Modelling of Grid-Connected Geared 2MW PMSG Wind Turbine Generator (1)

Modeling of Grid-Connected Di-rect-Driven 2MW PMSG Wind

Turbine Generator System

Presented by YU, DONGYOUNGCHOI, YOUNGSICK

CONTENTS• Modeling of Generator System

– Wind Turbine– MPPT– PMSG – FUZZY Controller– FUZZY Observer– SV-PWM

• Simulation Results

• Modeling of Grid-Side System– Super Capacitor– SV-PWM– PLL– Filter

• Simulation Results

Total System• Wind Turbine Generation System (with

PMSGωd

Wind Tur-bine

TorqueCon-

trollerBack-to-Back

Converter Controller

P, QCon-

troller

Vw : Wind speed Tw : Mech torqueωd : Design speed

ωe : Generator speed

Te : Generator torque

Vg : Generator voltageIg : Generator cur-rent

Vdc : DC-link volt-age Vgrid : Grid voltage

Igrid : Grid current

GridDC

TorqueCon-

trollerTower Con-

trol Unit

PitchCon-

troller

-Y Trans.

Generator Parts

Grid-Side Parts

Modeling of Generator SystemPMSG

Wind Tur-bine

Ian ,Ibn ,Icn

S1 ~ S6

SVPWMVqs

Iqs , Ids

h(ωe)

FUZZYOb-

server

FUZZYCon-

troller

h1, h2

Pe (Te * ωg) dt

To Grid

Iqs , Ids

Modeling of Generator System

Grid Side Model Parts

Modeling of Generator System• Parameters of Wind Turbine & PMSG

Parameters Unit

Air density [Rho] 1.205 [kg/m3]

Radius of wind turbine rotor [Rd]

38 [m]

Cut-in wind Speed 4 [m/s]

Cut-off wind speed 25 [m/s]

Rated wind speed 11.8 [m/s]

Gear ratio 1

Parameters for Wind Turbine

*refer to the Dynamic Modelling, Simulation and Analysis of an Offshore Variable-Speed Directly-Driven Permanent-Magnet Wind Energy Conver-sion and Storage System (WECSS) - Nicholas P. W. Strachan and Dragan Jovcic,

Modeling of Generator System• Parameters of Wind Turbine & PMSG

Parameters Unit

Number of poles [p] 22

Pole pairs [np] 11

Resistance of motor [Rs] 0.08 [Ohm]

Inductance of Generator [Ld =Lq]

0.334 [mH]

Inertia [J] 2.5e6 [kg.m2]

Equivalent Viscous Friction Coefficient [B] 0.001

Magnetic Flux (Electrical) [Lambdam] 136 [Wb]

Parameters for PMSG

Parameters Values Units

Rated Turbine Power 2 [MW]

Rated RPM of Turbine 42 [RPM]

Air Density [ρ] 1.205 [kg/m3]

Radius of Wind Turbine Rotor (Rt) 38 [m]

Cut-in Wind Speed 4 [m/s]

Cut-off Wind Speed 25 [m/s]

Rated Wind Speed (Vw) 11.8 [m/s]

Gear Ratio (ng) 1:1 -

Number of Poles [p] 22 -

Pole Pairs [np] 11 -

Resistance of Generator [Rs] 0.08 [Ω]

Inductance of Generator [Ls = Lds = Lqs] 0.334 [H]

Equivalent Inertia [J] 2.5e6 [kg·m2]

Equivalent Viscous Friction Coefficient [B] 0.001 [N·m·sec/rad]

Magnetic Flux (Electrical) [λm] 136 [V·sec/rad]

Rated Source-link Voltage [Vdc] 9200 [V]

Source-link Capacitance [Cdc] 3300 [uF]

Grid-Side Converter Output Voltage (Vac) 4000 [V]

LC Filter

Inductance [Lf] 0.55 [mH]

Capacitance [Cf] 727 [uF]

Cut-Off Frequency [fc] 250 [Hz]

Transformer Output Voltage (Vac) 22.9 [kV]

Transformer Ratio 5.7 N1:N2

Connection Type △-Y

Modeling of Generator System• Wind Turbine Model Block

),Cp(VR0.5P 3w

2W βλπ

Cp is utilization for Wind Power (0<Cp<1)

wdm /VRωλ

• Cp Calulation Model Block

In MPPT Tracking Area(Vw < 11.8 m/s),Cp should be al-ways maximum value, that is 0.4412.

