IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL 29, NO 6, JUNE 2014 2837 An SRF-PLL-Based Sensorless Vector Control Using the Predictive Deadbeat Algorithm for the Direct-Driven Permanent Magnet Synchronous Generator Li Tong, Xudong Zou, ShuShuai Feng, Yu Chen, Student Member, IEEE, Yong Kang, Qingjun Huang, and Yanrun Huang Abstract—This paper proposes an enhanced sensorless vector control strategy using the predictive deadbeat algorithm for a direct-driven permanent magnet synchronous generator (PMSG) To derive favorable sensorless control performances, an enhanced predictive deadbeat algorithm is proposed First, the estimated back electromotive force (EMF), corrected by a cascade compensator, was put into a deadbeat controller in order to improve the system stability, while realize the null-error tracking of the stator current at the same time Subsequently, an advance prediction of the stator current based on the Luenberger algorithm was used to compensate the one-step-delay caused by digital control Maintaining the system stability, parameters of the controller were optimized based on discrete models in order to improve the dynamic responses and robustness against changes in generator parameters In such cases, the proposed methodology of synchronous rotating frame phase lock loop (SRF-PLL), which applies the estimated back EMF, can observe the rotor position angle and speed without encoders, realizing the flux orientation and speed feedback regulation Finally, the simulation and experimental results, based on a 10-kW PMSG-based direct-driven power generation system, are both shown to verify the effectiveness and feasibility of the proposed sensorless vector control strategy Index Terms—Cascade compensator, predictive deadbeat control, sensorless vector control, synchronous rotating frame phase lock loop (SRF-PLL) I INTRODUCTION IND energy, being abundant in exploitation and pollution free in application, is always regarded as the alternative energy [1]–[3] for traditional fossil energy in large-scale power generation At present, mainstream wind energy conversion systems (WECS) are based on the doubly fed or directdriven technology [4], [5] As is well known, doubly fed WECS W Manuscript received August 7, 2012; revised November 7, 2012, April 21, 2013, and June 14, 2013; accepted June 27, 2013 Date of current version January 29, 2014 This paper was supported in part by the National Natural Science Fund for Excellent Young Scholars under Grant 51322704, and in part by the National Basic Research Program (973) of China under Project: 2012CB215100 Recommended for publication by Associate Editor R Kennel The authors are with the State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology Wuhan, Hubei 430074, China (e-mail: tongli19860729@gmail.com; xdzou@mail.hust.edu.cn; 715293926@qq.com; ayu03@163.com; ykang@ mail.hust.edu.cn; 1016709676@qq.com; 37940352@qq.com) Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org Digital Object Identifier 10.1109/TPEL.2013.2272465 applies a lower rating converter for control actions, but costs a lot in mechanical maintenance, especially the gearbox Comparatively, the direct-driven WECS, which universally applies the low speed suited permanent magnet synchronous generator (PMSG) [6], not only saves the costly gearbox, but is more efficient, reliable, and has better adaptability to grid faults [7], [8] Therefore, it has a very good application prospect To realize high efficiency in power generation of the PMSG, an encoder or a resolver is often employed to provide accurate information on rotor position angle and speed for high-performance vector control However, continuously ascending power grade and generator size make the mechanical sensors difficult to be installed and easily disturbed by terrible working environments These drawbacks greatly depress the reliability of the generator set and can even affect the safety and stability of the whole system Therefore, it is of great theoretical and practical application to study the sensorless vector control technology for the PMSG [9]–[14] As to the sensorless vector-controlled PMSG, both the rotor position and speed information are mandatory for the flux orientation and speed feedback regulation To extract the rotor position and speed information, two types of technology have been proposed One is the high frequency signal injection method [9] It makes use of the salient-pole effect of the generator to achieve the sensorless observation, and thus, is available even when the rotor speed falls down to zero However, this method is only confined to salient-pole generators, and the control performances will be depressed by the additionally incurred high frequency signals The other is the back EMF-based observation method [10]–[13] It is based on the generator model, and presents excellent dynamic and static responses inherently The main drawback of this technology is that, it fails to satisfy the precision requirements in extremely low speeds; however, a practical WECS will be started only when its wind turbine has reached a certain speed (i.e., corresponding to a certain cut-in wind velocity), so the imprecision in low speeds could be ignored By taking this practical limitation into consideration, the back EMF-based observation methods would be a better choice for wind power generation Obviously, precision of the back EMF estimation, which largely relies on the model parameters of the generator and tracking performances of stator current, shows profound influences on the overall performance of the sensorless vector control In a 0885-8993 © 2013 IEEE Personal use is permitted, but republication/redistribution requires IEEE permission See http://www.ieee.org/publications standards/publications/rights/index.html for more information 2838 Fig IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL 29, NO 6, JUNE 2014 System topology structure of the PMSG-based direct-driven WECS digital control system, control delay caused by current sampling, duty ratio