Electrical Power and Energy Systems 55 (2014) 562–571

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Real-time replication of a stand-alone wind energy conversion system:Error analysis

0142-0615/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.ijepes.2013.10.016

⇑ Corresponding author. Tel.: +33 476826384.E-mail addresses: ciprian.vlad@ugal.ro (C. Vlad), antoneta.bratcu@gipsa-lab.gre-

noble-inp.fr (A.I. Bratcu), iulian.munteanu@gipsa-lab.grenoble-inp.fr (I. Munteanu),silviu.epure@ugal.ro (S. Epure).

Ciprian Vlad a, Antoneta Iuliana Bratcu b,⇑, Iulian Munteanu b, Silviu Epure a

a ‘‘Dunarea de Jos’’ University of Galat�i, 47 Domneasca, 800008 Galat�i, Romaniab Grenoble Image, Speech, Signal and Automatic Control Laboratory (GIPSA-lab), Grenoble Institute of Technology, 11 Rue des Mathématiques, 38402 Saint-Martin d’Hères, France

a r t i c l e i n f o a b s t r a c t

Article history:Received 25 January 2013Received in revised form 13 September2013Accepted 12 October 2013

Keywords:Wind energy conversion systemsHardware-in-the-loop simulationVariable-speed operationFrequency-domain error analysisPermanent-magnet synchronous generator

This paper provides adequate information about the problem of real-time replicating in laboratory con-ditions. The dynamic behavior of stand-alone low-power wind energy conversion systems (WECS) inresponse to the wind speed variations and also to the electrical load variations is replicated. The inves-tigated system consists of a variable-speed wind turbine based on a permanent-magnet synchronousgenerator (PMSG), a diode bridge rectifier, a DC–DC step-down converter and a wide range DC load.Because of reduced noise level and better steady-state accuracy, a speed-driven hardware-in-the-loopphysical WECS simulator has been used to accomplish this task. Its significant drawback – that is, areduced bandwidth – has been significantly alleviated by using an enhanced software simulator structurewhich uses a feed-forward compensation of the inherent physical disturbance produced by the generatortorque variations. Both time-domain experimental results and a thorough frequency-domain error anal-ysis show good replication performance in the frequency range of variation of both wind speed and elec-trical load.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Because the primary resource of wind energy conversion sys-tems (WECS) varies stochastically, the experimental investigationof such systems – usually performed after the preliminary off-linesimulation analysis – must be rendered possible irrespective of theactual, uncontrollable wind conditions [1,2]. Laboratory investiga-tion under controlled wind conditions is aimed at, especially forcontrol purposes. Wind turbine physical simulators (WTPS) havethus become necessary, having as main goal to provide a physicalshaft replicating the dynamical behavior of a wind turbine definedby a given mathematical model.

Hardware-in-the-loop simulation (HILS) concept has been re-cently used for a wide palette of applications, including automotivesystems [3], power systems [4], power electronic converters [5],photovoltaic generators [6] and WECS [7–11]. In general, the struc-ture of a WTPS is based upon the HILS concept and supposes theclosed-loop connection of two subsystems, namely (see Fig. 1):

– A real-time software simulator (RTSS), which implements themathematical model of the simulated wind turbine and thatof the wind.

– An electromechanical tracking servo-system (TS), based uponan electrical motor (EM) offering the wind-like shaft, to be cou-pled to the electrical generator (EG) of the wind system.

The wind turbine’s mathematical model implemented in theRTSS is organized as a dynamical system whose output, y(t), is sendas reference to the TS. Depending of the output’s physical nature,the TS can be controlled in [12,13]:

– Rotational speed, when the reference of TS is the rotationalspeed computed within the RTSS, X(t); in this case the mea-sured (or else response) variable within the control loop is themotor torque, Tm(t) (usually, one uses the motor estimatedtorque).

– Torque, when the reference of TS is the wind turbine’s effectivetorque computed within the RTSS and the response variable isthe rotational speed, X(t).

