非凸约束下的分布式负载均衡：一种随机算法及其在电动汽车充电调度中的应用
Distributed Load Balancing with Nonconvex Constraints: A Randomized Algorithm with Application to Electric Vehicle Charging Scheduling
摘要：
针对实际非凸充电约束条件下的电动汽车调度问题，提出了一种分布式随机算法。该算法假设协调器的可用性，该协调器可以与所有EV通信。在算法的每次迭代中，协调器从EV接收试验性充电简档并计算广播控制信号。在接收到该广播控制信号之后，每个EV在其可容许的充电简档上生成概率分布，并且从该分布中采样以更新其暂定充电简档。我们证明了该算法收敛几乎肯定在有限的迭代充电配置文件。（算法收敛到的）最终充电曲线是随机的，即，这取决于实现。我们的特点是最终的充电配置文件-充电配置文件可以是一个实现的最终充电配置文件，当且仅当它是一个纳什均衡的游戏中，每个电动汽车寻求最小化的内积自己的充电配置文件和总电力需求。此外，我们提供了一个统一的次优性上界，缩放O（1/n）的电动汽车的数量n，为最终的充电配置文件的所有实现。
英文摘要：
To schedule a large number of EVs with the presence of practical nonconvex charging constraints, a distributed and randomized algorithm is proposed in this paper. The algorithm assumes the availability of a coordinator which can communicate with all EVs. In each iteration of the algorithm, the coordinator receives tentative charging profiles from the EVs and computes a broadcast control signal. After receiving this broadcast control signal, each EV generates a probability distribution over its admissible charging profiles, and samples from the distribution to update its tentative charging profile. We prove that the algorithm converges almost surely to a charging profile in finite iterations. The final charging profile (that the algorithm converges to) is random, i.e., it depends on the realization. We characterize the final charging profile---a charging profile can be a realization of the final charging profile if and only if it is a Nash equilibrium of the game in which each EV seeks to minimize the inner product of its own charging profile and the aggregate electricity demand. Furthermore, we provide a uniform suboptimality upper bound, that scales O(1/n) in the number n of EVs, for all realizations of the final charging profile.
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