refreshing, deadband, and other relevant factors will greatly deteriorate the control performances [15]; while deviations of the applied generator model parameters might further aggravate the system performances [16] Therefore, enhanced schemes for stator current control are needed to mitigate the negative effects caused by control delay and parameter variation At present, main control schemes aiming for PMSG include hysteresis control, synchronous frame proportional–integral (PI) control, and predictive control The hysteresis control has advantages such as fast dynamic response and simple digital implementation [17], [18]; however, effective measures should be taken to suppress the large current errors incurred by the irregular PWM operations The synchronous frame PI control presents excellent static tracking performance irrespective of operation conditions; but, its poor dynamics due to bandwidth limitation degrades the stator current control performances, and thus, the further delay compensation is required [15], [19] In comparison, the predictive control methods, aiming to control stator current with high accuracy in a short transient interval, can provide better dynamic responses and improved current wave form with less harmonics The direct predictive control (DPC) in [13] and [20]–[24], which applies the minimized cost function to select one of the only seven converter switching configurations, presents fast dynamics and robust static tracking performances against external factors However, several inevitable limitations exist, for example, the lower the current ripple amplitude is required, the smaller sampling period must be selected, which raises a very high real-time constraint Alternatively, the deadbeat-based predictive control [22], [25]–[28], which relies on the generator model to calculate voltage references and then translates them into corresponding switching configurations through the space vector modulation (SVPWM), largely reduces its real-time constraints to exhibit similar excellent dynamics and better static tracking performances Unfortunately, the deadbeat control is absolutely dependent on exact generator model, and its poor adaptability to nonideal factors such as control delay and parameter variation would make the calculated voltage vectors deviate from their expected values To obtain a better performance of sensorless vector control, an enhanced predictive deadbeat control is proposed in this pa- per Based on the discrete mathematic model of the PMSG, stator voltage references are derived from the current controller, and are further employed to estimate the back EMF Then, the estimated back EMF is applied to the SRF-PLL model to observe the rotor position and speed Meanwhile, the estimated back EMF is also put into the deadbeat controller after cascaded compensation, aiming to achieve the stability improvement and null-error tracking of stator current Finally, an advance prediction of stator current based on the Luenberger algorithm is adopted to alleviate the one-step-delay effect and parameter tolerance lying in the whole calculation process To achieve these goals, the paper is arranged as follows The system structure and discrete modeling of the flux-oriented PMSG is described in Section II Then, the principle of SRF-PLL-based sensorless observation is presented in Section III, followed by illustrations of the proposed predictive deadbeat control algorithm in Section IV Finally, comprehensive simulation and experimental results from the 10-kW PMSG-based prototype are presented in Section V, to verify the validity and feasibility of the proposed sensorless control strategy in a direct-driven WECS II SYSTEM STRUCTURE AND MATHEMATICAL MODELING A System Topology Structure Fig shows the PMSG-based direct-driven WECS Here, the wind turbine is in straightforward connection with the PMSG (surface-mounted or interior type), and the full-scale back-toback converters coupled with the dc-link capacitors are established between the generator and grid The isolating switch K1 is turned ON only when the preset cut-in wind velocity being detected, and the generator side converter (GSC) is started to perform relevant control strategies for efficient wind energy capture In the meantime, the network side converter (NSC) that links to the power network through the LC filter and isolating transformer maintains the dc-link voltage constant, achieving the high-quality active power delivery and occasional reactive power compensation On condition that the dc-link voltage has been well regulated, this paper focuses on studying the sensorless control technology for the PMSG TONG et al.: SRF-PLL-BASED SENSORLESS VECTOR CONTROL USING THE PREDICTIVE DEADBEAT ALGORITHM 2839 B Discrete Modeling of the PMSG Usually, a high-performance vector control scheme for the PMSG needs to be implemented in the synchronously oriented rotating frame, which relates to the rotor position angle By taking the stator current vector as Is (t) = [Isd (t) Isq (t)]T , the back EMF vector as Es (t) = [Esd (t) –Esq (t)]T , and the stator voltage vector as ur (t) = [ur d (t) ur q (t)]T (where subscripts “d” and “q” represent orthogonal state variables in the corresponding reference frame), then, the oriented state-space model of the PMSG in continuous state can be expressed as follows (in motor convention): d Is (t) = A · Is (t) + B · [ur (t) − Es (t)] dt A= −Rs /Ld Lq ωr /Ld −Ld ωr /Lq −Rs /Lq , B= 1/Ld 0 1/Lq (1.1) (1.2) where ωr represents the real rotor electrical angular velocity; Rs is the stator-phase resistance, and Ld and Lq are the d-axis and q-axis synchronous inductance, respectively, whose values differ from each other on condition of an interior PMSG In the discrete case, the sampling delay td is always taken into consideration Take the stator current for instance, the expected data sampling Is (t) at time t, in fact, equals to the sampling value IA D (t + td ) at the time (t + td ), i.e., Is (t) = IA D (t + td ) Accordingly, the general solution of the state-space model (1) can lead to the continuous stator current as follows: Is (t) = IA D (t + td ) = eA ·(t+t d −t ) · IA D (t0 ) t+t d + eA ·(t+t d −τ ) · B · [ur (τ ) − Es (τ )] dτ (2) t0 By replacing t0 and t in (2) with t0 = (kTs + td ) and t = (k + 1)Ts , the stator current in the discrete state is derived as follows: Is (k + 1) = eA ·T s · Is (k) +B· (k +1)T s +t d ur (τ ) · dτ k T +t d −B· (k +1)T s +t d Es (τ ) · dτ (3) k T +t d where “k” represents the sampling site in discrete time, k = 1, 2, 3, ., n, and Ts is the sampling period; besides, Is [(k + 1)Ts ] and Is (kTs ) have been simply noted as Is (k + 1) and Is (k) In the synchronized reference frame, the back EMF vector Es could be approximated as constant in two consecutive sampling periods, while the stator voltage vector ur varies along with the time for performing control actions Hence (k +1)T s +t d Es (τ )dτ = Ts · Es (k) (4.1) k T s +t d (k +1)T s +t d ur (τ )dτ = (Ts − td ) · ur (k) + td · ur (k + 1) k T s +t d (4.2) Fig Space vector diagram with sensor-less observed and permanent flux oriented reference frames By substituting (4) into (3) and applying the Taylor series expansion, the generalized discrete state-space model for PMSG can be derived as shown next Is (k + 1) = G · Is (k) + H · Es (k) + H · [(1 − δ) · ur (k) + δ · ur (k + 1)] G= − Ts Rs /Ld Ts Lq ωr /Ld −Ts Ld ωr /Lq − Ts Rs /Lq ,H= (5.1) Ts /Ld 0 Ts /Lq (5.2) where “δ” is defined as the ratio between the time delay and sampling period, i.e., δ = td /Ts III SRF-PLL-BASED SENSORLESS OBSERVATION When applying the “zero d-axis stator current control scheme” to the permanent flux oriented PMSG, the direct proportional relation between its electromagnetic torque and q-axis stator current can be found This feature makes the control performance of the PMSG similar to that of the dc-motor In such a case, if the sensorless vector control is applied, the rotor position angel must be exactly observed for the flux orientation Fig shows the space vector diagram with the expected permanent flux ψf oriented γ–δ reference frame (dashed line) and the sensorless observed d–q reference frame (solid line), which are assigned to rotate at the electrical angular velocities of ωr and ωe , respectively, with reference to the stationary α − β frame In the figure, “θr ” and “θe ” represent the actual and observed rotor position angels, respectively Initially, there exists an error between θr and θe (i.e., Δθ = θr −θr =0) Since that Es∗ (the reference of back EMF) is aligned on the γ axis, its orthogonal projections in d–q reference frame can be noted as Esd and Esq Accordingly, when Δθ is small enough, it can be considered that Δθ = Esd According to Fig 2, we can modify the d–q reference frame to make the d-axis align to γ-axis, which means θe = θr , and Δθ converges to zero Since Δθ = Esd , Esd can be used as the indicator to justify whether the d and γ axes have been aligned together or not To this, Es (k), the estimation of the back EMF, must be calculated first Using (5) and taking δ = 0, Es (k) 2840 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL 29, NO 6, JUNE 2014 as ∗ (k) = Esd Ld ∗ I (k + 1) − Ts sd Ld − Rs Ts ∗ (k) Isd ∗ (k) − ur d (k) − ωe Lq Isq Fig Block diagram of the SRF-PLL-based sensor-less observation can be rewritten as −1 Es (k) = Jm · Is (k) − Hm · Is (k − 1) − ur (k) Jm = Ldm /Ts + Rsm ωe Ldm − ωe Lq m Lq m /Ts + Rsm , −1 = Hm (6.1) Ldm /Ts 0 Lq m /Ts (6.2) In (6.1), the stator voltage ur (k) can be replaced with the previous output of the current controller rather than sampling the PWM format voltages directly; while the coefficient matrix −1 in (6.2) are based on measured generator paJm and Hm rameters The subscript “m” is defined to indicate the deviation ratio between measured and actual parameters, i.e., m = Lm /L = Rsm /Rs Once Esd is calculated from (6), the SRF-PLL can be designed Fig presents the sensorless observation model which incorporates the SRF-PLL and the estimated back EMF As seen in this figure, Esd is fed back and compared to its reference E ∗ sd , while the estimation error ΔEsd is sent to the PI regulator to derive the compensation term Δω; meanwhile, the q-axis component Esq calculated from (6) is also used to derive the feed-forward term by using ωFeed (k) = Esq (k)/[Ldm Isd (k) + ψf ] (7) Accordingly, the observed rotor speed could be figured out, as shown in (8) ω(k) = KP [ΔEsd (k) − ΔEsd (k − 1)] + KI ΔEsd (k) + ωFeed (k) (8) where Kp and KI are the proportional and integral coefficients of the PI controller in SRF-PLL To avoid the negative effect of high-frequency noise, the observed rotor speed ω in (8) needs to be filtered by a low-pass filter (LPF) After that, the observation of the rotor position angle can be achieved by integrating ωe (k) as expressed in (9) θe (k) = Ts · ωe (k) + θe (k − 1) (9) With the properly designed PI regulator and LPF [13] (as shown in Fig 3), characteristic performances such as dynamic response, disturbance dependence, and other relevant behaviors of the proposed observation method can be effectively improved However, it must be emphasized that the observation errors are primarily determined by the precision of the back EMF estimation Supposing that both the permanent flux orientation and null-error tracking of the stator current have been exactly ∗ could be written achieved, the referenced d-axis back EMF Esd (10) where superscript “∗” represents the reference value of corresponding state variable Recall that Δθ = Esd when Δθ is small enough, subtract the ∗ in (10), estimated back EMF Esd in (6) from its reference Esd then, the approximated expression for the sensorless observation error ε can be expressed as ∗ (k) − Esd (k)] ≈ −m ε ∝ [Esd + Ld + Rs Ts Isd (k) mLd ∗ Isd (k − 1) − ωe Lq Isq (k) − mIsq (k) Ts (11) As seen in (11), there are two major factors that will affect ε, namely the deviation ratio of the generator parameters and the static tracking errors of stator current control Since the measured generator parameters are uncontrollable, we should focus on improving