Grid voltage swell will cause transient DC flux component in the doubly fed induction generator (DFIG) stator windings, creating serious stator and rotor current and torque oscillation, which is more serious than influence of the voltage dip. It is found that virtual resistance manages effectively to suppress rotor current and torque oscillation, avoid the operation of crowbar circuit, and enhance its high voltage ride through technology capability. In order to acquire the best virtual resistance value, the excellent particle library (EPL) of dynamic particle swarm optimization (PSO) algorithm is proposed. It takes the rotor voltage and rotor current as two objectives, which has a fast convergence performance and high accuracy. Simulation and experimental results verify the effectiveness of the virtual resistance control strategy.

Many studies have focused on the impact of grid voltage sags [

DFIG can achieve HVRT by increasing hardware circuits and improving system control (Figure

DFIG equivalent circuit at static stator-oriented reference frame.

In the HVRT of DFIG, converter overcurrent can be avoided by using the crowbar on the rotor side, thus rapidly increasing the generator torque and generating an uncontrollable output of active and reactive power when the grid voltage swells. To solve these problems and ensure the excellent HVRT of the DFIG, this study analyzes the electromagnetic transient course of the DFIG under the grid voltage swell and examines the control strategy of active damping in the rotor converter according to the passive damping scheme of the series resistance of the generator rotor [

DFIG equivalent circuit is shown in Figure

The symbols and their corresponding meanings are as follows:

Subscripts

The rotor voltage can be calculated from (

Under normal condition, the rotor voltage term induced by the stator flux is expressed as

The rotor voltage at rotor terminal generated by the converter is expressed as

At

The stator flux under grid voltage swell is

The stator flux of (

If

Each component of the stator flux induces a corresponding component. A small component proportional to the slip is first induced by the forced flux. The small component rotates at slip frequency and achieves some Hertz. The second component induced by natural flux is important because it is proportional to

Virtual impedance control strategy is used to enhance HVRT capability and suppress the oscillation of DFIG during grid voltage swell [

Using stator flux as state variables, rotor current and stator voltage as input variables, stator flux state equation can be expressed as

The characteristic equation is expressed as

The damping factor

Given the relatively low stator resistance of megawatt generators, DFIG have the feature of underdamping. The system is prone to oscillation when the grid voltage swells because its natural oscillation frequency is close to the grid frequency. Therefore, system damping control, including both passive and active damping controls, should be considered. Thus, the virtual resistance control strategy was employed to increase the system damping and improve the dynamic HVRT performance of DFIG.

In a DFIG electromagnetic transient process motivated by a grid voltage swell, the rotor inducts strong back electromotive force (EMF) once the grid voltage swells because the rotor resistance and leakage impedance of the MW DFIG are relatively low. This strong EMF causes rotor overcurrent. Therefore, passive damping control is introduced; that is, dynamic series resistance is allocated to the side of the generator rotor. When the grid voltage swells, the passive damping of the dynamic series resistance of this generator rotor efficiently increases the system damping, reduces the peak oscillation of the rotor current, decreases the time constant of the rotor circuit, and quickly attenuates the rotor current. However, introducing a dynamic resistance increases system loss and reduces system efficiency, thus further complicating the resistance design. Therefore, a control algorithm that imitates the dynamic resistance (i.e., active damping control) should be considered.

To address the shortcomings of the practical dynamic resistance, active damping control based on virtual resistance can be adopted under a grid voltage swell to increase system resistance and improve the HVRT of the DFIG. A structural chart of the DFIG active damping control based on virtual resistance is shown in Figure

Block diagram of the DFIG control system based on virtual resistance.

For the analysis, the rotor side voltage can be reexpressed as

Block diagram of the current control system based on virtual resistance.

The rotor current closed loop controlled object transfer function

The switching frequency of the rotor side converter is usually high; thus, the delay of inertia can be neglected to simplify the analysis:

Assume that the virtual resistance is equal to

After the introduction of virtual resistance when (

The PI controller of the rotor current loop is designed by the internal model principle; before the introduction of virtual resistance the transfer function is expressed as

After the introduction of virtual resistance, the PI controller transfer function is expressed as

Before the introduction of virtual resistance, the rotor current closed loop transfer function is expressed as

After the introduction of virtual resistance, the rotor current closed loop transfer function is expressed as

Before the introduction of virtual resistance, the disturbance transfer function is expressed as

After the introduction of virtual resistance, the disturbance transfer function is expressed as

From (

The rotor equivalent circuit based on virtual resistance.

It is known that regulating virtual resistance can change the dynamic response of the rotor current control loop during grid voltage swell. Figure

Bode graph on disturbance with and without active damping strategy.

Step response of the disturbance transfer function with and without virtual resistance.

The root locus of the disturbance transfer function with and without virtual resistance.

