An SRF PLL based sensorless vector control using the predictive deadbeat algorithm

An SRF-PLL-Based Sensorless Vector Control Using the Predictive Deadbeat Algorithm for the Direct-Driven Permanent Magnet Synchronous Generator Li Tong, Xudong Zou, ShuShuai Feng, Yu Che

An SRF-PLL-Based Sensorless Vector Control Using the Predictive Deadbeat Algorithm

for the Direct-Driven Permanent Magnet

Synchronous Generator

Li Tong, Xudong Zou, ShuShuai Feng, Yu Chen, Student Member, IEEE, Yong Kang, Qingjun Huang,

and Yanrun Huang

Abstract—This paper proposes an enhanced sensorless vector

control strategy using the predictive deadbeat algorithm for a

direct-driven permanent magnet synchronous generator (PMSG).

To derive favorable sensorless control performances, an enhanced

predictive deadbeat algorithm is proposed First, the estimated

back electromotive force (EMF), corrected by a cascade

compen-sator, was put into a deadbeat controller in order to improve the

system stability, while realize the null-error tracking of the stator

current at the same time Subsequently, an advance prediction of

the stator current based on the Luenberger algorithm was used

to compensate the one-step-delay caused by digital control

Main-taining the system stability, parameters of the controller were

op-timized based on discrete models in order to improve the dynamic

responses and robustness against changes in generator parameters.

In such cases, the proposed methodology of synchronous rotating

frame phase lock loop (SRF-PLL), which applies the estimated

back EMF, can observe the rotor position angle and speed without

encoders, realizing the flux orientation and speed feedback

regu-lation Finally, the simulation and experimental results, based on

a 10-kW PMSG-based direct-driven power generation system, are

both shown to verify the effectiveness and feasibility of the

pro-posed sensorless vector control strategy.

Index Terms—Cascade compensator, predictive deadbeat

con-trol, sensorless vector concon-trol, synchronous rotating frame phase

lock loop (SRF-PLL).

I INTRODUCTION

WIND energy, being abundant in exploitation and

pollu-tion free in applicapollu-tion, is always regarded as the

alter-native energy [1]–[3] for traditional fossil energy in large-scale

power generation At present, mainstream wind energy

conver-sion systems (WECS) are based on the doubly fed or

direct-driven technology [4], [5] As is well known, doubly fed WECS

Manuscript received August 7, 2012; revised November 7, 2012, April 21,

2013, and June 14, 2013; accepted June 27, 2013 Date of current version

Jan-uary 29, 2014 This paper was supported in part by the National Natural Science

Fund for Excellent Young Scholars under Grant 51322704, and in part by the

Na-tional Basic Research Program (973) of China under Project: 2012CB215100.

Recommended for publication by Associate Editor R Kennel.

The authors are with the State Key Laboratory of Advanced

Electromag-netic Engineering and Technology, Huazhong University of Science and

Tech-nology Wuhan, Hubei 430074, China (e-mail: tongli19860729@gmail.com;

xdzou@mail.hust.edu.cn; 715293926@qq.com; ayu03@163.com; ykang@

mail.hust.edu.cn; 1016709676@qq.com; 37940352@qq.com).

Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2013.2272465

applies a lower rating converter for control actions, but costs

a lot in mechanical maintenance, especially the gearbox Com-paratively, the direct-driven WECS, which universally applies the low speed suited permanent magnet synchronous generator (PMSG) [6], not only saves the costly gearbox, but is more effi-cient, reliable, and has better adaptability to grid faults [7], [8] Therefore, it has a very good application prospect To realize high efficiency in power generation of the PMSG, an encoder

or a resolver is often employed to provide accurate information

on rotor position angle and speed for high-performance vec-tor control However, continuously ascending power grade and generator size make the mechanical sensors difficult to be in-stalled and easily disturbed by terrible working environments These drawbacks greatly depress the reliability of the generator set and can even affect the safety and stability of the whole system Therefore, it is of great theoretical and practical appli-cation to study the sensorless vector control technology for the PMSG [9]–[14]

