Harmonic Stability Analysis in Wind Farms

Esmaei l EbrahimzadehD e p a r t m e n t o f E n e r g y Te c h n o l o g y, A a l b o r g U n i v e r s i t y

e b b @ e t . a a u . d k

Outline

• Introduction

• Stability analysis

• Time-domain simulation results

• Conclusion

2Harmony Project, | Esmaeil Ebrahimzadeh|

Introduction

3

An ideal model

Power converter controllers can effect on stability

A model with considering the power converter controller

Harmony Project, | Esmaeil Ebrahimzadeh|

Grid-side power converter model

4

2 32 3

1.52 3

2 3

1.5 (1.5 ) (1.5 )12 10 120

1.5 (1.5 ) (1.5 )12 10 120

s

s s sT s

pwms s s

T T Ts s sG e

T T Ts s s

c 2 2i

pf

K sG Ks

Proportional plus Resonant (PR) current controllers

Approximated digital control delay

PMSG

Turbine

ACDC AC

DC

Power ConvertersLCL Filter

c,kI

gVGrid

Gcont,k(s) Gdelay,k(s)+-Iref,k(s)

Ig,k(s)

.Ig,k(s)

++

Gdamp,k(s)

PCC

damp, ,k d kG K

Harmony Project, | Esmaeil Ebrahimzadeh|

400-MW wind power plant as a case study

5

LCL Filter

LCL Filter

LCL Filter

LCL Filter

Parameter Value (P.U.)

LCL filterGrid-side inductor 8×10-4

Capacitor 40×10-6

WTG-side inductor 8×10-4

WT transformer Leakage inductance 3.18×10-4

33 kV cable (8 km)Shunt capacitance 7.841×10-6

Series inductance 1.802×10-4

Series resistance 0.022Three-winding

transformer Leakage inductance 3.8×10-4

150 kV cable (58 km)

Shunt capacitance 7.54 ×10-5

Series inductance 5.8×10-4

Series resistance 0.018Grid transformer Leakage inductance 4.46×10-4

AC filterResistance 2Inductance 10.612×10-6

Capacitance 9.55×10-5

Grid X/R ratio 10SCR 5, 8, or 2

Controller Ganis Kp 4Ki 1000

Sbase = 450 MVA Vbase = 150 kV fb = 50 Hz

• The network consists of four branches and each branch is represented by an aggregated 100-MW WT.

• The transformer is modeled by its short-circuit impedance.

• cables are modeled as a nominal π-model.

• Grid is represented by a simple Thévenin’s equivalent circuit.

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A large WPP as a MIMO control system

6

1

1 4 3(s) (s) (s) (s) G G G G

,1

,

(s)(s)

( )

(s)

g

ref

ref

ref n

VI

U s

I

1(s) (s) (s)o refV G U

1

2

(s)(s)

( )

(s)

o

m

VV

V s

V

111 12

22 ,2 ,2 2( 1) 2 221

,2 ,2 ,2 ,2 2 ,2 ,2 21

21

, ,

( )( ) ( )( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( )( )( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( )

( )( )( ) ( ) ( )

n

g g g

c pwm n n

c pwm k c pwm c pwm

n cn

c n pwm n n

Y sY s Y sY s Y s Y s

Y s G s G s Y s Y s Y sY sG s G s Y s G s G s Y s G s G s Y sG s

Y s GY sG s G s Y s

, , ( )

, , , ,

( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( )

n pwm n n n m n nn

c n pwm n n c n pwm n n

s G s Y s Y s Y sG s G s Y s G s G s Y s

1( 1) 1( )

2 ( 1) ,2 ,2 2 ( 1) 2 2 ( )

,2 ,2 2 ,2 ,2 22

( 1) ( ) , ,

, ,

( ) ( )( ) ( )

( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( )( )

( ) ( ) ( ) ( )( ) ( ) ( )

n n m

g g

n c pwm n n m

c pwm c pwm

n n n n m c n pwm n

c n pwm n n

Y s Y sY s Y s

Y s G s G s Y s Y s Y sG s G s Y s G s G s Y sG s

Y s Y s G s G sG s G s Y s

2( )

, ,

( 1)1 ( 1) 2 ( 1) ( 1)( 1) ( 1)( )

3 4

( )1 ( ) 2 ( ) ( )( 1)

( ) ( )( ) ( ) ( )

( ) ( ) ( ) ( ) ( )( ) ( )

( ) ( ) ( )

n m n

c n pwm n n

n n n n n n n n m

n m n m n m n n m n

Y s Y sG s G s Y s

Y s Y s Y s Y s Y sG s G s

Y Y s Y s Y s ( )( ) ( )

n m n mY s

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Influence of connection or disconnection of wind turbines on stability Case I: WT-1 is connected to the WPP and the other

three WTs are disconnected.

