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Circulating Current across Reactor under Dual Converter Formula

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The Circulating Current flows between the Rectifier and the Inverter through the DC link Reactor, Compensating for the Phase difference and Stabilizing the DC link Voltage. Check FAQs

i c = (\frac{1}{ω (dual) \cdot L r(dual)}) \cdot \int (e R, x, (α 1(dual) + (\frac{π}{6})), (ω (dual) \cdot t (dual)))

i_c - Circulating Current?ω_(dual) - Angular Frequency?L_r(dual) - Circulating Current Reactor?e_R - Instantaneous voltage Across Reactor?α_1(dual) - Delay Angle of First Converter?t_(dual) - Time?π - Archimedes' constant?

Circulating Current across Reactor under Dual Converter Example

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Here is how the Circulating Current across Reactor under Dual Converter equation looks like with Values.

Here is how the Circulating Current across Reactor under Dual Converter equation looks like with Units.

Here is how the Circulating Current across Reactor under Dual Converter equation looks like.

56.3308 = (\frac{1}{100 \cdot 2.3}) \cdot \int (4.32, x, (22 + (\frac{3.1416}{6})), (100 \cdot 30))

56.3308A = (\frac{1}{100rad/s \cdot 2.3H}) \cdot \int (4.32V, x, (22° + (\frac{3.1416}{6})), (100rad/s \cdot 30s))

56.3308 = (\frac{1}{100 \cdot 2.3}) \cdot \int (4.32, x, (22 + (\frac{3.1416}{6})), (100 \cdot 30))

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Circulating Current across Reactor under Dual Converter Solution

Follow our step by step solution on how to calculate Circulating Current across Reactor under Dual Converter?

FIRST Step Consider the formula

i c = (\frac{1}{ω (dual) \cdot L r(dual)}) \cdot \int (e R, x, (α 1(dual) + (\frac{π}{6})), (ω (dual) \cdot t (dual)))

Next Step Substitute values of Variables

∴

i c = (\frac{1}{100rad/s \cdot 2.3H}) \cdot \int (4.32V, x, (22° + (\frac{π}{6})), (100rad/s \cdot 30s))

Next Step Substitute values of Constants

∴

i c = (\frac{1}{100rad/s \cdot 2.3H}) \cdot \int (4.32V, x, (22° + (\frac{3.1416}{6})), (100rad/s \cdot 30s))

Next Step Convert Units

∴

i c = (\frac{1}{100rad/s \cdot 2.3H}) \cdot \int (4.32V, x, (0.384rad + (\frac{3.1416}{6})), (100rad/s \cdot 30s))

Next Step Prepare to Evaluate

∴

i c = (\frac{1}{100 \cdot 2.3}) \cdot \int (4.32, x, (0.384 + (\frac{3.1416}{6})), (100 \cdot 30))

Next Step Evaluate

∴

i c = 56.3307795320362A

LAST Step Rounding Answer

∴

i c = 56.3308A

Circulating Current across Reactor under Dual Converter Formula Elements

Variables

Constants

Functions

Circulating Current

The Circulating Current flows between the Rectifier and the Inverter through the DC link Reactor, Compensating for the Phase difference and Stabilizing the DC link Voltage.

Symbol: i_c

Measurement: Electric CurrentUnit: A

Note: Value can be positive or negative.

Formulas to find Circulating Current

Angular Frequency

Angular Frequency refers to the angular displacement per unit of time in a dual converter circuit.

Symbol: ω_(dual)

Measurement: Angular FrequencyUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Frequency

Circulating Current Reactor

Circulating Current Reactor is an inductive component that is deliberately introduced into the circuit to influence the behavior of circulating currents.

Symbol: L_r(dual)

Measurement: InductanceUnit: H

Note: Value should be greater than 0.

Formulas to find Circulating Current Reactor

Instantaneous voltage Across Reactor

The Instantaneous Voltage across Reactor refers to the Voltage present across the Reactor's terminals at a specific moment in Time.

Symbol: e_R

Measurement: Electric PotentialUnit: V

Note: Value can be positive or negative.

