modelling, control and simulation of an overall wind energy conversion system

Renewable Energy 28 (2003) 1169–1185www.elsevier.com/locate/renene

Modelling, control and simulation of an overallwind energy conversion system

Ph. Delaruea, A. Bouscayrola,∗, A. Tounzia, X. Guillauda,G. Lancigub

a L2EP Lille, USTL, 59655 Villeneneuve d’Ascq Cedex, Franceb Jeumont SA, 27 rue de l’Industrie, 59573 Jeumont Cedex, France

Received 27 May 2002; accepted 12 October 2002

Abstract

More and more conversion systems have been proposed to capture wind energy in order toproduce electrical power. In this paper, an energetic macroscopic representation is used todescribe such systems composed of very different parts. This representation yields the simul-ation model of the overall system based on energetic considerations. Moreover, a controlstructure can be deduced from this representation by simple inversion rules. Hence, the differ-ent strategies of wind turbine management can be shown by the theoretical control structure.In order to illustrate this modelling and control methodology a 750 kW wind energy conversionsystem is studied and simulated. 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Wind energy; Wind systems; Wind turbine, Control

1. Introduction

The wind energy conversion systems (WECS) have increasingly been developedover the last 10 years. Indeed, they offer energy without negative environmentalimpact. Constant-Speed Constant-Frequency (CSCF) systems were first developedusing a pitch angle control [1] in order to minimize the wind fluctuations on thetransfer power. CSCF systems generally use synchronous or squirrel cage induction

∗ Corresponding author. Tel.:+33-3-20-43-42-53; fax:+33-3-20-43-69-67.E-mail addresses: [email protected] (A. Bouscayrol); http://www.univ-lille1.fr/l2ep/

(A. Bouscayrol).

0960-1481/03/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.doi:10.1016/S0960-1481(02)00221-5

1170 Ph. Delarue et al. / Renewable Energy 28 (2003) 1169–1185

Nomenclature

Cp power coefficient of the wind turbinee electromotive force (V)f coefficient of viscous friction (N m s)F various forces (N)I various currents (A)J moment of inertia (kg m2)L various inductances (H)m various modulation coefficientsP various powers (W)r various resistances (�)R blade radius (m)sij switching functions of power electronics convertersS swept area of the blades (m2)T various torques (N m)u various voltages (V)v various speeds (m/s)l tip speed ratio� various rotation speeds (rad/s)r air density (kg/m3)

machines. Variable-Speed Constant-Frequency (VSCF) systems have been developedto reduce the influence of the wind fluctuations with variable speed machines. Thesegenerators can be squirrel cage induction or doubly fed induction machines [2–4].Variable-Speed Variable-Frequency (VSVF) systems improve the annual energy pro-duction [5] and are more flexible under various wind conditions and reduce thestresses of the turbine [6]. Nowadays, several solutions can be found, as a result ofthe design evolutions of aerodynamics, power electronics and electrical machines.The squirrel cage induction machine with two voltage-source-converters is the mostflexible conversion structure [7–11]. Synchronous machines with a high pole number[12] or Vernier reluctance machines for low speed [13] are also used in order toavoid the mechanical gearbox. Various control strategies are proposed to extractmaximum power from the wind [8–11,14] and to manage the system according tothe standard operating modes [15,16].

Hence, many different WECS are provided, with several power components usingdifferent technologies and knowledge: turbine, mechanical power train, electricalmachines and power electronics. They have to be simulated in order to providecomparisons for a critical choice. However, dynamic modelling of such complexsystems is not always made [17,18]. Indeed, if each part can easily be studied, thereare sometimes problems in connecting models of the devices, which are of a differentnature. Even if global softwares (saberTM, matlabTM, etc.) have adapted libraries

1171Ph. Delarue et al. / Renewable Energy 28 (2003) 1169–1185

and toolboxes, the connections of such elements cannot be made without a prelimi-nary study and sometimes they involve modifications of standard models.

The aim of this paper is to deal with a modelling and a control methodology inorder to simulate such WECS. This description [19] allows the subdivision of thewhole complex system into simple blocks which allows a synthetic and physicalrepresentation [20] based on the causality principle [21,22]. This methodology hasbeen successfully applied in the case of traction applications [23,24]. A first model-ling of a WECS with an induction generator has also been proposed [25]. In thispaper, the modelling of such a system is extended to its control design and simul-ation.

