International Journal of Electrical and Electronics Engineering Research (IJEEER) ISSN 2250-155X Vol. 3, Issue 2, Jun 2013, 29-40 Š TJPRC Pvt. Ltd.
DYNAMIC MODELING, ANALYSIS AND SIMULATION OF GRID CONNECTED DOUBLY FED INDUCTION GENERATOR BASED WIND POWER UNDER DIFFERENT OPERATING CONDITIONS JAGDEEP SINGH LATHER1, SUKHWINDER SINGH2 & SANJAY MARWAHA3 1
Associate Professor, Department of EE, National Institute of Technology Kurukshetra, Haryana, India
2
Assistant Professor, Department ECE, Ambala College of Engineering and AR, Ambala, Haryana, India 3
Professor, Department EIE, SLIET,Deemed-University, Sangrur, Punjab, India
ABSTRACT This paper presents a state space mathematical dynamic model of doubly fed induction generator based on phase voltages. A simulink model has been designed with the help of Matlab2010 in SimPowerSystem simulink tool to analyze the effect of different operating conditions on the performance of DFIG. Analysis of unbalance in grid voltage and some operating conditions such as sub synchronous, synchronous and super synchronous speed has been carried out. On the basis of simulation results obtained, discussions were carried out to explain the suitability and effectiveness of the analysis as compared to detailed line voltage model of the DFIG in Matlab demo. This paper also gives an overview on the requirements of suitable robust control design aspects to control various abnormal conditions and to maintain system stability and reliability.
KEYWORDS: DFIG, Wind Farm, Stability, Unbalanced Conditions INTRODUCTION With the advent of new technologies of variable speed wind turbine (DFIG and SG) with enhanced features to control and maintain constant power under uncertain and unbalanced circumstances make them very popular in the market. The market share of wind power increased over past few decades. DFIG had gain more popularity as compared to Synchronous generator (SG) because DFIG requires only 25-30% of the total nominal power rating of the generator, to operate control functions. So the control equipment rating is also small and which makes it more economical as compared to SG which requires power electronic control equipment of same rating as that of generator nominal power rating[1][5][6][7]. In recent years a lot of publications and research reports were submitted on wind technologies, which were entirely focused on mathematical modeling of DFIG based wind turbines. It include aerodynamic modeling of wind system, DFIG modeling, PWM modeling and modeling of Control system [4][7][8][9]. Matlab was used to simulate and test the mathematical model of DFIG and its performance under different uncertain conditions [15]-[18].In the previous studies many controllers were proposed to control of active power ,Reactive power compensation and other uncertain conditions are based on fuzzy control, discrete control based on trapezoidal rules, direct torque control, Neural Networks, Artificial Neural Networks, Evolutionary Strategy, Stator flux oriented control and PLL(Phase locked loop) control [6][22].However mathematical models of DFIG given in [1][3][4] and [12] provided more resemblance to practical or actual conditions but they were still based on different assumptions to simplify the expressions, So need to develop a more accurate mathematical model to explore practical and more accurate behavior of model to predict and to design more efficient control strategies. The main objectives covered in this paper are. 
To construct a state space mathematical model of the DFIG-Wind turbine system based on phase voltages.
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Jagdeep Singh Lather, Sukhwinder Singh &Sanjay Marwaha
To construct a Simulink model of DFIG-Wind turbine system.
Effect of different operating conditions such as grid voltage variation and DFIG speed variations has been carried out. In this paper a sixth ordered Mathematical model for DFIG was constructed by the use of first order differential
equations in continuous time frame with phase to ground voltages. Simulation results were obtained under different operating conditions.
MODELING OF DOUBLY FED INDUCTION GENERATOR Doubly Fed induction Generator DFIG) A Wound rotor asynchronous generator is known as DFIG machine. According to Park’s Transformation, the relation between stator Phase to ground Voltages van, vbn ,vcn and d-q-0 frame are given by following matrix equation(1) as[7][12]. v ans cos v bns cos( 2 / 3) cos( 4 / 3) v cns
Where
sin sin( 2 / 3) sin( 4 / 3)
1 v qs 1 v ds 1 v 0 s
(1)
is the angular displacement between stator phasor vans and q-axis running at synchronous speed.
