“…The mathematical model to find the optimal DC power flows with the addition of the security constraints can be characterized as follows (Carvalho et al., ; Azevedo et al., ): where α and β are weights regarding the objectives, f represents the vector of active power flow, p represents the vector of active power generation, R represents the diagonal matrix of resistances, represents the function associated with generation loss, A represents the network incidence matrix, T represents the network reactance matrix, d represents the demands for the active power, M represents the active power flow contingency matrix, N is the contingency matrix for generation, and are the limits on active power flow f , and are the limits on power generation p , and and are the limits on the security constraints.…”