The first part is devoted to the description of a studied wind generation system.In the second part, a control structure of this system is suggested according to inver-sion rules. The last part focuses on the transposition of the modelling and controlinto the matlab–simulinkTM software. Then simulation results are provided.

2. Modelling of a wind energy conversion system

The WECS studied is a VSVF structure. It ensures an energy conversion fromthe wind to an AC grid. An overall modelling is built, thanks to the energetic macro-scopic representation (EMR). As the modelling of the blade is often neglected, thispart is particularly detailed.

2.1. The wind energy conversion systems studied

The subscript of each power variable is associated with the physical element, fromwhere the variable comes. The different choices will be justified by the modellingof the global system.

The WECS is a fixed-pitch turbine with a horizontal axis and three blades. Agearbox ensures the adaptation between the rotation shaft of the blades (low speed)and the rotation shaft of the machine (high speed). In the system studied, the electro-mechanical conversion is provided by a permanent magnet DC machine instead ofthe AC machine classically used in wind generation system. The DC machine hasbeen chosen due to its simple electrical model. Hence, we can avoid a too complexrepresentation as this study is principally focused on the representation of the overallsystem. The electrical power produced supplies a capacitor, thanks to a four quad-rant-chopper. The DC voltage of the capacitor consists of a DC bus, which is con-verted to AC voltages by a three-phase power converter. Finally, after filtering theripples induced by the modulations of the converters, a three-phase transformeradapts the voltage magnitudes to those of the AC grid (Fig. 1).

2.2. Global modelling of the overall system

The EMR yields a synthetic description of complex systems based on the action–reaction principle between power devices [26]. The components (or sub-systems) of


Fig. 1. The WECS studied.

this representation are associated with each physical device. First, they are reducedto their global functions according to their internal causalities [19]. The powerbetween two connected blocks can be expressed by the product of their exchangevariables.

The EMR of the studied WECS is composed of several power components linkingthe wind to the AC grid, which are called upstream and downstream power sources(Fig. 2). Several elements, which will be detailed in the following part, can bepointed out:

� the blades (mechanical conversion function),� an equivalent shaft (mechanical accumulation function),� the gearbox (mechanical conversion function, which adapts the rotation speed),� the ideal machine (electromechanical function),� the winding of the machine (electrical accumulation function in the inductance),� the chopper (electrical conversion function, which yields the DC bus),� the capacitor (electrical accumulation function, which imposes the DC voltage),� the three-leg inverter (electrical conversion function),� an equivalent filter (electrical accumulation function of the inductances),� the three-phase transformer (electrical conversion function, which adapts the AC

voltages of the lines to those of the grid).

The elements, which induce energy accumulation, are all depicted by a rectangularpictogram. The elements, which induce energy conversion without energy accumu-lation, have different pictograms: triangular pictogram for mechanical conversion,

Fig. 2. EMR of the WECS studied.


circular pictogram for electromechanical conversion and square pictogram for electri-cal conversion.

Hence, this modelling gives a global overview of the energy modification in theWECS. Energy accumulation and conversion are differentiated. Indeed, this differ-ence is the basis of the suggested control methodology, as will be seen in thenext section.

2.3. Modelling of the blades

The wind power acting on the swept area of the blade S is a function of the airdensity r and the wind velocity vwind. The transmitted power Pblade is generallydeduced from the wind power using the power coefficient Cp

Pblade � Cp

12rSv3

wind. (1)

The power coefficient is a non-linear function of the tip speed-ratio l, whichdepends on the wind velocity and the rotation speed of the shaft �shaft (Fig. 3(a))

l �R�shaft

vwind, (2)

where R represents the blade radius. In the curve, lopt is the value of l which corres-ponds to the maximum of Cp.

As the transmitted power can be assumed to be the product of the torque and therotation speed of the shaft, an expression of the blade torque can be deduced from (1)

Tblade � Cp(l)12rS

v3wind

�shaft. (3)

But this classical modelling results in a problem. If the wind blows at zero rotationspeed, there is no blade torque and the system cannot start to run. To solve thisproblem, the rotation speed is replaced by the tip speed ratio (2)

Tblade �Cp(l)l

12rSRv2

wind. (4)

Fig. 3. Blade characteristics: (a) CP versus l/lopt, (b) CP/l versus l/lopt.


