,β)
This formula uses 1 Constants, 4 Functions, 10 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)
exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(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)
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
Average Thyristor Current Under AC Regulator - (Measured in Ampere) - Average Thyristor Current Under AC Regulator refers to the Mean Value of the Current flowing through the Thyristor over a Complete Cycle of the Alternating Current (AC) Waveform.
Supply Voltage - (Measured in Volt) - Supply Voltage of an AC Regulator refers to the Voltage provided by the Power Source to the regulator circuit.
Impedance - (Measured in Ohm) - Impedance is a Measure of the Total Opposition that an Electrical Circuit presents to the flow of Alternating Current (AC).
Phase Angle - (Measured in Radian) - Phase Angle typically refers to the Angular Displacement of the Waveform from its Zero crossing point.
Firing Angle - (Measured in Radian) - Firing Angle is the Angle of Delay Between the Zero Crossing of the AC Voltage Waveform and the triggering of the Thyristor.
Resistance - (Measured in Ohm) - Resistance is a measure of the opposition to current flow in any voltage regulator circuit. Its S.I unit is ohm.
Inductance - (Measured in Henry) - Inductance refers to the Property of a Circuit Element, typically an Inductor, that Opposes changes in the Current flowing through it by Inducing a Voltage in the Circuit.
Angular Frequency - (Measured in Radian per Second) - Angular Frequency is Defined as the Rate of Change of the Phase Angle of the Voltage or Current with Respect to Time.
Time - (Measured in Second) - Time is a fundamental parameter that measures the progression of events or changes in a system. It represents the elapsed time since the start of the waveform's cycle.
Extinction Angle of Thyristor - (Measured in Radian) - Extinction Angle of Thyristor is the angle of Delay between the Zero crossing of the AC Current Waveform and the point where the Thyristor naturally turns off due to the reversal of Voltage across it.
STEP 1: Convert Input(s) to Base Unit
Supply Voltage: 230 Volt --> 230 Volt No Conversion Required
Impedance: 3.37 Ohm --> 3.37 Ohm No Conversion Required
Phase Angle: 1.213 Radian --> 1.213 Radian No Conversion Required
Firing Angle: 1.476 Radian --> 1.476 Radian No Conversion Required
Resistance: 10.1 Ohm --> 10.1 Ohm No Conversion Required
Inductance: 1.258 Henry --> 1.258 Henry No Conversion Required
Angular Frequency: 314 Radian per Second --> 314 Radian per Second No Conversion Required
Time: 0.558 Second --> 0.558 Second No Conversion Required
Extinction Angle of Thyristor: 2.568 Radian --> 2.568 Radian No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Iav = ((sqrt(2)*Es)/(2*pi*Z))*int(sin(x-φ)-sin(α-φ)*exp((R/L)*((α/ω)-t)),x,α,β) --> ((sqrt(2)*230)/(2*pi*3.37))*int(sin(x-1.213)-sin(1.476-1.213)*exp((10.1/1.258)*((1.476/314)-0.558)),x,1.476,2.568)
Evaluating ... ...
Iav = 11.4926511298528
STEP 3: Convert Result to Output's Unit
11.4926511298528 Ampere --> No Conversion Required
FINAL ANSWER
11.4926511298528 11.49265 Ampere <-- Average Thyristor Current Under AC Regulator
(Calculation completed in 00.004 seconds)

Credits

Created by Siddharth Raj
Heritage Institute of Technology ( HITK), Kolkata
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3 AC Regulator Calculators

Average Thyristor Current under AC Regulator
Go Average Thyristor Current Under AC Regulator = ((sqrt(2)*Supply Voltage)/(2*pi*Impedance))*int(sin(x-Phase Angle)-sin(Firing Angle-Phase Angle)*exp((Resistance/Inductance)*((Firing Angle/Angular Frequency)-Time)),x,Firing Angle,Extinction Angle of Thyristor)
RMS Thyristor Current under AC Regulator
Go RMS Thyristor Current Under AC Regulator = (Supply Voltage/Impedance)*sqrt((1/pi)*int((sin(x-Phase Angle)-sin(Firing Angle-Phase Angle)*exp((Resistance/Inductance)*((Firing Angle/Angular Frequency)-Time)))^2,x,Firing Angle,Extinction Angle of Thyristor))
RMS Output Voltage under AC Regulator
Go RMS Output Voltage under AC Regulator = Supply Voltage*sqrt((1/pi)*int(Extinction Angle of Thyristor-Firing Angle+sin(2*Firing Angle)/2-sin(2*Extinction Angle of Thyristor)/2,x,Firing Angle,Extinction Angle of Thyristor))

Average Thyristor Current under AC Regulator Formula

Average Thyristor Current Under AC Regulator = ((sqrt(2)*Supply Voltage)/(2*pi*Impedance))*int(sin(x-Phase Angle)-sin(Firing Angle-Phase Angle)*exp((Resistance/Inductance)*((Firing Angle/Angular Frequency)-Time)),x,Firing Angle,Extinction Angle of Thyristor)
Iav = ((sqrt(2)*Es)/(2*pi*Z))*int(sin(x-φ)-sin(α-φ)*exp((R/L)*((α/ω)-t)),x,α,β)

Explain the Significance of Average Thyristor Current in AC Regulator Circuits?

