SUPERVISORY CONTROL OF GRID CONNECTED WIND POWER SYSTEMS TO GUARANTEE SAFE OPERATION

SUPERVISORY CONTROL OF GRID CONNECTED WIND POWER SYSTEMS TO GUARANTEE SAFE OPERATION Antoneta Iuliana BRATCU, Daniela Cristina CERNEGA and Iulian MUNTEANU Advanced Control Research Centre “Dunărea de Jos” University of Galaţi 47, Domnească, 800008-Galaţi, Romania Emails: {Antoneta.Bratcu, Daniela.Cernega, Iulian.Munteanu}@ugal.ro

Abstract: This article proposes a supervisor synthesis for a two level hierarchical control structure of a grid connected wind power system to ensure its safe and optimal operation. The global hybrid dynamics may roughly be captured into a hybrid automaton. The optimization tasks, specific to different operating regimes, are performed by the low level continuous controllers. A supervisor placed on a higher level must guarantee the safe transition from an operating regime to another, triggered by some discrete events. The interest is focused on the design problem on the higher level: the discrete event modelling and the supervisor design in the supervisory control framework. Copyright © 2006 IFAC Keywords: safety, supervisory control, discrete event dynamic systems, automata theory, hierarchical control.

1. INTRODUCTION Wind power systems (WPS) technology is a rapidly growing domain, the installed generation capacity was increasing averagely with 32% every year from 1998 to 2003. The modern technology has allowed the production costs reduction with more than 80% in the 1980s, so that the wind energy represents now a stable segment of the electrical energy market, supported by a mature technology (Burton, et al., 2001; Bathurst, et al., 2002). The wind energy conversion problem has a unitary-systemic character, imposing a global control approach, to ensure the system’s functionality and viability, as well as the provided energy quality. These requirements result from the exploitation experience and grid integration. The global WPSs’ performance (economical efficiency and integration capacity into energy grids) is presently aimed at, as briefly discussed next. Modelling of the exogenous signal, namely the wind, as a 3D non stationary random process, result in spectral models, allowing to identify two components in the wind speed: the steady-state, low frequency one, and the turbulent, high frequency one

(Van der Hoven model – Nichita, et al., 2002). The steady-state speed determines the available energy of a wind site. Dedicated spectral models (i.e. von Karman and Kaimal – Nichita, et al., 2002) exist for the turbulent component, the one inducing fatigue loads and rapidly cyclic aerodynamic and possibly damaging phenomena. Modelling of the WPSs in different regimes has as purpose the simulation analysis of their dynamic behaviour (Wilkie, et al., 1990), aiming further at solving the associated control problems (Novak and Ekelund, 1994; Welfonder, et al., 1997). The static operation of a wind turbine, depending on the average (steady state) wind speed, exhibits four zones (figure 1): I) for wind speeds smaller than the starting threshold ( vS ), the wind energy is not sufficient to move on the turbine (the provided power is zero); II) in the partial load zone – speeds larger than the start one, but smaller than the nominal one ( vn ) – the extracted power is proportional to the wind speed cubed (this zone is also called parabolic); III) in the full load zone – speeds larger than the nominal one ( vn ) and smaller than the safe

functioning limit ( vM ) – the harvested power is limited at its nominal value ( Pn ); IV) for wind speeds larger than the maximal operation speed the provided power becomes zero. PN

Pwt

II PS I vS 0

III vN

vM

IV v

Fig. 1. Power captured by a wind turbine versus average wind speed. Zones from figure 1 roughly correspond to the operating regimes (operational states) of a wind turbine. For the productive regimes – the partial and the full load zones – sufficiently good performing models are available. The normal operating regime is practically superposed on the partial load zone, for which multiple control objectives may be defined (Leithead, et al., 1991), in general cast into continuous optimal control problems, aiming at maximizing the conversion. The aerodynamic efficiency is expressed by the power coefficient, Cp, depending on the tip speed ratio, l (the ratio between the peripheral blade speed and the wind speed). In figure 2a) a typical Cp curve for a horizontal axis wind turbine (HAWT – Wilkie, et al., 1990) is shown, presenting a maximum for a well determined value of the tip speed, lopt. The power characteristics (figure 2b)) have a maximum for each value of the wind speed; all these maxima form the so called optimal regime characteristic (ORC, figure 2b)). 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

