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Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator



S. Babainejad and R. Keypour
 
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ABSTRACT

This study depicted the effect of electrical parameters of the induction generator on the transient voltage stability of a variable speed wind turbine. The dynamic behavior of a variable speed wind turbine connected to a simple network is tested and evaluated. The model of the variable speed wind turbine with doubly fed induction generator which has been developed as a compact block in the simulation tool MATLAB/SIMULINK, is used in this study for studding the dynamic behavior of the wind turbine. The simulation includes the induction generator, the aerodynamic model of the wind turbine rotor, the model of the convertor and the pitch control system. Using this model, a three phase fault is applied at the terminal of the wind turbine. The effect of the induction generator on the voltage stability of this simple case is evaluated and discussed. The considered parameters are the rotor resistance, the stator resistance, the leakage stator and rotor inductances and the mutual inductance. For each parameter, the terminal voltage, the generator rotor speed and the DC voltage of the converter are drawn. The results will be helpful to illustrate the transient stability phenomena in wind farms.

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  How to cite this article:

S. Babainejad and R. Keypour, 2010. Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator. Trends in Applied Sciences Research, 5: 267-278.

DOI: 10.3923/tasr.2010.267.278

URL: https://scialert.net/abstract/?doi=tasr.2010.267.278
 

INTRODUCTION

The worldwide concern about environmental pollution and the possible energy shortage has led to increasing interest in generation of renewable electrical energy. Wind energy generation is one way of electrical generation from renewable sources that uses wind turbine generators to convert the energy contained in flowing wind into electrical energy. Many different types of wind turbines exist in the electricity networks all over the world specially the variable speed types (Melício and Mendes, 2004; Sandra et al., 2008; Dusonchet et al., 2008; Yi and Ula, 2008; Slootweg et al., 2002). Although, fixed speed wind turbines are cheaper and simpler than the variable speed wind turbines (Dusonchet et al., 2008) but the ability of adaption the rotor speed to the actual wind speed in order to maximize energy production causes increasing interest in variable speed wind turbines specially in Doubly Fed Induction Generator Wind Turbine (DFIGWT). In recent years (Melício and Mendes, 2004). As a result of this, in the next future, these kinds of wind turbines may start to influence the behavior of electric power systems by interacting with conventional generation and loads. Voltage stability is one of the important subjects in power system stability studies (Kundur, 1994; Petru and Thiringer, 2002; Slootweg et al., 2001) and many trials have been made in this field to make the power system less sensitive to different electrical parameters in order to keep the power system stable after different faults occurred (Kundur, 1994; Heier, 1998; Dusonchet et al., 2008; Slootweg et al., 2002). In order to investigate the impact of wind turbine on power system dynamics, adequate simulation models are essential. This study describes the effect of electrical parameters of the induction generator on the transient voltage stability of a variable speed Wind Turbine with Doubly Fed Induction Generator (WTDFIG) connected to a simple grid. The model of WTDFIG has been implemented in the simulation tool MATLAB/SIMULINK. The simulation includes the induction generator, the shaft system, the aerodynamic model of the wind turbine rotor, the model of convertor system and the pitch control system.

MATERIALS AND METHODS

The study was conducted from March, 2009 to November, 2009.

Wind Turbine Model
The WTDFIG model is base on the following:

The induction generator is represented by the following Eq. 1 (Kundur, 1994):

Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
(1)

The stator electric values are indicated by the subscript s and the rotor electric values are indicated by the subscript r. v is a voltage, R is a resistance, I is a current, λ is a flux linkage. ω is the stator electrical frequency and s is the rotor slip. The flux linkages are given by Eq. 2 (Kundur, 1994):

Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
(2)

Ls, Lr and M are, respectively the stator and the rotor leakage inductance and the mutual inductance between the stator and rotor. The mutual inductance is shown by Lm in the rest of the study. The stator and rotor active power (Kundur, 1994; Melício and Mendes, 2004) are given by Eq. 3:

Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
(3)

The mechanical torque and the electrical torque are computed as follows Eq. 4 (Kundur, 1994; Melício and Mendes, 2004):

Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
(4)

The shaft system can be represented with lumped-mass system or the two-mass shaft model, in order to show the electromechanical interactions in the voltage stability (Akhmatov, 2003a). The electromechanical interactions are expressed by oscillations of the voltage, the generator current, the generator rotor speed and electromechanical parameters of the WTDFIG. The model equation of lumped-mass system in p.u. system is Eq. 5 (Dusonchet et al., 2008):

Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
(5)

The mechanical power of the turbine can be defined as Eq. 6 (Akhmatov, 2003b; Slootweg et al., 2002):

Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
(6)

where, ρ is the air density, D is the diameter of the area covered by the movement of the blades, v is the wind speed, cp is the power coefficient (Akhmatov, 2003b; Slootweg et al., 2002) cp(β,λi) is given by Eq. 7:

Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
(7)

Where:

Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
(8)

And:

Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
(9)

λ is the tip speed ratio, β is the pitch angle of rotor blades in degrees.

