comparison of fault-ride-through capability of dual and single-rotor wind turbines

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Technical note

Comparison of fault-ride-through capability of dual and single-rotor windturbines

E.M. Farahani, N. Hosseinzadeh*, M. EktesabiFaculty of Engineering and Industrial Sciences, Swinburne University of Technology, Hawthorn, 3122, VIC, Melbourne, Australia

a r t i c l e i n f o

Article history:Received 25 October 2011Accepted 7 June 2012Available online xxx

Keywords:Wind turbineTransient responseDual-rotor wind turbineEigenvalue analysisSpeed droop

a b s t r a c t

The majority of wind turbines currently in operation have the conventional concept design. That isa single-rotor wind turbine (SRWT) which is connected through spur gearbox to a generator. Recently,dual-rotor wind turbine (DRWT) has been introduced to the market. It has been proven that the steadystate performance of the DRWT system for extracting energy is better than the SRWT. But, a comparisonof fault-ride-through capability of these two types of turbines requires further research.

In this paper, the fault-ride-through capability of DRWT and SRWT are evaluated and compared whengenerating units are operating at constant pitch angle and constant speed modes. Constant pitch anglemode is simulated to investigate the natural damping of DRWT and SRWT. To verify the time domainsimulation results, damping characteristics of DRWT and SRWT are also compared through eigenvalueanalysis and speed droop characteristics of the control system. The accuracy of the aerodynamic model ofthe DRWT is enhanced by including the stream tube effect in the simulation. It was uncovered thatDRWT introduces higher damping torque to the network in both constant speed and constant pitch anglemodes. This advantage improves the transient performance of DRWT-based wind farms.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Wind energy is one of the fastest growing energy resources andit is going to have remarkable share in the energy market. Thus, theconsequences of the connection of wind turbine, specifically in theform of awind farm, to the electrical gridmust be investigated fromsteady state, dynamic and transient point of view. Differentapproaches have been introduced to improve the static anddynamic responses of the wind turbines [1,2].

The electrical, mechanical and aerodynamic performancequality of the wind turbine is very important to absorb energy asmuch as possible from wind. In this direction, a new wind turbinegenerator system (WTGS) has been recently introduced as shownin Fig. 1. This newWTGS, which is called as dual-rotor wind turbine(DRWT), has two sets of rotor systems and ismore efficient than theconventional single-rotor wind turbine (SRWT) from the energyextraction point of view [3]. Because most of the aerodynamictorque is generated from the tip portion of the blade, a relativelysmall auxiliary rotor which is positioned at the upwind location,would compensate for the less effective portion of the main rotorlocated downwind.

At the time of writing this paper, the authors could trace [4] asthe only reference about the dynamic performance of the dual-rotor system. Multi-body dynamics is the employed approach.Although in this paper a model is provided to present the detailedprocedures used to show the system dynamic and aerodynamic,however the authors did not compare the dynamic response of thedual-rotor wind turbine with a single-rotor wind turbine. Accord-ing to [4], the commercial types of dual-rotor wind turbines areable to generate power up to 1 MW.

Even though at the same wind speed and environmentalconditions the efficiency of the dual-rotor is higher, nevertheless itdoes not signify that the transient performance of DRWT is betterthan SRWT. Obviously, the transient behaviours of the dual-rotorand single-rotor wind turbines are different, because in the dual-rotor system the number, type and arrangement of the compo-nents are different.

The objective of this investigation is comparing synchronizingand damping torque introduced by DRWT and SRWT to thenetwork. For getting to this stage both type of wind turbines havebeen set up in PSCAD software. Drive train method has beenemployed for modelling the mechanical system of DRWT andSRWT. The electrical characteristics of generator, transformer,transmission line and power system used for DRWT and SRWT areidentical to have a fair comparison.

Synchronizing torque is mostly dominated by electromagnetictorque imposed by electrical side. Damping factor of generating

* Corresponding author. Department of Electrical and Computer Engineering,Sultan Qaboos University, Muscat, Oman.

E-mail addresses: [email protected], [email protected](N. Hosseinzadeh).

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Renewable Energy 48 (2012) 473e481


units is mostly influenced by their control systemmode and naturaldamping characteristic, which is imposed by mechanical drive. Toassess the transient response of DRWT and SRWT, when they areoperating in constant speed mode, a temporary three phase shortcircuit is applied to the power system and post-fault fluctuations ofthe variable of interest are recorded and compared. To verify thevalidity of the time domain simulation, the control system isapproximated by its speed droop characteristic and dampingfactors which are introduced by the control system are evaluatedanalytically.