So p.u. (per unit) values of stator phase voltages are given by equations (2)-(4)
v
qs p.u.
v
ds p.u.
v
2 3v ph base
cos * v ans vbns *[ 1 cos 3 sin ] v cns *[ 1 cos 3 sin ] 2 2 2 2
(2)
(3)
2 sin * v ans vbns *[ 1 sin 3 cos ] v cns *[ 1 sin 3 cos ] 2 2 2 2 3v ph base
0 s p.u .
2 3v ph base
12 *v v ans
bns
* 1 v cns * 1 2 2
(4)
Similarly, Rotor phase abc to qd0 transform referred to stator gives following equations.
cos * *[ 1 cos 3 sin ] v anr v bnr 2 2 v qr ' p.u. u * 3 v ph base v cnr *[ 1 2 cos 3 2 sin ]
(5)
cos * *[ 1 cos 3 sin ] v anr v bnr 2 2 v qr ' p.u. u * 3 v ph base v cnr *[ 1 2 cos 3 2 sin ]
(6)
2
2
v
0 r ' p.u .
u*
2 1 * *1 *1 3v ph base 2 v anr v bnr 2 v cnr 2
(7)
where r is the angular displacement between rotor phase Var and q-axis and r relative angular displacement between stator and rotor phase voltages. Where u=Ns/Nr turn ratio.
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Dynamic Modeling, Analysis and Simulation of Grid Connected Doubly Fed Induction Generator Based Wind Power Under Different Operating Conditions
In arbitrary reference frame d-q-0 the stator voltage equations for DFIG can be written as:
dqs
v
qs
v
ds
v
qs
qr '
v
dr '
sds RS iqs (8)
dds sqs RS ids dt
(9)
d0 s RS i0 s dt
dqr '
v
v
dt
qr '
dt
(s r )dr ' Rr 'iqr ' (10)
ddr ' (s r )qs Rr 'idr ' dt
(11)
d0 r ' Rr 'i0 r ' dt
(12)
v qs (t ) 0 ds v ds s (t ) 0 0s v 0s v qr ' 0 0 qr ' (t ) v dr ' 0 v 0 r ' (t ) dr ' (t ) 0r '
qs (t )
s 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 (s r ) 0
0 0 0 (s r ) 0 0
0 qs (t ) Rs 0 0 ds (t ) 0 0 0 s (t ) 0 qr ' (t ) 0 0 0 dr ' (t ) 0 0 ( t ) 0r '
0
0
0
0
Rs 0 0 0 0
0 Rs 0 0 0
0 0 Rr ' 0 0
0 0 0 Rr ' 0
iqs (t ) Lls LM i ( t ) 0 ds i0 s (t ) 0 L iqr ' (t ) M 0 idr ' (t ) 0 i0 r ' (t )
(13) 0 Lls LM 0 0 LM 0
0 0 Lls 0 0 0
LM 0 0 Llr ' LM 0 0
md (t ) =d-axis component of mutual flux. mq (t ) =q-axis component of mutual flux.
m =Resultant Mutual Flux Lad=Laq=Equivalent inductance seen from stator
Lmsat =Assumed value of inductance corresponds to mutual flux
m sat Where
at saturation.
0 iqs (t ) i (t ) 0 ds 0 i0 s (t ) 0 iqr ' (t ) 0 idr ' (t ) Rr ' i0 r ' (t )
0 LM 0 0 Llr ' LM 0
0 0 0 0 0 Llr '
1
qs (t ) ds (t ) 0 s (t ) qr ' (t ) dr ' (t ) 0 r ' (t ) (14)
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Jagdeep Singh Lather, Sukhwinder Singh &Sanjay Marwaha
qdo
s, r '
(t )
vqdos ,r '
= first order differential of flux linkages stator and rotor(referred to stator).
vector in qd0 frame of stator and rotor (referred to stator).
