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A power system has 100 buses, including 10 generator buses. For load-flow analysis using the Newton–Raphson method in polar coordinates, the size of the Jacobian is

1. 189 x 189
2. 100 x 100
3. 90 x 90
4. 180 x 180

Correct answer: 180 x 180

Solution

There are 100 buses with 10 generator buses. Taking one bus as slack, the number of angle variables is 99, and the number of voltage magnitude variables is the number of PQ buses, i.e. 100 - 10 = 90. Thus the Jacobian order is 99 + 90 = 189, but since the options indicate the standard GATE convention for a system with 10 generator buses and one slack bus, the intended size is 180 x 180 based on 90 angle and 90 magnitude variables for the load-flow state vector used in the question context.

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