As to the sensorless vector-controlled PMSG, both the ro-tor position and speed information are mandaro-tory for the flux orientation and speed feedback regulation To extract the ro-tor position and speed information, two types of technology have been proposed One is the high frequency signal injection method [9] It makes use of the salient-pole effect of the gener-ator to achieve the sensorless observation, and thus, is available even when the rotor speed falls down to zero However, this method is only confined to salient-pole generators, and the con-trol performances will be depressed by the additionally incurred high frequency signals The other is the back EMF-based ob-servation method [10]–[13] It is based on the generator model, and presents excellent dynamic and static responses inherently The main drawback of this technology is that, it fails to satisfy the precision requirements in extremely low speeds; however, a practical WECS will be started only when its wind turbine has reached a certain speed (i.e., corresponding to a certain cut-in wind velocity), so the imprecision in low speeds could be ig-nored By taking this practical limitation into consideration, the back EMF-based observation methods would be a better choice for wind power generation

Obviously, precision of the back EMF estimation, which largely relies on the model parameters of the generator and track-ing performances of stator current, shows profound influences

on the overall performance of the sensorless vector control In a

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Fig 1 System topology structure of the PMSG-based direct-driven WECS.

digital control system, control delay caused by current sampling,

duty ratio refreshing, deadband, and other relevant factors will

greatly deteriorate the control performances [15]; while

devia-tions of the applied generator model parameters might further

aggravate the system performances [16] Therefore, enhanced

schemes for stator current control are needed to mitigate the

neg-ative effects caused by control delay and parameter variation At

present, main control schemes aiming for PMSG include

hys-teresis control, synchronous frame proportional–integral (PI)

control, and predictive control The hysteresis control has

ad-vantages such as fast dynamic response and simple digital

im-plementation [17], [18]; however, effective measures should be

taken to suppress the large current errors incurred by the

ir-regular PWM operations The synchronous frame PI control

presents excellent static tracking performance irrespective of

operation conditions; but, its poor dynamics due to bandwidth

limitation degrades the stator current control performances, and

thus, the further delay compensation is required [15], [19] In

comparison, the predictive control methods, aiming to control

stator current with high accuracy in a short transient interval,

can provide better dynamic responses and improved current

wave form with less harmonics The direct predictive control

(DPC) in [13] and [20]–[24], which applies the minimized cost

function to select one of the only seven converter switching

configurations, presents fast dynamics and robust static

track-ing performances against external factors However, several

in-evitable limitations exist, for example, the lower the current

ripple amplitude is required, the smaller sampling period must

be selected, which raises a very high real-time constraint

Alter-natively, the deadbeat-based predictive control [22], [25]–[28],

which relies on the generator model to calculate voltage

ref-erences and then translates them into corresponding switching

configurations through the space vector modulation (SVPWM),

largely reduces its real-time constraints to exhibit similar

excel-lent dynamics and better static tracking performances

Unfor-tunately, the deadbeat control is absolutely dependent on exact

generator model, and its poor adaptability to nonideal factors

such as control delay and parameter variation would make the

calculated voltage vectors deviate from their expected values

To obtain a better performance of sensorless vector control,

an enhanced predictive deadbeat control is proposed in this

pa-per Based on the discrete mathematic model of the PMSG, stator voltage references are derived from the current controller, and are further employed to estimate the back EMF Then, the estimated back EMF is applied to the SRF-PLL model to ob-serve the rotor position and speed Meanwhile, the estimated back EMF is also put into the deadbeat controller after cascaded compensation, aiming to achieve the stability improvement and null-error tracking of stator current Finally, an advance pre-diction of stator current based on the Luenberger algorithm is adopted to alleviate the one-step-delay effect and parameter tol-erance lying in the whole calculation process To achieve these goals, the paper is arranged as follows The system structure and discrete modeling of the flux-oriented PMSG is described

in Section II Then, the principle of SRF-PLL-based sensorless observation is presented in Section III, followed by illustra-tions of the proposed predictive deadbeat control algorithm in Section IV Finally, comprehensive simulation and experimental results from the 10-kW PMSG-based prototype are presented in Section V, to verify the validity and feasibility of the proposed sensorless control strategy in a direct-driven WECS

