A review on position speed sensorless control for permanent magnet synchronous machine based wind energy conversion systems

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

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

direct-drive 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-the-art 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

direct-drive PMSG-based WECSs.

Index Terms— Direct drive, permanent-magnet synchronous

generator (PMSG), sensorless control, variable speed, wind

energy conversion system (WECS).

I INTRODUCTION

THE 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

domi-nant technology in the market since late 1990s [2]

How-ever, 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

gen-erators (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 6 MW [4], [5] Many wind turbine manufacturers, such as Vestas, Siemens Wind Power, GE Energy, Goldwind, etc have adopted the direct-drive 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 mechan-ical 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 micro-controller technologies, position/speed sensorless control for WECSs becomes feasible In the literature, a variety of optimal position/speed sensorless control strategies have been pro-posed 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 strate-gies 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 sensor-less 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 dis-cusses 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

Fig 1 Schematic diagram of a direct-drive PMSG-based WECS connected

to a grid or local load.

Fig 2 Direct-drive PMSG-based WECS with an MSC consisting of a diode

rectifier and a boost converter.

II COMMONLYUSEDPOWERELECTRONICCONVERSION

SYSTEMS INDIRECT-DRIVEPMSG-BASEDWECSs

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

volt-age 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 1 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

Fig 3 Direct-drive PMSG-based WECS with a two-level back-to-back PWM converter system.

Fig 4 Direct-drive PMSG-based WECS with a three-level NPC back-to-back converter system.

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., insulated-gate bipolar transistors and integrated insulated-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 gen-eration efficiency and reduced torque ripples and current harmonics [3], [9], [12] when compared with the WECS

in Fig 2 The cost to achieve these advantages is that the precise information of the rotor position/speed is needed Fig 3 shows a WECS equipped with two fully rated, two-level, 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 4 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 3 and 4 will be specifically discussed in Sections IV and V

III WINDSPEEDSENSORLESSCONTROL According to the aerodynamic model of a wind turbine, the

mechanical power P mcaptured by the wind turbine from wind can be expressed as

P m = 1

2ρ A r v3

Fig 5 Typical wind turbine torque-shaft speed characteristic curves for

different wind speeds and the OT curve.

whereρ is the air density, A r 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 = ω t R

where ω t 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 valueλopt 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=1

2ρ A r

R3C p max

λ3 opt

ω3

t = Koptω3

where C pmax is the maximum power coefficient, which is

obtained when the TSR is at the optimal value λopt.

According to P m = ω t · T m , the OT Toptof the wind turbine

can be expressed as follows:

Topt= 1

2ρ A r

R3C p max

λ3 opt

ω2

t = Koptω2

The WECS can be operated in the torque control mode with

an optimal reference torque signal obtained from (4) using the

Fig 6 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 5 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 6 shows typical wind turbine power–shaft speed char-acteristic 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 6 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]

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 P e by dP e If dP e/dω > 0, the

rotor speed keeps increasing and vice versa if dP e/dω < 0.

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

effi-ciency 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 2 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:

D k−1 = C1· sgn(D k−2) · sgn(P in ,k−1 − P in ,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; C1is 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 Koptin (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 Kopt is obtained,

the optimal power curve will be used as a reference for

deter-mining 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

Fig 7 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=

KoptVdc-opt2 ) of the output dc voltage Vdc-opt and current Idc-opt

of the MSC shown in Fig 2 Then, the WECS was controlled based on this optimal relationship

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 com-mand 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 grow-ing neural gas network [36], support-vector regression [37], backpropagation network [38], Gaussian radial basis function network (GRBFN) [39], and echo state network [40] Fig 7 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

ˆv w = b +

h



j=1

v jexp



−x − C j2

σ2

j



(8)

where x = [P m , ω t , β] is the input vector; C j R n andσ 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 ˆv w is the estimated wind speed The turbine

TABLE I

C OMPARISON OF D IFFERENT W IND S PEED S ENSORLESS MPPT A LGORITHMS [9], [16], [17]

mechanical power P m can be estimated from the measured

electrical output power; the turbine shaft speedω tcan 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

E FL Control

The FL control has been proved to be effective in MPPT

applications without the knowledge of wind turbine

charac-teristics 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

sig-nals [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 P e of the generator is estimated

If bothP e andω∗are positive, the search continues in the

same direction On the other hand, if a positiveω∗ leads to

a negativeP e, the direction of search reverses TheP eand

ω∗in the current step andω∗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 ROTORPOSITION/SPEEDSENSORLESSVECTOR

CONTROL FORPMSGs

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

e

ω

re

θ

Fig 8 Definitions of coordinate reference frames for PMSG modeling. these reference frames are shown in Fig 8 The dynamical model of a generic three-phase PMSG can be written in the

synchronously rotating dq reference frame as follows:

⎧

⎪

⎪

v d = R s i d + L d

d

dt i d − ω e L q i q

v q = R s i q +L q

d

dt i q + ω e L d i d + ω e ψ m

(9)

where v q andv d are the q- and d-axis stator terminal volt-ages, 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, ψ m is the flux linkage generated

by the permanent magnets, R s is the resistance of the stator windings, andω e is the electrical angular velocity of the rotor

The q- and d-axis flux linkages of the PMSG, ψ q andψ d, can be expressed as follows:

ψ d = L d i d + ψ m

The electromagnetic torque T e can be calculated by

T e =3

2p o

ψ m i q + (L d − L q )i d i q

(11)

where p o is the number of pole pairs The output electrical power can be calculated by

P e= 3

2(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:

v α

v β



= L + L cos(2θre) L sin θre

L sin θre L − L cos(2θre)



· d

dt

i α

i β



+R s i α

i β



+ K e · ω e· − sin θre

cosθre



(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

Fig 9 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, thenL will be zero, and (13) can be

further simplified as follows:

⎧

⎪

⎪

v α = R s i α + L d

dt i α − K e ω esinθre

v β = R s i β + L d

dt i β + K e ω ecosθre.

