Abstract-In this paper, we study unit commitment (UC) problems considering the uncertainty of load and wind power generation. UC problem is formulated as a chance-constrained two-stage stochastic programming problem where the chance constraint is used to restrict the probability of load imbalance. In addition to the conventional mixed integer linear programming formulation using Big-M, we present the bilinear mixed integer formulation of chance constraint, and then derive its linear counterpart using McCormick linearization method. Then, we develop a bilinear variant of Benders decomposition method, which is an easy-to-implement algorithm, to solve the resulting large-scale linear counterpart. Our results on typical IEEE systems demonstrate that (i) the bilinear mixed integer programming formulation is stronger than the conventional one; (ii) the proposed Benders decomposition algorithm is generally an order of magnitude faster than using a professional solver to directly compute both linear and bilinear chance-constrained UC models.
The thermodynamic properties of a working-fluid pair, composed of a refrigerant and an absorbent, greatly influence the performance of an absorption−refrigeration cycle. Particularly important is the solubility of the vaporized refrigerant in the absorbent. Using an isochoric saturation method, solubilities were measured for trans-1,3,3,3-tetrafluoropropeneand 1-methyl-3-octylimidazolium hexafluorophosphate ([Omim][PF 6 ]) from 283.15 to 343.15 K. Solubilities rise with a decrease in temperature and an increase in pressure. The highest solubility is in [Omim][PF 6 ], followed by [Hmim][PF 6 ], and [Bmim][PF 6 ]. The new data were correlated by the nonrandom two-liquid model and by the Krichevsky−Ilinskays equation; both provide good agreement with the experimental data. Estimates were given for total enthalpy, entropy, and Gibbs energy of dissolution.
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