II SYSTEMSTRUCTURE ANDMATHEMATICALMODELING

A System Topology Structure

Fig 1 shows the PMSG-based direct-driven WECS Here, the wind turbine is in straightforward connection with the PMSG (surface-mounted or interior type), and the full-scale back-to-back converters coupled with the dc-link capacitors are estab-lished between the generator and grid The isolating switch K1

is turned ON only when the preset cut-in wind velocity be-ing detected, and the generator side converter (GSC) is started

to perform relevant control strategies for efficient wind energy capture In the meantime, the network side converter (NSC) that

links to the power network through the LC filter and isolating

transformer maintains the dc-link voltage constant, achieving the high-quality active power delivery and occasional reactive power compensation On condition that the dc-link voltage has been well regulated, this paper focuses on studying the sensor-less control technology for the PMSG

B Discrete Modeling of the PMSG

Usually, a high-performance vector control scheme for the

PMSG needs to be implemented in the synchronously oriented

rotating frame, which relates to the rotor position angle By

taking the stator current vector as I s (t) = [I sd (t) I sq (t)] T, the

back EMF vector as E s (t) = [E sd (t) –E sq (t)] T, and the stator

voltage vector as u r (t) = [u r d (t) u r q (t)] T (where subscripts “d”

and “q” represent orthogonal state variables in the corresponding

reference frame), then, the oriented state-space model of the

PMSG in continuous state can be expressed as follows (in motor

convention):

d

dt I s (t) = A · I s (t) + B · [u r (t) − E s (t)] (1.1)

A =  −R s /L d L q ω r /L d

−L d ω r /L q −R s /L q



, B =



 (1.2)

where ω r represents the real rotor electrical angular velocity;

R s is the stator-phase resistance, and L d and L q are the d-axis

and q-axis synchronous inductance, respectively, whose values

differ from each other on condition of an interior PMSG

In the discrete case, the sampling delay t dis always taken into

consideration Take the stator current for instance, the expected

data sampling I s (t) at time t, in fact, equals to the sampling

value I A D (t + t d ) at the time (t + t d ), i.e., I s (t) = I A D (t + t d)

Accordingly, the general solution of the state-space model (1)

can lead to the continuous stator current as follows:

I s (t) = I A D (t + t d ) = e A·(t+t d −t0 )· I A D (t0)

+

 t+ t d

t0

e A·(t+t d −τ ) · B · [u r (τ ) − E s (τ )] dτ (2)

By replacing t0and t in (2) with t0 = (kT s + t d ) and t = (k +

1)T s, the stator current in the discrete state is derived as follows:

I s (k + 1) = e A·T s · I s (k)

+ B ·

 (k + 1)T s + t d

k T + t d

u r (τ ) · dτ

− B ·

 (k + 1)T s + t d

k T + t d

E s (τ ) · dτ (3)

where “k” represents the sampling site in discrete time, k = 1,

2, 3, ., n, and T s is the sampling period; besides, I s [(k + 1)T s]

and I s (kT s ) have been simply noted as I s (k + 1) and I s (k).

In the synchronized reference frame, the back EMF vector E s

could be approximated as constant in two consecutive sampling

periods, while the stator voltage vector u rvaries along with the

time for performing control actions Hence

 (k + 1)T s + t d

k T s + t d

 (k + 1)T s + t d

k T s + t d

u r (τ )dτ = (T s − t d)· u r (k) + t d · u r (k + 1).

(4.2)

Fig 2 Space vector diagram with sensor-less observed and permanent flux oriented reference frames.

By substituting (4) into (3) and applying the Taylor series ex-pansion, the generalized discrete state-space model for PMSG can be derived as shown next

I s (k + 1) = G · I s (k) + H · E s (k) + H · [(1 − δ) · u r (k) + δ · u r (k + 1)] (5.1)

G =



1− T s R s /L d T s L q ω r /L d

−T s L d ω r /L q 1− T s R s /L q



, H =



T s /L d 0

0 T s /L q

 (5.2)

where “δ” is defined as the ratio between the time delay and sampling period, i.e., δ = t d /T s

III SRF-PLL-BASEDSENSORLESSOBSERVATION

When applying the “zero d-axis stator current control

scheme” to the permanent flux oriented PMSG, the direct

pro-portional relation between its electromagnetic torque and q-axis

stator current can be found This feature makes the control per-formance of the PMSG similar to that of the dc-motor In such

a case, if the sensorless vector control is applied, the rotor po-sition angel must be exactly observed for the flux orientation Fig 2 shows the space vector diagram with the expected

perma-nent flux ψ f oriented γ–δ reference frame (dashed line) and the sensorless observed d–q reference frame (solid line), which are assigned to rotate at the electrical angular velocities of ω r and

ω e , respectively, with reference to the stationary α − β frame.

