RMS Harmonic Current for PWM Control Calculator

✖Armature Current DC motor is defined as the armature current developed in an electrical dc motor due to the rotation of rotor.ⓘ Armature Current [I_a]			+10% -10%
✖Number of Pulse in Half-cycle of PWM (Pulse Width Modulation) converter refers to the count of pulses generated within half of the waveform period.ⓘ Number of Pulse in Half-cycle of PWM [p]			+10% -10%
✖Harmonic Order is Defined as the the Integer Multiple of the Fundamental Frequency (f) of the PWM Signal. It indicates which Harmonic Component of the Current Waveform is being analyzed.ⓘ Harmonic Order [n]			+10% -10%
✖Excitation Angle is the angle at which the PWM Converter begins to Produce Output Voltage or Current.ⓘ Excitation Angle [α_k]			+10% -10%
✖Symmetrical Angle is the Angle at which the PWM Converter produces Symmetrical Output Waveforms with respect to the AC Input Waveform.ⓘ Symmetrical Angle [β_k]			+10% -10%

✖RMS nth Harmonic Current is the Effective Value of the Harmonic Component of the Current Waveform at a Frequency that is an Integer Multiple (n) of the Fundamental Frequency of the PWM Signal.ⓘ RMS Harmonic Current for PWM Control [I_n]

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Formula

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RMS Harmonic Current for PWM Control

Formula

`"I"_{"n"} = ((sqrt(2)*"I"_{"a"})/pi)*sum(x,1,"p",(cos("n"*"α"_{"k"}))-(cos("n"*"β"_{"k"})))`

Example

`"2.971044A"=((sqrt(2)*"2.2A")/pi)*sum(x,1,"3",(cos("3.0"*"30°"))-(cos("3.0"*"60.0°")))`

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RMS Harmonic Current for PWM Control Solution

STEP 0: Pre-Calculation Summary

Formula Used

RMS nth Harmonic Current = ((sqrt(2)*Armature Current)/pi)*sum(x,1,Number of Pulse in Half-cycle of PWM,(cos(Harmonic Order*Excitation Angle))-(cos(Harmonic Order*Symmetrical Angle)))
I_n = ((sqrt(2)*I_a)/pi)*sum(x,1,p,(cos(n*α_k))-(cos(n*β_k)))
This formula uses 1 Constants, 3 Functions, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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)
sum - Summation or sigma (∑) notation is a method used to write out a long sum in a concise way., sum(i, from, to, expr)

Variables Used

RMS nth Harmonic Current - (Measured in Ampere) - RMS nth Harmonic Current is the Effective Value of the Harmonic Component of the Current Waveform at a Frequency that is an Integer Multiple (n) of the Fundamental Frequency of the PWM Signal.
Armature Current - (Measured in Ampere) - Armature Current DC motor is defined as the armature current developed in an electrical dc motor due to the rotation of rotor.
Number of Pulse in Half-cycle of PWM - Number of Pulse in Half-cycle of PWM (Pulse Width Modulation) converter refers to the count of pulses generated within half of the waveform period.
Harmonic Order - Harmonic Order is Defined as the the Integer Multiple of the Fundamental Frequency (f) of the PWM Signal. It indicates which Harmonic Component of the Current Waveform is being analyzed.
Excitation Angle - (Measured in Radian) - Excitation Angle is the angle at which the PWM Converter begins to Produce Output Voltage or Current.
Symmetrical Angle - (Measured in Radian) - Symmetrical Angle is the Angle at which the PWM Converter produces Symmetrical Output Waveforms with respect to the AC Input Waveform.

STEP 1: Convert Input(s) to Base Unit

Armature Current: 2.2 Ampere --> 2.2 Ampere No Conversion Required
Number of Pulse in Half-cycle of PWM: 3 --> No Conversion Required
Harmonic Order: 3 --> No Conversion Required
Excitation Angle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Symmetrical Angle: 60 Degree --> 1.0471975511964 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_n = ((sqrt(2)*I_a)/pi)*sum(x,1,p,(cos(n*α_k))-(cos(n*β_k))) --> ((sqrt(2)*2.2)/pi)*sum(x,1,3,(cos(3*0.5235987755982))-(cos(3*1.0471975511964)))

Evaluating ... ...

