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A power system having 100 buses in which 20 are voltage controlled buses and 10 are generator buses. For the load flow study find the size of jacobian matrix –
  • a)
    169 × 169
  • b)
    200 × 200
  • c)
    190 × 190
  • d)
    188 × 188
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A power system having 100 buses in which 20 are voltage controlled bus...
size of jacobian matrix
= (2n – m – 2)× (2n – m – 2)
n = total number of buses.
m = voltage controlled buses + generator buses
generator bus
= 10-1=9 (∵ one slack bus)
m= 20 + 9 = 29
size of jacobian matrix = (2 x 100 - 29 - 2) x (2 x 100 - 29 - 2) x (2 x 100 - 29 - 2) = 169 x 169
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Most Upvoted Answer
A power system having 100 buses in which 20 are voltage controlled bus...
The size of the Jacobian matrix for a power system with n buses is given by n x n. In this case, there are 100 buses, so the Jacobian matrix will be a 100 x 100 matrix.

The fact that 20 buses are voltage controlled and 10 are generator buses does not affect the size of the Jacobian matrix. These are just additional constraints that need to be taken into account when solving the load flow equations.
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A power system having 100 buses in which 20 are voltage controlled buses and 10 are generator buses. For the load flow study find the size of jacobian matrix –a)169 × 169b)200 × 200c)190 × 190d)188 × 188Correct answer is option 'A'. Can you explain this answer?
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