• Pitch Angle Controller

Wind Speed (m/s)

5 10 15 20 25

2.1MW1.0

Nogeneration

Cut-in wind speed

Cut-off wind speed

Rated (Nominal) wind speed

MPPT Tracking Area

Constant Power Area

0.4412

Pitch Angle

• MPPT Model Block

Modeling of Generator System• MPPT Model Block

Genoptr K

MPPT equation

ωr opt : Optimum rotor speed [m/

s]Pgen : measured generated power [W]Kp opt : MPPT gain [W/(m/s}]

For keeping about 2MW stable power

MPPT_late : 10

Modeling of Generator System• Kp_opt Gain of each Condition (1)

Wind Speed (m/s)

5 10 15 20 25

2.1MW1.0

Nogeneration

Cut-in wind speed

Cut-off wind speed

MPPT Tracking Zone

Constant Power Zone

2.01e5

Kp_opt

23.99 rad/sec

Modeling of Generator System• Kp_opt Gain of each Condition (2)

Wind Speed (m/s)

5 10 15 20 25

2.1MW1.0

Nogeneration

Cut-in wind speed

Cut-off wind speed

MPPT Tracking Zone

Constant Power Zone

2.01e5

1.55e5Kp_opt

23.99 rad/sec

Modeling of Generator System• PMSM Model Block

Modeling of Generator System• Quadratic Mode by equation & sign of

Torque Torque

Genera-tor

ModeMotorMode

PMSM eq.

PMSG eq.

SimPowerSys-tem PMSG

Module

TloadTe

Te Tmech

PositiveTorque

Nega-tive

Torque

In Negative Torque Con-dition,

PMSM equation is oper-ate

By Generator Mode.

Te : Electrical Torque Tload : Load Torque

Tmech : Mechanical Torque

Modeling of Generator System• PMSM eq. & PMSG eq.

PMSM LOAD

mmmem TBT

meqsm2

e T*)(1/J)2p

((B/J)i/J)2p

ωλω

mmmem TBT

meqsm2

e T*)(1/J)2p

((B/J)i/J)2p

ωλω

: PMSM eq

: PMSG eq

Modeling of Generator System• PMSM eq. & PMSG eq.

ωeLdids

Fig. Equivalent d,q-axis Circuit of PMSM

ωeLqiqs ed =0

: PMSM eq.

: PMSG eq.

qdsdeqs

qqssqs eiLdt

diLiRV ω

qsqeds

ddssds iLdtdi

LiRV ω

qdsqeqs

qqssqs eiLdt

diLiRV ω

qsqeds

ddssds iLdtdi

LiRV ω

Modeling of Generator System• PMSG Model Block in SimPowerSystem module

Modeling of Generator System• Elecrtical Model in SimPowerSystem module

)i)iL(Li()2p

(1.5 dsqsqdqsm λ

Modeling of Generator System• Adc2qd Block

))V3(sin)V(2V(cos31

V bcbcabqs θθ ))V3cos()V(2V(sin31

V bcbcabds θθ

))V3(sin)V(2V(cos31

V bcbcabqs θθ

))V(V33

(sin)V(V31

)V(V32

(cos cnbncnbnbnan θθ

cnbnan )V

cos()V32

cos(Vcos32

πθπθθ

))cosV3()V(2V(sin31

V bcbcabds θθ

sin()V32

sin(V(sin32

sincosVsin31

cosV31

sincosVsin31

cosV(sin32

cnbnan

cncnbnbnan

πθπθθ

πθθππθθπθ

cnbnanqs )V

cos()V32

cos(Vcos32

V πθπθθ

cnbnands )V

sin()V32

sin(Vsin32

V πθπθθ

sin()32

sin(sin

cos()32

cos(cos

πθπθθ

Modeling of Generator System• qd2abc Block

θθ sinicosii dsqsa ))ii3(sin)i3i(0.5(cosi dsqsdsqsb θθ

θθ sinicosii dsqsa

))ii3(sin)i3i(0.5(cosi dsqsdsqsb θθ

dsqs )i32

sin()i32

cos( πθπθ

bac iii

dsqs )i32

sin()i32

cos( πθπθ

sin()32

1sincos

πθπθ

sin()32

sincos

πθπθ

sin()32

sin(sin

cos()32

cos(cos

πθπθθ

Coordinate transforma-tion is same as PMSG simulink equation’s Co-ordinate transformation axis

q axis

d axis

q axis

b-axisa’

a-axis

ac-axis

Modeling of Generator System• Mechanical model Block

• PMSG Model Block in PMSM eq.

PMSM LOADωm

mmmem TBT

mmqsmm T*(1/J)(B/J)i/J)2p

ωλω

mmqsmm T*)(1/J)2p

()(B/J)2p

(i/J)2p

ωλω

meqsm2

e T*)(1/J)2p

((B/J)i/J)2p

ωλω

• Iq, Id Model Block in PMSM eq.

