1

Abstract-- The paper presents dynamic modeling and simulation of a grid connected variable speed wind turbine (VSWT) using PSCAD/EMTDC, a widely used power system transient analysis tool. A variable speed wind generator with power electronics interface is modeled for dynamic simulation analysis. Component models and equations are addressed and their incorporations into the EMTDC are provided. Controllable power inverter strategies are intended for capturing the maximum power under variable speed operation and maintaining reactive power generation at a pre-determined level for constant power factor control or voltage regulation control. The component models and control schemes are constructed by user-define function provided in the simulation program. Simulation case studies provide the variable speed wind generator dynamic performance for changes in wind speed. This modeling work can be employed to evaluate impacts on power grid as well as the control scheme and output performance of a variable speed wind power system at the design state.

Index Terms— Grid connection, Maximum power capture, Power electronics interface, Reactive power control, Variable speed, Wind turbine

I. INTRODUCTION

RIABLE speed operation yields 20 to 30 percent more energy than the fixed speed operation, providing benefits

in reducing power fluctuations and improving var supply. Falling prices of the power electronics have made the variable speed technology more economical and common [1]. Such a wind turbine system as other types of dispersed generation is mostly connected to distribution feeders and the generation system cannot be easily connected to the electric power network without conducting comprehensive evaluations of control performance and grid impacts. This requires a reliable tool for simulating and assessing dynamics of a grid connected variable speed wind turbine.

The purpose of the work is to provide the capability of simulating and analyzing the dynamic performance and grid impacts of a variable speed wind energy conversion system using a reliable power system transient analysis program, PSCAD/EMTDC. The modeled system includes a fixed-pitch type wind blades, a direct-drive synchronous generator without a gear-box, and a controllable power electronics system, which consists of a six-diode rectifier and a IGBT voltage source inverter. The entire schematic diagram of the modeled wind generation is shown in Fig. 1. Models of the elements and the system control scheme are proposed in the form of mathematical equations and graphical control blocks and implemented in PSCAC/EMTDC [2]. Not only the large

base of built-in components available in the program but also user-defined models are used for assembling the wind turbine system. Overall control strategy and some major part of the system elements, i.e. wind turbine, are modeled by the user-define functions. The study results demonstrate the modeling work provide a reliable and useful simulation tool for evaluating the dynamic performance of a variable speed wind turbine integrated into power system.

SG

VSIRectif ierPower GridWind

Transformer

DC link

VSWT

Fig. 1. Schematic representation of modeled VSWT

II. EMTDC BASED MODELING

The variable speed wind turbine model consists of the following components.

- Wind model - Wind turbine - Synchronous Machine - Rectifier and voltage source inverter - Power electronics control

Fig.2 depicts the component blocks of a VSWT model.

WT SG POWER

ELECTRONICS

VBASE

VNOISE

VGUST

VRAMP

VWIND

WE

TM

CONTROL

EXC

WM EFIF

VEX_REF

VDC

PWT, QWT,

VWT, IWT

+

+

+ +

Fig. 2 Components of a VSWT simulation model

For modeling the shaft and synchronous generator, models

provided by the EMTDC program are used, and models of the wind speed, the wind turbine, power electronics block and the control block are built into the program by user define function of coding in FORTRAN or assembling the built-in elements and modules.

A. Wind Model

A wind model selected for this study is a four-component

Seul-Ki Kim, Eung-Sang Kim, Jae-Young Yoon and Ho-Yong Kim

PSCAD/EMTDC Based Dynamic Modeling and Analysis of a Variable Speed Wind Turbine

V

2

model [3], and can be described by equation (1).

VWIND = VBASE + VGUST + VRAMP + VNOISE (1) Where, VBASE = base wind speed [m/s]

VGUST = gust wind component [m/s] VRAMP = ramp wind component [m/s] VNOISE = noise wind component [m/s]

The base component is a constant speed and wind gust

component can be usually expressed as a sine or cosine wave function [4]. In this simulation, a combination of different cosine functions is used for wind gust. The ramp wind component can be represented by the built-in ramp function model of the program. The noise component of wind speed is defined in this study by a triangle wave function, of which frequency and magnitude are adjustable. Since there is a triangle wave generator available in the commercial version, it is used as a noise generator.

