Reactive Power Capability of the Wind Turbine with ... - IEEE Xplore

Reactive Power Capability of the Wind Turbine with Doubly Fed Induction Generator J. Tian1, 2, Student member IEEE, C. Su1, Member, IEEE, and Z. Chen1, Senior member, IEEE 1 Dept. Energy Technology, Aalborg University, 9220, Aalborg, Denmark 2

[email protected], [email protected], [email protected]

Sino-Danish Centre for Education and Research, 8000, Aarhus, Denmark

Abstract— With the increasing integration into power grids, wind power plants play an important role in the power system. Many requirements for the wind power plants have been proposed in the grid codes. According to these grid codes, wind power plants should have the ability to perform voltage control and reactive power compensation at the point of common coupling (PCC). Besides the shunt flexible alternating current transmission system (FACTS) devices such as the static var compensator (SVC) and the static synchronous compensator (STATCOM), the wind turbine itself can also provide a certain amount of reactive power compensation, depending on the wind speed and the active power control strategy. This paper analyzes the reactive power capability of Doubly Fed Induction Generator (DFIG) based wind turbine, considering the rated stator current limit, the rated rotor current limit, the rated rotor voltage limit, and the reactive power capability of the grid side convertor (GSC). The boundaries of reactive power capability of DFIG based wind turbine are derived. The result was obtained using the software MATLAB. Keywords— DFIG, grid codes, reactive power curves, voltage control, wind turbine

I.

INTRODUCTION

As the world embraces for a sustainable energy future, renewable power generation integration into the power grid is increasing rapidly. Among these renewable energy technologies, wind energy is the most rapidly growing one, and has been exploited and integrated in large scale. According to International Energy Agency, the global wind power capacity exceeds 238 GW, by the end of 2011. This is enough capacity to cover about 3% of the world’s electricity demand [1]. Nowadays, the DFIG and the permanent magnetic synchronous generator (PMSG) are the most commonly used generators in wind farms. Compared with PMSG, DFIG transfer electrical power to the grid both through the stator side and the rotor side. Since only a small part of the energy is transferred through the rotor side, the required capability of the back-to-back converter which is installed in the rotor side of DFIG is smaller than the full-scale converter used in a PMSGbased wind turbine. The stator of DFIG is connected to the grid directly, so that DFIG can compensate reactive power to the grid through its stator side [2].

978-1-4799-0224-8/13/$31.00 ©2013 IEEE

With the increasing integration of wind power into power grids, many requirements for wind power plants have been proposed in the grid codes. According to these grid codes, four most common requirements for the wind farms given by [3] are as follow: 

Active power and frequency control;



Reactive power and voltage control;



Fault ride through (FRT) capability;



Frequency and voltage operation range.

In order to fulfill these requirements, wind farm has to be able to provide a certain amount of reactive power to support the voltage control at the PCC. The conventional reactive power compensation devices like STATCOM and SVC will increase costs of the wind farm. On account of the variation of the wind speed, DFIG doesn’t operate at its full load condition all the time, so it can produce a certain amount of reactive power to the power grid. In order to fulfill the appeal of lowest possible cost and the highest possible efficiency for wind power applications, the reactive power capability of DFIG based wind turbine should be analyzed, so that advanced reactive power control strategy could be developed. The reactive power capability depends on the active power control strategy implemented in the wind turbine. Under normal operating condition, the wind turbine extracts wind energy in five separate regions as mentioned in section III. Under fault condition in the power grid, there are different control strategies. The most common used strategy is to use the crowbar system to short circuit the rotor circuit to limit the high currents in the stator and the rotor to protect the generator and the converter and provide a bypass for rotor current via a set of resistors connected to the rotor windings [4]-[5]. Another control strategy is to control the active power and reactive power directly to limit the stator current and rotor current at its safe operational regions [6]. Much research efforts have been put into the reactive power control and the voltage control at PCC in wind farms. In [7] the authors proposed a novel interface neurocontroller (INC) for coordinated control of the reactive power provided by STATCOM and grid side convertor (GSC), without considering the reactive power capability of DFIG. In [8] the

