Integrated Control for Small Power Wind Generator - MDPI

energies Article

Integrated Control for Small Power Wind Generator Hongliang Liu, Fabrice Locment

ID

and Manuela Sechilariu *

ID

Sorbonne University, Université de Technologie de Compiègne, EA 7284 AVENUES, Centre Pierre Guillaumat CS 60319, 60203 Compiègne CEDEX, France; [email protected] (H.L.); [email protected] (F.L.) * Correspondence: [email protected]; Tel.: +33-344-237-317 Received: 20 March 2018; Accepted: 8 May 2018; Published: 10 May 2018

Abstract: The control strategies of the small power wind generator are usually divided into the maximum power point tracking (MPPT) case, which requires the wind generator produce power as much as possible, and the power limited control (PLC) case that demands the wind generator produce a power level following the load requirement. Integration of these two operating cases responding to flexible and sophisticated power demands is the main topic of this article. A small power wind generator including the sluggish mechanical dynamic phenomenon, which uses the permanent magnet synchronous generator, is introduced to validate different control methods integrating MPPT and PLC cases and based on hysteresis control. It is a matter of an indirect power control method derived from three direct methods following perturb and observe principle as well as from a look-up table. To analyze and compare the proposed power control methods, which are implemented into an emulator of a small power wind generator, a power demand profile is used. This profile is randomly generated based on measured rapid wind velocity data. Analyzing experimental results, from the power viewpoint, all proposed methods reveal steady-state error with big amount of peak resulting from the nature of perturb and observe. Keywords: small power wind generator; power control method; power limited control; maximum power point tracking

1. Introduction After decades of development, the concern level about wind power research and application is still escalating. Being a clean and renewable energy resource, the wind power generator system extracts kinetic energy transforming into electrical form. While the wind energy source is apposite to provide the utility grid, small power wind systems can be used mostly as local distributed energy sources or one part of a microgrid since it is easy to be implemented and maintained. The scale of small power is defined by the power production level. In the United States of America, the wind energy system products lower than 100 kW are named small power wind systems; but, the criterion in Europe is 50 kW [1,2]. Due to its small size and light weight as well as its advances in aspects of reliability, energy density, and efficiency, the most used small power wind generator is the permanent magnet synchronous machine (PMSM) [3,4]. The small power wind energy system usually operates at maximum power point tracking (MPPT) case when wind velocity is lower than rated wind velocity; and constant power output is demanded when wind velocity is over rated wind velocity. However, being the local distributed energy source or a part of microgrid, the small scale wind energy system can also be required for the power limited control (PLC) case, at the range lower than rated wind velocity. Consequently, a general control strategy which could deal with both MPPT and PLC cases is necessary to be implemented. As discussed and presented in [5], the wind kinetic energy is converted into DC electrical energy by means of three possible solutions: the passive electrical structure using a three-phase diode bridge;

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the active structure using a controllable AC–DC converter; or the active structure using a controllable DC–DC converter with the three-phase diode bridge. Considering the energy conversion efficiency the tendency to decrease the financial cost, the active structure using DC–DC converter presented in [5] was selected in this paper. Several approaches for MPPT [3–11] and PLC [12–16] have been accomplished. Briefly, MPPT algorithms can be sorted into indirect and direct methods as summarized in [3,4]. The former type, indirect methods, indicates that the method relies on a precise mathematical model of the studied system. In [6], the ratio between the electrical output power and the value of DC voltage cube and the ratio between the DC current and the value of the DC voltage square are regarded as constant for all maximum power operating points. Based on these references, the DC voltage is controlled by a proportional-integral (PI) controller with a DC–AC converter at the grid side, while the rotational speed is controlled by another PI controller with an AC–DC converter at the generator side. In [7], the authors used the power coefficient (C p ) to make a lookup table to supply the reference of the mechanical rotational speed for different wind velocities. Also, this paper used electrical variables three-phase voltages estimating the rotational speed to avoid the usage of mechanical sensors. Both of these two indirect MPPT methods require pre-knowledge of studied system, and are sensitive to the parameter drift, which has not been discussed in these articles. Relatively, the direct method, such as the perturb and observe (P&O) principle used in [5,8] injects operating state disturbance into the system, and based on the system response, it determines the further direction of the variation of system operating point. Different from [5], in [8] it is considered only the mechanic inertia of generator, which is just 0.016 kg·m2 , thus the effect of the actually sluggish mechanic inertia of wind blades has been ignored. The direct MPPT method based on the P&O method presents more robustness and flexibility than the indirect method, since it does not require the mathematical model of the objective. However, the direct method usually asks designers with a good know-how level to make a tradeoff between response rapidity and stability. Some advanced algorithms such as the Neural Networks [9] can be used to estimate wind velocity or mechanical rotational speed and to establish a mathematical model of the system trained by a Particle Swarm Optimization method. This combination can avoid the requirement of expensive mechanical sensors and supply a highly precise model of the studied system; but the process of training the Neural Networks demands lots of preliminary work. The application of some advanced controlling techniques, such as the extended Kalman filter [10,11] also has been implemented for MPPT. Those techniques improved performances while increasing the complexity of application of those MPPT methods. The integrated control strategy of output power also has many approaches [12–16]. In [12], the authors use the variable step-size P&O method, which involves a sectional defined function modifying the output current of DC–DC converter to realize MPPT and a PI controller to realize PLC. Since [12] did not demonstrate the experimental verification, neither the power level of system nor the effect of the mechanical inertia are validated. Therefore, it is hard to determine if this combination is suitable to the small scale wind generator or not. In [13], a modified P&O method is selected for MPPT regulation. However, in this paper, PLC just means the constant power output when wind velocity is over the rated value of the studied system; in addition, a double loop PI control with a voltage inner loop and a power outer loop is implemented to achieve this objective. However, the inertia, combining the generator and the emulator of wind velocity and blades, is determined as 0.03 kg·m2 , which does not match the reality of real wind turbines. Thus, it means that [13] has not considered the influence of mechanical inertia which is an important factor focused on in our research. The sliding model control used in [14,15] that demands the system to meet a relatively logical relationship between the mechanical torque (being a ‘sliding surface’) and the actual electrical power, is independent of the mathematical information about the studied system. Hence, sliding model control, applied for the integrated power control, maintains strong robustness. However, similar to the P&O method, the sliding model control also just describes the movement of steady operating points of the wind generator; consequently, the dynamic process of electrical power respecting the change of mechanical

