IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL 1, NO 4, DECEMBER 2013 203 A Review on Position/Speed Sensorless Control for Permanent-Magnet Synchronous Machine-Based Wind Energy Conversion Systems Yue Zhao, Student Member, IEEE, Chun Wei, Student Member, IEEE, Zhe Zhang, Student Member, IEEE, and Wei Qiao, Senior Member, IEEE Abstract— Owing to the advantages of higher efficiency, greater reliability, and better grid compatibility, the directdrive permanent-magnet synchronous generator (PMSG)-based variable-speed wind energy conversion systems (WECSs) have drawn the highest attention from both academia and industry in the last few years Applying mechanical position/speed sensorless control to direct-drive PMSG-based WECSs will further reduce the cost and complexity, while enhancing the reliability and robustness of the WECSs This paper reviews the state-of-theart and highly applicable mechanical position/speed sensorless control schemes for PMSG-based variable-speed WECSs These include wind speed sensorless control schemes, generator rotor position and speed sensorless vector control schemes, and direct torque and direct power control schemes for a variety of directdrive PMSG-based WECSs Index Terms— Direct drive, permanent-magnet synchronous generator (PMSG), sensorless control, variable speed, wind energy conversion system (WECS) I I NTRODUCTION T HE total installed capacity of wind power is growing tremendously in the global market According to a report of the world wind energy association [1], the worldwide wind power installation has reached 254 GW by the end of June 2012 Among various wind energy conversion system (WECS) configurations, the doubly-fed induction generator (DFIG)-based variable-speed WECSs have been the dominant technology in the market since late 1990s [2] However, this situation has changed in the recent years with the development trend of WECSs toward larger power capacity, lower cost/kilowatt, increased power density, and the need for higher reliability More and more attention has been paid to direct-drive gearless WECS concepts Among different types of generators, the permanent-magnet synchronous generators (PMSGs) have been found to be superior owing to their advantages of higher efficiency, higher power density, Manuscript received June 1, 2013; accepted August 13, 2013 Date of publication September 4, 2013; date of current version October 29, 2013 This work was supported by the U.S National Science Foundation under Grant ECCS-0901218 Recommended for publication by Associate Editor Wenzhong Gao The authors are with the Department of Electrical Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588-0511 USA (e-mail: yue.zhao@ huskers.unl.edu; cwei@huskers.unl.edu; zhang.zhe@huskers.unl.edu; wqiao@ engr.unl.edu) 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/JESTPE.2013.2280572 lower maintenance costs, and better grid compatibility [3] The increased reliability and high performance make the direct-drive PMSG-based WECSs more attractive in multimegawatt offshore applications, where the WECSs are installed in harsh and less-accessible environments [3] Currently, there are a variety of commercial direct-drive PMSG-based WECSs in the market, with the power ratings ranging from hundreds of watts to MW [4], [5] Many wind turbine manufacturers, such as Vestas, Siemens Wind Power, GE Energy, Goldwind, etc have adopted the directdrive PMSG concept in their WECS products The variable-speed WECSs can be operated in the maximum power point tracking (MPPT) mode to extract the maximum energy from wind For this purpose, well-calibrated mechanical sensors, such as anemometers and encoders/resolvers, are indispensable to acquire the information of wind speed and generator rotor position/speed The use of mechanical sensors, however, increases the cost, hardware complexity, and failure rate of WECSs [6], [17] These problems can be solved by adopting position/speed sensorless control schemes With the development of advanced power electronics and microcontroller technologies, position/speed sensorless control for WECSs becomes feasible In the literature, a variety of optimal position/speed sensorless control strategies have been proposed for WECSs with different power electronic converters, leading to reduced production and maintenance costs, simple system design, and enhanced system robustness [8], [11]–[14] Moreover, much research effort in academia and industry has been devoted to sensorless control methods for motor drives [7], many of which are potentially applicable to WECSs This paper reviews position/speed sensorless control strategies for direct-drive PMSG-based WECSs Section II reviews the configurations of the commonly used power electronic conversion systems in direct-drive PMSG-based WECSs Section III reviews the state-of-the-art wind speed sensorless MPPT algorithms for direct-drive PMSG-based WECSs In Section IV, the rotor position/speed estimation methods for vector control of PMSGs are discussed Section V discusses the application of inherent motion-sensorless direct torque control (DTC) and direct power control (DPC) for position/speed sensorless control of direct-drive PMSG-based WECSs The challenges and future trends of position/speed sensorless control for direct-drive PMSG-based WECs are discussed in Section VI Section VII concludes this paper 2168-6777 © 2013 IEEE 204 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL 1, NO 4, DECEMBER 2013 Fig Schematic diagram of a direct-drive PMSG-based WECS connected to a grid or local load Fig Direct-drive PMSG-based WECS with a two-level back-to-back PWM converter system Fig Direct-drive PMSG-based WECS with a three-level NPC back-toback converter system Fig Direct-drive PMSG-based WECS with an MSC consisting of a diode rectifier and a boost converter II C OMMONLY U SED P OWER E LECTRONIC C ONVERSION S YSTEMS IN D IRECT-D RIVE PMSG-BASED WECSs Multipole low-speed PMSGs are the most commonly used generators in direct-drive variable-speed WECSs [9] To control the PMSG and regulate the frequency and voltage amplitude of the generated electricity to meet the grid code compliance requirements, full-scale power electronic converters are commonly adopted as the interface between the PMSG-based WECS and the power grid Fig shows the schematic diagram of a typical direct-drive PMSG-based WECS connected to a grid or local load, where the power electronic conversion system consists of an ac/dc rectifier, i.e., the machine-side converter (MSC), a dc link, and a dc/ac inverter, i.e., the grid-side inverter (GSI) The MSC is used to regulate the ac output power of the PMSG with variable voltage amplitude and frequency into dc power In addition, the MSC should have the capability of adjusting the current and torque of the PMSG to achieve shaft speed, power, or torque control for the PMSG The main function of the GSI is to maintain a constant dc-link voltage, control the reactive power that the WECS exchanges with the grid, and synchronize the ac power generated by the WECS with the power grid A variety of power converter topologies have been used in PMSG-based WECSs In this paper, the sensorless