...Contd from previous slide...Formation of the Jacobian Matrix

C. Formation of J₁₂

Let us define J₁₂ as

(4.46)

As evident from (4.33), the elements of J₂₁ involve the derivatives of real power P with respect to magnitude of bus voltage |V| . For i ≠ k , we can write from (4.38)

(4.47)

For i = k we have

(4.48)

Formation of J₂₂

For the formation of J₂₂ let us define

(4.49)

For i ≠ k we can write from (4.39)

(4.50)

Finally for i = k we have

(4.51)

We therefore see that once the submatrices J₁₁ and J₂₁ are computed, the formation of the submatrices J₁₂ and J₂₂ is fairly straightforward. For large system this will result in considerable saving in the computation time.