An important issue when using WTPS is how to assess its per-formance in terms of replication accuracy. Results related to this is-sue can be found in the literature; thus, in [12,13] it is shown thatthe dynamical properties of the wind-speed-to-rotational-speedtransfer are superior when the TS is torque-controlled, because atorque control loop is faster than a rotational speed control loop.The other way round, torque control has the drawback of introduc-ing noise, which affects the replication quality. This can easily be

Nomenclature

WECS wind energy conversion systemHILS hardware-in-the-loop simulationPMSG permanent-magnet synchronous generatorIM induction motorX rotational speedv wind speedk tip speed ratioCp(k) power coefficient of the wind turbineJwt inertia of the simulated wind turbineJtr total inertia of the physical simulatorTw wind torque

TG PMSG torqueTIM IM torqueVR rectified voltageIR rectified currentIDC load currentPwt wind turbine powerPDC electrical power measured at the chopper’s outputKXVR steady-state gain from X to the rectified voltageKT steady-state gain from rectified current to PMSG torque

C. Vlad et al. / Electrical Power and Energy Systems 55 (2014) 562–571 563

deduced if considering the turbine’s motion equation. In this case,the torque reference is the effective torque:

T�ef ¼ TwtðX;vÞ � JwtdXdt

;

where Twt(X, v) is the wind turbine torque, Jwt is the total inertia ofthe turbine-generator coupling and Jwt

dXdt is the dynamic torque.

This latter term of the above relation contains a derivative, whichamplifies noise. Use of filters in order to reduce noise also resultsin the bandwidth being reduced.

The goal of this paper is the WTPS’s frequency-domain errorassessment in dynamic regime. Two problems are approached, asfollows. The first is to establish a solution for improving the dy-namic properties of a rotational-speed-controlled WTPS. Becausethe noise level is quite low in this case – as the turbine’s dynamicalmodel implemented in the RTSS is strictly causal – improvement ofdynamics could render the speed control more attractive than thetorque control. The second problem approached is to establish asolution for global assessment of dynamic regimes of WTPS,namely by using frequency-domain models. It is well known thata generic fixed-pitch WECS has two dynamic transfer channels:from the wind speed to the rotational speed and from the electricalload (e.g., generator current or torque) to the rotational speed. Yet,the concerned literature deals with the wind speed synthesis andthe physical replication of the rotational speed variations in re-sponse to the synthesized wind speed, whereas the electrical loadinfluence on the WECS rotational speed is almost entirely omitted.

WECS based on permanent-magnet synchronous generatorwere investigated in recent researches, but most of them are in-tended for grid connected systems. In [14] is presented a simplecontrol strategy for an optimal extraction of output power fromgrid connected PMSG-based variable-speed wind energy conver-

Fig. 1. General structure of a real-time si

sion system. The electronics part consists in a diode bridge rectifierand a DC–DC boost converter. In [15,16] are illustrated the perfor-mance of a PMSG based wind system with back-to-back convertersfor grid interconnection.

The speed-driven simulation technique for 1:1 low-powerWECS has been reconsidered in this paper and an enhanced soft-ware simulator structure has been proposed. This technique isused to assess the real-time replication of the dynamic behaviorof a fixed-pitch rotor driving a genuine wind turbine permanent-magnet-synchronous-generator (PMSG) which supplies a mainlyresistive DC load through a customized power electronic interface.Its performance will be assessed not only in time-domain but alsousing the frequency-domain error evaluation method [12,13,17].

The paper is organized as follows. The next section describesthe structure of the studied WECS. The third section lists therequirements imposed to the WECS simulator and describes theproposed software simulator configuration. The fourth sectionillustrates the overall performance of the simulator by means oftime-domain results in various WECS regimes. Frequency-domainerror analysis is performed in the fifth section, emphasizing thefrequency range of accurate real-time replication. Conclusion andfuture issues are given in the final section, the sixth.

2. Structure of the considered stand-alone WECS

A low-power WECS, rated at about 1 kW at 11 m/s, is studied inthis paper (Fig. 2). This architecture allows the feeding of a low-voltage charge or inverter by using a minimum number of electro-chemical accumulators, meanwhile suitably controlling the tur-bine operating point and the accumulators charging current. Thewind turbine directly drives the PMSG; they are both taken from

mulator based on the HILS principle.

Fig. 2. Structure of the considered stand-alone WECS.

