  The charging processes of a large number of electric vehicles (EVs) require
coordination and control for the alleviation of their impacts on the
distribution network and for the provision of various grid services. However,
the scalability of existing EV charging control paradigms are limited by either
the number of EVs or the distribution network dimension, largely impairing EVs'
aggregate service capability and applicability. To overcome the scalability
barrier, this paper, motivated by the optimal scheduling problem for the
valley-filling service, (1) proposes a novel dimension reduction methodology by
grouping EVs (primal decision variables) and establishing voltage (global
coupled constraints) updating subsets for each EV group in the distribution
network and (2) develops a novel decentralized shrunken primal multi-dual
subgradient (SPMDS) optimization algorithm to solve this reduced-dimension
problem. The proposed SPMDS-based control framework requires no communication
between EVs, reduces over 43% of the computational cost in the primal
subgradient update, and reduces up to 68% of the computational cost in the dual
subgradient update. The efficiency and efficacy of the proposed algorithm are
demonstrated through simulations over a modified IEEE 13-bus test feeder and a
modified IEEE 123-bus test feeder.
