In this paper, a novel hybrid optimization approach, namely, gravitational particle swarm optimization algorithm (GPSOA), is introduced based on particle swarm optimization (PSO) and gravitational search algorithm (GSA) to solve combined economic and emission dispatch (CEED) problem considering wind power availability for the wind‐thermal power system. The proposed algorithm shows an interesting hybrid strategy and perfectly integrates the collective behaviors of PSO with the Newtonian gravitation laws of GSA. GPSOA updates particle’s velocity caused by the dependent random cooperation of GSA gravitational acceleration and PSO velocity. To describe the stochastic characteristics of wind speed and output power, Weibull‐based probability density function (PDF) is utilized. The CEED model employed consists of the fuel cost objective and emission‐level target produced by conventional thermal generators and the operational cost generated by wind turbines. The effectiveness of the suggested GPSOA is tested on the conventional thermal generator system and the modified wind‐thermal power system. Results of GPSOA‐based CEED problems by means of the optimal fuel cost, emission value, and best compromise solution are compared with the original PSO, GSA, and other state‐of‐the‐art optimization approaches to reveal that the introduced GPSOA exhibits competitive performance improvements in finding lower fuel cost and emission cost and best compromise solution.

Particle swarm optimization (PSO) has been proven to show good performance for solving various optimization problems. However, it tends to suffer from premature stagnation and loses exploration ability in the later evolution period when solving complex problems. This paper presents a sequential hybrid particle swarm optimization and gravitational search algorithm with dependent random coefficients called HPSO-GSA, which first incorporates the gravitational search algorithm (GSA) with the PSO by means of a sequential operating mode and then adopts three learning strategies in the hybridization process to overcome the aforementioned problem. Specifically, the particles in the HPSO-GSA enter into the PSO stage and update their velocities by adopting the dependent random coefficients strategy to enhance the exploration ability. Then, the GSA is incorporated into the PSO by using fixed iteration interval cycle or adaptive evolution stagnation cycle strategies when the swarm drops into local optimum and fails to improve their fitness. To evaluate the effectiveness and feasibility of the proposed HPSO-GSA, the simulations were conducted on benchmark test functions. The results reveal that the HPSO-GSA exhibits superior performance in terms of accuracy, reliability, and efficiency compared to PSO, GSA, and other recently developed hybrid variants.

Electric vehicles (EVs) are designed to improve the efficiency of energy and prevent the environment from being polluted, when they are widely and reasonably used in the transport system. However, due to the feature of EV’s batteries, the charging problem plays an important role in the application of EVs. Fortunately, with the help of advanced technologies, charging stations powered by smart grid operators (SGOs) can easily and conveniently solve the problems and supply charging service to EV users. In this paper, we consider that EVs will be charged by charging station operators (CSOs) in heterogeneous networks (Hetnet), through which they can exchange the information with each other. Considering the trading relationship among EV users, CSOs, and SGOs, we design their own utility functions in Hetnet, where the demand uncertainty is taken into account. In order to maximize the profits, we formulate this charging problem as a four-stage Stackelberg game, through which the optimal strategy is studied and analyzed. In the Stackelberg game model, we theoretically prove and discuss the existence and uniqueness of the Stackelberg equilibrium (SE). Using the proposed iterative algorithm, the optimal solution can be obtained in the optimization problem. The performance of the strategy is shown in the simulation results. It is shown that the simulation results confirm the efficiency of the model in Hetnet.

Electric vehicles (EVs) are designed to improve the power efficiency as well as it prevents the environment from being polluted, and thus they are widely and reasonably used in the power market. Thanks to mobile charging stations (MCSs), it provides the charging service to EVs more easily with higher payoff and lower consumption, compared with the fixed charging stations (FCSs). In this paper, we propose a dynamic contract-based strategy to apply the secured charging service from MCS in Internet of things (IoTs), considering incomplete information of EV users. Firstly, considering this charging system composed of multiple EV users and MCSs, we design the utility function of each one, where non-contract power are supplied to EV users besides the power in contract items in IoTs. Then, in order to maximize MCS's profits, an optimization problem is formulated to obtain the optimal contract items satisfying EV users' power demand. Thirdly, the optimal solution of this problem is efficiently achieved through the presented iterative search algorithm, considering the different types of EV users with different contract items. Finally, simulation results validate the effectiveness of our proposal and each of them in this charging system can be benefited.

The integration of smart grid and Internet of Things (IoT) has been facilitated with the proliferation of electric vehicles (EVs). However, due to EVs’ random mobility and different interests of energy demand, there exists a significant challenge to optimally schedule energy supply in IoT. In this paper, we propose a secure game theoretic scheme for charging EVs supplied by mobile charging stations (MCSs) in IoT, considering the dynamic renewable energy source. Firstly, the charging system composed of MCSs is developed to implement the charging service. Secondly, when the secure charging scheme of EV users is designed, the utility function of each entity in the charging system is formulated to express the trading relationship between EV users and MCSs. Moreover, with consideration of the competition and cooperation, we propose a Stackelberg game framework with sub-noncooperative optimization. Thirdly, the existence and uniqueness of both Stackelberg equilibrium (SE) and Nash equilibrium (NE) are theoretically analyzed and proved. Through the presented distributed energy scheduling algorithm, we can achieve the optimal solution. Finally, numerical results demonstrate the effectiveness and efficiency of our proposal through comparison with other existing schemes.

A path following control strategy for a four-wheel-independent-drive electrical vehicle (4WID-EV) based on backstepping and model predictive control is presented, which can ensure the accuracy of path following and maintain vehicle stability simultaneously. Firstly, a 2-DOF vehicle dynamic model and a path following error model are built and the desired yaw rate is obtained through backstepping. Then, a model predictive controller is adopted to track the desired yaw rate and obtain the optimal front wheel steering and external yaw moment. Meanwhile, an optimal torque distribution algorithm is carried out to allocate it to each tire. Finally, the effectiveness and superiority of the strategy is validated via CarSim–Simulink joint simulation. Results show that the strategy has higher following accuracy, smaller sideslip angle, and better yaw rate tracking.