=voltage
W = angular speed of stator and rotor flux linkages.
[L]= Self inductance and mutual inductances matrix.[R] and [is,r’]= Resistance and current matrices. Therefore, qs (t ) v qs (t ) 0 s ds (t ) v ds (t ) 0 s ( t ) 0 0s v 0 s (t ) 0 0 0 (t ) v qr '(t ) 0 0 qr ' v dr '(t ) 0 (t ) v 0 r '(t ) 0 dr ' 0r ' (t )
0 0 0 0 0 0 0 0 0 0 0 (s r ) 0 (s r ) 0 0 0 0
0 Rs 0 0 0 0 0 Lls LM 0 0 Rs 0 0 0 0 0 0 0 0 Rs 0 0 0 0 0 0 0 0 Rr ' 0 0 LM 0 0 0 0 0 Rr ' 0 0 0 0 0 0 0 0 Rr ' 0
0 Lls LM 0 0 LM 0
0 LM 0 0 Lls 0 0 Llr ' LM 0 0 0
0
0 LM 0 0 Llr ' LM 0
Llr ' 0 0 0 0 0
1
qs (t ) ds (t ) (t ) 0s qr ' (t ) (t ) dr ' 0 r ' (t )
(15)
Or can be written as qdo (t ) vqdo W [ Rs ,r ' ][ Ls ,r ' ]1 * qdo (t ) 66 s ,r ' 61 s ,r ' 61 s, r ' 61
(16)
Electro-Mechanical Model of DFIG From equation (16) flux linkages and phase currents were obtained using simulation model then electromechanical torque of DFIG can be obtained by using following expression as given below[7][12]. Te
3 p (ds iqs qs ids ) 2 2
(17)
The other torque which is given by the turbine to accelerate the rotor of DFIG known as mechanical torque and is denoted by Tm for generator operation Te acts opposite to Tm. So the net torque available to accelerate the rotor shaft of the generator depends upon the moment of inertia of the generator H, Tm, Te, angular speed Wr and damping toque as expressed by the following expression [7]. d ( wr / wb) 1 (Te Tm Fwr / wb) dt 2H
p.u.
(18)
wr wb
p.u
(19)
1 (Te Tm Fwr / wb).dt 2H
Where H is inertia constant, F damping coefficient and wb is base angular speed.
WIND TURBINE MODEL Aerodynamic Model The mechanical power produced by the turbine on interaction with wind depends upon swept area S of the air disk formed by the rotation of the turbine’s blades S, power coefficient of performance Cp(depends upon collective blade pitch angle
and tip to speed ratio ), air density and wind speed V. The expression for power extracted from wind is given
by [6][8][12] following equation. Pr
1 CP ( , ) SV 3 2
(26)
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Dynamic Modeling, Analysis and Simulation of Grid Connected Doubly Fed Induction Generator Based Wind Power Under Different Operating Conditions
Similarly torque produced is given by the equation as follows. Tr
1 CQ R( , ) SV 2 2
(20)
Hence the equation for thrust exerted on the tower Ft is given as follows. FT
1 CT ( , ) SV 2 2
(21)
Where Ct thrust coefficient, Cq is the torque coefficient ,R is the radius of the rotor. Cq=Cp/ and
=Rwr/V.
Where Wrt is the rotor speed of turbine. Figure.1 illustrate the variation of performance coefficients of Cp and Ct.
Cp
0. 5
0 -5 0 5 15 10 10
15 5
20 bet a 25
0
lambda
(a)
(b) Figure 1: (a), (b) Variations of Cp and Ct
SIMULATION MODEL OF WIND FARM To explore DFIG-wind turbine performance characteristics under different operating conditions a simulation model DFIG-Wind turbine in Sim Power System tool was constructed using MATLABR 2010.The model which was given in [12] is based on line voltages with D-Q frame. In [12] it is difficult to obtain zero sequence currents. In this model we have taken phase voltages to study performance of the DFIG.
