juan carlos ps ce 11

8/12/2019 Juan Carlos Ps Ce 11

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AbstractThis paper presents a comparative stability analysisof conventional synchronous generators and wind farms based on

double feed induction generators (DFIG). Based on an

appropriate DFIG wind generator model, PV curves, modal

analysis and time domain simulations are used to study the effect

on system stability of replacing conventional generation by

DFIG-based wind generation on the IEEE 14-bus benchmark

system, for both fixed power factor and voltage control

operation. The results show that the oscillatory behaviorassociated with the dominant mode of the synchronous generator

is improved when the DFIG-based wind turbine is connected to

the system; this improvement in the damping ratios is more

evident when the wind turbines are operated with terminal

voltage control.

Index TermsPower system stability, Wind power generation,Synchronous generators.

I. INTRODUCTION

OWDAYS, wind power energy is increasingly penetratingele electrical grids. This penetration is mainly driven by

policies, global warming concerns and better wind

technologies. The control capabilities of these newtechnologies are continuously improving to satisfy grid code

requirements, ensuring a safe operation under normal andfault conditions. Double feed induction generators (DFIGs) is

one of the most commonly used technologies nowadays, as

these offer advantages such as the decoupled control of active

and reactive powers and maximum power tracking. Thesecapabilities are possible due to the power electronic converters

used in this type of generator.

When the penetration of wind generation is high, it isimportant to keep these generators on line as much as possible

during grid disturbances as per grid code requirements.

Therefore, there is a significant interest in investigating the

dynamic performance and characteristics of the system underhigh penetration of wind generation.

Various studies have been carried out regarding modeling of

DFIG for stability analysis. In [2]-[6], different models of

DFIG-based wind generator farms are discussed andsimulations are performed. The tuning of the parameters of the

This work has been supported in part by MITACS and NSERC, Canada;

and the Universidad de Los Andes, Merida-Venezuela.J.C. Muoz and C. A. Caizares are with the Department of Electrical and

Computer Engineering, University of Waterloo, Waterloo, ON, Canada,

N2L3G1 ([email protected], [email protected]).

DFIG controllers is also addressed in various papers. Thus, in

[11], a tuning method to optimise the parameters of the DFIGcontrollers is proposed to improve small-and large-disturbance

stability performance. In [12], a methodology to tune damping

controllers based on eigenvalue sensitivities is presented.Reference [13] studies the increase in system transient

stability margins when DFIG generators are introduced instead

of cage generators. A complete analysis of transient stabilityconsidering the point of connection of the DFIG attransmission, subtransmission and distribution levels is

presented in [14]. In [15], the impact of the increased

penetration of DFIG-based wind turbines on small and

transient stability is assessed by replacing the DFIG by

synchronous generators and evaluating the sensitivity of theeigenvalues with respect to inertia. This methodology

identifies inter-area modes that are worsen, andelectromechanical modes whose damping is increased by the

penetration of DFIG based wind turbines. In [16], the steady

state voltage stability of power systems with high penetration

of wind turbines is studied using time-series ac power flowtechniques. The methodology used in [16] incorporates

resource and system assessment for wind power, unitcommitment and economic dispatch; the historical data of

loading and wind power output are time synchronized, and the

worst operating point is identified as the point when windgeneration feeds the largest portion of load. According to this

paper, the voltage control capabilities of the DFIG wind

turbines improve the voltage stability margin at distributionand transmission levels. Also, the eigenvalues trajectories as a

function of the load for a power system containing DFIGs are

computed in [17]. In this paper, the authors conclude that the

DFIGs do not participate in the unstable modes associatedwith oscillatory instability; a sensitivity analysis of the

eigenvalues with respect to the parameters of the active and

reactive power controllers is also carried out. Finally, in [18],a four generator test system is used to study the effect ofreplacing one synchronous generator by a wind farm on the

oscillation modes of the system, resulting in an increase of the

stability of the observed modes when wind farms areconnected.

