Solution of Newton-Raphson Load Flow

The Newton-Raphson load flow program is tested on the system of Fig. 4.1 with the system data and initial conditions given in Tables 4.1 to 4.3. From (4.41) we can write

Similarly from (4.39) we have

Hence from (4.42) we get

In a similar way the rest of the components of the matrix J₁₁⁽⁰⁾ are calculated. This matrix is given by

For forming the off diagonal elements of J₂₁ we note from (4.44) that

Also from (4.38) the real power injected at bus-2 is calculated as

Hence from (4.45) we have

Similarly the rest of the elements of the matrix J₂₁ are calculated. This matrix is then given as

For calculating the off diagonal elements of the matrix J₁₂ we note from (4.47) that they are negative of the off diagonal elements of J₂₁ . However the size of J₂₁ is (3 X 4) while the size of J₁₂ is (4 X 3). Therefore to avoid this discrepancy we first compute a matrix M that is given by

The elements of the above matrix are computed in accordance with (4.44) and (4.45). We can then define

Furthermore the diagonal elements of J₁₂ are overwritten in accordance with (4.48). This matrix is then given by

Finally it can be noticed from (4.50) that J₂₂ = J₁₁ (1:3, 1:3). However the diagonal elements of J₂₂ are then overwritten in accordance with (4.51). This gives the following matrix

From the initial conditions the power and reactive power are computed as

Consequently the mismatches are found to be

Then the updates at the end of the first iteration are given as

The load flow converges in 7 iterations when all the power and reactive power mismatches are below 10⁻⁶ .