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torque still needs to be avoided. At the same time, the determination of parameters of sliding model control requires experienced designers. In [16], the authors selected Tip Speed Ratio (TSR) as the feedback parameter of the P&O method, and then compare the actual value of TSR with the ideal value calculated by mathematical model of studied system. Nevertheless, even it used the principle of P&O, and the method still performs with weak robustness. Different from the achievement discussed above, the research objective of the present work focused on the more general and flexible limited power demands, which can be applied in power balancing of a microgrid [5,10,11], when the microgrid may include the small scale wind generator. This paper presents the modelling of a small power wind PMSM in order to validate the power control strategy methods with hysteresis control loop. Proposed power control methods are designed to cover MPPT and PLC operating cases. In addition, this study faces precisely the problem of the uncertainty of wind velocity and the demanded power amount from load. Therefore, regarding the robustness of the studied system, it should be considered beside the main focus which is the wind speed. One notes that, in this paper, the imposed wind reference is modeled on a real wind measurement with many variations in frequencies and amplitudes. The small power wind turbine is emulated by a test bench and several experiments are implemented to validate characteristics of all proposed methods. Finally, experimental results are given, compared, and analyzed, and strengths and weaknesses of each method are revealed together. The article is structured as follows. Section 2 presents the small power conversion system including the analysis of characteristics. The formulation of the research problem and proposed power control methods integrating MPPT and PLC operating cases are presented in Section 3. In Section 4, the capability and effectiveness of all methods are evaluated based on a test bench. Conclusions and further studies are given in Section 5 and the final section presents a nomenclature. 2. Small Scale Wind Energy Conversion System The study in this article concentrates on a system transforming electrical energy into DC form, allowing the output system to supply networks as follows: a DC grid, an AC grid by using an inverter, and microgrids with DC or AC bus [5,10,11]. The power conversion structure implemented for this study, shown in Figure 1 [5], comprises a three-phase diode bridge connected to a controllable DC–DC converter. Based on this combination, the optimization of energy is able to be realized by searching the maximum power operating point or limited power operating point. Due to their simplicity and robustness in application, P&O methods are chosen to be realized and studied in this article to deal with the issue of PLC which means the wind generation system generates the power value required by loads. The test bench of the small power wind energy conversion system, based on the emulator of a small power wind turbine, is presented in this section and then the distribution of steady-state working points is displayed and used to determine the control strategy. 2.1. Overview of Test Bench The test bench electric scheme is presented in Figure 1a. As presented in [5], a system that consists of a three-phase driver, a three-phase PMSM, and one dSPACE DS1104 control board emulates the dynamic behavior of wind and blades. A second PMSM is used as generator of whole wind energy conversion system. Generator’s output connects a three-phase diode bridge transforming electric energy from AC form into DC form. A capacitor CBUS is implemented to stabilize the voltage of DC bus. An inductance L and an Insulated Gate Bipolar Transistor (IGBT) module driving by dSPACE DS1104 are combined into a DC–DC boost convertor to realize the adjustment of operating point. A programmable electronic load (PEL), shown in Figure 1a, for which the CPEL is associated, emulates the power demand of user. The PEL keeps voltage at 400 V for all operating condition [5,10]. Detailed information of equipment of the test bench is given in Table 1 and all physic equipment is shown in Figure 1b.

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(a) 0.5 0.4

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Figure 1. (a) Test bench electric scheme; (b) Image of the test bench; (c) Power coefficient function. Figure 1. (a) Test bench electric scheme; (b) Image of the test bench; (c) Power coefficient function. Table 1. Detailed information of equipment. PMSM: permanent magnet synchronous machine; PEL: Table 1. Detailed information of equipment. PMSM: permanent magnet synchronous machine; PEL: programmable electronic load. programmable electronic load. Equipment Type Equipment TypeC3S063V2F10 Three-phase driver Parker PMSM driver Parker NX430EAJR7000 Three-phase Parker C3S063V2F10 Three-phasePMSM diode bridge SEMIKRON SKD 51/14 Parker NX430EAJR7000 Three-phase SEMIKRON SKD 51/14 CBUS bridge Capacitor diode 1 mF Capacitor C 1 mF 50 mH (267.5 mΩ) Inductance LBUS Inductance L 50 mH (267.5 mΩ) IGBT module SEMIKRON SKM100GB063D IGBT module SEMIKRON SKM100GB063D PEL Puissance+ PL-6000-A PEL Puissance+ PL-6000-A C Capacitor 1.1 mF Capacitor C 1.1 mF PEL PEL

2.1. Electrical Power Distribution 2.2. The emulating is is considered as as a 1akW system by emulating model model of ofthe thewind windenergy energyconversion conversionsystem system considered 1 kW system Bergey [5].[5]. The extracted amount ofofelectrical power pp by Bergey The extracted amount electricalpower powerisisbased based on on the aerodynamic power AERO AERO expressed by Equation (1): Equation (1): 1 p AERO = 1ρπR2 v3 c p , (1) 2 (1) pAERO   R2v3cp , 2 radius R is 1.25 m, the v indicates the wind where the density of air ρ is 1.23 kg/m3 , the blade velocity, and the c p is coefficient approached byisa 1.25 7th-order polynomial as  is 1.23 where the density of the air power kg/m3,that theisblade radius R m, the v indicatesfunction the wind in Equation (2). This power coefficient is given in Figure 1c; it shows the behavior of the emulated velocity, and the c p is the power coefficient that is approached by a 7th-order polynomial function wind turbine. The dynamic mechanical function [5] is given by Equation (3). as in Equation (2). This power coefficient is given in Figure 1c; it shows the behavior of the emulated wind turbine. The dynamic mechanical function [5] is given by Equation (3). 7 c p (λ) = ∑7 aK λK , (2) K =0 a  K cp      K , (2) K 0


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5 of 16 1 d (3)  pAERO  pEM   J  F .  dt 1 dΩ   R v , in which Ω is the In Equations (2) and (3), the λ (isp AERO the TSR calculated following − p EM + FΩ. (3) )=J Ω dt rotational speed used also in Equation (3), pEM is the electromagnetic power, J and F are In Equations (2) and (3), the λ is the TSR calculated following λ = RΩ/v, in which Ω is the 2 and the viscous damping equaling 0.06 separately the mechanical equaling 1.5is kg·m rotational speed used also ininertia Equation (3), p EM the electromagnetic power, J and F are separately Nm/rad. the mechanical inertia equaling 1.5 kg·m2 and the viscous damping equaling 0.06 Nm/rad. The The distribution distribution of of static static state state operating operating points points isis validated validated based based on on several several pre-research pre-research p experiments. Figure 2a,b presents the aerodynamic power and the electrical AERO BUS experiments. Figure 2a,b presents the aerodynamic power p AERO and the electrical power power ppBUS i following voltage uuBUS and the bus current as variables. The correlation of these following the the DC bus voltage and the bus current i as variables. The correlation of these two BUS BUS BUS powers, p AERO and and p BUS pisBUSdisplayed in Figure 2c. 2c. pAERO two powers, is displayed in Figure Energies 2018, 11, 1217

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(c) Figure and electrical power pBUS based Figure 2.2. (a) (a)Aerodynamic Aerodynamicpower power ppAERO based on on the the DC DC bus bus voltage voltage AERO and electrical power pBUS u ; (b) Aerodynamic power p and electrical power p based on the DC bus current i BUS; ; uBUS BUS; (b) Aerodynamic power pAERO AERO and electrical power pBUS BUS based on the DC bus current iBUS (c) Aerodynamic power p based on power p BUS . (c) Aerodynamic power pAERO AERO based on power pBUS .

