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