The present paper presents a comparative study of the effect

on stability of DFIG-based wind turbines vis-a-vis

conventional synchronous generators. PV curves are used foranalyzing static load margins, and the effect on the damping

ratio of the dominant mode of oscillation for the DFIG

operating at fixed power factor and terminal voltage control.

Comparative Stability Analysis of DFIG-based

Wind Farms and Conventional Synchronous

GeneratorsJ. C. Muoz, and C. A. Caizares,Fellow,IEEE

N

Power Systems Conference and Exposition, March 2011


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The presented studies are based on the IEEE 14-bus

benchmark system. Thus, in this system, one of the

synchronous generators is replaced by an aggregated DFIG-

based wind turbine of equivalent size. Simulations are carriedout using the Matlab-based toolbox (PSAT) [19], which

includes power flow, optimal power flow, continuation power

flow, small-disturbance stability and time domain simulation

tools.The rest of this paper is organized as follows: Section II

presents a brief description of the PSAT DFIG model and

associated controls. In Section III the study methodologies

used in this paper are briefly discussed. Section IV presentsand discusses the obtained simulations results. Finally, in

Section V the main conclusions of the present work are

discussed.

II. DFIG MODEL

The overall scheme for a wind farm based on DFIG is

depicted in Fig. 1. Thus, it is composed by two voltage fedPWM converters in back-to-back configuration. These

converters allow the decoupled control of the active andreactive power flow between the DFIG and the ac network by

adjusting the switching of the IGBTs. For this structure, the

equations of the double feed induction generator in terms ofthe d and q axes and neglecting the stator and rotor flux

transients can be written as [19]:

For the stator circuit:

(1)

(2)

For the rotor circuit:

1 (3)

1 (4)

where

, : d and q axes stator voltages;,: d and q axes stator currents;, : d and q axes rotor currents;

, : Stator and rotor resistances;: Stator self-reactance;: Rotor self-reactance;: Mutual reactance;: Rotor speed.

The wind turbine, generator shaft, and the gearbox is

modeled in [19] as a lumped inertia ; therefore, the motionequation can be represented by:

(5)

where

: Mechanical torque;: Electromagnetic torque.

This simplification in the inertia is valid only if it is assumed

that the controllers associated to the DFIG(s) are able to

quickly minimize the shaft oscillations [19]. The

electromagnetic torque is represented by:

(6)

Vector control schemes decouple the control of active andreactive power in the rotor. Thus, the active power P derived

from the wind turbine power-speed characteristic isassociated with the rotor current in the q axis as follows:

(7)

whereas the reactive power Q is associated with the rotorcurrent in the d axis trough the following voltage control

equation:

(8)

where

: Actual terminal voltage;: Desired terminal voltage.

This controller uses the current rotor speed to optimize theenergy extracted from the wind. Furthermore, for rotor speeds

greater than 1 p.u., the power is set to 1 p.u. and for rotor

speeds lower than 0.5 p.u. the power is set to zero. The limitsfor the rotor currents are then computed in PSAT as follows:

(9)

(10)

(11)

(12)

These limits are carefully selected to ensure a proper dynamicand steady state operation of the model.

Fig.1. DFIG overall scheme


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Four state variables can be identified in the DFIG model used

in [19]: , , , and . Where is the pitch angle. Thepitch angle control only operates for super-synchronous

speeds, and for sub-synchronous speeds the pitch control islocked. For the speed ranges used here, this pitch angle is

inactive and hence, not considered in this paper.It should be mentioned that the dynamics of the converter

are fast and are neglected. Therefore, the converter is

represented as a current source.

The wind is modeled by using the Weibull distributionavailable in [19], with a shape factor equal to two, which

results in a Rayleigh Distribution.

III. STUDY METHODOLOGY

The theoretical static load margin is computed in this paperby using PV curves. These curves are obtained in PSAT by

means of continuation power flows; this method uses

predictor-corrector steps to ensure convergence of thenonlinear algebraic equations that describe the power system,

avoiding the singularity of the Jacobian matrix near the

maximum loading point.