To evaluate and compare the natural damping characteristic ofDRWTand SRWT, the maximum short circuit period for which bothgenerating units are able to keep their stability are checked whilethe controller are deactivated and both DRWT and SRWT arerotating at constant pitch angle. To verify the simulation resultsregarding natural damping response, eigenvalue analysis isemployed using MATLAB software. The real portion of eigenvaluesis a good criterion for assessing the system natural damping.

Additionally, in calculating the aerodynamic torque, the streamtube effect behind the auxiliary rotor disk is neglected in Ref. [4].This simplification can affect the accuracy of the simulationsnegatively. In this paper, we have included the stream tube effectinto the dual-rotor aerodynamic model which improves theexactness of the aerodynamic model to be more realistic.

This paper is organized as follows: In Section 2 mechanicalmodels of different components of the DRWT and SRWT are pre-sented; In section 3 state space equations of turbine generator sethas been derived for eigenvalue analysis; Stream tube effect hasbeen discussed in section 4; The effect of pitch angle control ondamping torque is obtained analytically in section; 5 Computersimulation results are conducted in section 6. Although otherconfigurations of DRWT are introduced to enhance the perfor-mance of this technology, however, the focus of this paper is on theT gearbox type of DRWT. The authors intend to extend the studiesfor other types of dual-rotor wind turbines. For example, onepromising configuration is created if two rotors are directly coupled

to an asynchronous electrical machine: one rotor to the inductionwindings and the other rotor to the induced ones.

2. Mechanical dynamic model

In this section, the dynamic models of different components ofsingle and dual-rotor wind turbines are discussed. Fig. 2.a andFig. 2.b shows the elements of the single and dual-rotor windturbines, respectively.

2.1. Spur and bevel gears

Dynamic models for spur gearbox in SRWT and bevel gearboxemployed in DRWT are presented in Fig. 3 and Fig. 4 respectively.

By considering a zero backlash for the transmission system, thespur gearbox dynamic model which is the interface between twoparallel shafts, is considered to be as follows [5]:

J1:€q1 þ r1K12½r1q1 þ r2q2� þ r1d12hr1 _q1 þ r2 _q2

i¼ T1 � d1$ _q1

J2:€q2 þ r2K12½r1q1 þ r2q2� þ r2d12hr1 _q1 þ r2 _q2

i¼ T2 � d2$ _q2

(1)

where the definitions of parameters in Fig. 3 are as follows: J gearinertia; r gear radius; d damping coefficient between the gears; Kcontact points stiffness; T torque at the connection; q rotationalangle of gears;

Through comparing Figs. 3 and 4 there are number of dissimi-larities between the gearboxes used in single and dual-rotor windturbines. The differences are due to two main reasons. The majorcause is the difference between the numbers of the equipmentwhich are connected through the gearboxes and the minor one isrelated to the structure unlikeness of the spur and bevel gears suchas gear teeth formation [6]. Therefore, the dynamic model of gear-boxes employed in dual-rotor and single-rotor systemsare different.

Referring to Fig. 4, we have derived the bevel gearbox dynamicmodel, which links three shafts, as follows:

J1$€q1þr1$K12½r1$q1þr2$q2�þrav1d12hr1$ _q1þr2$ _q2

i¼T1�d1$ _q1

J2$€q2þr3K12½r1q1þr2q2�þr3$d12hr1$ _q1þr3 _q3

iþr3K23½r2q2þr3q3�þr3d32

hr2 _q2þr3 _q3

i¼T2�d2$ _q2

J3€q3þr3K23½r3q3þr2q2�þr3d23hr3 _q3þr2 _q2

i¼T3�d3$ _q3

(2)

Stiffness of the contact point is a time variable quantitydepending on the number of teeth which are engaged to each other.The stiffness variation for each cycle can be considered witha minimum value when one pair of teeth are engaged and

Fig. 1. Dual-rotor wind turbine.

Fig. 2. a. Single-rotor wind turbine, b. Dual-rotor wind turbine.

E.M. Farahani et al. / Renewable Energy 48 (2012) 473e481474


maximum value when there are two contact points. The profile ofthe stiffness is shown in Fig. 5 [7].