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authors proposed a coordinative control of the rotor side converter and the on-load tap changer to provide voltage control. In [9] the authors proposed that when there is a fault in the power grid, by reducing the active power production the DFIG based wind turbine can provide much more reactive power compensation to improve the system stability. In [10] the authors proposed a kind of DFIG based wind turbine reactive power control strategy during the fault period in the power grid, this analysis assume that the wind turbine is operating at its rated power. Some authors have analyzed the reactive power capability of DFIG based wind turbine. In [11] the authors investigated the influence of switching from Δ to Y coupling of the stator. In [12] the authors proposed an additional series grid-side converter connected in series with the stator winding of DFIG to ancillary compensate reactive power. A novel analysis method will be provided in this paper to obtain the reactive power capability of a single DFIG based wind turbine as the foundation of advanced reactive power control strategies. This paper will analyze the reactive power capability of a 2.4 MW DFIG based wind turbine. The analysis is based on the steady state model of DFIG, assuming that the DFIG is working at different wind speed operation point, and this analysis will be comply with an active power control strategy implemented in the wind turbine system. The result of the reactive power capability of a 2.4MW DFIG based wind turbine will consider the rated stator current limit, the rated rotor current limit, the rated rotor voltage limit, and the reactive power capability of GSC. The utilized wind turbine model and steady state DFIG model are introduced in section II. A two level PI control structure which is implemented in the wind turbine control systems is introduced in section III. The result of reactive power capability of DFIG based wind turbine is presented in section IV. And conclusions are drawn in section V. II.

1 P   πR 2C (  ,  ) v 3 t 2 p

where R is the radius of the blades,  is the air density, v is the wind velocity. The power conversion coefficient C p (  ,  ) can be expressed by (2) as a function of the blade pitch angle  and the tip-speed ratio  C p   ,    C1 (C2

1

i

 C3   C4  C5  C6 )(e

1

i

1

i

)

(2)



1

  C8 



C9 1 

(3)

3

the tip-speed ratio  is defined as 

r R

(4)

v

the constant coefficient C1 - C9 as shown in the appendix are given by [13]. With constant blade pitch angle, the maximum value of the power coefficient C p _ max would be obtained at a particular value of  , defined as opt . For maximum power point tracking (MPPT),  should be maintained at this optimal value. The maximum output power of the wind turbines Pt _ max can be expressed by Pt _ max 

1 2

(5)

ρπR 2 C p _ max v 3

Fig.2 shows the relationship between C p and  , with constant C p _ max  0.44

and opt  7.2 . All the other parameters of the wind turbine which are shown in the appendix are given by [14].

Cp

The basic configuration of a wind turbine with DFIG is shown in Fig.1. It is composed of blades, mechanical shaft system, gear-box, DFIG, crowbar, back-to-back converter, and its control system.

 C7

where

pitch angle   0 . It can be seen that

WIND TURBINE AND DFIG MODEL

(1)

0.5 0.4 0.3 0.2 0.1 0 -0.1

0 1 2 3 4 5 6 7 8 9 10 11 12 Lambda

Fig.2. Power coefficient C p versus tip speed ratio

Crowbar RSC

GSC



B. Steady State Model of DFIG The steady state model of DFIG which is shown in Fig.3 is given by [15], where Z eq / s is the equivalent impedance of the back-to-back converter.

Controller Fig.1. DFIG based wind turbine model

A. Model of the Wind Turbine Aerodynamics The mechanical power of the wind turbine can be calculated by

Assuming that the stator operates at unity power factor，the air-gap power transferred to the stator side can be calculated by

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Pag 

sTm

 3(Vs  I s Rs ) I s

P

III.