the current tracking performance so as to make Isd and Isq approach to their references as close as possible For this reason, the predictive deadbeat control, which has a better current tracking performance, will be discussed in the next section IV ANALYSIS AND DESIGN OF THE PREDICITVE DEADBEAT CONTROL ALGORITHM A Cascade Compensation The aim of applying the deadbeat algorithm here is to well control the stator current in the observed d−q reference frame, so that the sensorless vector-controlled PMSG can present favorable responses To so, the back EMF estimation Es (k) must be first solved according to (6), since that the actual back EMF can not be directly sampled −1 · Is (k − 1) − u∗r (k − 1) Es (k) = Jm · Is (k) − Hm (12) It is noted that the previous reference u∗r (k − 1) in (12) is used to replace the actual stator voltage ur (k) in (6) Then, the estimated back EMF Es (k) in (12) is applied in the deadbeat controller in (13), to achieve the null-error tracking of the stator current Accordingly, the stator voltage reference u∗r (k) in present kth sampling period can be calculated as follows: −1 −1 · Is∗ (k) − Hm Gm · Is (k) − Es (k) u∗r (k) = Hm (13) Equation (12) is calculated in the present kth sampling period, but lots of data sampling and calculation process will take up the most of time in the same kth period Therefore, the present calculation result u∗r (k) is always applied in the next sampling period (namely the “one-step-delay” control mode in digital control), to avoid incomplete control actions By doing so, the present stator voltage ur (k), which is generated by the GSC, is equal to the previous calculation result u∗r (k – 1) and can be TONG et al.: SRF-PLL-BASED SENSORLESS VECTOR CONTROL USING THE PREDICTIVE DEADBEAT ALGORITHM Fig Discrete block diagram of the dead-beat controlled system in observed d−q frame Fig Closed-loop characteristics of dead-beat control system with or without compensator (a) Maps of zeors and poles (b) Frequency response 2841 TABLE I MAIN PARAMETERS OF THE EXPERIMENT SYSTEM expressed as follows: −1 −1 · Is∗ (k − 1) − Hm Gm + Jm · Is (k − 1) ur (k) = Hm −1 + Hm · Is (k − 2) + u∗r (k − 2) (14) According to the control law (14) and the model (1), the discrete block diagram of the system can be drawn as Fig Obviously, (14) refers to the previous data information from the (k – 1)th and even (k – 2)th sampling period, and this may lead to potential stability problems To investigate the characteristic performances resulted by (14), seeFig Here, all the analysis is based on the measured generator parameters listed in Table I, and all these generator parameters are supposed to be accurately measured, i.e., m = 1.0 It is clearly seen that closed-loop poles of the system totally stay outside the unity circle, indicating system instability (see the poles denoted as “without compensation”) To avoid system instability, a compensator in (15) is employed in cascade with the back EMF estimation Es (k) to improve the system stability (see Fig 6) es (k) = a · es (k − 1) + b · Es (k − 1) (15) where “a” and “b” are the coefficients of the proposed cascade compensator With the cascade-compensation, the stator voltage reference u∗r (k) in Fig can be rewritten as follows: −1 −1 · Is∗ (k) − Hm Gm · Is (k) − es (k) u∗r (k) = Hm (16) For comparison, the characteristics after compensation are also shown in Fig From the figure, it can be found that the compensation effectively brings the unstable closed-loop poles back into the unity circle [see the poles denoted as “with compensation” in Fig 5(a)], leading to stability improvement Meanwhile, 2842 Fig IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL 29, NO 6, JUNE 2014 Discrete block diagram of the predictive deadbeat controlled system in observed d−q frame static performances of “unity gain and zero phase shift” [see the curve denoted as “with compensation” in Fig 5(b)] are derived and preserved, achieving the null-error tracking of the stator current However, it must be noted that these stable poles stay quite nearby the unity circle, which implicates poor dynamics and deficient stability margin against parameter changes Moreover, an unexpected resonance peak appears in the frequency responses [see Fig 5(b)] This resonance would probably invoke low-frequency oscillations in the stator current, resulting in severe torque ripples to make the PMSG terribly damaged B Luenberger-based Prediction According to the aforementioned analysis, it can be learned that the deadbeat control is quite sensitive to two factors: the time delay and the model parameters Since the parameter changes are unpredictable and unavoidable, it is of great necessity to further mitigate the effect of one-step control delay, which severely deteriorates the sensorless control performance Therefore, an advance prediction of the stator current based on the Luenberger algorithm is further proposed (see Fig 6) Is (k + 1) = (1 − D) · Is∗ (k) + D [2Is (k) − Is (k − 1)] (17) where “D” is defined as the predictive weight value, which is set to be in the range of [0, 1] By replacing the sampled stator current Is (k) in (16) with the predicted value Is (k + 1) in (17), the proposed predictive deadbeat control algorithm, which includes the back EMF estimation (13), cascade-compensation (15) and Luenberger prediction (17) can be finally expressed as follows: −1 u∗r (k) = Hm · [1 − Gm (1 − D)] Is∗ (k) − es (k) −1 − Hm Gm · D [2Is (k) − Is (k − 1)] (18) With a few mathematical manipulations, a fourth-order closedloop transfer function can be deduced Detailed derivation process is given in the Appendix And further ignore all the infinitely small terms, the simplified characteristic equation of the system can be rewritten as follows: λ(z) = a4 z + a3 z + a2 z + a1 z + a0 (19) where corresponding characteristic coefficients are set as: a4 = 1, a3 = –(1 + a), a2 = (2Dm + a − b), a1 = [b – (2 a + 1) Dm + bm], and a0 = (aDm – bm) It can be found that characteristic performances of the transfer function are mainly affected by two