This paper proposes an alternative robust observer-based linear control technique to maximize energy capture in a 4.8 MW horizontal-axis variable-speed wind turbine. The proposed strategy uses a generalized proportional integral (GPI) observer to reconstruct the aerodynamic torque in order to obtain a generator speed optimal trajectory. Then, a robust GPI observer-based controller supported by an active disturbance rejection (ADR) approach allows asymptotic tracking of the generator speed optimal trajectory. The proposed methodology controls the power coefficient, via the generator angular speed, towards an optimum point at which power coefficient is maximum. Several simulations (including an actuator fault) are performed on a 4.8 MW wind turbine benchmark model in order to validate the proposed control strategy and to compare it to a classical controller. Simulation and validation results show that the proposed control strategy is effective in terms of power capture and robustness.

The use of wind energy has a history of over a hundred years. Its applications include agriculture, milling, water pumping, and power production. In the 1970s, this technology started developing as an experimental technology. Nowadays, the conversion of wind energy into electrical energy by wind turbines is a mature technology that exhibits the highest growth rates among the renewable energy sources [

The main objective of wind turbines is to convert efficiently wind energy into electrical power. There are wind turbines available in a different number of configurations (vertical axis, horizontal axis, fixed speed, variable speed, etc.). The most used type for large-scale power production is the variable-speed horizontal-axis wind turbine (HAWT) with a two- or three-blade rotor [

Modern wind turbines are machines that require big efforts when maximizing wind energy capture, not only because of their highly nonlinear aerodynamics, but also because of the high efficiency required even when model uncertainties, external perturbations, or system faults are present. As a consequence, the efficiency of both power capture and power generation is strongly dependent on the selected control method [

A large number of control schemes to find the best way of solving the energy capture maximization problem for wind turbines at low-to-medium wind speeds have been proposed (see, e.g., [

Generalized proportional integral (GPI) control technique was started in 2000 by Fliess et al. [

GPI observer-based control of nonlinear uncertain systems is very much related to methodologies known as disturbance accommodation control (DAC) and active disturbance rejection control (ADRC). These approaches deal with the problem of cancelling, from the controller’s actions, endogenous and exogenous unknown additive disturbance inputs affecting the system. Perturbation effects are made available via a suitable linear or nonlinear estimation. The reader is invited to read the works by Johnson [

This work presents an alternative linear control technique based on GPI observers to maximize wind energy capture in variable-speed wind turbines operating at partial load. The proposed strategy uses a GPI observer to reconstruct the aerodynamic torque in order to provide a generator speed optimal trajectory to a robust GPI observer-based controller that regulates the power coefficient, via the generator torque, towards an optimum point at which the power coefficient is maximum. It is expected that the proposed GPI observer-based control technique adds robustness to the system and solves the control problem through linear active estimation and rejection of nonlinearities and perturbations of the wind energy conversion system (WECS).

This paper is organized as follows. In Section

Consider a wind turbine represented by a two-mass mechanical system as shown in Figure

Mechanical and aerodynamical characteristics of the wind turbine.

The power converter and generator dynamics are given by [

The following assumptions in relation to the system (

All the parameters of the WECS are known.

The pair

The generator angular speed

For sufficiently large positive integer

For a partial load-operating regime (operation in region 2), the main control objective is the maximization of wind power capture. This objective has a strong relation with the wind turbine power coefficient curve

In order to obtain the optimal reference

Given a positive integer

Now, the disturbance states

The next step is to design a GPI observer for the composite system in (

ADR-GPI observer-based controllers use an internal model approximation of the perturbation functions to reconstruct and reject the perturbations. Under this disturbance model approximation setting, several authors have applied it to different areas. Parker and Johnson used a first-order perturbation approximation to model wind speed perturbations in a wind turbine operating in region 3 [

The parameter

Supposing that Assumptions

By subtracting the proposed observer (

In order to obtain an ultimate bound for

GPI observers are bandwidth limited by the roots location of the estimation error characteristic polynomial. Generally, the larger the observer bandwidth is, the more accurate the estimation will be. However, a large observer bandwidth will increase noise sensitivity. Then, the selection of the roots of the estimation error characteristic polynomial affects the bandwidth of the GPI observer and also the influence of measurement noises on the estimations. Therefore, GPI observers are usually tuned in a compromise between disturbance estimation performance (set by the internal model approximation degree) and noise sensitivity.

