a new high-frequency injection method for sensorless ... · xu et al.:new high-frequency injection...

1556 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 5, SEPTEMBER/OCTOBER 2012

A New High-Frequency Injection Method forSensorless Control of Doubly Fed

Induction MachinesLongya Xu, Fellow, IEEE, Ernesto Inoa, Student Member, IEEE, Yu Liu, Student Member, IEEE, and

Bo Guan, Student Member, IEEE

Abstract—This paper introduces a new method to solve thesensorless control problem for a grid-connected doubly fed induc-tion machine (DFIM). The proposed method is based on high-frequency signal injection and the fact that the rotor of a DFIMcan be seen as the rotating secondary of an induction transformer.The commonly used sensorless technique based on stator-fluxlinkage, aside from being parameter sensitive, does not workduring fault ride through (FRT) conditions. Nevertheless, theproposed method is parameter independent and remains fullyfunctional during FRT conditions. Moreover, as opposed to otherhigh-frequency injection methods, the proposed method does notrequire rotor saliency. The mathematical principle of the pro-posed technique and its implementation are presented. Computersimulations and initial experimental results are also included forverification.

Index Terms—Doubly fed induction machines, fault ridethrough, high-frequency signal injection, power distributionfaults, sensorless control, wind power generation.

I. INTRODUCTION

ROTOR-CONTROLLED doubly fed induction machines(DFIMs) are widely used as generators in wind power sys-

tems in megawatt ratings due to several advantages. The mainone is the possibility of using power converters that are a frac-tion of the total power of the system. Since the reliability of thesystem increases with fewer components, significant effort hasbeen made to solve the sensorless control problem for DFIMs.The efforts can be broadly divided into two main groups. Thefirst group is the open-loop rotor-position estimators [1]–[3],in which the rotor position is directly estimated from the mea-sured voltages and currents by reference frame transformation.Unfortunately, open-loop estimators are highly sensitive to themachine parameters, and the accuracy of estimation is not guar-anteed [4]. The second group is based on adaptive control the-

Manuscript received October 6, 2011; revised January 15, 2012 andMarch 26, 2012; accepted March 29, 2012. Date of current versionSeptember 14, 2012. Paper 2011-IDC-532.R2, presented at the 2011 IEEEEnergy Conversion Congress and Exposition, Phoenix, AZ, September 17–22,and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY

APPLICATIONS by the Industrial Drives Committee of the IEEE IndustryApplications Society.

The authors are with the Department of Electrical and Computer En-gineering, The Ohio State University, Columbus, OH 43210 USA (e-mail:[email protected]; [email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIA.2012.2210015

ory [4]–[8]. Within this group, rotor-flux-based model referenceadaptive system (MRAS) observers [7], [8] have been widelystudied. The accuracy of the rotor-position estimation usingMRAS, compared to open-loop estimators, is less influenced byvariations of the machine parameters. However, both techniqueslose accuracy when the rotor speed approaches synchronousspeed because the back EMF in the rotor windings approacheszero around synchronous speed, analogous to the case of singlyfed induction machines running at zero speed. Hence, methodsbased on rotor-flux integration cannot give a satisfactory result[1], [9]. As a way to overcome this issue, several researchers[10], [11] have developed observers in which the stator-fluxlinkage, which is considered very stable for grid-connectedmachines, is used in the estimation process, as opposed to therotor-flux linkage. These methods are susceptible to machineparameter variations; hence, online estimators shall be used[12]. However, they are immune to the aforementioned problemat synchronous speed due to the fact that the grid to whichthe DFIM generators are connected remains relatively stable,which is true in most cases. Nevertheless, this assumption doesnot hold during fault ride through (FRT) conditions. In thesesituations, the highly distorted voltages and currents introducesignificant disturbances to the observers, which cannot keeptrack of the reference quantities utilized to determine the rotorposition. In consequence, these sensorless methods fail underFRT conditions.

