Small Signal Stability Analysis for a DFIG-Based Offshore Wind Farms Collected Through VSC-HVDC Transmission System

doi:10.4236/epe.2013.54B083

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Energy and Power Engineering, 2013, 5, 429-433

doi:10.4236/epe.2013.54B083 Published Online July 2013 (http://www.scirp.org/journal/epe)

Small Signal Stability Analysis for a DFIG-Based Offshore

W ind Farms Collected Thr ough VSC-HVDC

Transmission System

Kai Liao, Zhengyou He, Bin Sun, Yong Jia

School of Electrical Engineering, Southwest Jiaotong University, Chengdu, China

Email: [email protected]

Received April, 2013

ABSTRACT

This paper modeled a doubly fed induction generator (DFIG) - based offshore wind farm integrated through a voltage

source converter –based high voltage direct current (VSC-HVDC) transmission system, which is collected with infin ite

bus for small signal stability analysis. The control system of HVDC system is considered for the stability analysis. The

impact of the VSC control parameters on the network stability is studied. The lineared dynamic model is employed to

do small signal stability analysis by th e eigenvalue analysis. The locus of th e eigenvalue, which is corresponding to the

oscillation model is studied. Time domain si mulations conducted in Matlab/Simulink are used to validate the small sig-

nal stability analysis.

Keywords: DFIG; Offshore Wind Farm; VSC-HVDC; Small Signal Stability

1. Introduction

Because the advantages in speed control, reduced flicker,

and four-quadrant active and reactive power capabilities,

are primarily achieved via control of a rotor side con-

verter. Many large offshore wind farms based on DFIG

(Doubly fed induction generator) have been planned

around the world wide [1, 2]. The High-voltage dc (HVDC)

transmission is emerging as the prospective technology

to address the challenges associated with the integration

of future offshore wind power [3].

In [4] and [5], a VSC transmission system was used to

connect a 6-MWwind farm to the grid. VSC transmission

systems were also proposed in [6], for transmitting off-

shore wind power equipped fixed speed generators to the

grid. However, many large wind farms under develop-

ment will employ DFIG-based wind turbines whose op-

eration and response to net-work disturbances are sig-

nificantly different from other types of generators. In [7],

line commutated HVDC systems were used to connect a

large DFIG-based offshore wind farm into the grid. In [li

xue] described the use of VSC-HVDC transmission sys-

tem technology for connecting large DFIG-based wind

farms over long distance. New control strategies for

normal and grid fault conditions are proposed. To obtain

smooth operation, the wind farm side VSC is controlled

as an infinite voltage source that automatically absorbs

power generated by the wind farm and maintains a stable

local ac network.

The dynamic behavior of the doubly fed induction ge-

nerator (DFIG) has been investigated in many papers.

The majority of these studies are based on time-domain

simulations to show the impact on power syste m dynam-

ics [8,9], the performance of decoupled control and

maximum power tracking, the response to grid distur-

bances, the control methods to make the DFIG behave

like a synchronous generator [10-13], etc. Time-domain

studies offer a direct appreciation of the dynamic behav-

ior in terms of visual clarity. However, the time domain

simulation can’t observe all oscillation modals [14 ].

In [15], a model suitable for small-signal stability

analysis and control design of multi-terminal dc networks

is presented. A generic test network that combines con-

ventional synchronous and offshore wind generation

connected to shore via a dc network is used to illustrate

the design of enhanced voltage source converter (VSC)

controllers. The impact of VSC control parameters on

network stability is discussed and the overall network

dynamic performance assessed in the event of small and

large pert urbations .

In this paper, the grid-connected DFIG via VSC-HVDC

system is studied. The single-machine infinite-bus

(SMIB) approach is followed. The paper is organized as

follows. In Section II, the mathematical model is ob-

served. In Section III, modal analysis method and the

eigenvalue locus under different controller parameters is

K. LIAO ET AL.

430

studied. Sectio n IV p rese nt s the conclusion.

2. Modeling of Study System

The study system is shown in Figure 1 where a DFIG-

based wind farm (100MW form aggregation of 2 MW

units) is connected to a VSC-HVDC link.

