Fig. 2. Flow Chart of ABFLS IPM
Adaptive Barrier Parameter Update Strategy
The barrier parameter is usually chosen to be proportional to the current complementarity gap
 (20)
where is the centering parameter. has significant influence on the convergence of IPM algorithms. If is selected, the barrier parameter , the KKT equation (8), and further the Newton direction (9) are successively determined. In the PD algorithm,is simply set to a constant. In the PC and MCC algorithms, some simple heuristics are employed to update. The adaptive barrier parameter update strategy is originally proposed in [7], and it is firstly adopted in OPF problems with FACTS devices in this paper.
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