  The trending integrations of Battery Energy Storage System (BESS, stationary
battery) and Electric Vehicles (EV, mobile battery) to distribution grids call
for advanced Demand Side Management (DSM) technique that addresses the
scalability concerns of the system and stochastic availabilities of EVs.
Towards this goal, a stochastic DSM is proposed to capture the uncertainties in
EVs. Numerical approximation is then used to make the problem tractable. To
accelerate the computational speed, the proposed DSM is tightly relaxed to a
convex form using second-order cone programming. Furthermore, in light of the
continuous increasing problem size, a distributed method with a guaranteed
convergence is applied to shift the centralized computational burden to
distributed controllers. To verify the proposed DSM, real-life EV data
collected on UCLA campus is used to test the proposed DSM in an IEEE benchmark
test system. Numerical results demonstrate the correctness and merits of the
proposed approach.