Theanalysis analysisof ofthe theexperimental experimentalresults resultsgiven givenin inFigure Figure22indicates indicatesthat: that:(i) (i)operating operatingmaximum maximum The power points (MPPs) are not identical for p curves and p curves owing to losses ofpower power BUS curves and pAERO curves owing to losses of power points (MPPs) are not identical for pBUS AERO from the input side of PMSM to the output side of three-phase diode bridge; and (ii) for limited power from the input side of PMSM to the output side of three-phase diode bridge; and (ii) for limited demand, p AERO curves supply operating points different from p BUS curves. Thus, for integrated pAERO curves supply operating points different from pBUS curves. Thus, for power demand, power control strategy, p AERO curves are useless even as indirect references. Therefore, the control pAERO integrated power control strategy, curves are useless indirect Therefore, strategy and the regulating algorithm application have to takeeven into as account thisreferences. remark. Based on the the control strategy andcurves, the regulating algorithm have to take account this remark. characteristics of p BUS the variable chosenapplication to realize the change ofinto system’s operating point p Based on the characteristics of curves, the variable chosen to realize the change of system’s is the DC bus voltage. For each wind speed it is axiomatic that for one value of i BUS there are two BUS different working points the operating range. comparing i BUSvalue , the variable operating point is the DCwithin bus voltage. For each windConsequently, speed it is axiomatic that with for one of iBUS u is more suitable to be regarded as the reference variable, since each value of u presents BUS are two different working points within the operating range. Consequently, comparing BUS there witha iunique u , theoperating variable state. is more suitable to be regarded as the reference variable, since each value of BUS

BUS

u3.BUSProblem presents a unique operating state. Formulation Integration of MPPT and PLC cases is the main objective of this paper. The proposed principle of this power control method is to avoid the requirement of distinguishing the MPPT condition from the PLC condition. Based on different theories of direct and indirect MPPT methods, ways to realize the integration of MPPT and PLC methods are dissimilar and they are presented below.

Integration of MPPT and PLC cases is the main objective of this paper. The proposed principle of this power control method is to avoid the requirement of distinguishing the MPPT condition from the PLC condition. Based on different theories of direct and indirect MPPT methods, ways to realize the integration of MPPT and PLC methods are dissimilar and they are presented below. Energies 2018, 11, 1217 3.1. Control Loop

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Whatever the principle, power control methods can only describe movement of system’s 3.1. Control Loop points. Based on the characteristic of studied wind power conversion systems, the steady operating bus Whatever voltage uthe is selectedpower as thecontrol controlmethods variable.can Hence, explanations power BUS principle, only before describe movement of of proposed system’s steady control methods, the dynamic wind power conversion system withthe respect operating points. Based on the characteristic characteristicof ofwhole studied wind power conversion systems, bus u to the variation of needs to be analyzed first. To correctly operate the regulating algorithm, voltage u BUS is selected BUS as the control variable. Hence, before explanations of proposed power control methods, dynamic by characteristic whole wind system with respect the control loop the is regulated a hysteresisofcontroller duepower to its conversion good dynamic performance and to the variation of u needs to be analyzed first. To correctly operate the regulating algorithm, easy implementation [17]. Figure 3a,b show the response of the actual uBUS with respect to the BUS  the control loop is regulated by a hysteresis controller due controller, to its goodand dynamic performance and for the hysteresis respectively its enlarged variation of bus voltage reference u BUS easy implementation [17]. Figure 3a,b show the response of the actual u BUS with respect to the version. The power response as well as the three phase electrical variables response are analyzed variation of bus voltage reference u∗BUS for the hysteresis controller, and respectively its enlarged and presented in Figure 3c,d, with enlarge presentation of three-phase electric variables given in version. The power response as well as the three phase electrical variables response are analyzed and Figure 3e,f. presented in Figure 3c,d, with enlarge presentation of three-phase electric variables given in Figure 3e,f. u*

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Figure3.3. (a) (a) uuBUS response responseofofhysteresis hysteresiscontroller; controller;(b) (b)Enlarged Enlarged u uBUS response; response;(c) (c)Experimental Experimental Figure BUS BUS evolution iBUS; (d) , uBB, ,uuCC; ;(e) evolutionofofiiAA,,iiBB,,iiC and andi BUS ; (d)Experimental Experimentalevolution evolutionofofuu (e)Experimental Experimentalevolution evolution AA, u enlarged of i , i , i and i ; (f) Experimental evolution enlarged of u , u , u . i , iB , iC and BUS i ; (f) Experimental evolution enlarged of Au B, u C, u . enlarged of A A

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Then, different amplitudes of step input of u BUS were implemented into the test bench, based on 8 m/s wind velocity and the 150 V initial value of the bus voltage. In order to highlight the regulation time of p BUS response to the variation of u BUS , Figure 4 presents the relationship between the regulation time, variation value of p BUS , and the step input values of u BUS . The used values of step input of u BUS are: 10 V, 7.5 V, 5 V, and 2.5 V. Given the results given in Figure 3 and the discussion expressed in [18], one notes that the hysteresis controller is adequate for a rapid response. Indeed, the wave forms of currents and voltages may be considered as acceptable concerning the distortion. Therefore, mutual restraint resulting from


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Then, different amplitudes of step input of uBUS were implemented into the test bench, based onEnergies 8 m/s wind velocity and the 150 V initial value of the bus voltage. In order to highlight 7the 2018, 11, 1217 of 16 regulation time of pBUS response to the variation of uBUS , Figure 4 presents the relationship

Regulation time for 95% (s)

between the regulation time, variation value of pBUS , and the step input values of uBUS . The used the joint action of the power control methods and the hysteresis control algorithm has to be taken values of step input of uBUS are: 10 V, 7.5 V, 5 V, and 2.5 V. into account. 3 2 1 0 40 20 p (W) BUS

0

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u (V)

Figure 4.4. Relationship between voltage step input, power response Figure Relationship between voltage step input, power responseand andregulation regulationtime. time.