During the last decade, a clever technique based on high-frequency signal injection (HFI) has emerged as a possiblesolution to the sensorless problem at zero speed for singly fedinduction machines [13]. The literature review indicates that theHFI-based method has been investigated only once for DFIMapplications [14]. As expected, the accuracy of the resultsis not dependent on parameter uncertainties, and the methodworks at synchronous speed. Unfortunately, a large amount ofcomputational power was needed since a Fourier transform-based algorithm was used. In contrast to the approach in [14],this paper presents a new HFI method with a relatively simplealgorithm to solve the sensorless control problem of grid-connected DFIMs. In the proposed method, a high-frequencysignal is injected to the rotor windings to determine the rotorposition, while the rotor saliency information is not needed.The advantages of the proposed method include being immuneto parameter variations, very good performance at synchronousspeed and during FRT conditions, and ease of implementation.

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XU et al.: NEW HIGH-FREQUENCY INJECTION METHOD FOR SENSORLESS CONTROL OF DFIMS 1557

Fig. 1. Block diagram of a typical MRAS observer [10].

Several papers dealing with the control of the rotor currentsof a DFIM during FRT conditions have been written [15], [16],but the issue of rotor-position estimation during FRT conditionshas not been studied yet. The sensorless technique proposed inthis paper solves the rotor-position estimation problem duringFRT and other conditions.

After the introduction, Section II briefly introduces stator-flux-based MRAS observers and why, in their current form,they fail during FRT conditions. Section III describes the math-ematical principle of the proposed method, whereas Section IVpresents the implementation of its algorithm. Simulation andtesting results are shown in Sections V and VI, respectively.Section VII concludes this paper.

II. MRAS OBSERVERS DURING GRID FAULTS

Fig. 1 shows the block diagram of a typical MRAS observer.In summary, two signals that represent the same physical quan-tity, x and x̂, are generated by two different blocks. The firstblock does not depend on the quantity to be estimated, which,in the case of sensorless applications, is the rotor position,whereas the second block generates a signal that depends onit. Finally, the error between these two signals, ε, is usedto improve the accuracy of the estimation. In grid-connectedapplications, the stator flux is normally taken as a referencesignal since it depends on the grid voltage, which is normallyvery stable. Unfortunately, the stator-flux-based observer relieson the fact that the reference signal, x, changes relatively slowlyafter some sort of reference frame transformation. This hasto be the case so that a controller, normally a proportionalintegral (PI) controller, can be able to successfully track it.Nevertheless, during unbalanced FRT conditions, the phase andmagnitude of the machine stator-flux linkage change relativelyfast due to the now appearing negative component, whichrotates negatively at double grid frequency when seen from thepositive component reference frame.

Fig. 2 shows the simulation results of a stator-flux MRASobserver [10] during a two-phase-to-ground fault (on phases band c). The configuration used for the simulation is shown inFig. 3, and the machine parameters are given in Table I. Thesystem frequency of the simulated Matlab/Simulink model is60 Hz. The rotor-side converter is controlled to maintain a con-stant speed, which would be determined by a maximum-power-point-tracking algorithm, whereas the line-side converter iscontrolled to maintain a constant dc-bus voltage. The fault isintroduced at t = 0.8 s and is removed 200 ms later. As seenin Fig. 2(b), during the fault, the magnitude of the stator flux

Fig. 2. Simulation results in which the rotor is running at synchronous speed.As shown in Fig. 3, a two-phase-to-ground fault is introduced at t = 0.8 s for200 ms. The results show (a) the line-to-line stator voltage, (b) the stator-fluxlinkage magnitude and (c) phase, (d) the actual and the estimated rotor position,and (e) the error between these two. Idr is not identically zero during thefault.

Fig. 3. Configuration used to simulate and test experimentally the proposedsensorless algorithm under FRT conditions.

TABLE IPARAMETERS USED FOR SIMULATIONS AND EXPERIMENTS

is not constant. Moreover, the stator flux does not rotate ata constant angular velocity, as shown in Fig. 2(c), where theangular position of the stator flux is shown. As a consequence,the observer fails to properly estimate the rotor position, θr.Fig. 2(d) shows the actual and the estimated rotor position.Before t = 0.8 s, they overlap each other, and the error isalmost zero, as shown in Fig. 2(e). Nevertheless, by t ≈ 0.83 s,the error is close to 100◦. In this simulation, the actual rotorposition, not the estimated one, is used to control the rotor-sideconverter.