2.1. DFIG Generator

The one-phase equivalent electric circuit of the DFIG is

shown in Figure 2. The dynamic equations of DFIG are

usually described by transforming the machine ‘abc’

voltage equations into a synchronously rotating frame,

referred to as the ‘d-q’ frame.

For stability analysis, the generato rs are modeled as an

equivalent voltage source based on transient impedance.

The DFIG is modeled as

122

qs elel rel

qsel dsqsds

ss ss rss

elmrr el

qs qr

ss ss

di wRww w

iwi ee

dtw LwL TwL

wKw

wL wL



 



(1)

122

dselel rel

el qsdsdsqs

ss ss rss

elmrr el

ds dr

ss ss

diw Rw ww

wi iee

dtw LwL TwL

wKw

wL wL



 



(2)

2()

qs els r

el dsqselds

rs s

mrrel dr

de www

wRie we

dtTww

Kwv









(3)

2()

dselr s

el dsdselqs

rs s

mrrel qr

deww w

wRiewe

dtT ww

Kwv





 



(4)

Figure 1. The studied system structure.

Figure 2. The equivalent electric circuit of the DFIG.

where ds



and ds



are the equivalent internal q- and

d-axis voltages, respectively; ids and iqs are the stator q-

and d- axis currents, respectively. All the parameters are

converted to p.u.

2.2. Converter

Figure 3 illustrated a converter circuit diagram in ‘abc’

frame.

The dynamic model of the converter in ‘abc’ frame

can be modeled as

caaasa

cbbbsb

cccc sc

uii

uLiRiu

uii

























(5)

Use the Park transform as shown in (6), the dynamic

model in ‘d-q’ frame is shown in (7).

sinsin(120 )sin(120 )

3coscos(120 )cos(120 )

wt wtwt

Pwt wtwt





















(6)

mdcd mdsd

mqcq mqsq

iviu

dtL L L































(7)

where, Vc is the converter voltage and Vs is the grid volt-

age. Under PWM control, the amplitude of the converter

output fundamental voltage is controlled by the modula-

tion index as

cdc

VMV



 (8)

In ideal condition, the dc side transmission syste m can

be expressed as

()

dc dcd mdmq

Mi Mqi

dt CC

  (9)

where, the imd and imq are the d-and q- axis converter

current, respectively. M is the modulation index. Vdc is

the DC voltage and Idc is the DC current.





Figure 3. Converter circuit diagram.

K. LIAO ET AL. 431

2.3. Controller of Wind Farm Side Converter

The aim of the wind farm side converter controller sys-

tem is to maintain the wind farm network work at con-

stant frequency and voltage. One of the primary require-

ments for the WFVSC is to collect energy from the wind

farm. The output power of DFIG’s is contro lled by pow-

er electronic converters and MPPT system. The network

frequency variations have little influence on the power

generation. Therefore, to simplify the control system

design, the control strategy adopted here is to control the

wind farm side converter to resemble an infinite voltage

source with constant frequency, voltage amplitude, and

phase angle. The control block diagram for the wind

farm side converter is shown as Thus, as in the case

when a wind farm is connected to an infinite ac system,

the power generated by the wind farm is automatically

absorbed by the source resembled by the wind farm side

converters and then transmitted to the grid via the DC

lines. The main tasks for the WFVSC are then to collect

energy from the wind farm and to control the ac voltage

and frequency of the local wind farm network.

2.4. Controller of Grid Side Converter

The wind farm side converter collects energy from wind

farm and then transmit it to the power grid via the dc

transmission and grid side converter. For the normal op-

eration of a VSC transmission system, its dc link voltage

must be maintained at a constant value under all condi-

tions. A constant dc voltage indicates balanced active

power flow between the two sides. Abnormal dc link

voltage can cause the system to trip and disrupt its nor-

mal operation. Furthermore, to achieve this balance, the

grid side converter is assigned to control the dc voltage,

to ensure the energy collected by the wind farm side

converter is transmitted to the grid network. The control

system of the grid side conv erter is shown as Figure 5.

The current control loop is designed as:

()()

dpsd sdisd sd

ukiikii



 

dt

(10)

Figure 4. Control block diagr am of the wind farm side con-

verter.

()()

qp sqsqisqsq

ukiikii



 

dt

(11)



is designed as the dc voltage control loop and



designed as the connection bus voltage control loop.

