As to strong nonlinearity of doubly fed induction generators (DFIG) and uncertainty of its model, a novel rotor current controller with nonlinearity and robustness is proposed to enhance fault ride-though (FRT) capacities of grid-connected DFIG. Firstly, the model error, external disturbances, and the uncertain factors were estimated by constructing extended state observer (ESO) so as to achieve linearization model, which is compensated dynamically from nonlinear model. And then rotor current controller of DFIG is designed by using terminal sliding mode variable structure control theory (TSMC). The controller has superior dynamic performance and strong robustness. The simulation results show that the proposed control approach is effective.
With the development of wind generator technology, doubly fed induction generator (DFIG) has been the dominant technology used in wind power generation systems [
At present, low voltage ride-though (LVRT) of DFIG, which is one of main content of FRT, is studied widely and many improvement approaches are provided by scholars. However, there are seldom researchers to work on overcurrent of DFIG for improving FRT, which caused by power system disturbances. When a fault occurs in power system, overcurrent in the RSC of wind turbines will threaten the generator’s security, which even lead to a serious wind turbine generators tripping accident. So it is extremely important to maintain current in the rotor side converter in the DFIG during period of disturbances. There are some means to enhance the control ability of rotor current and FRT capacity of DFIG. The schemes reported in the literatures can be divided into two categories: (1) using hardware circuit, namely, placing crowbars protection at the RSC and additional bypass resistance in the DFIG structure [
The linear system control method is based on accurate model, and it does not have the robustness with the parameters. The compensate for the shortcomings of the linear controller, the nonlinear theory is applied to control for DFIG systems. In [
The linear sliding mode surfaceis generally chosen by traditional sliding mode control. The state of the system is force to be slide according to the predetermined trajectory, and gradually converge to zero, but tracking error of state does not converge to zero in the limited time. Therefore, terminal sliding mode control is put forward by some scholars. On the basis of the sliding mode control’s stability, it tries the best to improve the convergence speed of system [
The nonlinear controller with strong robust in the power system application is also more and more researcher's attention [
The rest part of the paper is organized as follows. Section
ESO is the important composition of autodisturbances-rejection controller [
Let
Then the expansion state equation of the system (
Then from (
For an arbitrarily changing
According to the definitions in (
The control variable is selected as follows:
Taking into account the tracking error of ESO and the limiting feature of controller,
The so-called terminal sliding mode control is the new terminal sliding surface, which contains nonlinear function, making the tracking error be able to converge to zero in finite time [
The traditional form of fast terminal sliding mode is as follows:
Due to the nonlinear part
The terminal SMC form is as follows:
The sliding mode control law can be designed from (
The model of DFIG-based wind turbines is studied in [
Equivalent circuit of a DFIG in the synchronous
The stator and rotor voltage in the synchronous
The stator and rotor flux linkage can be given as [
In order to reduce the destructiveness of DFIG overcurrent in the rotor winding or large overvoltage in the
Substituting (
Based on (
Substituting (
When power system failure occurred, the controller is designed based on (
Using (
Figure
Schematic diagram of proposed rotor current controller for a grid-connected DFIG system.
In a terminal SMC design, the SMC law and switching function are mainly considered [
Based on (
With the
By differentiating on both sides of (
The nonlinear factors
Using ESO to do feedforward compensation for the disturbance term of the controller
The second-order ESO for system can be expressed as follows:
The nonlinear function is defined as follows:
As stated earlier, the ESO is an observer which can estimate the uncertainties along with the states of the system, and make the disturbance rejected or compensated:
The disturbances
The control goal of the inner current control loops of
By differentiating (
According to (
According to the global fast terminal sliding mode as (
Terminal SMC is tracking trajectory, and the terminal SMC strategy with variable control structure can solve the steady-state and dynamically state error problem introduced by the external disturbances. The disturbance can be disposed, and it is more suitable for processing rotor current control of DFIG compared to other method.
In order to weaken the chattering when state variables rapidly approaching the sliding surface,
The nonlinear factors
Based on (
So far, control law can be defined as follows:
The schematic diagram of proposed terminal sliding mode controller based on ESO (T-SMCE) is shown in Figure
Schematic diagram of proposed terminal SMC based on ESO.
Design steps are shown in Figure
Flow diagram of proposed terminal SMC based on ESO.
In order to verify the validity of the proposed method, simulations of the proposed control scheme for a DFIG-based wind power generation system were carried out. It compares FRT capabilities of the proposed rotor current controller with the conventional PI controller. A 2 MW DFIG in a wind farm is connected to the transmission system through a 20 km distribution cable. The DFIG is rated at 2 MW with its parameters given in Table
Parameters of the simulated DFIG system.
Parameters | Value |
---|---|
Rated power | 2 MW |
Line-to-line voltage | 690 V |
Stator frequency | 50 Hz |
|
0.01 p.u. |
|
0.01 p.u. |
|
0.1 p.u. |
|
0.1 p.u. |
|
3.5 p.u. |
Pole pairs | 2 |
Acceleration time constant | 0.9408278 s |
Control parameters of terminal SMC regulator.