Case II: WT-1 and WT-2 are connected and other two WTs are disconnected.

Case III: Only WT-4 is disconnected.

Case IV: All WTs are connected.Case connected wind turbines in WPP Critical pole Frequency

I WT-1 -7.865±12173i 1937 HzII WT-1 and WT-2 -7.865±12173i 1937 Hz

III WT-1, WT-2, and WT-3 -14.977±5068.2i 806 Hz

IV WT-1, WT-2, WT-3, and WT-4 11.659 ±5267.1i 838 Hz

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Influence of the number of wind turbines on harmonic stability

8Case IV Case III

0.4 0.5 0.6 0.7 0.8 0.9

-0.2

0

0.2

Time (s)

WT-

1 C

urre

nt (p

u)

0.4 0.5 0.6 0.7 0.8 0.9

-0.2

0

0.2

Time (s)

WT-

2 C

urre

nt (p

u)

0.4 0.5 0.6 0.7 0.8 0.9

-0.2

0

0.2

Time (s)

WT-

3 C

urre

nt (p

u)

Case Critical pole

I -7.865II -7.865III -14.977

IV 11.659

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damp,k dG K

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-60

-40

-20

0

20

40

Damping gain

Rea

l par

t of c

ritic

al p

ole

Case I Case II Case III Case IV

SCR = 5

Real part of the critical pole in terms of damping controller gain (Kd) for different cases under SCR = 5.

9

Influence of the active damping on harmonic stability

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Kd = 0 Kd = 0.3

0.4 0.45 0.5 0.55 0.6 0.65 0.7

-0.2

0

0.2

Time (s)

WT-

1 C

urre

nt (p

u)

0.4 0.45 0.5 0.55 0.6 0.65 0.7

-0.2

0

0.2

Time (s)

WT-

2 C

urre

nt (p

u)

0.4 0.45 0.5 0.55 0.6 0.65 0.7

-0.2

0

0.2

Time (s)

WT-

3 C

urre

nt (p

u)

Kd = 0.75

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-60

-40

-20

0

20

40

Damping gain

Rea

l par

t of c

ritic

al p

ole

Case I Case II Case III Case IV

SCR = 5

Case Critical pole

I -7.865II -7.865III -14.977

IV 11.659

10

Influence of the active damping on harmonic stability

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Influence of grid impedance variations on stability

-20.000

-15.000

-10.000

-5.000

0

5.000

10.000

15.000

Case I Case II CaseIII Case IV

Rea

l par

t of c

ritic

al p

ole

SCR = 8SCR = 5SCR = 2

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Influence of grid impedance variations on stability

12

SCR = 2 SCR = 5

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75

-1

-0.5

0

0.5

1

Time (s)

Bus-

A Vo

ltage

(pu)

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75

-1

-0.5

0

0.5

1

Time (s)

Bus-

B Vo

ltage

(pu)

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75

-0.2

0

0.2

Time (s)

WT-

1 C

urre

nt (p

u)

-20.000-15.000-10.000-5.000

05.000

10.00015.000

Case I Case II CaseIII Case IV

SCR = 8SCR = 5SCR = 2

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damp,k dG K

Real part of the critical pole in terms of damping controller gain (Kd) for different cases under SCR = 2.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-60

-40

-20

0

20

40

Damping gain

Rea

l par

t of c

ritic

al p

ole

Case I Case II Case III Case IV

SCR = 2

13

Influence of the active damping on harmonic stability

Harmony Project, | Esmaeil Ebrahimzadeh|

Influence of the active damping on harmonic stability

14Case IV

0.4 0.5 0.6 0.7 0.8 0.9 1

-0.2

0

0.2

Time (s)

WT-

1 C

urre

nt (p

u)

0.4 0.5 0.6 0.7 0.8 0.9 1

-0.2

0

0.2

Time (s)

WT-

2 Cur

rent

(pu)

0.4 0.5 0.6 0.7 0.8 0.9 1

-0.2

0

0.2

Time (s)

WT-

3 Cur

rent

(pu)

0.4 0.5 0.6 0.7 0.8 0.9 1

-0.2

0

0.2

Time (s)

WT-

4 Cur

rent

(pu)

Case III Case II Case I

Kd = 0 Kd = 0.3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-60

-40

-20

0

20

40

Damping gain

Rea

l par

t of c

ritic

al p

ole

Case I Case II Case III Case IV

SCR = 2

Harmony Project, | Esmaeil Ebrahimzadeh|

Conclusion

• Both controller parameters of power converters and passive components of wind power plants can effect on harmonic stability.

• Connecting or disconnecting of the wind turbines in a wind power plant can vary the stability conditions.

• Impedance variations of main grid may change the stability of the system.

• Future work: Sensitivity analysis respect to the wind farm elements

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Thanks for your attention

16Harmony Project, | Esmaeil Ebrahimzadeh|