Question

A power system consists of 61 buses. If there are 20 PV buses in addition to PQ buses and a slack bus then the size of the Jacobian matrix is

• A. $100\times 100$
• B. $102\times 102$
• C. $99\times 99$
• D. $122\times 122$

Answer 1

The correct option is A $100\times 100$

Total buses = 61
There are 20 PV buses and one slack bus
Number of PQ buses = Total buses - (PV bus + slack bus) = 61-(20+1) = 40
$\therefore$ Size of jacobian matrix $=$(2PQ+PV) $\times$ (2PQ+PV)
$=$ (2 $\times$ 40 + 20) $\times$ (2 $\times$ 40 + 20 )
$=$ 100 $\times$ 100