arXiv subjects
Publications and source records attributed to Abdulaziz Alanazi.
Many classical $q$-series identities, such as the Rogers--Ramanujan identities, yield combinatorial interpretations in terms of integer partitions. Here we consider algebraically manipulating some of the classical $q$-series to yield natural combinatorial interpretations in terms of overpartitions. Bijective proofs are supplied as well.
This paper proposes a coordinated optimal scheduling model for hybrid AC/DC microgrids. The objective of the proposed model is to minimize the total microgrid operation cost when considering interactions between AC and DC sub-systems of the microgrid network. Nonlinear power flow equations for AC and DC networks have been linearized through a proposed model to enable formulating the problem by mixed integer linear programming (MILP) which expedites the solution process and ensures better solutions in terms of optimality. The proposed model is tested on the modified IEEE 33-bus test system. Numerical simulations exhibit the merits of the proposed coordinated AC/DC optimal scheduling model and further analyze its sensitivity to various decisive operational parameters.