Step Length Control

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

(5.12)

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,

(5.13)

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 ∥ ∞ .

(5.14)

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