• iq Model Block in PMSM eq.

Fig. Equivalent q-axis Circuit of PMSM

qdsdeqssqsqs

q eiLiRVdt

diL ω

di ωλω

qdsdeqs

qqssqs eiLdt

diLiRV ω

qdsdeqs

qsqssqs eiLdt

diLiRV ω

Vqs eq

ωeLdids

• id Model Block in PMSM eq.

Fig. Equivalent d-axis Circuit of PMSM

qsqeds

ddssds iLdtdi

LiRV ω

qsqeds

ddssds iLdtdi

LiRV ω

qsqedssdsds

d iLiRVdtdi

dtdi ω

ωeLqiqs ed =0

• PMSG Model Block

ωωλ

Dynamic equation of PMSM

• PMSG Model Block

Dynamic equation of PMSM

qse11ds8ds7ds

dse10qs6e5qs4qs

L3e2qs1e

ikVkiki

ikVkkiki

Modeling of Generator System• Signal Generator Model Block

Modeling of Generator System• FUZZY Controller Block

Vde rate limit : 2e4

Modeling of Generator System• FUZZY Controller Block (Nonlinear Con-

troller)

qse11ds7

dse10e5qs4

L3e2qs1

Tdsqse

ds2qs1

]k00[g,]0k0[g,]ii[xwhere

VgVgf(x)x

troller)

L3e2qs1e

i(x)h,(x)h,fieldVector

)Tkki(kk)ikkik(kVkk

Vkk)Tkki(kk)ikkik(k

)Tkki(kk)Vkikkik(k

again.atedifferenti usLet u,input the torelated directly not still is since

L3e2qs12dse10e5qs41eqs61

qs61L3e2qs12dse10e5qs41

L3e2qs12qe6dse10e5qs41

e2qs1e

ωωωω

ωωω

troller)

1ω21ω1d1

L3e2qs12dse10e5qs411e1

L3e2qs12dse10e5qs41e61

ekekωv

as vinput new thechoosing and,errortrackingabe(t)ω(t)ωeLet

)Tkωki(kk)iωkωkik(kf,ωvwhere,

)f(v)E(xu

)Tkωki(kk)iωkωkik(kωkk1

troller)

2ids_dds2

qse11ds72ds2ds2

qse11ds7ds8

qse11ds7dsds8

qse11ds8ds7ds

)ikik(f,iv,Vuwhere,

fv)E(xu

)ikik(ik1

ikikiVk

ikVkiki

troller)

)i(ikiv

)ωω(k)ω(ωkωv

iωkikihL

ωk)iωkωkik(kωkx

ikωhL

TkωkikωhL

h)(LLhL,(x)fxh

DerivateLie

vhLE(x)

ds_ddsidsds_d2

deω2deω1d1

qse11ds7ds2f

d2dse10e5qs41d2qs

L3d2qs1d1f

1)(iff

E(x),k0

0kkE(x)

troller)

vhLE(x)

dsidsqs11ds7k1

1dω2dω1dd2ds105qs4k1

ds_dds_d

ds_ddsidsds_dqs11ds7k1

1dω2dω1dd2ds105qs4k1

ikωikik

k))ωω(k)ω(ωkωω(kωikωkik

0,i0,i

)i(ikiωikik

k))ωω(k)ω(ωkωω(kωikωkik

Modeling of Generator System• FUZZY Observer Block

Modeling of Generator System• IPARK Block

cos-sin

sincosV

Modeling of Generator System• IPARK Block

cos-sin

sincosV

q axis

d axis

q axis

b-axisa’

a-axis

ac-axis

• Space-Vector PWM Model Block

• Tune for Space-Vector PWM

d axis

q axis

(001) (101)

(000)V0

)0,32(

)31,31()31,31(

)0,32(

)31,31(

θV*V max)

(tanVVV

Limitation of SVPWM Voltage is 2/3Vdc.