()(

sdpdc dcidc dc

ikVVkVVd

 

 

)t

(12)

()()

sqpGGiGG

ikVVkVVd

 

 

 (13)

According to (9), the modulation index M in dq frame

are give n as (14) and (15).

()

ddsdssq

LR sd

ui iv

VL L



 (14)

()

qqsqssd

LR sq

ui i v

VL L



 (15)

2.5. DFIG Control

The DFIG control is comprised by two PWM modulation

inverters connected back to back via a dc link. The con-

trol system is to ensure the stator frequency of DFIG

operates at a constant value, and constraint for maximum

power capture. So, the rotor side converter operates as a

controlled voltage source since it injects an ac voltage

with varying frequency to the rotor to keep the stator

voltage frequency be a constant value under varying

wind speed. The ac voltage of the rotor-side converter

depends on the control objectives. For grid-connected

dc ref

dref

ac ref

qref

PLL

()cos ref

s( )in ref

Inverter-side Controller

Current Controller

Voltage Controller

Figure 5. Control block diagram of the grid side converter.

dc,ref

k



G,ref

k



Figure 6. The control system of the grid side converter.

K. LIAO ET AL.

432

WECS applications, a sensible choice is to impose a con-

straint for maximum power capture (equivalent to air gap

power, electromagnetic torque, or speed constraint) and

another for the voltage control (reactive power con-

straint). These two objectives determine the DFIG rotor

voltage.

For the grid-side converter, the control has to be coor-

dinated so that the dc-link voltage is constant and the

desired sharing of reactive power with stator is achieved.

Usually, for minimum the converter rating, the reactive

power delivered to the grid only from the stator. So, the

there is no reactive power delivered to the grid and the

rotor side converter works at unity power factor.

In this paper the dynamic of the DFIG rotor is ignored.

The rotor side voltage, electromagnetic torque, rotor side

current and reactive and active power is constant.

3. Modal Analysis

The most direct way to assess small-signal stability is via

eigenvalue analysis of a model of the power system. In

this case, the “small-signal” disturbances are considered

sufficiently small to permit the equations representing the

system to be linearized and expressed in state-space form.

The model of a power system can be expressed as a set

of DAE. The linearized model of the test system can be

expressed in state-space form as

 xxB

u (16)

where x is the where is the state vector, u is the input

vector, A is the state matrix, and B is the input or control

matrix. The eigenvalue of the state matrix provide the

necessary information about the small-signal stability of

the system.

The purpose of th is study is to observe the influence of

VSC-HVDC control parameters on the small signal sta-

bility of the studied system. Vary the value of Kp1,

which is employed in the DC line voltage control in

VSC-HVDC system. The corresponding eigenvalue dis-

placements are shown in Figure 7. With a larger Kp, the

observations indicate that better damped for the oscilla-

tion modal.

Varying the control parameters of Ki, which can also

employed to DC voltage regulations. The corresponding

eigenvalue displacements are shown in Figure 8. The

analysis result indicates that the small Ki are better

damped and their oscillation frequencies are lover com-

pared to with large Ki controller.

The time domain simulation result is shown in Figure

9. Under a single phase fault in ac transmission line, the

transmission power of the bus, which collected the VSC

-HVDC system and wind farm operate at different con-

trol parameters is shown in the figure. The result of the

time domain simulation validates the results obtained

from the small-signal stability analysis above.

Figure 7. The eigenvalue locus under varying Kp.

Figure 8. The eigenvalue locus under varying Ki.

Figure 9. The time domain simulation result.

4. Conclusions

A lineared mathematical model for small signal stability

analysis of VSC-HVDC transmission system collected

with a DFIG based wind farm has been presented in this

paper. The lineared model is based the state-space mod-

els. The state matrix is employed to investigate the small

signal stability performance of the studied system

through the eigenvalue analysis. The eigenvalue locus

under different HVDC system control parameters is ob-

served. It was validated that using the small-signal stabil-

ity model, it was possible to design improved controllers

for the VSCs of the multi-terminal dc network, which

ensure stable network operation and enhanced dynamic

K. LIAO ET AL.

433

performance. The time domain simulation also validated

the analysis results.

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