Based on the four components, a wind speed model is constructed by integrating the built-in functions and logic circuits provided in the program.

B. Wind Turbine

The wind turbine is described by the following equation (2), (3) and (4).

WIND

M

V

Rωλ = (2)

3

35

32

21

2

1

λωρπ

ρπ

MP

WINDPM

CR

VCRP

=

= (3)

M

MM

PT

ω= (4)

where λ = tip speed ratio

ωM = blade angular speed [mechanical rad/s] R = blade radius [m] VWIND = wind speed [m/s] PM = mechanical power from wind blades [kW] ρ = air density [kg/m3] CP = power coefficient TM = mechanical torque from wind blades [N⋅m]

The mechanical torque obtained from equation (4) enters

into the input torque to the synchronous generator, and is driving the generator. CP may be expressed as a function of the tip speed ratio (TSR) λ given by equation (2) [5].

βλβ

λπβ )2(00184.03.013

)2(sin)0167.044.0( −−

−−−=PC (5)

where β is the blade pitch angle. For a fixed pitch type the

value of β is set to a constant value. Fig. 3 shows a user-defined wind turbine component and windows for entering data and parameters in this study.

Fig. 3. User defined component (wind turbine)

C. Synchronous Machine

The PSCAD/EMTDC provides a fully developed synchronous machine model, which is based on generalized machine theory [2] and with this model both sub-transient and transient behavior can be examined. It is considered that the synchronous generator is equipped with an exciter identical to IEEE type 1 model [6]. The exciter plays a role of meeting the dc link voltage requirement, as may be described by equation (6), for the three-phase voltage source inverter to create voltage waveforms with a nominal value of magnitude.

MAX

RMSACDC D

VV _22 ⋅

≥ (6)

where VDC = dc link voltage of power electronics

VAC_RMS = RMS value of the AC line to ground voltage of the inverter

DMAX = maximum duty cycle Since the synchronous generator is a direct drive type with

low speed and a high number of poles, the wind turbine and the generator are rotating at the same mechanical speed via the same shaft. Therefore, shaft dynamics can be characterized by a swing equation on a single mass rotating shown in equation (7). The shaft dynamics and the rotating mass can be represented by multi-mass torsional shaft model of PSCAD/EMTDC, which can be easily interfaced with the synchronous machine model.

WIND TURBINE

Tmw

Vwind

3

MEMM

M DTTdt

dJ ωω −−= (7)

where JM = a single rotating inertia [kg⋅m2]

TE = electric torque produced by generator [N⋅m] D = damping [J⋅s/rad]

In variable speed operation, the rotating speed of the wind

generator is not consistent with the electrical synchronous speed of the electric network and generally much slower than the speed. The electrical base frequency of the machine in the built-in models must be set to a value corresponding to the rated mechanical speed of the wind turbine specified by a manufacturer or a designer. Equation (8) and (9) give the value for the electrical base speed of the synchronous machine, ωB.

602TUR

B

RPMPf ⋅= (8)

60

2

TUR

BB

RPMP

f

⋅⋅=

=

π

πω (9)

where fB = electrical base frequency of the generator [Hz]

P = number of poles RPMTUR = mechanical rated speed of the turbine [rpm]

D. Power Electronics Control

Several types of power electronics interfaces have been investigated [7]. In this study, a combined system of a six-diode rectifier and a six-IGBT switch voltage source inverter, which is less expensive than others and commonly put into industrial use, has been modeled for AC-DC-AC conversion. The VSI is a voltage harmonic source in the point view of ac system and a harmonic filter need be placed appropriately to reduce the voltage harmonics it generates[8]. A L-C harmonic filter consisting of a series interconnection inductor and a parallel capacitor is located at the VSI terminal. Fig. 4 shows a rectifier and VSI system model that has been implemented in PSCAD/EMTDC. The six diodes rectifier converts ac power generated by the wind generator into dc power in an uncontrollable way and so control has to be implemented by the power electronics inverter. Current-controlled VSIs can generate an ac current which follows a desired reference waveform so can transfer the captured real power along with

Fig. 4. Rectifier and VSI model

controllable reactive power. For the modeling study, DQ control method that is widely used for VSI current control is employed. Variables in the ABC three phase coordinates may be transformed into those in the d-q reference frame rotating at synchronous speed by the rotational d-q transformation matrix [2]. In the three-phase balanced system, the instantaneous active and reactive power outputs, P and Q, of the wind turbine are described by equation (10).