• Space-Vector PWM Model Block

• Space-Vector PWM

)6006)to1Sectoris,(that6through1n(where,,TTTT

1ncossin

sincos(V

)sin3n

coscos3n

SectoranyatdurationtimeSwitching

πθπθ

θπθπ

• Switching Time of Space-Vector PWM

V1 V2 V7 V7 V2 V1 V0

T0/2 T0/2T0/2 T0/2T1 T2 T2 T1

ON Sequence OFF Sequence

(110)(010)

(001) (101)

(000)V0

Simulation Results• Simulation Result in Variable Speed

0 1 2 3 4 5 6 7 810

Time (sec)

0 1 2 3 4 5 6 7 822.5

Time (sec)

0 1 2 3 4 5 6 7 8-14

-4x 10

Time (sec)

est TL

0 1 2 3 4 5 6 7 88000

Time (sec)

0 1 2 3 4 5 6 7 8-450

Time (sec)

i qs (

0 1 2 3 4 5 6 7 8-100

Time (sec)

i ds (

Modeling of Grid System• Circuit for Grid Side Part

3-ØLoad

Trans-formerΔ - Ｙ

5.725 : 14kV /

22.8kV

InverterController

ia_PCC

ib_PCC

ic_PCC

ia_grid

ib_grid

ic_grid

Vab_iv

Vbc_iv

Vca_iv

Vab_in

Vbc_in

Vca_tn

22.9kV 3-Ø Line to Line

Voltage

Islanding Protector

Modeling of Grid System

Parameters Values Units

Rated Source-link Voltage [Vdc] 9200 [V]

Source-link Capacitance [Cdc] 3300 [uF]

Grid-Side Converter Output Voltage

(Vac)4000 [V]

LC Filter

Inductance [Lf] 0.55 [mH]

Capacitance [Cf] 727 [uF]

Cut-Off Frequency

[fc]250 [Hz]

Modeling of Grid System• Vdc equation

Cv Vdc

idciinv

The input DC current of the DC link is cal-culated by dividing the reference power to the DC voltage.

V invdcv

Pgen Pout

Modeling of Grid System• LC-fillter

uFCthenmHLso

fassume

offcutff

offcut

750,55.0,

,25020

CfVab_inv

Vbc_inv

Vca_inv

Vab_in

Vbc_in

Vca_in

Modeling of Grid System• LC-fillter Result

0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.66 0.68 0.7

Time(sec)

0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.66 0.68 0.7

Time(sec)

Modeling of Grid Control Sys-tem

-Y Trans.

VcIabc Vab

LocalLoad

+ -PI +

Vc_Nominal

Ids_refVds

Qmeasured

Qref PI+

- iqs_ref

Modeling of Grid System• Simulink Model Block Controller Part

Modeling of Grid System• Equvalant-Circuit of d-axis

Vds_in

Lf ωLfiqs

qsfindsds

invds iLVdt

diLV __

From In-veter

ToTrans-former

Modeling of Grid System• Equvalant-Circuit of d-axis

Vqs_in

Lf ωLfids

From In-veter

ToTrans-former

dsfinqsqs

invqs iLVdt

diLV __

Phase Locked Loop (PLL)

Modeling of Grid

1Sin_Cos

2*picos

RampGenerator

error w

FrequencyController

The most common PLL technique applied to three phase grid connected systems is based on an algorithm implemented in synchronous reference frame (dq). The structure of the dq PLL algorithm is represented like this:

Va,b,c

Vd*Loop Filter

f θ ω

dq abc

PLL con-troller

Transformation module

5. PV system Simulation

Where:CloseNeed: Need to CloseCloseNeed: Can CloseCloseOK: Close the switch

Algorithm for closed-swithching:

abs(θGrid- θPCC_out)<∆θ1

CloseCan=OFFCloseOK=OFFθPCC_out = θPCC_in

CloseNeed=ON

k=k+1θPCC_out = θPCC_in +k*∆θ2

Initialize CloseNeed=OFF, CloseCan=OFF,CloseOK=OFF, θPCC_out =0, k=0

CloseCan=ON

abs(θGrid)<∆θ3

CloseOK=ON;

DPC with SVPWM and PLL

5. PV system Simulation

DPC with SVPWM and PLL

Theta_Grid_in

Theta_PCC_in

CloseOK

CloseCan

CloseNeed

Sin_Cos_PCC_out

Theta_PCC_in

Theta_Grid_in

Sin_Grid

CloseOK

Theta_PCC_out

Theta_PCC_in

Theta_Grid_in

CloseCan

CloseNeedthupham3

3phTheta

Sin_Cos

3phTheta

Sin_Cos 3

CloseNeed

Vabc_3

Vabc_Grid

Vabc_3

CloseNeed

Theta_Grid_in

Theta_PCC_in

Sin_Cos_PCC_out

CloseNeed

CloseCan

CloseOK

Swithching Control

CloseNeed

Theta_PCC_in

Theta_Grid_in

CloseOK

CloseCan

Sin_Cos_PCC_outVabc_3

Vabc_Grid

CloseNeed

Modeling of Grid System

From Generator

S1 ~ S6

-Y Trans.L-C FilterVgrid

POWERCon-

troller( PI )