I_n = 2.97104384331933

STEP 3: Convert Result to Output's Unit

2.97104384331933 Ampere --> No Conversion Required

FINAL ANSWER

2.97104384331933 ≈ 2.971044 Ampere <-- RMS nth Harmonic Current

(Calculation completed in 00.020 seconds)

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< 19 Power Converter Characteristics Calculators

RMS Harmonic Current for PWM Control

Go RMS nth Harmonic Current = ((sqrt(2)*Armature Current)/pi)*sum(x,1,Number of Pulse in Half-cycle of PWM,(cos(Harmonic Order*Excitation Angle))-(cos(Harmonic Order*Symmetrical Angle)))

Average Output Voltage for PWM Control

Go Average Output Voltage of PWM Controlled Converter = (Peak Input Voltage of PWM Converter/pi)*sum(x,1,Number of Pulse in Half-cycle of PWM,(cos(Excitation Angle)-cos(Symmetrical Angle)))

Fundamental Supply Current for PWM Control

Go Fundamental Supply Current = ((sqrt(2)*Armature Current)/pi)*sum(x,1,Number of Pulse in Half-cycle of PWM,(cos(Excitation Angle))-(cos(Symmetrical Angle)))

RMS Output Voltage for Three Phase Semi-Converter

Go RMS Output Voltage 3 Phase Semi Converter = sqrt(3)*Peak Input Voltage 3 Phase Semi Converter*((3/(4*pi))*(pi-Delay Angle of 3 Phase Semi Converter+((sin(2*Delay Angle of 3 Phase Semi Converter))/2))^0.5)

RMS Supply Current for PWM Control

Go Root Mean Square Current = Armature Current/sqrt(pi)*sqrt(sum(x,1,Number of Pulse in Half-cycle of PWM,(Symmetrical Angle-Excitation Angle)))

RMS Output Voltage for Resistive Load

Go RMS Output Voltage 3 Phase Half Converter = sqrt(3)*Peak Phase Voltage*(sqrt((1/6)+((sqrt(3)*cos(2*Delay Angle of 3 Phase Half Converter))/(8*pi))))

RMS Output Voltage for Continuous Load Current

Go RMS Output Voltage 3 Phase Half Converter = sqrt(3)*Peak Input Voltage 3 Phase Half Converter*((1/6)+(sqrt(3)*cos(2*Delay Angle of 3 Phase Half Converter))/(8*pi))^0.5

RMS Output Voltage of Single Phase Thyristor Converter with Resistive Load

Go RMS Voltage Thyristor Converter = (Peak Input Voltage Thyristor Converter/2)*((180-Delay Angle of Thyristor Converter)/180+(0.5/pi)*sin(2*Delay Angle of Thyristor Converter))^0.5

RMS Output Voltage of Single Phase Semi-Converter with Highly Inductive Load

Go RMS Output Voltage Semi Converter = (Maximum Input Voltage Semi Converter/(2^0.5))*((180-Delay Angle Semi Converter)/180+(0.5/pi)*sin(2*Delay Angle Semi Converter))^0.5

Average Output Voltage for Continuous Load Current

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

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 of Single Phase Thyristor Converter with Resistive Load

Go Average Voltage Thyristor Converter = (Peak Input Voltage Thyristor Converter/(2*pi))*(1+cos(Delay Angle of Thyristor Converter))

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

DC Output Voltage of Second Converter

Go DC Output Voltage Second Converter = (2*Peak Input Voltage Dual Converter*(cos(Delay Angle of Second Converter)))/pi

DC Output Voltage for First Converter

Go DC Output Voltage First Converter = (2*Peak Input Voltage Dual Converter*(cos(Delay Angle of First Converter)))/pi

Average DC Output Voltage of Single Phase Full Converter

Go Average Voltage Full Converter = (2*Maximum DC Output Voltage Full Converter*cos(Firing Angle Full Converter))/pi

Average Output Voltage of Single Phase Semi-Converter with Highly Inductive Load

Go Average Voltage Semi Converter = (Maximum Input Voltage Semi Converter/pi)*(1+cos(Delay Angle Semi Converter))

Average Load Current of Three Phase Semi-Current

Go Load Current 3 Phase Semi Converter = Average Voltage 3 Phase Semi Converter/Resistance 3 Phase Semi Converter

RMS Output Voltage of Single Phase Full Converter

Go RMS Output Voltage Full Converter = Maximum Input Voltage Full Converter/(sqrt(2))

RMS Harmonic Current for PWM Control Formula

Define the Concept of Harmonic Order in the Context of PWM controlled converters?

