A Fully Distributed Approach to Optimal Energy Scheduling of Users and Generators Considering a Novel Combined Neurodynamic Algorithm in Smart Grid Chentao Xu and Xing He Abstract—A fully distributed microgrid system model is presented in this paper. In the user side, two types of load and plug-in electric vehicles are considered to schedule energy for more benefits. The charging and discharging states of the electric vehicles are represented by the zero-one variables with more flexibility. To solve the nonconvex optimization problem of the users, a novel neurodynamic algorithm which combines the neural network algorithm with the differential evolution algorithm is designed and its convergence speed is faster. A distributed algorithm with a new approach to deal with the inequality constraints is used to solve the convex optimization problem of the generators which can protect their privacy. Simulation results and comparative experiments show that the model and algorithms are effective. Index Terms—Differential evolution algorithm, distributed algori- thm, electric vehicle, neural network, zero-one variable.    I. Introduction I T is obvious that smart grid will occupy a very important position in the future distribution network system because it is more flexible, controllable, environmental than the conventional distribution network [1]. The users and generators can use the smart meters, advanced communication and control technologies to exchange information by the control center in the microgrid [2]. In general, at every time slot, the control center will announce the real-time price of energy according to the estimated demand, then the users will adjust their energy strategies for more benefits, which can decrease the demand at load peaks and increase demand at load valleys to make the distribution network system more stable and effective. At last the control center will buy the certain amount of energy from the generators according to their information [3]. Lee et al. [4] designed a smart lighting system for future smart grids. There are many types of loads in the user side and the models used to describe them are different. Haider et al. [5] analyzed the structure of the residential demand response systems and the load-scheduling techniques. Ihsan et al. [6] considered the generators with several types of renewable energy power. Xu et al. [7] structured the satisfaction function and designed the system model with three types of loads. Unlike gasoline car, there is huge market potential for electric vehicle (EV) because of its clean and environment-friendly advantages. It can be seen as energy storage devices at home with proper constraints. Karfopoulos and Hatziargyriou [8] gave two charging modes of centralized and distributed EV management control respectively. Luo et al. [9] combined two control strategies of series electric vehicles to get better fuel economy. Neural network has developed quickly as a tool for solving optimization problems. Qin et al. [10] constructed a one-layer recurrent neural network to solve the constrained convex optimization problems with complex-variables. Xia et al. [11] designed two projection neural networks with low dimension and complexity to solve the nonlinear programming problems. For general optimal problems with both equality and inequality constraints, Xia and Wang [12] gave some methods. Gao and Liao [13] presented a novel neural network to solve the generally constrained problems with fewer stability requirements. Han et al. [14] used an artificial neural network to solve the quadratic zero-one programming problems. For many distributed systems, traditional centralized neural network algorithms are limited because they take a lot of computation with poor flexibility, the single point of failure will lead to global crash, etc. [15]. Therefore, distributed neural network algorithms have been used more and more widely in recent years. Yi et al. [16] proposed a distributed gradient algorithm for constrained optimal problems. He et al. [17] put forward a second-order distributed continuous-time algorithm under a centralized framework. Jia et al. [18] proposed a neural network to solve the distributed nonsmooth optimization problems with inequality constraints over a multi-agent network. Guo et al. [19] considered a new distributed gradient-based algorithm to accelerate the convergence speed. Manuscript received November 10, 2019; revised January 17, 2020; accepted March 17, 2020. This work was supported by the Natural Science Foundation of China (61773320), Fundamental Research Funds for the Central Universities (XDJK2020TY003), and also supported by the Natural Science Foundation Project of Chongqing Science and Technology Commission (cstc2018jcyjAX0583). Recommended by Associate Editor Qinglai Wei. (Corresponding author: Xing He.) Citation: C. T. Xu and X. He, “A fully distributed approach to optimal energy scheduling of users and generators considering a novel combined neurodynamic algorithm in smart grid,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 7, pp. 1325–1335, Jul. 2021. The authors are with the Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China (e-mail: 415259822@qq.com; hexingdoc@swu.edu.cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JAS.2021.1004048 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 7, JULY 2021 1325