We propose an optimal operation strategy for an electric vehicle (EV) aggregator (AGG), which performs energy arbitrage in the energy market and provides ancillary services from aggregated EVs, while providing charging services to EVs to maximize the profit in a future energy market. We group EV batteries as several virtual batteries (VB) with respect to their departure time and stages to implement multiple schedules simultaneously in the multi-stage stochastic optimization (MSSO). They are continuously grouped and regrouped as EVs arrive and depart. We predict VB scenario trees of stepwise EV driving routes and optimize the decisions in responding to uncertain EV movements. The VB states change as EVs enter and exit through the stages, so we should indirectly track time-varying VB characteristics at each stage. Then, we distribute the regulation bids for the VBs to the individual EVs. To reduce mismatches between the bidding amounts for VBs and actual transacted amounts for EVs, we suggest a novel binary progressive hedging algorithm to quickly determine the VB operations. Based on data from historical vehicle statistics, we verify that our strategy with the MSSO model provides a higher profit to the AGG than two-stage stochastic models.

The purpose of this paper is to apply multistage stochastic programming to the transmission line expansion planning problem, especially when uncertain demand scenarios exist. Since the problem of transmission line expansion planning requires an intensive computational load, dual decomposition is used to decompose the problem into smaller problems. Following this, progressive hedging and proximal bundle methods are used to restore the decomposed solutions to the original problems. Mixed-integer linear programming is involved in the problem to decide where new transmission lines should be constructed or reinforced. However, integer variables in multistage stochastic programming (MSSP) are intractable since integer variables are not restored. Therefore, the branch-and-bound algorithm is applied to multistage stochastic programming methods to force convergence of integer variables.In addition, this paper suggests combining progressive hedging and dual decomposition in stochastic integer programming by sharing penalty parameters. The simulation results tested on the IEEE 30-bus system verify that our combined model sped up the computation and achieved higher accuracy by achieving the minimised cost.