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Additional resources for Überschall-Flugzeug Tu-144
T / T satisfies the conservation constraints in the static network N T . t/. t/ 2 V T . t / T is a flow in the time-expanded network N T . t/ be a corresponding function in the dynamic network N . t/ 2 V T be an arbitrary vertex in N T . t/ 2 V T at all times t, 0Ät ÄT e . Therefore, equality (i) holds for all v 2 V at all moments of time t, 0Ät ÄT e . t/ is a flow in the dynamic network N . It is easy to verify that a feasible flow in the dynamic network N is a feasible flow in the time-expanded network N T and vice-versa.
3, respectively. A. z C ˛aff zaff / I p . D . x; w; y; z/I (61) (62) until convergence test is satisfied. cI d w/k1 Ä "; 1 C kwk1 (63) the relative dual infeasibility given by dfeas D rf AT y 1 C kzk1 BT z 1 Ä "; (64) and the relative duality gap given by ˇ ˇ T ˇy c C zT d C x T r D ˇ ˇ ˇ Ä ": opt D 1 C ˇf y T c z T d x T r D ˇ The precision parameter " is set to 10 8 (65) . 2 Scaling Scaling of the objective and constraint functions is achieved by multiplying them with suitable constants so that the typical numerical values of the scaled functions in the optimization program are roughly of the same order of magnitude.
To avoid clutter, the subscript (ij) is dropped below. Based on the equivalent circuit in Fig. Âi Âsh /: (24) The first term in (24) is identical to the conventional load flow equation of a transmission device with series susceptance bij and shunt susceptance bsh . The last two terms can be used to define PiFD , an active power injection at bus i attributed to the FACTS device’s series and shunt voltage sources. Âj Âsh /; Âse /: (28) (29) By assuming lossless converter valves, the active power exchange among converters via the DC link is zero (Acha et al.