Question

The power system having 60 buses, 8 of them are generator buses and remaining are load buses. 6 load buses are having voltage constraint and become divergent at the first iteration. The size of Jacobian matrix is

• A. 110 $\times$ 110
• B. 111 $\times$ 111
• C. 105 $\times$ 105
• D. 120 $\times$ 120

Answer 1

The correct option is C 105 $\times$ 105

Total number of buses = 60
Generator buses including slack bus = 8
Number of PV buses = Generator bus - 1 slack bus
Number of PV buses = 8 - 1 = 7
6 load buses are having voltage constraint (fixed voltage). So these buses will be treated as PV buses.
Total number of PV buses = 7 + 6 = 13
Total number of load buses (PQ) = 60 - 13 - 1 (Slack bus)
Number of PQ buses = 46
size of Jacobian = (2 $\times$ PQ + PV)$\times$(2 $\times$ PQ + PV)
size of Jacobian = (2 $\times$ 46 + 13)$\times$(2 $\times$ 46 + 13) = 105$\times$105