564 C. Vlad et al. / Electrical Power and Energy Systems 55 (2014) 562–571

a Whisper WHI-200 wind system. The PMSG feeds a diode rectifierand a microprocessor-controlled step-down DC–DC converter. Theresistive DC load can be coupled to an accumulator. The turbinecan be controlled directly by the chopper duty ratio, a, or byimposing the load current, IDC, in order to modify its operatingpoint based upon measuring the load current, IDC, the rectifier out-put voltage, VR, and the turbine rotational speed, X.

The average wind turbine torque, Twt, is given by:

Twt ¼Pwt

X¼ 0:5pqv2R3CpðkÞ

k; ð1Þ

where Pwt is the wind turbine power, q is the air density, R is theblade length, v is the effective wind speed, k is the tip speed ratio(k = R �X/v) and Cp is the power coefficient. As it is well-known fromthe literature, Cp(k) and Twt(X) are unimodal curves [13]. The fol-lowing motion equation describes the interaction between the windtorque and the PMSG torque:

Jwt �dXdt¼ Twt � TG;

where Jwt is the total inertia of the turbine-PMSG coupling and thePMSG torque, TG, depends on both rotational speed and load cur-rent, IDC.

3. Requirements and configuration of the physical simulator

3.1. General requirements

The WECS has two inputs, i.e., the wind speed and the load.Depending on whether IDC is controlled or not, the load is ex-pressed either through the duty ratio value or through the loadcurrent reference. Next, the WECS output is the rotational speed,X, but note that either the output (load) power, PDC, or the rectifiervoltage, VR, may be taken as output.

The possibility of independently applying each of the two in-puts to the WECS must be ensured. The goal is to replicate theWECS dynamics as accurately as possible by the physical simulatorwithin the frequency range of interest. Unlike in most of worksfrom the literature, the investigated physical system (IPS) fromFig. 3 also contains the electrical components (i.e., the rectifierand the chopper) beside the mechanical subsystem.

The induction motor coupled physically with the PMSG mustreplicate the turbine behavior. Because of the necessity of comput-ing derivative of the rotational speed – already noisy due to therectified current abrupt variations – the torque-driven real-timesimulation solution is not suitable in this case. A speed-controlledsimulator was considered in this paper, whose general structure isgiven in [13]. Thus, a fast control loop was designed for the induc-

tion motor’s rotational speed, X, whose reference, X�, resultedfrom the wind turbine model, must be tracked by X much fasterthan the exogenous signals vary. This is not trivial, as the simula-tor’s and the WECS’s inertias are comparable. The turbine behavioris replicated by the real-time physical simulator, RTPS, composedof a software subsystem (RTSS in Fig. 3) which models the turbine(aerodynamics and motion equation) and a hardware subsystemcomposed of the induction motor (IM) and its drive [18] (Fig. 3).In [19] it is used an experimental bench of small power with a di-rect-torque-controlled 1.5 kW induction motor for a real wind tur-bine simulation and a directly coupled 1.5 kW PMSG. An energystorage control method is presented in order to improve the powerquality of the grid power system.

An important function of the RTSS is the real-time wind speedgeneration. The wind speed regime is adjustable in real timethrough the ControlDesk� interface accompanying the dSPACEboard DS 1103, which ensures the hardware/software support ofthe RTSS. The rig monitoring is possible due to the ControlDesk�

interface.

3.2. PMSG torque estimation

Because of cost-effective requirements, the described simulatordoes not use a torque transducer. The torque estimation providedby the Danfoss converter concerns the IM torque, TIM, equalingthe PMSG torque, TG, at steady state only. TIM and TG have differentdynamical behaviors; so TIM estimation is unreliable for being anestimation of TG to use for control purposes. More accurate estima-tion of the PMSG torque, TG, can be obtained by using the rectifiedcurrent, IR, quite easy to measure, based upon a proportionalityrelation of gain KT. Gain KT depends of the operating point (of thechopper’s duty ratio, a), as to a hyperbolic-like curve (Fig. 4), justi-fied by the influence of variable efficiencies of various elementswithin the conversion chain [20]. One can write:

TG ¼ KTðaÞ � IR; ð2Þ

where KT(a) was implemented as a look-up table in several effectivepoints identified experimentally by matching steady-state values ofTIM and KT � IR for different a.

