Analysis and Simulation of Wind Turbine Optimal Control Considering Wind Turbulence Characteristics

A maximum power point tracking (MPPT) algorithm of wind turbines considering wind turbulence characteristics is presented in this paper. The turbulence characteristics of natural wind are analyzed, and the natural wind speed model is established. A MPPT algorithm based on extremum-seeking control (ESC) is proposed, which considers the turbulence characteristics containing in wind speed. The goal of the MPPT algorithm is to keep the wind turbines running at the maximum wind energy utilization coefficient point stably. The algorithm is modeled and analyzed, and the simulation results show that the MPPT algorithm is correct and effective.


INTRODUCTION
With the scarcity of fossil energy and the restrictions on carbon dioxide emission in worldwide, renewable energy has become the developing trend to mitigate the fossil energy issue. Wind power as a kind of renewable energy, with clean, large storage capacity and ease of development etc., is widely developed and utilized. In various energy shares, the proportion of wind energy is increasing. Therefore, improving the efficiency and stability of wind turbines has important significance for the development and utilization of wind energy.
At present, domestic and foreign researchers have being done a series of studies on the efficiency of wind energy capture, and have made some achievements. For small wind turbines, Narayana et al. [1] combined the fuzzy control technique and the adaptive filtering technique to realize the maximum power point tracking of wind turbines. The results show that the algorithm can improve the wind energy utilization efficiency by 20%. RBF neural network and particle swarm algorithm were combined to realize the MPPT of small wind turbines, and the corresponding simulation model was established. The simulation results show that the algorithm can improve the utilization efficiency of small wind turbines to a certain extent [2]. Wang et al. [3] combined the disturbance signal and MPPT algorithm to improve the efficiency of MPPT algorithm. The calculation results show that this method can improve the efficiency of wind energy utilization for small wind turbines. The wind speed sensors installed on wind turbines can not accurately measure the wind speed at wind turbine locations because of the influence of wind rotor rotating airflow, which leads to that the MPPT algorithm relied on the measured wind speed can not accurately calculate the maximum power point of wind turbines. Therefore, Chen et al. [4][5][6] proposed the MPPT algorithm based on no-speed sensor vector control strategy, which uses the model reference adaptive system to accurately predict the rotation speed of wind rotor and then uses BP neural network to achieve the wind turbine maximum power point. Hill-climbing algorithm has the advantage of simplicity and practicality etc. However, this algorithm is prone to oscillate near the extreme points, which influences the stability of wind turbine operations. Thus, Hui et al. [7][8][9] combined hill-climbing algorithm and fuzzy logic control to solve the problem of the hill-climbing oscillations near the extreme points, and the efficiency of hillclimbing algorithm is improved. Esmaili et al. [10][11] did some researches about the operation principle of directdriven wind turbines, and proposed a corresponding MPPT control algorithm. Abdullah et al. [12] classified and summarized the current MPPT algorithms, which laid the foundation for the wind turbine MPPT technology researches.
Based on the existing maximum power tracking technology, a maximum power point tracking (MPPT) algorithm of wind turbines considering wind turbulence characteristics is presented in this paper. Firstly, the turbulence characteristics of natural wind are analyzed, and the natural wind speed model is established. Secondly, the principle that variable speed wind turbines convert wind energy into mechanical energy is analyzed, and the quantitative relationship between wind energy utilization coefficient and tip speed ratio is established. Finally, a MPPT algorithm of wind turbines considering wind turbulence characteristics is proposed, the goal of the MPPT algorithm is to keep the wind turbines running at the maximum wind energy utilization coefficient point stably. The algorithm is modeled and analyzed.

