**1. Introduction**

As an effective way of integrating distributed power generations and load, microgrids have obtained more and more attention as applications [1–4]. Due to the microgrid containing various distributed power sources, such as photovoltaic (PV), wind turbine (WT), and so on, the distributed power sources have their own different characteristics. The traditional control methods will be invalid to be used to solve the control problem of microgrids. Therefore, some new control strategies must be studied to deal with the microgrid control method. As of now, there are several results to realize the different control strategies in microgrids [5,6].

The traditional centralized control method needs a control center, through which the control order is sent. The receiving element obtains the signal sent from the control center and makes a process, then executes the relevant actions. However, with the large number of distributed power sources permeating into the microgrid, the traditional centralized control strategies may be ineffective to realize satisfactory results. On the other hand, once the control center is out of service, the whole system will be unable to work, which means an enormous loss. The distributed control method can easily avoid the above problem, the main reason being that the distributed control strategy does not need the control center, it is just used for the information exchange between one unit and its neighbors, finally obtaining a whole system of information sharing. If one or more of the units are out of service, the rest of the units can continue to process the information exchange, finally resulting in complete information sharing. Therefore, compared with the traditional control methods, the distributed control strategies

are superior [7,8]. In this paper, the distributed control method is utilized to solve the economic dispatch (ED) problem of the AC/DC hybrid microgrid.

On the other hand, with the rapid development of microgrid technology, the connection is closing between power grids, especially the relationship between the AC microgrid and the DC microgrid. Due to these two microgrids having different characteristics, the control methods and optimizing strategies are disparate. But the final goals are similar, that is, maintain the microgrid operating in a balanceable and safe state. The information exchange of the AC/DC hybrid microgrid is complicated and bidirectional, which is a challenging work.

In addition, the ED problem is significant for keeping the normal operation of the microgrid, and the rational dispatch is beneficial to reduce cost and increase profits. By power dispatching, the power demands between loads and generators are satisfied, and the stability of the power grid is enhanced. With the development of distributed control technology, the distributed consensus strategies are widely used to solve the ED problem. The proposed distributed method is also an exploration to realize the rational ED for the AC/DC microgrid.

#### **2. Literature Review**

It should be pointed out that the distributed consensus strategies have become promising technologies after decades of development. Up to now, there have been a large number of results about the applications of distributed control strategies. In Reference [9], by using the consensus algorithm, for an island microgrid, the optimal resource management strategy was presented. In Reference [10], the authors studied the power balance problem of the DC microgrid by using the consensus method. In References [11,12], the consensus algorithms were presented for solving the problems of the voltage stability and compensation in the microgrid, respectively. But the above references do not refer to the distributed hierarchical control thought. In Reference [13], for the DC microgrid, the distributed hierarchical control method was designed. A three-layer control framework for the static and dynamic performance of the microgrid was proposed in Reference [14]. In Reference [15], the distributed hierarchical control problem of the island microgrid was solved by proposing a network control scheme based on a robust communication algorithm. In Reference [16], by linearizing the input and output feedback, the second-order voltage problem in the microgrid was transformed into a second-order linear synchronization tracking problem, and a distributed hierarchical control strategy was developed. In Reference [17], a hierarchical control structure was developed for an autonomous microgrid, which could effectively adjust the photovoltaic output and realize the active balance in the considered microgrid. In Reference [18], for solving the problem of active regulation of the autonomous microgrid, the authors designed a two-stage controller and the optimal active power regulation controller. Although the above references are related to the hierarchical control thought, the object is simple microgrids, which does not involve the AC/DC hybrid microgrid.

With the development of research, many researchers have transferred their attention to the AC/DC hybrid microgrid. By using different study methods, more and more results about the AC/DC hybrid microgrid have been published [19–31]. In References [20,21], the voltage control problem was investigated by using different methods in the AC/DC hybrid microgrid. In References [22–24], the problems of power control and management of the AC/DC hybrid microgrid were discussed through different methods. For the interconnected microgrids, the authors designed an event-based consensus strategy for solving the coordinated power sharing problems in Reference [25]. In Reference [26], for solving the reactive power sharing and DC current sharing problem in the considered hybrid microgrids, a distributed coordination control method was developed. In References [27,28], two different bidirectional interlinking converters were studied for enhancing the transient performance of an islanded AC-DC hybrid microgrid. In Reference [29], an appropriate combinatorial optimization technique was proposed for solving the optimal sizing problem of AC-DC hybrid microgrids. In Reference [30], a straightforward and efficient method was studied to solve power flows' simultaneous problem of AC/DC hybrid microgrids.