3.3. Improvement of the real-time replication dynamics

Fig. 5 presents the block diagram of the enhanced speed-drivensimulation structure, which replicates in real time the dynamics ofa given wind turbine, described by a certain known wind torquecurve, Twt(v, X), and inertia Jwt. Its motion equation is softwaresimulated and the result is the value of the rotational speed notedby X�. The induction motor (IM in Fig. 3) – having the PMSG as load

VLT 5000

RTPS PMSG IM

Wind turbine model

3 ~

∗Ω

Ω

S nthetic wind speed

Wind turbine control

Power electronics Load

Motor drive

IMT ∗

Speed control

PMSG torqueestimation

GTvRI

IPS

Software environment on DS1103

RTSS

Utility grid

3 ~

DCI α DCV

Fig. 3. HIL simulator block diagram.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 111

1.5

2

2.5

3

3.5

4KT [Nm/A]

α [-]

Fig. 4. Proportional gain between rectified current and generator torque vs.chopper’s duty ratio.

C. Vlad et al. / Electrical Power and Energy Systems 55 (2014) 562–571 565

– is torque-driven in order to turn at the rotational speed reference,X�. Dynamics of the induction motor torque control loop may beequivalently represented as a first-order system; it is fed by torquereference T�IM and outputs torque realization TIM. This first-orderdynamic is very fast in relation to other dynamics in the system,so it can be omitted in further computations (this is why it is rep-resented by a dashed-line box in Fig. 5). The motion equation ofphysical simulator is characterized by total inertia Jtr and viscousfriction coefficient, Dtr, considered negligible.

Note that the PMSG torque, TG, influences the rotational speedon two channels: it is necessary for the speed reference computa-tion, meanwhile acting as a disturbance for this loop. The formerinfluence takes place in software, whereas the latter is a physicalone. In order to control dynamics of the first-order plant having

1Jtr sþDtr

as transfer function, a PI controller can be chosen – with

KpX as proportional gain and TiX as time constant – so that theclosed loop meet certain dynamical performance like bandwidthand overshoot [21]. As consequence, the closed-loop transfer func-tion from the disturbance TG to the output X contains a derivativeeffect at low frequencies:

H1ðsÞ ¼ HTG!XðsÞ ¼� TiX

KpXs

Jtr � TiX=KpX � s2 þ TiX � sþ 1ð3Þ

When particularizing Relation (3) for the case presented here(see Appendix A), one can note the insufficient damping of distur-bance and presence of phase lead at frequencies in the middle of

the variation range of interest (see the dotted-line Bode plots inFig. 6). Good disturbance rejection can theoretically be obtainedby increasing the proportional gain KpX, but also can be reachedif adding a feed-forward component in the control input [21] whileavoiding too large values of KpX. Because TG is a measurable distur-bance, it can be passed through a suitably chosen dynamical sys-tem G(s), represented as a grey-filled-in box in Fig. 5. Thetransfer function HTG!XðsÞ is thus modified as follows:

H2ðsÞ ¼ HGTG!XðsÞ ¼

GðsÞ � 1ð Þ � TiXKpX

s

Jtr � TiX=KpX � s2 þ TiX � sþ 1ð4Þ

The most conveniently G(s) � 1 can be configured as a three-de-gree-of-freedom lag-lead dynamical system for increasing themedium-frequency attenuation and compensating the phase lead(see the dashed-line Bode plots in Fig. 6a and b).

GðsÞ � 1 ¼ K � T1sþ 1T2sþ 1

; K < 1; T1 < T2 ð5Þ

The Bode plots of H2ðsÞ ¼ HGTG!XðsÞ are shown with solid lines in

Fig. 6. Note that just a simple attenuation gain, G(s) � 1 = K < 1,would be enough for solving the disturbance attenuation problem,but without reducing the phase lead at medium frequencies.

4. Time-domain performance of the simulator

4.1. Speed controller performance assessment

Two situations were investigated for showing the servo-systemperformances. First, a step variation of rotational speed was im-posed for 0.5 duty ratio (left column in Fig. 7). Secondly, a step var-iation of duty ratio was imposed for the speed of 40 rad/s (rightcolumn in Fig. 7).