(6)

where s is the stator synchronous speed, I s is the stator current, Vs is the stator voltage, Rs is the stator winding resistance, P is the number of pole pairs, and Tm is the mechanical torque which can be calculate by Tm 

Pt

(7)

r

where r is the rotor speed. Substituting (7) into (6), the stator current can be obtained by 2

Vs  Vs  Is 

4 Rss Pt 3Pr

(8)

2 Rs

The DFIG is fed from both the stator side and the rotor side. The stator is directly connected to the grid while the rotor is fed through a back-to-back converter which consists of two fourquadrant IGBT PWM converters including the rotor-side converter (RSC) and the GSC. A. Rotor Side Converter (RSC) Control System The RSC control scheme consists of two cascaded control loops. Implementing the stator voltage oriented reference frame, the inner current control loops regulates independently the d-axis and q-axis stator current components: ids and iqs , ids is used to control the active power, iqs is used to control the reactive power. The outer control loops regulates the rotor speed and the reactive power in order to control the active power and the reactive power independently. They are implemented using PI control method. The output signal vds _ ref

and vqs _ ref are sent to the PWM block to generate the control signal of RSC. The control block diagram is shown in Fig.4.

With the calculated magnitude of the stator current, we can use the equivalent circuit in Fig.3 to find the rotor current I r

r r _ ref

and the rotor voltage Vr . The voltage across the magnetizing branch can be calculated by Vm  Vs  I s ( Rs  js Lls )

Q s _ ref

Vm js Lm

(10)

The rotor current can be calculated by Ir  Is  Im

(11)

The rotor voltage can be calculated by Vr  sVm  I r ( Rr  jss Llr )

(12)

where Rr is the rotor winding resistance, Llr is the rotor leakage inductance, the slip s can be calculated by(13)



Vs 

s  r p s

Rs jX ls

 Vm 

Im

jX lr jX m Pag

Req / s

Vr /s jX eq / s 

Fig.3. Steady state model of DFIG

vqs _ ref

reactive power of GSC. The output voltage v dr _ ref and v qr _ ref are sent to the PWM block to generate the control signal of GSC. The control block diagram of GSC is shown in Fig.5. Depending on the rotor speed, when the generator is working at its super-synchronous mode, the DFIG produce active power from the rotor side, on the contrary, when the generator is working at its sub-synchronous mode the DFIG absorb active power from the rotor side.

v dc

vdc _ ref i r

Q g _ ref Qg

RSC 

iqs _ ref

vds _ ref

B. Grid Side Converter (GSC) Control System The GSC control scheme also consists of two cascaded control loops. Implementing the stator voltage oriented reference frame, the d-axis current idr is used to control the dc link voltage to control the rotor active power transferred to the power grid, and the q-axis current iqr is used to control the

(13)

Rr / s I r

ids iqs

Fig.4. The control block diagram of RSC

where Lm is the magnetizing inductance.

Is

is

(9)

The magnetizing current can be calculated by

s

ids _ ref

Qs

where Lls is the stator leakage inductance.

Im 

DFIG CONTROL SYSTEM

   Z eq / s  

idr _ ref idr iqr

vdr _ ref

iqr _ ref

vqr _ ref

Fig.5. The control block diagram of GSC

C. Control strategy of the wind power extraction For a 2.4 MW DFIG based wind turbine control system, the power extraction as a function of the wind speed is divided into different control regions as follow:

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

When the wind speed is lower than 3.5m/s, the wind turbine is halted.



When the wind speed is in the range of 3.5-5.5m/s, keep the rotor speed at 900 rpm constant, the slip will be 0.4 as a constant, the electric power generated by the DFIG increases with the wind speed growing up.

where Ps and Qs are the stator active power and the stator reactive power.



When the wind speed is in the range of 5.5-11m/s, implement MPPT control strategy.

Sr  Vr I r  Pr  jQr



When the wind speed is in the range of 11-12.1m/s, keep the rotor speed at 1800 rpm constant, the slip will be -0.2 as a constant. The electrical power generated by the DFIG increases to its rated value with the wind speed growing up.

(18)

The rotor apparent power can be calculated by *

(19)

where Pr is the rotor active power, and Qr is the rotor reactive power. The total active power of DFIG based wind turbine can be calculated by Ptot  Ps  Pr

(20)

When the wind speed is higher than 12.1m/s, implement pitch angle control strategy, keep the rotor speed at 1800rpm constant and the DFIG works at its rated power.

The stator reactive power capability versus the total active power with the rated stator current limit is shown in Fig.6 (a).