control schemes are reviewed for the power electronic conversion systems that have been well developed and widely adopted by wind turbine manufactures There are mainly three power converter topologies in the literature for the MSC: 1) an uncontrolled diode rectifier cascaded with a boost converter; 2) a fully-controlled two-level pulsewidth modulated (PWM) rectifier; and 3) a multilevel converter [9] The WECS with a diode rectifier and a boost converter, as shown in Fig 2, is renowned for its simple structure and low cost [10] The magnitude of the regulated dc output voltage of the diode rectifier is approximately proportional to the rotor speed of the PMSG [11] The functions of the boost converter are to step up and stabilize the dc voltage of the diode rectifier for the GSI as well as to regulate the rectifier/generator currents for MPPT control of the WECS Because the diode rectifier is a naturally commutated power converter, the voltages and currents of the PMSG cannot be fully controlled Therefore, the WECS equipped with such a converter system inherently does not need rotor position/speed sensors [12]–[14] Therefore, the main issue for sensorless control of this type of WECS is the MPPT control without wind speed measurements A detailed discussion on this aspect will be presented in Section III In a direct-drive WECS, if the power electronic converters consist of fully controllable switching devices, e.g., insulatedgate bipolar transistors and integrated gate-commutated thyristors, as shown in Fig 3, the speed, terminal voltage, and electromagnetic torque of the PMSG can be completely regulated, leading to improved control flexibility and generation efficiency and reduced torque ripples and current harmonics [3], [9], [12] when compared with the WECS in Fig The cost to achieve these advantages is that the precise information of the rotor position/speed is needed Fig shows a WECS equipped with two fully rated, twolevel, PWM converters connected back to back via a dc link This is the most frequently used power converter topology in variable-speed WECSs [9] Fig shows a WECS with two three-level, neutral-point clamped (NPC), PWM converters connected back to back via a dc link This configuration is primarily used in medium-voltage and high-power WECSs [3], [9], [16] Several manufacturers have released products based on this power converter topology [12], [15] The rotor position/speed sensorless control for the WECSs in Figs and will be specifically discussed in Sections IV and V III W IND S PEED S ENSORLESS C ONTROL According to the aerodynamic model of a wind turbine, the mechanical power Pm captured by the wind turbine from wind can be expressed as Pm = ρ Ar v ω3 C p (λ, β) (1) ZHAO et al.: REVIEW ON POSITION/SPEED SENSORLESS CONTROL 205 Fig Typical wind turbine torque-shaft speed characteristic curves for different wind speeds and the OT curve where ρ is the air density, Ar is the area swept by the blades, v ω is the wind speed, C p is the turbine power coefficient, β is the turbine blade pitch angle, and λ is the tip-speed ratio (TSR), which is defined by λ= ωt R vω (2) where ωt is the turbine shaft speed and R is the radius of the wind turbine rotor plane Normally, if β is fixed, there is an optimal value λopt at which the turbine will extract the maximum power from wind The purpose of sensorless MPPT algorithms is to control the shaft speed of the wind turbine so as to maintain the optimal TSR without the knowledge of wind speed The existing wind speed sensorless MPPT control methods can be mainly classified into the following five categories: 1) optimal torque (OT) control; 2) power signal feedback (PSF) control; 3) perturbation and observation (P&O) control; 4) wind speed estimation (WSE)-based control; and 5) fuzzy logic (FL) control [18], [19] A OT Control The principle of this method is to adjust the torque of the PMSG according to an optimal reference torque curve or lookup table, which is obtained through experimental tests [20]–[22] This method has been used in some disclosed patents of General Electric company for MPPT control of WECSs [23], [24] The maximum power that a wind turbine can extract from wind can be expressed by Pmax = R C p max ρ Ar ωt = K opt ωt3 λ3opt (3) where C pmax is the maximum power coefficient, which is obtained when the TSR is at the optimal value λopt According to Pm = ωt · Tm , the OT Topt of the wind turbine can be expressed as follows: Topt = ρ Ar R3 C p max ωt λopt = K opt ωt2 (4) The WECS can be operated in the torque control mode with an optimal reference torque signal obtained from (4) using the Fig Typical wind turbine power-shaft speed characteristic curves for different wind speeds and the optimal power curve measured or estimated turbine shaft speed signal Fig shows typical wind turbine torque–shaft speed characteristic curves and the OT curve for a WECS Although this control method is widely used in WECSs because of its simplicity, fast response, and high efficiency, it requires the information of air density and turbine mechanical parameters, which vary in different systems Moreover, the OT curve, which is mainly obtained via field tests, will change when the system ages This will affect the MPPT efficiency B PSF Control Fig shows typical wind turbine power–shaft speed characteristic curves According to (3), the curve of the maximum wind turbine power versus shaft speed (i.e., the optimal power curve) can be obtained and is shown in Fig as well Unlike the OT control, in the PSF control, the turbine shaft speed is measured or estimated to obtain the optimal power reference for the MPPT control during operation Some variations of this method have been proposed for PMSG-based WECSs In [25], the curves of the maximum electrical output power versus turbine shaft speed were obtained via field tests and applied for MPPT control of the WECS In [26], a MPPT method was proposed for a WECS using a diode rectifier (Fig 2) The maximum dc-side electrical power of the diode rectifier at a given wind speed is proportional to the cube of the dc-link voltage, and this maximum power versus dc voltage characteristic was stored in a lookup table for the real-time MPPT control A similar method was disclosed in a patent [27] In [28], an inverse method was used, in which the electrical output power was measured, and then the optimal turbine shaft speed reference was obtained from the optimal power curve for the MPPT control The stability analysis of the PSF control method in [21] was conducted in [29] It concluded that the PSF control method would provide robust and cost-effective MPPT control for WECSs C P&O Control The P&O method, also known as the hill-climb search (HCS) method, does not require any prior knowledge of the system and is totally independent of wind speed information and wind turbine characteristics [30] Therefore, it has been widely used in WECSs to search for the MPP [11], [31]–[33] 206 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL 1, NO 4, DECEMBER 2013 During the search process, the command of the generator rotor speed ω is continuously adjusted by a constant increment or decrement of dω in each step This