# Fast Decoupled¶

The fast decoupled method is a fantastic power flow algorithm developed by Stott and Alsac [FD]. The method builds on a series of very clever simplifications and the decoupling of the Jacobian matrix of the canonical Newton-Raphson algorithm to yield the fast-decoupled method.

The method consists in the building of two admittance-based matrices and which are independently factorized (using the LU method or any other) which then serve to find the increments of angle and voltage magnitude separately until convergence.

## Finding and ¶

To find we perform the following operations:

To find we perform the following operations:

## The fast-decoupled algorithm¶

• Factorize

• Factorize

• Compute the voltage module

• Compute the voltage angle

• Compute the error

• Check the convergence

• Iterate; While convergence is false and the number of iterations is less than the maximum:

• Solve voltage angles (P-iteration)

• Update voltage

• Compute the error (follow the previous steps)

• Check the convergence (follow the previous steps)

• If the convergence is still false:

• Solve voltage modules (Q-iteration)

• Update voltage

• Compute the error (follow the previous steps)

• Check the convergence (follow the previous steps)

• Increase the iteration counter.

• End

 [FD] Stott and O. Alsac, 1974, Fast Decoupled Power Flow, IEEE Trasactions PAS-93 859-869.