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International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 9, September 2015 ANALYSIS OF PMSG BASED WIND ENERGY CONVERSION SYSTEM OPERATING UNDER DIFFERENT GRID FAULT Kaki shanmukesh1, Mr.D.V.N.Ananth2 (PH.D) PG Scholar, Dept of EEE, VITAM Engineering College, Anandapuram, Visakhapatnam (Dt), A.P, India. 2 Assistant Professor, Dept of EEE, VITAM Engineering College, Anandapuram, Visakhapatnam (Dt), A.P, India. 1 ABSTRACT----- In the field of renewable energy generation has been observed wind energy. Where the technology is more rapid growth. It attracts attention as one of the most effective ways in terms of the cost of generating electricity from renewable energy sources. Voltage of the wind generator permanent magnet synchronous generator (PMSG) is directly driven by a variable due to the sporadic nature of wind energy. Voltage fluctuation and power of major concern in the connected network systems generate electricity using a wind converter list. Inverter is essential for interaction of from wind sources with Ac network. Synchronous generators used a variable speed the permanent magnet to extract the utmost of energy from wind energy conversion system. The is suggested common strategy for power control the permanent magnet synchronous generator a system based on wind energy conversion (WECS) operating under different the network conditions A unified power control strategy is proposed for the permanent magnet synchronous generator-based wind energy conversion system (WECS) operating under different grid conditions. In the strategy, the generator-side converter is used to control the dc-link voltage and the grid-side converter is responsible for the control of power flow injected into the grid. The generatorside controller has inherent damping capability of the torsional oscillations caused by drive-train characteristics. The grid-side control is utilized to satisfy the active and reactive current (power) requirements defined in the grid codes, and at the same time mitigates the current distortions even with unsymmetrical grid fault. During grid faults, the generator-side converter automatically reduces the generator current to maintain the dc voltage and the resultant generator acceleration is counteracted by pitch regulation. Compared with the conventional strategy, the with and without dc chopper, which is intended to assist the fault ride through of the WECS, can be eliminated if the proposed scheme is employed., the proposed strategy has quicker and more precise power responses, which is beneficial to the grid recovery The simulation results CHECK the effectiveness of proposed strategies. the power output of the permanent magnet synchronous generator (PMSG) of wind turbine systems. Index Terms—Active damping, grid fault, permanent magnetic synchronous generator (PMSG), power control, unbalanced voltage, wind energy conversion system (WECS). I. INTRODUCTION DURING the last decades, wind energy has grown rapidly and becomes the most competitive form of renewable energy. Among all kinds of wind energy conversion systems (WECSs), a variable speed wind turbine (WT) equipped with a multi pole permanent magnet synchronous generator (PMSG) is found to be very attractive and suitable for application in large wind farms [1], [2]. With gearless construction, such PMSG concept requires low maintenance, reduced losses and costs, and at the same time has high efficiency and good controllability. Currently, the PMSG-based WECS has been commercialized Fig. 1. Configuration of the PMSG-based WECS. By some WT manufactures, such as Siemens Power Generation and GE Energy, and its capacity can be as high as 3 MW. A typical configuration of the direct driven MW class PMSG based WECS is illustrated in Fig. 1 [3]–[5]. It consists of the mechanical system (aerodynamics, gearless drive train, and pitch angle control) and the electrical system (multi pole PMSG, full scale converter, and its control). The modelling and control of such a WECS have been widely discussed in the bibliography. Usually, the generator-side converter controls the power flow produced by the PMSG while the grid-side converter maintains the dc-link voltage to balance the input and output power [2]. Field-oriented control (FOC) and direct torque control are the most dominant strategies used in the generator side. The two strategies have similar dynamic responses and both of them allow separate control of the 3120 ISSN: 2278 – 7798 All Rights Reserved © 2015 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 9, September 2015 reactive and active current components (or flux and torque) of the generator [6]. In order to extract more power from the wind, the active current component (torque) is regulated so that the WECS tracks the maximum power point (MPP). The reactive current component can be controlled to zero in order to achieve the unity power factor operation of the PMSG. Alternatively, it can be regulated to maintain the stator voltage [7] or minimize the power loss of the generator [2]. The grid-side converter can also be controlled with FOC, in which the dq reference frame is usually aligned with the grid voltage vector [8]. Besides dc link voltage control, the grid-side converter can provide parts of reactive current (power) to