will lead to a variation of the output electrical power Pe by dPe If dPe /dω > 0, the rotor speed keeps increasing and vice versa if dPe /dω < Obviously, this method works well if the wind speed changes slowly and the increment dω is small In real-world applications, it may, however, fail to reach the MPP under rapidly changing wind conditions because of the large inertia of the wind turbines In addition, it is difficult to choose a suitable step size because a large step size leads to a faster response but inevitable oscillation around the MPP, whereas a small step size improves the MPP accuracy but reduces the speed of convergence Moreover, a fast wind speed variation always causes the rotor speed changing in a wrong direction Several advanced HCS-based MPPT control methods have been proposed for PMSG-based WECSs to improve the efficiency and mitigate or eliminate the aforementioned problems of the conventional P&O method In [31], a MPPT control method was proposed for the WECS shown in Fig The MPPT process is based on monitoring the output power of the generator and then directly adjusting the duty cycle of the dc–dc boost converter according to the result of comparison between two successive output power values The control law has been implemented based on the following principle: Dk = Dk−1 + Dk−1 Fig GRBFN-based WSE algorithm the optimal power curve corresponding to the current output power at the step k, and γ is a positive-definite gain Some of the methods combined the HCS algorithm and PSF control In [33], the data of MPP versus dc-link voltage were recorded and stored during the training process of an advanced HCS Then, the recorded data were used to generate a lookup table, which was used for fast MPPT execution In [11], a P&O method was used to search for the MPPs in the training mode of operation to obtain the optimal relationship (Idc-opt = K opt Vdc-opt ) of the output dc voltage Vdc-opt and current Idc-opt of the MSC shown in Fig Then, the WECS was controlled based on this optimal relationship (5) Dk−1 = C1 · sgn( Dk−2 ) · sgn(Pin,k−1 − Pin,k−2 ) (6) where k is the time index, D is the duty cycle, D is the change of the duty cycle; Pin is the input power value of the boost converter; C1 is a constant determining the convergence rate and accuracy of the algorithm, and sgn(·) is the signum function This method results in a better exploitation of wind energy, especially in the low wind speed range A similar MPPT method, which adjusts the duty cycle of a power converter, can be found in [34] Reference [32] proposed a novel solution to the problems of the conventional HCS algorithm It not only improves the tracking speed and accuracy but also ensures that the HCS always searches in the correct direction during wind speed variations This algorithm assumes that a wind turbine has a unique optimal power curve, as given by (3) During normal hill climbing, the K opt in (3) can be determined by measuring the corresponding output power and rotor speed of the PMSG when a MPP is detected Once the value of K opt is obtained, the optimal power curve will be used as a reference for determining the step size and the direction of the next perturbation For example, if the operating point lies on the right to the optimal power curve, the next perturbation will be decreasing ω in getting closer to the optimal power curve In addition, the step size of perturbation can be determined according to the distance between the operating point and the optimal power curve The control law can be formulated as follows: ∗ d(k + 1) = γ · [ω(k) − ω (k)] (7) where d(k + 1) is the duty ratio at step k + 1, ω(k) is the generator rotor speed at step k, ω∗ (k) is the abscissa of D WSE-Based Control In the traditional TSR control, the generator rotor speed reference is adjusted to follow the measured variable wind speed to maintain the TSR expressed by (2) at its optimal value, so as to ensure the maximum output power from the wind turbine In the WSE-based control, the wind speed is estimated and used to compute the optimal rotor speed command from the optimal TSR [6] The estimated wind speed can also be used to compute the optimal power command based on (1), where the wind turbine mechanical power can be estimated using the measured electrical output power and estimated shaft mechanical power losses [35] The generated optimal rotor speed/power command is then applied to the rotor speed/power control loop of the WECS control system Different WSE methods have been proposed using the growing neural gas network [36], support-vector regression [37], backpropagation network [38], Gaussian radial basis function network (GRBFN) [39], and echo state network [40] Fig shows a three-layer GRBFN used to provide a static nonlinear inverse mapping of the wind turbine aerodynamic model (1) to estimate the wind speed The overall input–output mapping for the GRBFN is given by h vˆw = b + v j exp − j =1 x − Cj σ j2 (8) where x = [Pm , ωt , β] is the input vector; C j R n and σ j R are the center and width of the j th RBF unit in the hidden layer, respectively, h is the number of RBF units, b and v j are the bias term and weight between the hidden and output layers, respectively, and vˆw is the estimated wind speed The turbine ZHAO et al.: REVIEW ON POSITION/SPEED SENSORLESS CONTROL 207 TABLE I C OMPARISON OF D IFFERENT W IND S PEED S ENSORLESS MPPT A LGORITHMS [9], [16], [17] ωe mechanical power Pm can be estimated from the measured electrical output power; the turbine shaft speed ωt can be either measured using sensors or estimated; the blade pitch angle β always remains constant in the MPPT region The parameters of the GRBFN are determined by an offline training process using a training data set generated from the WECS dynamic characteristics [6], [63] or an online training process using the data generated from a P&O method [65] Once trained, the parameters of the GRBFN are then fixed for real-time WSE θ re Fig E FL Control The FL control has been proved to be effective in MPPT applications without the knowledge of wind turbine characteristics and wind speed [41]–[44] It has the advantages of a universal control algorithm, fast convergence, insensitive parameters, and good immunity to noise and inaccurate signals [41] The fast convergence is achieved by adaptively decreasing the step size during the search process With the information of the increment/decrement of the generator rotor speed ω∗ , the corresponding increment/decrement of the electrical output power Pe of the generator is estimated If both Pe and ω∗ are positive, the search continues in the same direction On the other hand, if a positive ω∗ leads to a negative Pe , the direction of search reverses The Pe and ω∗ in the current step and ω∗ in the last step are described by triangular membership functions in the fuzzification stage, and then, a control law is produced based on a rule table, which finally generates a generator speed command signal after defuzzification In [42], a Takagi–Sugeno–Kang (TSK) fuzzy model was designed for wind speed sensorless MPPT based on a combination of a fuzzy clustering method, a genetic algorithm, and a recursive