The matrix obtained from the Branch-Node Incident Matrix by deleting the columns corresponding to the referenc

Question

The matrix obtained from the Branch-Node Incident Matrix by deleting the columns corresponding to the reference node is

Examoogle · Accepted Answer

Option B: Bus incidance matrix

Explanation & Concepts:
The Branch-Node Incidence Matrix (A) describes the relationship between branches and nodes in a network. By removing the column associated with the reference node (datum), we obtain the Reduced Incidence Matrix, also known as the Bus Incidence Matrix (A_bus).

Working Principle: In a network with 'n' nodes, one node is selected as the reference. The complete incidence matrix 'A' is of size (b x n). Deleting the column corresponding to the reference node reduces the size to (b x (n-1)), which is essential for forming the Y-bus matrix using the singular transformation $Y_{bus} = A^T Y_b A$.

Key Formulas: $Y_{bus} = A^T_{bus} Y_{branch} A_{bus}$ — Transformation to find bus admittance matrix; $A = [A_{bus} | A_{ref}]$ — Partitioning of incidence matrix

Key Points: The Branch-Node incidence matrix has a rank of (n-1) for a connected graph of 'n' nodes.; Deleting the reference node column makes the matrix non-singular and useful for power system analysis.; A column in the incidence matrix represents a node, and a row represents a branch.; Entries in the matrix are usually 1, -1, or 0 representing branch orientation.

Advantages: Allows direct calculation of nodal voltages.; Facilitates the formulation of Y-bus matrix for load flow studies.

Disadvantages: The matrix becomes sparse, but memory consumption increases for large networks.; Requires knowledge of network topology in matrix form.

Applications: Load flow analysis in power systems.; Short circuit studies and fault analysis.; Network topology identification.

Additional Info: The reference node is usually chosen as the slack bus in power system analysis.. Option A is incorrect as Node bus matrix is not a standard term in this context.. Option C is incorrect as the Branch incidence matrix typically refers to the full (n x b) matrix including the reference node.

Answer: B is correct — The Bus Incidence Matrix is the reduced form of the Branch-Node Incidence Matrix obtained by removing the reference node column.

Exam Tip: Remember that the Y-bus matrix is always symmetric for a linear network, which is a direct consequence of the properties of the Bus Incidence Matrix.

Examoogle · Answer

Option A: Node bus matrix

Examoogle · Answer

Option C: Branch incidance matrix

Examoogle · Answer

Option D: None of above

Correct Answer

Discussion (0)

Correct Answer

Related Questions

Discussion (0)