CHAPTER FOUR working with the A operator. Because all of the symmetrical components are balanced or symmetrical, all of the phasers can be described in terms of one phaser. And the operator. We usually choose the a phase simply for because it's easiest to do. And if we start with a positive sequence components, we can replace the B phase of the positive sequence components in terms of the a phase and the A operator. So we can say that the positive sequence B phase is equal to a squared v a one which means That's the eighth phase of the positive sequence multiplied by the a squared operator.
Moving on to the negative sequence components, and we will now look at the B phase of the negative sequence components. It can be written in terms of the a phase of the negative sequence of components, but the sequencing is reversed in this case. So we would have to say we can replace the VB sequence term by a sequence term shifted by just the A operator. In other words, v b two is equal to A operator times v a two. Moving on to the zero sequence impedance, since in the case of zero sequence components The phasers are equal magnitude and in the same direction, we can simply replace the V b phase of the zero sequence operator by just the a phase, we don't require a shift, because they're all in the same direction. So, one is equal to the other.
So, the B phase of the zero sequence component is equal to the a phase of the zero sequence component or in terms of an equation, the B zero is equal to b a zero. Shifting again back to the positive sequence impedance, we can replace the C phase in terms of the a phase using the A operator similarly, as we have done with the B phase, in this case, it's going to be the V c one is equal to the A operator the a one And moving on to the negative sequence, we can see that we can replace the C phase of the negative sequence in terms of the a phase negative sequence using the A operator, we can say that VC two is equal to a squared times V, a two. And finally, we can move on to the zero sequence. And we can also replace the C phase in terms of the a phase, again here, but we don't need the A operator in this case, because again, all of this hero sequence of phasers are in phase, so one equals the other.
So the c zero is equal to b, a zero. This ends chapter four