least-square optimization method The TSK fuzzy controller uses the measured rotor speed and electrical output power of the generator as two inputs and outputs the maximum power command signal This model has a high computational speed, low memory occupancy, and learning and fault-tolerance capability Table I compares the wind speed sensorless MPPT control algorithms discussed in this section IV ROTOR P OSITION /S PEED S ENSORLESS V ECTOR C ONTROL FOR PMSGs Definitions of coordinate reference frames for PMSG modeling these reference frames are shown in Fig The dynamical model of a generic three-phase PMSG can be written in the synchronously rotating dq reference frame as follows: ⎧ d ⎪ ⎨ v d = Rs i d + L d i d − ωe L q i q dt (9) ⎪ ⎩ v q = Rs i q + L q d i q + ωe L d i d + ωe ψm dt where v q and v d are the q- and d-axis stator terminal voltages, respectively, i q and i d are the q- and d-axis stator currents, respectively, L q and L d are the q- and d-axis inductances, respectively, ψm is the flux linkage generated by the permanent magnets, Rs is the resistance of the stator windings, and ωe is the electrical angular velocity of the rotor The q- and d-axis flux linkages of the PMSG, ψq and ψd , can be expressed as follows: ψd = L d i d + ψm ψq = L q i q The electromagnetic torque Te can be calculated by (11) Te = po ψm i q + (L d − L q )i d i q where po is the number of pole pairs The output electrical power can be calculated by Pe = (v q i q + v d i d ) (12) Using the inverse Park transformation, the dynamics of the PMSG can be modeled in the αβ stationary reference frame as follows: d iα vα L sin θre L + L cos(2θre ) = · vβ L sin θre L − L cos(2θre ) dt i β A Modeling of PMSGs and Problem Description A PMSG can be modeled using phase abc quantities Through proper coordinate transformations, the PMSG models in the dq rotating reference frame and the αβ stationary reference frame can be obtained The relationships among (10) +Rs iα iβ + K e · ωe · − sin θre cos θre (13) where θre is the rotor position angle, v α and v β are the α- and β-axis stator voltages, respectively, i α and i β are the 208 Fig IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL 1, NO 4, DECEMBER 2013 Position/speed estimation schemes for PMSGs based on fundamental-frequency model α- and β-axis stator currents, respectively, K e is the back electromotive force (EMF) constant, L = (L d + L q )/2, and L = (L d − L q )/2 If the saliency of the PMSG can be ignored, i.e., L d = L q , then L will be zero, and (13) can be further simplified as follows: ⎧ d ⎪ ⎨ v α = Rs i α + L i α − K e ωe sin θre dt (14) ⎪ ⎩ v = R i + L d i + K ω cos θ β s β β e e re dt If the rotor saliency, however, cannot be ignored, i.e., L d = L q , the dynamic analysis performed in the αβ stationary reference frame using (13) will be complex The dynamic model of a PMSG in the dq reference frame rotating synchronously with the rotor magnet flux can be expressed as (9), which shows how to control the current components by means of the applied voltage components through a vector control scheme for a PMSG-based WECS equipped with an active rectifier (Figs and 4) The reference values for the rectifier ac-side voltage vector can be generated using two independent proportional-integral (PI) current controllers with feedforward voltage compensation [45] The vector control requires the measurements of the stator currents, dc-bus voltage, and rotor position [46] In the conventional vector control for PMSGs, the rotor position is measured by electromechanical or optical position sensors The use of these sensors, however, increases the cost, size, weight, and hardware wiring complexity of the PMSG vector control system From the viewpoint of system reliability, mounting position sensors on rotor shafts will degrade mechanical robustness of the PMSGs As for WECS applications, because low-cost, reliable, and compact systems are always desired, the elimination of position/speed sensors is desired During the last decades, to overcome the drawbacks of sensor-based motor drives, much research effort has gone into the development of sensorless motor drives that have comparable dynamic performance with sensor-based motor drives Many position sensorless control schemes have been developed for permanent-magnet synchronous machines (PMSMs) used in applications such as electric-drive vehicles, home appliances, and etc Although little work has been reported on position sensorless vector control for PMSG-based WECSs, the methods developed for other industrial sensorless PMSM drives can be well transferred into the PMSG-based WECS applications Position sensorless vector control for the PMSGs used in direct-drive WECSs could be easier than those in other industrial applications because of several factors First, the difference between the d- and q-axis inductances of the PMSGs used in direct-drive WECSs is usually small Sensorless control of a nonsalient-pole PMSG is much easier than that of a PMSM with large saliency in the medium- and high-speed range Second, the operating ranges for the PMSGs used in WECSs are relatively limited and rarely reach the flux-weakening region Moreover, different from the PMSM applications, such as traction motors in electric-drive vehicles, in a WECS, the rotating speed of the PMSG is usually relatively stable and a large abrupt torque/speed change rarely happens This section reviews rotor position/speed estimation schemes applicable for PMSG vector control systems Some of these schemes have already been investigated for position sensorless control of PMSG-based WECSs Considering the operating range of a PMSG-based WECS, e.g., no power generation below the cut-in wind speed, this review mainly focuses on the medium- and high-speed ranges In this speed region, the methods based on the fundamental-frequency PMSG models are commonly used for rotor position and speed estimation Those methods can be generally grouped into two categories: 1) open-loop calculation and 2) closedloop observers, as shown in Fig Per previous discussion, the difference between d- and q-axis inductances is small for the PMSGs in wind applications Therefore, in this section, rotor position/speed estimation methods are discussed based on (14) In recent years, salient-pole PMSMs, e.g., interior PMSMs (IPMSMs) [47], [48], were also proposed for wind applications Using reconstructed machine models, e.g., the extended EMF model [49] and the active flux model [50], a salient-pole PMSM model can be converted into a model similar to a nonsalient-pole PMSM Therefore, the methods ZHAO et al.: REVIEW ON POSITION/SPEED SENSORLESS CONTROL 209 discussed in this section can also be applied to salient-pole PMSMs L sa = B Open-Loop Calculation The open-loop rotor position/speed estimation methods behave like real-time dynamic models of the PMSGs to receive the same control inputs as for the PMSGs and run in parallel with the PMSGs With the dynamic model of a PMSG, the states of interest, e.g., EMF, flux, and winding inductance, can be calculated, from which the rotor position and speed information can be extracted 1) Flux Linkage-Based Methods [51], [52]: At steady state where