Given the results given in Figure 3 and the discussion expressed in [18], one notes that the Due to the non-linearity of the system, as presented in Figure 4, the value of regulation time of hysteresis controller is adequate for a rapid response. Indeed, the wave forms of currents and output power p BUS responding the variation of u BUS is associated to the perturb step-size ∆u of u BUS voltages may be considered as acceptable concerning the distortion. Therefore, mutual restraint and the operating point. According to Figure 4, when demanded step input of u is big, e.g., +10 V, resulting from the joint action of the power control methods and the hysteresisBUS control algorithm +7.5 V, and even +5 V, the output power needs approximately 2.6 s to stable in the region about 5% of has to be taken into account. stable value of p BUS . For a decreased step input, e.g., +2.5 V, the value of the regulation time still rests Due to the non-linearity of the system, as presented in Figure 4, the value of regulation time of near to 2 s. output power pBUS responding the variation of uBUS is associated to the perturb step-size u of To implement the control strategy for all methods demanding information of p BUS and u BUS as uaccurate operating point. According to Figure 4, when demanded step Hz, input of uBUSbefore is big, BUS and the as possible, a low-pass filter, which uses a cut-off frequency of 6000 is added the e.g., +10 V, +7.5 V, and even +5 V, the output power needs approximately 2.6 s to stable in the entrance of direct methods. This is a compromise between the precision and the rapidity of tracking. . For method, a decreased steptime input, +2.5should V, the not value the regionIfabout 5% is of used stable of pBUS the p BUS byvalue the power control certain stepe.g., (which be of smaller than 2 s) has be added to avoid regulation timetostill rests near to 2 s.the dynamic process of p BUS response. However, for the method based the indirect this operating time stepdemanding is unnecessary, because used parameters To on implement theprinciple, control strategy for all methods information of pBUS and uBUSdo not include the p or any other parameters containing the high order dynamic characteristics. BUS a low-pass filter, which uses a cut-off frequency of 6000 Hz, is added before as accurate as possible,

the entrance of direct methods. This is a compromise between the precision and the rapidity of 3.2. Principle of Power Control Strategy Methods tracking. our previous studies [5,10,11], the PLC operating case means that the power output of IfBased the pon BUS is used by the power control method, certain time step (which should not be the small scale follow the demanded value by the users’ side. Thus, smaller than 2 s)wind has togenerator be addedshould to avoid the dynamic process of psupplied BUS response. However, for the the power control method should focus on the absolute value of the p DIFF = | p BUS − p LI M |, where method based on the indirect principle, this operating time step is unnecessary, because used p LI M is the asked power value and the p BUS is the measured actual power value, with the acceptable parameters do not include the pBUS or any other parameters containing the high order dynamic assumption that p LI M has been obtained. Figure 5 presents the proposed power controlling strategy characteristics. integrating both of MPPT and PLC cases. Dotted lines in this figure indicate the varying demanded value of power: the upper one shows the demanded values for MPPT case; the lower dotted line 3.2. Principle of Power Control Strategy Methods indicates the PLC case. Additionally, the solid line displays the power distribution for a given wind velocity. following P&O logic principle, theoperating proposedcase integrating power BasedThus, on our previousthe studies [5,10,11], the PLC means that thecontrol power methods output committed to minimize theshould value of the difference p DIFF . value supplied by the users’ side. ofwill thebe small scale wind generator follow the demanded the characteristics of thefocus wind on turbine, when thevalue demanded pDIFFof ppLIBUSM isplower Thus, According the powertocontrol method should the absolute of thevalue LIM , than the potential maximum power value, there are theoretically two operating points supplying where pLIM is the asked power value and the pBUS is the measured actual power value, with the the required power value. Considering the transfer of operating points, if the steady component of acceptable assumption that pLIM has been obtained. Figure 5 presents the proposed power operating currents is close to equipment’s physical limitations, the dynamic components of current controlling strategy both of MPPT and points PLC cases. Dotted lines in this indicate the resulting from theintegrating transfer between operating has high possibility for figure damaging devices. varying demanded valuethe of power: oneto shows theatdemanded values for MPPT case;side. the Therefore, in this work, system the willupper be forced operate the “low current–high voltage” lower Aiming dotted line indicates the PLC case. Additionally, the solid line displays the power distribution to realize the objective mentioned above, the operating region has been divided into four parts: I, II, III and IV which are defined by changes of variables ∆u BUS , ∆p BUS and ∆pdi f f presented in Figure 6 and Table 2.


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for a given wind velocity. Thus, following the P&O logic principle, the proposed integrating power 8 of 16 control methods will be committed to minimize the value of the difference pDIFF .

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Figure 5. Power controlling strategies.

According to the characteristics of the wind turbine, when the demanded value of pLIM is lower than the potential maximum power value, there are theoretically two operating points supplying the required power value. Considering the transfer of operating points, if the steady component of operating currents is close to equipment’s physical limitations, the dynamic components of current resulting from the transfer between operating points has high possibility for damaging devices. Therefore, in this work, the system will be forced to operate at the “low current– high voltage” side. Aiming to realize the objective mentioned above, the operating region has been divided into four parts: I, II, III and IV which are defined by changes of variables uBUS , pBUS and  p diff Figure 5. 5. Power Power controlling Figure controllingstrategies. strategies.

presented in Figure 6 and Table 2.

According to the characteristics of the wind turbine, when the demanded value of pLIM is lower than the potential maximum power value, there are theoretically two operating points supplying the required power value. Considering the transfer of operating points, if the steady component of operating currents is close to equipment’s physical limitations, the dynamic components of current resulting from the transfer between operating points has high possibility for damaging devices. Therefore, in this work, the system will be forced to operate at the “low current– high voltage” side. Aiming to realize the objective mentioned above, the operating region has been divided into four parts: I, II, III and IV which are defined by changes of variables uBUS , pBUS and  p diff (a) (b) presented in Figure 6 and Table 2. Figure 6. (a) Operating regions for power limited control (PLC) case; (b) Operating regions for Figure 6. (a) Operating regions for power limited control (PLC) case; (b) Operating regions for maximum power point tracking (MPPT) case. maximum power point tracking (MPPT) case. Table 2. Definition of four operating regions for PLC case. Table 2. Definition of four operating regions for PLC case. I II III

Variables

uBUS

↑ Variables

pBUS

↑ ∆u BUS ∆p BUS ↓ ∆p DIFF

↓ I

↑↓ ↑↑ ↓

↑

↑ III

↓↓

↑ ↑ ↑

↓↓ ↓

↑↓ ↓↓ ↓

↓

IV

IV ↑

↓

↓↓ ↑ ↑ ↓ ↑ pDIFF ↑ ↑ ↑ ↓ ↑ ↓ (a) (b) Based on the Table 2 and the Figure 6a, for example, after one step of perturbation, if the change Figure (a) Table Operating for power limited (PLC) (b) regions for on6.voltage, the and Figure 6a, for example, onecase; step of perturbation, if the change ofBased DC bus ,regions isthe positive, the change ofcontrol DCafter bus power, , is still positive and the 2uBUS pBUSOperating

