Security constrained economic dispatch using nonlinear Dantzig-Wolfe decomposition

Large-scale Unit Commitment under uncertainty

“…In Fu et al (2005) a ramp rate, fuel and emission constrained UC is solved. Having been used for a very long time, Lagrangian relaxation has been applied in particular to bUC Aganagic and Mokhtari (1997); Muckstadt and Koenig (1977); Merlin and Sandrin (1983); Cohen and Wan (1987); Aoki et al (1987); Yan et al (1993); Tong and Shahidehpour (1989); Zhuang and Galiana (1988);Fisher (1973); Nilsson and Sjelvgren (1996);Fan et al (2002); Shaw et al (1985); Borghetti et al (2001); Madrigal and Quintana (2000); Feltenmark and Kiwiel (2000); Fu et al (2005); Bertsekas et al (1983); Li and Shahidehpour (2003). However, other constraints have also been considered, such as Must Run/Off Yan et al (1993); Zhuang and Galiana (1988); Frangioni et al (2011), Fuel Aoki et al (1987; Tong and Shahidehpour (1989); Fu et al (2005); Cohen and Wan (1987), Ramp Rate Fu et al (2005); Cohen and Wan (1987); Yan et al (1993);Frangioni et al (2008Frangioni et al ( , 2011Borghetti et al (2003a, b); Li and Shahidehpour (2003); Aoki et al (1989), Reserve Aganagic and Mokhtari (1997); Cohen and Wan (1987), Hydro-Thermal Aoki et al (1987); …”

“…Early examples of the use of subgradient methods in UC are Fisher (1973), Muckstadt and Koenig (1977), Bertsekas et al (1983), Merlin and Sandrin (1983), Bard (1988) and Zhuang and Galiana (1988), possibly with modifications such as successive approximation techniques (Cohen and Wan 1987) or variable metric approaches (Aoki et al 1987). An early example of the use of CP is Aganagic and Mokhtari (1997). The two approaches are rather different: subgradient methods use very simple rules to compute the next dual iterate, whereas CP uses (possibly costly) linear programming (LP) problems for the same task, although hybrid versions have been devised (Tong and Shahidehpour 1989).…”

“…The offer-demand equilibrium constraints and reservoir balance equations are dualized, and the LD is maximized with a subgradient approach, with a heuristic step fixing the discrete hydro variables to recover a primal feasible hydro solution. In Aganagic and Mokhtari (1997) some transmission constraints are considered. In Li and Shahidehpour (2003) an alternative to ramping rate constraints in the model for thermal units, a so-called stress effect, is proposed.…”

Distributed Optimization-Based Dynamic Tariff for Congestion Management in Distribution Networks

“…However, this method is not suitable for the DDT method, because it requires the overall objective function. The same reason explains why the nonlinear Danzig-Wolfe decomposition method for security constrained economic dispatch (SCED) [25] is not suitable for the DDT method either. In addition, the abovementioned methods are not able to provide a price signal that can be easily understood by the aggregators as in the dual decomposition method, where the dual variables are also known as shadow prices.…”

Reserve-constrained economic dispatch: Cost and payment allocations

“…References [2][3][4][5][6][7][8][9] address diverse instances of the reserveconstrained economic dispatch and concentrate on providing solution techniques. The analytical results of this paper complement the results reported in these references.…”