diα /dt ≈ and diβ /dt ≈ 0, the stator and rotor flux vectors rotate synchronously Therefore, if the position angle of the stator flux can be calculated, the rotor flux angle can also be determined, which is the same as the rotor position angle According to (14), the voltage and current components in the stationary reference frame can be used to compute the stator and rotor flux linkages as follows: ψsα = ψsβ = a-phase resistance, and ea is the a-phase back EMF According to (16), L sa can be calculated as follows: (v α − Rs i α )dt v β − Rs i β dt and ψrα = ψsα − Li α ψrβ = ψsβ − Li β (15) where ψsα and ψsβ are the α- and β-axis stator flux linkages, respectively, and ψrα and ψrβ are the α- and β-axis rotor flux linkages, respectively Then, the rotor position can be calculated as θre = tan−1 (ψrβ /ψrα ) The accuracy of the fluxbased methods highly depends on the quality and accuracy of the voltage and current measurements Since integrators are needed in this method, the initial condition of the integration and integration drift are the problems that should be properly handled In addition, this method may work well in the steady state, but the transient performance is usually unsatisfactory Similar methods, called flux observers, were proposed in [53] and [54] for position sensorless control of PMSGs in WECSs, where phase-locked loops (PLLs) were used to extract the position information from the estimated rotor flux 2) Inductance-Based Methods [56]: The basic idea of this type of methods is that the spatial distribution of the phase inductance of a PMSG, especially the PMSG with a high saliency ratio, is a function of the rotor position The phase inductance can be calculated from the measured voltages and currents Then, the rotor position can be estimated from the calculated phase inductance using a lookup table In a PMSG control system, if the switching frequency is high enough, the values of the phase inductance and back EMF can be viewed as constant during a switching period Under this assumption, the dynamic voltage equation for phase a of a PMSG can be expressed as follows: v a = Ra i a + L sa di a + ea dt (16) where v a is the a-phase terminal voltage, i a is the a-phase current, L sa is the a-phase synchronous inductance, Ra is the v a − R a i a − ea di a /dt (17) where the instantaneous value of the back EMF ea can be evaluated using the calculated rotor position in the previous two control cycles, i.e., ea (k) = K e · [θre (k) − θre (k−1)]/ t According to the phase inductance obtained by (17), the rotor position can be obtained from a lookup table that was created to store the relationship between the rotor position and phase inductance The accuracy of the inductance-based methods also highly depends on the quality and accuracy of the voltage and current measurements Since the current and position derivatives need to be calculated in every switching cycle, the rotor position is highly subjected to the measurement noise In addition, this type of methods requires that the PMSG has a high saliency ratio, e.g., L q /L d > 2.5, and the performance will be poor for nonsalient-pole PMSGs 3) Algebraic Manipulation [57]: The basic idea of this method is to solve a set of equations formed by the PMSG model and coordinate transformations, because the rotor position can be expressed in terms of PMSG parameters and measured currents and voltages Specifically, the following coordinate transformations are required by this method: the Park transformations for the PMSG currents (18a) and voltages (18b) i d = i α cos θre + i β sin θre i q = −i α sin θre + i β cos θre (18a) v d = v α cos θre + v β sin θre v q = −v α sin θre + v β cos θre (18b) and the Clarke transformations for the PMSG currents (18c) and voltages (18d) iα = ia √ √ i β = −i b + ic (18c) vα = va √ √ v β = −v b + vc (18d) By manipulating (18) and PMSG equations (9), the rotor position can be calculated as follows: θre = tan−1 √ b−ic ) − 3ωe (L d − L q )i a v b −v c − Rs (i b −i c )− L d d(idt √ v a − Rs i a − L d didta +ωe (L d − L q )(i b −i c ) (19) The accuracy of this method is also strongly dependent on the accuracy of PMSG parameters and quality and accuracy of voltage and current measurements Since current derivatives also need to be calculated in every switching cycle, the rotor position is highly subjected to the measurement noise In conclusion, the open-loop calculation-based PMSG rotor position estimation methods are straightforward and easy to implement The resolution of the rotor position obtained from these methods is, however, limited by the numerical resolution, which depends on the sampling frequency and control-loop frequency of the system The accuracy of these methods is 210 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL 1, NO 4, DECEMBER 2013 for the observer to achieve a desired tracking performance With the estimated back EMF, the rotor position can be obtained by eˆα (22) θˆre = tan−1 − eˆβ Fig 10 Illustration of (a) linear observer, e.g., a disturbance observer, and (b) SMO for back EMF estimation of a PMSG strongly dependent on the accuracy of machine parameters and voltage and current measurements These methods are still useful, but may need to be improved using closed-loop observers discussed in the following section C Closed-Loop Observers In a closed-loop observer, both the control input of the plant and the tracking error of the observer, i.e., the error between plant and observer outputs, are often used as the input signals to the observer The observer gains are designed in forcing the observer output to converge to the plant output Thus, the estimated values for the states of interest can be forced to converge to their actual values In this sense, the closed-loop observer can be viewed as an adaptive filter, which has good disturbance rejection property and good robustness to the variations of PMSG parameters and current/voltage measurements In the literature, many observers have been proposed for rotor position/speed estimation, such as disturbance observers, sliding-mode observers (SMO), and extended Kalman filters (EKFs) 1) Disturbance Observers: The EMF or extended EMF can be estimated using disturbance voltage observers, as shown in Fig 10(a), in which the EMF is regarded as a kind of disturbance voltage These observers were usually designed based on the dynamic models of PMSGs in the αβ stationary reference frame From (14), the state-space equations of a PMSG can be express as follows: d iα −Rs /L i = · α + · iβ −Rs /L dt i β L vα vβ − eα eβ (20) where e = [eα ,eβ ]T = [−K e ωe sin(θre ), K e ωe cos(θre )]T is the vector of EMF terms In [58], based on the assumption that de/dt ≈ 0, a disturbance observer was designed as follows: d dt iˆα −Rs /L i = · α + · iβ −Rs /L L iˆβ vα vβ − eˆα eˆβ and d dt eˆα eˆβ =g· d dt iˆα − i α iˆβ − i β (21) where ^ denotes the estimated values and g is the observer gain, which can be designed using a pole assignment scheme A disturbance observer was also proposed in [49] for IPMSM applications based on the extended EMF model in the αβ stationary reference frame A similar observer design was proposed in [59] based on the extended EMF