factors: the predictive weight value “D” and the deviation ration “m” (variation of the generator parameters) By using Jury’s criterion as the stability restriction, the stable and unstable regions of system, which depends on “D” and “m,” can be unveiled As shown in Fig 7(a), the shaded region clearly defines the accessible stability field of the predictive deadbeat control For a certain value of “D,” the acceptable variation range of “m” is different For example, when D = 0.1, it allows “m” varying from 0.0 to 5.2 and the system remains stable, while D = 0.3, the variation range of “m” is narrowed from 0.0 to 2.1 This implies that a smaller D ensures the system stability with a larger parameter tolerance However, a small D will also lead to slow system responses, which can be seen in Fig 7(b) It is found that when D is decreased, tracks of the dominated poles move toward the low bandwidth region (see pole tracks from “4” to “1”), leading to slower dynamics but enlarged stability margin against parameter changes (i.e., starting point of a pole track stays nearby the origin point and far from the unity circle) Therefore, optimization designs of the predictive weight value “D” must compromise both the dynamic responses and system robustness In a long-term power generation, variations in the generator parameters are absolutely unpredictable and unavoidable due to the external changing working environments However, it is generally accepted that the initial controller can be designed on basis of accurately measured parameters Accordingly, considering that a ±50% variation happens to the generator parameters, i.e., m = [0.5, 1.5], the value D = 0.3 is finally selected with several comparisons Then, the closed-loop frequency response with D = 0.3 is depicted in Fig Obviously, the frequency responses are hardly affected even when “m” is changed from 0.5 to 1.5, as shown in Fig 8, therefore, robust control performances have been achieved TONG et al.: SRF-PLL-BASED SENSORLESS VECTOR CONTROL USING THE PREDICTIVE DEADBEAT ALGORITHM 2843 Fig Closed-loop characteristics of the predictive deadbeat control system defined by “D” and “m.” (a) Accessible operation filed (b) Pole trajectories with varied “D.” Fig Closed-loop frequency responses in accordance to varied generator parameters V SIMULATION AND EXPERIMENTAL RESULTS A Description of the Experimental System To testify the proposed strategy, a 10-kW prototype of the direct-driven WECS as shown in Fig was developed (see Fig 9) In the system, a prime motor with exclusive speed regulating system is employed to drive the PMSG [see Fig 9(a)], and the back-to-back converters coupled by dc-link capacitors [see Fig 9(b)] are constructed for power delivery Main parameters of the GSC and PMSG are provided in Table I The 32-bit float-point digital signal processor (DSP) TMS320F28335 is adopted to perform the proposed control algorithms onto GSC and NSC As shown in Fig 10, the stator currents Isa and Isb are sensed for the purpose of control actions, and the control blocks of 1, 2, and have been well designed in Sections III and IV To further realize the sensorless speed regulation, the cascade-compensated back EMF esq (k) in (15) is used to calculate the applicable speed feedback Since this paper mainly focuses on sensorless observation and stator current control, the calculation is only explained in the Appendix, and the designs of sensorless speed control loop is not further discussed here Practically, references of the inner current loop ∗ should be generated by the outer speed loop for the purpose Isq of maximum power point tracking (MPPT) In addition, the 11-bit optical encoder is reserved as the reference for verifying the sensorless observation Fig Prototype of direct-driven WECS (a) Prime motor and PMSG (b) Back to back converters Fig 10 PMSG Principle block diagram of the sensor-less vector control strategy for 2844 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL 29, NO 6, JUNE 2014 Fig 12 Simulated results of the robustness test with varied model parameters: (a) m = 0.5 and (b) m = 1.5 Fig 11 Simulated performances of the sensor-less controlled PMSG: (a) Dynamic responses and (b) Static responses B Simulation Verification In a real direct-driven WECS, the speed of the PMSG should be regulated by the speed control loop But, the PMSG in our setup is driven by the prime motor, and its speed regulation absolutely depends on the external control system However, the system functions can still be verified by the following three steps of verification Step (Verification of the sensorless vector control): To testify the performance of sensorless orientation and stator current control, the isolating switch K1 (see Fig 1) remains disconnected initially, and the outer loop of speed feedback regulation is removed Besides, the rotor speed of the prime motor is set ∗ is set at the amplitude of A Under such at 50 r/min, and Isq conditions, the dynamic and static responses of the proposed control system are simulated (as shown in Fig 11) As seen in Fig 11(a), when the isolating switch K1 is turned ON, the PMSG is immediately started into the mode of power generation By applying the optimized predictive weight value (i.e., “D” = 0.3) and exact generator parameters (i.e., “m” = 1.0), the sensorless observed rotor position angle θe (blue line) quickly tracks its reference angel θr (solid line) after a transient regulation Meanwhile, the three-phase stator currents Isabc quickly reaches to their static states with nearly ignorable overshoots, indicating favorable dynamics of the predictive deadbeat algorithm Subsequently, with the rotor speed and torque current being increased to 100 r/min and 10 A amplitude, respectively, as shown in Fig 11(b), the static observed position angle θe coincides with θr , and the stator currents still remain in wonderful static waveforms with almost null tracking errors Step (Verification of the system robustness): Then, the simulation when m = 0.5 and m = 1.5 is performed to testify the system