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ElectricalPower System

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

$Z_0 < Z_1 < Z_2$

$Z_1 < Z_2 < Z_0$

$Z_1 < Z_0 < Z_2$

$Z_0 > Z_1 > Z_2$

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower System

Option B

$Z_1 < Z_2 < Z_0$

Quick Summary:

In a standard three-phase power system, the positive sequence impedance ( $Z_1$ ) and negative sequence impedance ( $Z_2$ ) are generally equal for static components like lines and transformers ( $Z_1 = Z_2$ ). However, for rotating machines and in systems where grounding impedance influences the return path, the zero sequence impedance ( $Z_0$ ) is usually significantly larger than $Z_1$ and $Z_2$ because it depends heavily on the grounding method and the physical path of the return current.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$Z_1 = Z_2$ — for static equipment

$Z_0 = Z_{phase} + 3Z_n$ — where $Z_n$ is the neutral grounding impedance

⚙️ Working Principle

The positive and negative sequence currents encounter the same impedance in stationary networks. The zero-sequence current, however, flows through the neutral-to-ground path; the impedance of this path ( $Z_n$ ) is reflected as $3Z_n$ in the zero-sequence network, making $Z_0$ typically higher than $Z_1$ or $Z_2$ in solidly or impedance-grounded systems.

📌 Key Points

▸
Positive sequence ( $Z_1$ ) is the impedance offered to balanced phase currents.
▸
Negative sequence ( $Z_2$ ) is usually equal to $Z_1$ in static components.
▸
Zero sequence ( $Z_0$ ) includes the return path impedance through the ground/neutral.
▸
In transmission lines, $Z_0$ is usually 2 to 3 times larger than $Z_1$ .

✅ Advantages

▸
Ensures predictable fault current paths
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Allows for selective relay coordination

❌ Disadvantages / Limitations

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Higher ground fault currents in solidly grounded systems
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Increased risk of mechanical stress on windings during faults

🛠️ Applications / Uses

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Fault analysis in Power Systems
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Setting of Earth Fault Relays
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Protection relay coordination

📄 Additional Information

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In rotating machines, $Z_1 > Z_2 > Z_0$ might occur due to sub-transient effects, but for network impedance analysis under steady state, $Z_1 \approx Z_2 < Z_0$ is the standard relation.
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Option B represents the correct hierarchy where the zero sequence path is more resistive/reactive due to the return circuit.

📊 Diagram / Illustration

✅

B is correct — In a typical power system network, the zero sequence impedance is greater than the positive and negative sequence impedances because it incorporates the impedance of the return neutral path.

Core Concepts Used

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Symmetrical Components Power System Stability Grounding Impedance

💡 EXAM TIP

Always remember that $Z_1 = Z_2$ for static components like transformers and lines; only $Z_0$ changes significantly based on grounding configuration.

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