Fig. 7a shows a good tracking of the speed reference (rising timeof about 0.1 s). The overshoot is under 5% and remains so for differ-ent operating points. The associated control effort (Fig. 7b) empha-sizes the IM torque variation as estimated by the Danfoss converter(light-color plot). The PMSG torque, TG, computed using the meth-od from Section 3.2, is also given (dark-color plot). Note that thetwo variables have the same steady-state value.

In the second case, when a duty ratio step is applied (see the TG

evolution in Fig. 7d), the rotational speed deviation from the refer-

Fig. 5. Double influence of the generator torque on the rotational speed tracking loop that ensures the real-time simulation of a given wind turbine dynamics.

10-2

10-1

100

101

102

103

-80

-70

-60

-50

-40

-30

-20

-10

0

frequency [rad/s]

– H1(s) G(s)–1 H2(s)

-100

-50

0

50

100 – H1(s)G(s)H2(s)

(b) TG → Ω phase Bode plot [deg]

−1

K 2

1T

1

1T

(a) TG → Ω gain Bode plot [dB]

10-2

10-1

100

101

102

103

frequency [rad/s]

Fig. 6. Bode plots corresponding to the influence of the generator electromagnetictorque, TG, as measurable disturbance in the rotational speed tracking loop –improvement of disturbance rejection by using a lag-lead dynamical system.

566 C. Vlad et al. / Electrical Power and Energy Systems 55 (2014) 562–571

ence is under 10%, barely overpassing the noise level. The IM tor-que evolution, TIM, compensates for the PMSG load variation in or-der to reject the system disturbance (Fig. 7d, light-color plot). Thedynamic regime lasts for less than 0.5 s. The speed noise level isabout 1 rad/s.

4.2. Turbine simulator performance assessment at deterministic windspeed variations

Fig. 8 shows the simulator behavior around a typical operat-ing point, on the right side of the torque curve. Two cases werestudied. First, the emulated WECS experiences wind speed steps(of 1 m/s) at constant load current (left column of Fig. 8). Sec-ondly, step variations of the load current (of 2 A) were appliedat constant wind speed (right column of Fig. 8). The WECS mod-el responds by changing the speed reference of the inductionmotor. In Fig. 8a and d one can see accurate tracking of theWECS speed model (light plot). Fig. 8b and e shows the PMSGtorque (dark plot) and the wind turbine torque (light plot).The noisier driving torque, TIM, is also represented with light col-or. In Fig. 8b the wind torque has a sudden change due to thewind speed step variation, and then it follows the turbine newtorque characteristic as the rotational speed varies. Fig. 8c showsthe electrical variables’ evolutions at the rectifier output. Thevoltage (light plot) increases with the wind speed as the rota-tional speed (and so the PMSG electromagnetic force) increases.As the load current is maintained constant, the duty ratio reduc-tion decreases, further decreasing the rectifier current, IR (darkplot). IR evolution leads to a slight reduction in the PMSG torque(Fig. 8b).

The right column of Fig. 8 presents the simulator response toload current variations. Fig. 8d and e shows the turbine operatingpoint migration. As the current increases, the torque increasesand the speed consequently decreases, the operating point evolvestowards the maximum-torque point. Further increase in load maylead to unstable operation due to the operating point migration onthe right side of the torque curve. Fig. 8f shows the rectifier outputvariables’ evolutions.

(a)

(b)

(c)

(d)

[ ]NmGT

[ ]NmIMT

[ ], rad/s∗Ω Ω

[ ], rad/s∗Ω Ω

[ ]NmIMT

[ ]NmGT

[ ]st [ ]st

Fig. 7. Servo-system performance: left column – rotational speed varies from 40–50–40 rad/s at 0.5 duty ratio: (a) rotational speed (dark plot) against its reference, X�, (b) IMtorque (light plot) and PMSG electromagnetic torque (dark plot); right column – duty ratio varies as 0.3 ? 0.5 ? 0.3 at 40 rad/s rotational speed, (c) rotational speed (darkplot) against its reference, X�, (d) IM torque (light plot) and PMSG torque (dark plot). (For interpretation of the references to color in this figure legend, the reader is referred tothe web version of this article.)

