Two methods used in the solution of load flows are the Gauss Seidel and the Newt

Question

Two methods used in the solution of load flows are the Gauss Seidel and the Newton Raphson. In a few brief sentences, discuss one or two of the relative merits of these two methods. The Newton Raphson method can be used to solve n nonlinear algebraic equations of the form f(x) = c The aim is to determine the n variables x_i given the values of the n constants c_i and the functions f_i. Suppose we are using Newton Raphson to solve the load flow problem for a 5 bus power system made up of a swing bus, two PV bus and five PQ busses. What is the value of n? What are the variables x_i which are to be evaluated? What are the c_i?

Explanation / Answer

Part 1)

Gauss Seidel method for solution of load flows.

The Gauss-Seidel method is an iterative algorithm for solving a set of non-linear algebraic equations. It is one of the methods used in load flow studies. In this method, a solution vector is assumed and one of the equations is used to obtain the revised value of a particular variable. The rate of convergence of the Gauss Seidel method is slow (linear convergence characteristic), requiring a considerably greater number of iterations to obtain a solution. Advantage of the Gauss Seidel method is the ease of programming and most efficient utilization of core memory.

Newton Raphson Method for solution of load flows.

It is an iterative method which approximates a set of non-linear simultaneous Taylor’s series expansion and the terms are limited to the first approximation. Its programming logic is considerably more complex and it has the disadvantage of requiring a large computer memory even when a compact storage scheme is used for the Jacobian and admittance matrices. However For large systems the Newton Raphson method is faster, more accurate and more reliable than the Gauss Seidel method or any other known method

Part 2)

Number of bus power system(n) 5

P-V(load np) bus is 2

P-Q(generator ng) bus is 5

value of n=np+ng+1=5+2+1=8

Ci are the constants which are PV loads (2 PV buses).

Xi are to be determined for PQ buses(5 unknowns)

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