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Sparsity of YBUS

In a power flow study of a big power system, the YBUS matrix is
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Answer & Explanation
Correct AnswerB. Sparse matrix

Quick Explanation

Each power-system bus is directly connected to only a small fraction of all other buses. Therefore most off-diagonal elements of the bus-admittance matrix are zero, making YBUS a sparse matrix for a large network. Hence option B.

Formula / Key Relation

Yij=0 when buses i and j have no direct branch connection
Sparsity of YBUS explanatory diagram

Detailed Explanation

Correct Answer

B — Sparse matrix

Concept and Reasoning

Each power-system bus is directly connected to only a small fraction of all other buses. Therefore most off-diagonal elements of the bus-admittance matrix are zero, making YBUS a sparse matrix for a large network. Hence option B.

Calculation / Key Relation

Yij=0 when buses i and j have no direct branch connection

Exam Takeaway

Large power-network YBUS is sparse because connectivity is local.

Common Mistake

Do not call YBUS full merely because every bus participates in the system solution.

Quick Trick

Large power-network YBUS is sparse because connectivity is local.

Common Mistake

Do not call YBUS full merely because every bus participates in the system solution.

Exam Tip

Large power-network YBUS is sparse because connectivity is local.

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