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fina******nIIIIIINNNNNNceTTTTTTdIIIIII,,,,,,bNNNNNN******y******aaaaaatFFFFFFtttttthiiiiiiAAAAAerrrrrrooooooaaaaaannnnnnnnnnnFuuuuuuCCCCCCaaaaaadddddennnnnnlllllloooooodhhhhhhrrrrrIIIIIIrrrrrreoooooonnnnnneeeeerrrrrrrffffffssssssaaaaaeeeeeeaeeeeeettttttssssssiiiiiilrrrrrrRRRRRpppppptttttt------MuuuuuuooooooGGGGGGiiiiittttttnnnnnnvvvvveeeeeeieeeeeenddddddaaaaassssssooooooiiiiiiieeeeeerrrrrsnnnnnnfffffflllllltoooooggggggllllllIIIIIIrssssssnnnnnnlllllyccccccaaaaaaaaaaaddddddhhhhhhouuuuuu*******uuuuuuaaaaaafttttttssssssaaaaahhhhhhffffffEttttttttttttoooooonnnnnrrrrrrciiiiiieeeeeerrrrrrdddddaaaaaao......::::::VVVVVVllllllnaaaaaaAAAAATTTTTT......ogggggg,,,,,,meeeeeedddddaaaaaaBBBBBBccccccrrrrrmmmmmmirrrrrrhhhhhhciiiiieeeeeennnnnnbbbbbbaaaaammmmmmAooooooiiiiiinnnnneeeeeefeeeeeellllllfrrrrrroooooorrrrrraGGGGG@@@@@@gggggghhhhhhiryyyyyyaaaaaaaaaaaiiiiiis,,,,,,vvvvvveeeeeemmmmmMMMMMMaeeeeeeeeennnnnneeeeeenbbbbbeeeeee......,,,,,,dooooooiiiiinnnnnnGGGGGGeeeeerrrrrrddddddCrrrrrggggggeeeeeeooooool*****rrrrrrizzzzzzmmmmmmm*****aaaaaa,,,,,,aaaaaaaAAAAAAtnnnnnneyyyyyyrrrrrrggggggAeeeeeecnnnnnntittttttoiiiiiinnnnnnnaaaaaa(BMWK) 2ttttacaciicciaiaehhethehedtdtLttdLLLdcittaTcoTevaecocTcovaaaveveheTotLdaoeTvctaciLttdtehcoavTecccctsAtttAssAAscAsttssssTsTsssTTpppppdapppaasdtddaTspadpcstsATpapdcccccccAAAcAAcAcrrrrrriiiiiisssshshhhhshhhhhrrrrrr4uuuuuullllllyyyyyyllllllooottotttootoooooollooooooggggvvvvgvgvhhhhhhnnnnnnaaaaaaaaaaaaffffffyyyyyyoooooaaaaaaaoooooaaoeeeeeeaaaaaahhhhhhhhhhhhooooooaaaaaaaaaaeeeeeelllllleeeeee0aaaaaannnnnnrrrrrrssssssooooooeeeeeeaaaaaannnnnnnnnnnnnnnnnnnnnnnnnnnnnttttttnnnnnttttttddddddnnnnmmmmnmnmaaaaaannnnnwwwwwwrrrrrrrrrrrrmmmmmmeeeeeeiiiiiittttttaaaaaasssssswwwwwweeeeee5hhhhhttthttttttthhhhhheeeeeerrrrrrssssssggggggnnnnnneeeeeeddddddccccccttttttccccccssssssssssssttttttddddddaaaaaatttttteeeeeeeeeeeerrrrrrmmmmmm-wwwwww,,,,,,eeeeeeeeeeeeaaaaaassssssrrrrrraaaaooooaooaccccchhhhhchiiiiiiiiiiiittttttppppppaaaaaallllllaaaaaaeeeeeeeiieieieeieirrrrrrdddddd8,,,,,,mmmmmmiiiiiimmmmmmrrrrrrllllllccccccddddddeeeeeeiiiiiiccccccyyyyyyooooooddddddttttttnnnnnnnnnnnneeeeeeeeeeeessssssiiiiiiiiiiiiuuuuuuccccccssssssjjjjjj......iiiiii9tttttteeeeeeeeeeeeeeeerrrrrrhhhhhhttttttmmmmmmccccccaaaaaaooooooeeeeeeaaaaaavvvvvvuuuuuuttttttssssssaaaaaawwwwwwuuuuuudddddd,,,,,,hhhhhhiiiiiittttttooooooeeeeee6......ggggggmmmmmmnnnnnnooooooddddddrrrrrrbbbbbbhhhhhheeeeeeAAAAAAeeeeeehhhhhhcccccccccccrrrrrrllllllsssssseeeeeerrrrrrtttttttttttteeeeee((((((3cccccceeeeeennnnnnTTTTTTuuuuuuhhhhhhnnttttttppppppnnnnnneeeeeeeeeeeeeeeeeeeeeyyyyyyiiiiiiaaaaaapppppphhhhhhBBBBBBoooooo,,,,,,ppppppeeeeeellllllmmmmmmnnnnnnttttttddddddnnnnnnffffffccccccssssssddddddtttttteeeeeeooooooiiiiiieeeeerrrrrrccccccoooooorrrrrrhhhhhhCllllllnnnnnnrrrrrhhhhhheeeeeeddddddaaaararrrraraaaaaaiiiiiirrrraaaassssssttttttnnnnnneeeeeemmmmmmddddddooooooaaaaaayyyyyyooooooddddddooooooeeeeeeffffffvvvvvviiiiiieeiiiiiiaaaaaassssssoooooooooeeeeeeoeeeeeerrrrrrrrrrrrllllllcccccchhhhhhottttttKKKKKtcccclKlTttAmssmcAscmTTAsfTcsclAtfccfmmltTTmftAlclfAfsnnnnnnCeeeeee(aaaaaarrrrrrssssssccccccnnnnnnddddddiiiiiilllllliiiiiimmmmmmeeeeeebbbbbbhhhhhhiiiiiieeeeeehhooohhohooheeeeeeffffffhssssssaaaaaarrrrrriiiiiiddddoooododooooooopttttttoooooooooooollllllssssssnnnnnnooooooottttttmmmmmmaaaaaaeeeeeennnnnnnnnnnttttttmmmmmmoooooossssssaaaaaassssssiiiiiihhhhhhaaaaaeeeeeeeeeeeessorrrrrruuuuuueeeeeeeeeeeebbbbbbaaaaaaffffffeerririiirriiraaaaaaeeeeeesssssshhhhhhnnnnnnyteeeeddddedednnnnnncccccclllllluuuuuuddddddooooooiiiiiinmmnmnmmnmnntttttteeeeeetttt''''''ssssssrrrrrrttttttnnnnnnrrrrrrnnnnnntyyyyyyrrrrrrmmmmmmeeeeeeccccccssssssbbbbbbssssssxxxxxxvvvvvvssssssrrrrccccccpeeeeeennnnnnrrrrrrttttttsssssshhhhhhr((((((oooooollllllooootttttteeeeeeaaaaaaeeeeeehhhhhheeeelllllloooooopaaaaaaiiiiiieeeeeettttttbbbbbbeeeeeessssssaaaaaaaaaaaaiiiiii......iiiiiiwwwwwwittttttGGGGGGttttttoooooottttttddddddnnnnnnoooooottttttiiiiiiiiiii((((((eeeeeeggggggssssssyaaaaaatttttrrrrrrrrrrrrmmmmmmllllll,,,,,,iiiiiissssssppppppeeeeeeooooooghhhhhhccccccnnnnnnmmmmmmcccccceeeeeerrrrrrsppppppssssssssssssnnnnnniiiiiiiiiiiiHHHHHHuuuuuullllllhhhhhhsssssseeeeeeooooooTTTTTTeeeeeeooooooffffffvvvvvvttttttttttttddddddtttnnnnnn222222nnnnnhrrrrrrrnnnnnnnnnnnnaaaaaaooooooaaaaaaiiiiiillllllaaaaaannnnnn:tttttt......eeeeeeeeeeeennnnnbbbbbbeeeeeeoooooocccccciiiiiirrrrrrssssssaaaaaannnnnneeeeeeoooooowwwwwwaaainnnnnniiiiiieeeeeeiiiiii/llllll000000iiiiiitttttttmmmmmmsssssshhhhhhttttttuuuuuuiiiiiiaaaaaacccccceeeeeeiiiiiimmmmmmmmmmmmpppppp,,,,,,iiiiiieeeeeerrrrrrwwwwwwTTTTTTddddddeeeeeelllllleeeeeemmmmmmgoooooo/rrrrrrllllllcccccczzzzzzccccrrrrrrnnnnnnbbbbbbccmmmmmmyyyyyyggggggmmmmmmvvvvvvppppppnnnnnnuuuuuueeeeee111111ssssssccccccttttttddddddceeeeeebbbbbbeeeeeesssssshhhhhhwwwwwweeeeee©ooooooiiiiiieeeeeettttttooooooheeeeeetttttteeeeeennnnnntttttpppppphhhhhh::::::oooooojjjjjjiiiiii,,,,,,bbbbbbeeeeeeyyyyyyeeeeeemmmmmmeeeeeeddddddbbbbbbpppppphhhhhh111111eeeeeeeeeeeerrrrrrrhhhhhhbbbrrrrrruuuuuussssssiiiiiiyyyyyyddddddoooooonnnnnnppppppnneeeeeetttttt......rrrrrrppppppaaaaaauuuuuutoooooo......aaaaaahhhhhhiiiiiiffffffrrrrrrcccccciiiiiiessssssAAAAAAiiiiiinnnnnnhhhhhheeeeeeeeeeeellllll::::::nnnnnnoooooouuuuuu))))))111111eeeeeerrrrrreeeeeeaaaaaaaaaaaa2ttttttnnnnnnddddddiiiiiieeessssssoooooopppppprrrrrrHHHHHHiiiimmmmmmrrrrrrssssssllllllTTTTTTttttttssssssrrrrrrssssssiiiiiia©eeeeeessssssddddddnnnnnnrrrrrrsssshhhhhhttttttlllllleeeeeetttttt0llllllrrrrrrrrrsssststttttseeeeee......ccccccttttttwwwwwwrrrrrreeeeeessssssccccccttttttLLLLLLoooooorrrrrrttttttnnnnnnuuuuuuhhhhhhttttnnnnnnoooooorrrrrruuuuuueeeeeettttttaaaaaappppppllllllpppppptttttcccccctddddddttttiiiiiiooooooiiiiii,,,,,,......ttttttaaaaaa2eeeeeeeeeeeeuuuuuuhhhhhhtttttteeeeeettttttIIIIIIooooooyyyyyy,,,,,,iiiiiihhhhhhuuuuuuooooooaaaaaaioooooorrrroooororocccccclllllleeeeeeccccccoooooossssssccccccccccccaaaaaaccWWWWWaaaaaattttttaaaaaaaaaaaauuuuuuooooooaaaaaarrrrrrnnnnnnmmmmmmNNNNNNnnnnnn3nnnnnnccccccvAAAAAA222222iiiiiiddddddyyyyyydddddd2eeeeeeeeeeeennnnnneeeeeemmmmmmllllllrrrrrrddddddooooooeeeeeennnnnnnnnnnnaaaaaaoooooonnnnnnaaaaaaiiiiiiooooooaaaaaaccccccmmmmmmrrrrrrllllllrrrrrr((((((aaaaaarrrrrrppppppiiiiiissssssoooooiiiiiirrrrrrttttttccccccttt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Peer review under responsibility of International Federation of Automatic Control.