Ｘ grid

Ia ,Ib ,Ic

Va ,Vb, Vc

LocalLoad

• Block Diagram of Normal Mode (Grid Connected)

PQ Load

PQ PCC PQ Grid

Modeling of Grid System• Simulink Model Block Normal Mode (Grid Connected)

Modeling of Grid System• Simulation Result Normal Mode (Grid Connected) LOAD

0.5 0.55 0.6 0.65 0.7 0.75 0.8-4

Time(sec)

a_Load [V]

Vb_Load

Vc_Load

0.5 0.55 0.6 0.65 0.7 0.75 0.8-100

Time(sec)

i abc_

ia_Load

ib_Load

ic_Load

0.5 0.55 0.6 0.65 0.7 0.75 0.8-1

Time(sec)

Load [W]

Modeling of Grid System• Simulation Result Normal Mode (Grid Connected) PCC

0.5 0.55 0.6 0.65 0.7 0.75 0.8-4

Time(sec)

a_PCC [V]

Vb_PCC

Vc_PCC

0.5 0.55 0.6 0.65 0.7 0.75 0.8-200

Time(sec)

i abc_

ia_PCC

ib_PCC

ic_PCC

0.5 0.55 0.6 0.65 0.7 0.75 0.8-1

Time(sec)

PCC [W]

Modeling of Grid System• Simulation Result Normal Mode (Grid Connected) Grid

0.5 0.55 0.6 0.65 0.7 0.75 0.8-4

Time(sec)

rid [V

a_Grid [V]

Vb_Grid

Vc_Grid

0.5 0.55 0.6 0.65 0.7 0.75 0.8-200

Time(sec)

i abc_

ia_Grid

ib_Grid

ic_Grid

0.5 0.55 0.6 0.65 0.7 0.75 0.8-1

Time(sec)

Grid [W]

Modeling of Grid System• Simulink Result Fault Mode (Stand Alone) PCC

0.7 0.75 0.8 0.85 0.9 0.95 1-4

Time(sec)

a_Load [V]

Vb_Load

Vc_Load

0.7 0.75 0.8 0.85 0.9 0.95 1-100

Time(sec)

i abc_

ia_Load

ib_Load

ic_Load

0.7 0.75 0.8 0.85 0.9 0.95 1-1

Time(sec)

Load [W]

Modeling of Grid System• Simulation Result Fault Mode (Stand Alone) PCC

0.7 0.75 0.8 0.85 0.9 0.95 1-4

Time(sec)

a_PCC [V]

Vb_PCC

Vc_PCC

0.7 0.75 0.8 0.85 0.9 0.95 1-200

Time(sec)

i abc_

ia_PCC

ib_PCC

ic_PCC

0.7 0.75 0.8 0.85 0.9 0.95 1-1

Time(sec)

PCC [W]

Modeling of Grid System• Simulation Result Fault Mode (Stand Alone) Grid

0.7 0.75 0.8 0.85 0.9 0.95 1-4

Time(sec)

rid [V

a_Grid [V]

Vb_Grid

Vc_Grid

0.7 0.75 0.8 0.85 0.9 0.95 1-200

Time(sec)

i abc_

ia_Grid

ib_Grid

ic_Grid

0.7 0.75 0.8 0.85 0.9 0.95 1-1

Time(sec)

Grid [W]

Modeling of Grid System• Simulink Result Reconnecting Mode LOAD

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7-4

Time(sec)

a_Load [V]

Vb_Load

Vc_Load

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7-100

Time(sec)

i abc_

ia_Load

ib_Load

ic_Load

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7-1

Time(sec)

Load [W]

Command Reconnecting Synchronized PLL

Modeling of Grid System• Simulation Result Reconnecting Mode PCC

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7-4

Time(sec)

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7-200

Time(sec)

i abc_

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7-1

Time(sec)

Va_PCC

Vb_PCC

Vc_PCC

ia_PCC

ib_PCC

ic_PCC

Modeling of Grid System• Simulation Result Reconnecting Mode GRID

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7-4

Time(sec)

rid [V

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7-200

Time(sec)

i abc_

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7

Time(sec)

Grid [W]

Va_Grid

Vb_Grid

Vc_Grid

ia_Grid

ib_Grid

ic_Grid

Modeling of Grid System• Simulation Result Reconnecting Mode

1.35 1.4 1.45 1.5 1.55 1.60

Time(sec)

PCC [rad]

ThetaGrid

1.35 1.4 1.45 1.5 1.55 1.60

Time(sec)

Command ConnectingSynchronized PLL

Modelling of Grid-Connected Geared 2MW PMSG Wind Turbine Generator (1)

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