Neural Network Compensation Control for Output Power Optimization of Wind Energy Conversion System Based on Data-Driven Control

Abstract

Due to the uncertainty of wind and because wind energy conversion systems (WECSs) have strong nonlinear characteristics, accurate model of the WECS is difficult to be built. To solve this problem, data-driven control technology is selected and data-driven controller for the WECS is designed based on the Markov model. The neural networks are designed to optimize the output of the system based on the data-driven control system model. In order to improve the efficiency of the neural network training, three different learning rules are compared. Analysis results and SCADA data of the wind farm are compared, and it is shown that the method effectively reduces fluctuations of the generator speed, the safety of the wind turbines can be enhanced, the accuracy of the WECS output is improved, and more wind energy is captured.

1. Introduction

In recent years, the global wind industry has grown rapidly, wind energy has become one of the most important renewable energy sources, installed capacity growth rate of wind turbines has become more than 25% annually, and wind energy has been widely applied to water irrigation [1], urban power supply [2], and many other fields. However, there are still some difficult issues in wind energy control technology: how to get maximum power output of wind turbine is one of the main concerns. Domestic and foreign scholars have done a lot of research on capturing the largest wind energy; the most common control strategy is maximum power point tracking control (MPPT) [3]. The maximum wind energy is captured by controlling the output error of the wind generator speed, when the wind speed changes. PI control [4, 5], LQG control [6, 7], and Fuzzy sliding mode control [8] are commonly used as the control methods. However, the parameters of PI controller are almost adjusted through a large number of experiments. They will be affected by the change of load and wind speed, and therefore, PI regulator will lose the flexibility at this time. The LQG control method does not have high modeling accuracy, so the error of system output is too large. Fuzzy sliding mode control cannot reduce the chattering phenomenon; it will lead to low accuracy and poor robust performance.

Data-driven control theory has gradually become a hot research area for domestic and foreign scholars [9–14]. The data-driven control theory can be used to design a controller for a complex nonlinear system whose model is unknown. The control method has general applicability and is successfully applied to many fields, such as flight control [15, 16], pattern recognition [17], and robot control [18, 19].

However, the shortcomings of the data-driven controller are parameter perturbation and excessive computing. The data-driven approach is improved by many well-known scholars [20–23]. A new data-driven controller is designed in the literature [20]; the method uses only measured input and output data of the controlled plant and guarantees bounded input and bounded output stability. It can be known by comparing this data-driven approach with the general adaptive control approach. The method has practical application value and can be combined with other control methods, and thus the cost of the controller is greatly reduced.

Neural networks have independence—not relying on accurate mathematical model of the system—and a strong classification ability for spatial data model. In fact, neural networks have been successfully applicated to wind power control systems [24–30]. Literatures [24–26] introduce the neural network predictive control in the application of the WECS, using neural network predictive controller to compensate system output errors that are caused by uncertainty parameters in WECS; disturbance output is reduced when the wind turbine is at run time. Literatures [31, 32] introduce observers applied to wind turbines; robust performance and dynamic performance of the WECS can be improved by the observers. When wind speed is larger, power output may exceed the rated value; this will cause high wind turbine torque load. Power output quality of the WECS is optimized by controlling the blade pitch angle in literatures [27, 28], so the wind turbine shutdown and overload can be reduced. There exist analytical models of wind turbines as in [33–36] and models based on input output data as in [29, 30, 37], and in the paper, the second case is considered. Literatures [29, 30, 37] introduce data-driven controller designed for the WECS based on neural network, this method collects wind farms data by supervisory control and data acquisition (SCADA) system, such as wind energy utilization coefficient, wind generator speed, and wind speed. Using data-driven control to identify input and output of the controlled object, different control methods are used to regulate WECS output; the results proved that this method can be effectively applied to different wind turbines.

Data-driven controller for the WECS based on neural network compensation control is designed in this paper. Firstly, a 10 min data of wind turbine was selected by SCADA system; the data-driven control system Markov parameters can be obtained by input and output data of the WECS. Secondly, the controller gain can be obtained by closed solution of differential Riccati.

In order to improve the WECS control precision and capture more wind energy, a neural network compensator is designed to counteract dynamic disturbances caused by unkown parameters of the WECS, different neural network learning rules are selected in the training process, and another neural network is used to optimize the wind energy utilization coefficient and reduce the mechanical shocks on the WECS. Analysis results show that this way more wind energy can be captured and safety of the wind turbine can be enhanced.