REACTIVE POWER LIMITS

QGSC   S GSC 2  Pr 2

Considering the rated stator current limit, the rated rotor current limit, the rated rotor voltage limit, and the reactive power capability of GSC, the reactive power capability boundaries of DFIG is derived, with the output active power controlled by the strategies introduced in section III. A. Rated Stator Current Limit The stator voltage and stator current are given by Vs  Vs 0



I s  I s _ real  jI s _ imag

The total reactive power capability combining the stator reactive power capability and the GSC reactive power capability versus the total active power with the rated stator current limit is shown in Fig.6 (b).

(14) (15)

where Vs is the amplitude of Vs , I s _ real is the stator active power current component, I s _ imag is the stator reactive power current component. To get the reactive power capability boundary limited by the rated stator current, with the given wind speed v , I s _ real can be calculated by (8), then the maximum I s _ imag can be calculated by I s _ imag _ max   I s _ rate 2  I s _ real 2

(16)

s

s  NPv_ opt / R s

where N is the gearbox ratio. The rotor voltage can be obtained by (12). The stator apparent power can be calculated by

2.4 2 1.6 1.2 0.8 0.4 0 -0.4 -0.8

s=0.4 MPPT s=-0.2

3 2.5 2 1.5 1 0.5 0 -0.5 -1

s=0.4 MPPT s=-0.2

0 0.2 0.4 0.6 0.8 1

0 0.2 0.4 0.6 0.8 1

Ptot [p.u.]

Ptot [p.u.]

(a)

(b)

Fig.6. Reactive power capability with rated stator current limit

B. Rated Rotor Current Limit Combining (9), (10) and (11), (22) can be derived.

where I s _ rate is the rated stator current. Then, the rotor current can be obtained by (11). Complying with the active power control strategy intruduced in section III, combine (4) and (13) , the slip s can be calculated by

(21)

where SGSC is the capacity of the converter.

Q tot [p.u.]

IV.

The reactive power capability of GSC can be calculated by

Q s [p.u.]



*

S s  Vs I s  Ps  jQs

Ir  Is 

Vs  I s ( Rs  js Lls ) js Lm

(22)

The amplitude of rotor current can be expressed by I r  I r _ real 2  I r _ imag 2

(17)

(23)

where I r _ real is the rotor active power current component, I r _ imag is the rotor reactive power current component.

To get the reactive power capability limited by the rated rotor current, with the given wind speed v , I s _ real can be

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calculated by (8), and make I r as the rated rotor current, combining (8), (15), (22), (23), I s _ imag can be calculated. Then the total active power and the stator reactive power can be obtained by (20) and (18) separately. The stator reactive power capability versus the total active power with the rated rotor current limit is shown in Fig.7 (a).

The stator reactive power capability versus the total active power with the rated rotor voltage limit is shown in Fig.9 (a). The total reactive power capability combining the stator reactive power capability and the GSC reactive power capability versus the total active power with the rated rotor voltage limit is shown in Fig.9 (b).

s=0.4 MPPT s=-0.2

0 0.2 0.4 0.6 0.8 1

2.8 2.4 2 1.6 1.2 0.8 0.4 0 -0.4 -0.8 -1.2 -1.6

s=0.4 MPPT s=-0.2

0 0.2 0.4 0.6 0.8 1

Ptotal [p.u.] (a)

Fig.8. Rotor voltage versus total reactive power and slip

Ptot[p.u.] (b)

Qs [p.u.]

Fig.7. Reactive power capability with Rated Rotor Current Limit

C. Rated Rotor Voltage Limit Combining (12), (17) and (22), (24) can be derived. Vr  s(Vs  I s ( Rs  js Lls )) V  I ( R  js Lls )  (Is  s s s )( Rr  jss Llr ) js Lm

(24)

The amplitude of the rotor voltage can be expressed by

s=0.4 MPPT

0.2 0.5 0.8 1.1

1.5 1 0.5 0 -0.5 -1 -1.5

s=0.4 MPPT

0.2 0.5 0.8 1.1

Ptot [p.u.]

Ptot [p.u.]

(a)

(b)

Fig.9. Reactive power capability with the rated rotor voltage limit

(25)

where Vr _ real is the d-axis component of the rotor voltage, Vr _ imag is the q-axis component of the rotor voltage.