↓ ↓ ↑

↑

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↓ ↑ ↑

↑

maximum power point, tracking (MPPT) of DC bus voltage, is positive, thecase. change of DC power, ∆p still positive and the BUS positive, change of is also the operating point canbus be identified atBUS this, is moment in the region pDIFF ∆u change of p DIFF is also positive, the operating point can be identified at this moment in the region II. II. So, since it is desired to drive the system the “low current–high voltage” side, the Table 2. Definition of fouroperating operating at regions for PLC case. So, next sinceperturbation it is desiredstep to drive the system operating at the “low current–high voltage” side, the next is selected as positive again. Variables step is selected I II III IV perturbation as positive again.  u ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ TheBUSFigure 6a and Table 2 indicate the power limited demand conditions, for which the demanded valueis lower than↑ the potential maximum power ↓value. The↓Figure 6b ↑and Table 3↓ present the pBUS ↓ ↑ ↑ region definition demand conditions. It is↓ obvious that, to these conditions, pDIFF of the MPPT ↓ ↑ ↑ ↓ ↑ two operating ↑ ↓ operating regions can be defined by same rules. Therefore, P&O algorithms based on these operating regions’Based definition uniformly two of after MPPT and PLC. Based on trends changes on thecan Table 2 and thecover Figure 6a,conditions for example, one step of perturbation, if theofchange of of ∆uDC , ∆pvoltage, , power control based on P&O theory the direction BUSbus BUS , ∆p DIFF , is positive, themethods change of DC bus power, , is still positive and the of uBUS pBUSdetermine change of system operating state. change of pDIFF is also positive, the operating point can be identified at this moment in the region

II. So, since it is desiredTable to drive the system operatingregions at the for “low current–high voltage” side, the 3. Definition of operating MPPT case. next perturbation step is selected as positive again. Variables ∆u BUS ∆p BUS ∆p DIFF

I

↑ ↑ ↓

IV

↓ ↓ ↑

↑ ↓ ↑

↓ ↑ ↓

Variables

Energies 2018, 11, 1217

I

IV

uBUS pBUS

↑

↓

↑

↓

↑

↓

↓

↑

pDIFF

↓

↑

↑

↓

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3.2.1. Fixed Step-Size 3.2.1. Fixed Step-Size In order to validate the control strategy mentioned above, one simple experiment was In order to validate the control strategy mentioned simple experiment wasprofiles, designed. designed. Figure 7 present the selected wind velocity above, and theone demanded power value as Figure 7 present the selected wind velocity and the demanded power value profiles, as as well as experimental results of actual electrical power, u BUS and the perturb step-size. Thewell profile experimental results of actual electrical power, u BUS and the perturb step-size. The profile of p LI M of pLIM demands 250 W, which is lower than the maximum power level for given wind velocity, demands 250 W, which is lower than the maximum power level for given wind velocity, and 378 W, and 378 is the power maximum power is to confirm this strategy with which is W, thewhich maximum level. Thelevel. first The step first is tostep confirm this strategy works works with fixed fixed perturbation step-size. perturbation step-size. p 600

LIM

p

BUS-F

(W)

400 200 0 0

50

(a) u 300

100

150

100

150

(b) u

BUS-F

-F

10

250

5 (V)

(V)

Time (s)

200

0

150

-5

100 0

-10 0

50

Time (s)

100

150

(c)

50

Time (s)

(d)

Figure 7. Fixed step-size: (a) wind velocity profile; (b) evaluations of pBUS ; (c) evaluations of u BUS ; Figure 7. Fixed step-size: (a) wind velocity profile; (b) evaluations of p BUS ; (c) evaluations of u BUS ; u . (d)evaluations evaluationsof of∆u. (d)

According to results in Figure 7, it is clear that the principle presented in Section 3.2 works According to results in Figure 7, it is clear that the principle presented in Section 3.2 works properly for identifying the actual operating region and detecting the moving direction of properly for identifying the actual operating region and detecting the moving direction of perturbation. perturbation. However, obviously, fixed perturbation step-size cannot drive the system producing However, obviously, fixed perturbation step-size cannot drive the system producing stable power stable power output; so, using variable perturbation step-size is the next object to be implemented. output; so, using variable perturbation step-size is the next object to be implemented. 3.2.2. Improved Variable Step-Size Designed with Newton–Raphson Technique Following the logic of MPPT variable step-size method [3,18], Newton–Raphson method is one worthwhile method of calculating variable step-size for power control method integrating MPPT and PLC cases. Based on the theory of Newton–Raphson method, p DIFF is regarded as one function of bus voltage, p DIFF = f (u BUS ). Thus, the calculation of variable step-size matches the following iterative methodology for each k step: ∆p DIFF (k) = p DIFF (k ) − p DIFF (k − 1),

(4)

∆u BUS (k) = u BUS (k) − u BUS (k − 1),

(5)

∆u = Sign × | p DIFF (k)/(∆p DIFF (k )/∆u BUS (k))|,

(6)

u BUS− REF = ∆u + u BUS (k).

(7)

The value of Sign is determined based on Table 2. When the system works in I, II or III region, its value equals one; otherwise, the system works in IV region and the value Sign equals minus one. To avoid the convergence of variable step-size at the low voltage–high current operating conditions

u BUS  REF  u  u BUS  k  .

(7)

The value of Sign is determined based on Table 2. When the system works in I, II or III region, otherwise, the system works in IV region and the value Sign equals minus one. 10 of 16 To avoid the convergence of variable step-size at the low voltage–high current operating conditions whose region is located at the left side of maximum power operating points, the variable step-size whose region is located at the left side of maximum power operating points, the variable step-size calculating method is used when system works in III and IV operating regions. calculating method is used when system works in III and IV operating regions. Figure 8 presents the experimental results of Newton–Raphson method under the same Figure 8 presents the experimental results of Newton–Raphson method under the same experimental condition as in Figure 7. experimental condition as in Figure 7. its value equals Energies 2018, 11, 1217one;

p 600

LIM

p

u

BUS-NR

250 (V)

(W)

400 200 0 0

BUS-NR

300

200 150

50

Time (s)

100

100 0

150

50

(a)

Time (s)

100

150

(b) u

-NR

10

(V)

5 0 -5 -10 0

50

Time (s)