Fig. 4. (a) Representation of a 3− ϕ DFIM in which the rotor is rotated by35◦. Only the phase a windings in the stator and rotor are shown. (b) Phaserelation between the stator and rotor voltages for the rotor position of Fig. 4(a).

III. THEORETICAL ANALYSIS

A. Principle of Operation

The proposed method is based on the principle that a DFIMworks as a transformer in which the relative position betweenthe primary and secondary windings changes as the rotor ro-tates. In other words, the phase difference between the statorand rotor voltages in a DFIM is a function of the rotor position.Hence, if a high-frequency signal is injected into the rotorwinding, the corresponding signal obtained from the statorwinding will contain the rotor-position information. This idea isexemplified in Fig. 4, in which the rotor is displaced by 35◦ withrespect to the stator axis. The diagram of Fig. 4(a) representsphase a of the stator and rotor windings of a three-phase two-pole DFIM. As seen in Fig. 4(b), the phase difference betweenthe phase voltages is a function of the angular displacement ofthe rotor. If the machine were single phase, the induced voltagemagnitude would vary as the rotor moves, but for a three-phasemachine, the induced voltage maintains a constant magnituderegardless of the angular displacement of the rotor.

B. Mathematical Analysis

The mathematical model is developed in this section. Thewinding arrangement for a two-pole three-phase Y-connectedsymmetrical induction machine is shown in Fig. 5. Three-phase stator windings are identical, sinusoidally distributed, anddisplaced by 120◦ with Ns equivalent turns and resistance rs.

Fig. 5. Pictorial representation of a DFIM.

Fig. 6. Per-phase equivalent circuit of a grid-connected DFIM with highfrequency injected in the rotor. Vg = 0 for the analysis at high frequency.

The three-phase rotor windings are also identical, sinusoidallydistributed, and displaced by 120◦ with Nr equivalent turns andresistance rr. As shown in Fig. 5, θr represents the angulardifference between the axis of the winding phase a in the statorand that of phase a in the rotor.

The superposition principle is used for the following analy-sis; therefore, it is assumed that only high-frequency voltage ispresent and injected into the rotor circuit, as shown in Fig. 6with the assumption of Vg = 0. Referring all the rotor variablesto the stator in the a-b-c reference frame, the voltage equationsof the machine can be written as

�Vabcs = rs ·�iabcs +d�λabcs

dtand

�V ′abcr = r′r ·�i′abcr +

d�λ′abcr

dt(1)

where

[�Vabcs]T = [Vas Vbs Vcs],

[�V ′abcr

]T= [V ′

ar V′br V

′cr]

[�λabcs]T = [λas λbs λcs],

[�λ′abcr

]T= [λ′

ar λ′br λ

′cr]

[�iabcs]T = [ias ibs ics],

[�i′abcr

]T= [i′ar i

′br i

′cr] . (2)

The flux linkage is defined as(�λabcs

�λ′abcr

)=

([Ls] [Lsr]

[Lsr]T [L′

r]

)(�iabcs�i′abcr

). (3)


The inductance matrices are

[Ls] =

⎛⎝Lls + Lms − 1

2Lms − 12Lms

− 12Lms Lls + Lms − 1

2Lms

− 12Lms − 1

2Lms Lls + Lms

⎞⎠

[Lsr] =Lms

⎛⎝ cos θr cos

(θr+

2π3

)cos

(θr− 2π

3

)cos

(θr− 2π

3

)cos θr cos

(θr+

2π3

)cos

(θr+

2π3

)cos

(θr− 2π

3

)cos θr

⎞⎠

[L′r] =

⎛⎝L′

lr + Lms − 12Lms − 1

2Lms

− 12Lms L′

lr + Lms − 12Lms

− 12Lms − 1

2Lms L′lr + Lms

⎞⎠ .