Fig. 4. Modelling of the blades: (a) internal description and (b) EMR.

A new coefficient, the torque coefficientCT(l) � CP(l) /l, can then be defined. Italso has a non-linear evolution with respect to l, but it avoids the singularity at zerorotation speed. This coefficient is sometimes used to define the torque [7,27]. Usingan extrapolation method for the lower values of l, we obtain, for l � 0, a non-zerovalue of Cp /l (Fig. 3(b)). Then, when the wind is blowing, a small torque acts onthe blades and the rotation occurs.

Moreover, a blade velocity vblade and a tangential force Ftang can also be definedaccording to the blade radius R

� vblade � R�shaft

Tblade � RFtang

. (5)

If we take the previous considerations into account, the model of the blades canbe described as shown in Fig. 4(a). This internal description leads to the externalexchange variables of the macroscopic representation of the blades (triangular picto-gram, Fig. 4(b)).

2.4. Modelling of the mechanical parts

As both mechanical shafts are linked by the gearbox (mgear gear ratio), there isonly one state variable [20]. An equivalent shaft is so defined [25]. It yields therotation speed of the shaft, �shaft, from the gear torque, Tgear, and the blade torque(J, moment of inertia and f, coefficient of viscous friction)

Jshaft

ddt

�shaft � Tblade�Tgear�fshaft�shaft (6)

with

Jshaft � J1 �J2

m2gear

fshaft � f1 �f2

m2gear

.

This element is depicted by a rectangular pictogram with an oblique bar accordingto the EMR (Fig. 5). This representation indicates an energy accumulation: thisdevice yields a rotation speed of the shaft which is a state variable.

Fig. 5. EMR of the mechanical parts.


Fig. 6. EMR of the DC machine.

The gearbox is a mechanical converter, which adapts the rotational speed, �gear,and the torque, Tgear, with the gear ratio, mgear

��gear � mgear�shaft

Tgear � mgearTdcm

. (7)

2.5. Modelling of the electrical machine

The electromechanical conversion (circular pictogram, Fig. 6) of the DC machinelinks its torque, Tdcm, to the armature currents idcm, and the e.m.f., edcm, to the speed,�gear, through the flux coefficient kf

�Tdcm � kfidcm

edcm � kf�gear

. (8)

The winding of the machine is an accumulation element, which yields the machinecurrent from the e.m.f. and the chopper supply voltage, uchop (rdcm, Ldcm resistanceand inductance of the winding)

Ldcm

ddt

idcm � edcm�uchop�rdcmidcm. (9)

2.6. Modelling of the electrical parts

The power converters are modelled by their switching functions, sij (1 for closedswitch and 0 for open switch) and their modulation functions, mi [28]. First, thepower converters can be modelled in mean values. Hence, the switching and modu-lation functions are replaced by their mean values calculated on the switching period(0�sij�1 and �1�mi�1).

The chopper leads to an electrical conversion without energy accumulation. It isthus depicted by a square pictogram (Fig. 7). Its inputs and outputs can be modelledby classical relations

Fig. 7. EMR of the electrical part.


�uchop � mchopucap

ichop � mchopidcm

with mchop � schop11�schop21. (10)

The three-phase inverter is modelled in the same way

�uinv � minvucap

iinv � mtinviline

with minv � �sinv11�sinv31

sinv21�sinv31�. (11)

The DC bus voltage capacitor is an accumulation element, which yields the capaci-tor DC voltage ucap from the inverter current iinv and the chopper current ichop

Ccap

ddt

ucap � ichop�iinv�ucap / rcap, (12)

where rcap is an equivalent resistor to take the converter losses into account.The association of the filter inductances and the transformer inductances leads to

a common accumulation element: their currents are common state variables. It yieldstwo independent currents iline � [iline1iline2]t (the third is a combination of the twoothers) from the inverter voltages uinv � [uinv13uinv23]t and the transformer voltagesutrans � [utrans13utrans23]t [25]

lline

ddt

iline �13�2 �1

�1 2� (uinv�utrans)�rlineiline. (13)

