ts-fuzzy controlled dfig based wind energy...

Abstract— This paper focuses on the implementation of the TS

(Tagaki-Sugino) fuzzy controller for the active power and the DC capacitor voltage control of the Doubly Fed Induction Generator (DFIG) based wind generator. DFIG system is represented by a third-order model where electromagnetic transients of the stator are neglected. The effectiveness of the TS-fuzzy controller on the rotor speed oscillations and the DC capacitor voltage variations of the DFIG damping controller on converter ratings of the DFIG system is also investigated. The results of the time domain simulation studies are presented to elucidate the effectiveness of the TS-fuzzy controller compared with conventional PI controller in the DFIG system. The proposed TS-fuzzy controller can improve the fault ride through capability of DFIG compared to the conventional PI controller.

Index Terms—Doubly Fed Induction Generator (DFIG), Wind Turbine (WT), dynamic system stability, TS fuzzy controller, damping controller.

I. INTRODUCTION

RECENTLY there has been a growing amount of interest in wind energy conversion systems (WECS). Among various other techniques of wind power generation, the doubly fed induction generator (DFIG) has been popular because of its higher energy transfer capability, low investment and flexible control [1]. DFIG is different from the conventional induction generator in a way that it employs a series voltage-source converter to feed the wound rotor. The feedback converters consist of Rotor side converter (RSC) and Grid side converter (GSC). The control capabilities of these converters give DFIG an additional advantage of flexible control and stability over other induction generators.

The dynamic behavior of DFIG has been investigated by several authors in the past. A third order model for transient stability using PSS/E has been reported in [2]. Furthermore, the detailed model of the grid connected DFIG has been presented in [3] whereas the modal analysis has been discussed in [4]. The change in modal properties for different operating conditions and system parameters is discussed in [4]. However, the detailed

S. Mishra is with the Department of Electrical Engineering at IIT Delhi,

India. (email: [email protected]) Y. Mishra is with the School of ITEE, The University of Queensland,

Australia and presently also a visiting scholar at The University of Tennessee, Knoxville, TN, USA. (email: [email protected]; [email protected])

Fangxing Li is with the Department of Electrical Engineering, The University of Tennessee, Knoxville, TN, USA. (email: [email protected])

Z. Y. Dong is with the Department of Electrical Engineering, Hong kong Polytechnic University, Hong Kong (email: [email protected])

model for the converters and the controllers was either neglected or overly simplified. The performance of decoupled control of active and reactive power of DFIG is presented in [5]. The control methods for DFIG to make it work like a synchronous generator and the fault ride through behavior have been reported in [6] and [7] respectively.

The DFIG control strategy is based on conventional Proportional Integral (PI) technique which is well accepted in the industry. The decoupled control of DFIG has following controllers namely Pref , Vsref , Vdcref and qcref. These controllers are required to maintain maximum power tracking, stator terminal voltage, DC voltage level and reactive power level at GSC respectively. However, the intelligent controllers like fuzzy and neural network controllers, capturing the system operators’ experience, outperform the conventional PI controllers and have been reported in the past [8-16]. The TS-fuzzy logic control has been successfully applied for UPFC in [17] for a multi machine power system.

The fuzzy logic approach provides the design of a non-linear, model free controller and hence, can be used for the coordinated control of RSC and GSC in the DFIG system. The Mamdani type fuzzy logic controller may not be able to provide superior control over a wide range of operation [18]. Instead, a Takagi-Sugeno (TS) type fuzzy controller can provide a wide range of control gain variation by utilizing both linear and non-linear rules in the consequent expression of the fuzzy rule base [18]. As new methods have been outlined for the design of TS fuzzy controllers, the purpose of this paper is to highlight the application of TS fuzzy controllers to provide regulation of the active power output and DC capacitor voltage of the DFIG. The simulation results presented highlight the effectiveness of the TS-fuzzy controller in damping rotor speed oscillations and in controlling the DC voltage variations.

According to the present grid code, the wind farm should be able to ride through any fault in the system. Hence fault ride through capability is required by the system operators as mentioned in [11]. Therefore, the contributions of this paper are: (i) to study the effectiveness of the TS-fuzzy controller on the variation of the DC voltage across capacitor and rotor speed oscillations (ii) the efficacy of the TS-fuzzy controller in improving the fault ride through capability of the system. This paper is structured as follows: Section II presents the modeling of the DFIG system. The detailed control methodology is discussed in Section III. Section IV describes the TS-fuzzy controller and its application to the DFIG. Section V discusses simulation and results followed by conclusions in Section VI.