10.1016/j.ifacol.2023.10.317



11256



Andrea Rivarola et al. / IFAC PapersOnLine 56-2 (2023) 11255–11260



The prevention of aeroacoustic noise by using control has been studied, e.g., in (Cardenas-Dobson and Asher, 1996) and in (Møller and Pedersen, 2011). Moreover, several contributions are devoted to mitigate the aeroacoustic noise by using the pitch control system. For example, some implementations of individual pitch control dedicated to attenuate noise can be found in (Bertagnolio et al., 2014; Maizi et al., 2017) and (Mackowski and Carolus, 2021).

The above-mentioned contributions to reducing noise do not take into account the general case that individual pitch control is not always available in real wind turbines. Moreover, they also do not consider the trade-off between maximum power extraction and minimal noise emission. Thus, these two aspects are considered in the present work, where noise mitigation and power extraction are compromised by using multi-objective optimization in a similar way as used in (Gambier, 2017), for collective pitch control and tower damping control. Hence, a control loop for the attenuation of noise is optimally combined with the collective pitch control.

The rest of the paper is structured as follows: Section 2 is devoted to present the necessary fundamentals of acoustic noise from wind turbines, and in Section 3, the control issues are discussed. The control system topology and the design are described in Section 4, whilst a numerical study on a 5 MW reference wind turbine, including the simulation results, is the subject of Section 5. Finally, conclusions are drawn in Section 6.



2. WIND TURBINE ACOUSTIC NOISE FUNDAMENTALS

As it was already mentioned, the field of wind turbine acoustic noise is vast and complex. Therefore, the interest in the current section is to describe the basic aspects in order to understand the problem, so that the needs can be satisfied in this work. The interest is to obtain a prediction model to estimate the noise and the formulation of an objective function as a performance index, which can be used in the optimization problem.



2.1 Prediction Models

Many noise prediction models have been proposed in the specialized literature. These models have been classified by (Lowson, 1992), where three classes are distinguished: Class I for very simple stationary models, Class II for models of middle complexity, which include some parameters of the wind turbine, and Class III for models with full information about the noise process associated with the wind turbine. A comparison of the different models is provided by (Zidan et al., 2014). The interest here lies primarily in the simple Class I models. The most important ones are:

Lowson’s Model

The model of (Lowson, 1992) is given by



LwA = 10 log10 PwT + 50 ,



(1)



where LwA is the A-weighted sound power level of the source and



PwT is the rated power of the wind turbine in Watts.



Hau’s Model



In (Hau et al., 1993), a simple model depending on rotor diameter D is proposed. The formula is given by



= LwA 20 log10 D + 72 .



(2)



Hagg’s Model

The model suggested by (Hagg et al., 1992) includes the tip speed, i.e.,



LwA = 50 log10 vtip +10 log10 D − 4 .



(3)



Since that for the tip speed applies, vtip = 0.5 D ωr, with ωr as the rotor speed, (3) can be reformulated in terms of the rotor speed, namely



= LwA =



50 50



log10 log10



(0.5D (ωr ) +



ωr ) +10 60 log10



log10 D − 4 D −19.0515



.



(4)



The three formulas are evaluated for a 5 MW reference wind turbine with a rotor radius of 63 m. As real data, the simulation data provided by the high-resolution model implemented in OpenFAST is used (Bortolotti et al., 2020). The results are shown in Figure 1.



Figure 1. Results for the prediction of the sound power level



As it is pointed out in (Wagner et al., 1996), these formulas are very inaccurately and cannot be used if exactitude is required. However, they can be readjusted for a particular case if measurement data is available. In the case of real-time control, the prediction can be complemented by sensor data.

The last equation is useful because ωr is a measurable state variable, and therefore, the sound power level LwA is variable, calculable, and dependent on the pitch control system. Hence, this model has been selected for this first study.

The above-presented models correspond to the emission places. Since the important aspect is the sound power level at the receiver position, the model has to be complemented by a propagation model. This is presented in the following subsection.



2.2 Propagation Models



The choice of a propagation model follows the same criterion as for the prediction model, i.e., simplicity and dependence of useful variables from the control point of view. A detailed treatment of the topic can be found in (Wagner et al., 1996).



