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Examoogle • User • info@examoogle.com • EE-2024-8821
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In an unbalanced 3-phase system, the currents are measured as Iₐ = zero, Ib = 6∠60° and Ic = 6∠–120°. The zero sequence, positive sequence and negative sequence components will be
Zero, (3 – j3), (– 3 + j3)
Zero, ( – 3+ j3), ( 3 – j3)
Zero, ( – 9+ j 33), (9 – j33)
Zero, ( 9 – j33), (– 9 + j33)
Zero, ( – 9+ j 33), (9 – j33)
Quick Trick: Remember the operator 'a' (1 at 120 deg) and 'a squared' (1 at 240 deg). Since Ia=0, the sum of sequence components (I0+I1+I₂) must be zero, which is immediate for options with opposite real/imaginary parts.
Remember the operator 'a' (1 at 120 deg) and 'a squared' (1 at 240 deg). Since Ia=0, the sum of sequence components (I0+I1+I₂) must be zero, which is immediate for options with opposite real/imaginary parts.
Calculate Zero Sequence Component (I0)
I0 = (1/3) * (Ia + Ib + Ic). Given Ia = 0, Ib = 6(0.5 + j0.866) = 3 + j5.196, Ic = 6(-0.5 - j0.866) = -3 - j5.196. Sum = 0 + (3-3) + j(5.196-5.196) = 0. Hence I0 = 0.
Calculate Positive Sequence Component (I1)
I1 = (1/3) * (Ia + aIb + a2Ic). Since a = -0.5 + j0.866 and a² = -0.5 - j0.866, substituting the values yields I1 = (1/3) * [0 + (-0.5+j0.866)(3+j5.196) + (-0.5-j0.866)(-3-j5.196)]. Calculating this results in -9 + j3*sqrt(3).
Calculate Negative Sequence Component (I₂)
I₂ = (1/3) * (Ia + a2Ib + aIc). Using the property that I0+I1+I₂ = Ia = 0, we get I₂ = -(I0+I1). Since I0=0, I₂ = -I1 = -(-9 + j3sqrt(3)) = 9 - j3sqrt(3).
A: Calculated values for components do not match the standard transformation matrix results. B: The signs for the real and imaginary parts are swapped relative to the positive sequence. D: Incorrect signs for the real/imaginary parts of the positive sequence component.
C is correct because the sequence components sum to Ia=0, and the positive sequence calculation (1/3)(Ia + aIb + a2Ic) yields (-9 + j3sqrt(3)) and negative sequence yields (9 - j3sqrt(3)).
In sequence component problems, always check if I0+I1+I₂ equals the original Ia. If Ia=0, I1 must be the negative of I₂, which immediately narrows down options.