TS-fuzzy controlled DFIG based Wind Energy Conversion Systems

S. Mishra, Senior Member, IEEE, Y. Mishra, Student Member, IEEE, Fangxing Li, Senior Member IEEE, Z. Y. Dong, Senior Member, IEEE

978-1-4244-4241-6/09/$25.00 ©2009 IEEE

Authorized licensed use limited to: UNIVERSITY OF TENNESSEE. Downloaded on October 27, 2009 at 16:57 from IEEE Xplore. Restrictions apply.

II. MODELLING OF DFIG

The grid connected single machine infinite bus system is as shown in Fig. 1. The stator and rotor voltages of the doubly excited DFIG are supplied by the grid and the power converters respectively.

Simulation of the realistic response of the DFIG system requires the modeling of the controllers in addition to the main electrical and mechanical components. The components considered include, (i) turbine, (ii) drive train, (iii) generator and (iv) the converter system.

Fig. 1. DFIG system.

A. Turbine

The turbine in DFIG system is the combination of blades and hub. Its function is to convert the kinetic energy of the wind into the mechanical energy, which is available for the generator. In general the detailed models of the turbine are used for the purpose of design and mechanical testing only.

The stability studies done in this paper do not require detailed modeling of the wind turbine blades and hence it is neglected in this paper. Inputs to the wind turbine are the wind speed, pitch angle and the rotor speed and the output from the wind turbine is the mechanical torque.

B. Drive train

In stability studies, when the response of a system subjected to any disturbance is analyzed, the drive train system should be modeled as a series of rigid disks connected via mass-less shafts. The two-mass drive train model is considered for the stability studies of DFIG system and the dynamics can be expressed by the differential equations below [4],

2 tt m sh

dH T T

dt

ω = − (1)

2 rg sh e

dH T T

dt

ω = − (2)

( )twt r B

d

dt

θ ω ω ω= − (3)

twsh tw

dT K D

dt

θθ= +

(4)

where tH and

gH [s] are the turbine and generator inertia, tω

and rω [p.u] are the turbine and DFIG rotor speed, and shT is

the shaft torque, mT is the mechanical torque and eT is the

electrical torque. twθ [rad] is the shaft twist angle, K[p.u./rad]

the shaft stiffness, and D[p.u. s/rad] the damping coefficient.

C. Generator

The most common way of representing DFIG for the purpose of simulation and control is in terms of direct and quadrature axes (dq axes) quantities, which form a reference frame that rotate synchronously with the stator flux vector [3].

''

' ''

0

1[ ( ) ]

q ms d s dr

rr

q s s qs

dE Ls E v

dx L

E X X iT

ω ω= − +

− − −

(5)

''

' ''

0

1[ ( ) ]

d ms q s q r

r r

d s s q s

d E Ls E v

d x L

E X X iT

ω ω= −

− + −

(6)

Whereas, the parameters are defined as: s s ss s mX L x Xω= = + ,

2' ( )ms s ss

rr

LX L

Lω= − and '

0rr

r

LT

R= . The algebraic equations can be

expressed as

' 's d ds q qsP E i E i= − − (7)

' 's d qs q dsQ E i E i= − (8) ' 'd s ds s qs dsE r i X i v= − + + (9) ' 'q s qs s ds qsE r i X i v= − − + (10)

where s is the rotor slip; sP is the output active power of the

stator of the DFIG; ssL is the stator self-inductance; rrL is the

rotor self-inductance;mL is the mutual inductance; sω is the

synchronous angle speed;sX is the stator reactance; sx is the

stator leakage reactance; rx is the rotor leakage reactance; 'sX is

the stator transient reactance; 'dE and '

qE are the d and q axis

voltages behind the transient reactance, respectively; '0T is the

rotor circuit time constant; dsi and qsi are the d and q axis stator

currents, respectively; dsv and qsv are the d and q axis stator

terminal voltages, respectively; drv and qrv are the d and q axis

rotor voltages, respectively;sQ is the reactive power of the stator

of the DFIG. The voltage equations and the flux linkage equations of the DFIG are based on the motor convention.

D. Converter model

The converter model in DFIG system comprises of two pulse width modulation invertors connected back to back via a dc link. The rotor side converter (RSC) is a controlled voltage source as since it injects an AC voltage at slip frequency to the rotor. The grid side converter (GSC) acts as a controlled voltage source and maintains the dc link voltage constant. The power balance equation for the converter model can be written as:

r gc dcP P P= + (11)

where rP , gcP , dcP are the active power at RSC, GSC and DC


link respectively, which can be expressed as,

r dr dr qr qrP v i v i= + (12)

gc dgc dgc qgc qgcP v i v i= + (13)

dcdc dc dc dc

dvP v i Cv

dt= = − (14)

III. CONTROLLERS FOR DFIG

This section describes the controllers used for the DFIG system. As mentioned above, there are two back to back converters hence we need to control these two converter sides. Primarily, these controllers are known as RSC and GSC controllers. For controlling the aerodynamic power beyond certain point, pitch angle controller is used. This section also introduces a new auxiliary control signal which is added to the active power control loop to enhance the damping. This is known as the damping controller.