2. Problem Description

Wind speed and wind direction are uncontrollable variables while, wind generator speed and torque are controllable variables [29, 30, 37, 38]. The SCADA system of wind turbines is shown in Figure 1; the system can monitor multiple wind farm data, for example, wind turbines, grid data, and substation data. Data of output power, wind generator speed, wind generator torque, and wind speed is selected in this paper.

Figure 1 

SCADA system for wind farm.

Wind farm data collected is given in Table 1; 10 min data is used in this paper, the data from 2010/07/02 00:10:00 A. to 2010/07/20 02:20:00 AM. 𝑣(𝑡−1) is wind speed data of previous sampling time period, and 𝑃_𝑎(𝑡−1) is wind generator data of previous sampling time.

Table 1 

10 min sample data of SCADA system.

According to the literature [1], the relationship between wind energy utilization coefficient and tip speed ratio can be known. As in Figure 2, the tip speed ratio reaches optimum value, the maximum wind energy utilization coefficient 𝐶_𝑝max is around 0.47, tip speed ratio optimum value is around 7, and blade pitch angle is around 0 degree; the figure has general applicability to the variable speed constant frequency wind turbine: Γ(Ω𝑡)=𝐶𝑣(𝑡)²𝐶_Γ(𝜆),_𝑤(𝑡)=𝑃^𝑤(𝑡)𝑃Γ(𝑡)_𝑤,(𝑡)=𝐶𝑅𝑣(𝑡)³𝐶_𝑃(𝜆).(1) Letting, 𝐶=0.5𝜋𝜌𝑅³, in (1), Γ is wind wheel torque, 𝜌 is air density, 𝑅 is radius of the wind wheel, and 𝑣 is wind speed. The relationship between wind speed and wind turbine power output is shown in Figure 3, 𝐶_Γ(𝜆) is torque coefficient, 𝜆 is tip speed ratio, 𝜆=Ω_𝑊𝑅/𝑣, Ω_𝑊 is rotor speed, and 𝐶_𝑝(𝜆) is wind energy utilization coefficient. The relationship between 𝐶_Γ(𝜆) and 𝐶_𝑝(𝜆) can be expressed as 𝐶_Γ(𝜆)=(𝐶_𝑝(𝜆))/𝜆.

Figure 2 

Wind energy utilization coefficient versus tip speed ratio.

Figure 3 

Wind speed versus wind generator power.

There are multiple unknown parameters and uncertainties in the WECS, the system has strong nonlinear characteristics, and its model is difficult to be established. Using the equivalent model and ignoring a number of uncertainties are often the solutions; however, the modeling accuracy is greatly reduced and seriously affects the control effect. Data-driven control only needs system input and output data. So, data-driven control model for the wind power system can be expressed as 𝑦_𝑗=𝑓_𝑗𝑄_𝑗,𝑅_𝑗,𝑢_𝑗,𝑥_𝑗,𝑀_𝑖𝑗,𝑗=1,2,3,𝑖=1,2...𝑁,(2) where 𝑦_𝑗 is wind generator power output. Because three groups of data are selected for the experiment, 𝑗=3,𝑗 can be selected as a different value according to actual needs. 𝑥_𝑗 is system state, including wind generator speed, wind generator torque, and wind speed. 𝑢_𝑗 is the system control input. 𝑄_𝑗 and 𝑅_𝑗 are positive semidefinite symmetric weight matrices, 𝑀_𝑖𝑗=𝐂_𝑗𝐀^{𝑗(𝑖−1)}𝐁_𝑗, where 𝑀_𝑖𝑗 are wind power control system Markov parameters: 𝐽=𝜀𝑦^𝑇𝑗𝑄_𝑗𝑦_𝑗+^𝑁−1_𝑘=0𝑦^𝑇𝑗𝑄_𝑗𝑦_𝑗+𝑢^𝑇𝑗𝑅_𝑗𝑢_𝑗.(3)