model in an estimated dq reference frame The stability of a disturbance observer can be guaranteed by selecting proper observer gains Because machine parameters are needed in the observers’ models, the variations of those parameters will slightly affect the accuracy of the position estimation, especially when both the d- and q-axis inductances have cross saturation In addition, the quality of voltage and current measurements could also affect the performance of disturbance observers A similar disturbance observer can be found in the PMSG wind turbine control system in [60] 2) Sliding-Mode Observers: An SMO is an observer whose inputs are discontinuous functions of the errors between the estimated and measured system states If a sliding manifold is well designed, when the trajectories for the states of interest reach the designed manifold, the sliding mode will be enforced The dynamics for the states of interest under the sliding mode depend only on the manifold chosen in the state space and are not affected by system structure or parameter accuracy Advantages such as high robustness to system structure and parameter variations make the SMO a promising solution for sensorless control of PMSMs Still using (14) to model a PMSG, an SMO [61] [Fig 10(b)] was designed as follows: d dt vα iˆα −Rs /L iˆ = · α + ˆi β ˆ −Rs /L L vβ iβ ˆ ωc i − iα · k · sgn α − 1+l s + ωc iˆβ − i β (23) where ωc is the cutoff frequency of the low-pass filter (LPF); l is the observer feedback gain; and k is the gain of the switching terms In this case, the sliding surface is designed T as S = iˆα − i α , iˆβ − i β By properly selecting l and k, V = 1/2·S T · S > and d V /dt < can be guaranteed, so as the observer stability If the sliding mode is enforced, the back EMF components can be estimated by eˆα eˆβ = k (1 + l) · ωc iˆ − i α · sgn α ˆ s + ωc iβ − iβ (24) Then, the rotor position can be calculated using (22) Many variations of (23) can be found in the literature, e.g., using a saturation function or a sigmoid function to replace the sgn function to mitigate the chattering problem The design of the sliding surface can also be different In addition, several online adaption schemes [62] have also been proposed to improve the observer robustness to machine parameter variations A similar SMO was designed based on the extended EMF model for IPMSM applications [63] ZHAO et al.: REVIEW ON POSITION/SPEED SENSORLESS CONTROL 211 where xˆ = xˆ1 xˆ2 Aˆ = −Rs /L d L q ωˆ e /L d −L d ωˆ e /L q −Rs /L q The adjustable model uses the estimated speed to correct the estimation of the matrix A The adaptive mechanism for rotor speed update can be expressed as follows: Fig 11 Schematic diagram of a MRAS-based speed estimator t ωˆ e = k1 i d iˆq − i q iˆd − ψm i q − iˆq L d dτ However, in practical applications, the attractive features of the SMO, such as robustness to machine parameter and load variations, will degrade if the system has a low sampling ratio and control-loop frequency As discussed in [64], the performance of the SMO without oversampling is much worse than the case with oversampling A solution to this problem is the quasi-SMO [63] with a discretized convergence law Compared with the disturbance observers, which are the examples of linear state observers using continuous-state feedback, the SMO is a representative of nonlinear observers using the output of a discontinuous switching control as the feedback If the gains of the switching functions are tuned well, the SMO will have better dynamic performance than the disturbance observers Well-designed LPFs are, however, needed in the SMO to mitigate the oscillating position errors due to the unwanted noise caused by switching functions As an attractive candidate for position sensorless control, the SMO has also been applied to PMSGs for wind applications [65], [66] 3) Model Reference Adaptive System-Based Methods: The model reference adaptive system (MRAS) is an effective scheme for speed estimation in motor drives In a MRAS, as shown in Fig 11, an adjustable model and a reference model are connected in parallel The output of the adjustable model is expected to converge to the output of the reference model using a proper adaption mechanism If the output of the adjustable model tracks that of the reference model accurately, the internal states of these two models should be identical In [67], the reference model was formulated as follows: d x = A·x+u dt (25) where x= x1 x2 = i d + ψm L d iq u= u1 u2 = (v d L d + ψm ) L 2d vq L q A= −Rs L d L q ωe L d −L d ωe L q −Rs L q The adjustable model was defined as d xˆ = Aˆ · xˆ + u dt (26) +k2 i d iˆq − i q iˆd − ψm i q − iˆq L d + ωe (0) (27) The stability of the MRAS and convergence of the speed estimation can be guaranteed by the Popov super stability theory [67] Per previous discussion, if the tracking errors between the states of the adjustable and reference models are close to zero, the estimated speed in (27) can be viewed as the actual speed Then, the rotor position can be obtained by integrating the estimated rotor speed There are other options for designing the reference model For example, a disturbance observer and an SMO were used as the reference model in [49] and [68], respectively, and the corresponding adaptive mechanisms for rotor speed adaption are also different 4) EKF-Based Methods: As an extension of the Kalman filter, which is a stochastic state observer in the least-square sense, the EKF is a viable candidate for online estimation of rotor position and speed of a PMSM In the EKF algorithm, the system state variables can be selected in either a rotating [69] or a stationary [70] reference frame, i.e., x = [i d , i q , ωe , θre ]T and x = [i α , i β , ωe , θre ]T , respectively A standard EKF algorithm contains three steps: a) prediction; b) innovation; and c) Kalman gain update Due to the stochastic properties of the EKF, it has great advantages in robustness to measurement noise and parameter inaccuracy However, tuning the covariance matrices of the model and measurement noise is difficult [69] In addition, the EKF-based algorithms are computationally intensive and time consuming, which makes the EKF hard to be implemented in industrial drives D Position/Speed Extraction Methods Per the review in Sections IV-B and C, by selecting a suitable method, position/speed related states, such as back EMF or flux, can be estimated Then, appropriate position/speed extraction methods are needed to obtain the rotor position and speed information from these estimated states If the two orthogonal back EMF components eˆα and eˆβ are obtained, the simplest and most straightforward method to calculate the rotor position is using (22) However, this method is an openloop method, which is quite sensitive to the input noise In addition, if the output of the observer is a position error signal, which is a function of the difference between the estimated and actual rotor positions, (22) cannot be used In addition to (22), the PLL-based and angle tracking observers are also effective methods Many applications of these methods can be found in the literature for rotor position extraction in PMSG-based WECS control