Without virtual resistance

With virtual resistance

The rotor current objective function is as follows:

The rotor voltage objective function is as follows:

Obviously, there are two objective functions, the current and voltage. This paper adopts the method of important objective and satisfied constraints to simply the objective functions. Let the current objective function as the first optimization goal when the grid voltage swell is less than 0.3 pu. Let the voltage objective function as the first goal when the grid voltage swell is greater than 0.3 pu. Meanwhile, make the satisfaction function as a constraint condition. The constraint value is described as follows:

In particle swarm optimization (PSO) algorithm, the particles are optimized by changing the speed and position of the particles. As the algorithm proceeds, the effective distance between particles will be diminished, and the particle concentration increased. The particles with small Euclidean distance will iterate repeatedly, prone to premature convergence and lead the PSO algorithm to the local best solution, which affect the speed of convergence and the precision of algorithm. Hence, it is necessary to adjust the particle concentration in PSO algorithm. The particle concentration is associated with the degree of similarity between particles. The degree of similarity between particles is decided by two aspects: the Euclidean distance between two particles:

When

The probability of retained particles is

The probability of retained particles is determined by the concentration and the fitness of particle

The particles with larger fitness value inevitably contain some key information. Hence, this paper adopts probabilistic method to keep some excellent particles, and then these excellent particles iterate into the next generation with large probability. It not only avoids the blind search of the algorithm but also can improve the convergence speed.

The steps to establish the excellent particle library (EPL) are as follows: after each iteration of particle swarm optimization (PSO), the PSO can produce two best solutions (denoted as fitness) which are

In a static environment, on the basis of local and global optimal solutions, the particles can finally find the optimal value in the solution space through iterative formula. But because the rotor voltage and current of doubly fed induction generator change at any time, the dynamic improvement is introduced to adapt to the changes of the current environment.

The achievement of dynamic PSO is as follows: first of all, the solution space is divided into

If

Probability to be selected is related to the concentration of the particles. Both the current and voltage in the objective function are to find the minimum values, so opposite to (

The detailed algorithm simulation steps are as follows.

Initialize the particle parameters, which include the searching space, the particle numbers

Establish the EPL according to (

Supposing the EPL is made up of

The velocity and position of each particle are updated by the following equation:

Regulate the particle concentration. Select

Use the excellent particles in EPL to replace the particles of larger fitness. In this way a new generation of particle swarm is generated, and then go to Step

End the iteration.

Supposing the initial voltage of the stator

Fitness curve.

From Figure

Through the comparison of three kinds of PSO algorithm, this paper put forward the EPL of the dynamic PSO algorithm by modifying the distance between the particles, adjusting the particle concentration, avoiding the repeated computation in the process of PSO algorithm, and saving a lot of time to make the algorithm fast convergence.

In conclusion, the EPL of dynamic PSO algorithm is suitable for calculating the virtual resistance values in different rotor speeds and different voltage swells. In practical application, the virtual resistance can be selected according to the current rotor speed and voltage swell.

Simulations were performed using MATLAB based on the system configuration shown in Figure

Figures

Rotor current, voltage with variable damping control in subsynchronization.

Rotor current and voltage with 0.5 pu virtual resistance

Rotor current and voltage with 1.5 pu virtual resistance

Rotor current, voltage with variable damping control in synchronization.

Rotor current and voltage with 0.5 pu virtual resistance

Rotor current and voltage with 1.5 pu virtual resistance

Rotor current and voltage with variable damping control in supersynchronization.

Rotor current and voltage with 0.5 pu virtual resistance

Rotor current and voltage with 1.5 pu virtual resistance

Experimental tests of the virtual resistance control strategy were performed on a laboratory setup of the 11 Kw DFIG system to further verify the effectiveness of the proposed strategy. A 15 Kw AC motor driving the DFIG at desired speed was used to emulate wind turbine. A TMS320LF28335 DSP was employed to control the rotor side converter and the grid side converter. The switching frequency for both converters was set at 5 kHz, with a sampling frequency of 10 kHz. PM100CLA120 was used for the switching device. The waveforms are acquired by a DPO4032 digital oscilloscope.

The main parameters of DFIG are as follows: the stator resistance

Figures

Rotor current and voltage with variable damping coefficient in subsynchronization.

Rotor current and voltage with 0.5 pu virtual resistance

Rotor current and voltage with 1.5 pu virtual resistance

Rotor current and voltage with variable damping coefficient in synchronization.

Rotor current and voltage with 0.5 pu virtual resistance

Rotor current and voltage with 1.5 pu virtual resistance

Rotor current and voltage with variable damping coefficient in supersynchronization.

Rotor current and voltage with 0.5 pu virtual resistance

Rotor current and voltage with 1.5 pu virtual resistance

This paper analyzes the DFIG electromagnetic transient process under a grid voltage swell, introduces active damping control to DFIG rotor excitation control based on passive damping control, and proposes an improved control strategy for variable damping and the acquisition of virtual resistances on the basis of the EPL of dynamic PSO algorithm. Due to the rapidity and accuracy of the algorithm, the virtual resistance value is more accurate. The control method based on active damping inhibited the rotor current oscillation caused by the grid voltage swell, reduced the effect of electromagnetic torque oscillation in the system during HVRT, and reduced the crowbar motion and its adverse effects. Variable damping control over the effect of different rotation speeds and the range of grid voltage swell in the system improved the HVRT control of DFIG.

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

The project was supported by National Natural Science Foundation of China (51277050).