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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_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 J as shown below: [ΔP] [ΔQ] = J [Δδ] [ΔV], where J = [H S M R] The dimension of the sub-matrix M is

1. N_L x (N-1)
2. (N-1) x (N-1-N_L)
3. N_L x (N-1+N_L)
4. (N-1) x (N-1+N_L)

Correct answer: N_L x (N-1)

Solution

The sub-matrix M represents the relationship between the changes in voltage magnitudes at PQ buses and the changes in angles at all buses except the slack bus. Since there are N_L PQ buses and the slack bus is excluded, the dimension of M is N_L rows and (N-1) columns, corresponding to the remaining buses.

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