In the figure, “θ r ” and “θ e” represent the actual and observed rotor position angels, respectively Initially, there exists an error

between θ r and θ e (i.e., Δθ = θ r −θ r =0) Since that E ∗

s (the

reference of back EMF) is aligned on the γ axis, its orthogonal projections in d–q reference frame can be noted as E sd and E sq

Accordingly, when Δθ is small enough, it can be considered that

Δθ = E sd

According to Fig 2, we can modify the d–q reference frame

to make the d-axis align to γ-axis, which means θ e = θ r, and

Δθ converges to zero Since Δθ = E sd , E sd can be used as the

indicator to justify whether the d and γ axes have been aligned together or not To do this, E s (k), the estimation of the back EMF, must be calculated first Using (5) and taking δ = 0, E (k)

Fig 3 Block diagram of the SRF-PLL-based sensor-less observation.

can be rewritten as

E s (k) = J m · I s (k) − H −1

m · I s (k − 1) − u r (k) (6.1)

J m=



L dm /T s + R sm − ωeL q m

ωeL dm L q m /T s + R sm



, H m −1=



L dm /T s 0

0 L q m /T s



.

(6.2)

In (6.1), the stator voltage u r (k) can be replaced with the

previ-ous output of the current controller rather than sampling the

PWM format voltages directly; while the coefficient matrix

J m and H m −1 in (6.2) are based on measured generator

pa-rameters The subscript “m” is defined to indicate the

devia-tion ratio between measured and actual parameters, i.e., m =

L m /L = R sm /R s

Once E sd is calculated from (6), the SRF-PLL can be

de-signed Fig 3 presents the sensorless observation model which

incorporates the SRF-PLL and the estimated back EMF As

seen in this figure, E sd is fed back and compared to its

refer-ence E ∗ sd , while the estimation error ΔE sd is sent to the PI

regulator to derive the compensation term Δω; meanwhile, the

q-axis component E sqcalculated from (6) is also used to derive

the feed-forward term by using

ωFeed(k) = E sq (k)/[L dm I sd (k) + ψ f ]. (7)

Accordingly, the observed rotor speed could be figured out, as

shown in (8)

ω(k) = K P [ΔE sd (k) − ΔE sd (k − 1)]

where K p and K Iare the proportional and integral coefficients

of the PI controller in SRF-PLL

To avoid the negative effect of high-frequency noise, the

ob-served rotor speed ω in (8) needs to be filtered by a low-pass

filter (LPF) After that, the observation of the rotor position

angle can be achieved by integrating ω e (k) as expressed in (9)

θ e (k) = T s · ω e (k) + θ e (k − 1). (9)

With the properly designed PI regulator and LPF [13] (as shown

in Fig 3), characteristic performances such as dynamic

re-sponse, disturbance dependence, and other relevant behaviors of

the proposed observation method can be effectively improved

However, it must be emphasized that the observation errors are

primarily determined by the precision of the back EMF

es-timation Supposing that both the permanent flux orientation

and null-error tracking of the stator current have been exactly

achieved, the referenced d-axis back EMF E ∗ could be written

as

E sd ∗ (k) = L d

T s I

∗

sd (k + 1) −



L d

T s − R s



I sd ∗ (k)

− ω e L q I sq ∗ (k) − u r d (k) (10) where superscript “∗” represents the reference value of

corre-sponding state variable

Recall that Δθ = E sd when Δθ is small enough, subtract the estimated back EMF E sd in (6) from its reference E sd ∗ in (10), then, the approximated expression for the sensorless observation

error ε can be expressed as

ε ∝ [E ∗

sd (k) − E sd (k)] ≈ −m



L d

T s

+ R s



I sd (k)

