## 1 Introduction  
The rapid development of smart electricity utilization techniques has enabled more and more electrical appliances to participate in demand response. Through electricity price or economic incentives, electrical appliances are used to respond to grid dispatching and operation needs, and the stability of power systems is improved [1; 2; 3].  
Incentive-based demand response encourages and guides customers to participate in demand response projects by adopting economic compensation or preferential price policies. Direct load control (DLC) is a common method of demand response that switches on/off the electrical appliances or adjusts the power consumption of the electrical appliances by remote control [4; 5; 6]. The customers participating in the control will receive economic compensation or electricity price discount. An intelligent home provides more advanced technology for the interaction between customers and the power grid. The control of the electrical appliances is according to the types of electrical appliances, the characteristics of the electrical appliances, and the usage habits of the customers.  
The conventional centralized control method requires the control center to operate the entire system. It not only imposes a heavy burden on the control center, but also is unable to guarantee the reliability of the systems. When the number of customers changes, the parameters in the system need to be changed. Compared with the drawbacks of the conventional centralized control method,one of the advantages of the distributed control strategy is that the various parts of the system can be flexibly distributed without centralized management of the control center. Only one or several controlled nodes in the system need to be taken as the dominant nodes to receive control information. Global information is shared between two adjacent nodes, which is beneficial to improve the reliability of the system and avoid communication congestion in the control center. This distributed control strategy is adopted in DLC, and the objective load power of the DLC is allocated to each customer according to the incremental cost consensus (ICC) algorithm, so that the optimal power allocation of the DLC is realized. Therefore, the distributed management and scheduling methods will be able to replace the conventional centralized scheduling mode to a certain extent.  
A distributed optimal resource management based on the consensus algorithm is proposed in [7; 8]. A distributed consensus-based economic dispatch with transmission losses is presented in [9]. The decentralized control of thermostatic loads for flexible demand response is considered in [10]. The conventional power generation units for power allocation according to the ICC algorithm under the different conditions of centralized control and distributed control is considered in [11]. Other research works on consensus control of demand-side resources can be found in [12; 13; 14; 15; 16; 17]. However, the references mentioned above do not consider comprehensively the load modeling. The managing of the loads only considers the continuous response characteristics of the loads, but does not consider the discrete response characteristics of the on/off loads [18; 19; 20]. In view of the above problems, this paper proposes a distributed control strategy based on a multi-agent consensus algorithm.  
The rest of this paper is as follows: Section 2 provides the overall framework of the proposed method. The objective function and the ICC algorithm formulations are provided in Section 3. Section 4 contains the simulation results and the convergence analysis. Finally, Section 5 concludes this paper.