[ ]st [ ]st

[ ], rad/s∗Ω Ω [ ], rad/s∗Ω Ω

[ ]NmwtT [ ]NmwtT[ ]NmGT

[ ]NmGT

[ ]NmIMT[ ]NmIMT

[ ]VRV

[ ]VRV

[ ]x10 ARI[ ]x10 ARI

(a) (d)

(b) (e)

(c) (f)

Fig. 8. Wind turbine simulator responses: left column – case when wind speed varies as 7 ? 8 ? 7 m/s at fixed load current, IDC, of 11 A: (a) rotational speed (dark plot) andits reference, X�, (b) wind torque, Twt (light plot), PMSG torque, TG (dark plot) and IM torque, TIM (noisy), (c) rectifier output voltage, VR (light plot) and rectifier current, IR;right column – case when the load current varies as 11 ? 13 ? 11 A at fixed wind speed (8 m/s): (d) rotational speed (dark plot) and its reference, X�, (e) wind torque, Twt

(light plot), PMSG torque, TG (dark plot) and IM torque, TIM (noisy), (f) rectifier output voltage, VR (light plot) and rectifier current, IR. (For interpretation of the references tocolor in this figure legend, the reader is referred to the web version of this article.)

C. Vlad et al. / Electrical Power and Energy Systems 55 (2014) 562–571 567

(a) (f)

[ ]st[ ]st

[ ], rad/s∗Ω Ω

[ ]m /sv

[ ], rad/s∗Ω Ω

[ ]NmwtT[ ]NmGT [ ]NmwtT[ ]NmGT

[ ]VRV [ ]VRV

[ ]x5 ARI [ ]x10 ARI

[ ]WwtP

[ ]WDCP [ ]WDCP

[ ]WwtP

[ ]m/sv

(b) (g)

(h) (c)

(d) (i)

(e) (j)

Fig. 9. System behavior at random wind speed of mean 7.5 m/s: left column – duty ratio fixed at 0.5: (a) wind speed evolution, (b) rotational speed (dark plot) and itsreference, X�, (c) wind torque, Twt (dark plot), PMSG torque, TG (light plot), (d) rectifier output voltage, VR (light plot) and its current, IR, (e) wind turbine power, Pwt (dark plot)and electrical power measured at the chopper’s output, PDC (light plot); right column – load current fixed at 11 A: (f) wind speed evolution, (g) rotational speed (dark plot) andits reference, X�, (h) wind torque, Twt (dark plot), PMSG torque, TG (light plot), (i) rectifier output voltage, VR (light plot) and its current, IR, (j) wind turbine power, Pwt (darkplot) and electrical power measured at the chopper’s output, PDC (light plot). (For interpretation of the references to color in this figure legend, the reader is referred to theweb version of this article.)

568 C. Vlad et al. / Electrical Power and Energy Systems 55 (2014) 562–571

4.3. Turbine simulator performance assessment at stochastic windspeed variations

Fig. 9 presents the emulated behavior as wind speed variespseudo-randomly with average value of 7.5 m/s. Because simulator

can be used in two ways – namely with duty ratio input and withIDC current input respectively – two case studies were considered:when the chopper duty ratio is constant (left column) and whenthe load current is constant (right column). In the second casethe time evolution was zoomed. Note that the wind speed varia-

C. Vlad et al. / Electrical Power and Energy Systems 55 (2014) 562–571 569

tions (Fig. 9a and f) are sufficiently slow (due to its bounded spec-trum) such that the speed reference to be perfectly tracked (Fig. 9band g).

In the first case (left column), the load induced by the quitelarge value of duty ratio a = 0.5 is important, therefore rotationalspeed values are quite low. The load is not stiff and PMSG torquefollows the wind torque which varies strongly with the wind speed(Fig. 9c). This leads to quite large variations of rectifier current(Fig. 9d) and so to large variations of output electrical power(Fig. 9e). In conclusion, electrical power follows wind speedvariations.