3. Data-Driven Control Methodology

Lemma 1 (see [39]). The closed solution of differential Riccati equation is 𝐗(𝑘)=𝐂⋅(𝑘𝐑)^𝑇(𝑘𝐐)(+𝑘)𝐒𝐂(𝑘()𝑘_𝑇)−𝐂(𝑘)^𝑇𝐐(𝑘)𝐒(𝑘)𝐐(𝑘)𝐒(𝑘)⁻¹𝐒(𝑘)^𝑇𝐐(𝑘)𝐂(𝑘),(4) where 𝐂(𝑘)=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣𝐂𝐂𝐂𝐀𝐀²𝐂𝐀⋮_𝑁−𝑘𝐒(𝑘)=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣𝐂𝐀𝐂𝐂⋮𝐀𝟎𝐁𝐁_{𝑁−𝑘−1}𝐂⋯⋮𝟎𝐁⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦,⋱⋱⋱⋯⋱⋱⋯⋮⋮⋮𝟎𝐁𝐂𝐀^{𝑁−𝑘−2}𝐁⋯𝐂𝐁𝟎⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦,(5)𝐒(𝑁)=𝟎, 𝐑(𝑘)=diag(𝐑,𝐑,…,𝐑) is block diagonal matrix with dimensions (𝑁−𝑘+1)⋅𝑚 and 𝐐(𝑘)=diag(𝐐,𝐐,…,𝐐) is block diagonal matrix with dimensions (𝑁−𝑘+1)⋅𝑙.

Theorem 2. For given Markov parameters of the WECS, after introduction of a closed solution of the differential Riccati equation, the data-driven controller can be expressed as：𝑈(𝑘)=𝐆(𝑘)𝐱_𝑐(𝑘),𝑗=1,2,3,(6) where 𝐆(𝑘) is the data-driven controller gain 𝐱_𝑐(𝑘) is the data-driven controller state 𝐆(𝑘)=−𝑅+𝜽(𝑘+1)^𝑇Ω(𝑘+1)𝜽(𝑘+1)⁻¹𝐱×𝜽(𝑘+1)^𝑇Ω(𝑘+1),_𝑐(𝑘)=𝐂(𝑘+1)𝐀𝐱(𝑘)=⎡⎢⎢⎢⎢⎢⎢⎣𝐂𝐂𝐀𝐀²𝐂𝐀⋮_𝑁−𝑘⎤⎥⎥⎥⎥⎥⎥⎦𝐱(𝑘),(7) where Ω(𝑘+𝜽(1𝑘)+=1)𝐐×=(𝐑𝑘𝐂(+𝑘(𝑘1++)1−1))𝐐+𝐁(𝐒𝑘=(𝑘++𝐌1)1_𝟏𝐒)_𝑇𝐌(𝑘_𝟐+⋯1)𝐌_𝑁−𝑘^𝑇,𝐐(𝑘+1)𝐒(𝑘+1)⁻¹𝐒(𝑘+1)=×⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣𝐒(𝐌𝑘𝟎+1)^𝑇𝐐⋯(𝑘+1⋯),⋯𝟎_𝟏𝐌𝟎⋱⋮_𝟐𝐌⋮𝐌⋮_𝟏⋱⋱⋱⋱⋮⋮_{𝑁−𝑘−1}𝐌_{𝑁−𝑘−2}⋯𝐌_𝟏𝟎⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦(𝐒(𝑁)=𝟎),(8) where 