This study investigates a hybrid hierarchical multi-agent system for distributed cooperative voltage control in active distribution networks. The hybrid hierarchical multi-agent system adopts on-load tap-changing (OLTC) agents for the distribution transformers and feeder control section (FCS) agents for the distributed generators (DGs). The objective is to minimize the voltage deviations over the network. The FCS agents also have the objective of minimizing reductions in DG power output. A

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... squares method is used for curve fitting to achieve the two objectives. The OLTC agent receives voltage information from the FCS agents to evaluate the state of the voltage in each feeder and the distribution network and cooperates with the FCS agents to control the voltage of the network. The FCS agents exchange the fitted curve parameters and basic information on the DGs with other agents to achieve the objectives. The effectiveness of the proposed distributed cooperative voltage control scheme is verified through simulations. Depending on the network voltages obtained by the OLTC agent, different operations are executed to prevent voltage limit violations and to minimize the voltage deviations and reductions in the DG power outputs. control, a global optimum may not be reached because each agent considers only its own objectives. Distributed control is more suited than centralized control to active distribution networks [11] . In [12], a distributed generator dispatching scheme for voltage support in distribution feeders was studied. Ref. [13] proposed a voltage regulation algorithm assuming remote terminal units at each DG and feeder capacitor. In [14] and [15], a voltage control protocol for a load tap changer and a DG was investigated; however, certain important voltage control devices were not included. Refs. [16] and [17] studied integrated control methods for active and reactive power for photovoltaic generators. However, only local control and external commands from PV inverters were studied, and optimizing the voltage over the entire network was not considered. Voltage optimization algorithms must be adaptive in an active distribution network. In [18] [19] [20] , a genetic algorithm was applied to solve a voltage control problem. In [21], evolutionary particle swarm optimization was used, and in [22] and [23], a local learning algorithm combined with nonlinear programming was investigated. However, these algorithms require large amounts of data, have communication delays, and are subject to communication blocks. In this study, a multi-agent-based method for distributed cooperative control of the voltages in active distribution networks is investigated. In this approach, the OLTC, the outputs of the reactive compensation devices and the DGs are adjusted according to the network state to prevent voltage limit violations, minimize voltage deviations, and maximize the DG active power outputs in the distribution network with various loads and feeders. Curve fitting is used to approximate the relations between voltage and power, and these curves are used to determine the control actions. The proposed method reduces the amount of data transmitted between agents, shortens the computation times, and finds a global minimum. The effectiveness of the proposed distributed cooperative voltage control scheme and curve-fitting method are verified through simulations.