Load Flow By Newton-Raphson Method power system analysis free lecture notes pdf

There are three concepts are used in Load flow by newton rapson method.

Load Flow Algorithm

Formation of the Jacobian Matrix

Solution of Newton-Raphson Load Flow

(4.27)

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. 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).