C p (λ)

a)

4.5 4.0 3.5 3.0

Pwt [ kW ]

b) ORC

2.50 2.0 1.5

λ opt 2

4

6

8

10

λ

1.0 0.5 12 0

7 m/s 5 m/s

5

9 m/s

10 15 20

W [ rad/s ]

25 30 35 40 45

Fig. 2. a) Power coefficient versus the tip speed ratio; b) Power characteristics. Curves from figure 2, only valuable in the partial load zone, suggest a harvested wind energy maximisation problem formulation: the turbine must ideally operate on the ORC (at the optimal value of the tip speed), irrespectively of the wind speed. To this, one can add the variable fatigue load reduction, to ensure a certain reliability level of the mechanical parts. Various approaches exist for solving one or many objectives from those above: Maximum Power Point Tracking (MPPT – Datta and Ranganathan, 2003; Wang, 2004), suitable especially under uncertainties, including on the static characteristic; use of the intelligent control techniques (Abo-Khalil, et al., 2004; Zhang, et al., 2004), when there are uncertainties about the static model; sliding mode techniques (De Battista, et al., 2000), when the uncertainties refer to the dynamic model; gain scheduling techniques (Ekelund, 1997; Bianchi, et al., 2005), for adapting the control law depending on the average wind speed; frequency robust control

techniques (Rocha and Filho, 2003). Control laws based upon some mixed (energy-reliability) optimisation criteria (Novak and Ekelund, 1994; Ekelund, 1997) can be designed to comply with the fatigue minimisation. Supervisory control of WPSs is related to their global, “high-level” operation. Transitions between different operating zones, turbine’s functioning in regimes distinct from the normal ones, as well as its behaviour under extreme dynamical loads, are ensured by a supervisor (Burton, et al., 2001). Concerning the design control problem at this level, the literature is however extremely poor in publications. Kana, et al. (2001) and Young, et al. (2003) present points of view closer to a global control approach. Studies on supervisory control of the WPSs seem to be still at the beginning. The system approached in this paper is an average power (dozens of kW) variable speed fixed pitch asynchronous generator based HAWT, which will be supervised in order to force a set of safe operation specifications to be met. The model used will be a hybrid automaton, whose discrete states are issued by an as exhaustive as possible enumeration of the operating regimes, each of which is equipped with a continuous controller for specific optimization tasks. So, the global control structure has a hybrid dynamic on two decision levels. In this paper the interest is given to the higher level design problem. The rest of the paper is organised as follows. The second section explains the necessity of a hierarchical control for the approached WPSs. A discrete event model is built in the third section, to be used in the fifth section for designing a supervisor to guarantee the safe operation, using the general framework briefed in the fourth section. The last section is dedicated to conclusion and future work. 2. CONTROLLED GRID CONNECTED WPS AS A HYBRID DYNAMIC SYSTEM To reduce the wind turbines operation costs requires an automated and remote controlled operation. An appropriate control strategy allows improving the system’s reliability, yielding both maintenance costs’ reduction and harvested power growth. The reliability can be improved at two levels of action: 1) at low level, by controlling the captured power at variable speed, and 2) at a higher level, by ensuring the safe operation, regardless from the wind conditions (by rejecting mainly the extreme wind turbulences). The above cited works show that the continuous dynamics of the partial load zone (figure 1) can be controlled for conversion optimization. In the other zones the control subsystems are less complex. Because of the wind’s randomness, the WPS may often change the operating point from an operational state to another, potentially affecting the proper operation. One may naturally think of a supervisor to assist the system’s safe transition among different operational states, equipped with continuous controllers. This one must be placed on a higher level to “see” the system being driven by certain discrete events, which trigger the transitions

