GATE Electrical Engineering (EE) 2021 Solved Papers

Consider a power system consisting of N number of buses. Buses in this power system are categorized into slack bus, PV buses and PQ buses for load flow study. The number of PQ buses is N ${}_{\mathit{L}}$. The balanced Newton-Raphson method is used to carry out load flow study in polar form. H, S, M, and R are sub-matrices of the Jacobian matrix $\mathit{J}$ as shown below:
$\left[\begin{array}{c}∆\mathit{P}\\ ∆\mathit{Q}\end{array}\right]=\mathit{J}\left[\begin{array}{c}∆\mathit{\delta }\\ ∆\mathit{V}\end{array}\right];$ where $\mathit{J}=\left[\begin{array}{cc}\mathit{H}& \mathit{S}\\ \mathit{M}& \mathit{R}\end{array}\right]$
The dimension of the sub-matrix $\mathit{M}$ is: