This paper proposes an adaptive gain second-order sliding mode control strategy to track optimal electromagnetic torque and regulate reactive power of doubly fed wind turbine system. Firstly, wind turbine aerodynamic characteristics and doubly fed induction generator (DFIG) modeling are presented. Then, electromagnetic torque error and reactive power error are chosen as sliding variables, and fixed gain super-twisting sliding mode control scheme is designed. Considering that uncertainty upper bound is unknown and is hard to be estimated in actual doubly fed wind turbine system, a gain scheduled law is proposed to compel control parameters variation according to uncertainty upper bound real-time. Adaptive gain second-order sliding mode rotor voltage control method is constructed in detail and finite time stability of doubly fed wind turbine control system is strictly proved. The superiority and robustness of the proposed control scheme are finally evaluated on a 1.5 MW DFIG wind turbine system.
In the 21st century, as human population grows and nonregeneration energy is rapidly consumed, climate warming and environmental degradation problems become increasingly serious. Renewable energy such as wind energy, hydroenergy, and nuclear energy is highly favored. Particularly, wind energy, as one of the clean renewable energy sources, is attracting more and more attention [
Among the many adopted wind power technologies, doubly fed induction generator (DFIG) has been widely used in the wind power industry and dominated the market due to its excellent operating performances such as light weight, small size, highly cost effective, and small capacity of converter. In order to enhance generating efficiency, wind energy conversion optimization is one of the key issues in the DFIG wind power generation control system [
Many scholars study various control methods for optimizing wind energy conversion [
Sliding mode control is a nonlinear robust control method and has already successfully applied to doubly fed wind turbine system [
Higher-order sliding mode can cancel the requirement of compelling relative degree to be one, enhance sliding accuracy, attenuate chattering phenomenon, and make control effective continuous [
In this context, to face the stringent specifications of maximum wind power tracking and reactive power control problems of doubly fed wind turbine system where the uncertainties are subjected to fast variations, this paper proposes a new adaptive control gain second-order sliding mode scheme. It is not necessary to know the upper bound of uncertainty in advance by choosing suitable sliding function and designing adaptive gain second-order sliding mode controller. Control parameters can be adjusted according to variation of uncertainty upper bound. The control objectives of maximum wind power tracking and reactive power regulation are achieved by controlling rotor voltage, and the output chattering is greatly restrained.
This paper is organized as follows. Section
Structure diagram of doubly fed wind turbine system is shown in Figure
Schematic diagram of doubly feed wind turbine system.
According to Betz’ Law, the captured mechanical power of wind turbine is
Power conversion efficiency
Wind turbine mechanical power can also be defined as
Dynamic characteristics of doubly fed wind turbine system can be accurately described via fifth-order differential equations [
The fifth differential equation is kinematic equation:
For achieving decoupling control,
Reactive power is expressed as
In the constant power zone, the objective is to adjust pitch angle to maintain wind turbine system operating at rated power, while, in the partial load zone, the objective is to track maximum wind energy. Control objectives of this paper are to achieve maximum wind power tracking and reactive power regulation according to grid demand and tolerance range of wind power system.
The pitch angle
The relation between power coefficient and tip speed ratio.
When wind turbine operates at maximum power point (
The objective of maximum wind power tracking control is further presented as achieving
For doubly fed wind turbine system (
For tracking maximum wind power and regulating reactive power, the sliding variables are chosen as
To calculate first-order time derivative of
Then there exist positive constants
According to sufficient condition for finite time stability of super-twisting algorithm [
It is observed that uncertainty upper bounds are needed when designing rotor voltage second-order sliding mode controller, yet the upper bounds are usually unknown in practical wind power system and hard to be estimated. Overestimation of these upper bounds may lead to conservative choice of controller parameters which will produce more control effective, aggravate control chattering, and shorten service cycle of wind turbines.
Adaptive control gain can deal with unknown uncertainty upper bound problem and further restrain rotor voltage chattering. Here
Due to the existence of parameter uncertainty and external disturbance,
Carrying out feedback control for system (
In practice, parameters
Then aiming at formula (
Thus, uncertain function
Second-order sliding mode control problem of system (
Theorem
In order to achieve optimal torque tracking of doubly fed wind power system,
To bring in new state vector
Then formula (
Formula (
Considering
It is observed that if
To choose Lyapunov function
To calculate time derivative of Lyapunov function (
Considering formulas (
Considering
To guarantee positive definiteness of matrix
Then, if
In view of formulas (
Then
To combine formulas (
Considering inequation
One solution of formula (
Hence,
(
To choose
Take note that
(
It is worth noting that the expression under
The symbol
When
Namely,
Simulation verification of the proposed control scheme is carried out based on MATLAB platform. Nominal parameters of doubly fed wind turbine system are
Gradient wind speed model can be described by formulas (
Figure
Gradient wind speed.
Optimal torque tracking under fixed gain.
Reactive power regulation under fixed gain.
Optimal torque tracking under adaptive gain.
Reactive power regulation under adaptive gain.
Rotor voltage in
Rotor voltage in
Rotor current in
Control gain under adaptive gain.
The random wind speed variation is shown in Figure
Random wind speed.
Optimal torque tracking.
Reactive power regulation.
Rotor voltage in
Rotor current in
For achieving maximum wind power tracking and reactive power regulation of doubly fed wind turbine system, this paper proposed an adaptive gain second-order sliding mode control scheme. Firstly, the system model is established. Then second-order sliding mode rotor voltage controllers are designed after detailed description of the two control objectives. Considering the circumstance of unknown uncertainty upper bound, adaptive gain second-order sliding mode rotor voltages controllers are designed, and finite time stability is proved in detail. Finally, simulation experiments under gradient wind and random wind verify that the proposed control strategy can achieve optimal torque tracking and reactive power regulation and is robust to parameter uncertainties such as network voltage, network frequency, rotor resistance, and mutual inductance. The proposed control method also makes rotor control voltage continuous and the control chattering is greatly restrained.
The authors declare that they have no conflicts of interest.
This work was supported by National Natural Science Foundation of China under Grants 61375084 and 61773015, Doctoral Scientific Research Initial Foundation of Shandong Jiaotong University, Jinan Science and Technology Innovation Program of Shandong, China, under Grant 201401203, and Key Program of Natural Science Foundation of Shandong Province ZR2015QZ08.