between the operational states. Its role is to switch between the low level continuous controllers, such that the transitions take only place according to certain imposed safety specifications. Given the safety specifications, the design problem will be stated in the supervisory control classical approach (Ramadge and Wonham, 1987; Wonham and Ramadge, 1987; Ramadge and Wonham, 1989). By identifying all the possible operating regimes, a discrete event model (automaton) of the WPS will be yielded, with transitions triggered by either controllable or uncontrollable events. The supervisor will result as a discrete event system also, able of disabling the action of certain controllable events. It will practically reproduce in its transition structure a certain part of the plant’s behaviour, namely the admissible behaviour, determined by the safety specifications (Mînzu and Cernega, 2001). 3. DISCRETE EVENT MODEL OF A GRID CONNECTED WPS The Van der Hoven wind speed model is adopted (Nichita et al., 2002): v = vs + vt, where vs and vt are the steady-state, low frequency and the turbulent, high frequency wind speed, respectively. The energy extraction is based on vs (this component appears in fact on the abscissa of figure 1). The two components can be separated by filtering. The minimum allowed and the maximum allowed rotational speed of the low speed shaft are supposed known, Wm and WM. The modelling method has been recently first presented by Bratcu, et al., (2006). The productive regimes are those of partial and of full load. The “normal” operation is practically that of the partial load region (wind speed between vS and vN and rotational speed between Wm and WM). Four kinds of uncontrollable (but measurable) phenomena are considered as disturbing the productive operation: high turbulence, gusts, vibrations and over-speed because of load losing. The turbulence may be high for a long time, whereas gusts last short by their nature. Both vibrations and over-speed must not last in any case longer than a maximal duration. In absence of any disturbance, the productive states are equipped with normally operating continuous controllers. Depending on grid requirements, three types of such controllers are here considered: for energetic optimization (generically denoted as MPPT – having two versions, for partial load and for full load respectively), for speed tracking and for power tracking. The last two types are the same for both partial load zone and for full load zone too. If a disturbance occurs, some other controllers must act for compensating it: turbulence, gust, vibration and over-speed controllers – all of them having different versions for partial load and for full load, except the turbulence controller, which is necessary only in partial load operation. Surpassing the nominal power is called overload, a phenomenon impossible to alleviate by control action. The turbine can suffer it only for a short time; it practically must be stopped as soon as the overload is detected. Other uncontrollable situations, imposing the turbine’s stop, are the occurrence of a major failure from any

state and the absence of any controller during a maximally admissible duration. The STOP state must be accessible from any other state by means of a manual command. So, one can identify four kinds of states necessary for modelling a grid connected asynchronous generator based WPS as an automaton: · functional states: WT – waiting, S – start, MPPTPL – MPPT controller in partial load, TPL – turbulence controller in partial load, GPL – gust controller in partial load, STPL – speed tracking in partial load, PTPL – power tracking in partial load, MPPTFL – MPPT controller in full load, GFL – gust controller in full load, STFL – speed tracking in full load, PTFL – power tracking in full load; · extreme operation states: OSPL, – over-speed in partial load, OLPL – overload in partial load, OVPL – operation under vibrations in partial load, OSFL – over-speed in full load, OLFL – overload in full load, OVFL – operation under vibrations in full load; states OSPLT, OLPLT, OVPLT, OSFLT, OLFLT and OVFLT are the same as above, but with timer (introduced for control purposes, as detailed in section 5); · temporary states: TSS – temporary state before start, DSPL – decision state in partial load, DSFL – decision state in full load, TS1¸TS12 temporary states between different operation states or between operation states and failure states; · failure states: CF – controllers failure, FA – failure analysis, STOP – reset all the counters and all the controllers; the class of “catastrophic” states is included in this class: IMF – irreversible mechanical failure (instability due to exponential growth of the rotational speed), IEF – irreversible electrical failure (because of the overload). Let S be the set of all events associated to transitions between the above states. These events are either controllable, which can be influenced by a control action, or uncontrollable, which are fully independent of any control action. These are: · controllable events, whose set is usually denoted by Sc: c1 – turbine’s activation (entering in waiting state); c2 – start command; c3 – enabling the partial load MPPT controller; c4 – enabling the full load MPPT controller; c5 – enabling the speed tracking controller; c6 – enabling the power tracking controller; c7 – enabling the partial load turbulence controller; c8 – enabling the partial load gust controller; c9 – enabling the full load gust controller; c10 – enabling the over-speed controller; c11 – enabling the vibrations controller; c12 – disabling the current controller; c13 – external alarm in case of failure; c14 – emergency stop; c15 – manual stop, c16 – start counting, c17 – continue counting; · uncontrollable events, whose set is habitually denoted by Su: u1 – W grows to Wm; u2 – vs grows to vS; u3 – vs reduces to vS; u4 – vs grows to vN; u5 – vs reduces to vN; u6 – vs grows to vM; u7 – high turbulence detected (vt grows to vt_threshold known); u8 – the turbulence reduces; u9 – gust detected; u10 – gust disappearance; u11 – over-speed (W grows to WM); u12 – over-speed quitted (W reduces to WM); u13 – half over-speed maximum time overtaken (either the over-speed controller does not work, or it cannot

