4.Electrical --Dynamic modeling .full

DYNAMIC MODELING, ANALYSIS AND SIMULATION OF GRID CONNECTED

DOUBLY FED INDUCTION GENERATOR BASED WIND POWER UNDER DIFFERENT

OPERATING CONDITIONS

JAGDEEP SINGH LATHER1, SUKHWINDER SINGH

2 & SANJAY MARWAHA

3

1Associate Professor, Department of EE, National Institute of Technology Kurukshetra, Haryana, India

2Assistant Professor, Department ECE, Ambala College of Engineering and AR, Ambala, Haryana, India

3Professor, 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.

International Journal of Electrical and

Electronics Engineering Research (IJEEER)

ISSN 2250-155X

Vol. 3, Issue 2, Jun 2013, 29-40

© TJPRC Pvt. Ltd.

30 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].

0

cos sin 1

cos( 2 / 3) sin( 2 / 3) 1

cos( 4 / 3) sin( 4 / 3) 1

qsans

bns ds

cns s

vv

v v

v v

(1)

Where is the angular displacement between stator phasor ansv and q-axis running at synchronous speed.

So p.u. (per unit) values of stator phase voltages are given by equations (2)-(4)

. .

2 3 31 1cos * *[ cos sin ] *[ cos sin ]2 2 2 23qs p u ans bns cns

ph base

v v v vv

(2)

. .

2 3 31 1sin * *[ sin cos ] *[ sin cos ]2 2 2 23ds p u ans bns cns

ph base

v v v vv

(3)

0 . .

2 1 1 1* * *2 2 23s p u ans bns cns

ph base

v v v vv

(4)

Similarly, Rotor phase abc to qd0 transform referred to stator gives following equations.

' . .

31cos * *[ cos sin ]2 2 2*

3 31*[ cos sin ]2 2

anr bnr

qr p u

ph basecnr

uv v

vv v

(5)

' . .

31cos * *[ cos sin ]2 2 2*

3 31*[ cos sin ]2 2

anr bnr

qr p u

ph basecnr

uv v

vv v

(6)

0 ' . .

2 1 1 1* * * *2 2 23r p u anr bnr cnr

ph base

uv v v vv

(7)

rwhere 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.

Dynamic Modeling, Analysis and Simulation of Grid Connected Doubly Fed Induction 31

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:

qs

s ds S qsqs

dR i

dtv

(8)

dss qs S dsds

dR i

dtv

(9)

00

sS sqs

dR i

dtv

'

' ' ''( )

qr

s r dr r qrqr

dR i

dtv

(10)

'' ''

( )drs r qs r drdr

dR i

dtv

(11)

0 '' 0 ''

rr rqr

dR i

dtv

(12)

0

'

'

0 '

( )

( )0 0 0 0 0( )

0 0 0 0 0

( ) 0 0 0 0 0 00

0 0 0 0 ( ) 0( )' 0 0 0 ( ) 0 0

0 0 0 0 0 0( )

'

( )0 '

qsqs s

dsds

s

s rqr

s rdr

r

tqs

ttds

ts

tqr

tdr

tr

v

vvv

vv

0 0

'' '

'' '

'0 ' 0 '

( )0 0 0 0 0

( ) ( )0 0 0 0 0

( ) ( )0 0 0 0 0

0 0 0 0 0( ) ( )

0 0 0 0 0( ) ( )

0 0 0 0 0( ) ( )

qss

s dss

s ss

rqr qr

rdr dr

rr r

i tR

t i tR

t i tR

Rt i t

Rt i t

Rt i t

(13)

1

0 0

'' '

'' '

'0 ' 0 '

( ) ( )0 0 0 0

( ) ( )0 0 0 0

( ) ( )0 0 0 0 0

0 0 0 0( ) ( )

0 0 0 0( ) ( )

0 0 0 0 0( ) ( )

qs qsls M M

ds dsls M M

s sls

M lr Mqr qr

M lr Mdr dr

lrr r

i t tL L L

i t tL L L

i t tL

L L Li t t

L L Li t t

Li t t

(14)

( )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

msatL =Assumed value of inductance corresponds to mutual flux

msat at saturation.

Where

32 Jagdeep Singh Lather, Sukhwinder Singh &Sanjay Marwaha

( ), '

tqdos r = first order differential of flux linkages stator and rotor(referred to stator).

, 's rqdov =voltage

vector in qd0 frame of stator and rotor (referred to stator). 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,

( )

( )

0 ( )

'( )

'( )

0 '( )

( )

0 0 0 0 0( )

0 0 0 0 0

( ) 0 0 0 0 0 00

0 0 0 0 ( ) 0( )' 0 0 0 ( ) 0 0

0 0 0 0 0 0( )

'

( )0 '

qs ts

ds ts

s t

s rqr t

s rdr t

r t

tqs

tds

ts

tqr

tdr

tr

v

v

v

v

v

v

1

''

''

''

( )0 0 0 00 0 0 0 0

(0 0 0 00 0 0 0 0

0 0 0 0 00 0 0 0 0

0 0 0 00 0 0 0 0

0 0 0 00 0 0 0 0

0 0 0 0 00 0 0 0 0

qsls M Ms

dsls M Ms

lss

M lr Mr

M lr Mr

lrr

tL L LR

tL L LR

LR

L L LR

L L LR

LR

0

'

'

0 '

)

( )

( )

( )

( )

s

qr

dr

r

t

t

t

t

(15)

Or can be written as

, ' , '

1

, ' , '6 66 1 6 1

6 1

( ) [ ][ ] * ( ), ' s r s rqdo s r s r qdot v W R L tqdos r

(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].

3( )

2 2e ds qs qs ds

pT i i (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].

( / ) 1( / ) . . (18)

2

re m r

d w wbT T Fw wb p u

dt H

1( / ). . (19)

2

re m r

wT T Fw wb dt p u

wb H

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.

31P ( , )

2r PC SV (26)

Dynamic Modeling, Analysis and Simulation of Grid Connected Doubly Fed Induction 33

Generator Based Wind Power Under Different Operating Conditions

Similarly torque produced is given by the equation as follows.

21( , )

2r QT C R SV (20)

Hence the equation for thrust exerted on the tower Ft is given as follows.

21( , )

2T TF C SV (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.

0

5

10

15

-5

0

5

10

15

20

25

0

0.5

lambda

beta

Cp

(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 35

Generator Based Wind Power Under Different Operating Conditions

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 37

Generator Based Wind Power Under Different Operating Conditions

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.

38 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 39

Generator Based Wind Power Under Different Operating Conditions

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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.