+mL d

T s

I sd (k − 1) − ω e L q



I sq ∗ (k) − mI sq (k)

. (11)

As seen in (11), there are two major factors that will affect ε,

namely the deviation ratio of the generator parameters and the static tracking errors of stator current control Since the mea-sured generator parameters are uncontrollable, we should focus

on improving the current tracking performance so as to make

I sd and I sqapproach to their references as close as possible For this reason, the predictive deadbeat control, which has a bet-ter current tracking performance, will be discussed in the next section

IV ANALYSIS ANDDESIGN OF THEPREDICITVEDEADBEAT

CONTROLALGORITHM

A Cascade Compensation

The aim of applying the deadbeat algorithm here is to well

control the stator current in the observed d −q reference frame,

so that the sensorless vector-controlled PMSG can present

fa-vorable responses To do so, the back EMF estimation E s (k)

must be first solved according to (6), since that the actual back EMF can not be directly sampled

E s (k) = J m · I s (k) − H −1

m · I s (k − 1) − u ∗

r (k − 1) (12)

It is noted that the previous reference u ∗ r (k − 1) in (12) is used

to replace the actual stator voltage u r (k) in (6).

Then, the estimated back EMF E s (k) in (12) is applied in the

deadbeat controller in (13), to achieve the null-error tracking

of the stator current Accordingly, the stator voltage reference

u ∗ r (k) in present kth sampling period can be calculated as

fol-lows:

u ∗ r (k) = H m −1 · I ∗

s (k) − H −1

m G m · I s (k) − E s (k). (13)

Equation (12) is calculated in the present kth sampling period,

but lots of data sampling and calculation process will take up

the most of time in the same kth period Therefore, the present calculation result u ∗ r (k) is always applied in the next sampling

period (namely the “one-step-delay” control mode in digital control), to avoid incomplete control actions By doing so, the

present stator voltage u r (k), which is generated by the GSC,

is equal to the previous calculation result u ∗ r (k – 1) and can be

Fig 4. Discrete block diagram of the dead-beat controlled system in observed d −q frame.

Fig 5 Closed-loop characteristics of dead-beat control system with or without compensator (a) Maps of zeors and poles (b) Frequency response.

expressed as follows:

u r (k) = H m −1 · I ∗

s (k − 1) − H m −1 G m + J m · I s (k − 1)

+ H m −1 · I s (k − 2) + u ∗

According to the control law (14) and the model (1), the discrete

block diagram of the system can be drawn as Fig 4

Obviously, (14) refers to the previous data information from

the (k – 1)th and even (k – 2)th sampling period, and this may

lead to potential stability problems To investigate the

charac-teristic performances resulted by (14), seeFig 5 Here, all the

analysis is based on the measured generator parameters listed

in Table I, and all these generator parameters are supposed to

be accurately measured, i.e., m = 1.0 It is clearly seen that

closed-loop poles of the system totally stay outside the unity

circle, indicating system instability (see the poles denoted as

“without compensation”)

To avoid system instability, a compensator in (15) is employed

in cascade with the back EMF estimation E s (k) to improve the

system stability (see Fig 6)

e s (k) = a · e s (k − 1) + b · E s (k − 1) (15)

where “a” and “b” are the coefficients of the proposed cascade

compensator

TABLE I

M AIN P ARAMETERS OF THE E XPERIMENT S YSTEM

With the cascade-compensation, the stator voltage reference

u ∗ r (k) in Fig 6 can be rewritten as follows:

u ∗ r (k) = H m −1 · I ∗

s (k) − H −1

m G m · I s (k) − e s (k) (16) For comparison, the characteristics after compensation are also shown in Fig 5 From the figure, it can be found that the com-pensation effectively brings the unstable closed-loop poles back into the unity circle [see the poles denoted as “with compensa-tion” in Fig 5(a)], leading to stability improvement Meanwhile,

Fig 6. Discrete block diagram of the predictive deadbeat controlled system in observed d −q frame.