accomplish its task); u19 – functional failure; u20 – no active controller after a known authorized maximum delay, Dtmax (time out).

accomplish its task); u14 – overload (power larger than the nominal one); u15 – half overload maximum time overtaken; u16 – vibrations above the admissible limit detected; u17 – vibrations disappearance; u18 – half vibration maximum time overtaken (either the vibrations controller does not work, or it cannot u3 u3

u3

c16

OVPL

u 17

c2

u 18

c12

u 16 n4

u4 u 11 u7

u11

TPL

u9

c3 c12

TS 6

u 16 TS2 c12 u9 u7 c6 c 12 u 9 PTPL u 16

u7

STPL

TS10

DSPL

TS 11

c8 c5

c12

TS1

u5

u5 u14

c16

GFL TS 12

u15

OLPLT

u9

c15

u 10

CF

c14

GPL

c14 c14

OLPL

u15 c14

c17

c4

u10

OLFLT

c9 c12

c12

u4

OLFL

u9

c15

u 19

u19

u19

PTFL u 16

· events: controllable

c15

uncontrollable c15

c1

c14

FA

u 19

catastrophic

u 16

STFL u14

failure

u9

u9

c15

STOP

MPPTFL

c5

u4 c15

of extreme operation

c6

c16

IEF

temporary

c12

TS3

· states: functional

u6

DSFL

u 20

u20

u5

u16

TS 7

c12

c12

TS 5 u12

u12

c10

c17

TS 9

c12

c16

OSFL

c12

LEGEND

OSFLT u13

c17

c10

c12

c7 c12

u8

c15

OSPL

u12

MPPTPL

c11

IMF

u13

u17 u17

u1

c16

TS4 u12

OVFL

u18

S

OSPLT

u3

u3

c16

OVFLT

TSS

c11

TS 8

u3

u2

OVPLT

u17

u16

c1

WT

u3

Figure 3 shows the discrete event model of a grid connected asynchronous generator based WPS.

u19

u 19

u19

c13

to external display

Fig. 3. Grid connected asynchronous generator based WPS modelled as an automaton. 4. GENERAL SUPERVISORY CONTROL FRAMEWORK 4.1 A two level hierarchical control structure The supervisor must ensure the closed loop system to always meet the safety specifications. A general two level hierarchical control structure can be proposed, where plant G is a hybrid dynamical automaton, whose discrete states are the operational states (OS), above identified; their set is noted by Q (figure 4). Each vector field fi(×), continuous with bounded derivatives, describes a closed loop continuous dynamics. The event producing the transition between states OSi and OSj is denoted by eij. w Î S*

SUPERVISOR S (S,Y) state y g = W(y) control input qÎQ s state feedback Event filtering Y(s,y)Î {0,1} PLANT G (discrete) state q . OSi x = fi (×)

eji eij

…

. OSj x = f j (×) . OSk x = f k (×)

WIND POWER SYSTEM AS DISCRETE EVENT SYSTEM

Fig. 4. The supervisor in a two level hierarchical control structure.