The harmonic order represents the number of times the frequency of a particular harmonic component is a multiple of the fundamental frequency. Mathematically, the nth harmonic has a frequency that is n times the fundamental frequency.

How to Calculate RMS Harmonic Current for PWM Control?

RMS Harmonic Current for PWM Control calculator uses RMS nth Harmonic Current = ((sqrt(2)*Armature Current)/pi)*sum(x,1,Number of Pulse in Half-cycle of PWM,(cos(Harmonic Order*Excitation Angle))-(cos(Harmonic Order*Symmetrical Angle))) to calculate the RMS nth Harmonic Current, The RMS Harmonic Current for PWM Control formula is defined as the effective value of the harmonic component of the current waveform at a frequency that is an integer multiple (n) of the fundamental frequency of the PWM signal. RMS nth Harmonic Current is denoted by I_n symbol.

How to calculate RMS Harmonic Current for PWM Control using this online calculator? To use this online calculator for RMS Harmonic Current for PWM Control, enter Armature Current (I_a), Number of Pulse in Half-cycle of PWM (p), Harmonic Order (n), Excitation Angle (α_k) & Symmetrical Angle (β_k) and hit the calculate button. Here is how the RMS Harmonic Current for PWM Control calculation can be explained with given input values -> -4.058521 = ((sqrt(2)*2.2)/pi)*sum(x,1,3,(cos(3*0.5235987755982))-(cos(3*1.0471975511964))).

FAQ

What is RMS Harmonic Current for PWM Control?

The RMS Harmonic Current for PWM Control formula is defined as the effective value of the harmonic component of the current waveform at a frequency that is an integer multiple (n) of the fundamental frequency of the PWM signal and is represented as I_n = ((sqrt(2)*I_a)/pi)*sum(x,1,p,(cos(n*α_k))-(cos(n*β_k))) or RMS nth Harmonic Current = ((sqrt(2)*Armature Current)/pi)*sum(x,1,Number of Pulse in Half-cycle of PWM,(cos(Harmonic Order*Excitation Angle))-(cos(Harmonic Order*Symmetrical Angle))). Armature Current DC motor is defined as the armature current developed in an electrical dc motor due to the rotation of rotor, Number of Pulse in Half-cycle of PWM (Pulse Width Modulation) converter refers to the count of pulses generated within half of the waveform period, Harmonic Order is Defined as the the Integer Multiple of the Fundamental Frequency (f) of the PWM Signal. It indicates which Harmonic Component of the Current Waveform is being analyzed, Excitation Angle is the angle at which the PWM Converter begins to Produce Output Voltage or Current & Symmetrical Angle is the Angle at which the PWM Converter produces Symmetrical Output Waveforms with respect to the AC Input Waveform.

How to calculate RMS Harmonic Current for PWM Control?

The RMS Harmonic Current for PWM Control formula is defined as the effective value of the harmonic component of the current waveform at a frequency that is an integer multiple (n) of the fundamental frequency of the PWM signal is calculated using RMS nth Harmonic Current = ((sqrt(2)*Armature Current)/pi)*sum(x,1,Number of Pulse in Half-cycle of PWM,(cos(Harmonic Order*Excitation Angle))-(cos(Harmonic Order*Symmetrical Angle))). To calculate RMS Harmonic Current for PWM Control, you need Armature Current (I_a), Number of Pulse in Half-cycle of PWM (p), Harmonic Order (n), Excitation Angle (α_k) & Symmetrical Angle (β_k). With our tool, you need to enter the respective value for Armature Current, Number of Pulse in Half-cycle of PWM, Harmonic Order, Excitation Angle & Symmetrical Angle 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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