Newton-Raphson Method
For Power Flow Analysis
• Most widely used method for solving simultaneous nonlinear algebraic equation
• Is a successive approximation procedure based on an initial estimate of the
unknown and the use of Taylor’s series expansion
• 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. The N-R method is more accurate, and is insensitive to factors like slack
bus selection, regulating transformers etc. and the number of iterations required
in this method is almost independent of the system size.
• 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.
• Let consider the solution of the one-dimensional equation :
Example 1
Use Newton-Raphson method to find the root of the equation given below .
Assume an initial estimation of x(0)= 6.
The MATLAB plot command is used to plot f(x) = x3-6x2+9x-4 over a range of
0 to 6 as shown in figure .The intersection of f(x) with the x-axis results in the
roots of f(x).From the figure , two of the roots are found to be 1 and
4.Actulally , there is a repeated root at x=1.
Staring with an initial estimate of x(0)= 6, we extrapolate along the tangent to
its intersection with the x-axis and take that as the next approximation . This
is continue until successive x-values are sufficiently close.
Example 2
Graphically, the solution to this system is
represented by the intersections of the circle
x12+x22=4 with the curve ex1+x2 =1 . Figure show
that these are near (1,-1.7) and (-1.8,0.8)
Example 3
Video on Newton Raphson Method
• https://www.youtube.com/watch?v=8IZeluWrW
ME
• https://www.youtube.com/watch?v=8ruTV8dtbF
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