robustness As shown in Fig 12, the PMSG rotates at a fixed speed of 100 r/min, while its torque current reference Fig 13 PMSG Simulated speed regulation of the sensor-less vector controlled ∗ Isq is suddenly increased from to 10 A and then decreased to A again It can be seen that neither the dynamic nor static performances are influenced, except for slight deviations between θe and θr in the short transitions, indicating satisfactory robustness of the proposed control scheme Step (Verification of the speed feedback regulation): Finally, the speed feedback regulation is also performed to test the overall system performance, and corresponding simulation results are presented in Fig 13 When the speed references ωref increases from 30 to 150 r/min, the stator current IS A responds immediately and reaches to its limitations (±6 A peak value) rapidly to accelerate the process of speed regulation, while the TONG et al.: SRF-PLL-BASED SENSORLESS VECTOR CONTROL USING THE PREDICTIVE DEADBEAT ALGORITHM Fig 14 Fig 15 2845 Dynamic performances of sensor-less controlled PMSG Fig 16 Tracking errors of the stator current in d-q frame Fig 17 Lissajous figure of the observed back EMF in α − β frame Static performances of sensor-less controlled PMSG observed mechanical angular speed ωm e converges to the reference smoothly Furthermore, it is just due to the exact observation of the rotor position angle, the speed can be maintained at 150 r/min with the very small empty-load torque current Similarly, excellent sensorless control performances can also be found in the process of deceleration C Experimental Results The experiments under the same conditions as the simulations are also performed Here, the digital to analog chip was employed to acquire the encoder-generated and sensorless observed rotor position angels and speeds Similar to the “step 1” in the simulation, experimental verifications without the outer loop of speed feedback are shown in Figs 14 and 15 In comparison to Fig 11, similar excellent responses of the stator current control were derived In addition, static tracking errors of stator current in d–q frame and the Lissajous figure of the observed back EMF in α − β frame are also shown in Fig 15 As shown in Figs 16 and 17, both the small tracking errors (Isd err and Isq err ), which are no more than 0.1 A, and the approximated circle prove excellent performances of the proposed control scheme Subsequently, the robustness experiments as “step 2” in the simulation are performed As shown in Figs 18 and 19, similar robustness performance can be obtained with the optimized weight value “D = 0.3.” In Fig 20, the predictive weight value “D” is set at 0.5, and “m” is suddenly changed from 1.0 to 1.5 It can be seen that the state of “D = 0.5” and “m = 1.0”, which is located at point A in Fig 7(a), still maintain the system stable Once “m” is switched to 1.5, corresponding state moves into the unstable region (see point B in Fig 7(a)) Accordingly, the stator current, observed angle θe and its reference θr were all distorted, as shown in Fig 20 This result proves the relationship given in Fig 7(a), namely the increased value of “D” leads to a decreased tolerant range of parameter changes Without doubts, rationally compromised controller designs are required to satisfy practical applications Finally, the speed feedback regulation is also performed, as “step 3” in the simulation Here, the prime motor was stopped but still connected to the PMSG as a great inertia link, while the PMSG is adversely operated into the states of electromotion Fig 21 exhibits the comprehensive performances of the sensorless vector controlled PMSG in a speed regulation, where Ur A B , IS A , ωm e , and ωm r represent the stator voltage, stator current, the observed and the encoder-generated rotor mechanical angular speeds, respectively Apparently, stable speed feedback regulation is realized and similar regulating performances 2846 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL 29, NO 6, JUNE 2014 Fig 18 Robustness experiments: Dynamic performances by suddenly increased power generation (a) D = 0.3, m = 0.5 (b) D = 0.3, m = 1.5 Fig 19 Robustness experiments: Dynamic performances by suddenly decreased power generation (a) D = 0.3, m = 0.5 (b) D = 0.3, m = 1.5 Fig 20 Robustness experiments with increased predictive weight value “D.” Dynamic performances by suddenly increased model parameters “m.” Fig 21 Speed regulation of the sensor-less controlled PMSG 1—ω m r , rotor speed from encoder 2—IS A , stator current in Phase A 3—ω m e , observed rotor speed 4—U r A B , measured stator line voltage Fig 22 Transient performances in the acceleration as Fig 13 can be observed For details, short scopes of the two speed changing processes are also presented in Figs 22 and 23 Due to the nonperfect soft connection between the prime motor and the PMSG [see the shaft in Fig 9(a)], rotation of the prime motor slightly lags behind responses of the stator current; therefore, a small speed fluctuation appears in the transition Ignoring this, the overall performance is almost the same as the simulation, and satisfactory dynamic and static performances of the proposed control scheme are totally obtained To further present information for the concerned accuracy of speed tracking, errors of speed tracking and position observation during transient and steady states are shown in Figs 24 and 25, respectively In steady states (see periods “I” and “III”), the observed mechanical angular speed ωm e accurately follow its reference ωref , and the observed position angle θe maintains TONG et al.: SRF-PLL-BASED SENSORLESS VECTOR CONTROL USING THE PREDICTIVE DEADBEAT ALGORITHM 2847 clusions are summarized as follows: 1) The proposed methodology of SRF-PLL which applies the estimated back EMF can achieve fast observations of the rotor position and speed with satisfying accuracy; 2) With properly designed controller, the proposed control scheme based on predictive deadbeat algorithm allows the sensorless vector-controlled