The ideal transformer is an electrical converter (square pictogram) between thefilter and the grid. It links the transformer voltages to those of the grid ugrid �[ugrid13ugrid23]t, and the transformer current itrans � [itrans1itrans2]t to those of the line,

with the transformer ratio mtrans

�utrans � mtransugrid

itrans � mtransiline

. (14)

3. Control of a wind energy conversion system

The aim of the wind generation control is to ensure the management of the power,which is delivered by the wind. But, as this system is directly connected to the grid,the reactive power has to be controlled too. Moreover, the voltage of the DC bus isa sensitive variable for the design of the power converter and the DC capacitor. Thisvoltage also has to be controlled.

As a result of inversion rules, a maximum control structure (MCS) is deducedfrom the EMR of the system. It consists of control blocks, which have to inversethe local function of each power component. Two other control blocks have to bebuilt in order to define the references of the MCS from the power references: theactive power management (APM) and the reactive power management (RPM).


3.1. Maximum control structure

A control structure of the system studied is defined from its EMR according toinversion rules [19]. An element, which accumulates energy, needs a controller toinverse its physical function. An element without energy storage can be inverteddirectly (inverse mathematical operation). In the following figures, the inversionfunctions are depicted with continuous lines, and disturbance rejections withdashed lines.

The inversion rules are applied to the EMR of the wind generation system. Itleads to its MCS (Fig. 8). All control blocks can contain classical operations: pulsewidth modulations (PWM) for the converters, current controllers for the machineand the lines, etc. This control structure points out the variables to be measured.Some of them cannot be directly measured and estimation algorithms have to beadded in a supplementary step (as the machine e.m.f., edcm, is estimated through thespeed measurement, �gear-mes). But the estimation algorithms are not presented inthis paper.

For example, relation (8) is directly inverted in order to produce the referencecurrent, idcm-ref, from the reference torque, Tdcm-ref, as follows:

idcm-ref �1kf

Tdcm-ref. (15)

In the case of relation (9), as the current is a state variable, a controller is neededto define the reference voltage, uchop-ref. Moreover, the disturbance variable, edcm, istaken into account and rejected externally to the controller

uchop-ref � Cont( idcm-ref�idcm-mes)�edcm-mes. (16)

Cont(xref�xmes) is the controller associated to the variable x. The overall controlequations are provided in Ref. [29].

One can remark that the MCS needs torque and current references. As the technicalspecifications give only power and capacitor voltage references, other blocks haveto be inserted in the control chain.

3.2. Active power management

A simple relation can be found between the converted power, Pconv, and the torqueof the gear, Tgear

Fig. 8. MCS of the WECS studied.


Fig. 9. Converted power versus rotation speed.

Pconv � Tgear�shaft. (17)

The torque reference can be deduced from the following power relation:

Tgear-ref �Pconv-ref

�shaft-mes. (18)

The converted power, Pconv, versus the rotation shaft speed, �shaftr, for differentwind velocities (Fig. 9) shows that a maximum curve can be obtained for eachoperating point (continuous line). By associating this maximum power curve and theassociated rotation speed, a look-up table is built; it gives the optimum power fromthe rotation speed (Fig. 10). As the power is divided by the rotation speed, a newlook-up table is built with the rotation speed as input and the reference torque asoutput (Fig. 10). This look-up table gives the reference torque directly from the speedmeasurement for a maximum power strategy; maximum power generation and speedlimitation for high wind velocity.

A more complex strategy can be deduced from the first one. Indeed, in most windgenerators, several operating modes have to be defined [15]. If the wind velocity istoo high or low, the wind turbine is turned off. For low wind velocity, the controlhas to allow a maximum power extraction. For high wind velocity, a constant valueis imposed on the rotation speed. The APM block has to be changed.

Fig. 10. APM block.


3.3. Reactive power management

If the desired reactive power is assumed to be zero and if sinusoidal absorptionis needed, the active power can be expressed by the r.m.s. value of the voltage grid,Vgrid, and the transformer current, Itrans. If the power losses are neglected in theconverter switches and in the lines, this power is equal to the one of the DC bus.

P � 3VgridItrans�ucapiinv. (19)

With these assumptions, there is a direct relation between the r.m.s. value of theabsorbed current and that of the inverter. On the other hand, the voltage capacitoris defined through the inverter and the chopper current.

