If Ia1 is the positive sequence current of an alternator and Z1, Z2 and Z0 are the sequence impedances of the

Question

If Ia1 is the positive sequence current of an alternator and Z1, Z2 and Z0 are the sequence impedances of the alternator. The drop produced by the current Ia1 will be

Examoogle · Accepted Answer

Option A: $I_{a1} Z_1$

Explanation & Concepts:
In symmetrical component analysis, the positive, negative, and zero sequence networks of an alternator are decoupled from each other. Each sequence current produces a voltage drop only across its corresponding sequence impedance.

Working Principle: According to the principle of superposition in power systems, an unbalanced polyphase network can be decomposed into three balanced networks. The positive sequence current $I_{a1}$ encounters only the positive sequence impedance $Z_1$ of the generator. Since the networks are independent, $I_{a1}$ does not produce any drop across $Z_2$ or $Z_0$.

Key Formulas: $V_{a1} = I_{a1} Z_1$ — Positive sequence voltage drop; $V_{a2} = I_{a2} Z_2$ — Negative sequence voltage drop; $V_{a0} = I_{a0} Z_0$ — Zero sequence voltage drop

Key Points: Sequence networks are mutually independent in a balanced generator.; Positive sequence impedance ($Z_1$) is usually distinct from negative ($Z_2$) and zero ($Z_0$) impedances.; The alternator generates only positive sequence voltages internally; negative and zero sequence voltages are zero under normal internal conditions.

Advantages: Simplifies analysis of unsymmetrical faults; Allows for independent calculation of sequence quantities

Applications: Symmetrical Fault Analysis; Unsymmetrical Fault Analysis (L-G, L-L, L-L-G)

Additional Info: Options B, C, and D are incorrect because they imply coupling between sequence networks, which does not occur within the alternator itself during sequence current calculation.. The total voltage at the terminal is a combination of these sequence components, but the specific drop attributed to $I_{a1}$ is strictly $I_{a1}Z_1$.

Answer: A is correct — The positive sequence current $I_{a1}$ flows through the positive sequence network and creates a voltage drop equal to $I_{a1} Z_1$.

Exam Tip: Always remember that sequence networks are isolated. If you are asked about sequence voltage at a bus during a fault, the network connections change, but the local drop within the machine remains dictated by the local sequence current and impedance.

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Option B: $I_{a1} (Z_1 + Z_2)$

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Option C: $I_{a1} (Z_1 + Z_2 + Z_0)$

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Option D: $I_{a1} (Z_2 + Z_0)$

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