In [7] an exact equation has been formulated for modelling thevibratory effects of spur gearbox. But this accuracy is pointless forevaluating the dynamic performance of the whole wind turbinesystem. So, it is possible to calculate the average value of the stiff-ness and employ it as a constant for simplicity without affecting thevalidity of our studies. The average stiffness is given in (3):

Kav ¼ Kmax$ðε� 1Þ$Trd þ Kmin$ð2Trd � εÞTrd

(3)

where: ε: contact ratio; Kmin: minimum stiffness; Kmax: maximumstiffness; Trd: stiffness cycle time

The contact ratio of the spur gear is presented in [8]:

ε ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2b � R2a

qþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir2b � r2a

q� ðRa þ RbÞ$sin a

p$mg$cos a(4)

where: Ra: wheel base circle radius; Rb: wheel external radius;ra: pinion base circle radius; rb: pinion external radius; rc: distancebetween the centers of two base circles; a: pressure angle;mg: module of the gear;

To calculate the contact ratio of bevel gear through (4), theequivalent spur gear corresponding to the bevel gear must beobtained. The method is described in [8].

The damping coefficient of spur and bevel gears are given by [9]:

dz ¼ 2$x$

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiεspur$Kmin$J1$J2J2$r21 þ J1$r22

s(5)

Where, x is the damping rate which varies between 3% and 17%,depending on the material type.

2.2. Shaft and rotor system

As shown in Fig. 2, dual and single-rotor wind turbines havedifferent arrangements of the shafts, rotors and blades. So theinvestigation of a basic mechanical system comprising two rotorswhich are connected to each other by a shaft can pave the way forstudying the more complicated systems. Fig. 6 shows a basicmechanical system [10]. The shaft is modelled by a damper anda spring. The rotors are presented by masses and dampers.where: Tls, Trs, Tem, Ta: torques in different sides of the system.

dr, dg, dls: damping coefficient of the elements. Kls: shaft stiffness.ug, ur: angular velocity of the masses.

First-order differential equation is employed to demonstrate thedynamic of the rotors:

Jr _ur ¼ Ta � Tls � KrurJg _ug ¼ Ths � Tem � Kgug

(6)

The equation which describes the effect of the shaft on thedynamic on the whole system is as follows:

Tls ¼ Blsðqls � qrsÞ þ Klsðuls � ursÞ (7)

2.3. Blade bending model

New designs of wind turbine continue to increase in rotor size inorder to extract more power from wind. As the rotor diametersincrease, the rotor structure is more flexible and blades woulddominate the dynamic of the mechanical drive train of the windturbine. The combination of the hub and blades can be presented bya twomassmodel. Fig.7 shows thedrive trainmodelof theblades [11].

Eq (8) define the dynamic behaviour of the two mass model ofthe hub and blade combination. Jflex presents the momentuminertia of the flexible part of the blade and Jrigid shows themomentum inertia of the rigid part of the blade. Two masses arecoupled together by the blade stiffness Kblade.

Jflex€qblade¼Tm�Kbladeðqblade�qhubÞ�dbladeðublade�uhubÞ

Jrig€qhub¼�Kbladeðqhub�qbladeÞ�dbladeðuhub�ubladeÞ

�Kshðqhub�qshÞ�dshðuhub�ushÞ(8)

where:qblade, qhub, qsh are the rotating angle of the blades, hub and shaft,

respectively. ublade, uhub, ush are the rotating speed of the blades,hub and shaft, respectively.

Fig. 3. Dynamic model of one stage spur gear box.

Fig. 4. Dynamic model of the 2 stage bevel gear with 3 shafts.

Fig. 5. The profile of the stiffness.

Fig. 6. Mechanical elements for modelling the shaft.

E.M. Farahani et al. / Renewable Energy 48 (2012) 473e481 475


By having the fundamental equations of each mechanicalelement such as shaft, rotor, gearbox and blades, it is possible toobtain the dynamic behaviour of the whole mechanical system fordual and single-rotor wind turbines. The all-inclusive plot whichshows the relationship betweenmechanical elements in both typesof the turbines is given in Fig. 8, where the torques and speeds withindex “s” and “d” indicate the variables in single and dual-rotorsystems, respectively.

