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ElectricalPower System

The positive, negative and zero sequence impedances of a solidly grounded system under steady state condition always follow the relations

$Z_1 > Z_2 > Z_0$

$Z_1 < Z_2 < Z_0$

$Z_0 < Z_1 < Z_2$

None of the above

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower System

Option A

$Z_1 > Z_2 > Z_0$

Quick Summary:

In a solidly grounded synchronous generator or system, the positive sequence impedance ( $Z_1$ ) is typically greater than the negative sequence impedance ( $Z_2$ ), and the negative sequence impedance is greater than the zero sequence impedance ( $Z_0$ ). This sequence of magnitudes ( $Z_1 > Z_2 > Z_0$ ) is a fundamental characteristic of standard rotating machinery under fault conditions.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$Z_1 = R_1 + jX_{d}''$ — Positive sequence impedance

$Z_2 = R_2 + jX_2$ — Negative sequence impedance ( $X_2 \approx X_{d}''$ )

$Z_0 = R_0 + jX_0$ — Zero sequence impedance

⚙️ Working Principle

The positive sequence impedance represents the machine's impedance to balanced loads. The negative sequence impedance is smaller because the armature reaction flux, rotating at synchronous speed in the opposite direction of the rotor, effectively induces currents that demagnetize the rotor path, reducing the effective reactance. Zero sequence impedance ( $Z_0$ ) is usually the lowest because it is limited only by leakage reactance and the path of the grounding system, and it lacks the flux linkage through the main rotor magnetic circuit.

📌 Key Points

▸
Positive sequence impedance ( $Z_1$ ) includes the effect of main flux linkage.
▸
Negative sequence impedance ( $Z_2$ ) is smaller due to the high-frequency nature of the armature reaction on the rotor cage.
▸
Zero sequence impedance ( $Z_0$ ) is highly dependent on the grounding method and the path return impedance.
▸
The relation $Z_1 > Z_2 > Z_0$ is the standard convention for synchronous generators.

✅ Advantages

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Predictable behavior during unsymmetrical faults.
▸
Essential for calculating fault current magnitudes accurately using symmetrical components.

❌ Disadvantages / Limitations

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Values can change during transient and sub-transient states.
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Highly dependent on machine construction.

🛠️ Applications / Uses

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Fault analysis in Power Systems.
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Setting of numerical distance and directional relays.

📄 Additional Information

▸
The provided answer in the source is $Z_1 > Z_2 > Z_0$ . Note that in some literature, specifically for transmission lines, the relation might vary, but for synchronous machines, this is the established order.
▸
Option B suggests $Z_1 < Z_2 < Z_0$ , which is physically incorrect for standard rotating electrical machines.

📊 Diagram / Illustration

✅

A is correct — In a standard synchronous generator, the sequence impedances follow the relation $Z_1 > Z_2 > Z_0$ .

Core Concepts Used

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Symmetrical Components Sequence Impedances Synchronous Machine Characteristics

💡 EXAM TIP

Always verify if the question refers to a generator or a transmission line; while for generators $Z_1 > Z_2 > Z_0$ is standard, transmission lines have $Z_0 > Z_1 = Z_2$ due to the return path through ground.

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