The relationship between the amplitude of rotor voltage, the total reactive power and the slip is shown in Fig.8. Comparing with the rated rotor voltage which is presented by the orange plain, it can be seen that the rated rotor voltage limits the maximum reactive power production only when the slip is larger than 0.31 which is presented by the blue wireframe, and there is no reactive power absorption limit by the rated rotor voltage.

D. Reactive Power Capbility of DFIG Complying with the active power control strategy intruduced in section III, combining the rated stator current limit, the rated rotor current limit, the rated rotor voltage limit, and the reactive power capability of GSC, the reactive power boundaries of DFIG can be derived and is shown in Fig.10. It can be seen that the reactive power production is limited by the rated rotor current and the rated rotor voltage, the reactive power absorption is limited by the rated stator current.

To get the reactive power capability limited by the rated rotor voltage, with the given wind speed v , I s _ real can be calculated by (8). Make Vr as the rated rotor voltage, combining (15), (24), (25), I s _ imag can be calculated. Then the total active power and the stator reactive power can be obtained by (20) and (18) separately.

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Qtot [p.u.] and Slip

Vr  Vr _ real 2  Vr _ imag 2

1.5 1 0.5 0 -0.5 -1 -1.5

Qtot [p.u.]

2.1 1.8 1.5 1.2 0.9 0.6 0.3 0 -0.3 -0.6 -0.9 -1.2

Q tot[p.u.]

Qs [p.u.]

The total reactive power capability combining the stator reactive power capability and the GSC reactive power capability versus the total active power with the rated rotor current limit is shown in Fig.7 (b).

1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1.2

Rated rotor voltage limit Rated rotor current limit Rated stator current limit Slip

0 0.2 0.4 0.6 0.8 1 Ptot [p.u.]

Fig.10. Reactive power capability of DFIG based wind turbine.

V.

CONCLUSION

VIII. REFERENCES

This paper analyzed the reactive power capability of a single DFIG based wind turbine. The analysis is based on the steady state model of DFIG and the active power control strategy implemented in the DFIG based wind turbine system. Considering the rated stator current limit, the rated rotor current limit, the rated rotor voltage limit, and reactive power capability of GSC, the reactive power capability of a 2.4 MW wind turbine was presented. The reactive power capability of a DFIG based wind turbine is the foundation for developing novel reactive power control strategy in wind farms to provide reactive power support according to the increasingly strict requirements of the grid codes. When there is a fault in the power grid, the wind turbine control system will change the active power production and the reactive power production and absorption to realize the low voltage ride through (LVRT) capability or high voltage ride through (HVRT) capability. In this case the reactive power capability might be different, which will be considered as the future work further this paper. VI. TABLE I.

TABLE II.

[3]

[4]

[5]

[6]

[7]

[9]

WIND TURBINE PARAMETERS value 2.4 MW 42m 3.5m/s-12.1m/s 100 0.73, 151, 0.58, 0.002, 2.14 13.2, 18.4, 0.02, 0.003 0.44, 7.2

[10]

[11]

[12] [13]

DFIG PARAMETERS

Parameter Rated Stator Power Rated Stator Phase Voltage Rated Stator Current Rated Rotor Current Rated Rotor Phase Voltage Rated Stator Frequency Rated Rotor Speed Nominal Rotor Speed Range Rated Slip, Turn Ratio Number of Pole Pairs Stator Winding Resistance Rotor Winding Resistance Stator Leakage Inductance Rotor Leakage Inductance Magnetizing Inductance

[2]

[8]

APPENDIX

Parameter Rated Mechanical Power Rotor Diameter Wind Speed Range Gearbox ratio C1, C2, C3, C4, C5 C6, C7, C8, C9 CpMax, Lambda_CpMax

[1]

value 2MW 398.4 V (rms) 1760 A (rms) 1823 A (rms) 488 V (rms) 50 Hz 1800 rpm 900-1800 rpm -0.2, 2.94 2 2.6 mΩ 2.9 mΩ 87 μH 87μH 2.5 mH

[14] [15]

VII. ACKNOWLEDGMENT The authors gratefully acknowledge the contributions of Prof. Bin Wu and Prof. Gonzalo Abad to the electric power industry.

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