Differential Evolution (DE) is a simple and efficient optimizer, especially for continuous optimization. For these reasons DE has often been employed for solving various engineering problems. On the other hand, the DE structure has some limitations in the search logic, since it contains too narrow a set of exploration moves. This fact has inspired many computer scientists to improve upon DE by proposing modifications to the original algorithm. This paper presents a survey on DE and its recent advances. A classification, into two macro-groups, of the DE modifications is proposed here: (1) algorithms which integrate additional components within the DE structure, (2) algorithms which employ a modified DE structure. For each macro-group, four algorithms representative of the state-of-the-art in DE, have been selected for an in depth description of their working principles. In order to compare their performance, these eight algorithm have been tested on a set of benchmark problems. Experiments have been repeated for a (relatively) low dimensional case and a (relatively) high dimensional case. The working principles, differences and similarities of these recently proposed DE-based algorithms have also been highlighted throughout the paper. Although within both macro-groups, it is unclear whether there is a superiority of one algorithm with respect to the others, some conclusions can be drawn. At first, in order to improve upon the DE performance a modification which includes some additional and alternative search moves integrating those contained in a standard DE is necessary. These extra moves should assist the DE framework in detecting new promising search directions to be used by DE. Thus, a limited employment of these alternative moves appears to be the best option in successfully assisting DE. The successful extra moves are obtained in two ways: an increase in the exploitative pressure and the introduction of some randomization. This randomization should not be excessive though, since it would jeopardize the search. A proper increase in the randomization is crucial for obtaining significant improvements in the DE functioning. Numerical results show that, among the algorithms considered in this study, the most efficient additional components in a DE framework appear to be the population size reduction and the scale factor local search. Regarding the modified DE structures, the global and local neighborhood search and self-adaptive control parameter scheme, recently proposed in literature, seem to be the most promising modifications.

Recent advances in differential evolution: a survey and experimental analysis

To improve the use of lithium-ion batteries in electric vehicle (EV) applications, evaluations and comparisons of different equivalent circuit models are presented in this paper. Based on an analysis of the traditional lithium-ion battery equivalent circuit models such as the Rint, RC, Thevenin and PNGV models, an improved Thevenin model, named dual polarization (DP) model, is put forward by adding an extra RC to simulate the electrochemical polarization and concentration polarization separately. The model parameters are identified with a genetic algorithm, which is used to find the optimal time constant of the model, and the experimental data from a Hybrid Pulse Power Characterization (HPPC) test on a LiMn2O4 battery module. Evaluations on the five models are carried out from the point of view of the dynamic performance and the state of charge (SoC) estimation. The dynamic performances of the five models are obtained by conducting the Dynamic Stress Test (DST) and the accuracy of SoC estimation with the Robust Extended Kalman Filter (REKF) approach is determined by performing a Federal Urban Driving Schedules (FUDS) experiment. By comparison, the DP model has the best dynamic performance and provides the most accurate SoC estimation. Finally, sensitivity of the different SoC initial values is investigated based on the accuracy of SoC estimation with the REKF approach based on the DP model. It is clear that the errors resulting from the SoC initial value are significantly reduced and the true SoC is convergent within an acceptable error.

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Evaluation of Lithium-Ion Battery Equivalent Circuit Models for State of Charge Estimation by an Experimental Approach

An adaptive Kalman filter algorithm is adopted to estimate the state of charge (SOC) of a lithium-ion battery for application in electric vehicles (EVs). Generally, the Kalman filter algorithm is selected to dynamically estimate the SOC. However, it easily causes divergence due to the uncertainty of the battery model and system noise. To obtain a better convergent and robust result, an adaptive Kalman filter algorithm that can greatly improve the dependence of the traditional filter algorithm on the battery model is employed. In this paper, the typical characteristics of the lithium-ion battery are analyzed by experiment, such as hysteresis, polarization, Coulomb efficiency, etc. In addition, an improved Thevenin battery model is achieved by adding an extra RC branch to the Thevenin model, and model parameters are identified by using the extended Kalman filter (EKF) algorithm. Further, an adaptive EKF (AEKF) algorithm is adopted to the SOC estimation of the lithium-ion battery. Finally, the proposed method is evaluated by experiments with federal urban driving schedules. The proposed SOC estimation using AEKF is more accurate and reliable than that using EKF. The comparison shows that the maximum SOC estimation error decreases from 14.96% to 2.54% and that the mean SOC estimation error reduces from 3.19% to 1.06%.

