Section VI:  Load Flow By Newton-Raphson Method

• Load Flow Algorithm
• Formation of the Jacobian Matrix
• Solution of Newton-Raphson Load Flow

Let us assume that an n -bus power system contains a total n_p number of P-Q buses while the number of P-V (generator) buses be n_g such that n = n_p + n_g + 1. Bus-1 is assumed to be the slack bus. We shall further use the mismatch equations of ΔP_i and ΔQ_i given in (4.9) and (4.10) respectively. The approach to Newton-Raphson load flow is similar to that of solving a system of nonlinear equations using the Newton-Raphson method: At each iteration we have to form a Jacobian matrix and solve for the corrections from an equation of the type given in (4.27). For the load flow problem, this equation is of the form

(4.30)

where the Jacobian matrix is divided into submatrices as

(4.31)

It can be seen that the size of the Jacobian matrix is ( n + n_p − 1) x ( n + n_p −1). For example for the 5-bus problem of Fig. 4.1 this matrix will be of the size (7 x 7). The dimensions of the submatrices are as follows:

J₁₁: (n - 1) ´ (n - 1), J₁₂: (n - 1) ´ n_p, J₂₁: n_p ´ (n - 1) and J₂₂: n_p ´ n_p

The submatrices are

	(4.32)
	(4.33)
	(4.34)
	(4.35)