“…The control variables of such problems in addition to generator production rates may include the voltage angles of the buses (Conejo and Aguado, 1998), transformation ratios, states of flexible ac transmission systems (FACTS) (Hingorani, 1993;Hingorani, Gyugyi, and El-Hawary, 2000;Song and Johns, 1999) which affect the transmission performance of power lines, and switching variables which alter the topology of the transmission network (Fisher, O'Neill, and Ferris, 2008;Hedman, O'Neill, Fisher, and Oren, 2008;O'Neill, Hedman, Krall, Papavasiliou, and Oren, 2010). These optimal transmission switching models, which formulate the optimization as a mixed integer problem, usually assume n − 1 contingency reliability (Hedman, O'Neill, Fisher, and Oren, 2009) (in general, n is the number of system components), which means that the effects of single line and generator failures on the network are included in the analysis.…”