3. SRWT and DRWT state space model

To prove the validity of our studies regarding transient responseof the dual and single-rotor wind turbines, the damping character-istic of DRWT and SRWT can be evaluated through eigenvalueanalysis. The location of the eigenvalues in each system is a powerfulaid to predict the damping factor of the system. For getting to thisstage, the state space of induction generator, single-rotor and dual-rotorwind turbinesmust be calculated and combined appropriately.Both dual-rotor and single-rotor systems including inductiongenerator should be linearized over the operating point.

3.1. Induction generator model

A 4th order dynamic model of an induction generator (IG) is asfollows:

_xG ¼ AG$xG þ BG$uG (9)

where xG ¼ ½iqs; ids; iqr; idr�T ; uG ¼ ½vqs; vds; vqr; vdr�T .

The expressions of AG and BG are listed in [12].

3.2. Turbine model

The state space model associated with dual and single-rotorwind turbines is presented in (10) as follows:

_xT ¼ AT$xT þ BT$uT (10)

where state and input variables in dual-rotor systems can beidentified based on Fig. 8.

xDRWT ¼ ½ud0; ::::::;ud7; dd0; :::::; dd7�TuDRWT ¼ ½Td0; Td3; Td7�T

(11)

The same is true for state and input variables for single-rotorwind turbines:

xSRWT ¼ ½uS0; ::::;uS4; dS0; :::; dS4�TuSRWT ¼ ½TS0; TS4�T

(12)

Mechanical state variables (xs, xd) and electrical state variables(xG) should be linked together through electromagnetic torqueprovided by generator (TS4, Td7). The normal format of electro-magnetic torque (Te) is shown in (13):

Te ¼ Lm�idr:iqs � iqr:ids

�(13)

Fig. 7. a) Three blades connected to the hub b) Equivalent torsional representation.

Fig. 8. General mechanical block diagram of variable speed wind turbine.



Equation (13) is a nonlinear equation and can’t be used as a statevariable. The linear format of Te is composed of electrical statevariables as follows:

Te ¼ Lm�idr0Diqs þ iqs0Didr � iqr0Dids � ids0Diqr

�(14)

With idr0, iqr0, ids0, idr0 as the initial values of the generatorstator and rotor currents. TS4 in us and Td7 in ud must be replaced bytheir linear format which is presented in (14). Mechanicalparameters for both SRWT and DRWT can be estimated with highaccuracy through the equations suggested by [13]. The estimationis feasible by identifying obvious parameters which are easilyaccessible such as the length of main and auxiliary blades, ratingpower, gearbox ratio, etc.

4. Aerodynamic model for DRWT

Aerodynamic model of DRWT is different from SRWT to someextent. Since thewindwhich is flowing through themain turbine inDRWT is disturbed by the auxiliary turbine, then stream tube effectmust be included in the aerodynamic torque calculations for DRWT.Through (15) aerodynamic torque introduced by the blades is asfollows:

TM ¼ 0:5r$p$R5$CP$u2M=l3 (15)

With R blade radius, l the tip speed ratio, r the air density anduM the mechanical speed of the rotor. Cp can be calculated asfollows [16]:

CPðl; bÞ ¼ 0:517�116li

� 0:4b� 5�$e

�21li þ 0:0068l

1li

¼ 1lþ 0:08b

� 0:035

b3 þ 1

(16)

With b is pitch angle.Same method can be followed for main and auxiliary turbines.

Tip speed ratios for the main and auxiliary turbines are calculatedthrough (17) & (18), respectively.

lAux ¼ uAux$RAux=V1 (17)

lMain ¼ uMain$RMain=VM (18)

where V1 is the wind speed on auxiliary wind turbine and VM is thespeed of the unified wind on main turbine. So, the essentialelement for calculating the tip speed ratio is wind speed on themain and auxiliary turbines. Obtaining the wind speed on auxiliaryturbine is straight forward. However, calculation of wind speed onmain turbine requires further investigation.

In dual-rotor wind turbine, after the free upstream flowwith theundisturbed speed V1 passing the auxiliary rotor disk, the down-stream flow velocity distribution is assumed to be composed of twoparts, i.e. the disturbed and the undisturbed portions with thespeed of V0

2 and V1, respectively. This phenomenon is shown inFig. 9.a. In [4] the expansion of the stream tube behind the auxiliaryrotor disk was neglected. To have more precise results, calculationsperformed in [4] must be revised by considering the expansioneffect, as shown in Fig. 9.b.

