Consider a power system with buses, of which are generator buses and the remaining are load buses (where there is no generation). Assume that there are no reactive power-limit violations at the generator buses. What is the size of the Jacobian matrix in the Newton-Raphson load flow method?
ANSWER
The Jacobian matrix has size , option (B).
Official answer: BSource: Official answer key, GATE 2026 EE (IIT Guwahati)
Count the bus types. The generator buses include one slack (reference) bus, so there are PV buses. The load buses are PQ buses. Hence .
The slack bus has both and specified. It adds no unknowns and no mismatch equations to the Newton-Raphson iteration.
Each PV bus has specified. With no reactive power-limit violation it stays a PV bus, so its only unknown is . It gives one equation, the real-power mismatch . The PV buses together contribute unknowns and equations.
Each PQ bus has both and unknown. It gives two equations, the mismatches and . The PQ buses together contribute unknowns and equations.
The Jacobian relates the mismatch vector to the corrections in the unknowns, so it is square. Its size is the number of unknowns: .
Substitute : .
The Jacobian is therefore , which is option (B).
KEY IDEA
The size of the Newton-Raphson Jacobian equals the number of unknowns. The slack bus has none, each PV bus has one () and each PQ bus has two ( and ). The generator buses include the slack bus.
WATCH OUT FOR
Treating all generator buses as PV buses and forgetting that one of them is the slack bus. That gives , which is not among the options. Another slip is counting the slack bus's and as unknowns, which gives (A).
From the GATE 2026 EE paper. Every question of this paper · Download the full paper · All 10 Per unit & load flow questions, with notes