the grid [9]. With increasing penetration of wind energy into the grid, the power system enforces more regulations on the grid integration of the WECSs [10]–[14]. These codes require the WECSs to behave more and more as the conventional power plants in the power system. One important rule is that the WECS should be able to stay operating during grid disturbances or faults and provide ancillary services in order to support the utility. In order to be compliant with the grid codes, additional measure, such as the dc chopper, is required to assist the system operation during grid disturbances [4], [15].With no more control effort, the dc chopper can dissipate the unbalanced power between the generator and the grid when grid fault happens. Considering the worst scenario (the grid voltage drops to zero), the power rating of the dc chopper should be full scale (in MW class) [15]. Such a strategy can hardly satisfy the requirements of some grid codes as will be shown in this paper. For the sake of eliminating the dc chopper, a variable structured controller is designed in [16] and [17]. Such controller varies the generator-side power control from the MPP tracking to the reduced power output when the grid fault is detected. Nevertheless, the controller cannot provide enough torsional damping for the WECS in some instances as denoted in [18]. To reserve the fault ride through (FRT) capability while obtaining enough torsional damping, a novel control strategy is proposed in [3] and [19]. Instead of controlling the active power flow, the generator-side converter is utilized to maintain the dc-link voltage while the grid-side converter is controlling the active power to the grid. Besides the power controller, additional active damping loop, consisting of a notch filter and a phase compensator, is designed to ensure a positive damping for the torsional vibration. As verified by the simulations in [19], such a strategy can successfully assist the FRT of the WECS during symmetrical grid faults. However, the strategy is complex and its performance relies on the system parameters. Moreover, such a solution can hardly be adaptive to the unsymmetrical grid faults scenario that is much more common in the power system. This paper proposes a unified power control strategy for the MW class PMSG based WECS operating under different grid conditions, including unsymmetrical grid faults. In the strategy, the generator side converter maintains the dc-link voltage, while providing inherent damping for the torsional oscillations. Compared with the conventional strategy, in the proposed strategy, the dc chopper can be eliminated. In comparison with the variable-structured control scheme, the proposed strategy can provide enough torsional damping for the WECS and has a quicker and more precise current (power) response during grid faults. Compared with the scheme in [19], no system parameter is required for the proposed strategy, which results in the simple implementation and good robustness. Moreover, the distortions of the current injected into the grid can be mitigated with the strategy so that the power quality is improved when unsymmetrical grid fault occurs. The simulation results verify the analyses and the effectiveness of the proposed strategy. II. SYSTEM MODELING AND ANALYSIS MW class multi pole PMSG-based WECS has relatively soft shafts [3]. The eigen frequency of the drive train is rather low and within the bandwidth that is normally taken into account in power system dynamic simulations [3], [20]. A multi mass model representation of the drive train is, therefore, essential in order to properly illustrate the dynamic impact of WTs on the grid. Although the three- or higher mass model can be used in the transient performance study of the WECS, the twomass model is accurate enough to yield acceptable results [20]. Because of no inherent damper in the conventional PMSG, the damping factor of the shaft is neglected. The mechanical system of the WECS can be expressed as follows [3], [21], [22]: where, ωh, ωg are the rotational speed of theWT and the generator; Jh, Jg are the turbine inertia and generator inertia, respectively; θ is the electrical angle of the shaft; K is the stiffness of the shaft; and Twt is the mechanical torque that can be expressed as Twt = KwCq v2 (2) 3121 ISSN: 2278 – 7798 All Rights Reserved © 2015 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 9, September 2015 The PMSG model can be expressed in the synchronous frame as follows, in which the d-axis is aligned to the generator rotor frame and the corresponding q-axis is 90◦ leading [23] ids =1/Ld vds – Rs/Ld ids + Lq/Lid npωg iqs iqs =1/Lq vqs − Rs/Lq iqs − Ld/Lq npωg ids – ψrnpωg/Lq Tg =1.5np [ψr iqs + (Ld − Lq ) ids iqs] (3) where Ld, Lq are d-, q-axis inductances, respectively; Rs is the resistance of the stator windings; vds, vqs, and ids, iqs are d-, q-axis voltages and currents, respectively ;ψr is the amplitude of the flux induced by the permanent magnets of the rotor in the stator phases; and np is the number of pole pairs. If the PMSG is assumed to have equal d-, q-axis inductances (Ld ≈ Lq ), the generator torque Tg is proportional to the q-axis current iqs. Because of huge inertias of the generator and turbine, the mechanical dynamics is much slower than the electrical ones. In