𝐑(𝑘+1)=diag(𝐑,𝐑,…,𝐑) is block diagonal matrix with dimensions 𝑚(𝑁−𝑘) and 𝐐(𝑘+1)=diag(𝐐,𝐐,…,𝐐) is block diagonal matrix with dimensions 𝑙(𝑁−𝑘). 𝐀_𝑗,𝐁_𝑗,and𝐂_𝑗 of the Markov parameters 𝑀_𝑖𝑗 can be obtained by the input 𝑢_𝑗 and output 𝑦_𝑗, and the column vectors 𝐮_𝑗(𝑘) and 𝐲_𝑗(𝑘) are formed by 𝑝-Step input and output data from the beginning of the {𝑢_𝑗,𝑦_𝑗}: 𝑈𝑌_𝑗(𝑘)=𝐮_𝑗1(𝑘)⋯𝐮_𝑗𝑝−1(𝑘+𝑝−1)^𝑇,𝑗=1,2,3,(9)_𝑗(𝑘)=𝑦_𝑗1(𝑘)⋯𝑦_𝑗𝑝−1(𝑘+𝑝−1)^𝑇,𝑗=1,2,3.(10) Then, matrices 𝐘_𝑗 and 𝐕_𝑗 in (11) can be formed by the input data and output data. The relationship between input and output data can be expressed as (12) 𝐘𝐕_𝑗=𝐲_𝑗1(𝑘+𝑝)⋯𝐲_𝑗𝐿(𝑘+𝑝+𝐿),𝑗=1,2,3,_𝑗=⎡⎢⎢⎢⎢⎣𝐮^𝑗𝐮(𝑘)⋯𝐮_𝑗(𝑘+𝐿)_𝑗𝑝𝐲(𝑘+𝑝)⋯𝐮_𝑗𝑝(𝑘+𝑝+𝐿)_𝑗𝐏(𝑘)⋯𝐲_𝑗𝐿(𝑘+𝐿)⎤⎥⎥⎥⎥⎦,𝑗=1,2,3,(11)_𝑗1𝐓_𝑗𝑝𝐏_𝑗2=𝐘^𝑗𝐕^𝑇𝑗𝐕_𝑗𝐕^𝑇𝑗⁺,𝑗=1,2,3,(12) where 𝐏_𝑗2𝐏_𝑗1=𝐎_𝑗𝑝𝐁_𝑗𝑝+𝐌_𝑗𝐓_𝑗𝑝,𝐁_𝑗𝑝=−𝐎_𝑗𝑝𝐌_𝑗,𝐌_𝑗=−𝐴^𝑝𝑗𝐎^+𝑗𝑝,𝐎_𝑗𝑝=𝐀_𝑗𝑝−1𝐁_𝑗⋯𝐀_𝑗𝐁_𝑗𝐁_𝑗,=⎡⎢⎢⎢⎢⎢⎢⎣𝐂^𝑗𝐂_𝑗𝐀_𝑗𝐂_𝑗⋮𝐀_𝑗𝑝−1𝐓⎤⎥⎥⎥⎥⎥⎥⎦𝑗=1,2,3,_𝑗𝑝=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣𝐂0⋯⋯⋯0^𝑗𝐂𝐁_𝑗0⋱⋮_𝑗𝐂𝐀⋮_𝑗𝐁_𝑗𝐂⋮_𝑗𝐁_𝑗⋱⋱⋱⋱⋮⋮_𝑗𝐀_𝑗𝑝−2𝐁_𝑗𝐂_𝑗𝐀_𝑗𝑝−3𝐁_𝑗⋯𝐂_𝑗𝐁_𝑗0⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦𝑗=1,2,3.(13)𝐏_𝑗1, 𝐏_𝑗2, and matrix 𝐓_𝑗𝑝 can be obtained by solving (9); when 𝑝=𝑁+1, the WECS Markov parameters 𝑀_𝑖𝑗 can be extracted from 𝐓_𝑗𝑝.