Based on (

In relation to the simplified system (

For a sufficiently large positive integer

The unknown input perturbation

Then, it is possible to augment the simplified system in (

It is desired that the generator angular speed

Given Assumptions

By subtracting the proposed GPI observer (

Following the same idea of the proof of Theorem

Assume that there is an accurate estimation of

Such law asymptotically and exponentially forces the closed loop system tracking error

By replacing (

Since the relative order of the WECS is one and system order is three, zero dynamics come into play and in consequence are analyzed. Considering the third-order system dynamics defined in (

Note that for the GPI observer-based control strategy defined in (

The simulations are carried out using a benchmark model for wind turbine control implemented in MATLAB/Simulink. This benchmark model was published by Odgaard et al. in [

For wind speeds between 0 and 12.5 m/s, the turbine is controlled to operate in region 2. The wind profile used has an average hub-height wind speed of 8.68 m/s and a turbulence intensity of 12%. The test bench defines a standard torque control strategy for the operation in region 2 with the following control law:

The proposed aerodynamic torque GPI observer (

GPI observer for aerodynamic torque estimation:

GPI observer-based control:

Closed loop system schema of the proposed control strategy.

The estimate of the aerodynamic torque obtained by the GPI observer in (

Aerodynamic torque estimation results: (a) aerodynamic torque, (b) generator speed optimal trajectory, (c) aerodynamic torque estimation error, and (d) generator speed trajectory estimation error.

The simulation results of the proposed control strategy are shown in Figure

Simulation results of the proposed GPI observer-based control: (a) wind profile, (b) generator angular speed, (c) tracking error, (d) aerodynamic power captured, and (e) power coefficient.

Figures

The performance of each control system is compared using an aerodynamic efficiency index

The benchmark model [

The fault considered is an offset, denoted as

Figure

Simulation results on power converter fault.

It is observed in Figure

In this paper, a linear active disturbance rejection control strategy based on two GPI observers for maximum wind energy capture of variable-speed wind turbines operating at partial load has been proposed. In order to create the generator speed optimal trajectory towards an optimum point at which the WECS power coefficient is maximum, an ADR philosophy-based GPI observer was developed to estimate the aerodynamic torque and its first derivative. Then, an ADR philosophy-based GPI observer-based controller was designed, and it was able to absolutely and arbitrarily bound the generator speed tracking error.

The proposed design strategy solved the control problem based on linear active estimation of possible nonlinearities and perturbations of the WECS, and these accurate estimations were used by a simplified linear control law, in which the captured wind energy was maximized.

It was shown through simulation tests on a fully nonlinear benchmark model that the proposed dual GPI observer control strategy maximized the captured wind energy even when an actuator fault was applied. This is a demonstration of some robustness added by the GPI observer-based control.

Since performance of wind turbines is significantly affected by the used control strategy, considering new alternative linear control strategies that can improve the performance of the WECS is a motivation to use, adapt, and evaluate linear GPI observer-based controllers to operate wind turbines at partial load.

It is worth noting that the proposed control strategy is related to exact feedback linearization, but there are some important differences between both strategies which give advantages to GPI observer-based control, such as the following: (a) GPI observer-based control does not require system state measurements, (b) any mismatch between the system model and the real system is lumped together in a perturbation function that is estimated and rejected on line, (c) GPI observers are capable of estimating a certain number of perturbation function derivatives (useful to determine