The eigenvalues from the linearization of the differential

algebraic equations that describe the dynamic operation of the

power system are used to perform stability studies around theequilibrium points of the PV curves [20]. This paper focuses

in small oscillatory phenomena, which can be associated with

Hopf Bifurcations (HB). These types of bifurcations areidentified by the presence of a complex pair of eigenvalues

crossing the imaginary axes of the complex plane when the

loading level slowly changes. Here, the damping ratios are

used to identify proximity to these bifurcations, which is

defined for the i-th eigenvalue of the state matrix as follows:

(13)

Moreover, by using participation factors, a better

understanding of the states that influence the dominant or

critical modes can be achieved [20].

Time domain simulations are also carried out using PSATwith the aim of studying the system dynamic behaviour under

contingency (large-disturbance) operation. These simulations

are based on the numerical integration of the differential-algebraic equations that describe the dynamic operation of the

system, and also allow to study the effect on all system

variables of wind speed variations.

IV. RESULTS

The following three study cases are addressed here:Case A corresponds to the IEEE 14-bus system with

synchronous generators, as depicted in Fig. 2. This

benchmark system, described in detail in [21], is comprised

of two synchronous generators providing active and reactivepower connected at Buses 1 and 2, and three synchronous

condensers connected at Buses 3, 6 and 8. Automatic voltage

regulators (AVR) Type II are incorporated in each machine.

The model for the synchronous generator connected at Bus 1is a 5th order model, and the models for the generator

connected at Bus 2 and all the synchronous condensers are

6thorder models. The system base load is 259 MW and81.4 MVAR. In all simulations, the load are represented

using exponential recovery dynamic models.

In Case B, the 60 MVA synchronous generator located atBus 2 in Case A is replaced by an aggregated DFIG-based

wind turbine of equivalent size and limits, operating at unity

power factor. The corresponding collector system is shownin Fig. 3; two transformation stages are modeled: one from

480 V to 25 kV and the other one from 25kV to 69kV.Detailed data for the DFIG-based wind turbine, wind model

and collector system can be found in the Appendix.

In Case C, the DFIG is assumed to operate under terminalvoltage control.

Fig.3. DFIG Collector system (PSAT).

Fig. 2. IEEE 14 bus system (PSAT).


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Normal and single contingency (Line 2-4 trip) operation are

considered for each study case.

A. Case A

Figures 4 and 5 depict PV curves for normal and

contingency operation respectively. Observe that the static

load margin in this case under normal operating condition is

435 MW, while for contingency operation this margin is

reduced to 391 MW. Moreover, HBs are identified for aloading level of 341 MW and 329 MW for normal and

contingency operation, respectively. The participation factors

associate the AVR of the generator connected at Bus 1 withthis oscillatory instability, which has a frequency of 1.32 Hz

for normal operating condition and 1.31 Hz for contingency

operation.Time domain simulations for a Line 2-4 trip at 1s at a

loading level of 332 MW is shown in Fig. 6. Notice from this

figure the oscillatory instability predicted by the eigenvalue

analysis.

B. Case B

The static load margin for Case B under normal operation is

depicted in Fig. 4. This margin is 424 MW, which is 2.53%

lower than the static load margin for Case A. This reduction ismainly due to the DFIG unity power factor operation, which

does not allow for the control of the terminal voltage. As it can

be seen from Fig. 5, a similar observation can be made for the

system under contingency conditions, where the static load

margin becomes 382 MW, which represents a 2.30%reduction with respect to Case A for the same operating

conditions.

The eigenvalue analysis for Case B shows an important

improvement in the dominant mode damping ratios associatedwith the generator connected at Bus 1. Indeed, for the same

loading levels corresponding to the HBs in Case A (341 Mw

and 329 MW), the damping ratios become 1.91% and 1.82%

for normal and contingency operation, respectively, at similarfrequencies as before. The participation factors do not link the

DFIG state variables with the oscillatory modes, which is

consistent with the observations reported in [17].

