ABSTRACT
Using slack variables ω to transform inequality constraints into equality constraints and adding barrier penalties to the original objective function, the Lagrangian is given by
Z
I I
I I
G spec−( )a b P cP2 λ
−
⎡
⎣
⎢⎢⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥⎥⎥ −
∑ P V V−
Z Z+
( )− −P P T G G G
Z Z
SZ
( )P P
( )V V )(V V
−
++ ω
2 −
−
l ( )+ + + + +i S
ω
μ i
(12)
where μk > 0 is the Interior Point Algorithm (IPA) barrier parameter that monotonically decreases to
zero as iterations progress. Based on the KarushKuhn-Tucker (KKT) optimality condition, a set of nonlinear equations can be derived from (12), and the corresponding set of linear correction equations can be derived in sequence by applying the Newton’s method (G.L. Torres et al. 1998, W.M. Lin et al. 2002, W.M. Lin et al. 2008). The OPF algorithm can be summarized in the flowchart of the PCIPA in Figure 2.
