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Fast Decoupled Power Flow Algorithm

Learn about faster power flow algorithms and the benefits of using decoupled methods. Understand handling iteration schemes and approximations for real and reactive power flow equations. Explore advantages and disadvantages of decoupled algorithms.

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Fast Decoupled Power Flow Algorithm

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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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