systems [54], [55] 212 Fig 12 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL 1, NO 4, DECEMBER 2013 Block diagram for a PLL-based position extraction method Fig 13 A typical PLL-based position extraction method is shown in Fig 12, where Msinθre and Mcosθre are the orthogonal input signals, e.g., the estimated EMF components, where M is the amplitude If the difference between the estimated and actual positions is small, the following relationship can be obtained Msin θre cos θˆre − Mcos θre sin θˆre = Msin θre − θˆre ≈ M θ (28) A PI regulator can be used to estimate the rotor speed from M θ Then, the rotor position can be obtained using a speed integrator The transfer function of the PLL can be expressed as follows: k p s + ki θˆre = (29) θre s + k p s + ki The dynamic behavior of (29) depends on the PI gains, which can be determined by appropriately placing the poles of the characteristic polynomial of the transfer function If the output of the state observer is already a function of θ , it can be used directly by the PLL as an equivalent term to M θ The rotor speed can be obtained directly from a MRASbased method, such as (27), or a PLL method Alternatively, rotor speed can be simply and effectively estimated from rotor position using a moving average algorithm However, due to the time-delay properties of the moving average algorithm, a phase lag will exist between the estimated and actual rotor speeds To mitigate this issue, a torque feedforward based speed correction can be used [71] V DTC AND DPC FOR D IRECT-D RIVE PMSG-BASED WECSs A Direct Torque Control As a promising control scheme, the DTC is primarily developed for high-performance electric motor drive systems In contrast to the vector control, the DTC adopts the electromagnetic torque and stator flux linkage as the control variables It not only achieves a faster torque response but also avoids the coordinate transformations and current decoupling computation in the vector control Therefore, the DTC is an inherent motion-sensorless control strategy [72] ABB successfully launched the first commercial DTC drive product in 1995 [73], and then DTC wind turbine converters joined ABB’s product family [74] For WECS applications, one advantage of adopting the DTC is that the outer speed control loop in the vector control can be eliminated using a torquecommand sensorless MPPT algorithm [75] The schematic Schematic diagram of a DTC for a PMSG-based WECS diagram of the DTC for a PMSG-based WECS is shown in Fig 13 At each sampling instant, according to the differences between the reference and actual torques and stator flux linkages, an optimal stator voltage vector will be selected directly from a switching table to restrain the torque and flux within the hysteresis bands However, due to the use of the hysteresis comparators and discrete-time controllers, the unpredictable torque and current ripples of the PMSG cannot be neglected This drawback may increase the mechanical stress on the turbine shaft, reduce the turbine life, and produce much acoustic noise [9] Using a three-level NPC converter instead of a two-level converter may improve the performance of the DTC under stead-state operation [76] An alternative is to integrate the space–vector modulation (SVM) into the DTC [66], [75] However, according to the characteristics of the DTC [72], the modified SVM-DTC cannot be considered a genuine DTC scheme B Direct Power Control The DPC, which follows the idea of the DTC, also gains the advantages such as fast dynamic response, no coordination transformation, simple implementation, and high robustness to parameter variations [77], [78] Compared with the DTC, the DPC is used to control the GSI instead of the MSC and the control variables in the DPC are instantaneous active power and reactive power, which makes the DPC suitable and promising for either generation control or grid connection in microgrid applications [79] The DPC was initially proposed for three-phase PWM rectifiers and then was naturally adopted for DFIG-based WECSs [80] Nevertheless, there are few studies on the DPC for directdrive PMSG-based WECSs reported in the literature The schematic diagram of the conventional DPC for a GSI is shown in Fig 14 Similar to the DTC, the main drawbacks of the DPC are high power and current ripples The performance of a DPC would become worse when the operating points are close to the power limits of the GSI [79] To mitigate the weakness of the DPC, some trials have been devoted to improving and optimizing the switching table [78], [79], [81] Some research has been conducted to lower the total harmonic distortion (THD) and achieve a fixed switching frequency using PI regulators integrated with a space–vector PWM scheme [82], or a model-based predictive control instead of the hysteresis controllers [83] In [84], the DPC was applied for controlling a three-level GSI with inductor-capacitor-inductor filters for the ZHAO et al.: REVIEW ON POSITION/SPEED SENSORLESS CONTROL Fig 14 Schematic diagram of a DPC for a PMSG-based WECS application to a PMSG-based WECS, in which an uncontrolled diode rectifier and a dc–dc boost converter were adopted to form the MSC Therefore, the overall control system of the PMSG and the power electronic converters can be treated as a rotor position/speed sensorless control scheme The use of PI controllers and space–vector PWM indeed reduces the power and current ripples, but the merits of simple implementation and fast dynamic response in the conventional DPC are lost VI C HALLENGES AND F UTURE T RENDS From the review and discussion in the previous three sections, it can be seen that the position/speed sensorless control technology for direct-drive PMSG-based WECSs has been extensively studied with a surge of interests being prompted by the availability of more powerful digital signal processing devices However, despite the aforementioned developments, there are still challenges, which limit the applications of some of the aforementioned sensorless control algorithms in real-world WECSs Significant research effort is desired to overcome the challenges Among the existing wind speed sensorless MPPT techniques, the OT and PSF are the most mature ones The implementation of the OT and PSF techniques, however, requires prior knowledge of the WECSs Moreover, the accuracy of these MPPT methods is affected by system parameter variations caused by the aging of the WECSs Compared with the OT and PSF methods, the advanced HCS method is independent of system characteristics, but has slower tracking speed and lower robustness to disturbances and abrupt changes in wind speed conditions Further studies can be carried out to combine the existing methods, such as the combination of HCS and PSF or HCS and OT, which will enable the WECS to learn the MPPs online without the need of field tests and switch to the fast and smooth MPPT control after the MPPs are learned Moreover, advanced wind speed sensorless MPPT algorithms based on computational intelligence (e.g., artificial neural networks, FL, etc.) are capable of fast online learning of MPPs and adaption to system dynamic characteristics variations caused by the