On the other hand, as the basis for ensuring the economic and reliable operation of microgrids, the economic dispatch (ED) problem has also attracted special attention, and lots of results based on consensus algorithms have been developed [32,33]. In Reference [34], for solving the ED problem, the authors proposed a consensus-based algorithm for learning about the mismatch. In Reference [35], for the islanded microgrids, a new consensus-based method was developed, where the incremental cost of every agent is taken as the consensus variable, so their proposed method could quickly converge to the optimal solutions. In Reference [36], for solving the ED issue, an improved distributed consensus algorithm was proposed, where the feedback gains of the algorithm could be different and time varying. In Reference [37], considering the delay effect in the optimal operation of microgrids, the ED problem was discussed based on the consensus algorithm. In Reference [38], in the framework of hierarchical distributed theory, considering the power limitation of the DC microgrid, a constrained economic dispatch method was proposed. As for the ED problem for the AC/DC hybrid microgrid, some results have been developed. In Reference [39], for the considered hybrid microgrid, by considering the properties of AC and DC subsystems and the deficiencies in concentrated optimization, a management system based on consensus and coordination optimization was developed for the safe and economic operation. For discussing the economic operation of the hybrid AC/DC microgrid, a distributed control framework was proposed in Reference [40]. In References [41,42], a distributed economic dispatch method was developed based on the so-called finite-step consensus method, which could reach to the optimal solutions in finite steps. However, up to now, there are few results discussing hierarchical distributed strategy for the ED problem of the AC/DC hybrid microgrid. By fully taking into account the characteristics of the AC sub-grid and the DC sub-grid, how to connect the relationship between them and propose a reasonable control algorithm is an important issue for solving the ED problem for the AC/DC hybrid microgrid, which is an interesting and challenging topic.

Based on the above analysis and discussions, in this paper, a distributed two-layer consensus algorithm is proposed to investigate the ED problem of the AC/DC hybrid microgrid in detail. At first, the whole nodes of the AC/DC hybrid microgrid will be divided into two parts, that is, the leadership layer nodes and the tracking layer nodes. Then, by using the proposed consensus strategy, the data of the leadership layer and the tracking layer are uniformly processed to achieve the same increment cost (IC) of each node, which means that the ED problem is realized. Finally, some case study results and discussions are presented to demonstrate the usefulness of the developed hierarchical strategy.

The remainder of the article is arranged as follows: The optimal scheduling model for the considered AC/DC hybrid microgrid is presented in Section 3. In Section 4, for solving the ED problem, the two-layer consensus algorithms are proposed with or without constraints, respectively. In Section 5, the case study is designed to demonstrate the usefulness of the proposed distributed method. In the end, our main conclusions are given in Section 6.

## **3. Optimal Scheduling Model for the AC**/**DC Hybrid Microgrid**

#### *3.1. Structure Information of the AC*/*DC Hybrid Microgrid*

In this paper, we mainly focus on the isolated AC/DC hybrid microgrid. Figure 1 presents the structure information of the considered model in this paper, which mainly contains an AC sub-grid, a DC sub-grid, and a power conversion unit that is in-lined between sub-grids. The wind turbine (WT) is connected to the micro-grid AC bus, and the solar photovoltaic unit (PV) is connected to the micro-grid DC bus, while the energy storage unit (BS) and the AC/DC load unit (Load) are in both parts. The AC sub-grids and DC sub-grids are connected by an AC/DC bidirectional converter (IC) between the AC bus and the DC bus, and M1 is an AC/DC tie line power monitoring point. The dashed lines in Figure 1 indicate the communication links between the various units.

To promote the utilization efficiency of the renewable energy and ensure reliable power supply, the operation of the isolated AC/DC hybrid microgrid is able to be grouped into three levels: (1) The distributed generations in the AC sub-grid and DC sub-grid are used for realizing power self-balancing

in the region, (2) through the commutation tie line, the AC sub-grid and DC sub-grid can realize inter-area power balance, and (3) the electric energy transfer and peak-shaving are realized by charging and discharging the energy storage unit.

**Figure 1.** The structure of the considered AC/DC hybrid microgrid.
