In order to improve the performance of a doubly fed induction generator (DFIG) system, we put forward a high performance nonlinear passivity-based control (PBC) method on DFIG. Firstly, we build a PBC mathematical model for DFIG. We design the passive controller for the inner loop in the control system based on passivity theory. Then we calculate the rotor’s control voltages which are modulated afterwards to pulse to control the rotor side converter. The maximal wind energy capture is effectively realized. The rotor speed and DFIG currents fast track their expected values. The independent regulation of the stator active power and reactive power is achieved. Finally we perform simulations to verify the effectiveness of the proposed method. Furthermore, we employ the Wigner-Ville distribution (WVD) and continuous wavelet transform (CWT) as two time-frequency representation methods to indicate that the proposed method in the paper performs well from the perspective of energy distribution in time and frequency domain.

Recently, owing to the depletion of fossil fuels such as oil, natural gas, and coal, and the serious environmental pollution caused by fossil fuels burning, the development and utilization of wind energy which is renewable and completely green is of great significance throughout the world. The doubly fed induction generator (DFIG), which can operate on variable-speed constant-frequency (VSCF) mode, has been widely studied revealing its excellent performance [

Compared to the traditional vector control method, the passivity-based control (PBC) theory has shown superior control performance. From the point of view of energy, PBC theory seeks the energy function related to the controlled variable. Based on the designed passive controller, the energy function tracks the expected energy function so as to achieve the control objective. In detail, the reactive component in the energy dissipation of the system is configured in order to force the system’s total energy to track the expected energy function. Therefore, the stability of the system is ensured, and the system’s state variables asymptotically converge to their set values, and also the outputs of the controlled object asymptotically converge to their desired values. Compared to the linearization control method, the superiority of the PBC method lies in the designed passive controller which focuses on the natural properties of the object. Accordingly, the system’s robustness is effectively improved, and the control law designed for PBC controller ensures that the system is globally stable with no divergent singular point.

Based on the above advantages of PBC theory, passivity control of an asynchronous motor has been studied and some significant progress has been made [

In order to solve the above problems, in this paper we propose a nonlinear PBC method with high performance for the DFIG system. We build the PBC model of a DFIG and prove its passivity. Then we design the passive controller for the inner loop based on passivity theory. Furthermore, we perform simulation experiments to verify the effectiveness of the proposed method.

On the other hand, DFIG system signals are time series signals. Time series analysis has attracted a great deal of attention from different research fields. Time-frequency representation can simultaneously present the energy characteristics in time and frequency plane. In this paper we implement the Wigner-Ville distribution (WVD) and continuous wavelet transform (CWT) as two time-frequency representation methods to analyze the DFIG system’s signals. The results indicate that our proposed method performs well from the perspective of energy distribution in time and frequency domain.

The organization of this paper is as follows. Section

The VSCF DFIG wind power generation system is shown in Figure

Schematic diagram of the DFIG wind power generation system.

According to the aerodynamics principle, for a given wind speed

We define the wind energy utilization coefficient

The tip speed ratio

When the blade pitch angle

Corresponding to

Figure

Schematic diagram of the two-phase rotating reference frame.

The voltage equation is

The flux-linkage equation is

Substituting (

The electromagnetic torque equation is

The motion equation of the DFIG is

Based on PBC theory, from (

From the above, we can see that

When the system works, there exists a winding capacitance effect between the stator winding and rotor winding. Because its value is small, we ignore this winding capacitance effect in the following. The energy function

By derivation of (

Since the matrix

Through integration of (

In order to achieve a stator flux linkage orientation, the control objectives for the DFIG system are as follows:

Electromagnet torque asymptotic track:

Stator flux linkage orientation and asymptotic track:

In the two-phase rotating reference frame, the expected electromagnetic torque is calculated as follows:

From the control objectives, we have

In the control system based on stator flux linkage orientation, the stator’s active power and reactive power are in direct proportion to the active component and reactive component of the stator current, respectively.

We describe the expected stator’s reactive power

Thus, the

We define the expected state variables

In accordance with (

We calculate the eigenvalues of the matrix

We know that

By derivation of (

According to Lyapunov stability theory, if

Then, from the condition

Substitute

In order to reach a satisfactory dynamic performance, that is to say, to have fast convergence to the expected value, we add a damper to (

According to the theory above, we construct the schematic diagram of a passivity-based control for the DFIG system shown in Figure

Schematic diagram of the passivity-based control for the DFIG system.

In order to verify the effectiveness of our proposed strategy, according to the theory above, we construct a simulation model of the wind power generation system using MATLAB/SIMULINK. The simulation condition is as follows. The initial wind speed is 3 m/s. At

Simulation results: (a) actual rotor speed and expected rotor speed waves of the DFIG, (b) rotor current wave, (c) stator current wave, (d)

Figure

Figure

Figure

Figure

From the above simulation results we have acquired the signals of the DFIG. We use WVD and CWT to analyze these signals to demonstrate the effectiveness of our proposed method from the perspective of energy distribution in time and frequency domain. The WVD of a signal

We can also express the frequency-domain WVD of

In order to test the signal’s additivity property, we have written a WVD program in MATLAB. The test signal is

WVD of the test signal.

The analyzing function of continuous wavelet transforms (CWT) is a wavelet

More details on the WVD and CWT methods can be found in [

WVD results: (a) WVD of the rotor current signal and (b) WVD of the stator current signal.

CWT results: (a) CWT of the rotor current signal and (b) CWT of the stator current signal.

Regarding the results of the WVD, from Figure

The primary frequency of the stator current signal in Figure

Turning to the results based on CWT, Figure

The CWT result of stator current signal in Figure

In order to improve the performance of the DFIG system, in this paper, we have investigated and proposed a nonlinear PBC strategy on the DFIG. We have built a PBC model of the DFIG in a two-phase rotating reference frame and designed the passive controller for the inner loop. Then we have calculated the rotor control voltages. Furthermore, our simulations and time-frequency representation results have verified that the rotor speed and DFIG currents fast track their expected values and that the independent regulation of stator active power and reactive power is achieved. In summary, we have drawn the following conclusions:

The proposed method is simple and has strong robustness.

The static and dynamic performances of the whole system have been improved.

The independent regulation of the stator active power and reactive power has been achieved.

Both time-frequency representation methods (WVD and CWT) can be successfully used to analyze the DFIG system’s signals.

In this paper, we have chosen time-frequency representation to analyze our signals aiming to observe the energy distribution in time-frequency plane. We also note the recent development on nonlinear time series analysis. Methods such as recurrence plots [

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work has been supported by “the Fundamental Research Funds for the Central Universities (2014MS89) and (13MS72)” and “the Natural Science Foundation of Hebei Province (E2015502012)”.