II. NATURAL WIND SPEED MODEL
The natural wind speed is random, which can be described by Van der Hoven wind speed spectrum model, as shown in Fig. 1. Fig. 1 shows that the Van der Hoven wind speed spectrum model is composed of the mid-long term wind speed PAPER ANALYSIS AND SIMULATION OF WIND TURBINE OPTIMAL CONTROL CONSIDERING WIND TURBULENCE CHARACTERIS… and the short-time wind speed (the dotted line part in Fig.  1, the wind speed spectrum curve from the beginning of 10min to the right). Short-time wind speed is the main factor that influences the dynamic characteristics and wind energy capture efficiency of wind turbines. Therefore, the wind speed model established in this paper is the shorttime wind speed model.

( )
K is the gain of the transfer function, and its formula is given as equation (5).
Where, S T is the sampling time of white noise, and it can be configured. ( ) , B x y is beta function. The Von Carman filter in equation (3) is the non integer order filter, and the calculation process of the non integer order filter is difficult. Therefore, we use the improved Von Carman filter in this paper. The improved Von Karman filter has the integer order transfer function. The efficiency of the improved von Karman filter is same with the non integer order filter, but the calculation process becomes simple. The improved filter transfer function expression formula is shown as equation (6).
Based on the above knowledge, the calculation process of turbulence can be shown in Fig. 2.   v t is 14m/s, standard deviation is bigger than that of the average wind speed 7m/s. The above simulation results prove the correctness of the established turbulence model.  Wind turbines are the equipment that can convert wind energy into mechanical energy. The size that wind turbines convert wind energy into mechanical energy is related to wind speed 3-th power, and the relationship can be expressed as equation (7).
In equation (7), WT P is the wind turbine mechanical power; ! is the air density; R is the rotor radius; v is the wind speed; ! is the pitch angle; ! is the tip speed ratio; p C is the wind energy utilization coefficient of wind turbines. The relationships among p C , ! and ! are expressed as equations (8).  This paper focuses on the MPPT technology of variable speed wind turbines. In order to facilitate the analysis of the main issues, the variable speed wind turbines are assumed to operate at below the rated wind speed during the study. Under this condition, the pitch angle is zero degree, and the size of p C is only related to ! . The rela-tionship between p C and ! can be shown in Fig. 6. It can be seen from Fig. 6 that the wind energy utilization coefficient p C is a monopole function of the tip speed ratio ! . Thus, it is possible to achieve the maximum wind energy utilization coefficient max p C and the optimum tip speed ratio opt ! .

A. Principle of Extremum-seeking Control
It can be known from the relationship between p C and ! in Fig. 6 that p C has a unique maximum wind energy utilization coefficient max p C in the change process of tip speed ratio ! . Therefore, we could use extremum-seeking control algorithm to search the optimal tip speed ratio value opt ! in which the wind energy utilization coefficient p C can obtain maximum max p C . Fig. 8 is a schematic diagram of extremumseeking control. In Fig. 8, ( ) s s h + is high-pass filter; k s is integrator; ! is the output signal of wind energy utilization coefficient p C after high-pass filter; ! ! is the output signal of ! after superimposed sinusoidal; a is the amplitude of excitation signal; ! ! is the estimated value of the optimal tip speed ratio opt ! [13].
The output value of ( ) p C ! is filtered by the high-pass filter in Fig. 8. Equation (11) can be achieved by demodulating the filter output value using signal wave sin( ) wt .
In equation (12), the last 4 terms on the right side are high-frequency components. The four terms attenuate greatly after integral computation and can be neglected. Because the value of opt ! is constant, thus the equation that can be achieved. Therefore, equation (12) can be simplified as equation (13). . Accordingly, the wind turbine MPPT algorithm is completed.