100

150

(c)

uBUS Figure 8. 8. Canonical Evaluations of ofpBUS ; (b) Evaluations of of ; (c); Figure Canonical Newton–Raphson Newton–Raphsonmethod: method:(a)(a) Evaluations p BUS ; (b) Evaluations u BUS  u Evaluations of . (c) Evaluations of ∆u. p is Basedon onFigure Figure8,8,when whenp pLIM equals equals250 250 which means PLC case, variation Based W,W, which means thethe PLC case, thethe variation of of p BUSBUS LI M is significant; even when equals W, MPPT case, variation of the stationary component significant; even when p LI MpLIM equals 380380 W, MPPT case, the the variation of the stationary component of the MPP is not obvious soItmuch. is when clear that when thevalue maximum value of pof the MPP is not obvious so much. is clearItthat the maximum of perturbation BUS around BUSparound step-size is selected big, as 10 V, such the perturbation cannot significantly to perturbation step-size is such selected big, as 10 V, the step-size perturbation step-size cannot converge significantly zero (shown in Figure 8). in If, Figure the maximum value of perturbation step-size is reduced, effect of converge to zero (shown 8). If, the maximum value of perturbation step-sizethe is reduced, convergence perturbation is notstep-size improved butsignificantly the seeking but speed a new the effect of of convergence ofstep-size perturbation is significantly not improved thetoseeking steady-state will clearly also be decreased. speed to a new steady-state will clearly also be decreased. According to experimental results such as in Figure 8, direct application of Newton–Raphson method cannot converge properly. This is due to the fact that the rate of change of the power respect to the voltage, around operating points of limited power, is usually high, comparing to the response of power nearby MPP with same size of perturbation step. Therefore, one improved Newton–Raphson variable step-size iterative methodology is introduced as follows: gradi (k) = ∆u = Sign ×

p BUS (k ) − p BUS (k − 1) , u BUS (k ) − u BUS (k − 1)

| p DIFF (k)/(∆p DIFF (k)/∆u BUS (k))| , with | gradi (k )| ≥ 1, | gradi (k)| u BUS− REF = ∆u + u BUS (k).

(8)

(9) (10)

Based on the results presented in Figure 8, the calculation iteration (Equations (4)–(7)) of variable step-size around the MPPs naturally converge smooth, since, at that place, the distribution of operating points has a large range where the change of power is not significant for at least one perturb. So, dividing classic Newton–Raphson calculation iteration by the gradient of the actual power respecting DC bus voltage could reduce the power transition if the operating goal is PLC. Taking into account the modification in Equation (10), it can be stated that with this variable step-size algorithm, this method can deal with the convergence of variable step-size for both conditions of MPPT and PLC.

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3.2.3. Variable Step-Size with Fuzzy Logic Another well-known technique of variable perturbation step-size is the fuzzy logic method [3,18], which can handle robust and nonlinear control requirements. However, one notes that this method requires in-depth knowledge concerning the system. Fuzzy logic is based on the input space and the output space mapping through logical actions. As usual, in this work, the process is divided into three phases: the fuzzification, the fuzzy reasoning, and the defuzzification. Same as the method presented in Section 3.2.2, the fuzzy logic method is introduced into the calculation of variable step-size. So, gradi (k) and p DIFF (k ) are chosen as two inputs of fuzzy logic method as presented in Equation (11): (

e1 = gradi (k) =

p BUS (k )− p BUS (k −1) u BUS (k )−u BUS (k −1)

e2 = p DIFF (k)

.

(11)

During the fuzzification phase, the inputs and outputs numerical values are expressed in fuzzy sets. All points in input space are translated into the “code” in form of the degree of membership which can equal any values between 0 and 1. Considering the universe of discourse of the inputs and the output normalized into [–1, 1], Figure 9b–d present the fuzzy subsets corresponding to the inputs e1 ∈ {bn; n; z; p; bp} and e2 ∈ {n; z; p}, and to the output s ∈ {−; 0; +}. Aiming to accomplish fuzzy logic as simple as possible, following the principle presented in Figure 9a, these input variables, the gradi (k ) is normalized into e1 by gain K1 , and p DIFF (k) is normalized into e2 by gain K2 . However, there is possibility to adjust values of K1 and K2 , to obtain a normalized interval rather than [–1, 1], which can lead to a better regulating performance (presented in Section 4). Forms of membership function were selected as triangular and trapezoidal functions to simplify the study. For e1 , a group of five subsets is demonstrated to separate its value range for MPPT and PLC cases. Parameters of each membership function are determined based on experimental tests. The Figure 9e shows the fuzzy reasoning surface of the proposed fuzzy logic and the Table 4 explains the “if–then” reasoning role. The step of “if” describes a fuzzy area in the input space and the step “then” step states the output in the fuzzy area. With a logical operator, membership functions values, evaluating the degree of each activated rule, summarize the degree of satisfaction for the “if” step of each rule. Subsequently, the fuzzy set in the “then” step of each rule is determined. Finally, outputs of each rule are aggregate into one fuzzy set. The Mamdani Fuzzy Inference System using the fuzzy toolbox is applied in this work. The defuzzification wishes to “convert” the fuzzy set resulted from the fuzzy reasoning into a numerical value between 0 and 1. Then this value is anti-normalized to be ∆u by Ks . Several defuzzification operators are mentioned in [19]; however, the most used operator is the centroid, or center of gravity, which is chosen in this study, such as the implemented methods mentioned above. Figure 10 presents the experimental results of fuzzy logic method under the same operating condition as presented in Figures 7 and 8. Table 4. Fuzzy rule table.

s

e1 (gradi)

Big Negative (bn) Negative (n) Zero (z) Positive (p) Big Positive (bp)

e2 (pDIFF ) Negative (n)

Zero (z)

Positive (p)

0 + + + 0

0 0 0 0 0

0 − − − 0

Energies 2018, 11, 1217 Energies 2018, 11, x FOR PEER REVIEW

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12 of 17

(a) n z p Degree of Membership

Degree of Membership

bn n z p bp 1 0.8 0.6 0.4 0.2 0 -1

-0.8

-0.6

-0.4

-0.2

0 e1

0.2

0.4

0.6

0.8

1

1 0.8 0.6 0.4 0.2 0 -1

-0.8

-0.6

-0.4

-0.2

(b)

0.2

0.4

0.6

0.8

1

(c)

0 +

1

1

0.8 0.6

s

Degree of Membership

-

0 e2

0

0.4

-1 1

0.2 0 -1

-0.8

-0.6

-0.4

-0.2

0 s

0.2

0.4

0.6

0.8

0.5

e 0 1

1

-0.5

(d)

-1 1

0.5

0 e

-0.5

-1

2

(e)

Figure 9. Fuzzy logic: (a) structure of fuzzy logic; (b) membership of e1; (c) membership of e2; (d) Figure 9. Fuzzy logic: (a) structure of fuzzy logic; (b) membership of e1 ; (c) membership of e2 ; 13 of 17 (d) membership of s; (e) surface of fuzzy reasoning role.

Energies membership 2018, 11, x FOR ofPEER s; (e) REVIEW surface of fuzzy reasoning role.

(V)

(W)

The Figure 9e shows the fuzzy reasoning surface of the proposed fuzzy logic and the Table 4 u p p LIM reasoning BUS-FL explains the “if–then” role. The step of “if”300 describes a fuzzy areaBUS-FL in the input space and 600 the step “then” step states the output in the fuzzy area. With a logical operator, membership 250 functions values, evaluating the degree of each activated rule, summarize the degree of satisfaction 400 for the “if” step of each rule. Subsequently, the fuzzy set in the “then” step of each rule is 200 200 determined. Finally, outputs of each rule are aggregate into one fuzzy set. The Mamdani Fuzzy 150 Inference System using the fuzzy toolbox is applied in this work. 0 0

50

Time (s)

100

150

100 0

Table 4. Fuzzy rule table.