SIMULATION STUDIES UNDER VARIOUS OPERATING CONDITIONS To study and explore the observations from simulation results we have taken various operating conditions such as generator’s rotor running with under synchronous speed, Synchronous speed and super synchronous speed ,effect of capacitor voltage Vdc of the 3-phase converter on the grid side rotor voltages and currents .Also the effect of grid voltage dip incorporated in the system to study stability issues. Under Synchronous Speed Operation In this mode of operation rotor of DFIG is running at less than synchronous speed the permissible limits for variable speed Wind turbine based on DFIG is +30% and -30% of synchronous speed. Below synchronous speed converter fed current signals to rotor circuit to produce flux in the rotor in direction to strength the stator flux. Reactive power from stator of the DFIG maintained to negligible magnitude (Q0 =0) [6]-[12].
34
Jagdeep Singh Lather, Sukhwinder Singh &Sanjay Marwaha
Figure 2: The Variation of wr, Pitch, Tm and Tem when Generator Shaft Speed is Reduced Suddenly From the figure 2 it is observed that when speed of generator reduced suddenly then electromechanical torque developed by generator tends to speed up the shaft in reverse direction as motor mode. Tm becomes positive.
Figure 3: Active and Reactive Power Flow To increase speed of the rotor flux to synchronous speed converter increase the frequency of currents fed to the rotor and maintain Vr/Fr ratio same, this is the desire condition. To obtain simulation results in this condition i.e. below permissible speed, the wind turbine and generator’s initial speeds are assumed to be 0.3 p.u of base speed of synchronous speed of the generator. The initial value of slip is assumed to be 0.6. At t=0.25 sec rotor speed increases in motoring mode hence active and reactive power becomes negative as in motoring mode.
Dynamic Modeling, Analysis and Simulation of Grid Connected Doubly Fed Induction Generator Based Wind Power Under Different Operating Conditions
35
Figure 4: Stator, Rotor Currents and Converter dc Voltage At Synchronous Speed To obtain the performance characteristics of the DFIG at synchronous speed we have taken wind turbine and generator’s initial speeds are to be 1 p.u. of base synchronous speed of generator. The initial value of slip is set to be 0.
Figure 5: (A) Grid Voltage Stator & Rotor Current, Active, Reactive Power and Vdc
36
Jagdeep Singh Lather, Sukhwinder Singh &Sanjay Marwaha
Figure 5: (B) Rotor Current, Rotor Speed, Pitch Angle, Tm and Tem Variations under Synchronous Speed The above figure shows that all the parameters vary in more stable conditions at this speed. Above Synchronous Speed (Super Synchronous) In this mode of operation wind turbine and generator’s initial speeds are set to be 1.2 p.u. of base synchronous speed of generator. The initial value of slip is assumed to be 0.2.
Figure 6: (A) Grid Voltage Stator Current, Rotor Current, Active and Reactive Power, Converter Voltage
Dynamic Modeling, Analysis and Simulation of Grid Connected Doubly Fed Induction Generator Based Wind Power Under Different Operating Conditions
37
Figure 6: (B) Rotor Speed, Pitch Angle, Tm and Tem Variations with above Synchronous Speed Mode At t=0.25 sec variation in pitch angle is observed because the Tem(Electromechanical torque) and Tm(mechanical torque) tends to increase to positive direction to reduce generator speed as it goes above synchronous speed. Variations occurred in magnitude and frequency of rotor current to control generator speed to desired limit. Voltage Dip in Power Supply The simulation study for voltage dip a voltage dip is applied at t=0.03 to 0.3 p.u. of rated grid side voltage. It is assumed that generator is running above synchronous speed with similar conditions as were used in part c).
