Load Flow Order of Jacobian Matrix Power System

[jaus tail]

I'm studying Newton Raphson Method in Load Flow Studies. Book has defined Jacobian Matrix and it's order as: N + N_p - 1
N = Total Number of Buses
N_p = Number of P-Q Buses

But in solved example they've used some other formula. I'm not sure if it's right.

Shouldn't order be: N + Np - 1
N = 40
Np = number of P-Q buses = (total number of buses) - (number of P-V buses) - slack bus = 40 - 9 - 1 = 30
So order = N + Np - 1 = 40 + 30 - 1 = 69
Order = 69 X 69
But none of the option is this.
Why have they ignored slack bus in the formula?

 

[anorlunda]

It has been a long time since I did this, but I think you are correct 69x69.

 

[Baarken]

From: http://nptel.ac.in/courses/Webcourse-contents/IIT-KANPUR/power-system/chapter_4/4_10.html

The size of the Jacobian matrix is $(n+n_p-1) \times (n + n_p -1)$

I believe you are correct.

 

[jaus tail]

So I guess book answer is wrong. Thanks.

 

[HenryD8]

slack bus is also voltage controlled bus, so the book is correct