(14)

If the rotor saliency, however, cannot be ignored, i.e.,

L d = L q, the dynamic analysis performed in theαβ 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

com-ponents through a vector control scheme for a PMSG-based

WECS equipped with an active rectifier (Figs 3 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

compensa-tion [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

compa-rable dynamic performance with sensor-based motor drives

Many position sensorless control schemes have been

devel-oped 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) closed-loop observers, as shown in Fig 9 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

discussed in this section can also be applied to salient-pole

PMSMs

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 di α /dt ≈ 0 and di β /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:

ψ s α=(v α − R s i α )dt

ψ s β = 

v β − R s i β

dt

and

ψ r α = ψ s α − Li α

whereψ s α andψ s β are theα- and β-axis stator flux linkages,

respectively, and ψ r α and ψ r β are the α- and β-axis rotor

flux linkages, respectively Then, the rotor position can be

calculated asθre= tan−1(ψ r β /ψ r α ) The accuracy of the

flux-based 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 = R a i a + Lsa

di a

where v a is the a-phase terminal voltage, i a is the a-phase

current, L is the a-phase synchronous inductance, R is the

a-phase resistance, and e a is the a-phase back EMF According

to (16), Lsa can be calculated as follows:

Lsa= v a − R a i a − e a

where the instantaneous value of the back EMF e a can be evaluated using the calculated rotor position in the previous

two control cycles, i.e., e a (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 follow-ing coordinate transformations are required by this method: the Park transformations for the PMSG currents (18a) and voltages (18b)

i d = i αcosθre+ i βsinθre

i q = −i αsinθre+ i βcosθre (18a)

v d = v αcosθre+ v βsinθre

v q = −v αsinθre+ v βcosθre (18b) and the Clarke transformations for the PMSG currents (18c) and voltages (18d)

i α = i a

i β = −i b

√

3+ i c

√

v α = v a

v β = −v b

√

3+ v c

√

By manipulating (18) and PMSG equations (9), the rotor position can be calculated as follows:

θre = tan−1

v b −v c − R s (i b −i c )−L d (i b−ic )

dt −√3ω e (L d −L q )i a

√

3

v a − R s i a −L d di dt a



+ω e (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

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

distur-bance 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

dt

i α

i β



= −R s /L 0

0 −R s /L



· i i α

β

 +1

L · v v α

β



− e e α

β



(20)

where e = [e α ,e β]T = [−K e ω esin(θre), K e ω ecos(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

i α

ˆi β



= −R s /L 0

0 −R s /L



· i α

i β

 +1

L · v v α

β



− ˆe ˆe α

β



and

d

dt

ˆe α

ˆe β



= g · d

dt

i α − i α

ˆi β − i β



(21)

where ^ denotes the estimated values and g is the observer

gain, which can be designed using a pole assignment scheme

for the observer to achieve a desired tracking performance With the estimated back EMF, the rotor position can be obtained by

ˆθre= tan−1

−ˆe α

ˆe β



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

addi-tion, 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

i α

ˆi β



= −R s /L 0

0 −R s /L



· i ˆi β α

 + 1

L

v α

v β



−



1+ l ω c

s + ω c



· k · sgn i ˆi α β − i − i α β



(23)

whereω c 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

as S = ˆi α − i α , ˆi β − i βT By properly selecting l and k,

V = 1/2·S T ·S > 0 and dV/dt < 0 can be guaranteed, so as

the observer stability If the sliding mode is enforced, the back EMF components can be estimated by

ˆe α

ˆe β



= k (1 + l) · ω c

s + ω c · sgn ˆi i β α − i − i β α .



. (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]

Fig 11 Schematic diagram of a MRAS-based speed estimator.

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

exam-ples 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

effec-tive 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

dt x = A · x + u (25) where

x = x1

x2



= i d + ψ m



L d

i q



u = u1

u2



= (v d L d + ψ m )L2d

v q



L q



A = −R s



L d L q ω e



L d

−L d ω e



L q −R s



L q



.

The adjustable model was defined as

d

where

ˆx = ˆx1

ˆx2



ˆA = −R s /L d L q ˆω e /L d

−L d ˆω e /L q −R s /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:

ˆω e =

 t

0

k1



i d ˆi q − i q ˆi d − ψ m



i q − ˆi q



L d



d τ

+k2



i d ˆi q − i q ˆi d − ψ m



i q − ˆi q



L d



+ ω e (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 , ω e , θre]T

and x = [i α , i β , ω e , 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 mea-surement 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 suit-able 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 ˆe α and ˆe β are obtained, the simplest and most straightforward method to calculate the rotor position is using (22) However, this method is an open-loop 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]

Fig 12 Block diagram for a PLL-based position extraction method.

A typical PLL-based position extraction method is shown in

Fig 12, where Msin θre and Mcos θre 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 θrecos ˆθre−Mcos θresin ˆθre= Msinθre− ˆθre



≈ Mθ.

(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:

ˆθre

θre = k p s + k i

s2+ k p s + k i (29) 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 ofθ, it can

be used directly by the PLL as an equivalent term to M θ.

The rotor speed can be obtained directly from a

MRAS-based 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 DTCANDDPCFORDIRECT-DRIVE

PMSG-BASEDWECSs

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

elec-tromagnetic 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

decou-pling 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

torque-command sensorless MPPT algorithm [75] The schematic

Fig 13 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 rec-tifiers and then was naturally adopted for DFIG-based WECSs [80] Nevertheless, there are few studies on the DPC for direct-drive 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