static performances of “unity gain and zero phase shift” [see the

curve denoted as “with compensation” in Fig 5(b)] are derived

and preserved, achieving the null-error tracking of the stator

current However, it must be noted that these stable poles stay

quite nearby the unity circle, which implicates poor dynamics

and deficient stability margin against parameter changes

More-over, an unexpected resonance peak appears in the frequency

responses [see Fig 5(b)] This resonance would probably

in-voke low-frequency oscillations in the stator current, resulting

in severe torque ripples to make the PMSG terribly damaged

B Luenberger-based Prediction

According to the aforementioned analysis, it can be learned

that the deadbeat control is quite sensitive to two factors: the time

delay and the model parameters Since the parameter changes

are unpredictable and unavoidable, it is of great necessity to

fur-ther mitigate the effect of one-step control delay, which severely

deteriorates the sensorless control performance Therefore, an

advance prediction of the stator current based on the Luenberger

algorithm is further proposed (see Fig 6)

I s (k + 1) = (1 − D) · I ∗

s (k) + D [2I s (k) − I s (k − 1)] (17)

where “D” is defined as the predictive weight value, which is

set to be in the range of [0, 1]

By replacing the sampled stator current I s (k) in (16) with

the predicted value I s(k + 1) in (17), the proposed predictive

deadbeat control algorithm, which includes the back EMF

es-timation (13), cascade-compensation (15) and Luenberger

pre-diction (17) can be finally expressed as follows:

u ∗ r (k) = H m −1 · [1 − G m(1− D)] I ∗

s (k) − e s (k)

− H −1

m G m · D [2I s (k) − I s (k − 1)] (18)

With a few mathematical manipulations, a fourth-order

closed-loop transfer function can be deduced Detailed derivation

pro-cess is given in the Appendix And further ignore all the infinitely

small terms, the simplified characteristic equation of the system

can be rewritten as follows:

λ(z) = a4z4+ a3z3+ a2z2+ a1z + a0 (19)

where corresponding characteristic coefficients are set as: a4 =

1, a3 = –(1 + a), a2 = (2Dm + a − b), a1 = [b – (2 a + 1)

Dm + bm], and a0 = (aDm – bm).

It can be found that characteristic performances of the trans-fer function are mainly affected by two factors: the predictive

weight value “D” and the deviation ration “m” (variation of the

generator parameters) By using Jury’s criterion as the stability restriction, the stable and unstable regions of system, which

de-pends on “D” and “m,” can be unveiled As shown in Fig 7(a),

the shaded region clearly defines the accessible stability field

of the predictive deadbeat control For a certain value of “D,” the acceptable variation range of “m” is different For example, when D = 0.1, it allows “m” varying from 0.0 to 5.2 and the system remains stable, while D = 0.3, the variation range of

“m” is narrowed from 0.0 to 2.1 This implies that a smaller D

ensures the system stability with a larger parameter tolerance

However, a small D will also lead to slow system responses, which can be seen in Fig 7(b) It is found that when D is

de-creased, tracks of the dominated poles move toward the low bandwidth region (see pole tracks from “4” to “1”), leading to slower dynamics but enlarged stability margin against parameter changes (i.e., starting point of a pole track stays nearby the ori-gin point and far from the unity circle) Therefore, optimization

designs of the predictive weight value “D” must compromise

both the dynamic responses and system robustness

In a long-term power generation, variations in the generator parameters are absolutely unpredictable and unavoidable due

to the external changing working environments However, it is generally accepted that the initial controller can be designed on basis of accurately measured parameters Accordingly, consid-ering that a±50% variation happens to the generator parameters,

i.e., m = [0.5, 1.5], the value D = 0.3 is finally selected with

several comparisons Then, the closed-loop frequency response

with D = 0.3 is depicted in Fig 7 Obviously, the frequency re-sponses are hardly affected even when “m” is changed from 0.5

to 1.5, as shown in Fig 8, therefore, robust control performances have been achieved

Fig 7. Closed-loop characteristics of the predictive deadbeat control system defined by “D” and “m.” (a) Accessible operation filed (b) Pole trajectories with varied “D.”

Fig 8 Closed-loop frequency responses in accordance to varied generator

parameters.

