This paper proposes a novel cooperative charging strategy for a smart charging station in the dynamic electricity pricing environment, which helps electric vehicles (EVs) to economically accomplish the charging task by the given deadlines. This strategy allows EVs to share their battery-stored energy with each other under the coordination of an aggregator, so that more flexibility is given to the aggregator for better scheduling. Mathematically, the scheduling problem is formulated as a constrained mixed-integer linear program (MILP) to capture the discrete nature of the battery states, i.e., charging, idle and discharging. Then, an efficient algorithm is proposed to solve the MILP by means of dual decomposition and Benders decomposition. At last, the algorithm can be implemented in a distributed fashion, which makes it scalable and thus suitable for large-scale scheduling problems. Numerical results validate our theoretical analysis.

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A novel method called alternating convex optimization is presented to synthesize unequally spaced linear arrays with minimum element spacing constraint. In this method, the problem of synthesizing an unequally spaced array is formulated as a sequence of alternating convex optimization problems, and the excitation vector and auxiliary weighting vector are alternately chosen as the optimization variables. The minimum spacing constraint for considering the physical element antenna size can be easily imposed in this alternating optimization process. Two examples for synthesizing unequally spaced linear arrays with focused and shaped patterns are provided to validate the effectiveness and advantages of the proposed method.

Abstract-We formulate an optimal scheduling problem for battery swapping that assigns to each electric vehicle (EV) a best station to swap its depleted battery based on its current location and state of charge. The schedule aims to minimize total travel distance and generation cost over both station assignments and power flow variables, subject to EV range constraints, grid operational constraints and AC power flow equations. To deal with the nonconvexity of power flow equations and the binary nature of station assignments, we propose a solution based on second-order cone programming (SOCP) relaxation of optimal power flow (OPF) and generalized Benders decomposition. When the SOCP relaxation is exact, this approach computes a globally optimal solution. We evaluate the performance of the proposed algorithm through simulations. The algorithm requires global information and is suitable for cases where the distribution network, stations, and EVs are managed centrally by the same operator. In Part II of the paper, we develop distributed solutions for cases where they are operated by different organizations that do not share private information.