5.4 Step Length Control

Step length control is a key element affecting the computational efficiency of a continuation method. It affects the continuation method with two issues: (1) speed – how fast the corrector converges to a specified accuracy, and (2) robustness – whether the corrector converges to a true solution given a predicted point. Matpower’s continuation power flow can optionally use adaptive steps, where the step size σ  is adjusted by a scaling factor α  within the limits specified.

 j+1     j j              j+1
σ    = α σ  ,    σmin ≤ σ    ≤ σmax

This scaling factor αj  for step j  is limited to a maximum of 2 and is calculated from an error estimation between the predicted and corrected solutions γj  as follows,

             (         )
  j            𝜖cpf             j
α  =  1 + βcpf  γj −  1  ,    α  ≤  2,

where βcpf   is a damping factor, 𝜖cpf   is a specified tolerance, and γj  is given by

  j   ∥∥( j+1  j+1)   (  j+1  ˆj+1)∥∥
γ  =  ∥ x   ,λ     −  xˆ   ,λ    ∥ ∞ .