Formulas to find Instantaneous voltage Across Reactor

Delay Angle of First Converter

Delay angle of first converter here refers to the delay angle of thyristors of the first converter in the dual converter.

Symbol: α_1(dual)

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Delay Angle of First Converter

Time

Time provides a framework for understanding the sequence of events, durations, intervals, and the relationships between different moments.

Symbol: t_(dual)

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Time

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: int(expr, arg, from, to)

Other formulas in Single Phase Dual Converters category

Go DC Output Voltage for First Converter

V out(first) = \frac{2 \cdot V in(dual) \cdot (\cos (α 1(dual)))}{π}

Go DC Output Voltage of Second Converter

V out(second) = \frac{2 \cdot V in(dual) \cdot (\cos (α 2(dual)))}{π}

Go Instantaneous Circulating Current

i r(dual) = \frac{2 \cdot V in(dual) \cdot (\cos (ω (dual) \cdot t (dual)) - \cos (α 1(dual)))}{ω (dual) \cdot L r(dual)}

How to Evaluate Circulating Current across Reactor under Dual Converter?

Circulating Current across Reactor under Dual Converter evaluator uses Circulating Current = (1/(Angular Frequency*Circulating Current Reactor))*int(Instantaneous voltage Across Reactor,x,(Delay Angle of First Converter+(pi/6)),(Angular Frequency*Time)) to evaluate the Circulating Current, The Circulating Current across Reactor under Dual Converter refers to the current that flows through the reactor due to the phase difference between the firing angles of the rectifier and the inverter in the dual converter system. Circulating Current is denoted by i_c symbol.

How to evaluate Circulating Current across Reactor under Dual Converter using this online evaluator? To use this online evaluator for Circulating Current across Reactor under Dual Converter, enter Angular Frequency (ω_(dual)), Circulating Current Reactor (L_r(dual)), Instantaneous voltage Across Reactor (e_R), Delay Angle of First Converter (α_1(dual)) & Time (t_(dual)) and hit the calculate button.

FAQs on Circulating Current across Reactor under Dual Converter

What is the formula to find Circulating Current across Reactor under Dual Converter?

The formula of Circulating Current across Reactor under Dual Converter is expressed as Circulating Current = (1/(Angular Frequency*Circulating Current Reactor))*int(Instantaneous voltage Across Reactor,x,(Delay Angle of First Converter+(pi/6)),(Angular Frequency*Time)). Here is an example- 56.33078 = (1/(100*2.3))*int(4.32,x,(0.38397243543868+(pi/6)),(100*30)).

How to calculate Circulating Current across Reactor under Dual Converter?

With Angular Frequency (ω_(dual)), Circulating Current Reactor (L_r(dual)), Instantaneous voltage Across Reactor (e_R), Delay Angle of First Converter (α_1(dual)) & Time (t_(dual)) we can find Circulating Current across Reactor under Dual Converter using the formula - Circulating Current = (1/(Angular Frequency*Circulating Current Reactor))*int(Instantaneous voltage Across Reactor,x,(Delay Angle of First Converter+(pi/6)),(Angular Frequency*Time)). This formula also uses Archimedes' constant and Definite Integral (int) function(s).

Can the Circulating Current across Reactor under Dual Converter be negative?

Yes, the Circulating Current across Reactor under Dual Converter, measured in Electric Current can be negative.

Which unit is used to measure Circulating Current across Reactor under Dual Converter?

Circulating Current across Reactor under Dual Converter is usually measured using the Ampere[A] for Electric Current. Milliampere[A], Microampere[A], Centiampere[A] are the few other units in which Circulating Current across Reactor under Dual Converter can be measured.

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Circulating Current across Reactor under Dual Converter Formula

Circulating Current across Reactor under Dual Converter Example

Circulating Current across Reactor under Dual Converter Solution

Circulating Current across Reactor under Dual Converter Formula Elements

Other formulas in Single Phase Dual Converters category

How to Evaluate Circulating Current across Reactor under Dual Converter?

FAQs on Circulating Current across Reactor under Dual Converter

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