why 3 phase voltage is 415 volts

 

Hi friends, today's topic is the case of 3 phase AC supply, if one phase is 230 volt, then 3 phase should give 690 volts, then How it comes 400 volts? so today I will explain, that how 400 volts comes?why 3 phase voltage is 440 volts

        Additions are of 2 types,                                                                                                                 

              \ 1) scalar addition

                   This method is used in schools, if 230 is written 3 times, then addition will be 690, this is called scalar addition, 

                 

2)  Vector addition

         

        Here also  230, three times, but I have shown the direction also here, the arrow is there, this means, that  all 230 have same direction, now if we add all these 3 quantities, then also 690 will come with an arrow, so if quantity has direction also, then the addition of these, will be done using vector addition method, see Both methods addition is 690, that is because, the direction of all 3 quantity is the same,

 

2 phase voltage

       if all these 3 have a different direction, then what will happen, let us see,

          Here also same 230 is shown, this quantity has direction also, so it is called vector, that is why it is called vector addition, I have shown 2 quantities here, both do not have the same direction. if we add these two, then 460 will not come, if it were scalar, then 460 will come, what will be the addition here? see, the addition  230 and  230, will make 400, so we get 400 from 2 vectors itself,In above all have the same direction, so 690 is the addition, here it is not adding to give 460, this is called vector addition.

 

how to calculate phase to phase voltage

     Above I explained vector addition, now I will explain about vector difference, this difference is used in 3 phase supply, if we measure voltage using a multimeter, between 2 points, then we get the voltage difference, it will not be voltage addition, that is why, we are talking about voltage difference,

        here I have shown 2 vectors, the difference between these 2 vectors, will also be 400, both are different direction, the difference between these two is 400, this 400 is used in the AC supply, the addition is not applicable, I told about the addition to you only for knowledge, so that I could explain the difference to you.

        I have shown 2 phases here, the difference is 400, if these two 230 were scalar, then the difference will be zero not 400, as these are not scalar, these are vectors, so the difference is coming 400,

440 volt 3 phase wiring diagram

      Now I showed 2 phases, I have shown the 3rd phase also here, see,

       3 rd phases are not required to get  400, 2 phases itself will give 400, the difference of 2 phases is 400, but, this 400 is just one phase, if you want 3 phase, 400 volts line to line, then all 3 phases are required, if you want just 1 phase 400 volts, then two-phase input is sufficient, if all 3 phases are there, then the difference of any 2 phases, will be 400 and difference  is also 400, see, like this, so 3 phases are not needed to get 400, 2 phase itself will give 400,

      Concept 230 + 230 + 230 = 690 is for scalar, 690 will not be in the vector, 3 phase supply has vector quantities, as they have direction, direction word is used only to explain, actually, they are all phasor quantities, the angle is called phase angle, but all calculation is done as per vector, so all 3 results will be 400, understand, all three 400, value is 400 for all 3 phase, but all 3 phase have different directions.

     

3 phase voltage calculation formula

    Now we can calculate these, using mathematics also, if one phase of the 3 phase supply, is 230 v, so

230*1.782=398 or 230*= 398

 

the result will be 398 volts, this 398 is written as 400 for simplicity, addition or subtraction, the value will come 400, provided, the angle is 120 degree, whatever phase voltage will be there, vector difference will come root 3 times, this 400 is called line to line voltage,

         I will explain to you once more, the difference between scalar & vector, if both 230, are scalar quantities, then addition will be 460, but if they are vector and the angle is 120 degree, then vector addition will be 400, if the angle is different, then this 400 will change also, similarly, in the case of difference or subtraction, if the 2 phase are vectors, then the difference will not be zero, but it will come 400, provided the angle is 120 degree, if the angle is different, then this 400 will change,

      If  two phase were scalar, then the difference of two 230 will be zero, so scalar & vector have lot of difference, here, the scalar difference will come zero, but vector difference will be 400, scalar difference method is used, If quantities are scalar, scalar does not have direction, but  the direction is there, so vector.

      Now you will ask, that you told, the difference is 400 V, but 440 V is written everywhere, what is that 440 volts, this 400 or 230 V will be changing, 230 will give 400, but if the voltage increases by 10%, 10% of 400 will be 40, if the voltage is 10% more, then 400 + 40 will give 440, so if these voltages are 10% more, then 400 will become 440 volts, that is what written many places, if you measure the voltage with a multi-meter, then even 440 may not come, you may not get even 400, as voltage is changing, if this is 230, then you get 400, if this 230 changes, then this 400 will change also, these all 3 will not be added, as these are not scalar, these are vector or phasor.

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