The ISO 9613 (ISO-9613, 1993; ISO-9613, 1996) serves as the basis for modelling the propagation of sound waves. The sound pressure level at the receiver location is calculated for each source by



LpA = LwA + Lcf − A ,



(5)



where LwA is already defined in the previous subsection, Lcf is a correction factor in dB (zero for the radiation into the free space), and A is the attenuation in dB. Moreover, the attenuation A is composed of several factors, such as, for instance,



A = Agd + Aatm + Agr + Abar + Ao .



(6)



The factor Agd is the attenuation caused by geometric divergence. It can be defined for hemispherical spreading, spherical spreading, or cylindrical spreading, i.e.,



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Agd,h = 10 log10 (2π (d / d0 )2 ) = 20 log10 (d / d0 ) + 8dB Agd,s = 10 log10 (4π (d / d0 )2 ) = 20 log10 (d / d0 ) +11dB (7) Agd,c = 10 log10 (2π (d / d0 )) = 10 log10 (d / d0 ) + 8dB



with d as the distance to the receiver in meters. d0 is a reference distance (normally 1 m), 10 log10(2π) ≈ 8 dB and 10 log10(4π) ≈11 dB. The distance d can be computed by considering the hub height hh of the wind turbine and the horizontal distance ld to the receiver as



=d ld2 + hh2 .



(8)



The atmospheric attenuation Aatm is given by



Aatm = α d



(9)



with α as atmospheric absorption in dB/m, which depends on the frequency, temperature, humidity, and pressure. d is the distance in meters. Other factors that can be considered are, for instance, ground absorption (Agr), screening (Abar), as well as other possible factors (Ao). According to (Lovtidende, 2017), another factor is, for example, the sound insulation Aσ.



Factors Agr, Aσ, and α are frequency-dependent parameters, which are normally expressed for each central frequency of the 1/3-octave bands (see (Lovtidende, 2017)). For each band, applies (5), and the total sound pressure level is obtained from



(∑ ) LpA,tot = 10 log10



10 . n



LpA (i)/10



i =1



(10)



In the sense of formulating simple models, it is commonly assumed that the propagation takes place in a spherical spread, i.e., the sound pressure level suffers an attenuation of 6 dB per distance doubling (Møller and Pedersen, 2011). For the spherical spreading, the Aweighted sound pressure level (SPL) LpA is formulated by



LpA = LwA − 20 log10 (d / d0 ) −α d −11 dB .



(11)



A typical value for α is 0.005 dB/m (Rogers et al., 2006).



In the downwind direction, the spherical assumption is valid for distances closer to the machine. For distances larger than 200 m, the propagation presents a cylindrical spread, which means that the decay rate is about 3 dB per distance doubling (Hubbard and Shepherd, 1991). The cylindrical propagation for distances greater than 200 m can be modeled by using



L=pA LwA − 20 log10 (200m /1m) −10 log10 (d / 200m) −α d −11dB + Ag ,(12)



(Møller and Pedersen, 2011). Ag is a ground effect correction (1.5 dB for onshore and 3 dB for offshore machines). The Danish standard (Lovtidende, 2017) proposes a propagation equation for low-frequency noise given by



LpA = LwA −10 log10 (hh2 + d 2 ) −α hh2 + d 2 − Aσ − AgLF −11dB + Ag .(13)

∆LgLF, and ∆Lσ are ground effect and sound isolation at low frequencies, respectively. Propagation model results for the same example are presented in Figure 2.



2.3 Ambient Acoustic Noise

Ambient acoustic noise lebels ranged from about 30 dB(A) in rural and suburban zones to 120 or more dB(A) in urban and commercial



110 A-weighted sound pressure level LpA [dB(A)]



100



Spheric spread Cylindrical spread



90



Danish standard



80



70



60



50



400 100 200 300 400 500 600 700 d [m]



Figure 2. Results for the models of sound propagation



areas (Fitzell and Phil, 2019). Zones closer to wind farms are normally characterized by suburban settlements. Thus, it is possible to assume a noise level fluctuating between 30 and 48 dB(A) (Hansen and Hansen, 2020).



Moreover, the wind interaction with the foliage in rural settings produces an A-weighted broadband sound pressure, which is almost proportional to the base 10 logarithm of the wind speed (Fégeant, 1999), namely,



LpAwind = K1 log10 (vw ) + K2 .