)(2

3,)(

2

3DQQDQQDD IVIVQIVIVP −=+= (10)

where VD = d-axis voltage at the wind turbine

VQ = q-axis voltage at the wind turbine ID = d-axis current at the wind turbine IQ = q-axis current at the wind turbine.

Here, VQ is identical to the magnitude of the instantaneous

voltage at the wind generation system and VD is zero in the rotating d-q coordinates, so the equation (10) may be contracted into simpler equation (11).

DOQO IVQIVP2

3,

2

3 −== (11)

where |VO| is the instantaneous voltage magnitude of the wind turbine system. Since the voltage remains at a level of the grid AC voltage and the voltage variation is very small compared to changes in the magnitude of IQ and ID, P and Q are mainly subject to the d-axis current and q-axis current respectively. Fig. 5 illustrates DQ control decouples real and reactive components and enables real power and reactive power to be separately controlled by specifying the respective reference values of PREF and QREF for the both power outputs and independently adjusting the magnitude of the d-axis current IQ and that of the q-axis current ID. The reference values PREF and QREF of the wind generation are specified by what VSI’s control strategies are taken for real and reactive power output.

The firing signals are generated by the sine pulse width modulation (SPWM) technique. The desired current vector IABC_REF and the actual output current vector IABC_WT of the wind system are compared and the error signal vector IERR is compared with a triangle waveform vector to create the switching signals.

DQ

to

ABC

IA_REF

IB_REF

IC_REF

PI

PIID_REF

IQ_REFPREF

PWT

QREF

QWT

OR

VMAG

+

-

+-

SPWM

generator

Firing Signals

IQ_UPPER

IQ_LOWERID_UPPER

ID_LOWER

PREF & QREF

generator

WTUR

+-

comparator

firing signals

IABC_REF

IABC_WT

IERR

Triangle signals

SPWM

generator

Fig. 5. Current control scheme of a voltage source inverter

4

Fig. 6. Current control block

Fig. 6 shows the current control model for this modeling

study and Fig. 7 depicts the window boxes of the user-defined component of the real and reactive power reference generator to enter the basic parameters of the wind turbine, options of control modes and some desired values. Fig. 8 presents the SPWM switching signal generator to give firing pulses into the IGBT switches of the VSI.

Fig. 7. User defined component of P and Q reference generator

Fig. 8. SPWM switching control

E. Capturing the maximum power

The maximum aerodynamic power available from wind energy can be described by equation (12) and it can be depicted by Fig. 9. This simply means that the maximum power may be achieved by varying the turbine speed with varying wind speed such that at all times it is on the track of the maximum power curve [1], [9]. One way of enabling the maximum power capture is to specify the reference value of real power for the inverter control as the available maximum power multiplied by the inverter efficiency, as shown in equation (13).

3

35

2

1M

OPT

MAXPMAX

M

CRP ω

λπρ= (12)

MAXMREF PP η= (13)

Where CPMAX = the maximum power coefficient

λOPT = value of λ where CPMAX = CP (λOPT)

η = electrical loss in generator and inverter

Tu rb in e s p e e d [ ra d / s ]

0

Mechanical power

V3

V2

V1

ωM

PM

PM

MAX

Fig. 9. Power vs turbine speed curve

F. Reactive Power Control

Various control modes can be used for determining the amount of reactive compensation to provide. Possible control modes include power factor, kvar, current and voltage. Constant power factor mode and voltage regulation mode are implemented in this analysis.

In constant power factor control (PFC) mode, the reference

5

Fig. 10. VSWT implemented in PSACD/EMTDC

value of the reactive power of the wind turbine, QREF, may be specified by equation (14).