the case, the electrical system can be simply modelled as follows: where Tg, T* g are the generator electrical torque and its reference; Xdc = 12 V 2 dc, Cdc, Vdc are the dc-link capacitance and voltage; Pout, P∗ out are the output power and its reference from the gridside converter; ts, t_ s is the equivalent time constants of the generator torque and grid side converter. By implementing the control structure in [2] and [19], the performance of the whole system can be evaluated based on its small-signal model deduced from (1), (2), and (4) [18]. As concluded in [18], resonance can be excited by mechanical or electrical load changes with either control structure, which will result in torsional vibrations and system instability. Strategies in [2] cannot provide enough damping for the WECS when the constant or smoothed power production is required. The active damping scheme presented in [3] needs to know the shaft resonant frequency and it is non effective if the WECS operates at power smoothing mode [18]. From the FRT capability point of view, the control structure in [19] is preferred because the active and reactive power in the grid side can be directly controlled. As a result, not only symmetrical, as in [19], but also unsymmetrical fault can be handled by the grid-side converter. The dc chopper can be substantially derated or eliminated and it is unnecessary to vary the controller structures when grid fault occurs. This results in a unified structure for the power control of the WECS. III. DESIGN OF THE UNIFIED POWER CONTROL FOR THE MW CLASS PMSGBASED WECS The increasing penetration of wind power in the utility leads to a continuous evolution of grid interconnection requirements. Basically, the WECSs are requested to operate robustly in different grid situations and to provide ancillary services in order to behave as a conventional power plant. The unified power control scheme for the MW class PMSG based WECS is designed to satisfy the grid requirements explained in this section. In the scheme, the generator-side converter is controlled to maintain a constant dc-link voltage and actively damp the torsional oscillation. The grid-side converter can regulate the positive- and negativesequence output power as required by the power system operator (PSO) under different grid conditions. If a grid fault happens, to keep the dclink voltage constant, the generator side converter control starts to reduce the generator power and thus the power flow to the dc link, by decreasing the stator current. The power surplus is buffered in kinetic energy of the large rotating masses and is reflected in the acceleration of the generator. The acceleration can be counteracted by the pitch control when the generator speed increases above its rated value. A. Controller Design of the Generator-Side Converter In the WECS, usually Jh >> Jg >> max(ts, t’s, Cdc), so the dynamic responses of the WECS can be classified into three time scales. Based on the singular perturbation theory, the slow and fast dynamics will not affect each other as they have different response time scale [24]. Therefore, the fast dynamic is supposed to be fast enough to converge to its steady state instantaneously when discussing the slow dynamic. Similarly, the slow dynamic is neglected in the study of fast dynamic. As a result, the control of the WECS can be designed based on the following three sub models: 3122 ISSN: 2278 – 7798 All Rights Reserved © 2015 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 9, September 2015 Dynamic model (9) will be stable if kh > 0. In (7), responses of Tg and Xdc are independent. Tg responses stably with a positive ts . Substituting (8) into (7) and ignoring the high-order items, if z = X* dc − Xdc, we have Dynamic model (10) is stable if kp > tski . Fig. 2. Torque characteristics of the WT. Based on the perturbation theory, the whole system can be stabilized by controller (8) if all the subsystems are stable or (11) holds true. The proposed scheme has inherent oscillation damping capability since the damping torque is provided with the generator speed feed forward in which X*dc = 1/2V *2dc , V * dc is the reference of the dc-link voltage and the symbols with superscript “-” represent the quasi-steady value of the state variables. Design the reference of the generator torque as T*g = kh (t) ωg (8) where kh (t) = _kp + ki _ _ (X*dc − Xdc) and kp, ki are the proportional and integral coefficients. The slowest model (5) behaves as a first-order system. Fig. 2 shows the typical torque characteristics of the WT. Considering the generator torque as Tg1 , the WECS has two possible steady operation points, in which point “B” is stable and “C” is unstable. Regarding ωg =  ̄ωg = ωh in (8), dynamics model (5) is stable if kh > ∂Twt/∂ωh . The conclusion can also be identified from the fact that there is unique cross point “B” between torque characteristic and line OB in Fig. 2. Model (6) is a second-order system and its transfer function with the control input (8) is as follows: Fig. 3. Control diagram of the generator-side converter. In order to behave as the first-order dynamic, the PMSG is controlled with vector control techniques [3]. By aligning the d-axis of the rotating reference frame on the rotor flux, the control of the generator torque and stator voltage can be decoupled. The control diagram of the generator-side converter is depicted in Fig. 3. The PI regulator of the dc-link voltage controller has upper and lower limits in order to satisfy (11). Equation (8) is the input of the vector controller and i* ds can be set to zero to avoid demagnetization of the permanent magnetic. The rotor flux angle θr for the frame transformation and the generator speed _ωg in (8) can be estimated based on the back electromotive force of the PMSG, which results in the sensor less implementation of the proposed scheme [25]. 