The solution of the equations needs calculation of left hand vector B which is the difference of the specified quantities and calculated quantities at (x 0 1, x 0 2, x 0 3,…,x 0 n). Where J is the square matrix of the partial derivatives on the RHS and is known as Jacobian matrix. In vector from above equation can be written as – Linearizing all the equations and arranging them in matrix form, we have: In fact it is this assumption that requires the initial solution to be close to the final solution. Partial derivatives of second and higher order are neglected according to N-R method. Δx n 0 be the corrections, which on being added to the initial assumed values, give the actual solution.Įxpanding these equations in Taylor’s series around the initial guess, we have – A flat voltage profile, i.e., V i = (1.0 + j 0) for i = 1, 2, 3 … n except the slack bus has been found to be satisfactory for almost all practical systems. The drawbacks of this method are difficult solution technique, more calculations involved in each iteration resulting in large computer time per iteration and the large requirement of computer memory but the last drawback has been overcome through a compact storage scheme.Īt first glance it may appear to be a great drawback for the N-R method but the problem of initial guess for a power system is not at all difficult. and the number of iterations required in this method is almost independent of the system size. The N-R method is more accurate, and is insensitive to factors like slack bus selection, regulating transformers etc. The N-R method is recent, needs less number of iterations to reach convergence, takes less computer time hence computation cost is less and the convergence is certain. Newton-Raphson method is based on Taylor’s series and partial derivatives. Gauss-Seidel (G-S) is a simple iterative method of solving n number load flow equations by iterative method. Many advantages are attributed to the Newton-Raphson (N-R) approach. In fact, among the numerous solution methods available for power flow analysis, the Newton-Raphson method is considered to be the most sophisticated and important. The power flow problem can also be solved by using Newton-Raphson method.
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