Question

The dimension of the sub-matrix $M$ in the Newton-Raphson Jacobian is \(\underline{\hspace{2cm}}\).

• A. $N_L \times (N-1)$
• B. $(N-1) \times (N-1-N_L)$
• C. $N_L \times (N-1+N_L)$
• D. $(N-1) \times (N-1+N_L)$

Hint:

In NR load flow, rows correspond to PQ buses (Q equations) and columns to all non-slack angle variables.

Answer 1

The Correct Option is A

Jacobian matrix in polar NR load flow consists of submatrices:
$H \rightarrow (N-1)\times(N-1)$,
$S \rightarrow (N-1)\times N_L$,
$M \rightarrow N_L \times (N-1)$,
$R \rightarrow N_L \times N_L$.
$M$ relates reactive power mismatches at PQ buses ($N_L$ rows) to voltage angle changes at non-slack buses ($(N-1)$ columns).
Thus, size of $M$ is $N_L \times (N-1)$.
Final Answer: (A) $N_L \times (N-1)$