Study of transient stability for parallel connected inverters in microgrid system works in stand...

1

Study of transient stability for parallel connected inverters in Microgrid system works in stand-alone

F. Andrade, J. Cusido, L. Romeral, J. J. Cárdenas

Page|2


Introduction

[1] Networks have been undergoing significant changes in the last few years due to the growth of distributed generation (DG)

Page|3


Inverters can be classified in current source inverters (CSI) or voltage-source inverters (VSI).

Microgrid conceptthe Microgrid is defined as an aggregation of loads and microsources operating like single system providing both power and heat.

• Studies Stability

Page|4


[Vásquez et al., 2009], [Guerrero et al, 2004] , [Guerrero et al, 2006] , [Coelho et al, 2002], Pogaku et al, 2007], [Nikkhajoei y Iravani, 2007]

• Studies Stability

Page|5


[Vásquez et al., 2009], [Guerrero et al, 2004] , [Guerrero et al, 2006] , [Coelho et al, 2002], Pogaku et al, 2007], [Nikkhajoei y Iravani, 2007]

Page|6


• OutlineNon-linear

model

Lyapunov Function

Small Signal Result

Page|7


• A Mathematical model

Ren

ewab

leSo

urce

1

Filter 1Inverter 1 Inverter 2

Ren

ewab

leSo

urce

2

Filter 1

1V

1I

2V

2I

1Z 2Z

3Z

qqddi IVIVsP

dqqdi IVIVsQ

sPs

sP if

f

sQs

sQ if

f

Page|8


• A Mathematical model

Ren

ewab

leSo

urce

1


Ren

ewab

leSo

urce

2

Filter 1

1V

1I

2V

2I

1Z 2Z

3Z

Pk p 0

QkVV v 0

droop curves (f vs P and V vs Q)

