Calculate the active and reactive components of the current in each phase of a starconnected 500

Calculate the active and reactive components of the current...

Key Concepts

Active Power

Active power, often measured in kilowatts (kW), is the component of electrical power that performs useful work such as running motors or lighting lamps. It represents the real energy consumed in performing tasks and is calculated from the product of voltage, current, and the cosine of the phase angle between them.

Reactive Power

Reactive power, measured in kilovolt-amperes reactive (kVAR), is the component of power that oscillates between the source and the reactive components (like inductors and capacitors) in the system. It does not perform any useful work but is necessary to maintain the magnetic and electric fields in AC systems.

Power Factor

Power factor is the cosine of the phase angle between the voltage and current waveforms and indicates the efficiency with which the current is being converted into useful work. A power factor of 0.8, for instance, signifies that 80% of the total current contributes to active power while the remaining 20% is involved in reactive power.

Three-Phase Systems

Three-phase systems consist of three AC voltages that are equal in magnitude and frequency but are phase-shifted by 120° relative to each other. These systems are widely used in power generation and distribution due to their efficiency in transmitting power and providing a steady load.

Star Connection

A star connection (or Y-connection) is a common method of linking the phases in a three-phase system where one end of each phase winding is connected together to form a neutral point. This configuration defines the relationship between line and phase voltages, which is essential for calculating phase currents and analyzing power distribution in the system.

Phasor Analysis

Phasor analysis is a technique used in AC circuit analysis to represent sinusoidal voltages and currents as rotating vectors (phasors) in the complex plane. This approach simplifies the calculation of magnitude and phase relationships, making it easier to analyze active and reactive power components, especially in three-phase star-connected systems.

Transcript

00:01 In this question, we have a 3 -phase star -connected alternator whose line voltage is equal to 5 ,000 volts.

00:11 And this alternator is supplying 3 ,000 kilowatt -power -8 power -factor lagging load.

00:22 Because here nothing is mentioned about the nature of power factor.

00:26 That's why i assume that the power factor is lagging.

00:30 Now by using this information i draw this figure here we have a three phase alternator which is connected in a star and it is supplying power to a load whose rating is 3 ,000 kilowatt and power factor of load is equal to 0 .8 lagging.

00:52 And in this question we need to calculate the value of ia, i, b, c.

00:57 Now we know active power drawn by the power.

01:00 Load is given by p is equal to root 3 vl i .l coz phi.

01:09 Here the value of p is equal to 3 ,000 kilowatt is equal to root 3 ,000, the value of vl is equal to 5 ,000, the value of il is unknown and the value of cos -5 is equal to 0 .8.

01:30 And by solving this, we obtain the value of il is equal to 433 .012 amp.

01:43 Because here power factor is 0 .8 lagging.

01:49 So that's why the angle of current il is equal to negative cos inverse 0 .8.

02:00 And this will become equal to il is equal to 433 .012 negative 36 .86 amper.

02:18 Here this is the line current of phase a because when we calculate line current by using this formula then by default this current is equal to ia means this current is the current flowing in the line a...

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