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Dynamic and Stability Improvement of a

Wind Farm Connected to Grid Using UPFC

M. Tarafdar Hagh, A. Lafzi and A. Roshan MilaniElectrical Department, University of Tabriz, Tabriz, Iran

Abstract - Wind power exploitation development to provide

Electricity has had more acceleration in recent years in compare

with other sources of providing electrical energy in the world.Since, regions with the potential of wind energy are notnecessarily close to consumers ,analyzing and modeling of windfarms in order to distribute system load and to study theelectrical and mechanical changes of them is important in many

aspects and generally ,wind farms which are connected toelectricity system by radius and local grids, will face possibility of transferring provided power of wind farms problem when theposition of consumers is far from mentioned units where, usingFACTS devices are considered in order to keep stability and tocreate provided Electricity transferring conditions to consumers.In this paper, a wind farm modeling and UPFC using are studiedto solve the wind farms power transmition problems.

I. I NTRODUCTION

Because of electrical grids development, specially windenergy usage and wind farms construction and connectingthem to general electricity grid, optimum use of existing gridsand dynamic stability increase of them has a specialimportance. UPFC (unified power flow control) with theability in unified power controlling is able to control the activeand reactive power flowing by the line, independently and cancorrect the parameters like terminal voltage and load angelusing UPFC in a single grids requires exact studies on it’sinstallation in the grid [1]. Different models for UPFC areintroduced in various studies, which one of the ideas isdetailed model appliance in which, all switches dynamic ismodeled, this method is not suitable for dynamic studies

because it requires a long time to be simulated [2]. The other method is using current injection sources for UPFC analysis.This method’s weak point is it’s appliance in a specifiedfrequency and so electrical parts dynamics are omitted [3, 4].

In this paper structure and UPFC functional basics under stable conditions and induction generator model and windturbine model is mentioned initially and then the effect of UPFC connected to a sample wind farm, in respect windvelocity changes and wind farm distance to grid and power flow are studied.

II. STEADY STATE MODEL OF THE UPFC

Unified power flow control (UPFC) is able to control activeand reactive power flow the transmition line and bus voltageregulating synchronously. Fig.1 shows UPFC schematic whichcontains a parallel ac/dc voltage source converter and a seriesdc/ac voltage source which are connected by a dc capacitor.

UPFC is combination of a parallel reactive power compensator (STATCOM) and a series compensator (SSSC).Series converter has the ability to control voltage angel andamplitude that regulate the active and reactive power flow of transmition line by voltage injection. Parallel converter

provides the real power required by the series converter,converted between the grids. Dc capacitor provides the

possibility of converting the real power between two

converters [5]. Stable function of UPFC with two seriesvoltage source converters VB<įB and parallel VE<įE with their equivalent impedances is shown in Fig. 2.

Fig 1.UPFC structure.

Fig 2. Steady state model of UPFC.

978-1-4244-1706-3/08/$25.00 ©2008 IEEE.

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In this model series voltage source and parallel voltagesource equivalence condition can be shown from the followingequation.

)1(PB+PE=0

Mentioned equation shows that, in the stable model, no

active power is converted between system and UPFC. XB ˬ

XE and Zkm parameters are in respect the transmition lineimpedance, parallel and series voltage sources impedances.Active and reactive power flows in transmition line can beexpressed by:

)2(

∗

∗

¸̧ ¹

·¨̈©

§

+

−−==

¸̧ ¹

·¨̈©

§ −+

+

−+==

Bkm

k Bmmmk mmk

e

E k

Bkm

m Bk k kmk km

jX Z

V V V V I V S

jX

V V

jX Z

V V V V I V S

..

..

*

*

Where B BV δ ∠ and E E V δ ∠ are the control variables of

UPFC. There are equality and inequality power constraints andinequality voltage constraints of the UPFC, which are given by(3) and (4).Shunt voltage and power constraints:

)3(( )

max

max

22

E E

E E E

V V

S Q P

≤

≤+

Series voltage and power constraints:

)4(( )

max

max

22

B B

B B B

V V

S Q P

≤

≤+

Where, SEmax and SBmax are the power limits for the shunt

and series voltage sources, and VEmax and VBmax are the limitson their voltage magnitudes [6]. Series and parallel converter control system acts in the way that output voltage converters

response to internal reference variants v pqref for seriesconverter and i pq ref for parallel converters correctly as thecontrol main structure. Series converter generates voltage

vector (v pq) with demanded amplitude and angle by input

reference. This voltage injection always is directly to affect onthe power flow on the line. Applied PI control system for series converter is shown in Fig. 3.

Fig 3. Series converter control system.

III. WIND TURBINE MODEL

The mathematical relation for the mechanical power extraction from the wind can be expressed as follows:.

)5(32

2

1

ω ρπ V C R P pm=

Where, Pm is the extracted power from the wind, ȡ is the air

density, R is the blade radius (m), VȦ is the wind speed (m/s)and Cp is the power coefficient which is a function of tip speedratio, Ȝ , and blade pitch angle, ȕ (deg). Cp can be shown fromthe following equation [7]. Simulation of wind farm controlmodel is shown in Fig. 4.

)6(( ) λ β λ 17.02 6.5022.0

2

1 −−−= eC p

)7(

B

V ω

λ ω =

Fig 4. Dynamic model of wind turbine.

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IV. I NDUCTION GENERATOR MODEL

Induction generator is modeled using d-q equations as below.