Here, the supervisor design disregards the continuous phenomena inside of the discrete states. The supervisor and the plant are both discrete event dynamical systems (DEDS), driven by the same event sequence, w (input signal). S=SuÈSc is the total set of events, uncontrollable and controllable, and S* is the set of all sequences composed of elements of S. The supervisor S is an automaton, S, plus a function, W, which establishes for each state y a control input, g=W(y), and forces the behaviour of G to comply with the imposed specifications, by forbidding certain controllable events (the uncontrollable events are always authorized). The filtering block effectively prevents the forbidden controllable events to produce, by means of the command function, Y. Noting the next event by s, then: Y(s,y)=1, if s is either uncontrollable, or controllable and enabled, and Y(s,y)=0 otherwise. The supervisory action is in fact performed by the pair S = (S, Y). 4.2 Existence conditions for the supervisor The model used here for a DEDS is a logical one. The set of all possible event sequences form the possible behaviour of a DEDS plant, suitably described by a formal language L, or by its recognizing automaton, G, defined as G = (Q, S, d, q0,

Qm), where d: Q´S ® Q is the (partial) transition function, q0 is the initial state and QmÍQ is the subset of marker states, representing some accomplished tasks. The marker language, denoted by Lm(G), contains all the event sequences driving to marker states. Let L(S/G) be the language of the closed loop system. Theorem 1 (Ramadge and Wonham, 1987): For a plant modelled by automaton G and language L(G), having Lm(G) as marked language and KÍLm(G) as imposed specifications, a supervisor S exists such that L(S/G)=K, iff: 1) K is Lm-closed (i.e. K ÇLm(G)=K, where K is the prefix closure of the language K); 2) K is controllable (i.e. SuÇL(G)Í K ). 4.3 Systematic supervisor design Definition 1. Automaton B=(S, XB, xB, x0, Xm) is a restriction of automaton A=(S, XA, xA, x0, Xm) if two conditions hold: a) XBÌXA; b) xB(s,x)=xA(s,x), " xÎXB and " sÎS for which xA(s,x) is defined. Definition 2. Let A=(S, XA, x, x0, Xm) and B=(S, XB, x, x0, Xm) be two automata, such that B is a restriction of automaton A. A state xÎ XB is called uncontrollable in relation with automaton A if exists uÎSu for which xA(u,x) Î XA–XB. The cyclic working processes include the systems capable to restart (i.e., their marked states are the same as the initial ones). As the specifications language always meets the relation KÌLm(G)ÌL(G), then it is possible to consider the supervisor state set XÌQ. This assumption matches the case when the specification is a constraint for the automaton process. Given the plant G as a process with cyclic working, the physically possible behaviour, L(G), the marked behaviour, Lm(G), and the specifications language, K, the algorithm below – SCCWA (Supremal Controllable for Cycling Working Automata – Cernega and Mînzu, 2002) – computes the supremal controllable language of K (it is assumed that the initial state is not uncontrollable). SCCWA: Step 0. Let S0 be identical to G: S0 = (X0, S, x0, q0, Qm), where X0ºQ,, x0 º d. Step 1. The recognizer S1 for the language KÌLm(G)ÌL(G) defined by S1=(X1, S, x1, q0, Xm), X1Ì X0, is constructed. Step 2. i=1. Step 3. Set Ci of uncontrollable states of Si in relation with Si-1 is computed. If Ci ¹Æ, then go to Step 4, else S=Si and STOP. Step 4. Automaton Si+1 is constructed, by removing from Si the uncontrollable states and the transitions to them. Automaton Si+1 is defined by Si+1=(Xi+1, S, xi+1 , q0, Qm), where Xi+1=Xi– Ci . Si+1 is a restriction of Si. Step 5. If Xi+1¹Æ, then i=i+1, go to Step 3; else STOP. If language K is controllable, the algorithm stops at Step 1. The automaton computed at each iteration is a