If the loading level is increased, an HB can be observed at a386 MW total load level in normal operating condition. This

corresponds to a 25% increase in the dynamic load margin

with respect to Case A. Moreover, HBs are not observed forcontingency conditions.

The above eigenvalue discussion is consistent with the time

domain simulations depicted in Fig. 6. Thus, observe that theoscillations in this case are completely damped after 25 s.

C. Case C

The DFIG-based wind turbine with terminal voltage controloperation delivers the reactive power required to keep the

voltage at terminals constant at 1.09 p.u. The limits for this

reactive power are set so that they are similar to the replacedsynchronous generator limits. As can be seen in Fig. 4, the

static load margin for Case C under normal operating

condition is 431 MW; this value is slightly lower than theCase A static load margin, but 1.6% greater than the margin

observed for the DFIG operating at unity power factor.

Moreover, in contingency operation, the static load margin for

Fig. 4. PV curves for normal operation.

Fig. 5. PV curves for contingency operation.

Fig. 6. Bus 14 voltage.


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Case C becomes 387 MW, which is 1.3% greater than the

corresponding margin for unity power factor operation.The normal and contingency operation dominant mode

damping ratios for the same loading levels associated with theHBs in Case A are 2.59% and 2.50%, respectively. These

values are roughly 74% greater than those obtained for the

DFIG with unity power factor operation. As a result,oscillatory instabilities are not observed in Case C.

Figure 6 further demonstrates the better damping response in

this case by means of time domain simulations. Observe that

oscillations are damped faster than in Case B.

Figure 7 illustrates the power output variations associatedwith wind speed changes for the DFIG operating at terminal

voltage control. The output power oscillation at 1s is mostly

the result of the voltage drop when Line 2-4 is tripped; afterthis oscillation is damped, the output power is controlled tooptimize the energy extracted from the wind speed shown in

Fig. 8. Figure 9 depicts the DFIG reactive power support;

notice that the reactive power changes to regulate the terminalvoltage and thus increase system security.

Results of a sensitivity study of the dominant-mode damping

ratios with respect to the DFIG voltage controller gain canbe seen in Table I. Observe that there is a linear correlation

between the gain and the oscillatory mode damping ratios.This correlation suggests that by properly tuning the voltagecontroller gain, DFIGs equipped with voltage control

TABLE IDOMINANT-MODE DAMPING AS A FUNCTION OF THE DFIGVOLTAGE

CONTROLLER GAIN (NORMAL OPERATION CONDITION AT 341MW

LOADING)

Dominant-mode DampingRatio (%)

10 1.67

11 1.86

12 2.0513 2.23

14 2.41

15* 2.59

16 2.76

17 2.92

18 3.08

19 3.24

20 3.39

* Base DFIG voltage controller gain

TABLE IIDOMINANT-MODE DAMPING AS A FUNCTION OF THE WIND POWER

PENETRATION (NORMAL OPERATION CONDITION AT 341MWLOADING)

Wind PowerPenetration (MW) Dominant-modeDamping Ratio (%)

5 0.89

10 1.14

15 1.39

20 1.64

25 1.88

30 2.12

35 2.36

40* 2.59

45 2.81

50 3.04

* Base synchronous generator power output

Fig.7. DFIGs output power.

Fig. 8. Wind speed.

Fig. 9. Reactive power output.


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capabilities can properly damp the oscillatory modes,

eliminating the occurrence of oscillatory instability associatedwith HBs.

Table II shows the sensitivity of the dominant mode

damping ratio with respect to the wind power penetration.

These results suggest that as wind power penetrationincreases, the damping ratio of the dominant mode improves.

For this study, the wind power output connected at Bus 2 was

gradually increased from 5 MW to 50 MW at a 342 MWloading level. These wind power output levels range between

1.33 to 15% of the total system generated power.