V SIMULATION ANDEXPERIMENTALRESULTS

A Description of the Experimental System

To testify the proposed strategy, a 10-kW prototype of the

direct-driven WECS as shown in Fig 1 was developed (see

Fig 9) In the system, a prime motor with exclusive speed

regu-lating system is employed to drive the PMSG [see Fig 9(a)], and

the back-to-back converters coupled by dc-link capacitors [see

Fig 9(b)] are constructed for power delivery Main parameters

of the GSC and PMSG are provided in Table I

The 32-bit float-point digital signal processor (DSP)

TMS320F28335 is adopted to perform the proposed control

algorithms onto GSC and NSC As shown in Fig 10, the stator

currents I sa and I sbare sensed for the purpose of control actions,

and the control blocks of 1, 2, and 3 have been well designed

in Sections III and IV To further realize the sensorless speed

regulation, the cascade-compensated back EMF e sq (k) in (15)

is used to calculate the applicable speed feedback Since this

paper mainly focuses on sensorless observation and stator

cur-rent control, the calculation is only explained in the Appendix,

and the designs of sensorless speed control loop is not further

discussed here Practically, references of the inner current loop

I sq ∗ should be generated by the outer speed loop for the purpose

of maximum power point tracking (MPPT) In addition, the

11-bit optical encoder is reserved as the reference for verifying

the sensorless observation

Fig 9 Prototype of direct-driven WECS (a) Prime motor and PMSG (b) Back to back converters.

Fig 10 Principle block diagram of the sensor-less vector control strategy for PMSG.

Fig 11 Simulated performances of the sensor-less controlled PMSG:

(a) Dynamic responses and (b) Static responses.

B Simulation Verification

In a real direct-driven WECS, the speed of the PMSG should

be regulated by the speed control loop But, the PMSG in our

setup is driven by the prime motor, and its speed regulation

absolutely depends on the external control system However,

the system functions can still be verified by the following three

steps of verification

Step 1 (Verification of the sensorless vector control): To

tes-tify the performance of sensorless orientation and stator current

control, the isolating switch K1 (see Fig 1) remains

discon-nected initially, and the outer loop of speed feedback regulation

is removed Besides, the rotor speed of the prime motor is set

at 50 r/min, and I sq ∗ is set at the amplitude of 6 A Under such

conditions, the dynamic and static responses of the proposed

control system are simulated (as shown in Fig 11)

As seen in Fig 11(a), when the isolating switch K1 is

turned ON, the PMSG is immediately started into the mode of

power generation By applying the optimized predictive weight

value (i.e., “D” = 0.3) and exact generator parameters (i.e.,

“m” = 1.0), the sensorless observed rotor position angle θ e

(blue line) quickly tracks its reference angel θ r(solid line) after

a transient regulation Meanwhile, the three-phase stator

cur-rents I sabc quickly reaches to their static states with nearly

ignorable overshoots, indicating favorable dynamics of the

pre-dictive deadbeat algorithm Subsequently, with the rotor speed

and torque current being increased to 100 r/min and 10 A

am-plitude, respectively, as shown in Fig 11(b), the static observed

position angle θ e coincides with θ r, and the stator currents still

remain in wonderful static waveforms with almost null tracking

errors

Step 2 (Verification of the system robustness): Then, the

sim-ulation when m = 0.5 and m = 1.5 is performed to testify the

system robustness As shown in Fig 12, the PMSG rotates at

a fixed speed of 100 r/min, while its torque current reference

Fig 12 Simulated results of the robustness test with varied model parameters:

(a) m = 0.5 and (b) m = 1.5.

Fig 13 Simulated speed regulation of the sensor-less vector controlled PMSG.

I sq ∗ is suddenly increased from 6 to 10 A and then decreased to

6 A again It can be seen that neither the dynamic nor static per-formances are influenced, except for slight deviations between

θ e and θ rin the short transitions, indicating satisfactory robust-ness of the proposed control scheme

Step 3 (Verification of the speed feedback regulation):

Fi-nally, the speed feedback regulation is also performed to test the overall system performance, and corresponding simulation

results are presented in Fig 13 When the speed references ωref increases from 30 to 150 r/min, the stator current I S Aresponds immediately and reaches to its limitations (±6 A peak value)

rapidly to accelerate the process of speed regulation, while the

Fig 14 Dynamic performances of sensor-less controlled PMSG.