Figure 7: Grid Voltage Stator Current, Active and Reactive Power, Converter Voltage with a Voltage Dip in the Grid Voltage From the above figure7. Variations were observed in stator current, active and reactive power and also in converter voltage.
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Jagdeep Singh Lather, Sukhwinder Singh &Sanjay Marwaha
Figure 8: Rotor Current, Generator’s Rotor Speed, Pitch Angle, Tm and Tem Variations with Above Synchronous Speed Mode From the above figure 8 variations are observed in generator speed, pitch angle, Tm and Tem are observed which indicates that as generator speed goes down pitch angle increases to increase generator speed to desired speed.
CONCLUSIONS AND FUTURE SCOPE The conclusions were drawn in different cases a),b),c) and d) pertaining to different operating conditions.
In case a): The pitch angle gets saturated at max level 27 deg unable to control and maintain generating mode. Tem becomes very large as under this condition generator draws large current from stator and rotor side connected to grid as shown in figure 4. Hence generator has to cut down from supply.
In case b): The frequency of rotor fed currents and their magnitudes were observed to be very small. Pitch angle is almost zero. There are small variations in the generator’s speed. Both active and reactive powers are positive as shown in fig.5 (a,b) i.e. DFIG is working in generating mode.
In case c): Due to generator’s rotor running at above synchronous speed , it deliver more active and reactive power to grid. The pitch angle variations are small as shown in fig 6(a,b).
In case d): Due to dip in grid voltage active and reactive power generated by goes down. Hence converter voltage experiences a small dip but due to rotor currents it regain its predefined rated voltage level of 1150V. Both stator and rotor currents were goes down as grid side voltage as shown in fig 7 and 8. In all the above cases dc voltage level of the converter need to be stabilized. Also the torque variations are needed
to be smooth out as these variation are difficult to be judge in continuous model. In the future new advanced control strategies are required to stabilize the performance of DFIG based wind turbine.
Dynamic Modeling, Analysis and Simulation of Grid Connected Doubly Fed Induction Generator Based Wind Power Under Different Operating Conditions
39
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19. Seif Eddine Ben Elghali, Mohamed El HachemiBenbouzid, “High-Order Sliding Mode Control of a Marine Current Turbine Driven Doubly-Fed Induction Generator” IEEE Journal of Oceanic Engineering, vol. 35, no. 2, pp-402-411,April 2010 20. LinglingFan, Rajesh Kavasseri, “Modeling of DFIG-Based Wind Farms for SSR Analysis”, IEEE Transactions on Power Delivery, vol. 25, no. 4, pp-2073-2082,october 2010. 21. Alvaro Luna, Francisco,David and Pedro “ Simplified modeling of a DFIG for transient studies in wind power applications” IEEE Transactions on Industrial Electronics, vol.58,No. 1.,pp. 9-20, January 2011. 22. Lihui Yang, Zhao Xu and Zhao Yang “ Oscillatory stability and eigenvalue sensitivity analysis of a DFIG wind turbine system” IEEE Transactions on energy conversion, vol.26,no.1,pp. 328-338,March 2011. 23. Lixing Wei,Russel J. Kerkman and Richard “ Analysis of IGBT power cycling capabilities used in DFIG wind power system” IEEE Transactions on Industry applications, vol.47, no.4,pp. 1794-1801,July 2011.
APPENDICES Appendix-A Generator Data: Power Rating= 1.5 MW. Nom. Power= 1.5/.9 MVA , L-L volt=575V. and freq.=60 Stator [ Rs,Lls ] (p.u.): [ 0.023 0.18]; Rotor [ Rr',Llr' ] (p.u.): [ 0.016 0.16], Lm(p.u.)=2.9, Inertia constant, friction factor, and pairs of poles=[0.685,0.01(p.u),3] Converter Data:DC_Nom voltage=1150V, C=10000e-6 Turbine Data and Drive Train : Pmec=1.5 MW, Inertia Constant=4.32, Shaft mutual Damping=1.5.