State-of-Charge Estimation of the Lithium-Ion Battery Using an Adaptive Extended Kalman Filter Based on an Improved Thevenin Model

State of charge estimation of lithium-ion batteries using the open-circuit voltage at various ambient temperatures

Battery technology is the bottleneck of the electric vehicles (EVs). It is important, both in theory and practical application, to do research on the modeling and state estimation of batteries, which is essential to optimizing energy management, extending the life cycle, reducing cost, and safeguarding the safe application of batteries in EVs. However, the batteries, with strong time-variables and nonlinear characteristics, are further influenced by such random factors such as driving loads, operational conditions, in the application of EVs. The real-time, accurate estimation of their state is challenging. The classification of the estimation methodologies for estimating state-of-charge (SoC) of battery focusing with the estimation method/algorithm, advantages, drawbacks, and estimation error are systematically and separately discussed. Especially for the battery packs existing of the inevitable inconsistency in cell capacity, resistance and voltage, the advanced characterizing monomer selection, and bias correction-based method has been described and discussed. The review also presents the key feedback factors that are indispensable for accurate estimation of battery SoC, it will be helpful for ensuring the SoC estimation accuracy. It will be very helpful for choosing an appropriate method to develop a reliable and safe battery management system and energy management strategy of the EVs. Finally, the paper also highlights a number of key factors and challenges, and presents the possible recommendations for the development of next generation of smart SoC estimation and battery management systems for electric vehicles and battery energy storage system.

Critical Review on the Battery State of Charge Estimation Methods for Electric Vehicles

State of charge estimation based on evolutionary neural network

According to the aerodynamical characteristic of the wind turbine, a maximum power point tracking (MPPT) is necessary to get high efficiency for wind power conversion, which means that the rotating speed of wind turbine should be adjusted in the real time to capture maximum wind power. Because of the fast variation of wind speed and the heavy inertia of generator, the MPPT control of wind generation is much challengeable. A new MPPT control scheme has been developed for permanent magnetic (PM) generator driven by a three-phase inverter to generate 350 V direct current power to the DC bus line. The main differences between the method used in the proposed MPPT system and other techniques used in the past are as follows: (1) the tracking step is variable according to the change of wind speed; (2) in order to avoid the dead time effect of the inverter the MPPT control is synchronized to the rotating speed of the generator; (3) a low pass filter is used at the output of the MPPT controller to decrease the fluctuation of the rotating speed reference. The resulting system has high-efficiency, lower-cost and fast, stable tracking speed. The experimental results show that it can track as fast as 0.2Hz variation of wind speed and increases the output wind power as much as 48%. As a result, the efficiency of the generation has been improved evidently.

A new maximum power point tracking control scheme for wind generation

Differential evolution (DE) is a recently invented global optimization algorithm. In this paper, a new differential evolution algorithm, self-adaptive chaos differential evolution (SACDE) with chaos mutation factor and dynamically changing weighting factor and crossover factor is presented. The evolution speed factor and aggregation degree factor of the population are introduced in this new algorithm. In each iteration process, the weighting factor is changed dynamically based on the current aggregation degree factor, and the crossover factor is changed dynamically based on the current evolution speed factor. The chaos mutation factor is introduced to avoid falling into the local optimum. DE and SACDE are tested with two well-known benchmark functions. The experiments show that the convergence speed of SACDE is significantly superior to DE, the convergence accuracy is also increased.

Self-Adaptive chaos differential evolution

Support vector machine based battery model for electric vehicles

The utilization of motor-in-wheel in the electric vehicle (EV) is a very important research topic. In order to simplify the control of EV, a new system is proposed by Guilin Tao, which changes the traditional configuration and control strategy of direct-wheel-driven EV. In this system two permanent-magnet-brushless dc motors (PMBDCMs) are connected directly in serial, in order to cut down the differential algorithm thoroughly in velocity control strategy. This structure can realize the differential automatically when the EV runs on the smooth road at low speed. But this structure considers the characters of the motor only, which is an ideal system. EV is a complex electromechanical system, and its work condition is also complex. The variation of the external condition and the work condition of operation can affect the operation of motor, so the state of the EV will change. In this paper, according to the change of the work condition and road condition, combined with the dynamics of EV, this problem was well studied. The neural network PID control mode was used in this paper, and by means of the Matlab/Simulink and the experimental verification, it reveals that this method can enhance the safety and stability of this system.

Cao Binggang

Papers

State of charge estimation based on evolutionary neural network

A new maximum power point tracking control scheme for wind generation

Self-Adaptive chaos differential evolution

Support vector machine based battery model for electric vehicles

Driving and control of torque for direct-wheel-driven electric vehicle with motors in serial