Parameters | Value |
---|---|
|
150 |
|
50 |
|
50 |
Control parameters of PI regulator.
Parameters | Value |
---|---|
|
0.0499 |
|
0.0128 |
Control parameters of ESO regulator.
Parameters | Value |
---|---|
|
100 |
|
0.5 |
|
0.0016 |
|
300 |
|
0.25 |
|
0.0016 |
The rotor current will rise rapidly and more exceed the rate value, if there is a fault at some points inside the transmission system. Thus DFIG must be maintained to a sustained grid-connected until the fault is cleared. The control method is mainly studied in this paper, which is to reduce rotor overcurrent of DFIG under power grid disturbances. Therefore, the outer power control loops of rotor side and grid side converters are constant. The mechanical parts of wind turbine are simulated based on the optimal power-speed curve [
Assume that a three-phase short-circuit fault occurs in high voltage side bus of DFIG step-up transformer at 1 s and the failure lasts for 0.12 s. At the condition that the proposed rotor current controller has or not, we compare the voltage of grid-connected, the rotor current and electromagnetic torque of DFIG’s response to three-phase short-circuit fault respectively in Figures
The overcurrent in the rotor side converter is greatly weakened under the three-phase short-circuit fault. As shown in Figures
The possibility that a serious wind turbine generators tripping accident caused by fault is reduced. Enhanced transient performances are similar to the conventional PI. Under power system fault, the proposed approach reduced threat for generator security operation caused by the overcurrent in the rotor side converter for wind turbine. It can enhance the control ability of the rotor current and improve the stability and the grid-connected operation ability of the wind turbines. The superiority of the designed controller is verified in this paper.
The rotor current curve of a DFIG in the direct axis.
The rotor current curve of a DFIG in the quadrature axis.
The electromagnetic torque curve of DFIG.
The voltage curve of grid-connected.
When system is in the steady-state operation, a load shedding fault occurs, causing a step response, wherein the active power load in power grid suddenly sags 60% at 1 s. The voltage of grid-connected, the rotor current, and electromagnetic torque of DFIG dynamic response to load shedding without and with the proposed rotor current controller are compared in Figures
As shown in Figures
The rotor current curve of DFIG in the direct axis.
The rotor current curve of DFIG in the quadrature axis.
The electromagnetic torque curve of DFIG.
The voltage curve of grid-connected.
In order to compare original PI method with the proposed method about computation time analysis objectively, the following discussion is carried out. Due to DFIG which has overcurrent protection when the amplitude of overcurrent in the rotor side converter achieves protection threshold, it will trigger protection and seriously may lead to a wind turbine generators tripping accident for DFIG. As shown in Figures
In addition, total time taken from the control start to the standard values is defined as
The comparison analysis of
Parameters | PI | The proposed approach |
---|---|---|
|
1.26 | 1.26 |
|
1.21 | 1.21 |
|
1.22 | 1.22 |
|
1.13 | 1.14 |
The comparison analysis of
Parameters | PI | The proposed approach |
---|---|---|
|
1.28 | 1.28 |
|
1.29 | 1.29 |
|
1.27 | 1.27 |
|
1.31 | 1.32 |
The rotor current curve of a DFIG in the direct axis under three-phase short circuit fault.
Compared with the original PI control, the proposed method increased the computational burden. However, the influence on the system caused by nonlinear factors is reduced. The increasing logic judge for DFIG caused by overshoot is reduced. Thus the computational burden of the proposed method is decreasing. So the
In the simulation, a load shedding fault is happened, causing a step response with the active power load in power grid suddenly drops 10%, 30%, 60%, and 90% at 1 s, respectively. The dynamic responses of DFIG in rotor current under different load shedding proportion with the proposed ESO-terminal SMC are compared in Figure
The rotor current curve of a DFIG in the quadrature axis under different load shedding proportion.
As shown in Figure
In order to validate the influence of the experiment results caused by
The rotor current curve of a DFIG in the direct axis under different
The rotor current curve of a DFIG in the quadrature axis under different
The rotor current curve of a DFIG in the direct axis under different
In addition, when
It is proved that the ranges of
As shown in Figure
The nonlinear rotor current controller is introduced in this paper, which is designed by combining the advantages of ESO and terminal SMC theory. It enhances FRT capabilities of DFIG-based wind power generation system. ESO compensates internal and external disturbances of system dynamically and it has reduced the complexity of the controller and with strong practicability and robustness. Terminal sliding mode makes a design of controllers to simplify and improve the convergence speed. ESO-terminal SMC has the advantages of rapid response and insensitive for disturbances. A nonlinear rotor current control law with good robustness and better dynamic quality is obtained. The proposed ESO-terminal SMC has very fast transient response that will effectively eliminate the overcurrent in the rotor side converter and limit electromagnetic torque in the DFIG fluctuations, with strong adaptability. Simulation results show that the proposed rotor current control scheme enables the DFIG to successfully comply with FRT regulations. The proposed control method is easy to be realized in engineering.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors gratefully acknowledge the support of National Natural Science Foundation of China (no. 51377017) and Changjiang Scholars and Innovative Research Team in University (IRT1114).