3123 ISSN: 2278 – 7798 All Rights Reserved © 2015 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 9, September 2015 B. Controller Design of the Grid-Side Converter As the generator and grid are decoupled by the back-to-back converter, the grid disturbances would not affect the operation of the generator-side converter. The grid side converter should take the responsibility to keep the WECS running properly even with grid faults. In order to extract the symmetrical sinusoid currents from the WECS and improve the power quality during unsymmetrical grid faults, where · represents the dot product and × denotes the cross product; the symbols with superscript “+” represent the positive sequence variables. Since only positive-sequence powers are controlled in such a strategy, the currents injected into the grid only contain positive sequence components so that the current distortions are mitigated [27]. C. Design of the Pitch Controller Fig. 4. Control diagram of the grid-side converter. the positive-sequence active and reactive power are regulated in the proposed strategy. The control diagram is illustrated in Fig. 4. The control of the grid-side converter is also based on the vector control techniques, in which the rotating reference frame is aligned to the positive sequence grid voltage vector. The positive- and negativesequence components of the grid voltage can be separated with the second-order generalized integrator-based phase locked loop [26]. The angle of the positive-sequence grid voltage vector θ+ is then applied to the frame transformation and control. With such a strategy, the positive-sequence active and reactive powers of the grid-side converter, Pout,pos ,Qout,pos, can be controlled independently by the d-, q-axis currents id,g , iq,g. In Fig. 4, Pout,pos, Qout,pos, can be calculated with the following equations: The pitch control is activated once the generator speed increases above its rated value and the power extracted from the wind energy subsequently reduces. Due to the nonlinear aerodynamic characteristics of the WT, pitch angle control is quite difficult. Conventional linear controller cannot provide satisfactory performance in a wide wind speed range [28]. Controller with gain scheduling may be effective but the gains are hard to tune. In [28] and [29], the authors proposed a robust pitch controller based on inverse-system theory. The controller is simple to implement and is robust to the system parameter deviations. Fig. 5 shows its control diagram. It consists of an inverse-system based control block for the nominal system control and a robust compensator to mitigate the control error caused by the parameter deviations [28]. The controller is employed in the paper and the details can be found in [28]. IV. SIMULATION RESULTS The simulations are carried out in MATLAB/ Simulink to verify the aforementioned analysis and the effectiveness of the proposed strategy. The models of the MW class PMSG-based WECS shown in Fig. 1 are included in the simulations. The drive train is modelled as two-mass mechanical system as described in (1). The converter is modelled as a digital system with 1kHz switching frequency and 10-kHz sampling frequency. Parameters of the WECS for the simulations are listed in the Appendix. Fig. 5. Control diagram of the pitch angle. 3124 ISSN: 2278 – 7798 All Rights Reserved © 2015 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 9, September 2015 its dynamic will affect the reactive current response once the converter rating is reached. The active current control of strategy A is not as flexible as the other strategies since the generator-side converter always operates at the MPP. As a result, it cannot provide the reduced iq defined in Fig. 9 after t = 1.5 s, in contrast to the capability. Fig. 6. Wind speed profile. 4.1 Operation in Normal Grid situation Two control strategies, one is the conventional scheme in [2] and the other is the proposed scheme, are compared through simulations when the grid is normal. In both strategies, the grid side converter is controlled to operate at the unity power factor mode and output smoothed active power. A random wind with the profile shown in Fig. 6 is utilized in the simulation. The responses in terms of the gridside active and reactive power, dc-link voltage, generator torque, turbine, and generator speed are presented in Fig. 7. As shown in Fig. 7(a), the generator speed is oscillating at 2.01 Hz and the system tends to be unstable with the conventional scheme. In accordance with [18], the conventional scheme cannot provide enough damping for the WECS when the smoothed or constant power is produced. In contrast, the proposed scheme can actively damp the speed or power oscillations to improve the system stability. 