A. Rotor side converter (RSC) controller

The RSC is used to control the wind turbine output power and the voltage measured at the grid terminals.

The power is controlled such that it follows a pre-defined power-speed characteristics, named tracking characteristic. This characteristic is illustrated by the ABCD curve in Fig. 2 superimposed to the mechanical power characteristics of the turbine obtained at different wind speeds. The speed of the turbine ωr is measured and the corresponding mechanical power of the tracking characteristic is used as the reference power for the power control loop. The tracking characteristic is defined by four points: A, B, C and D. From zero speed to speed of point A the reference power is zero. Between point A and point B the tracking characteristic is a straight line. Between point B and point C the tracking characteristic is the locus of the maximum power of the turbine (maxima of the turbine power versus turbine speed curves). The tracking characteristic is a straight line from point C and point D. The power at point D is one per unit (1 p.u.). Beyond point D the reference power is a constant equal to 1 p.u. The power control loop is illustrated in Fig. 3. For RSC, the d-axis of the rotating reference frame used for d-q transformation is aligned with air-gap flux. The actual electrical output power, measured at the grid terminals of the wind turbine, is added to the total power losses (mechanical and electrical) and is compared with the reference power obtained from the tracking characteristic. A Proportional-Integral (PI) regulator is used to reduce the power error to zero. The output of this regulator is the reference rotor current Iqr_ref, that must be injected in the rotor by the RSC. This is the current component that produces the electromagnetic torque Tem. The actual Iqr component is compared to Iqr_ref and the error is reduced to zero by a current regulator (PI). The output of this current controller is the voltage Vqr generated by the RSC. The voltage at grid terminals is controlled by the reactive power generated or absorbed by the RSC. The reactive power is exchanged with the grid, through the generator. In the exchange process, generator absorbs reactive power to supply its mutual and leakage reactance. The excess of reactive power is sent to the grid or to RSC. The control loop is shown in Fig. 4. The wind turbine control implements the V-I characteristic illustrated in Fig. 5. As

long as the reactive current stays within the maximum current values (-Imax, Imax) imposed by the converter rating, the voltage is regulated at the reference voltage Vref.

Fig. 2. Turbine characteristics and tracking characteristic.

Fig. 3.RSC active power controller

Fig. 4. RSC grid voltage controller.

B. Grid side converter (GSC) controller

The GSC is used to regulate the voltage of the DC capacitor. The control schematic is illustrated in Fig. 5. The d-axis of the rotating reference frame used for d-q transformation is aligned with the positive sequence of grid voltage. This controller consists of: (i) a measurement system measuring the d and q components of AC currents to be controlled as well as the DC voltage (

dcV ); (ii) an outer regulation loop consisting of a DC

voltage regulator. The output of the DC voltage regulator is the reference current Idgc_ref for the current regulator (Idgc is the current in phase with grid voltage which controls active powerflow); (iii) an inner current regulation loop consisting of a current regulator. The current regulator controls the magnitude and phase of the voltage generated by converter (Vgc) as shown in Fig. 6.


Fig. 5. Grid side converter control (DC capacitor voltage control).

Fig. 6. Grid side converter control (Reactive power control).

C. Pitch angle controller

The pitch angle is kept constant at zero degree until the speed reaches point D speed of the tracking characteristic. Beyond point D the pitch angle is proportional to the speed deviation from point D speed. The construction of the pitch angle controller is shown in Fig. 7.

Fig. 7. Pitch angle controller.

IV. DESIGN OF TS FUZZY CONTROLLER FOR DFIG

The fuzzy controllers are conventional non-linear controllers and can produce satisfactory results when constructed properly using the experience of the system operator. The design of fuzzy logic controller consists of (i) determining the inputs, (ii) setting up the rules and (iii) the design method for converting the rules into a crisp output signal, known as defuzzification. First of all, the input signal, in this case is the error and rate of change of error signal, is measured and depending on the crisp value of the signal, it can be expressed in terms of the degree of membership of the fuzzy sets. The shape of the fuzzy sets can be determined by the expert knowledge of the system. The next step is to construct the fuzzy rules, again based on the expert knowledge of the control problem, to accommodate all the possible combinations of memberships.

