Matpower employs all of the standard steady-state models typically used for power ﬂow analysis. The AC models are described ﬁrst, then the simpliﬁed DC models. Internally, the magnitudes of all values are expressed in per unit and angles of complex quantities are expressed in radians. Internally, all oﬀ-line generators and branches are removed before forming the models used to solve the power ﬂow, continuation power ﬂow or optimal power ﬂow problem, and all buses are numbered consecutively, beginning at 1. Conversions to and from this internal indexing is done by the functions ext2int and int2ext. The notation in this section, as well as Sections 4 and 6, is based on this internal numbering, with all generators and branches assumed to be in-service. Due to the strengths of the Matlab programming language in handling matrices and vectors, the models and equations are presented here in matrix and vector form.