The multi-period version of the optimal power flow can tackle the power dispatch problem of modern distribution system with distributed renewable energy sources and energy storage system. In this paper, a communication-efficient decentralized optimization algorithm (DOA) for the multi-period optimal power flow problem is presented. Firstly, the power management of modern distribution system is modelled as a linear conic optimization problem based on the conically relaxed power flow equations. Secondly, some ancillary variables at the junction bus are introduced to decompose the distribution system into several separate parts. Moreover, the DOA based on the extended version of Alternating Direction Method of Multipliers (ADMM) is proposed. The DOA evolves by partial local message exchanges without central coordination. Finally, the colouring scheme, which is in accord with the network colouring used in communication protocols to avoid packet collisions, is applied in the decentralized algorithm as well.