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Newton raphson

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Ahmed M. Elkholy

The document discusses the Newton-Raphson method for finding the solutions of nonlinear equations. It describes how the method uses Taylor series expansion to linearize the function around an initial guess. It then finds the next estimate as the initial guess minus the ratio of the function value to the derivative value. The method repeats this process iteratively until converging to a solution. Examples of applying Newton-Raphson to power flow problems are presented.

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Newton Raphson 11/5/2016 2
NEWTON-RAPHSON METHOD Consider the solution of the one-dimensional If (0) is an initial estimate of the solution, and (0) is a small deviation from the correct solution. Then we have math 11/5/2016 3
Expanding by Taylor's series then we have Assuming the error (0) is very small, the higher-order terms can be neglected because of Then math NEWTON-RAPHSON METHOD 11/5/2016 4
the first iteration will be math NEWTON-RAPHSON METHOD 11/5/2016 5
NEWTON-RAPHSON METHOD math 11/5/2016 6
Power flow NEWTON-RAPHSON METHOD 11/5/2016 7
Power flow NEWTON-RAPHSON METHOD J1 11/5/2016 8
Example NEWTON-RAPHSON METHOD 11/5/2016 9
Power flow NEWTON-RAPHSON METHOD J2 11/5/2016 10
Example NEWTON-RAPHSON METHOD 11/5/2016 11
Power flow NEWTON-RAPHSON METHOD J3 11/5/2016 12
Example NEWTON-RAPHSON METHOD 11/5/2016 13
Power flow NEWTON-RAPHSON METHOD J4 11/5/2016 14
Example NEWTON-RAPHSON METHOD 11/5/2016 15
Power flow NEWTON-RAPHSON METHOD 11/5/2016 16
Example NEWTON-RAPHSON METHOD 11/5/2016 17
Example NEWTON-RAPHSON METHOD 11/5/2016 18
Example NEWTON-RAPHSON METHOD 11/5/2016 19
Example NEWTON-RAPHSON METHOD (n -1) x (n -1)) 11/5/2016 20
Example NEWTON-RAPHSON METHOD (n - 1) x (n - 1- m) 11/5/2016 21
Example NEWTON-RAPHSON METHOD ( n - 1 - m) x ( n - 1) 11/5/2016 22
Example NEWTON-RAPHSON METHOD ( n - 1 - m) x ( n - 1 - m) 11/5/2016 23
Example NEWTON-RAPHSON METHOD 11/5/2016 24
Thank you11/5/2016 25

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