PF

PFPQ REFREF

21−⋅= (14)

Where PF is power factor and PREF is the reference value of real power output of the VSWT.

In voltage regulation (VR) mode, reactive power compensation is controlled in such a manner that the voltage magnitude of the VSWT-connected bus being kept constant at a specified level. The reference magnitude of the voltage to be regulated must be set as the nominal voltage of the AC grid where the wind turbine is considered as being interconnected.

Whether the mode controls constant power factor or voltage, the reactive power capability of a VSWT is limited. Such a limitation is required to be considered in the modeling study. The reactive capability limits of the wind turbine used in this study are determined by MVA rating of the inverter which may be described by equation (15).

22INVINVLIMITS PSQ −±= (15)

Where QLIMITS, PINV and SINV are the reactive power limits, the real power output and MVA rating of the inverter respectively.

III. SIMULATION RESULTS

The proposed model is implemented into PSCAD/EMTDC software and simulated for analyzing the dynamic behaviors of a wind turbine with varying wind conditions. Fig. 10 shows a VSWT model implemented in PSCAD/EMTDC. Also, both types of reactive compensation, constant power factor control and voltage regulation control, were simulated to compare the impacts on the bus voltage of the wind turbine. In power factor control the set value is unity and in voltage regulation the desired voltage is set to 1.005 pu. A high pole modular synchronous generator which has 42 pole pairs is considered as the wind generator. The rating capacity is chosen to be 1MVA. The rated speed of the rotor is chosen to be 26.8 rpm.

The rated wind speed is 12.35 m/s. the cut-in and cut-out speeds are 6 m/s and 25 m/s respectively. The switching frequency of the grid interface inverter is 7.2 kHz. It is assumed that the system operates in a balanced condition.

The VSWT has been connected to the power grid at 0.5 [sec]. The wind speed curve used for this study is shown in Fig. 11. The turbine angular speed variation respoding to varying wind speed is shown in Fig. 12(a). It is observed that at the instance when the wind turbine was integrated oscillations in the turbine speed occurred and gradually damped. The speed swings still remained as subsychronous oscillations, whose frequency is approximately 20[Hz], as shown in Fig. 12(b). The phenomenon comes from the interaction between the mechanical torque applied on the wind turbine and the electrical torque produced by the power system. Such oscillations can be damped below the appropriate level by employing damping factors. Fig. 13 presents the power coefficient profile corresponding to change in the turbine speed. It can be demonstrated by observing the power coefficient reaching the maximum value of 0.44 that the turbine speed has been well controlled to capture the maximum energy with varying wind speed. Fig. 14 shows the mechanical torque into and electrical torque from the wind generator. The real and reactive power output of the wind turbine in power factor control with varying wind speed is shown in Fig. 15. Inertia smoothing effects are apparent in the real power curve. Fig. 16 presents magnitude of the voltage at the terminal of the wind turbine in constant power factor. It should be noted that the voltage is varying with power fluctuations and the power variations result from changes in wind speed. Fig. 17 shows the dc link voltage. The current reference is well being tracked by the actual current, as shown in Fig. 18. The voltage waveforms at the primary busbar (0.69kV side) of the VSWT transformer are shown in Fig. 19.

In order to see the voltage control capability in VR mode, a sudden increase of reactive load by 600kVar at the second winding busbar (22.9kV side) of the VSWT transformer was applied. In such a case, the terminal voltages and reactive power outputs in PFC and VR modes were compared. Figs. 20 and 21 show the results of PFC and VR operation respectively.

At the moment of adding the additional load, the terminal

6

Wind Speed

[sec] 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 ...

6.0

7.0

8.0

9.0

10.0

11.0

12.0

13.0

14.0

m/s

Wind Speed

Fig. 11. Wind speed for case study

Turbine Speed

[sec] 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 ...

2.00

2.20

2.40

2.60

2.80

[mech

. ra

d/s]

Wtur

(a) Turbine angular speed (0-40 sec)

Turbine Speed

[sec] 15.00 15.10 15.20 15.30 15.40 15.50 15.60 15.70 15.80 15.90 16.00 ...