restriction of that computed at the previous iteration, so Si+1 is a restriction of S0. If the algorithm stops at Step 5, there is no controllable language included in K. Theorem 2 (Cernega and Mînzu, 2002). Automaton S resulted from algorithm SCCWA is the recogniser of the supremal controllable language of K, supC(K). 5. SUPERVISOR DESIGN FOR SAFE OPERATION OF A WPS 5.1 From safety specifications to desired behaviour In the studied case, the automaton G is that of figure 3, i.e. G = (Q, S, d, q0, Qm), where the set of events, S, is described in section 3. Here, q0, the initial state, is STOP. The set of marked states, Qm, contains all the functional states corresponding to the basic goal of the turbine (energy production), plus the STOP state: Qm={MPPTPL, TPL, PTPL, STPL, GPL, GFL, STFL, PTFL, MPPTFL, STOP}. Automaton G models a cyclic working process having the initial state as a marked state. The safe operation means to avoid the catastrophic states, IMF and IEF. IMF would be accessible from the over-speed states (OSPL, OSFL) and from operation under vibrations (OVPL, OVFL), whereas IEF would be accessible from the overload states (OLPL, OLFL). Since there is no controller acting in overload states, the emergency stop (event c14) must be forced from these states, after a technically acceptable time interval, in order to avoid the overheating destruction. The mechanical destruction (IMF) can be avoided by forcing the stop after counting a part (e.g., a half) of the maximum admissible time of abnormal operation (in over-speed or under vibrations), which is a well known value. Thus, in figure 3, states OVPLT, OVFLT, OSPLT, OSFLT, OLFLT, OLPLT, containing timers, were introduced. The desired behaviour, K, is recognized by automaton S1, S1 = (X1, S, d, x0, Xm), where X1=Q–{IMF, IEF}, x0=q0, Xm=Qm. 5.2 Supervisor design For the supervisory design, Step 0 to Step 2 are already done. For the supervisor existence, it remains to check the Lm-closure (Step 3) and the controllability (Step 4). For the first point, one must prove that K ÇLm(G)=K. The transition structure of the automaton shows that there is no prefix of a string from K leading to a marked state not belonging to the specification language. So, this latter is Lmclosed. As for the controllability of K, one can note that C1 = Æ . States TS10, TS11 and TS12 are not uncontrollable, as event c17 is controllable. So, supC(K) = K and K is controllable. The fifth step of the algorithm yields the binary command function, Y, to be specified for each pair (controllable event, state) for which the (partial) transition function is

defined. In this case, Y(ci,x)=1, for all the states xÎX1 and for all the controllable events, except: Y(c17,TS10) = Y(c17,TS11) = Y(c17,TS12) = 0. For the rest of the supervisor states, the command function Y(ci,x)=“don’t care”. 6. CONCLUSION AND FUTURE WORK A discrete event model of a grid connected WPS to ensure its safe operation is proposed in this article. The discrete states model the possible operating regimes of the turbine and embed the low level continuous controllers, which perform some optimization tasks. The interest was focused on designing the supervisor on the higher control level, which must guarantee the safe transition between the operating regimes. The safe operation was expressed as avoiding some dangerous states (i.e., irreversible failures). The design problem was stated in the supervisory control framework. The existence conditions of a supervisor were checked out. The supervisor was effectively constructed using an algorithm for computing the supremal controllable language for a class of cyclic working automata. Future research will be focused on embedding the supervisor in a two level hierarchical hybrid control architecture. The closed loop system will be validated by both numerical and real time simulation. REFERENCES Abo-Khalil, A.G., D.-C. Lee and J.-K. Seok (2004). Variable speed wind power generation system based on fuzzy logic control for maximum output power tracking. In: Proceedings of 2004 IEEE 35th Annual Power Electronics Specialists Conference – PESC 04, 3, 2039–2043. Bathurst, G.N., J. Weatherill and G. Strbac (2002). Trading Wind Generation in Short Term Energy Markets. IEEE Transactions on Power Systems, 17(3), 782 – 789. Bianchi, F.D., R.J. Mantz and C.F. Christiansen (2005). Gain scheduling control of variablespeed wind energy conversion systems using quasi-LPV models. Control Engineering Practice, 13(2), 247-255. Bratcu, A.I., I. Munteanu, D.C. Cernega (2006). Modélisation à évènements discrets d’un système éolien à vitesse variable en vue de la commande supervisée. Actes de la 6ième Conférence Francophone de Modélisation et Simulation – MOSIM’06, Lavoisier (Eds.: M. Gourgand, F. Riane, CD-ROM). Burton, T., D. Sharpe, N. Jenkins and E. Bossanyi (2001). Wind Energy Handbook. John Wiley & Sons. Datta, R. and V.T. Ranganathan (2003). A Method of Tracking the Peak Power Points for a Variable Speed Wind Energy Conversion System. IEEE Transactions on Energy Conversion, 18(1), 163–168. De Battista, H., R.J. Mantz and C.F. Christiansen (2000). Dynamical Sliding Mode Power Control of Wind Driven Induction Generators. IEEE Transactions on Energy Conversion, 15(4), 451457.