(14)



According to (Rogers et al., 2006), the wind produces ambient noise varying between 25 dB(A) (calm conditions) to 42 dB(A).



3. CONTROL OF WIND TURBINES

As previously mentioned, the main noise sources are the trailing edges of the blades and the rotational speed, which both change according to the pitch control system. Thus, noise generation and the control of the rotational speed are closely related. Therefore, in order to understand the control problem associated with the noise mitigation of a wind turbine, wind turbine control in general has to be clarified first. These aspects are briefly undertaken in this section.

3.1 General Aspects of Wind Turbine Control

Since the operation of an upstream horizontal-axis variablespeed variable-pitch wind turbine is widely known (see, for example, (Burton et al., 2011; Manwell et al., 2009; Bianchi et al., 2007; Gambier, 2022), it is just briefly discussed in the sequel. Based on wind speed, the operation of the machine can be divided into four adjacent zones. The wind turbine cannot convert energy in the first region because the wind speed is lower than the cut-in value for which the machine was designed. When the wind speed goes above the cut-in value, the operation moves to the second region, where the wind speed is appropriate for energy conversion without reaching the rated values. The control objective is to maximize power by tracking the optimal characteristic curve of the generator.

If the wind speed increases over the rated value, the machine enters Region III, where it stays as long as the wind speed does not reach the cut-out threshold. In this region, the control objective is to maintain constant the rotational speed (and indirectly, power) by pitching the rotor blades to the feather. Over the cutout value, the wind turbine goes into Region IV, where it must be shut down in order to protect its integrity.

On the other hand, the transition zones between Regions I and II as well as between Regions II and III are often called Region I½ and Region II½, respectively. The difference between both transition regions is given by the corresponding set-points. All regions are described in Figure 3.

3.2 Speed Control in Region I and II

In Regions I and II, the wind speed is low enough that the rotational speed is also low, and therefore, no control is generally needed for it. However, sometimes it is required to control the



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Figure 3. Operational regions of large wind turbines, (Gambier, 2022)



rotational speed. In such a case, this can be carried out by using the generator torque, as is illustrated in Figure 4.



ωg,setpoint



β



Tg,rated



Wind ωg



+ Tg Turbine – Controller −



Figure 4. Rotational speed control diagram for Region I and II



3.2 Speed Control in Region III

In Region III, the main control objective is to regulate the rotational speed and the power conversion to the rated values. This is accomplished by including a second control loop that keeps the rotational speed constant by pitching the blades collectively. The collective pitch controller and the corresponding control loop are shown in Figure 5 (see (Gambier, 2021)).



Figure 5. Rotational speed control diagram for Region III

When the system reaches the steady state, the controller output is equal to zero, but the pitch angle has to be equal to the necessary angle to maintain the rotational speed at the rated value for the current wind speed. This is obtained by including β0. In other words, β0 is the value of the pitch angle, which yields a rated rotor speed ωr,rat, for the corresponding wind speed.

4. WIND TURBINE CONTROL FOR NOISE MITIGATION

4.1 General Concepts

Regulation in Germany for onshore installations requires a minimum distance of 400 m and thresholds of 55 dB(A) and 40 dB(A) for day and night, respectively (Nieuwenhuizen and Köhl, 2015). In addition, these threshold values refers to the total noise. This means that if the ambient noise is louder for a while, then the wind turbines have to be quieter in order to maintain the noise limit.

From the practical point of view, the regulation is satisfied by including in the supervisory control system two fixed operational modes: “normal operation” for the day and “power limited” for the night. Thus, the operation is switched between these two modes according to the time of day indicated by the clock in the supervisor. In the following, another control concepts for the noise mitigation are proposed.

4.2 Control in Region III

First, the concept has been developed for Region III because this is the zone of high wind speed and, consequently, the noisiest. The



idea is to implement a tracking control system such that the power conversion takes place adaptively in order to maximize power while maintaining the sound threshold below the limit.