4.2 Operation with Symmetrical Grid Faults The FRT capabilities of the following three control schemes during symmetrical grid voltage sags are compared in this section. Strategy A: the conventional scheme with and without dc chopper [2]. Strategy C: the proposed scheme without dc chopper scheme with and without dc chopper [17]. The “E-On Netz” voltage dip profile, shown in Fig. 8, is employed in the simulations. As requested, reactive current must be provided if the voltage dip is more than 10% of the rated value and no active current should be injected to the grid for voltage fewer than 0.5 per unit (pu) [11]. The resultant active and reactive current support during the fault is defined in Fig. 9. The wind speed remains 12 m/s during the fault and the simulation results are illustrated in Fig. 10. As shown in Fig. 10(a), the grid-side active and reactive current (iq , id ) controlled with the proposed strategy can track the profile defined in Fig. 9 very well. In contrast, strategies A and B can hardly provide satisfactory results because the active current (power) is indirectly controlled and Fig. 7. System responses under normal grid condition. (a) Conventional scheme. (b) Proposed scheme Fig. 8. Voltage drop profile from E-On Netz. 3125 ISSN: 2278 – 7798 All Rights Reserved © 2015 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 9, September 2015 Fig. 10.1 PMSG speed, torque and stator current parameters for TLG fault Conventional technique with and without chopper Fig. 9. Active and reactive current support in the event of grid fault defined in E.on code. strategies Aand B. In the generator side, strategy A outputs a constant maximal power while strategies B and C reduce the power extraction during the fault. The active power of PMSG (Pg ) responds quicker with strategy B in comparison with C because it is directly controlled. In contrast to strategy B, strategy C controls the dc-link voltage Vdc with the generator-side converter. Usually, the generator side has larger time constant than grid side. Due to this, slower response and larger fluctuations can be found in the dc-link voltage when strategy C is employed. In Fig. 10.2, the fullscale dc chopper is activated during the fault to consume the generator power in strategy A. The chopper can be eliminated in strategies A and C since the output power of the PMSG is actively reduced by the strategies during grid fault. The surplus power in the turbine is buffered in the rotating masses and the resultant generator acceleration is counteracted by the pitch control Conventional technique with and without Fig. 10.2 DC link capacitor voltage during DLG fault In Figure above shows plots of the power produced from the PMSG, , and the real and reactive power injected into the utility grid, and . chopper Conventional technique with and without chopper However, the average model provides significant savings in computational time com-pared to the other models. Proposed with chopper and without chopper 3126 ISSN: 2278 – 7798 All Rights Reserved © 2015 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 9, September 2015 Fig.10.3 generator parameters like speed, torque and current output waveforms with and without chopper circuit with TLG fault .proposed with chopper and without chopper In Fig 10.5 above, the full-scale dc chopper is activated during the fault to consume the generator power in strategy A. Fig.10.5 stator three phase voltage & current output waveforms with and without chopper circuit with TLG fault Hence the output power of the PMSG is actively reduced by the strategies during grid fault. The surplus power in the turbine is buffered in the rotating masses and the resultant generator acceleration is counteracted by the pitch control 4.3 Operation With Unsymmetrical Grid Faults Fig.10.4 DC capacitor voltage waveforms with and without chopper circuit with TLG fault Usually, unsymmetrical grid fault happens more often than the symmetrical faults. During unsymmetrical voltage sags, the negative-sequence voltage can lead to second-order harmonics in the injected currents. In addition to handling the overvoltage of the dc capacitor during the fault, additional efforts should be spent on mitigation of current harmonics. With the three strategies, the system responses during unsymmetrical grid faults are illustrated in Fig. 11. In the simulation, the wind speed remains at 12 m/s and a 150 ms phasephase short circuit is applied on the transmission line at t = 1 s, which results in 85% positivesequence voltage sags and 50% negativesequence voltage jump at the connection point of the WECS. The WECS is requested to produce 1 pu reactive currents and no active currents during the fault. 