The TS-fuzzy controller differs from the Mamdani-fuzzy in its rule consequent. The linguistic rule consequent is made variable by means of its parameters. As the rule consequent is variable, the TS fuzzy control scheme can produce an infinite number of gain variation characteristics. In essence, the TS fuzzy controller is capable of offering more and better solutions to a wide variety of non-linear control problems. The

quadrature-current component of the RSC, qr refi − , and the

direct-current component of the GSC, dgc refi − , are controlled by

active power deviation and DC voltage deviation respectively as shown in Fig. 8 and Fig. 9 respectively.

Fig. 8. Rotor side controller with TS fuzzy controller.

Fig. 9. Grid side converter DC voltage controller with TS fuzzy controller. The active power and DC voltage deviations are fuzzified using two input fuzzy sets P (positive) and N (negative). The membership function used for the positive set is defined by (15) and can be represented as shown in Fig. 10.

(15)

Where, ( )ix k denotes the input to the fuzzy controller at the kth

sampling instant given by

1( ) ( ) refx k e k P P= = − or DC ref DCV V− − (16)

2 ( ) ( )x k e k= ∫ (17)

The membership functions for 1x and 2x is shown in Fig.11.

The values of 1L and

2L are chosen on the basis of the

maximum value of real power or DC voltage error and the integral of the error. The maximum value of errors and its integral is determined observing these variations by running the programs once with the PI controllers.

Fig. 10. Membership functions.


Fig. 11. TS Fuzzy control scheme with error and integral of error.

The TS fuzzy controller uses the four simplified rules as Rule 1: If

1( )x k is P and 2( )x k is P then

1 1 1 1 2 2( ) ( ( ) ( ))u k K a x k a x k= + (18)

Rule 2:

If 1( )x k is P and 2 ( )x k is N then 2 2 1( ) ( ( ))u k K u k= (19)

Rule 3:

If 1( )x k is N and 2 ( )x k is P then 3 3 1( ) ( ( ))u k K u k= (20)

Rule 4:

If 1( )x k is N and 2 ( )x k is N then 4 4 1( ) ( ( ))u k K u k= (21)

In the above rule base 1u , 2u , 3u , and 4u represent the

consequent of the TS fuzzy controller. The output of the TS

fuzzy controller is defined as follows:

4

1

4

1

( )

( )j j

j

jj

u k

u k

μ

μ

=

=

=∑

∑

(22)

V. SIMULATION RESULTS AND DISCUSSION

The TS fuzzy controller was implemented in DFIG power

control and DC voltage control, in MATLAB/SimPower Systems environment, while the parameters of the wind turbine (WT) with DFIG are given in the Appendix. The parameters of all the other controllers are taken from the MATLAB DFIG system model and are modified to improve the response of rotor speed and DC oscillations. Using hit and trial method, the parameters of active power and DC voltage control loops are adjusted to achieve the lowest possible peaks for rotor and DC voltage oscillations. Then, the tuned TS-fuzzy controllers are compared with these PI parameters of the DFIG model. The Single Machine Infinite Bus (SMIB) system shown in Fig.12 is taken for the case study and the simulations are performed to verify the effectiveness of the TS fuzzy and the damping controller in improving the transient stability, the system damping and the fault ride-through capability of the WT with DFIG.

Fig. 12. SMIB system.

A. Effect of TS fuzzy controller at wind speed 10m/s

The damping of the wind turbine with DFIG using TS Fuzzy controller and PI controller in its power control loop and DC voltage control loop is compared under 3-phase bus fault at Bus B1, which is cleared after 120 ms. The wind speed is kept constant 10 m/s. The improvement in the dynamic response of rotor speed oscillations with TS fuzzy compared to the PI controller is shown in Fig. 13. The change in the response of the real power with the implementation of the TS-fuzzy controller is hardly noticed as in Fig 14.

Fig. 13. Variation of rotor speed following a fault.

300 300.2 300.4 300.6 300.8 301 301.2 301.4 301.6 301.8 302

-0.2

0

0.2

0.4

0.6

0.8

Time(sec)

Rea

l po

wer

(pu)

with TS fuzzy controllerwith PI controller

Fig. 14. Variation in electrical power output at 10 m/s for 120ms fault. The oscillations in the DC link capacitor voltage are also

compared. The positive peak value of DC link voltage with the PI controller is 1600 V, whereas this is reduced to only 1400 V in the case of TS-fuzzy controller as shown in the Fig. 15. The improvement is beneficial for the operation of converters, since this reduces the stress on the RSC and GSC converters. Moreover, the oscillation/peak in the DC link capacitor voltage beyond the protection limit would trip the convertors. With the implementation of TS-fuzzy controller, the system will not reach the threshold and hence can sustain the fault for longer duration, thereby enhancing the system stability margin.


