For the past few years, wind energy is the most popular non-traditional resource among renewable energy resources and it’s significant to make full use of wind energy to realize a high level of generating power. Moreover, diverse maximum power point tracking (MPPT) methods have been designed for varying speed operation of wind energy conversion system (WECS) applications to obtain optimal power extraction. Hence, a novel and meta-heuristic technique, named enhanced atom search optimization (EASO), is designed for a permanent magnet synchronous generator (PMSG) based WECS, which can be employed to track the maximum power point. One of the most promising benefits of this technique is powerful global search capability that leads to fast response and high-quality optimal solution. Besides, in contrast with other conventional meta-heuristic techniques, EASO is extremely not relying on the original solution, which can avoid sinking into a low-quality local maximum power point (LMPP) by realizing an appropriate trade-off between global exploration and local exploitation. At last, simulations employing two case studies through Matlab/Simulink validate the practicability and effectiveness of the proposed techniques for optimal proportional-integral-derivative (PID) control parameters tuning of PMSG based WECS under a variety of wind conditions.

To meet the increasing demand for energy in this century and reduce the pollution caused by coal and oil power plants, there is an urgent need for a sustainable and environmentally friendly source of green energy. Under the background that coping with global climate change has become the international mainstream issue, energy transformation with the development of renewable energy as the main content has become the development strategy of many countries and regions [

Since the 1980 s, global wind power technology has been continuously developing at a high speed. Wind power generation technology has experienced the stages of constant speed constant frequency (CFCF) and variable speed constant frequency (VSCF) [

Although wind resources are abundant, the output power of wind turbine is unstable thanks to the change of wind speed. For the sake of solving this problem, the maximum power point tracking (MPPT) algorithm is usually used to enhance the efficiency of WECS [

Besides, a MPPT control method with constant tracking bandwidth is designed, which aims at overcoming the disadvantage that the traditional power feedback method would reduce the tracking bandwidth [

On the other hand, the continuous flow of air in nature forms the wind, which can be seen that the wind will be affected by the circulation. In addition, temperature, pressure and so on are also indirect factors affecting the wind. The result of the above factors is that the wind power generation system has the characteristics of time-varying and nonlinear. In addition, the fan will also be affected by multiple factors, resulting in inaccurate system model parameters [

It’s worth noting that fuzzy control algorithm is a common algorithm in nonlinear intelligent control algorithm. Besides, fuzzy control algorithm does not need precise mathematical model, so it is very suitable for strongly nonlinear systems such as wind power generation. Wei et al. [

The rest of the paper is arranged as follows. The Modelling of PMSG system is presented in

As shown the framework of a PMSG system in

The power coefficient _{P}(

where _{m} is the mechanical rotation speed, _{wind} is the wind speed.

Then power coefficient _{P}(

And the electrical power generated by WT can be denoted as

where

The dynamic equations of stator voltage in d-q axis are given as [

where _{d} and _{q} stand for d-q axis inductances, _{s} means stator resistance, _{d} and _{q} denote d-q axis stator currents, _{d} and _{q} represent d-q axis stator voltages, _{f} denotes permanent flux. And _{e} = _{m} represents electrical speed where _{e} is magnetic flux,

Under steady-state conditions, the system

where _{d} and _{q} represent d-q axis steady-state stator voltages, _{d} and _{q} denote d-q axis steady-state stator currents.

Moreover, electromagnetic torque _{e}, stator active power _{s}, and reactive power _{s} can be described by

The dynamics model of mechanical shafting system can be represented by

where _{tot} denote the entire inertia of drive train, _{m} means the mechanical torque, _{e} stands for the electromagnetic torque,

Optimal tip speed ratio method is a commonly MPPT mechanism in current research. The optimal power coefficient _{opt} and the fixed value pitch angle

Hence, mechanical rotation speed needs to keep its optimum value

In this work, pitch angle _{opt} = 7.4, and optimal power coefficient

At this end, the description of optimal power curve can be obtained as

where

EASO is improved by original ASO algorithm [

The potential energy between two interactive atoms can be characterized by Lennard Jones (L-J) potential energy [

where _{ij}) and _{ij} are the potential energy and the interaction force of _{ij} denotes the Euclidian distance between the _{j} and _{i} mean the locations of the

The potential energy of the atom is thoroughly determined by the proportional relation (

where _{ij}(_{max} is the maximum iterations number, _{max} and _{min} are the maximum and minimum distance ratios, and _{best} is the suit of the optimal

According to ^{′}. For the sake of balancing interaction force (i.e., global search and local exploitation), EASO has carried out the following improvements compared with original ASO, yields

where _{best}(

As shown in

Geometric constraint is introduced to maintain the stability of molecular structure. Suppose each atom can bond to the optimal atom, then the geometric constraint for the

where _{i} is the geometric constraint for the _{i} is the constraint force for the

Each atom will move to an updated location under the combined action of interaction forces and geometric constraints. The acceleration of each atom according to Newton’s second law can be given by

where _{i}(_{worst}(

The position of each atom can be denoted by

where _{i}(

EASO is used to optimize the parameters of three PID control loops in

where the value range of proportional gains _{Pi}, integral gain _{Ii}, and differential gains _{Di} are [0,1000], [0,1000], and [0,200], respectively. Moreover, simulation time _{wind} varies between 8 m/s and 12 m/s, and weight coefficient _{1} = _{2} = 0.25.

