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ProblemSet6

ProblemSet6 - connected to bus D is equal to 5 MW at a pf...

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1 Problem Set #6 Power-flow solutions, Gauss-Seidel Method, and Newton-Raphson Method 6-1 (Keyhani Lecture) Using Gauss elimination and back substitution, solve = 3 2 1 14 2 5 2 12 4 0 3 10 3 2 1 x x x 6-2 (Keyhani Lecture) Use Newton-Raphson to find one solution to the polynomial equation f ( x )= y , where y =0 and f ( x )=3 x 3 +4 x 2 +5 x +6. Start with x (0)=1.0 and continue until ε < ) 1 ( ) 1 ( ) ( i x i x i x (6.1) is satisfied, where ε =0.001. 6-3 (Keyhani Lecture) Use Newton-Raphson to find a solution to = + 5 . 0 2 . 1 ) cos( 2 1 2 1 x x e x x where x 1 and x 2 are in radians. a) Start with x 1 (0)=1.0 and x 2 (0)=0.5 and continue until Equation (6.1) is satisfied with ε =0.005. b) Show that Newton-Raphson diverges for the example if x 1 (0)=1.0 and x 2 (0)=2.0. 6-4 (Grainger and Stevenson, Jr. Chapter 8, Prob 8.10)

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