According to the mass flow rate theory:

V 02$A

02 ¼ V2$A1 (19)

Therefore, to obtain the area of the disturbed wind (A02) on the

main turbine disc, it is necessary to calculate the disturbed windvelocity V0

2 just next to the main turbine. Based on the (20), it ispossible to estimate the amount of the wind speed at any pointbetween the auxiliary and main blades [14].

V 02 ¼ V1

1� 1� ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1� Cpp2

�1þ 2:xffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1þ 4:x2p �!

(20)

where, V02 is the speed of the disturbed wind next to main blade and“x” is the distance between the main and auxiliary turbines. Bysubstituting the obtained V0

2 into (19), the area of A02 at any perfor-mance of the auxiliary rotor (differentCP) is achievable. One approachfor examination of the dynamic functioning of the dual-rotor is toanalyse the rotorswhich aerodynamically are independent fromeachother. In other words, the authors of Ref. [4] treated the flow enteringthe auxiliary andmain rotors as two independent uniformflowswiththe speed of V1 and VM, respectively. This matter is shown in Fig. 10.The equivalent uniform flow entering the main rotor (VM) producesthe same aerodynamic torque which is obtainable from the summa-tion of the disturbed (V0

2) and undisturbed (V1) winds.Equation (21), by employing A0

2 and V02, gives out the value of

the uniformwind speed (VM) on the main rotor at any performanceof the auxiliary rotor [4]:

r$V 032 $A0

2 þ r$V31 $�A2 � A0

2� ¼ r$V3

M$A2 (21)

VM from (21) should be replaced in (18) for calculating the mainturbine tip speed ratio.

5. Damping effect of pitch angle control

The conventional blade pitch angle control strategies are cat-egorised mainly as; a) Generator power control and b) Generatorrotor speed control. During the fault, electrical power drops downto a very low value and generators accelerate. Throughout the

Fig. 9. a. Stream tube effect is neglected. b. Stream tube effect is included.



fault, constant speed wind turbines increase the pitch angle toreduce the captured aerodynamic power to keep the speedconstant. On the other hand, constant power wind turbinesdecreases the pitch angle to restore the electric power and thisreaction pushes the generator to accelerate more which is harmfulfor the stability of the generator. During normal operation, a windturbine is usually working in constant power mode to extractmaximum energy from wind. In case of any faulty condition, thecontrol system is switched to constant speed mode [15]. The blockdiagram of pitch control in constant speed mode is presented inFig. 11.

The dynamic of the generator speed can be written as:

2$H$D _ur ¼ DTm � DTe � Dr$Dur (22)

where, Dr is rotor damping factor, Tm is torque from prime moverand Te is electromagnetic torque.

To simplify the analysis of the damping effect of the speed modeon the wind turbine, the control system in Fig. 11 is replaced bya droop characteristic curve of torque versus speed. In this paper,both main and auxiliary turbines vary the captured aerodynamictorque for regulating the power in DRWT through the droop curve.Based on this scheme, the simplified relationship between thegenerator speed and mechanical torque over the operating pointcan be illustrated as follows:

DTm ¼ �Kmain$Dur � Kaux$Dur (23)

where Kmain and Kaux are droop constants of main and auxiliaryturbines aerodynamic torques over operating point respectively.

According to (24), electromagnetic torque (Te) can be decom-posed into damping torque and synchronizing torque [17]:

DTe ¼ Ts$Ddþ Td$Dur (24)

By substituting (23) and (24) in (22), it is possible to obtain thedamping factor of the DRWT which is the coefficient of Dur. Thedamping factors for DRWT are presented in (25).

DDRWT ¼ ðTd þ Dr þ Kmain þ KauxÞ (25)

If same procedure is followed for SRWT then damping factor is:

DSRWT ¼ ðTd þ Dr þ KmainÞ (26)

Kaux is equal to zero for SRWT.From (25) and (26), it is obvious that in constant speed opera-

tion mode DRWT presents more damping compared to SRWT infaulty condition. To verify the validity of the simplifications, whichis made in this section, both DRWT and SRWT must be modelledand transient response of the wind turbines must be simulated toassess their damping characteristics.

6. Simulation results

The objective of this study is to investigate and compare thedynamic behaviour of the dual and single-rotor wind turbines fromdifferent aspects. Both dual and single-rotor wind turbines are set upin PSCAD software. To facilitate, a simple power system has beenchosen which is shown in Fig. 12. The dynamic model of the windturbines are established based on the component models presentedin previous sections. The generators are connected to the powersystemthrougha stepuptransformeranda100kmtransmission line.The parameters of generator and mechanical systems are listed inAppendix A. Pitch angle control which is employed in this investi-gation regulates the speed of the wind generator. The followingsimulation results compare the capabilities of the dual and single-rotor wind turbines in the context of transient stability performance.

