 Hello, friends welcome to the new post. In this post, we will have a detailed look at Balanced Three-Phase Circuits Voltage and Current Calculation.  the system having the same magnitude of three phases but with a difference of one twenty-degree of phase, the angle is called a balanced three-phase system. Here we are going to discuss the details about the voltage and current flowing in this system.

Generally, a three-phase system is used for the transmission of volts from one point to other from generation to load end. So let get started

## Balanced Three-Phase Circuits Voltage and Current Calculation

• In a power system, the power is generated through the use of three-phase generators.
• The load linked to the three phases of generators is balanced it means the impedance values are the same.
• in the below figure the generator configured with wye connection having natural wire n. • To understanding of this circuitry let us assume that the value of impedance and load is zero and also between points 0 and n also zero
• the resultant circuitry of this generator has emf in very phase and denoted with a circle.
• Each emf is configured in a series combination to the resistance and inductive reactance linked to Zd.
• The points x y and z are reference points
• and terminals of generated with f g h
• In this circuitry, the value of emf denoted with Exo, Eyo, and Ezo has equal magnitude and separated with one twenty degree of angle
• Let suppose that value of every emf is one hundred volts then Eao was taken as a reference then we have
• Exo = 100∠0V
• Eyo = 100∠240V
• Ezo = 100∠120V
• Here phase equation is fgh.
• In other words Exo leads  Eyo by one twenty-degree and Eyo leads by  Ezo one twenty degrees.
• In below figure, we can see the phase sequence • The voltage about the terminal is given here.
• Vfo=Exo-IfnZd
• Vgo=Eyo-IgnZd
• Vho=Ezo-IhnZd
• as o and n has the same value of potential so Vfo Vgo Vho has the same value of Vxn, Vyn, Vzn
• Equation of line current are mention here • Exo, Eyo Ezo has the same value of and one twenty-degree phase difference.
• Vfo, Vgo Vho also has hs same values and one twenty degrees phase difference
• In below figure you can see the 3 currents flowing in the system having balance configuration. In figure denoted as b their closed triangle is shown. • So the curent flowing in the neutral is zero.
• in case of nonbalance load, the current summation is zero and the current is passing among the points n and o.
• in the non-balance system, there is not the same potential till they are linked to 0 value of impedance.
• Due to phase variation in the voltage and current in case of a balanced three-phase system, it is easy to simple to use such a technique that denoting th phasor through one twenty degrees.
• The outcome of the product of 2 complicated numbers is the multiple of their magnitude and angle sum
• If the complicated number denoting phasor is multiplied to a complex number of unity magnitude and angle θ the resultant complex number denotes phasor equal to real phasor parted with the angle of θ.
• The complex number if unity value and angle is a function which that moves the phasor at which it works with angle
• In math the operator, j caused the rotation of ninety degrees and operator -1 that results in one eight degrees.
• 2 continues usage of operator J results in 90+90 that results in j x j cause to rotation at an angle off one-eighty degree.
• The a alphabet is generally used to represent the function that results in the movement of one twenty degrees anti-clock wises.
• This function is a complex number having a unity value having an angle of one twenty-degree and works as • If we use function a two time then phasor will be moved with the angle of two forty degrees.
• With using three times angle move to three-sixty degrees • In below diagram, we can see the phasor denotation having different values of a. • The line to lin voltage for below circuitry are Vfg, Vgh and Vhf • Following the path from f to g to the point n we have
• Vfg=Vfn+Vgn=Vfn-Vgn
• as the Exo and Vfn has not the same phase so we are replacing Vxn in place of Exo
• So in the below diagram shows the phasor diagram of voltage to neutral and vlaeu of Vfg is given here.

• In case of function we have

Vgn=a2Vgn

Vfg=Vfn-a2Vfn

• phasor equation
• In the case of phasor Vfg leading the Vfn through an angle of thirty degrees and has √3  has a large value.
• Other value of line to line can be found through using this method  In the above figure we can all values of line to line volts
• the value of balance their phase line to line volts of three-phase circuitry same to √3 time the magnitude of line to neutral

So that is all about the Balanced Three-Phase Circuits Voltage and Current Calculation. If you have any further query ask in the comments box. See you in the next post

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