The wind turbine and the doubly fed induction generator are shown briefly in Fig. 1.

The relation between cp and λ is normally established by the cp/λ curve. The cp/λ characteristics, for different values of the pitch angle, are shown in Fig. 2.

To connect a variable speed wind turbine to the grid, always a power electronic converter is necessary. This causes extra investment and additional losses (Mutschler and Hoffmann, 2002). On the other hand, with converter-fed variable speed wind turbine, adaption of the rotor speed to the actual wind speed in order to maximize energy production would be possible (Mutschler and Hoffmann, 2002).


Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
Fig. 1:

Schematic of doubly fed induction generator wind turbine

Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
Fig. 2:

Performance coefficient versus tip speed ratio characteristics, for different values of the pitch angle


Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
Fig. 3:

Schematic of generic control loop

The voltage or the reactive power at grid terminals is controlled by the reactive current flowing in the converter of the generator side as shown in Fig. 3.

The converter of the grid side is used to regulate the voltage of the DC bus capacitor as shown in Fig. 3. In addition, this model allows using the grid side converter to generate or absorb reactive power.

The pitch angle is kept constant at zero degree until the speed reaches point D speed of the tracking characteristic. Point D shows the maximum speed that the wind turbine could work in. WTDFIG could work form 0.7 p.u. till 1.2 p.u. of the nominal speed of the induction generator. Point D is equal to 1.2 p.u. of the nominal speed of the generator. Beyond point D the pitch angle is proportional to the speed deviation from point D speed. For those speeds which are above point D the pitch angle would be set at the maximum degree and for those beyond point D, it would be set at 0 degree as shown in Fig. 4.

The blade-angle is between the minimal value, βmin = 0 degree and the maximal pitch value, βmax = 24 degree.

The induction generator is connected to a low voltage stiff grid through a transformer and line impedance, Z.

Using the described model above, a three-phase fault is applied close to the wind turbine and would be cleared automatically by fixing the transition times in the related block. The effect different electrical parameters of the induction generator on the voltage stability of this simple case is evaluated and discussed. The considered parameters are the stator and rotor resistance, the leakage stator and rotor inductance and the mutual inductance. For each parameter, the terminal voltage and the generator rotor speed are drawn.

Case Study
The parameters of the WTDFIG, the transformer and the electric line are listed in Table 1-3.


Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
Fig. 4:

The pitch angle controller block

Table 1:

Generator specifications

Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator

Table 2:

Grid specifications

Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator

Table 3:

Wind turbine specifications

Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator

RESULTS AND DISCUSSION

Stator Resistance
The effect of different values of stator resistance is shown in Fig. 5a-c. The model is tested for different values of resistance (Rs1, Rs2, Rs3) and the following results are obtained for a fault clearing time 0.2 sec. The considered stator resistance values are:

Rs1= Rs/2 = 0.024 p.u.
Rs2= Rs = 0.048 p.u.
Rs3= 2Rs = 0.096 p.u.

where, Rs is the rated stator resistance of the modeled generator. The goal is to test the transient behavior of the model in the values above and beyond this nominal resistance.

As is shown in the Fig. 5. The system is more unstable when stator resistance increases. The lumped-mass shaft model is used in the simulation; therefore, the rotor speed oscillations are not that much noticeable. The rotor speed oscillations were more obvious if the tow-mass model was taken in to account (Dusonchet et al., 2008). A fixed speed wind turbine shows the same reaction to increase of the stator resistance (Dusonchet et al., 2008), so the both kind of wind turbine become more unstable when stator resistance increases but the fluctuations of the terminal voltage and rotor speed are more obvious in WTDFIG. Ac voltage schematic in Fig. 5 shows that the system needs much more time to become stable after the fault occurrence when the stator resistance increases.

Leakage Stator Inductance
The effect of different values of stator reactance is shown in Fig. 6a-c. The model is tested for different values of reactance (Ls1,Ls2,Ls3) and the following results are obtained for a fault clearing time 0.2 sec. The considered stator resistance values are:

Ls1= Ls/2 = 0.038 p.u.
Ls2= Ls = 0.076 p.u.
Ls3= 2Ls = 0.152 p.u.

where, Ls is the rated value of the stator inductance assumed in the simulation. The purpose is to test the transient behavior of the model in the values above and beyond this nominal inductance.

As shown in Fig. 6, voltage stability decreases for decreased values of stator inductances. As described earlier that the system is more stable when lumped-mass shaft system is used in the model. Oscillation in the shaft system, excited by the grid disturbance, can lead to fluctuation of the generator rotor speed and also to fluctuations of the electric parameters of the induction generator in two-mass model (Dusonchet et al., 2008).

Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
Fig. 5:

(a-c) Terminal voltage, generator rotor speed and DC voltage of the convertor, respectively after three-phase short circuit fault for different values of stator resistance


Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
Fig. 6:

(a-c) Terminal voltage, generator rotor speed and DC voltage of the convertor, respectively after three-phase short circuit fault for different values of stator inductance


Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
Fig. 7:

(a-c) DC voltage of the convertor, terminal voltage and generator rotor speed, respectively with better visualization for different values of stator inductance

In comparison with fixed speed wind turbine which become more stable when the stator reactance decreases (Dusonchet et al., 2008), the WTDFIG become more unstable in the same situation. Figure 7a-c show the DC voltage of the convertor, terminal voltage and rotor speed with better visualization.

Mutual Inductance
The effect of different values of stator resistance shown in Fig. 8. The model is tested for different values of resistance (Lm1, Lm2, Lm3) and the following results are obtained for a fault clearing time 0.2 sec. The considered stator resistance values are:

Lm1= Lm/2 = 1.9 p.u.
Lm2= Lm = 3.8 p.u.
Lm3= 2Lm = 7.6 p.u.

where, Lm is the rated value of the mutual inductance, assumed in the simulations.


Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
Fig. 8:

(a-c) Terminal voltage, generator rotor speed and DC voltage of the convertor, respectively after three-phase short circuit fault for different values of mutual inductance

As shown in(Fig. 8a-c), the system is more unstable when mutual inductance increases. A fixed speed wind turbine becomes more stable in the same situation (Dusonchet et al., 2008).

Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
Fig. 9:

(a-c) DC voltage of the convertor, generator rotor speed and terminal voltage, respectively after three-phase short circuit fault for different values of rotor inductance


Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator

Fig. 10:

(a-c) DC voltage of the convertor after three-phase short circuit fault for different values of rotor inductance

Rotor Inductance
Figure 9a-c show the voltage fluctuation and generator rotor speed for different values of the rotor inductance (Lr1, Lr2, Lr3). The three-phase short circuit fault occurs at t = 10 sec close to the wind turbine and would be cleared 0.2 sec later.

The considered rotor inductance values are:

Lr1= Lr/2 = 0.06 p.u.
Lr2= Lr = 0.12 p.u.
Lr3= 2Lr = 0.24 p.u.

where, Lr is the rated value of the rotor inductance, assumed in the simulation.

Figure 10a-c shows the DC voltage of the convertor, terminal AC voltage and rotor speed with better visualization. In this case the system is more unstable when rotor inductance decreases. A fixed speed wind turbine shows the different behavior in the same case. It becomes more unstable when the rotor inductance increases and the fluctuations of the terminal voltage and generator rotor speed are more obvious in a fixed speed wind turbine (Dusonchet et al., 2008).

Rotor Resistance
At last, the same test is done for different value of rotor resistance (Rr1, Rr2, Rr3) and the following results are obtained.

Rr1= Rr/2 = 0.09 p.u.
Rr2= Rr = 0.12 p.u.
Rr3= 2Rr = 0.24 p.u.

where, Rr is the rated value of the rotor resistance, assumed in the simulation.

In comparison with a fixed speed wind turbine which becomes more stable when rotor resistance increases (Dusonchet et al., 2008) a variable speed wind turbine with doubly fed induction generator becomes more unstable (Fig. 11a-c).


Image for - Analysis of Transient Voltage Stability of a Variable Speed Wind Turbine with Doubly Fed Induction Generator Affected by Different Electrical Parameters of Induction Generator
Fig. 11:

(a-c) Generator rotor speed, DC voltage of the convertor and terminal voltage, respectively after three-phase short circuit fault for different values of rotor resistance

CONCLUSIONS

The effect of different electrical parameters of the induction generator on the voltage stability of this simple case after applying a short-circuit fault close to the wind turbine, has been evaluated and discussed in this study. Voltage stability depends on the induction generator parameters, such as the stator resistance, the stator reactance, the mutual reactance, the rotor resistance and the rotor reactance. In comparison of a fixed speed wind turbine which needs reduced stator resistance, stator reactance and rotor reactance and increased mutual reactance and rotor resistance (Dusonchet et al., 2008) for an increase of voltage stability, a decrease of voltage stability in a doubly fed induction generator wind turbine is occurred when there is increased stator resistance, decreased stator inductance, increased mutual inductance, decreased rotor inductance and increased rotor resistance. So these two kinds of wind turbines show opposite reactions to the same variances in all of the electrical parameters of an induction generator except stator resistance. The voltage oscillations were completely clear in AC and DC voltage diagrams after a three phase fault is applied. Because of using lumped-mass shaft system the fluctuations in rotor speed weren’t noticeable. According to similar studies (Dusonchet et al., 2008) using two-mass shaft system makes the model more unstable, but for further comparisons the model needs to be developed for two-mass shaft system.

ACKNOWLEDGMENT

The authors would like to express their appreciation to Elecrtical Department Laboratory of Semnan University for providing facilities of this study and also the reviewers for their helpful comments.

REFERENCES

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