)8(

sd dArqrqr rq

rqdArd rd r rd

sd d sq sq s sq

sqd sd sd s sd

dt

d i RV

dt

d i RV

dt

d i RV

dt d i RV

λ ω λ

λ ω λ

λ ω λ

λ ω λ

−+=

−+=

−+=

−+=

)9(md dA ω ω ω −=

)10(

)(2

rqrd rd rqem ii P

T λ λ −==

)11(

mecheq Lemdt

d J T T ω =−

Here, Vrd, Vrq, ird, irq, Ȝ rd, Ȝ rq are stator quantities and Vsd,Vsq, isd, isq, Ȝ sd, Ȝ sq are rotor quantities. Ȧd is synchronousreference frame speed and Ȧm is rotor speed in electricalradians per second. Here it is to be noted that TL is load torque,

but for modeling the induction machine as generator it is

considered as negative torque [8].

V. TEST SYSTEM MODEL

Studied wind farm in this paper has six, 1.5 mega wattturbine, mentioned units are connected to consumer by a400/20 KV transformer and a 25 km, 20 KV line andconnected to grid by a 132/20 KV transformer.

Generators used in this model are squirrel cage Inductiongenerators and stator windings are connected to the griddirectly and in order to compensate a part of required reactive

power, capacitor bank is used at the junction point. Simulatedmodel is shown in Fig.5. In this figure sample system

containing wind farm model and its turbines, is shown together with the other elements. Wind turbines are studied in windvelocity changes conditions and also reactive and active power flow control in the presence of UPFC and without that isexamined in modeling. Wind velocity changes affects and

studying its effects on the system dynamics has been modeledtogether with the wind farm power changes.

Fig 5. Test system model.

Wind velocity has been modeled linearly from 8 m/s to 11m/s in 8 seconds. In this period of time, output power increaseof units at the nominal value is modeled by the wind turbines’

pitch angel control.Induction generators required reactive power is determined400 KVAR by capacitor banks connected to 400 volt terminals

for each induction generator couple. It’s obvious that invarious power generation conditions more reactive power is

provided by the grid. Wind velocity initial conditions isconsidered 8 m/s for wind turbines that increase to 11 m/s atthe 2, 4, 6 sec, in respect. Initially that increase dynamicconditions of wind farm is studied according to the directconnection of wind turbines.

A. System study with direct connection condition (no UPFC)

In this conditions according to the great distance betweenthe consumers and generation units and weakness of the unitsconnections to the electrical system, generated power proper transmition possibility is not provided. Modeling conclusions

and wind farms induction generators output is shown in Fig. 6.As you see, units output power increase by wind velocity

increase. As the nominal power is extractable at 9 m/s windvelocity, so in modeling under condition that wind velocityincrease more, wind farm pitch angel control, increases the

blades angel and controls them to create the possibility of out put power maintains that this issue is seen at 4 second at Fig.(6-d) for the first turbine. Above conditions are modeled attimes 6 sec and 8 sec for 2nd and 3rd turbines in respect.

Also, units required reactive power increase demand is inadditions to the constant capacity installed on their terminals isshown in Fig. (6-b), as you see, wind velocity increase and infollow units generating power absorb from the grid. At the

time 6 sec, third group wind farms are modeled in condition of generating increase. In approximately 8 sec, pitch anglecontrol condition is provided for it.Fig. 7 indicate electrical changes of the wind farms connection

point to the grid. As you see, wind velocity increase, thatfigure (7-b) shows the reactive power absorbed from the grid.

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Fig. 11, shows the voltage amplitude and UPFC seriesconverter angel which is provided to keep the generating

power flow to grid under system conditions. As you see, after UPFC applying to the system at t=6 s, output voltage hasincreased in 0.1 pu in order to keep the power flow. According

to above modeling, UPFC function in stability of wind farmsconnection to grid is very important.

Fig 10. Fig (10-a) and (10-b) show active and reactive power of wind farm busand Fig (10-c) and (10-d) show voltage and current of wind farm bus with

UPFC.

Fig 11. Fig (11-a) shows converter voltage magnitude of UPFC, Fig (11-b)

shows UPFC series converter angel.

VI. CONCLUSION

In recent years, wind energy operation to generate electrical power has had a great improve. Transmition conditions studyand using wind energy in electrical grids and connection of wind farm to grid is function of power system topology. Using

FACTS devices in order to transmit maximum wind farmgenerated power by keeping their stability under varioussystem conditions is considered. In this paper UPFC functionin wind farms generated maximum transmission power isstudied.

R EFERENCES

[1] N.Tambey, M.L.Kotharri, “Damping of power system oscillations withunified power flow controller (UPFC)”, IEE Prroc. Transm. Distri. , Vol. 150,

NO. , March 2003.[2] C.T.Chang, Y.Y.Hsu, ”Design of UPFC controllers and supplementarydamping controller for power transmission control and stability enhancement

of a longitudinal power system ”, IEE Proc. ,Gene. ,Disti. ,Vol. 149 ,NO. 4,July 2002.[3] Z.J.Meng, P.L.So, “A Current injection UPFC model for enhancing power

system dynamic performance”, IEEE Transaction on Power Systems 2000.[4] D.Z.Fang, H.F.wang, “Application of the injection modeling approach to

power flow analysis for systems with unified power flow controller”,

Electrical Power and Energy Systems 2001.

[5] Papic .I.Zunko.P, Povh,D, “Basic control of unified power flowcontroller”, IEEE Transactions on Power Systems, pp. 1734_1354, 1997.

[6] Bei Xu, Ali Abur, “Satate estimation of systems with embedded FACTSdevices”, IEEE Bologona Power Tech Conference, Italy, June 2003.[7] Woei_Luen, Yaun Yih, "Controller design for an induction generator

driven by a variable speed wind turbine", IEEE Transaction on Energyconversion, Vol 21, No 3, 2006.[8] Nitin N. Joshi, N.Mohan, “ Application of TCSC in Wind Farm

Application” , IEEE Conference, Speedam 2006.

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