B. Wind Turbine Extremum-seeking Process
The phase relationship between the wind energy utilization coefficient ( ) p C ! and the tip speed ratio ! is shown in Fig. 9. In the processes of searching the maximum value of ( ) p C ! , letting the tip speed ratio ! superimpose a sinusoidal excitation signal that the frequency is ! and the amplitude is a . Accordingly, the output value of ( ) p C ! also has a sinusoidal variation. When the operation point is located on the left side of the maximum value point max p C , the wind energy utilization coefficient function ( ) p C ! will increase as the tip speed ratio ! increases, the phase ! of ( ) p C ! and ! is less than 2 ! . When the operation point is located on the right side of the maximum value point max p C , the wind energy utilization coefficient function ( ) p C ! will decrease as the tip speed ratio ! increases, the phase ! of ( ) p C ! and ! is more than 2 ! .
When the operation point is located at the maximum value point max p C , the phase ! of ( ) p C ! and ! is equal to 2 ! .
The operational status of wind turbines and the direction of tip speed ratio ! can be determined by analyzing the size of the phase ! . As a power source for wind power generation system, wind speed has high frequency turbulence. The high frequency turbulence can result in the tip speed ratio of wind turbines change. In the process of maximum power point tracking by using extremum-seeking control algorithm, because of the interference of the high frequency turbulence, the output superposition signal has high frequency random components. It is difficult to separate the standard sinusoidal signal from the output superposition signal. Therefore, a new method is proposed to realize the extremum-seeking control algorithm in this paper, and the turbulence is used to instead of sinusoidal signal as the excitation signals in the method.
According to the measurement data, we can obtain generator power G P , generator rotational speed G ! , wind speed v , transmission efficiency! and transmission ratio G K . The tip speed ratio !( ) t and the wind energy utilization coefficient C ( ) p t can be calculated according these measurement data. The calculation process is shown in equation (14).
Where, k is the integral constant, the value size of k determines the search speed and accuracy. When  The simulation system structure of variable speed wind turbines is shown in Fig. 10. Wind turbine, anemometer, gearbox, generator, control system and power system are contained in Fig. 10. The anemometer is used to measure wind speed of wind turbines, and provide data support for constructing the MPPT algorithm considering wind turbulence characteristics.   Fig. 12 is the tip speed ratio of variable speed wind turbines. From the figure we can clearly see that with the change of wind speed, the MPPT algorithm considering wind turbulence characteristics can make the wind turbine running smoothly in the vicinity of the optimal tip speed ratio. The fluctuation range of tip speed ratio is small, so that the wind turbine can capture more wind energy. In the same time, the wind turbine runs stability.  Fig. 13 shows the wind energy utilization coefficient of wind turbines. From the figure we can clearly see that the MPPT algorithm considering wind turbulence characteristics can make the wind energy utilization coefficient of wind turbines running smoothly above 0.4. The MPPT algorithm considering wind turbulence characteristics not only improves the utilization efficiency of wind energy, but also ensures the stability of the wind turbine operation. ! . This means that the wind turbine operates at the vicinity of the maximum wind energy utilization coefficient. Accordingly, the maximum power point tracking considering wind turbulence characteristics is proved to be effective. From the above analysis, the MPPT algorithm considering wind turbulence characteristics can make the variable speed wind turbines running in the vicinity of the maximum wind energy utilization coefficient. It realizes the optimization control of wind turbines, and keeps the wind turbines to run stably.

VII. CONCLUSIONS
Based on the existing maximum power tracking technology, a MPPT algorithm considering wind turbulence characteristics is presented in this paper. Firstly, the turbulence characteristics of natural wind are analyzed, and the natural wind speed model is established. Secondly, the principle that the variable speed wind turbines convert wind energy into mechanical energy is analyzed, and the quantitative relationship between the wind energy utilization coefficient and the tip speed ratio is established. Finally, a MPPT algorithm considering wind turbulence characteristics is presented, the goal of the MPPT algorithm is to keep the wind turbines running at the maximum wind energy utilization coefficient point stably.
The algorithm is modeled and analyzed, and the simulation results show that the MPPT algorithm considering wind turbulence characteristics can make the wind energy utilization coefficient of wind turbines running smoothly above 0.4. It improves the utilization efficiency of wind energy, and reduces the fluctuation of wind turbines.