Two control system topologies can satisfy this purpose. Both use two controllers: the collective pitch controller (CPC) and the active sound damping controller (ASDC). The first topology connects the controllers in a cascade configuration. The second does it in the parallel configuration. Both configurations are shown in Figure 6.



ωg,rat



Lsp eL ASDC −



Lenv



Sound



LpA



Prediction and Propagation



eω −



CPC



βcpc β−

asdc



β0β1 β2 β3



βa1

Pitch βa2 actuators βa3



Wind ωg Turbine



Torque Tg Controller



Actuator Tga



(b)



Figure 6. Control system for pitch control and noise mitigation. (a) Cascade configuration. (b) Parallel configuration

The cascade configuration subordinates the speed control loop to the noise level control loop. Thus, the power reduction is forced until the maximum allowable noise limit is reached. The maximum value in the saturation block is set to the rated rotational speed. This ensures that the speed does not exceed its rated value if the noise level is very low. Hence, this yields a hard maintenance of the allowable noise level.

In the parallel configuration, both controllers compete without, a priori, one prevailing over the other. However, if the noise level increases, its control error and control signal decrease, and then the pitch angle increases, reducing the speed and consequently the noise level. In this case, it is about a soft maintenance of the allowable noise level because no limit is imposed. The relative importance of the control loops is managed by assigning priorities.



In all cases, controllers must work coordinately to achieve the best possible result. One way to achieve this is to tune the parameters of both controllers together as players of a cooperative game using MOO (multi-objective optimization, see, e.g., (Gambier, 2017)).



The multi-objective optimization algorithm minimizes by using simulation data the following objective functions



∫ ∫ Jω



=



tf



1 − t0



t e tf



2



t0



ω



dt



and



JL



= tf



1 − t0



tf t0



t



eL2



dt .



(15)



The result is a Pareto front, as portrayed in Figure 7.



Figure 7. Illustrative Pareto front for the MOO problem

All points on the Pareto front are equivalently optimal, but only one point has to be chosen. Selecting a point closer to the vertical axis prioritizes the CPC and, contrarily, a point more distant to it emphasizes the ASDC.



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4.3 Control in Region I and II

Regions I and II are characterized by a low rotational speed and, therefore, noise mitigation is not necessary. However, if the machine is likewise too noisy in Regions I and II, the control concepts and design technique proposed for Region III can be integrated with the control scheme of Figure 4 to introduce noise mitigation there.

The major distinction lies in the fact that the control variable is injected into another type of actuator and must therefore be scaled differently, requiring entirely new parameter tuning.

5. NUMERICAL STUDY

The approach for reducing the acoustic noise proposed in the previous section is now analysed by means of a numerical simulation example.

5.1 Experimental Setup for the Simulation Experiments

For the numerical study, the NREL 5MW reference wind turbine (Jonkman et al., 2009) has been chosen because it satisfies the characteristics of a typical onshore machine.

The conventional three-bladed, horizontal axis, clockwise, upwind, variable-speed and variable-pitch machine has a 126m-diameter rotor with 61.5 m-long blades. The hub height is 90 m and the generator has an efficiency of 94.4%, which corresponds to a mechanical power of 5.30 MW. The maximum power factor Cp is 0.482 and it is reached at a tip-speed ratio of 7.55. The gearbox ratio is 97:1, such that the rated rotor speed of 12.1 rpm yields a generator speed of 1173.7 rpm for a rated wind speed of 11.4 m/s. The cut-in rotational speed is ωr,ci = 6.9 rpm. This leads, according to (4), to a noise emission that varies between 99.4 and 112.1 dB(A).

5.2 Scenario for the Numerical Study

Both proposed control system topologies are compared with the classic speed limitation approach. The comparison is carried out by considering the energy produced in kWh during the night operation. Moreover, three cases are considered for the classic approach: In the optimistic case, the ambient noise is supposed to be low enough that the rotational speed can be increased up to the maximum allowed value for a noise of 40 dB(A); in the pessimistic case, the ambient noise is high and the rotational speed is set to the minimum allowed value; and in the third case, the ambient noise is average.