A PI (Proportional Integral) controller can be used to control the DC voltage. Ityields the inverter current reference, iinv-ref. This is then transformed into the trans-former magnitude current reference, Itrans-ref, using Eq. (19). Itrans-ref is multiplied bythe unitary sine wave obtained by a grid voltage measurement. The transformer cur-rent references are thus defined without shift angle between the voltage (Q � 0) andthat without harmonics (Fig. 11).

4. Simulation of a wind energy conversion system

A 750 kW wind generation system has been deduced from the Jeumont Industrysystem J48, (synchronous generator). The turbine has a blade radius of 24 m. ThisWECS is connected to 20 kV grid.

4.1. Simulation transposition

The modelling and the control of the studied WECS (see Fig. 8) and the manage-ment blocks are directly transposed to the matlab–simulinkTM software (Fig. 12).Hence, the suggested methodology gives precious help to the simulation design. Allblocks can be internally described with their mathematical relations. An example isgiven for the blades (Fig. 13).

4.2. Simulation results

Simple tests are provided in order to validate the modelling and control method-ology. First, the blades are locked, in order to charge the DC capacitor. Secondly,

Fig. 11. RPM block.


Fig. 12. matlab–simulinkTM model and control of the WECS studied.

Fig. 13. matlab–simulinkTM model of the blade.

the mechanical brake action is cancelled and the blades begin to rotate. A table ofan actual wind velocity is used as input for the simulation, between 10 and 19 m/s(Fig. 15).

4.2.1. Reactive power managementThe DC bus voltage is initially fixed at 975 V (voltage value due to the diode

bridge when switches are turned off). Then, the DC bus voltage increases to itsnominal value using a PI controller (Fig. 14). After that, one can notice that the DCvoltage remains at a constant value in spite of the wind fluctuations. Sinusoidal linecurrents are also controlled by PI controllers and they are in phase with line-to-neutral voltages (Q � 0) (Fig. 16).

4.2.2. Active power managementThe blade speed (Fig. 17) increases under the wind action and reaches 2.6 rad/s.

During this period, the blade torque, Tblade, is greater than the machine torque, Tdcm

(Fig. 19).One can notice that the blade speed is quasi-constant after the transient state. This

is due to Tdcm � ref � f(�shaft) table which corresponds to a maximum power strategyand parabolic evolution, which leads to a constant blade speed when the wind velo-


Fig. 15. Wind velocity.

Fig. 14. Capacitor voltage.

city is greater than 10 m/s. The obtained power fluctuates with the wind velocity(Fig. 18).

5. Conclusions

An overall wind generation system has been described with the help of the EMR.This description yields a synthetic view of the overall system according to the causalrelations of its components. A MCS of the wind generation system has been deducedfrom its EMR by logical inversion rules. Of course, the MCS possesses a maximumof control operations and measurements. It is the first necessary step for a morepractical structure, which can be deduced by adapted simplifications and variable


Fig. 16. Line currents and voltages.

Fig. 17. Blade speed.

estimations. The MCS shows the controllers and the sensors (or estimationalgorithms) which are needed in such a system. Moreover, management blocks haveto be defined in order to connect references of physical variables and power refer-ences.

The model and control of the WECS have been very easily transposed in simul-ation software such as matlab–simulinkTM. The global simulation software allowsus to study the influence of each control operation (disturbance rejection, controllerdesign, and parameter variation), and of the wind fluctuations. Moreover, differentmanagement strategies can now be compared. Indeed, the inversion of power compo-nents cannot be avoided because they are based on the action–reaction principle andon the natural causality of energy accumulation. So, the management blocks are thekey to the different control strategies, and many solutions can be defined.


Fig. 19. Torque evolutions.

Fig. 18. Power evolution.

The studied wind generation system is a virtual system. As a result of the flexibilityof the EMR and the MCS, the DC machine and the chopper can be easily replacedby an AC machine and a three-leg rectifier [25]. The MCS can be built in the sameway; only the machine control and the rectifier control have to be modified. Onecan notice that practical control structures can be deduced for the MCS [29]. Ofcourse, other WECS can be modelled in the same way. The studies can then bemore complete by taking into account wind gusts and other practical problems [30].

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