(a) s

(V)

e1 (gradi)

Big Negative 10 (bn) Negative (n) 5 Zero (z) 0 Positive (p) -5 (bp) Big Positive

Negative u (n) -FL 0 + + + 0

50

e2 (pDIFF) Zero (z) 0 0 0 0 0

Time (s)

100

150

(b) Positive (p) 0 0

-10 0 wishes

50 the fuzzy set 100resulted from 150the fuzzy reasoning into a The defuzzification to “convert” Time (s) numerical value between 0 and 1. Then this value (c) is anti-normalized to be  u by Ks. Several defuzzification operators are mentioned in [19]; however, the most used operator is the centroid, or umentioned Figure (a) ; (b) (c)Evaluations Evaluations of∆u. . center of gravity, which is chosenofof inppthis such asof implemented methods BUS BUS Figure10. 10. (a)Evaluations Evaluations (b) Evaluations Evaluations ofthe uuBUS ;;(c) of BUS ; study, above. Figure 10 presents the experimental results of fuzzy logic method under the same operating in Figures 7 and 8. 4. condition Analysis as of presented Comparative Results

In order to compare above-mentioned power control methods, a real wind velocity is considered as the wind velocity input, presented in Figure 11a, from data measured by Météo France, in Compiegne, France, on 15 January 2015, during 15 min; this real wind velocity profile is the same as in [18]. Furthermore, the pLIM profile was chosen based on the potential maximum power and the physical minimum power of the test bench, as presented in Figure 11b. The selected wind profile and power limited profile highlight a strained condition with rapid changes.

-10 0

50

Time (s)

100

150

(c) Figure 10. (a) Evaluations of pBUS ; (b) Evaluations of u BUS ; (c) Evaluations of

Energies 2018, 11, 1217

u .

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4. Analysis of Comparative Results 4. Analysis of Comparative Results In order to compare above-mentioned power control methods, a real wind velocity is In order as to compare above-mentioned control a real wind velocity is considered as considered the wind velocity input, power presented in methods, Figure 11a, from data measured by Météo the wind in velocity input, presented 11a,2015, fromduring data measured France, in Compiegne, France, Compiegne, France, onin15Figure January 15 min; by thisMétéo real wind velocity profile is France, on as 15in January 2015, duringthe 15 min; realwas wind velocity profile is the same as in [18]. pLIM this the same [18]. Furthermore, profile chosen based on the potential maximum Furthermore, the p profile was chosen based on the potential maximum power and the physical LI M power and the physical minimum power of the test bench, as presented in Figure 11b. The selected minimum power the test bench, as presented 11b. The selected wind changes. profile and power wind profile andof power limited profile highlightinaFigure strained condition with rapid limited profile highlight a strained condition with rapid changes. pMAX pMIN pLIM

v

9

600 400

7 (W)

(m/s)

8

6

200

5

0

4 0

150

300

450 Time (s)

(a)

600

750

900

0

150

300

450 Time (s)

600

750

900

(b)

v ;(b) Figure (b)p pMAX, ,p pMINand andp pLIM . Figure 11. 11. Profile Profile of: of: (a) (a)the theselected selected v; MI N LI M . MAX Underthese theseexperimental experimentalconditions, conditions,several severalexperimental experimentaltests testsare areintroduced introducedto tocompare compareall all Under above-mentioned power control methods whose characteristics are given as follow: above-mentioned power control methods whose characteristics are given as follow:

• • •

Fixedstep-size: step-size:step-size step-sizeequals equals10 10V,V,7 7V,V,5 5VVand and2.5 2.5V.V. Fixed Improvedvariable variablestep-size step-sizedesigned designedwith withNewton–Raphson Newton–Raphsontechnique: technique: maximum maximum value valueofof Improved step-size equals 10 V, 7 V, 5 V and 2.5 V. step-size equals 10 V, 7 V, 5 V and 2.5 V. Variablestep-size step-sizebased basedon onfuzzy fuzzylogic: logic:the thecombination combinationofofparameters parameters(K(K,1K , K,2,KK)s)respectively respectively Variable s 1 2 equal: (4.5, (4.5, 17.5, 10), (5,(5, 15,15, 7), (5, (5,7), 20,(5, 10),20, (10, 20,(10, 7), and 20, 10). equal: 17.5,7), 7),(4.5, (4.5,17.5 17.5 10), 7), 15, (5, 10), 15, (5, 10),20,(5,7),20, 10), 20, (10, 7), and (10, 20, 10). As key variable, pDIFF is used to analyze characteristics of each method. Referencing

statistical ‘mean’, defined as average value, andofthe ‘variance’, thestatistical expected As keyconcepts, variable,the p DIFF is used to analyze characteristics each method. indicating Referencing value of the the ‘mean’, squareddefined deviation from the mean, arethe calculated toindicating compare dynamic and value steady-state concepts, as average value, and ‘variance’, the expected of the squared deviation from the mean, are calculated to compare dynamic and steady-state characteristics of different power control methods. At first, to all methods based on the P&O theory, a sampling method is a sampling time equals two seconds, is applied to filter the peak of each perturbation step of P&O (marked as ‘Mean sampling’ and ‘Variance sampling’). Then, the overall comparison (marked as ‘Mean overall’ and ‘Variance overall’) is calculated and analyzed also. Based on those parameters, results for the optimal one test of each kind of method are collected and presented in Figure 12. The ‘Mean’ and ‘Variance’ of those selected tests are listed in Table 5. Summarizing all presented results, under complex conditions of wind velocity and power demands variation, all three methods based on the P&O principle matched the design target of this integrating power control method. Those methods perform weakly in the view of dynamic, resulting from the mechanical inertia which cannot be ignored; but, overall, their steady-state errors are tiny. From fixed step-size to improved Newton–Raphson method calculating variable step-size till to fuzzy logic method, the dynamic noise is reduced significantly, meanwhile the change of whole steady-state error is not much, in the ‘overall’ view. Considering the complexity of implementing each power control method, fixed step-size and improved Newton–Raphson method has just one parameter needing to be determined: the value or the maximum limit of step-size. In theory, variable step-size calculated by fuzzy logic has a greater possibility to perform better, since it contains several parameters to be modified. However, this greater freedom increases the complexity of determination of those parameters, which demands a rich experience of application.