The test time is from 2010/07/21 00:30:10 AM to 2010/07/29 00:25:30 AM, corresponding control input data and output data set are {𝑢₁,𝑦₁},{𝑢₂,𝑦₂},{𝑢₃,𝑦₃} and The original power output and the optimized power output are shown by Figures 4(a)–4(c). It can be seen that data-driven controller can effectively identify wind turbine power output and control precision achieves the desired effect.

(a) Wind speed versus wind generator speed

(b) Wind generator torque versus wind speed

(c) Wind generator torque versus wind generator speed

Figure 4 

Power output.

4. Neural Network Optimization

As shown in Figure 2, the tip speed ratio can be adjusted by controlling wind generator speed to improve wind energy utilization coefficient 𝐶_𝑝. Wind generator speed is optimized by neural network compensator to improve wind energy capture efficiency. Neural network performance evaluation [40–43] is expressed as (14) 𝐽=min𝐸^∞𝑡=0𝑂_𝑡𝑖−𝑂_𝑖²d𝑡,(14) where 𝑂_𝑡𝑖 is the target output of the compensator and 𝑖=1,2,…,𝑛. 𝑂_𝑖 is the actual output of the compensator, which is Δ𝑢_𝑗𝑛𝑛(𝑘) in (17). Neural networks have many learning rules; different learning rules lead to different training efficiency, OUTSTAR learning rules are used to train neural network compensator in this paper, which is intended to generate an m-dimensional desired output vector. Weight vector Δ𝑊_𝑘 of OUTSTAR learning rule can be expressed as Δ𝑊_𝑘=𝜂𝑑−𝑊_𝑘.(15) Before adding the data-driven controller, open-loop input data which constitutes the matrix𝐘_𝑗  and output data which constitutes the matrix𝐕_𝑗  are collected, row vector of matrix𝐕_𝑗  and matrix𝐘_𝑗 must be linearly independent. Inputs of the neural network compensator are 𝑒_𝑗(𝑘−1), 𝑦_𝑗(𝑘−1), and Δ𝑢_𝑗(𝑘);Δ𝑢_𝑗(𝑘) is the error between data-driven controller current input 𝑢(𝑘,𝑥_𝑗) and previous input 𝑢(𝑘−1,𝑥_𝑗). Output of the compensator is Δ𝑢_𝑗𝑛𝑛(𝑘); Δ𝑢_𝑗𝑛𝑛(𝑘) is the error between neural network current input 𝑢_𝑗𝑛𝑛(𝑘,𝑥_𝑗) and previous input 𝑢_𝑗𝑛𝑛(𝑘−1,𝑥_𝑗)∶Δ𝑢Δ_𝑗𝑛𝑛𝑢_𝑗(𝑘)=𝑢𝑘,𝑥_𝑗−𝑢𝑘−1,𝑥_𝑗,(16)(𝑘)=𝑢_𝑗𝑛𝑛𝑘,𝑥_𝑗−𝑢_𝑗𝑛𝑛𝑘−1,𝑥_𝑗.(17) The method has general applicability, so randomly wind turbine 1, wind turbine 2, and wind turbine 3 are selected as the study objects, and learning rules of EBPA and LMS are used to train the neural network compensator also. Equation (18) give the wind turbine output power mean absolute error (MAE), the standard deviation of mean absolute error (SD of MAE), the relative mean absolute error (RMAE), and the standard deviation of relative mean absolute error (SD of RMAE), where 𝑦_𝐾 is control output, 𝑦₀ is instance value, and n is sample number. It can be seen that the model built on the collected data is stabler with the OUTSTAR learning rules. Output error with different training rules is given in Table 2: MAE=∑^𝑛𝐾=1||𝑦_𝐾−𝑦₀||STDofMAE=𝑛,∑^𝑛𝐾=1𝑦_𝐾−𝑦₀²RMAE=∑_𝑛𝐾=1𝑛,||𝑦_𝐾−𝑦₀||𝑛𝑦₀STDofRMAE=,∑^𝑛𝐾=1𝑦_𝐾−𝑦₀/𝑦₀²𝑛.(18)

Table 2 

Output error with different training rules.

5. Analysis and Results

The original value and optimal value of wind energy utilization coefficient are compared in Figure 5, it can be known wind energy captured is increasing by adjusting tip speed ratio value, as the tip speed ratio is close to the optimal value, the value of wind energy utilization coefficient is increasing. Wind turbine 1 is taken as study object, and a 5-17-1 neural network is selected to optimize wind energy captured by the wind wheel. Figure 6(a) gives the original and optimal generator speeds. It can be seen that the optimal generator speed is stabler than the original one. Figure 6(b) gives the original and optimal power output. It can be seen that the optimal power is more than the original one.

(a) Tip speed ratio

(b) Wind energy utilization coefficient

Figure 5 

Wind energy utilization coefficient versus tip speed ratio.

(a) Power output

(b) Generator speed

Figure 6 

Optimized output.

6. Conclusion

In this paper, data-driven controller for the WECS is designed based on neural network, Markov parameters of the data-driven controller can be obtained by input and output data of the WECS. To overcome the inadequacy of data-driven control, neural network compensator is used to compensate for the deviation output of wind power data-driven control system; the results show that the system stable performance is improved.

10 min data of wind farm SCADA system is collected, including wind generator power output, wind generator speed, wind energy utilization coefficient, and tip speed ratio. The method first determines the WECS Markov parameters, the system output is controlled by adjusting the data-driven controller gain, and the neural network is trained by different neural network learning rules. The results show that the generator speed fluctuations can be reduced, the security of wind turbine operation is high, more wind energy is captured, and the method is relatively simple and easy to understand.