IV.CONCLUSIONS

A comparative stability analysis based on PV curves, modalanalysis and time domain simulations of DFIG-based wind

generators replacing synchronous generators has been carried

out for the IEEE-14 bus system. The obtained results showthat the oscillatory behaviour associated with the dominant

mode of the synchronous generator is improved when the

DFIG-based wind turbine is connected to the system, which is

consistent with similar observations by other authors. This

improvement in the damping ratio is more evident for DFIGwind turbines operating with terminal voltage control.

Moreover, the static load margins are not significantly affected

when the DFIG-based wind turbine with voltage control

operation replaces an equivalent synchronous generator; thesmall differences could be accredited to the impedances of the

collector system. However, when the DFIG is operated with

unity power factor, static load margins are reduced; thus,negatively affecting the system security.

APPENDIX

TABLE III

DFIGPARAMETERS

Power rating Sn(MVA) 60.0

Voltage rating Vn(kV) 0.480

Frequency ratingfn (Hz) 60.0

Stator resistanceRs(p.u.) 0.01

Stator reactance Xs(p.u.) 0.10

Rotor resistanceRr(p.u.) 0.01

Rotor reactance Xr(p.u.) 0.08

Magnetization reactance Xm(p.u.) 3.00

Initial constant Hm (kWs/kVA) 3.00

Pitch control gainK (p.u.) 10

Pitch control time constant Tp(s) 3

Voltage control gainKV(p.u) 15

Power control time constant Te(s) 0.01

Rotor radiusR (m) 75

Number of polesp 4

Number of Blades nb 3Gear box ratio GB 1/89

Pmax(p.u.) 0.9

Pmin(p.u.) 0.0

Qmax (p.u.) 0.35

Qmin(p.u.) -0.219

TABLE IV

WIND MODEL PARAMETERS

Wind model type Weibull

Distribution

Average wind speed vA (m/s) 14.50

Air density (kg/m3) 1.225

Filter time constant (s) 4

Sample time for wind measurements t

(s)

0.1

Scale factor for Weibull distribution c 20

Shape factor for Weibull distribution k 2

Frequency step f (Hz) 0.2

TABLE IVCOLLECTOR SYSTEM PARAMETERS

First transformation stage

Voltage ratio (kV/kV) 0.480/25

Resistance (p.u.) 0.00

Rectance (p.u.) 0.1

Fixed tap ratio (p.u./p.u.) 1.00

Second transformation stage

Voltage ratio (kV/kV) 25/69


Rectance (p.u.) 0.1

Fixed tap ratio (p.u./p.u.) 1.00Transmission line

Length of Line (km) 0*


Reactance (p.u.) 0.017

Susceptance (p.u.) 1e-3

* Zero indicates to PSAT that the line parametersare given in p.u.

REFERENCES

[1] V. Akhmatov, Analysis of dynamic behavior of electric powersystems with large amount of wind power, Ph.D. dissertation,

Technical Univ. Denmark, Lyngby, Denmark, 2003.[2] J. G. Slootweg, H. Polinder, and W.L. Kling, Dynamic modeling of a

wind turbine with doubly fed induction generator, inProc.2001 IEEE

Power Eng. Soc. SummerMeeting, pp.644-649, Jul. 2001.

[3] I. Erlich, J. Kretschmann, J. Fortmann, S. Mueller-Engelhardt, and H.Wrede, Modeling of wind turbines based on doubly-fed induction

generators for power system stability studies, IEEE Trans. PowerSyst., vol. 22, pp. 909-919, Aug. 2007.

[4] Dynamic Modeling of Doubly-Fed Induction Machine Wind-Generators, DIgSILENT GmbH, Germany, Aug. 2003. [Online].

Available: http//www.digsilent. de/images/Company/news/DFIGRev1.pdf.

[5] Y. Lei, A. Mullane, G. Lightbody, and R. Yacamini, Modeling of thewind turbine with a doubly fed induction generator for grid integration

studies, IEEE Trans. Energy Convers., vol. 21, pp. 257264, Mar.2006.