2.200

2.220

2.240

2.260

2.280

[mech

. ra

d/s]

Wtur

(b) Subsynchronous oscillation (15-16 [sec] period of curve (a)) Fig. 12. Turbine speed of wind turbine

POWER COEFFICIENT

[sec] 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 ...

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.400

0.450 Cp

Fig. 13. Power coefficient CP

Torque

[sec] 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 ...

0.00

0.20

0.40

0.60

0.80

1.00

1.20

[PU

]

Mechnical Torque Electrical Torque

Fig. 14. Mechanical and electrical torque

VSWT OUTPUT

[sec] 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 ...

-0.4k

-0.2k

0.0

0.2k

0.4k

0.6k

0.8k

1.0k

1.2k

kW

/ kV

ar

Real Power of VSWT Reactive Power of VSWT

Fig. 15. Real and reactive power of VSWT in PFC mode

Terminal voltage (PFC mode)

[sec] 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 ...

0.9850

0.9900

0.9950

1.0000

1.0050

1.0100

1.0150

1.0200

volta

ge [

pu]

Vmag

Fig. 16. Terminal bus voltage in PFC mode

DC link Voltage

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 ...

2.00

2.20

2.40

2.60

2.80

[kV]

V_dc

Fig. 17. DC link voltage

Currents

[sec] 4.0000 4.0010 4.0020 4.0030 4.0040 4.0050 4.0060 4.0070 4.0080 ...

-50

0

50

100

150

200

250

300

350

400

450

A

Reference Current (phase A) Actual Current (phase A)

Fig. 18. Current reference and actual current

Voltage Waveforms

[sec] 4.000 4.020 4.040 4.060 ...

-1.3k

-1.0k

-0.8k

-0.5k

-0.3k

0.0

0.3k

0.5k

0.8k

1.0k

1.3k

V

Va Vb Vc

Fig. 19. Voltage waveforms at primary busbar of VSWT transformenr

Terminal voltage (PFC mode)

[sec] 0.00 0.50 1.00 1.50 2.00 2.50 3.00 ...

0.9850

0.9900

0.9950

1.0000

1.0050

1.0100

1.0150

volta

ge [

pu]

Vmag

(a) Terminal voltage magnitude

Reactive Power (PFC mode)

[sec] 0.00 0.50 1.00 1.50 2.00 2.50 3.00 ...

-700

-600

-500

-400

-300

-200

-100

0

100

[kVar

]

Reactive Power of VSWT Reactive power into Grid

(b) Reactive generation of VSWT and reactive injection into grid Fig. 20. Case of PFC operation with reactive load connected at 1 [sec]

7

Terminal voltage (VR mode)

[sec] 0.00 0.50 1.00 1.50 2.00 2.50 3.00 ...

0.9850

0.9900

0.9950

1.0000

1.0050

1.0100

1.0150

volta

ge [

pu]

Vmag

(a) Terminal voltage magnitude

Reactive Power (VR mode)

[sec] 0.00 0.50 1.00 1.50 2.00 2.50 3.00 ...

-400

-300

-200

-100

0

100

200

300

400

[kVar

]

Reactive Power of VSWT Reactive power into Grid

(b) Reactive generation of VSWT and reactive injection into grid Fig. 21. Case of VR operation with reactive load connected at 1 [sec]

voltage made a sudden drop in Fig. 20(a). It’s just because the VSWT produced zero reactive generation as programmed to generate unity power factor and the power system supplied such amount of reactive power, as shown in Fig. 20(b). On the other hand VR operation kept the voltage at the specified level, as shown in Fig. 21(a). It should be noted in Fig. 21(b) that the VSWT shared the added reactive demand by supplying about 300kVar to the power grid.

IV. CONCLUSIONS

A dynamic model of a variable speed wind generation with power electronic interface was proposed for computer simulation study and implemented in a widely used power system transient analysis program, PSCAD/EMTDC. Component models of a VSWT and its control scheme have been built by using user define functions and built-in components provided in the software. A wind model was integrated into the modeling to see the wind impact. Dynamic responses of the wind turbine to varying wind speeds and under different reactive control schemes were simulated and analyzed based on the modeled system.