3127 ISSN: 2278 – 7798 All Rights Reserved © 2015 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 9, September 2015 Conventional technique with and without chopper Conventional technique with chopper and without chopper Fig. 10.8 PMSG speed, torque and stator current parameters for DLG fault Fig. 10.6 PMSG speed, torque and stator current parameters for SLG fault Conventional technique with chopper and without chopper Fig. 10.7 DC link capacitor voltage during SLG fault Conventional technique with chopper and without chopper Conventional technique with chopper and without chopper Fig 10.9 DC link capacitor voltage during SLG fault 3128 ISSN: 2278 – 7798 All Rights Reserved © 2015 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 9, September 2015 Proposed Control Scheme Without & With Chopper Fig.11.2 DC capacitor voltage waveforms with and without chopper circuit with SLG fault Fig.11 generator parameters like speed, torque and current output waveforms withand without chopper circuit with SLG fault Fig.11.3 Grid terminal three phase voltage & current output waveforms with and without chopper circuit with SLG fault Fig.11.1 Mechanical torque output waveforms with and without chopper circuit with SLG fault 3129 ISSN: 2278 – 7798 All Rights Reserved © 2015 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 9, September 2015 Fig.11.4 generator parameters like speed, torque and current output waveforms withand without chopper circuit with SLG fault Fig.11.6 stator three phase voltage & current output waveforms with and without chopper circuit with DLG fault Fig11.5 DC capacitor voltage waveforms with and without chopper circuit with DLG fault Fig 11.7 Grid terminal three phase voltage & current output waveforms with and without chopper circuit with DLG fault The direct and quadrature axis current waveforms without and with chopper are shown in Fig. 7.14. As denoted, the positive- and negative-sequence components Vabcg,pos, Vabcg,neg in the grid voltage Vabc,g can be separated successfully with the presented scheme. Because the power control is not designed on the positive-sequence synchronous frame, the output currents with strategies A and B are highly distorted in Fig.8.14. In contrast, strategy C results in sinusoidal and symmetrical grid currents even with the unsymmetrical grid fault. 3130 ISSN: 2278 – 7798 All Rights Reserved © 2015 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 9, September 2015 CONCLUSION The converter-based WECS has the potential to improve the transient stability of the power system because of its quickpower response. However, the rating of power devices limits its applications. In order to make maximal use of such systems, advanced control technique should be developed to satisfy the requirements of the power systems. The conventional control strategy for the PMSG-based WECSis mainly designed to promise the proper operation of the generator. In the strategy, the generator torque (power) is directly controlled while the grid side power is indirectly regulated. The disturbance at the generator side will aggravate the power responses at the grid side, which is not desired by the PSO. The basic idea of the proposed strategy is to first satisfy the power system requirements under different grid conditions. In the strategy, the active/reactive current (power) is directly regulated through the grid-side converter. In order to provide enough oscillation damping, additional active damping loop is integrated into the generator-side controller. Compared with the conventional or variable-structured control strategies, the proposed one has the quickest and most precise grid-side current(power) responses. During grid fault, no dc chopper or controller switching is necessary with the strategy and the current distortions can be mitigated when the unsymmetrical grid fault occurs. Moreover, the proposed strategy requires no system parameters and is simple to implement, which makes it attractive for the engineering practice. However, such a strategies sacrifices the response of the generator-side variables and leads to the fluctuation of the dc-link voltage. It is believed that a large dc-link capacitor can be helpful to improve the system performance if the proposed strategy is employed. APPENDIX PARAMETERS OF THE PMSG-BASED WECS Parameters of the WECS in the simulations are converted to a pu system and the real values can be derived by multiplying each pu value and the base value. The system base values are defined as follows [30]: where the variables with subscript “b” represent the base values; P, V, I, f are the power, voltage, current, and electrical frequency, respectively; Z,L,C are the impedance, inductance, and capacitance, respectively; ω,Ω are the electrical and mechanical angular frequencies, respectively; T is the torque; J,K are the inertia and stiffness, respectively; np is the pole pairs of PMSG; and ψr is the amplitude of the flux induced by the permanent magnets of the rotor. Base power Pb (MVA) 1.5 Base voltage Vb (V ) 690/√3 Base frequency fb (Hz) 11.5 Pole pairs of PMSG np 40 Nominal WT mechanical power (pu) 1.1 Nominal WT speed (pu) 1.2 WT inertia constant (pu) 4.8 PMSG inertia constant (pu) 0.5 Shaft stiffness (pu) 2 Rated generator torque (pu) 1 Rated generator power (pu) 1 Rated generator line voltage (pu) 1 Rated generator speed (pu) 1 Generator inductance in the d frame (pu) 0.7 Generator inductance in the q frame (pu) 0.7 Generator stator resistance (pu) 0.01 Flux of the permanent magnets (pu) 0.9 DC-link capacitance (pu) 1 Line inductance (pu) 0.1 Rate wind speed (m/s) 12 REFERENCES [1] M. Chinchilla, S. Arnaltes, and J. C. Burgos, “Control of permanent-magnet generators applied to variable-speed wind-energy systems con-nected to the grid, ”IEEE Trans. Energy Converse., vol. 21, no. 1, pp. 130– 135, Mar. 2006. [2] H. Polinder, F. F. A van der Pijl, and P. 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