The behaviour of thewind turbines, whenpitch angle control is inoperation, are simulated following a grid three phase short circuit of0.3 s at t ¼ 120 s on the secondary side of the step up transformer.

The informationwhich is provided byFig.13 is an overviewaboutthe responses of the variables during the fault and post-fault period.Responses of variables relative to SRWT are distinct by bolded linewith circles standon them. Squares are standingonDRWTvariables.Fig.13a shows that the damping torque provided by DRWT is higherthe SRWT. From the figure it is clear that the amplitude of the firstswing of both generators speed are identical. The reason is that thesynchronizing torque introduced by the electrical networkewhichhelps keeping the generators stable during their first swinge is thesame for the two systems. It is because electrical quantities areidentical in DRWT and SRWT prior to the occurrence of the fault.From Fig. 13b it is clear that the voltage in dual-rotor system canrecover faster than single-rotor. The reason is the differencebetween the generator speed settling time in single and dual-rotorsystems. According to Fig. B.1 in appendix B, terminal voltage isinversely proportional to the slip. The generator speed in SRWTtakes longer to be recovered to its nominal value, so does theterminal voltage in single-rotor system. Fig.13 confirms the effect ofconstant speed mode of the pitch control on the level of dampingwhich was investigated in Section 5.

As can be seen from Fig. 13c and d, active and reactive powersalso have larger oscillations during the post-fault period for theSRWT in comparison with the DRWT. Since pre-fault operatingpoint of active and reactive power influences the post-fault oscil-lations, then to have a fair comparison we assume that active andreactive power generated by the dual-rotor and single-rotorsystems are the same before the fault.

The pitch angle control mode is not the only reason for higherdamping level of DRWT. The simulation is rerun at the same faultduration when the pitch control system is disabled and windturbine is rotating at constant pitch angle. Fig. 14 shows the SRWTbecomes unstable after removing the fault. According to Fig. 14a,the generator speed swings and generator faces over speed. On the

Fig. 10. Two rotors are aerodynamically independent.

Fig. 11. Generator constant speed pitch control system.



Fig. 13. Dynamic response of the wind turbine to a three phase grid short circuit when system stays stable.

Fig. 14. Instability of single-rotor wind turbine when pitch angle control is disabled.

SRWTWindGen

#1 #2PI

COUPLED

SECTION

ABC->G

TimedFaultLogic

RL

DRWT

GenWind #1 #2

PI

COUPLED

SECTION

ABC->G

TimedFaultLogic

RL

a b

Fig. 12. Simple power grid connected to either single-rotor or dual-rotor wind turbine.



other hand, the DRWT resumes its variables to the pre-fault levelsand continues its power generation. In case of any large generatorspeed oscillation, the auxiliary turbine acts as a flywheel. The mainpurpose of flywheel in mechanical systems is to smooth out thedestructive oscillations. Therefore, the flywheel damping effect ofthe auxiliary turbine on post-fault generator speed oscillations isanother reason of higher damping torque in DRWT. If the fault lastsmore than 0.39 s, then dual-rotor system is also unstable. There-fore, DRWT is more resistive against network disturbances. In thisinvestigation the fault-ride-through capabilities of DRWT andSRWT are calculated based on parameters in tables A.1 to A.3.

To verify the results given out by Fig. 14, eigenvalue is a veryhandy solution. MATLAB function (eig) is the tool to calculate theeigenvalues of a state space model of DRWT and SRWT. The initialvalues of the generator currents are achievable through abc-dq0transformation function in PSCAD after running the timedomain simulation. Table 1 illustrates the eigenvalues of bothDRWT and SRWT systems. The data presented in this table revealsthat number of eigenvalues introduced by DRWT is more thanSRWT. Since the mechanical parameters of main turbines inDRWT and SRWT are the same and the generators are identical,then some of the natural frequencies in both systems are quiteclose together.

For the pairs of natural frequencies presented by DRWT andSRWT, which are close enough, real part of eigenvalue in DRWT ismore negative. This matter signifies that installing the auxiliaryturbine in DRWT increases the damping factor of the naturalfrequencies which are common between DRWT and SRWT. Forexample, natural frequency in third row in DRWT and naturalfrequency in second row of SRWT are almost the same. However,since real part for DRWT is higher, the oscillations caused by thisnatural frequency would be damped faster compared to SRWT.This verifies the simulation results presented in the previoussections.