In the view point of electric utilities, grid interface of intermittent generation sources such as wind turbines has been a challenge that can cause lower power quality in power systems. So comprehensive impact studies are absolutely necessary before wind turbines being added to real networks. Also, users who intend to install wind turbines in networks must ensure their systems meet the requirements for grid connection. Therefore, the work done in this study provides a reliable tool for evaluating the performance of variable speed wind turbines and their impacts on power networks in terms of dynamic behaviors as a preliminary analysis for their actual integrations and operations.

V. REFERENCES [1] Mukund R. Patel, Wind and Solar Power Systems. CRC Press, USA.

,1999, pp. 81-82.

[2] Manitoba HVDC Research Center, PSCAD/EMTDC Power System Simulation Software User’s Manual, Version 3, 1998 release.

[3] P. M. Anderson and Anjan Bose, “Stability Simulation of Wind Turbine Systems”, IEEE Trans. Power Apparatus and systems, Vol. PAS-102, No. 12, pp. 3791-3795, December 1983.

[4] Reynolds, Michael G.. “Stability of Wind Turbine Generators to Wind Gusts”, Purdue University Report TR-EE 79-20.

[5] A. Murdoch, R. S. Barton, J. R. Winkelman, S.H. Javid, "Control Design and Performance Analysis of a 6 MW wind Turbine Generator", IEEE Trans. on Power Apparatus and Systems, Vol. PAS-102, No. 5, pp.1340-1347, May 1983.

[6] IEEE Committee Report, “Computer Representation of Excitation Systems”. IEEE Trans. on Power Apparatus and Systems, Vol. PAS-87, no. 6, June 1968.

[7] Z. Chen and E. Spooner, “Grid Power Quality with Variable Speed Wind Turbines”, IEEE Trans. Energy Conversions, vol. 16, No. 2, pp. 148-154, June 2001.

[8] Z. Chen and S. B. Tennakoon, “Harmonic filter considerations for voltage source inverter based advanced static Var compensator”, UPEC’92, Bath, UK, pp. 640-643, Sept. 1992.

[9] Eduard Muljadi and C. P. Butterfield, “ Pitch-Controlled Variable-Speed Wind Turbine Generation”, IEEE Trans. on Industry Applications, Vol. 37, No. 1, pp. 240-246, January/February 2001.

[10] E. Spooner, A. C. Williamson, and G. Catto, “Modular design of permanent-magnet generators for wind turbines”, IEE Proc.ㅡ B, Electric Power Applications, vol. 143, no. 5, pp. 388-395, Sept. 1996.

VI. BIOGRAPHIES

Seul-Ki Kim received B.S and M.S degree in electrical engineering from Korea University, korea in 1998 and in 2000 respectively. Since 2000, he has been working as a researcher in power system research group of Korea Electrotechnology Research Institute (KERI). His research interests are grid-connection of wind turbines, voltage stability analysis and power flow analysis.

Eung-Sang Kim received B.S degree in electrical engineering from Seoul National University of Technology, and M.S and Ph. D degree in electrical engineering from Soong-sil University. Currently, he has been working as a principal researcher in power system research group of Korea Electrotechnology Research Institute. His research interests are power quality, dispersed generating system integration and grid-connection of dispersed generations.

Jae-young Yoon is the head of the Power System Research Group at the Korea Electrotechnology Research Institute . He received his BSc., MSc. and Ph.D degree in electrical engineering from Busan National University. Since 1987, he has been working in the research field of power system analysis including custom power systems. His research areas are power system modeling, analysis and evaluation including system interconnection study.

Ho-yong Kim is with the Korea Electrotechnology Research Institute as a Principle Research Engineer since 1986. He is currently a Director of Power System Research Lab. He received BS degree from Seoul National University, Korea in 1979 and MS, Ph.D. from University of Texas at Austin ,USA in 1982 and 1985 respectively. His main research areas are distribution automation and AI applications to power systems and Power System Interconnection.