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The line current in a three phase unbalanced load are Ia = 4 + j6, Ib = 2 - j2, Ic = -3 + j2, then zero sequence component of current will be
- a)3 + j6
- b)9 + j10
- c)1 + j2
- d)3 - j6
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The line current in a three phase unbalanced load are Ia = 4 + j6, Ib ...
Concept:
The relation between the line currents in terms of the symmetrical components of currents is given below.
The relation between the line currents in terms of the symmetrical components of currents is given below.
Ia0 = Zero Sequence Component of Current
Ia1 = Positive Sequence Component of Current
Ia2 = Negative Sequence Component of Current
a = 1∠120°, which represents the rotation of 120° in the clockwise direction.
a2 = 1∠-120° or 1∠240° in anticlockwise direction or clockwise direction, respectively.
1 + a + a2 = 0
Calculation:
Given that
Ia = 4 + j6, Ib = 2 - j2, Ic = -3 + j2
Zero sequence component of current,
∴ I0 = 1 + j2 A
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The line current in a three phase unbalanced load are Ia = 4 + j6, Ib ...
Zero Sequence Component of Current in Unbalanced Load
Given values:
Ia = 4 + j6
Ib = 2 - j2
Ic = -3 + j2
To find the zero sequence component of current, we need to calculate the average of the three phase currents.
Step 1: Calculate the average of the three phase currents
Iavg = (Ia + Ib + Ic) / 3
= (4 + j6 + 2 - j2 - 3 + j2) / 3
= (3 + j6) / 3
= 1 + j2
Step 2: The zero sequence component is given by the equation:
I0 = (Ia + Ib + Ic) / 3 - Iavg
= (4 + j6 + 2 - j2 - 3 + j2) / 3 - (1 + j2)
= (3 + j6) / 3 - (1 + j2)
= 3/3 + j6/3 - 1/3 - j2/3
= 1 + j2 - 1/3 - j2/3
= 1 - 1/3 + j2 - j2/3
= 2/3 + j4/3
Therefore, the zero sequence component of current is 2/3 + j4/3, which is expressed as 1 + j2 in rectangular form.
Hence, the correct answer is option 'C' - 1 + j2.
Given values:
Ia = 4 + j6
Ib = 2 - j2
Ic = -3 + j2
To find the zero sequence component of current, we need to calculate the average of the three phase currents.
Step 1: Calculate the average of the three phase currents
Iavg = (Ia + Ib + Ic) / 3
= (4 + j6 + 2 - j2 - 3 + j2) / 3
= (3 + j6) / 3
= 1 + j2
Step 2: The zero sequence component is given by the equation:
I0 = (Ia + Ib + Ic) / 3 - Iavg
= (4 + j6 + 2 - j2 - 3 + j2) / 3 - (1 + j2)
= (3 + j6) / 3 - (1 + j2)
= 3/3 + j6/3 - 1/3 - j2/3
= 1 + j2 - 1/3 - j2/3
= 1 - 1/3 + j2 - j2/3
= 2/3 + j4/3
Therefore, the zero sequence component of current is 2/3 + j4/3, which is expressed as 1 + j2 in rectangular form.
Hence, the correct answer is option 'C' - 1 + j2.
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Question Description
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