[6] L.M. Fernandez, F. Jurado, and J.R. Saenz, Aggregated dynamicmodel for wind farms with doubly fed induction generator wind

turbines, Renewable Energy, vol.33, no.1, pp. 129-140, Jan. 2008,[Online]. Available: http// www.sciencedirect.com.

[7] W. Qiao, Dynamic Modeling and control of Doubly Fed InductionGenerators Driven by Wind Turbines, inProc. 2009 IEEE/PES Power

Systems Conference and Exposition, pp.1-7, Mar. 2009.

[8] P. Ledesma, and J. Usaola, Effect of Neglecting Stator Transients inDoubly Fed Induction Generators Models,IEEE Trans. Energy Conv.,

vol. 19, pp. 459-461, Jun. 2004.[9] F. Mei and B. Pal, Modal analysis of grid-connected doubly fed

induction generators,IEEE Trans. Energy Conv., vol. 22, pp. 728-736,

Jun. 2007.

[10] J.G. Slootweg, Wind power: Modeling and Impact on Power SystemDynamics, Ph.D. dissertation, Delft University of Technology, Delft,

Netherlands, 2003.


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[11] F. Wu, X.-P. Zhang, K. Godfrey, and P. Ju, Small signal stabilityanalysis and optimal control of a wind turbine with doubly fed

induction generator, in Proc. 2007IET Gener. Transm. Distrib., pp.751-760, Sep. 2007.

[12] L. Sigrist and L. Rouco, Design of Damping Controllers for doublyFed Induction Generators Using Eigenvalue Sensitivities, in Proc.

2009IEEE/PES Power Systems Conference and Exposition, pp. 1-7,

Mar. 2009.

[13] M. V. A. Nunes, J. A. P. Lopes, H. H. Zurn, U. H. Bezerra, and R. G.Almeida, Influence of the variable-speed wind generators in transient

stability margin of the conventional generators integrated in electrical

grids,IEEE Trans. Energy Conv.,vol. 19, pp. 692, Dec. 2004.[14] Ch. Eping, J. Stenzel, M. Poller, and H. Muller, Impact of Large Scale

Wind Power on Power System Stability. DIgSILENT GmbH,

Germany, Apr. 2005. [Online]. Available: http//www.digsilent.de/

Consulting/Publications/PaperGlasgow_DIgSILENT.pdf.

[15] D. Gautam, V. Vittal, and T. Harbour, Impact of Increased Penetrationof DFIG-Based Wind Turbine Generators on Transient and SmallSignal Stability of Power Systems, IEEE Trans. Power Syst., vol. 24,

pp. 1426-1434, Aug. 2009.

[16] E. Vittal, M. OMalley, and A. Keane, A Steady-State VoltageStability Analysis of Power Systems With High Penetrations of Wind,

IEEE Trans. Power Syst., vol. 25, pp. 433-442, Aug. 2009.

[17] H.A. Pulgar-Painemal and P.W. Sauer, Power system modal analysisconsidering doubly-fed induction generators, in Proc.2010 Bulk

Power System Dynamics and Control (iREP) Symposium, pp. 1-7, Aug.

2010.

[18] J.J. Sanchez-Gasca, N.W. Miller, and W.W. Price, A modal analysisof a two-area system with significant wind power penetration, inProc.

2004 IEEE PES Power Systems Conf. Expo.,pp. 1148-1152.

[19] F. Milano, PSAT, Matlab-based Power System Analysis Toolbox,2010, [Online]. Available: http:// www.power.uwaterloo.ca/~fmilano/.

[20] A. Gomez-Exposito, A. J. Conejo, and C.A. Caizares, ElectricEnergy Systems: Analysis and Operation ,vol. I. Boca Raton: CRC

press, 2009, pp. 428-452.

[21] S. K. M. Kodsi and C. A. Caizares, Modeling and simulation of IEEE14 bus system with Facts controllers, Tech. Rep., Univ. Waterloo, ON,Canada, [Online] Available: http://www.power.uwaterloo.ca.,

Mar.2003.

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