A generalized Benders decomposition approach to reactive source planning in power systems

Semidefinite relaxation and generalised benders decomposition to solve the transmission expansion network and reactive power planning

“…In order to use the GBD, the MINLP model presented in Section 2 is rewritten including semidefinite structures based in [22,23,32,33]. The matrix structure of X t, o is shown in Fig.…”

“…This section presents the convex SDP slave problem S t, o κ for a stage t, operating condition o and iteration κ, based in [33], as shown in (26)- (32). Where S t, 0 κ represents the normal operation condition, and S t, o κ represents the contingency operation condition (in the existing or candidate lines).…”

Deterministic Global Optimization

“…l'vlixed-Integer Nonlinear Optimization problems are encountered in a variety of applications in all branches of engineering and applied science, applied mathematics, and operations research. These represent very important and active research areas that include: (Bloom, 1983;Rouhani et al, 1985); (iv) the chip layout and compaction (Dorneigh and Sahinidis, 1995); (v) the topology optimization of transportation networks (Hoang, 1982); and (vi) the optimal scheduling of thermal generating units (Geromel and Belloni, 1986). …”

Generalized Benders Decomposition for one Class of MINLPs with Vector Conic Constraint

“…Along this line, Geoffrion [11] generalized the Benders decomposition to a broader class of problems where the parameterized subproblem need no longer be a linear programming. Rouhani et al [26] and Floudas and Ciric [9] used the generalized Benders decomposition approach to solve MINLPs which are modelled from practical problems of reactive source planning in power systems and heat exchanger network synthesis respectively. It is noted that Hooker and Ottosson studied logice-based Benders decomposition, one extension of Benders decomposition, and applied this method to planning and scheduling.…”