PMSG to present excellent dynamic and static performances, and satisfactory robustness against changes in the generator parameters; 3) The stable and accurate speed feedback regulation experiments on such a sensorless vector-controlled PMSG substantially verified its feasibility in practical direct-driven wind power generation Fig 23 APPENDIX Transient performances in the deceleration A Derivations of the Closed-Loop System Transfer Function By performing the “z transformation” on formulas (1), (6), (15), and (18), the generated z-formed transfer functions in the sensorless observed d–q reference frame are expressed as follows: z− 1− Ts R s Ld,q Isd,q (z) = + Fig 24 Accuracy of speed tracking for sensor-less speed regulation Esd,q (z) = ± Ts ur d,q (z) Ld,q Ts ˜ Ts ωe Lq ,d Esd,q (z) ± Isq ,d (z) (20) Ld,q Ld,q Ldm (1 − z −1 ) + Rsm Isd,q (z) Ts − ωe Lq ,dm Isq ,d (z) ∓ ur d,q (z) (z − a)esd,q (z) = bEsd,q (z) u∗r d,q (z) = Ld,q m − Ts −D (21) (22) Ld,q m − Rsm Ts Ld,q m − Rsm Ts ∗ (z) (1 − D) Isd,q (2 − z −1 )Isd,q (z) ∗ −1 ∓ ωe Lq ,dm (1−D)Isq ,d (z)+D(2 − z ) ×Isq ,d (z)]∓ esd,q (z) (23) Fig 25 Accuracy of position observation for sensor-less speed regulation identical to the actual encoder-generated position information θr In transient states (see period “II”), the speed tracking error ωerr presents similar convergence procedure as in the simulation Meanwhile, small position errors Δθ (less than 0.3 rad) appear in the transitions, but gradually decreases to zero along with the speed tracking procedure It can be learned that satisfying accuracy in the sensorless speed regulation is also ensured with the proposed control scheme VI CONCLUSION This paper proposes an enhanced sensorless vector control strategy for the PMSG in direct-driven WECS, and the main con- Then, substitutions of (20), (21), and (22) into (23) can result in the complete closed-loop transfer function of the discrete system (see Fig 6) as in (24), shown at the top of the next page Accordingly, the closed-loop characteristic equation could be attained as shown in (6) Equation (25), shown at the top of the next page B Calculation of Observed Speed Feedback Based on the measured permanent flux ψf , the sensorless observed rotor mechanical angular speed ωm e (k) for feedback regulation is derived as follows: ωm e (k) = esq (k) N · ψf where N is the number of pole pairs for the PMSG (26) 2848 ⎡ ⎢ ⎢ ⎢ ⎣ IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL 29, NO 6, JUNE 2014 z4 − + a − + b 1− Ts R s Ld,q = [m − m − ± Ts R s Ld,q z + 2Dm − Ts R s Ld,q − (2a + 1)Dm − Ts R s Ld,q +a 1− Ts R s Ld,q Ts R s Ld,q + bm + bm ⎤ − b z2 Ts Rs Ld,q z + aDm − Ts R s Ld,q − bm ⎥ ⎥ ⎥ Isd,q (z) ⎦ Ts ωe Lq ,d Ts ∗ ˜sd,q (z) m(1 − D)(z − az)Isq (z − az − bz)E ,d (z) ± Ld,q Ld,q ∗ (z) ∓ (1 − D)](z − az)Isd,q Ts ωe Lq ,d z − (a + 2mD) z + (2amD + mD + mb − b) z − amD Isq ,d (z) Ld,q ⎡ ⎢ λ(z) = ⎢ ⎣ z4 − + a − + b 1− Ts R s Ld,q Ts R s Ld,q z + 2Dm − Ts R s Ld,q − (2a + 1)Dm − Ts R s Ld,q REFERENCES [1] F Blaabjerg, M Liserre, and K Ma, “Power electronics converters for wind turbine systems,” IEEE Trans Ind Appl., vol 48, no 2, pp 708– 719, Mar 2012 [2] M Chinchilla, S Arnaltes, and J C Burgos, “Control of permanentmagnet generators applied to variable-speed wind-energy systems connected to the grid,” IEEE Trans Energy Convers., vol 21, no 1, pp 130– 135, Mar 2006 [3] F Blaabjerg, R Teodorescu, and M Liserre, “Overview of control and grid synchronization for distributed power generation systems,” IEEE Trans Ind Electron., vol 53, no 5, pp 1398–1409, Oct 2006 [4] R Teodorescu, M Liserre, and P Rodriguez, Grid Converters for photovoltaic and Wind Power Systems, 2nd ed New York, NY, USA: Wiley, 2011 [5] M Liserre, R Cardenas, and M Molinas, “Overview of multi-mw wind turbines and wind parks,” IEEE Trans Ind Electron., vol 58, no 4, pp 1081–1095, Apr 2011 [6] E Spooner and A C Williams, “Direct coupled permanent magnet generators for wind turbine applications,” IEE Proc Electron Power Appl., vol 143, no 1, pp 1–8, Mar 1996 [7] H Li and Z Chen, “Overview of different wind generator systems and their comparisons,” IET Renewable Power Generat., vol 2, no 2, pp 123–128, Jun 2008 [8] A.D Hansen and G Michale, “Multi-pole permanent magnet synchronous generator wind turbines’ grid support capability in uninterrupted operation during grid faults,” IET Renewable Power Generat., vol 3, no 3, pp 333– 348, Sep 2009 [9] N Bianchi, S Bolognai, and J H Jang, “Comparison of PM motor structures and sensorless control techniques for zero-speed rotor position detection,” IEEE Trans Ind Electron., vol 22, no 6, pp 2466–2475, Nov 2007 [10] M Boussak, “Implementation and experimental investigation of sensorless speed control with initial rotor position estimation for interior permanent magnet synchronous motor drive,” IEEE Trans Power Electron., vol 20, no 6, pp 1413–1422, Nov 2005 [11] W Qiao, X Yang, and X Gong, “Wind speed and rotor position sensorless control for direct-drive PMG wind turbines,” IEEE Trans Ind Electron., vol 48, no 1, pp 3–11, Jan 2012 [12] H Kim, J B Son, and J Y Lee, “A high-speed sliding-mode observer for the sensor-less speed control of PMSM,” IEEE Trans Ind Electron., vol 47, no 3, pp 1337–1343, Jan 2011 [13] M Prendl and E Schaltz, “Sensorless model predictive direct current control using novel second-order PLL observer for PMSM drive systems,” IEEE Trans Ind Electron., vol 58, no 9, pp 4087–4095, Sep 2011 [14] F Genduso, R Miceli, and C Rando, “Back EMF sensorless-control algorithm for high-dynamic performance PMSM,” IEEE Trans Ind Electron., vol 57, no 6, pp 2092–2100, Jun 2010 +a 1− Ts R s Ld,q + bm + bm (24) ⎤ − b z2 Ts Rs Ld,q z + aDm − Ts R s Ld,q − bm ⎥ ⎥ (25) ⎦ [15] T Senjyu, K Uezato, and T Funabashi, “An adaptive dead-time compensation strategy for voltage source inverter fed motor drives,” IEEE Trans Power Electron., vol 20, no 5, pp 1150–1160, Sep 2005 [16] M Hinkkanen, T Tuovinen, and L Harnefors, “A combined position and stator-resistance observer for salient PMSM drives: design and stability analysis,” IEEE Trans Power Electron., vol 27, no 2, pp 601–609, Feb 2012 [17] M Mohseni, S M Islam, and M A Masoum, “Enhanced hysterisis-based current regulators in vector control of DFIG wind turbines,” IEEE Trans Power Electron., vol 26, no 1, pp 223–234, Jan 2011 [18] C N.