The receiver is located 400 meters away from the wind turbine, and the aerial-ground-environmental conditions have a sound attenuation of 58.7 dB(A). The German legislation allows a total noise level of up to 55 dB(A) during the day and 40 dB(A) at night for small settlement areas.

The operation takes place in Region III with an effective wind speed changing between 11.5 and 21 m/s, including tower shadow and turbulence of 10%, for 30 minutes (see the profile as the grey line in Figure 9b).

5.2 Control System Design

All controllers are implemented as PI control laws (proportional-integral) with a back-calculation anti-windup mechanism. The controller parameters are obtained by using the method described in 4.2. The classic approach is tuned, however, by using simulation-based single objective optimization for the rotor speed control loop. Controller gains are summarized in Table 1. Notice that the parallel configuration has two values for Kiω. The fist is for day operation and the other one is for night operation.



Table 1. Controller Parameters



Gains Classic Approach Cascade Approach



KpL



--



KiL



--



-0.5383 -41.88 × 10-5



KaL



--



0.5



Kpω



1.51



1.64



Kiω



0.653



0.5631



Kaω



8.0



0.5



Parallel Approach -0.4866

-9.573 × 10-5 0.7

-1.937 0.5631 0.0

0.7



5.3 Simulation Results and Analysis

The simulation is started with four minutes in the day operation and then it is switched into the night operation. In total, the whole simulation lasts 30 minutes. The results for the classic approach are shown in Figure 8.



60 Sound pressure level [dB(A)]



50



40



30



20



10



00



5



10



15



Sound legal limit SPL (Optimistic case) SPL (Average case) SPL (Pessimistic case) Background noise



20



25 t [min] 30 (a)



(b) Figure 8. Results for the classic approach. (a) SPL. (b) Rotor speed.



It is appreciated that the control system can only keep the noise at the correct level in the optimistic situation, i.e., when the minimum environmental noise occurs. If some leeway is given, the average case might also be acceptable. The power restriction is not required during daytime operation since the SPL is less than 55 dB(A) for the rated rotor speed.



The results for both proposed approaches are presented in Figure 9.



Sound pressure level [dB(A)] Piecewise effective stochastic wind speed [m/s] 60



50



40



30



20



10



00



5



Rotor speed [rpm]



13



12 10



9



8 7



6 5



4



30



5



Reference SPL cascade approach SPL parallel approach Background noise



10



15



20



25 t [min] 30 (a)



Effective stochastic wind speed [m/s] 22



Rated rotor speed Rotor speed, cascade app. Rotor speed, parallel app. Wind speed



10



15



20



20



18



16



14



12



10



8



6



4



25



t



[min]



30



2 (b)



Figure 9. Results for the new approaches. (a) SPL. (b) Rotor speed.



Figure 8b also shows that, by design, the rotor speed is kept constant independently of the sound pressure level. This is the main difference



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with respect to the new approaches, where the rotor speed is adjusted in order to maintain the SPL at the allowed level but at the maximum possible rotor speed. This is observed in Figure 9b.

The converted energy in kWh for all cases is shown in Table 2. The optimistic case yields the maximum conversion, assuming very low ambient noise. This is not realistic and should not be used. In the pessimist case, the noise is high and the assumption leads to an anti-economic low result. The average case exceeds the permissible limit when noise is high and it should be avoided if the regulations are very strict. The new approaches guarantee threshold compliance by means of variable rotation speed, where the cascade approach performs better than the parallel approach.



Table 2. Energy converted by the different approaches in 30 minutes



Classic Approach

Cascade Approach Parallel Approach



Energy in kWh



Optimistic case Pessimistic case



3750.4



2941.9



3601.0



3535.6



Average case 3559.2



7. CONCLUSIONS

In this work, two approaches for the control of wind turbines under noise restrictions with minimum losses in the energy conversion are studied. Both perform better than the classic approach. However, the cascade configuration is slightly superior. The parameter tuning is carried out by using multi-objective optimization. In the next research steps, more sophisticated models for the propagation as well as noise measurements in a Hardware-in-the-Loop system and realtime operation will be studied.

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