The average thyristor current is crucial as it provides insights into the load placed on the thyristor during operation. This knowledge aids in designing and analyzing the AC regulator circuit, ensuring that the thyristor operates within its safe operating limits. Overall, the concept of average thyristor current is significant for optimizing the performance and reliability of AC regulator circuits."

How to Calculate Average Thyristor Current under AC Regulator?

Average Thyristor Current under AC Regulator calculator uses Average Thyristor Current Under AC Regulator = ((sqrt(2)*Supply Voltage)/(2*pi*Impedance))*int(sin(x-Phase Angle)-sin(Firing Angle-Phase Angle)*exp((Resistance/Inductance)*((Firing Angle/Angular Frequency)-Time)),x,Firing Angle,Extinction Angle of Thyristor) to calculate the Average Thyristor Current Under AC Regulator, The Average Thyristor Current under AC Regulator formula is defined as the mean value of the current flowing through the thyristor over a complete cycle of the alternating current (AC) waveform. Average Thyristor Current Under AC Regulator is denoted by Iav symbol.

How to calculate Average Thyristor Current under AC Regulator using this online calculator? To use this online calculator for Average Thyristor Current under AC Regulator, enter Supply Voltage (Es), Impedance (Z), Phase Angle (φ), Firing Angle (α), Resistance (R), Inductance (L), Angular Frequency (ω), Time (t) & Extinction Angle of Thyristor (β) and hit the calculate button. Here is how the Average Thyristor Current under AC Regulator calculation can be explained with given input values -> 11.49265 = ((sqrt(2)*230)/(2*pi*3.37))*int(sin(x-1.213)-sin(1.476-1.213)*exp((10.1/1.258)*((1.476/314)-0.558)),x,1.476,2.568).

FAQ

What is Average Thyristor Current under AC Regulator?
The Average Thyristor Current under AC Regulator formula is defined as the mean value of the current flowing through the thyristor over a complete cycle of the alternating current (AC) waveform and is represented as Iav = ((sqrt(2)*Es)/(2*pi*Z))*int(sin(x-φ)-sin(α-φ)*exp((R/L)*((α/ω)-t)),x,α,β) or Average Thyristor Current Under AC Regulator = ((sqrt(2)*Supply Voltage)/(2*pi*Impedance))*int(sin(x-Phase Angle)-sin(Firing Angle-Phase Angle)*exp((Resistance/Inductance)*((Firing Angle/Angular Frequency)-Time)),x,Firing Angle,Extinction Angle of Thyristor). Supply Voltage of an AC Regulator refers to the Voltage provided by the Power Source to the regulator circuit, Impedance is a Measure of the Total Opposition that an Electrical Circuit presents to the flow of Alternating Current (AC), Phase Angle typically refers to the Angular Displacement of the Waveform from its Zero crossing point, Firing Angle is the Angle of Delay Between the Zero Crossing of the AC Voltage Waveform and the triggering of the Thyristor, Resistance is a measure of the opposition to current flow in any voltage regulator circuit. Its S.I unit is ohm, Inductance refers to the Property of a Circuit Element, typically an Inductor, that Opposes changes in the Current flowing through it by Inducing a Voltage in the Circuit, Angular Frequency is Defined as the Rate of Change of the Phase Angle of the Voltage or Current with Respect to Time, Time is a fundamental parameter that measures the progression of events or changes in a system. It represents the elapsed time since the start of the waveform's cycle & Extinction Angle of Thyristor is the angle of Delay between the Zero crossing of the AC Current Waveform and the point where the Thyristor naturally turns off due to the reversal of Voltage across it.
How to calculate Average Thyristor Current under AC Regulator?
The Average Thyristor Current under AC Regulator formula is defined as the mean value of the current flowing through the thyristor over a complete cycle of the alternating current (AC) waveform is calculated using Average Thyristor Current Under AC Regulator = ((sqrt(2)*Supply Voltage)/(2*pi*Impedance))*int(sin(x-Phase Angle)-sin(Firing Angle-Phase Angle)*exp((Resistance/Inductance)*((Firing Angle/Angular Frequency)-Time)),x,Firing Angle,Extinction Angle of Thyristor). To calculate Average Thyristor Current under AC Regulator, you need Supply Voltage (Es), Impedance (Z), Phase Angle (φ), Firing Angle (α), Resistance (R), Inductance (L), Angular Frequency (ω), Time (t) & Extinction Angle of Thyristor (β). With our tool, you need to enter the respective value for Supply Voltage, Impedance, Phase Angle, Firing Angle, Resistance, Inductance, Angular Frequency, Time & Extinction Angle of Thyristor 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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