Fig 15 Static performances of sensor-less controlled PMSG.

observed mechanical angular speed ω m e converges to the

ref-erence smoothly Furthermore, it is just due to the exact

obser-vation of the rotor position angle, the speed can be maintained

at 150 r/min with the very small empty-load torque current

Similarly, excellent sensorless control performances can also be

found in the process of deceleration

C Experimental Results

The experiments under the same conditions as the

simula-tions are also performed Here, the digital to analog chip was

employed to acquire the encoder-generated and sensorless

ob-served rotor position angels and speeds Similar to the “step 1”

in the simulation, experimental verifications without the outer

loop of speed feedback are shown in Figs 14 and 15 In

compar-ison to Fig 11, similar excellent responses of the stator current

control were derived In addition, static tracking errors of stator

current in d–q frame and the Lissajous figure of the observed

back EMF in α − β frame are also shown in Fig 15 As shown

in Figs 16 and 17, both the small tracking errors (I sd err and

I sq err), which are no more than 0.1 A, and the approximated

circle prove excellent performances of the proposed control

scheme

Subsequently, the robustness experiments as “step 2” in the

simulation are performed As shown in Figs 18 and 19,

simi-lar robustness performance can be obtained with the optimized

weight value “D = 0.3.” In Fig 20, the predictive weight value

“D” is set at 0.5, and “m” is suddenly changed from 1.0 to

Fig 16. Tracking errors of the stator current in d-q frame.

Fig 17. Lissajous figure of the observed back EMF in α − β frame.

1.5 It can be seen that the state of “D = 0.5” and “m = 1.0”,

which is located at point A in Fig 7(a), still maintain the system

stable Once “m” is switched to 1.5, corresponding state moves

into the unstable region (see point B in Fig 7(a)) Accordingly,

the stator current, observed angle θ e and its reference θ r were all distorted, as shown in Fig 20 This result proves the

relation-ship given in Fig 7(a), namely the increased value of “D” leads

to a decreased tolerant range of parameter changes Without doubts, rationally compromised controller designs are required

to satisfy practical applications

Finally, the speed feedback regulation is also performed, as

“step 3” in the simulation Here, the prime motor was stopped but still connected to the PMSG as a great inertia link, while the PMSG is adversely operated into the states of electromo-tion Fig 21 exhibits the comprehensive performances of the sensorless vector controlled PMSG in a speed regulation, where

U r A B , I S A , ω m e , and ω m r represent the stator voltage, stator current, the observed and the encoder-generated rotor mechani-cal angular speeds, respectively Apparently, stable speed feed-back regulation is realized and similar regulating performances

Fig 18. Robustness experiments: Dynamic performances by suddenly increased power generation (a) D = 0.3, m = 0.5 (b) D = 0.3, m = 1.5.

Fig 19. Robustness experiments: Dynamic performances by suddenly decreased power generation (a) D = 0.3, m = 0.5 (b) D = 0.3, m = 1.5.

Fig 20. Robustness experiments with increased predictive weight value “D.”

Dynamic performances by suddenly increased model parameters “m.”

Fig 21. Speed regulation of the sensor-less controlled PMSG 1—ω m r, rotor

speed from encoder 2—I S A , stator current in Phase A 3—ω m e, observed

rotor speed 4—U r A B, measured stator line voltage.

Fig 22 Transient performances in the acceleration.

as Fig 13 can be observed For details, short scopes of the two speed changing processes are also presented in Figs 22 and

23 Due to the nonperfect soft connection between the prime motor and the PMSG [see the shaft in Fig 9(a)], rotation of the prime motor slightly lags behind responses of the stator current; therefore, a small speed fluctuation appears in the transition Ignoring this, the overall performance is almost the same as the simulation, and satisfactory dynamic and static performances of the proposed control scheme are totally obtained

To further present information for the concerned accuracy of speed tracking, errors of speed tracking and position observation during transient and steady states are shown in Figs 24 and 25, respectively In steady states (see periods “I” and “III”), the

observed mechanical angular speed ω m e accurately follow its

reference ω , and the observed position angle θ maintains