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Decoupled Power Flow Algorithms

Decoupled Power Flow Algorithms. Lecture #23 EEE 574 Dr. Dan Tylavsky. We know that for the full Newton power flow we interleave P, P and , Vas shown. N. H. P. . Q. V. J. L. An alternate ordering which will still preserve the quasi-diagonal dominance property is:.

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Decoupled Power Flow Algorithms

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  1. Decoupled Power Flow Algorithms Lecture #23 EEE 574 Dr. Dan Tylavsky

  2. We know that for the full Newton power flow we interleave P, P and , Vas shown.

  3. N H P  Q V J L • An alternate ordering which will still preserve the quasi-diagonal dominance property is: • Symbolically we can write this as: • The draw back to this ordering is the increased fill.

  4. Consider the following 3 bus system: • Conventional Ordering: • No Fill • New Ordering: • Much Fill

  5. Claim: • There exists only weak coupling between: • P and V, • Q and ; • (Said another way, changes in P have little effect on Q and vice versa.) • hence N and J can be ignore. • Recall the Jacobian is a linear approximation, ignoring N and J, simply makes the approximation less accurate.

  6. k i Rik+j Xik Vi/i V/k Pik+j Qik • Let’s show that this approximation is reasonable. • Recall the equations for power flow through a transmission line: • For typical power system branches: • X/R >> 1. • ik <200. • Let’s investigate how this allows us to approximate the real and reactive power flow equations.

  7. 0 0 (i-i) • Starting with the real power flow equation: • For X/R >> 1: • For ik < 200:

  8. 1 0 • For the reactive power flow equation: • For ik < 200: • For X/R >> 1: (Recall Bik<0)

  9. These equations imply:

  10. The decoupled equations become: • Where: • There are various ways of handling the iteration scheme. A popular way is:

  11. q=0 Did buses Switch Types? Did buses Switch Types? Y Y Is q>3? Is q>3? N N N N Converged? |Pqmax|, |Qqmax|<? Converged? |Pqmax|, |Qqmax|<? Y Y Create Output Create Output N Perform bus type switching Perform bus type switching Solve Update Bus Angle q+1= q+  q N N N Solve Update Bus Angle Vq+1= Vq+ V q q=q+1 Y Begin as with Newton-Raphson

  12. Full Newton (-Raphson) Log(max(P,)) Decoupled Convergence Tolerance Iteration Number • The decoupled algorithm looses quadratic convergence and resorts to linear (geometric convergence.

  13. The advantages of the decoupled algorithm: • Less calculations: • Full Newton O(N3/3) • Decoupled O(2*(N/2)3/3)=O(N3/12) • Disadvantages: • Convergence is unreliable. • Improved Convergence through Fast Decoupled Power Flow Algorithm.

  14. The End

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