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The conventional volt-VAR control (VVC) in distribution systems has limitations in solving the overvoltage problem caused by massive solar photovoltaic (PV) deployment. As an alternative method, VVC using solar PV smart inverters (PVSIs) has come into the limelight, which can respond quickly and effectively to solve the overvoltage problem by absorbing reactive power. However, the network power loss, that is, the sum of line losses in the distribution network, increases with reactive power. Dynamic distribution network reconfiguration (DNR), which hourly controls the network topology by controlling sectionalizing and tie switches, can also solve the overvoltage problem and reduce network loss by changing the power flow in the network. In this study, to improve the voltage profile and minimize the network power loss, we propose a control scheme that integrates the dynamic DNR with volt-VAR control of PVSIs. The proposed control scheme is practically usable for three reasons: Primarily, the proposed scheme is based on a deep reinforcement learning (DRL) algorithm, which does not require accurate distribution system parameters. Furthermore, we propose the use of a heterogeneous multiagent DRL algorithm to control the switches centrally and PVSIs locally. Finally, a practical communication network in the distribution system is assumed. PVSIs only send their status to the central control center, and there is no communication between the PVSIs. A modified 33-bus distribution test feeder reflecting the system conditions of South Korea is used for the case study. The results of this case study demonstrates that the proposed control scheme effectively improves the voltage profile of the distribution system. In addition, the proposed scheme reduces the total power loss in the distribution system, which is the sum of the network power loss and curtailed energy, owing to the voltage violation of the solar PV output. [ABSTRACT FROM AUTHOR]