Question

The Y-bus matrix of a 100-bus interconnected system is 90% sparse. Hence the number of transmission lines in the system must be:

• A. 450
• B. 500
• C. 900
• D. 1000

Hint:

The sparsity of the Y-bus matrix can help estimate the number of transmission lines in an interconnected system.

Answer 1

The Correct Option is A

In a system with \(n\) buses, the number of transmission lines (branches) is typically related to the sparsity of the Y-bus matrix. The sparsity indicates the proportion of the matrix that is zero, and for an \(n\)-bus system, the number of non-zero elements in the matrix is approximately \(0.5n(n-1)\). In this case, with 90% sparsity, the number of transmission lines can be estimated as: \[ \text{Transmission lines} = \frac{0.1 \times n(n-1)}{2} \] Substituting \(n = 100\), we get: \[ \text{Transmission lines} = \frac{0.1 \times 100(100-1)}{2} = 450 \] Thus, the number of transmission lines in the system is 450.