a sampling method is a sampling time equals two seconds, is applied to filter the peak of each perturbation step of P&O (marked as ‘Mean sampling’ and ‘Variance sampling’). Then, the overall comparison (marked as ‘Mean overall’ and ‘Variance overall’) is calculated and analyzed also. Based on those parameters, results for the optimal one test of each kind of method are collected and Energies 2018, 11, presented in 1217 Figure 12. The ‘Mean’ and ‘Variance’ of those selected tests are listed in Table 5. 14 of 16 pBUS-F pBUS-NR pBUS-FL

800

250 (V)

(W)

600 400 200 0 0

uBUS-F uBUS-NR uBUS-FL

300

200 150

100

200

300

400 500 Time (s)

600

700

800

100 0

900

100

200

300

(a) u-F u-NR

400 500 Time (s)

600

700

800

900

700

800

900

(b) u-FL

pDIFF-F pDIFF-NR pDIFF-FL

200

10 100 (W)

(V)

5 0 -5

-100

-10 0

0

100

200

300

400 500 Time (s)

600

700

800

900

-200 0

(c)

100

200

300

400 500 Time (s)

600

(d)

Figure12. 12.Evaluations Evaluationsof ofexperimental experimentalresults resultsfor forselected selectedtest: test:(a) (a) evaluation evaluation of of p pBUS; (b) ; (b)evaluation evaluation Figure BUS u BUS; (c) ; (c) evaluation (d) evaluation u ; evaluation ofofu BUS evaluation of of ∆u;(d) of pof DIFFp. DIFF . Table Table5.5.Means Meansand andvariances variancesfor forall allpower powercontrol controlmethods. methods.

Method Method Fixed 10 V Fixed Variable 10 7 VV Variable 7 V Fuzzy (10, 20, 7) Fuzzy (10, 20, 7)

Mean Sampling Mean Sampling 0.1383 0.1383 0.1296 0.1296 0.1613 0.1613

Variance Sampling Variance Sampling 14.9045 14.9045 21.4507 21.4507 19.0379 19.0379

Mean Overall Mean Overall 0.1347 0.1347 0.1326 0.1326 0.1662 0.1662

Variance Overall Variance Overall 39.5348 39.5348 26.0033 26.0033 22.0579 22.0579

Summarizing all presented results, under complex conditions of wind velocity and power 5.demands Conclusions variation, all three methods based on the P&O principle matched the design target of this integrating power control control methods method. based Those on methods perform weakly in the view ofimproved dynamic, Three power the P&O principle (fixed step-size; resulting from the mechanical inertia which cannot be ignored; but, overall, their steady-state errors Newton–Raphson variable step-size and variable step-size based on fuzzy logic) have been studied, are tiny. From fixed step-size to improved Newton–Raphson method calculating variable step-size designed, and then implemented into a test bench highlighting the sluggish mechanical inertia and till to fuzzy logic method, theproblem dynamicintegrating noise is reduced significantly, change dealing with the power control MPPT and PLC cases.meanwhile This study the concerns theof whole steady-state error is not much, in the ‘overall’ view. small power wind energy conversion system. Considering the based complexity of implementing each power control method, fixed and One experiment, on designed wind and power demand profile, was used to step-size validate the improved Newton–Raphson method has justanother one parameter needing to be determined: thevelocity value or basic function of each method. In addition, experiment, using a measured wind the maximum limit of step-size. In theory, variable calculated by fuzzy logic has a greater profile and one calculated power demand profile, wasstep-size implemented to compare characteristics of all possibility to perform better, since containsand several parameters be modified. However, this proposed methods. Evaluations of allitmethods several statisticaltoindices of key variable p DIFF greater freedom increases the complexity of determination of those parameters, which demands were calculated and analyzed. All power control methods present good steady-state characteristics,a richtheir experience application. are limited by the sluggish mechanical inertia and the control loop’s but dynamicofcharacteristics capability. Furthermore, some of the complex control algorithms, such as fuzzy logic used in this work, have the potential to achieve better performance. Moreover, the studied system uses a PMSM assembly, three-phase diode bridge, and converter with a hysteresis control, which makes it one of the most robust “drivers”. The future research direction is to improve the dynamic characteristics of the control loop, to suppress the effect from the sluggish mechanical inertia. In addition, a deep robustness analysis may be conducted taking into account unmodeled dynamics, or associated couplings and uncertainties. This can significantly improve the performance of methods based on the P&O principle.

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Author Contributions: All authors have conceived and designed the system, performed the experiments, and analyzed the data. All authors contributed jointly to the writing and preparing revision of this manuscript. All authors have read and approved the manuscript. Conflicts of Interest: The authors declare no conflict of interest and the founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the result.

Nomenclature v CBUS L CPEL p AERO cp R ρ λ J F p BUS u BUS i BUS u∗BUS u A , u B , uC i A , i B , iC ∆u p LI M p DIFF ∆u BUS ∆p BUS ∆p DIFF p BUS− F u BUS− F ∆u− F u BUS− REF p BUS− NR u BUS− NR ∆u− NR gradi(k) K1 K2 KS p BUS− FL u BUS− FL ∆u− FL p DIFF− F p DIFF− NR p DIFF− FL p MAX p MI N

Wind velocity Capacitor at the DC bus Inductance at the DC bus Capacitor as the Programmable Electronic Load side Harvested aerodynamic power Power coefficient Blade radius Air density Tip speed ration Equivalent inertia of blades and hub Viscous damping coefficient Electrical DC BUS power of experimental platform Electrical DC BUS voltage of experimental platform Electrical DC BUS current of experimental platform Reference of DC BUS voltage of experimental platform Three-phase voltages Three-phase currents Perturbation step-size Demanded power value for power limited control Difference between the actual and demanded power Change of DC bus voltage Change of DC bus power Change of the pDIFF Experimental DC bus power for fixed perturb step-size method in Figure 7 Experimental DC bus voltage for fixed perturb step-size method in Figure 7 Experimental evaluation of ∆u in Figure 7 Calculated reference of DC bus voltage for variable step-size method Experimental DC bus power for variable perturb step-size method in Figure 8 Experimental DC bus voltage for variable perturb step-size method in Figure 8 Experimental evaluation of ∆u in Figure 8 Ratio between the change of electrical power and the change of voltage Gain for normalizing the first input of fuzzy logic method Gain for normalizing the second input of fuzzy logic method Gain for antinormalizing the output of fuzzy logic method Experimental DC bus power for fuzzy logic method in Figure 10 Experimental DC bus voltage for fuzzy logic method in Figure 10 Experimental evaluation of ∆u in Figure 10 Evaluation of pDIFF for the fixed step-size perturbation and observation method Evaluation of pDIFF for the variable step-size perturbation and observation method Evaluation of pDIFF for the fuzzy logic method Theoretical maximum value of DC bus power based on the wind velocity curve in Figure 11a Theoretical minimum value of DC bus power based on the wind velocity curve in Figure 11a

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References 1. 2. 3. 4. 5.

6.

7.

8.

9.

10.

11.

12. 13. 14. 15.

16.

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