In the second case (right column) current IDC determines a loadsmaller than in the first case, leading to larger rotational speed val-ues (Fig. 9d). As load current IDC is supposed constant, outputpower PDC is also constant (Fig. 9j). The load is stiff in this case, rec-tifier current presents small variations and so does PMSG torque(Fig. 9h–i). Wind speed variations are no longer followed by PMSGtorque and the quite large differences with respect to wind torqueare likely to determine rotational speed variations within a rangelarger than in the first case.

4.4. Real-time replication of starting and braking regimes

Fig. 10 shows the simulated WECS behavior at starting on theleft column and at electromagnetic braking on the right column.At starting, a low load variation was applied at 0.1 duty cycleand wind speed of 6 m/s. The operating point migrates to the right

[ ]st

[ ], rad/s∗Ω Ω

[ ]NmwtT

[ ]NmGT[ ]NmIMT

[ ]VRV

[ ]x100 ARI

(a)

(b)

(c)

Fig. 10. Wind turbine simulator starting and electromagnetic brake regimes: left column(dark plot) and its reference, X�, (b) wind torque, Twt (light plot), PMSG torque, TG (dark plcurrent, IR; right column – electromagnetic brake regime at wind speed fixed at 7 m/s andreference, X�, (e) wind torque, Twt (dark plot), PMSG torque, TG (noisy), (f) rectifier outputo color in this figure legend, the reader is referred to the web version of this article.)

side of the turbine torque curve and is characterized by low steady-state values of the wind torque and quite high rotational speed(Fig. 10a and b). Fig. 10c shows the electrical variables evolutionsin this regime: quite large voltage and small steady-state currentvalues.

The braking regime was obtained for a fixed wind speed of7 m/s and a step variation of duty cycle between 0.2 and 0.9. Dueto the quite large load, the turbine operating point moves to theleft side of the torque curve, at low values of rotational speedand torque (Fig. 10d and e). The PMSG torque varies in step to alarge value that cannot be provided by the turbine at the actualwind speed and the system brakes.

5. Frequency-domain error analysis

The simulator performance around a typical operating pointwas studied against the one predicted by the linearized modelfor a frequency range larger than two decades. The physical simu-lator was submitted to small-amplitude variable-frequency sinu-soidal variations of its exogenous signals, the wind speed and theload current reference. The amplitude and phase lag of the rota-tional speed as output signal were measured for each frequencyvalue. Bode plots were plotted for both input–output channels(Fig. 11a–d).

The replication performance on each influence channel isjudged in relation to the frequency spectrum of its respective exog-enous signal. Fig. 11a and b illustrate good simulation quality on

[ ]st

[ ], rad/s∗Ω Ω

[ ]NmwtT

[ ]NmGT

[ ]VRV

[ ]x5 ARI

(d)

(e)

(f)

– start regime at low load value and wind speed fixed at 6 m/s: (a) rotational speedot) and IM torque, TIM (noisy), (c) rectifier output voltage, VR (light plot) and rectifierat a duty cycle step variation from 0.2 to 0.9: (d) rotational speed (dark plot) and its

t voltage, VR (light plot) and rectifier current, IR. (For interpretation of the references

10-2

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102

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10

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25

frequency [rad/s]

(a) Wind-speed-to-rotational-speed steady-state gain [dB]

modelphysical simulator

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frequency [rad/s]

(c) Load-current-reference-to-rotational-speed steady-state gain [dB]

modelphysical simulator

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modelphysical simulator

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0

frequency [rad/s]

(d) Load-current-reference-to-rotational-speed phase lag [degrees]

modelphysical simulator

Fig. 11. Real-time simulation performance in the frequency domain – simulator vs. linearized model Bode plots obtained around the operating point described by v = 7 m/s,I�DC ¼ 11 A and X = 56.17 rad/s: (a and b) wind-speed-to-rotational-speed channel; (c and d) load-current-reference-to-rotational-speed channel.

570 C. Vlad et al. / Electrical Power and Energy Systems 55 (2014) 562–571

the first channel in the frequency range of interest. The maximumgain error is below 1 dB and is placed within the bandwidth(Fig. 11a). Phase lag errors are very small (Fig. 11b). Both gain errorand phase lag error increase with the frequency.