300 301 302 303 304 305 306 307 308 309

1.18

1.19

1.2

1.21

1.22

1.23

1.24

Time(sec)

Rot

orsp

eed(

pu)

with TS fuzzy controllerwith only PI controller

300 300.05 300.1 300.15 300.2 300.25 300.3

1000

1100

1200

1300

1400

1500

1600

Time(sec)

DC

-Lin

k V

olta

ge(v

)


Fig.15. DC Voltage variation at 10m/s for 120 ms fault.

300 300.05 300.1 300.15 300.2 300.25 300.3 300.35 300.4 300.45

0

500

1000

1500

Time(sec)

DC

cap

acito

r vo

ltage


Fig. 16. DC Voltage variation at 10m/s for 180 ms fault.

When the fault duration is increased to 180 ms, the DC Link capacitor voltage of DFIG with PI controller is going towards negative (-200 V) which will initiate the trip circuit to trip the DFIG from the grid. Whereas, the TS-fuzzy controller keeps the DC voltage positive thereby prevents the tripping of protection relays. This is shown in Fig. 16. Hence, with the help of TS fuzzy controller in DFIG fault ride through capability is improved.

B. Effect of TS fuzzy controller at wind speed 14m/s

The performance of the TS-fuzzy controller is investigated at the changes wind speed. Fig. 17 shows the comparison of the PI and the TS-fuzzy controller with the wind speed of 14 m/s. TS-fuzzy is has better response by bringing rotor speed to the steady state value quickly.

Fig. 17. Rotor speed oscillations followed by a 3 phase fault at 120kv bus.

VI. CONCLUSION

A TS-fuzzy controller is developed for controlling the active power and DC capacitor voltage of the DFIG based WT system. It is observed that the damping of the rotor oscillations are improved with the implementation of TS-fuzzy controller compared to its counterpart PI controller. The positive and negative peak oscillations in DC capacitor voltage, following a 3 phase fault, is reduced to only 1400V and 500V in the case of TS-fuzzy controllers. Instead, these peaks are 1600V and -200V for the conventional PI controller. This reduction in the peak rise in the DC link voltage would not only help in reducing the stress on RSC and GSC convertors but would also help in designing the appropriate protection system for the reliable/secure operation of the DFIG system. =This would, in turn improve the fault ride through capability of DFIG as the system can sustain the fault for longer duration of time compared to PI controllers.

Fuzzy controllers, in contrast to the conventional PI controllers, can take care of the non-linearity in the control law and hence are known to have better performance than PI under variable operating conditions. Moreover, the TS-fuzzy is better than the mamdani type fuzzy controllers in terms of the number of fuzzy sets for the input fuzzification, number of rules used and the number of coefficients to be optimized. Therefore, in this paper, the TS-fuzzy based controller is proposed for the active power and DC voltage control loops of the DFIG system. Furthermore, the application of these controllers for the multimachine DFIG systems would be tested and hence would be the next part of our research.

VII. APPENDIX - PARAMETERS OF WIND TURBINE SYSTEM

(a) Turbine data Nominal wind turbine mechanical output power in MW =9 Pitch angle controller gain =500 Maximum rate of change of pitch angle (deg/sec) =2 Inertia constant of turbine in seconds =2 (b) Generator data Nominal power in MVA = 10 Nominal voltage (L-L) in volts = 575 Stator resistance in p.u. =0.00706 Stator inductance in p.u. =0.171 Rotor resistance in p.u. =0.005 Rotor inductance in p.u. =0.156 Magnetizing inductance =2.9 Inertia constant in seconds =0.4 Friction factor or damping factor in p.u. =0.01 Pair of poles (P) =3 (c)Converter data Converter maximum power in p.u. =0.5 Grid side coupling inductor inductance and resistance in p.u =0.15 and 0.0015, respectively. Nominal DC voltage in volts =1200 DC capacitor value in mF = 60 (d)Controller data Grid voltage regulator gains KP

=1.25 and KI =300


Droop sX in p.u. = 0.02

Power regulator gains KP=2 and KI =10

DC bus voltage regulator gains KP= 0.002 and KI = 0.05

Grid side converter current regulator gains KP=1 and KI =100

Rotor side converter current regulator gains KP=0.3 and KI = 8 Damping controller proportional gain KP

=12 (e)TS fuzzy controller coefficients

Power controller K1 =2.5, K2 =2.1, K3 =1.0, and K4 =0.5

DC voltage controller K1 =1.0, K2 =0.5, K3 =5.0, and K4 =5.0

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