Answer to Question #226503 in Electrical Engineering for Alock kumar

Question #226503

Show that, "Three unbalanced phasors of a 3- system can be resolved into three balanced system of phasors."


1
Expert's answer
2021-08-19T08:27:02-0400


Consider an unbalanced phasor has shown in (a). The positive, negative, and zero sequence are shown in (b), (c), and (d) respectively.

Let's define the a-operator

a=ej120°=12+j32a2=ej240°=12j32a=e^{j120\degree}=-\dfrac{1}{2}+j\dfrac{\sqrt{3}}{2}\\ a^2=e^{j240\degree}=-\dfrac{1}{2}-j\dfrac{\sqrt{3}}{2}\\

from (b)

Vb1=a2Va1Vc1=aVa1V_{b1}=a^2V_{a1}\\ V_{c1}=aV_{a1}\\

from (c)

Vb2=aVa2Vc2=a2Va2V_{b2}=aV_{a2}\\ V_{c2}=a^2V_{a2}

from (d)

Va0=Vb0=Vc0V_{a0}=V_{b0}=V_{c0}



Va=Va0+Va1+Va2Vb=Vb0+Vb1+Vb2Vb=Va0+a2Va1+aVa2Vc=Vc0+Vc1+Vc2Vc=Va0+aVa1+a2Va2V_{a}=V_{a0}+V_{a1}+V_{a2}\\ V_{b}=V_{b0}+V_{b1}+V_{b2}\\ V_{b}=V_{a0}+a^2V_{a1}+aV_{a2}\\ V_{c}=V_{c0}+V_{c1}+V_{c2}\\ V_{c}=V_{a0}+aV_{a1}+a^2V_{a2}\\



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