Page|9


• working in the time domain

ifpf Pk

ifvf QkVV

Page|10



ifpf Pk

ifvf QkVV

qd jVVV

cosVVd

sinVVq

d

q

V

Varctan

Page|11



ifpf Pk

ifvf QkVV

qd jVVV

cosVVd

sinVVq

d

q

V

Varctan

22qd

qddq

VV

VVVV

22qd VVV

Page|12


• A Generator

QV

VkVVV

QV

VkVVV

Pk

qfvqfdq

dfpqdfd

fpf

We have a set of equations which describe the behavior of each inverter

Page|13


• The whole system

22

22222222

22

22222222

222222

11

11111111

11

11111111

111111

QV

VkVVV

QV

VkVVV

Pk

QV

VkVVV

QV

VkVVV

Pk

qfvqfdq

dfpqdfd

fpf

qfvqfdq

dfpqdfd

fpf

• The network

Page|14


Ren

ewab

leSo

urce

1


Ren

ewab

leSo

urce

2

Filter 1

1V

1I

2V

2I

1Z 2Z

3Z

2

2

1

1

22221212

22221212

12121111

12121111

2

2

1

1

2

1

323

331

2

1

q

d

q

d

q

d

q

d

V

V

V

V

GBGB

BGBG

GBGB

BGBG

I

I

I

I

E

E

YYY

YYY

I

I

• The network

Page|15


Ren

ewab

leSo

urce

1


Ren

ewab

leSo

urce

2

Filter 1

1V

1I

2V

2I

1Z 2Z

3Z

2

2

1

1

22221212

22221212

12121111

12121111

22

22

11

11

2

2

1

1

00

00

00

00

q

d

q

d

dq

qd

dq

qd

V

V

V

V

GBGB

BGBG

GBGB

BGBG

VV

VV

VV

VV

Q

P

Q

P

Page|16


• The whole system

26

25

6253672

625

635266

26

256554616

26

25

6253572

625

635256

26

255564515

26

25

625342

625

63523

26

252414

23

22

6253372

322

635236

23

223521313

23

22

6253272

322

635226

23

222531212

23

22

625342

322

63523

23

222111

XX

XXXXX

XX

XXXXXXXXXXXX

XX

XXXXX

XX

XXXXXXXXXXXX

XX

XXXX

XX

XXXXXXXX

XX

XXXXX

XX

XXXXXXXXXXXX

XX

XXXXX

XX

XXXXXXXXXXXX

XX

XXXX

XX

XXXXXXXX

• Study of Stability for the Microgrid by means of Lyapunov’s method

Page|17


• System

Page|18


Ren

ewab

leSo

urce

1


Ren

ewab

leSo

urce

2

Filter 1

1V

1I

2V

2I

1Z 2Z

3Z

Variable Value unitLine transmission (Z3) 0.5+3i Ω

Local load (Z1) 13+6i ΩLocal load (Z2) 25+13i Ω

Cut-off freq. of measuring filter (ωf) 37.7 rd/sFrequency droop coefficient (kp) 0.0005 rd/s/W

Voltage droop coefficient (kv) 0.0005 V/VARNominal frequency 377 rd/s

• Study of Stability for the Microgrid by means of Lyapunov’s method

• Lyapunov‘s Funtion

Page|19


26

25

26

25

24

23

22

23

22

21)(

XX

XXD

CX

XX

XXB

AXXV

kk

XXV 0)(

0)0( V

0)0( f

• Lyapunov‘s Funtion

Page|20


26

25

26

25

24

23

22

23

22

21)(

XX

XXD

CX

XX

XXB

AXXV

kk

XXV 0)(

0)0( V

0)()()()()()(

66

55

44

33

22

11

XX

XVX

X

XVX

X

XVX

X

XVX

X

XVX

X

XV

0)( XVdt

d

• Using Matlab for find the values

Page|21


066

2/126

2555

2/126

25

4433

2/123

2222

2/123

2211

XXXXFXXXXE

XCXXDXXXCXXXXBXAX

• Eigenvalues of lineal system

Page|22


XAX~~

15.032.29.154006.0061.00

42.25.3686.9097.0954.00

97.034.07.37956.0097.00

000005.154

157.094.00217.057.360

944.0157.00936.0466.07.37

A

;5.37;7.377.35;9.26;8.10;0 654321

• Simulation results of a DG Microgrid system by means of Power Electronics tools

Page|23


0.5 1 1.5 21500

1600

1700

1800

1900

2000

2100

2200

t(s)

kW

P Power Elect. model

0.5 1 1.5 2-500

0

500

1000

t(s)

VAR

Q Power Elect. model

L=8mHL=0.5mHL=5mH

L=8mHL=5mHL=0.5mH

• Simulation results of a DG Microgrid system by means of Nonlineal model.

Page|24


0.5 1 1.5 2-500

0

500

1000

t(s)

VA

R

Q Nonlineal Model

0.5 1 1.5 21600

1700

1800

1900

2000

2100

2200

t(s)

kW

P Nonlineal Model

L=8mHL=5mHL=0.5mH

L=8mHL=5mHL=0.5mH

• Study of stability by means of Lyapunov function and root locus plot.

Page|25


0 0.2 0.4 0.6-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0Lyapunov function Plot

t(s)-40 -30 -20 -10 0 10

-30

-20

-10

0

10

20

30Root locus Plot

0

L=8mH

L=0.5mHL=8mH

L=0.5mH

L=8mH

L=0.5mH

L=8mH

L=0.5mH

L=8mH

L=0.5mH

0)( XV

• Conclusions

• A nonlinear state-space model of a Microgrid.

• It has analyzed the model by means of both stability studies: Lyapunov function and root locus plot.

• Using that Lyapunov function, we can determined the region of asymptotic stability.

Page|26


Thank you for your Attention

Page|27


Date post:	24-Jun-2015
Category:	Technology
Upload:	fundacio-ctm-centre-tecnologic
View:	597 times
Download:	1 times

Study of transient stability for parallel connected inverters in microgrid system works in stand...

Technology