And the convergence criterion of EASO can be given as

where ε=10^{−6} is convergence error, _{k} and _{k−1} are the fitness function value of the

At this end, the designed PID controllers for PMSG are expressed as follows:

The overall flowchart of EASO based PID control for PMSG is denoted in

The described EASO is compared with genetic optimization (GA) [

where _{d} and _{d} are the lower range and upper range of the

The optimal PID controller parameters obtained by three algorithms after 30 runs are depicted in _{q} and d-axis voltage _{d} are limited to [−0.65, 0.65] (p.u.). Lastly, the simulation is constructed on MATLAB/Simulink 2019a with Intel^{R} CoreTMi5 at 2.5 GHz and 16 GB RAM of a personal computer.

Technique | _{P1} |
_{I1} |
_{D1} |
_{P2} |
_{I2} |
_{D2} |
_{P3} |
_{I3} |
_{D3} |

GA | 766.63 | 542.36 | 38.73 | 155.63 | 81.63 | 9.21 | 345.63 | 261.63 | 5.63 |

PSO | 796.74 | 631.53 | 80.25 | 187.36 | 69.52 | 8.15 | 353.35 | 239.52 | 4.15 |

EASO | 868.36 | 501.63 | 112.52 | 204.52 | 102.52 | 6.14 | 268.24 | 218.25 | 8.21 |

Four successive step-variation wind speed signals from 8 m/s to 12 m/s are exected to WECS, and the simulation outcomes of three algorithms are given in _{m}, active power _{e} and d-axis current _{d}. Especially, the convergence time of _{e} of GA, PSO, and EASO during the second step-variation are 3.04, 3.98, and 4.12 s, respectively. The maximum overshoot of _{m} of GA, PSO, and EASO during the third step-variation are 5.93%, 3.93% and 1.20%, respectively. And the maximum overshoot of _{d} of GA, PSO, and EASO from _{P}of EASO is the largest which can capture the largest wind energy.

The low-frequency random-variation wind signals from 7 m/s to 11 m/s is exhibited in _{P} compared with other methods, which demonstrates the best MPPT performance. And EASO shows the smallest oscillation of all the controlled variables during the whole simulation time due to the adaptive update of dynamic optimization results based on Euclidian distance ratio.

In this case, the high-frequency random-variation wind signals from 6 m/s to 12 m/s (see in _{P} at its optimal value and get the smallest overshoot of _{m}, _{e}, and _{d} during the whole simulation time thanks to its appropriate balance between global search and local exploration.

Integral absolute error (IAE) indices describe the error accumulation of controlled variable relative to its reference value over a period of time _{d} of EASO is only 69.50% and 81.33% of that of GA and PSO in step-variation of wind. The IAE_{d} of EASO is only 91.07% and 86.18% of that of GA and PSO in low-frequency random-variation wind. What’s more,

Case | IAE indices | GA | PSO | EASO |

Step-variation of wind | IAE_{d} |
0.2131 | 0.1821 | |

IAE_{r} |
0.3798 | 0.4235 | ||

Low-frequency random-variation wind | IAE_{d} |
0.1814 | 0.1917 | |

IAE_{r} |
0.8063 | 0.797 | ||

High-frequency random-variation wind | IAE_{d} |
0.2704 | 0.2414 | |

IAE_{r} |
0.9736 | 0.9722 |

Wind energy, as a gift of nature, is a green and pollution-free energy that can be used, which also has played an increasingly significant role in power generation. However, wind power system is a very complex nonlinear time-varying system, how to realize the MPPT control of WECS is very meaningful. Although a large number of MPPT strategies have been developed for PMSG based WECS, these techniques are basically less efficient and difficult in searching the MPP. In this paper, a novel and prominent meta-heuristic algorithm named EASO is adopted for optimal power extraction of PMSG based WECS, which major novelties/outcomes can be summarized as follows:

(1) In contrast to typical MPPT technique (namely, GA and PSO), EASO can efficiently escape being sinking into low-quality LMPP for PMSG based WECS since it owns a strong global search ability;

(2) Compared with independent meta-heuristic algorithms, EASO can successfully obtain a dynamic balance between global exploration and local exploitation because it can adaptively adjust the weight between the exploration and exploitation based on the dynamic optimization results. Therefore, FASO is more prone to converge to a higher-quality optimal solution with a faster speed for MPPT under varieties of wind speed profiles;

(3) EASO is adopted for optimal PID control parameters tuning of PMSG based WECS for MPPT under varying wind conditions. Three case studies through Matlab/Simulink verify that EASO possesses the lowest tracking error and control costs in all cases

(4) Notable that EASO obtains the smallest IAE indices which indicates the best tracking performance. Specially, the IAE of EASO is only 69.50% and 81.33% of that of GA and PSO in step-variation of wind. Moreover, the IAE_{r} of EASO is only 96.58% and 96.72% of that of GA and PSO in high-frequency random-variation wind.

Future studies will focus on the following aspects:

(1) This paper mainly carries on the theoretical analysis of WECS based on PMSG. Compared with the real wind power generation system, the established model still own some defects. The two wind conditions adopted are relatively single and have not yet accurately simulated the natural wind conditions. How to achieve maximum wind energy tracking under natural wind conditions still needs further research;

(2) Comprehensive experiments like hardware-in-the-loop (HIL) experiment based on a dSpace will be carried out to confirm the practicality and meliority of EASO.