aging of the WECSs The applications of the computational intelligence-based methods are, however, currently limited by their relatively high computational costs With the availability and cost reduction of higher performance processors, these methods will be good options for efficiency optimization and performance improvement of WECSs There are two major challenges in designing rotor position/speed sensorless control algorithms for the PMSGs used 213 in the drive–drive WECSs First, the operating conditions of a WECS always change from time to time because of the intermittent nature of wind energy This requires the sensorless control algorithms to achieve satisfactory steady-state and dynamic rotor position/speed estimation precision over the entire speed range of the WECS This requirement, however, cannot be met by a single sensorless control technique [85] and may need different control techniques for different operating conditions In addition, because a WECS is connected to a power grid or feeds a load as a stand-alone system, the performance of the sensorless control algorithms under abnormal or fault conditions, e.g., grid/load unbalance or short circuits, should be examined and evaluated To the best of the authors’ knowledge, few studies have been done on these subjects for sensorless control in the literature Therefore, more research needs to be launched to overcome these two major challenges in the rotor position/speed sensorless control of the PMSGbased WECSs The application of the inherent motion-sensorless DTC and DPC in PMSG-based WECSs is promising and attractive Further studies are, however, needed to solve the problems such as irregular torque, power and current ripples, and high THD VII C ONCLUSION The demand of highly reliable wind power with lower production and maintenance costs will make position/speed sensorless control a promising technique in WECS applications This paper has reviewed the most recent progress in the field of position/speed sensorless control schemes for directdrive PMSG-based WECSs First, the mainstream power electronic converter topologies used in direct-drive PMSGbased WECSs were reviewed Then, the existing wind speed sensorless MPPT methods, including the OT control, PSF control, P&O control, WSE-based control, and FL control, were discussed To the best of the authors’ knowledge, the most commonly used wind speed sensorless MPPT methods are the OT and PSF controls, depending on the selection of the control commands These wind speed sensorless MPPT methods generate the optimal rotor speed, torque or power references for the control systems of the PMSGs, which can then use either a rotor position/speed estimation-based sensorless vector control or direct torque or direct power control to track the MPPs of the WECSs without using generator rotor position/speed sensors In the fully controlled rectifier-based PMSG WECSs, the SMO is a good candidate for the rotor position estimation used in the vector control system The inherent motion-sensorless DTC and DPC provide promising and attractive alternatives for position/speed sensorless control of PMSG-based WECSs When applying position/speed sensorless control algorithms to direct-drive PMSG-based WECSs, various critical 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variable-speedtype turbines,” IEEE Trans Ind Electron., vol 56, no 1, pp 69–77, Jan 2009 [85] F Spinato, P Tavner, G van Bussel, and E Koutoulakos, “Reliability of wind turbine subassemblies,” IET Renew Power Generat., vol 3, no 4, pp 387–401, Dec 2009 216 IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL 1, NO 4, DECEMBER 2013 Yue Zhao (S’10) received the B.S degree in electrical engineering from Beijing University of Aeronautics and Astronautics, Beijing, China, in 2010 He is currently pursuing the Ph.D degree in electrical engineering from the University of NebraskaLincoln, Lincoln, NE, USA He was a Graduate Student Researcher in 2011 and 2012 and a summer Product Engineering Intern in 2013 with John Deere Electronic Solutions, Fargo, ND, USA His current research interests include electric machines and drives, power electronics, and control Mr Zhao is a member of Eta Kappa Nu He was a recipient of the Best Paper Prize of the 2012 IEEE Transportation Electrification Conference and Expo Chun Wei (S’12) received the B.S degree in electrical engineering from Beijing Jiaotong University, Beijing, China, in 2009, and the M.S degree in electrical engineering from North China Electric Power University, Beijing, China, in 2012 He is currently pursuing the Ph.D degree in electrical engineering at the University of Nebraska-Lincoln, Lincoln, NE, USA His current research interests include wind power technology, power electronics, and renewable energy systems Zhe Zhang (S’10) received the B.S degree in electrical engineering from Xi’an Jiaotong University, Xi’an, China, in 2010 He is currently pursuing the Ph.D degree in electrical engineering from the University of Nebraska-Lincoln, Lincoln, NE, USA His current research interests include control of wind energy conversion systems, power electronics, and motor drives Wei Qiao (S’05–M’08–SM’12) received the B.Eng and M.Eng degrees in electrical engineering from Zhejiang University, Hangzhou, China, in 1997 and 2002, respectively, the M.S degree in high performance computation for engineered systems from Singapore-MIT Alliance, Singapore, in 2003, and the Ph.D degree in electrical engineering from Georgia Institute of Technology, Atlanta, GA, USA, in 2008 He has been with the University of NebraskaLincoln (UNL), Lincoln, NE, USA, since August 2008, where he is currently an Associate Professor in the Department of Electrical Engineering His current research interests include renewable energy systems, smart grids, microgrids, condition monitoring and fault diagnosis, energy storage systems, power electronics, electric machines and drives, and computational intelligence for electric power and energy systems He is the author or coauthor of three book chapters and more than 120 papers in referred journals and international conference proceedings Dr Qiao is an Associated Editor of the IEEE T RANSACTIONS ON I NDUS TRY A PPLICATIONS , an Associate Editor of the IEEE J OURNAL OF E MERG ING AND S ELECTED T OPICS IN P OWER E LECTRONICS , and the Chair of the Sustainable Energy Sources Technical Thrust of the IEEE Power Electronics Society (PELS) He is the Publications Chair of the 2013 IEEE Energy Conversion Congress and Exposition He was the Technical Program Co-Chair and Publications Chair of the 2012 IEEE Symposium on Power Electronics and Machines in Wind Applications (PEMWA) and the Technical Program Co-Chair and Finance Co-Chair of PEMWA 2009 He was the recipient of a 2010 National Science Foundation CAREER Award, the 2010 IEEE Industry Applications Society (IAS) Andrew W Smith Outstanding Young Member Award, the 2012 UNL College of Engineering Faculty Research & Creative Activity Award, the 2011 UNL Harold and Esther Edgerton Junior Faculty Award, and the 2011 UNL College of Engineering Edgerton Innovation Award He has received four Best Paper Awards from IEEE IAS, PES, and PELS