7. Conclusions

In this paper, by using PSCAD/EMTDC software, transientresponse of dual and single-rotor wind turbines have been evalu-ated and compared. The stream tube effect is included in aero-dynamic torque calculation which was ignored in previous work inliterature. So, the dual-rotor wind turbine (DRWT) aerodynamicmodel in this paper is more accurate compared to the previousinvestigations. The results of the methods uncovered that theDRWT presented higher damping torque to the network comparedto single-rotor wind turbine (SRWT) in both constant speed modeand constant pitch angle mode (Natural response):

� Constant Speed Mode: Based on time domain simulationresults the damping torque of DRWT, which is introduced tothe network, is higher than SRWT when they are operating inconstant speed mode. Speed droop method also signifies thatdamping torque of DRWT is higher during unstable situationwhen both main and auxiliary turbines contribute to keep thespeed constant by regulating their pitch angle. For droopanalysis, the action of the control system on the speed variationis approximated by a droop curve.

� Constant Angle Mode: To investigate and compare the naturalresponses of DRWT and SRWT, both turbines operated atconstant pitch angle. Timedomain simulation results illustratedthat fault-ride-through capability of DRWT is higher than SRWTin this operating mode. The reason is the flywheel effect of theauxiliary turbine during the imbalance condition to damp outthe oscillations. To verify the natural response of the turbines,eigenvalue analysis was employed. It was shown that by addingthe linear equations related to auxiliary turbine, the real part ofthe eigenvalues moved leftward in complex plane while theirimaginary parts stay almost constant. This means more damp-ing in the DRWT responses compared to the SRWT.

By using dual-rotor wind turbines, both steady state and tran-sient performance of the wind farm would be enhanced.

Appendix A

Table 1Eigenvalues presented by DRWT and SRWT.

DRWT SRWT

1 �0.9228 � j 0.2737 �0.4583 � j 0.34352 �0.1440 � j 0.8543 �0.3748 � j1.66033 �0.4211 � j 1.6606 �10.6351 � j 4.96044 �1.2357 � j 2.6463 �9.5895 � j190.66515 �11.3546 � j 5.0993 �8.0281 � j312.676 �10.8854 � j 190.6042 07 �9.1439 � j312.67 �11.64018 0 �673.23309 �3.6866 �1271.610 �11.388211 �689.529512 �1292.613 �2131.4

Table A.1Electrical parameters of induction generator.

Rated voltage 0.69 kVRated power 1.5 MVAMoment of inertia 3 sFrequency 50 HzMachine damping 0.3 p.u.Stator resistance 0.066 p.u.Stator leakage reactance 0.1 p.u.Rotor resistance 0.05 p.u.Rotor reactance 0.2 p.u.Unsaturated magnetizing reactance 2.5 p.u.

Table A.2Parameters of the network system.

Transformer ratio 0.69/63 kVBase MVA 2 MVAPositive sequence reactance 0.3 p.uLine length 100 kmLine resistance 0.1781E-3 U/mLine inductive reactance 0.514E-3 U/mLine capacitive reactance 27354.48 M U*m

Table A.3Mechanical parameters of gear box and turbine

Spur base circle radius r1 ¼ 0.1 m r2 ¼ 1 mBevel base circle radius rav1 ¼ 0.1 m rav2 ¼ 0.5 m rav3 ¼ 1 mSRWT blade diameter 51 mDRWT blade diameters Main ¼ 51 m Aux. ¼ 26.4 mRotor damping factor Single ¼ main ¼ 3 Aux. ¼ 1.5 p.u.Blade damping factor Single ¼ main ¼ 2 Aux. ¼ 1.0 p.u.Rotor inertia momentum Single ¼ main ¼ 0.28e5 Aux. ¼ 0.8e4 kg m2

Blade inertia momentum Single ¼ main ¼ 0.1E5 Aux. ¼ 0.16E4 kg m2

Effective blade stiffness 0.21e6All shaft stiffness’s 2.5e5All shaft damping factors 0.6 p.u.



Appendix B

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Fig. B.1. Voltage versus slip in induction machine.


comparison of fault-ride-through capability of dual and single-rotor wind turbines

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