-M Ho, V S P Cheung, and H S.-H Chung, “Constant-frequency hysteresis current control of grid-connected VSI without bandwidth control,” IEEE Trans Power Electron., vol 24, no 11, pp 2484–2495, Nov 2009 [19] K H Kim and M J Youn, “A simple and robust digital current control technique of a PM synchronous motor using time delay control approach,” IEEE Trans Power Electron., vol 16, no 1, pp 72–82, Jan 2001 [20] M Rivera, A Wilson, and C A Rojas, “A comparative assessment of model predictive current control and space vector modulation in a direct matrix converter,” IEEE Trans Ind Electron., vol 60, no 2, pp 578–588, Feb 2013 [21] M Preindl, E Schaltz, and P Thogersen, “Switching frequency reduction using model predictive direct current control for high-power voltage source inverters,” IEEE Trans Ind Electron., vol 58, no 7, pp 2826–2835, Jun 2011 [22] F Morel, X F Lin-shi, and J M Retif, “A comparative study of predictive current control schemes for a permanent magnet synchronous machine drive,” IEEE Trans Ind Electron., vol 56, no 7, pp 2715–2728, Jul 2009 [23] P Cortes, M Kazmierkowski, and R Kennel, “Predictive control in power electronics and drives,” IEEE Trans Ind Electron., vol 55, no 12, pp 4312–4324, Dec 2008 [24] J Rodriguez, J Pontt, and C A Silva, “Predictive current control of a voltage source inverter,” IEEE Trans Ind Electron., vol 54, no 1, pp 495–503, Feb 2007 [25] J M E Huerta, J Castello, and R G Gil, “An adaptive robust predictive current control for three-phase grid-connected inverters,” IEEE Trans Ind Electron., vol 58, no 8, pp 3537–3546, Aug 2011 [26] J M E Huerta, J Castello, and R G Gil, “A synchronous reference frame robust predictive current control for three-phase grid-connected inverters,” IEEE Trans Ind Electron., vol 57, no 3, pp 954–962, Mar 2010 [27] J C Moreno, J M E Huerta, and R G Gil, “A robust predictive current control for three-phase grid-connected inverters,” IEEE Trans Ind Electron., vol 56, no 6, pp 1993–2004, Jun 2009 [28] L Malesani, P Mattavelli, and S Buso, “Robust dead-beat current control for PWM rectifiers and active filters,” IEEE Trans Ind Appl., vol 35, no 3, pp 954–962, May 1999 TONG et al.: SRF-PLL-BASED SENSORLESS VECTOR CONTROL USING THE PREDICTIVE DEADBEAT ALGORITHM Li Tong was born in JiangXi Province, China, in 1986 He received the B.S and M.S degrees in electrical and electronic engineering from the Huazhong University of Science and Technology, Wuhan, China, in 2007 and 2009 respectively, where he is currently working toward the Ph.D degree His main research interests include power electronic converters, control of electric machine, wind energy generation system, and power quality control Xudong Zou was born in Hunan Province, China, in1974 He received the Ph.D degree in electrical engineering from the Huazhong University of Science and Technology (HUST), Wuhan, China, in 2005 He is currently an Associate Professor in the Department of Applied Power Electronic Engineering, HUST His main research interests include the wind power generation system, flywheel energy, and power electronic converters ShuShuai Feng was born in Henan, China, in 1988 He received the B.S degree in electrical engineering from the Harbin Institute of Technology, Harbin, China, in 2010, and the M.S degree in power electronics and drive from the Huazhong University of Science and Technology, Wuhan, China, in 2013 Since 2013, he has worked as an R&D Engineer in 704 research institute of China Shipbuilding Industry Corporation, Shanghai, China His research interests include power electronic converters and renewable energy Yu Chen (S’09) received the B.E and Ph.D degrees in electrical and electronic engineering from the Huazhong University of Science and Technology, Wuhan, China, in 2006 and 2011, respectively From March 2008 to March 2009, he was an Intern in GE Global Research Center, Shanghai, China In September 2011, he joined the Huazhong University of Science and Technology as a Lecturer His research interests include the power electronic converter topologies, soft switching techniques, converter modeling, the fault diagnosis techniques, and the wind energy power-conversion system 2849 Yong Kang was born in Hubei Province, China, on October 16, 1965 He received the B.E M.E, and Ph.D degrees from the Huazhong University of Science and Technology, Wuhan China, in 1988, 1991, and 1994, respectively In 1994, he joined the Huazhong University of Science and Technology as a Lecturer and was promoted to Associate professor in 1996 and to Full Professor in 1998 He is currently the Head of the College of Electrical and Electronic Engineering, Huazhong University of Science and Technology He is the author of more than 60 technical papers His research interests include power electronic converter, ac drivers, electromagnetic compatibility, and their digital control techniques Qingjun Huang was born in Hubei Province, China, in 1984 He received the B.S the M.S degrees in electrical and electronic engineering from the Huazhong University of Science and Technology, Wuhan, China, in 2006 and 2011, respectively, where he is currently working toward the Ph.D degree His main research interests include power electronic converters, control of electric machine, and renewable energy generation system Yanrun Huang was born in Henan, China, in 1987 He received the B.S degree in electrical engineering from Northwestern Polytechnical University, Xi’an, China, in 2010, and the M.S degree in power electronics and drive from the Huazhong University of Science and Technology, Wuhan, China, in 2013 Since 2013, he has worked as an Electrical Engineer in Henan Electric Power Company, Zhengzhou, China His research interests include power electronic converters and renewable energy