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Power Flow

Power Flow. Usage. New generation sites Projected load growth New transmission line locations Interconnections with other system Various load conditions, such as peak and off-peak The impact of losing major components. Basic considerations. How to get the bus admittance matrix.

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Power Flow

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  1. Power Flow

  2. Usage • New generation sites • Projected load growth • New transmission line locations • Interconnections with other system • Various load conditions, such as peak and off-peak • The impact of losing major components

  3. Basic considerations • How to get the bus admittance matrix. • Representation of a transformer • Its elements in the [Ybus] matrix Yii : the sum of all the admittances connected to the i-th bus Yij : (-1) times of the admittance between the i and j-th bus

  4. Transformer q p a:1 [Ybus] elements Equivalent circuit

  5. Newton-Raphson Method • It solves nonlinear equations. • One of iterative methods • It approximates the function as a linear function. • Prior knowledge : Taylor Series

  6. Newton-Raphson Method - Concept Problem : Solve exact solution

  7. Newton-Raphson Method - Single Variable Taylor series (the 1st order) Next point

  8. N-R Method - Multi-Variable Case Problem Taylor’s approximation To be the solution

  9. Programming - General • Variable • address and value • Array • Loop (for, while, ..) • Branch (if, if-else ) • Escape from Loop (break, continue)

  10. Example 1 : Newton-Raphson /* Newton Rahpshon method f(x)=x^2-3x+2 */ niter=10; x=3; for(i=1;i<=niter;i++){ f=x^2-3*x+2; df=2*x-3; x1=x -(df)^(-1)*f; msgprint(x1); f=x1^2-3*x1+2; if(abs(f)<0.00001) break; x=x1; }

  11. Example 2 : Newton-Raphson // Newton Rahpshon method f1(x)=x1^2+4x2^2-4=0 // f2(x)=x1-x2=0 niter=10; x1=0.2; x2=0.2; Jacob=zeros(2,2); f1=x1^2+4*x2^2-4; f2=x1-x2; for(i=1;i<=niter;i++){ Jacob(1;1)=2*x1; Jacob(1;2)=8*x2; Jacob(2;1)=1; Jacob(2;2)=-1; newx=[x1;x2]-inv(Jacob)*[f1;f2]; msgprint(newx); x1=newx(1); x2=newx(2); f1=x1^2+4*x2^2-4; f2=x1-x2; if(abs(f1)+abs(f2)<0.0001) break; }

  12. Power Equation Power equation at the i-th bus Generation Load Injected power to the network Another expression

  13. Load Flow Problem Number of variables = Number of gen. buses + 2 * Number of load buses Required number of equations = Number of gen. buses + 2 * Number of load buses

  14. Power Equation Load Bus Generator Bus

  15. 1 2 slack bus 3 Example – 3 Bus System

  16. Power Flow Problem For all buses (except slack bus) Only for load buses

  17. Update Update of voltage magnitudes and angles. where,

  18. Elements of Jacobian matrix Off-diagonal elements of each sub-matrix

  19. Elements of Jacobian matrix diagonal elements of each sub-matrix

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