Cernega, D.C. and V. Mînzu (2002). The Computation of the Supremal Controllable Language for an Assembly Workstation. In: Proceedings of the IFAC Symposium on Large Scale Systems: Theory and Applications – LSS 2001, Pergamon-Elsevier, 343-348. Ekelund, T. (1997). Modeling and Linear Quadratic Optimal Control of Wind Turbines. Ph.D. Thesis, Chalmers University of Göteborg, Sweden. Kana, C.L., M. Thamodharan and A. Wolf (2001). System Management of a Wind-Energy Converter. IEEE Transactions on Power Electronics, 16(3), 375-381. Leithead, W.E., S. De la Salle and D. Reardon (1991). Role and objectives of control for wind turbines. In: IEE Proceedings-C, 138(2), 135-148. Mînzu, V. and D. Cernega (2001). Discrete event dynamical systems – approaches and applications. EDP Publishing, Bucharest (in Romanian). Nichita, C., D. Luca, B. Dakyo and E. Ceangă (2002). Large Band Simulation of the Wind Speed for Real Time Wind Turbine Simulators. IEEE Transactions on Energy Conversion, 17(4), 523-529. Novak, P. and T. Ekelund (1994). Modeling, Identification and Control of a Variable Speed HAWT. In: Proceedings of the European Wind Energy Conference, 441-446. Ramadge, P.J. and W.M. Wonham (1987). Supervisory Control of A Class of Discrete Event Processes. SIAM Journal of Control & Optimization, 25(1), 206–230. Ramadge, P.J. and W.M. Wonham (1989). Modular Feedback Logic for Discrete Event Systems. SIAM Journal of Control & Optimization, 25(5), 1202– 1218. Rocha, R. and L.S.M. Filho (2003). A multivariable Hinfinity control for wind energy conversion systems. In: Proceedings of 2003 IEEE Conference on Control Applications – CCA 2003, 1, 206-211. Wang, Q. (2004). An Intelligent Maximum Power Extraction Algorithm for Inverter-Based Variable Speed Wind Turbine Systems. IEEE Transactions on Power Electronics, 19(5), 1242–1249. Welfonder, E., R. Neifer and M. Spanner (1997). Developpement and Experimental Identification of Dynamic Models for Wind Turbines. Control Engineering Practice, 5(1), 63-73. Wilkie, J., W.E. Leithead and C. Anderson (1990). Modeling of Wind Turbines by Simple Models. Wind Engineering, 4, 247-274. Wonham, W.M. and P.J. Ramadge (1987). On the Supremal Controllable Language of a Given Language. SIAM Journal of Control & Optimization, 25(3), 637–659. Young, W.F., J.E. Stamp and J.D. Dillinger (2003). Communication vulnerabilities and mitigations in wind power SCADA systems. In: American Wind Energy Association WINDPOWER 2003 Conference, Austin, Texas, 15 pages. Zhang, X.-F., D.-P. Xu and Y.-B. Liu (2004). Adaptive optimal fuzzy control for variable speed fixed pitch wind turbines. In: Proceedings of the Fifth World Congress on Intelligent Control and Automation – WCICA 2004, 3, 2481-2485.