Fig. 11c and d allow assessing the simulation quality on the sec-ond channel in the frequency range of the load current referencevariations. In this case also the gain difference is around 1 dB alongthe whole frequency range of interest (Fig. 11c). Phase lag errorsare placed around 2� (Fig. 11d). Both gain and phase lag errors in-crease with the frequency, and differences are more obvious thanin the case of the first channel.

To conclude, one can identify a frequency value that suggeststhe limits of the real-time simulation good performance: it is situ-ated around 10 rad/s for both transfer channels. So the WECS’sdynamical behavior submitted to exogenous variations faster than10 rad/s will be simulated the less accurately the larger the fre-quency is.

As predicted in [13], a speed-driven wind turbine simulatorshould have worse dynamic performance than a torque-drivensimulator. However, the enhanced speed-driven simulation struc-ture proposed in this paper has very good dynamic performance,as Fig. 11 suggests, close to performance of torque-driven simula-tors (see also results reported in [17]). Moreover, unlike torque-driven simulators, the proposed structure offers better replicationin the low-frequency domain, i.e., almost zero steady-state error.

6. Conclusion

This paper has proposed a new real-time software simulatorstructure that enhances the performances of a speed-driven WECShardware-in-the-loop simulator by significantly enlarging itsbandwidth.

A WECS composed of a low-power fixed-pitch wind turbine ro-tor that drives a PMSG has been considered. This supplies a mainly

resistive DC load through an uncontrolled rectifier and a buck DCpower stage. By imposing either the converter duty ratio or theoutput current, this latter allows the variable-speed regime ofthe turbine rotor.

The WECS model states that the generator torque influences therotational speed only through the motion equation. Yet, in thespeed-driven simulator structure, it has been shown that there isa second influence channel by means of the simulator rotatinghardware. This second influence, acting like a disturbance, hasbeen alleviated by a new software simulator structure containinga supplementary feed-forward control branch. Thus, introductionof a lag-lead compensator of the estimated generator torque hasled to improved emulation bandwidth and hence to well-perform-ing WECS dynamical replication whose accuracy is close to that oftorque-driven real-time simulations. A cheap and sufficiently accu-rate estimation of the PMSG electromagnetic torque based uponmeasuring the rectified current was preferred instead of using atorque transducer.

Good real-time replication was obtained for both wind-speed-to-rotational-speed and generator-torque-to-rotational-speedtransfer channels in the frequency range of interest, covering var-iation domains of both exogenous signals. The results have alsobeen assessed in the frequency domain by plotting the experimen-tally-obtained WECS simulator Bode characteristics against thoseof the WECS linearized model.

Appendix A

A.1. Aerodynamic subsystem and drive train

Air density q = 1.25 kg/m3, tip speed ratio optimal value kopt = 7,blade length R = 1.15 m, power efficiency coefficient maximum va-lue Cpmax(kopt) = 0.476, torque coefficient maximum valueCTmax = 0.075, the torque CT polynomial function approximation:

C. Vlad et al. / Electrical Power and Energy Systems 55 (2014) 562–571 571

CT(k) = a6 � k + a5 � k + a4 � k + a3 � k + a2 � k + a1 � k + a0, wherea0 = 0.0061, a1 = �0.0013, a2 = 0.0081, a3 = �0.97477 � 10�3,a4 = �6.5416 � 10�5, a5 = 1.3027 � 10�5, a6 = �4.54 � 10�7, gear box(drive train) ratio i = 1, Jwt = 0.2 kg �m2.

A.2. Permanent-magnet synchronous generator

Ratings: 1 kW, 48 V; number of pole pairs p = 5.

A.3. Load and chopper

Load resistance Rload = 1.94 X; chopper inductance Lb_ch = 0.02 -H and resistance Rb_ch = 0.8 X.

A.4. Induction machine

Jtr = 0.0894 kg �m2; ratings: 3 kW, 400 V, 50 Hz, 960 rot/min,7.6 A.

A.5. Control parameters

Real-time simulation sampling time Te = 0.5 ms; speed PI con-troller: gain KpX = 2.25, time constant TiX = 0.0833 s; DC currentPI controller: gain KpI = 0.02, time constant TiI = 0.01 s.

Steady-state gain from X to DC voltage: KXVR = 1.27.

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