Since the frequency of the injected high-frequency signal,ωhf , is several times higher than the fundamental frequency ofthe machine, with rr � Xr, the rotor voltage in (1) becomes�V ′abcr ≈ d�λ′

abcr/dt. Hence, if a balanced voltage set

�Vabcr = Vhf

⎡⎣ cos(ωhft)cos

(ωhft− 2π

3

)cos

(ωhft+

2π3

)⎤⎦ (4)

is applied to the rotor’s terminals, the rotor-flux linkages will be

�λ′abcr =

Vhf

ωhf

⎡⎣ sin(ωhft)sin

(ωhft− 2π

3

)sin

(ωhft+

2π3

)⎤⎦ . (5)

From (3), the rotor current becomes

�i′abcr = [L′r]

−1 �λ′abcr − [L′

r]−1

[Lsr]T�iabcs. (6)

Hence, replacing �iabcr by (6) and solving (3) for �λabcs, itfollows that

�λabcs=[Ls]�iabcs−[Lsr] [L′r]

−1[Lsr]

T�iabcs+[Lsr][L′r]

−1�λ′abcr.

Therefore, the stator voltage becomes

�Vabcs ≈d�λabcs

dt= [Ls]

d�iabcsdt

− [Lsr] [L′r]

−1[Lsr]

T d�iabcsdt

+ [Lsr] [L′r]

−1 d�λabcr

dt− d[Lsr]

dt[L′

r]−1

[Lsr]T�iabcs

−[Lsr][L′r]

−1 d[Lsr]T

dt�iabcs+

d[Lsr]

dt[L′

r]−1�λ′

abcr. (7)

The first three terms in (7) represent the so-called transformervoltage, whereas the last three terms are the speed voltage,which is a voltage proportional to the speed of variation of themutual inductance. The grid is represented by an ideal voltagesource in series with an inductance, which accounts for the lineimpedance, Vg and Lg , respectively. As mentioned earlier, ahigh-frequency voltage source, Vhf , is connected to the rotor,and assuming that the machine is not in saturation, the principleof superposition can be applied. For convenience of analysis,the grid voltage is assumed to be zero, i.e., Vg = 0. Hence, thestator voltage and current are related by

�Vabcs = −Lgd�iabcsdt

(8)

Fig. 7. Block diagram of algorithm describing the implementation of theproposed observer. The stator voltage is filtered by a BPF centered at ωhf .

where the minus sign is needed since the current was initiallydefined for motor operation. After several algebraic manipula-tions aided by the computer algebra system Maple, in whichthe trigonometric identity cosu · sin v = (1/2)[sin(u+ v)−sin(u− v)] is used extensively, the stator voltage becomes

�Vabcs =N1

D1

⎡⎣

cos(ωhft+ θr)

cos(ωhft− 2π

3 + θr)

cos(ωhft+

2π3 + θr

)⎤⎦ (9)

where N1 = 3LmsVhfLg(ωr + ωhf) and

D1 = ωhf (2L′lrLls + 3L′

lrLms

+ 3LlsLms + 3LgLms + 2L′lrLg) .

To obtain (9) from (7) and (8) is conceptually straightfor-ward but very algebraically tedious. In essence, the inductancematrices, currents, and flux vectors given by (5), (6), and (8)are replaced in (7), and the whole expression is simplified.As expected, the result is a rotating space vector of constantmagnitude, which is what (9) represents.

Assuming that Lls = L′lr, Lg ≈ Lls [17], [18] and since

ωhf � ωr and 9Lms � 4Lls, (9) can be simplified to

�Vabcs ≈Vhf

3

⎡⎣

cos(ωhft+ θr)

cos(ωhft− 2π

3 + θr)

cos(ωhft+

2π3 + θr

)⎤⎦ . (10)

The result on (10) agrees with the assessment that, at highfrequency, the stator currents are governed predominately bythe stator and rotor leakage inductances [19] since, after as-suming similar values for leakage and line inductances, thestator voltage is one-third of the injected voltage. Comparing(4) and (10), it becomes apparent that the rotor position, i.e.,θr, is encoded in the high-frequency voltage at the stator.

IV. EXTRACTION OF ROTOR-POSITION INFORMATION

A. Algorithm Implementation

The rotor angular information is obtained by implementingthe simple algorithm shown in Fig. 7. The measured statorvoltage is filtered by a bandpass filter (BPF) centered at the highfrequency injected in the rotor, i.e., ωhf . The angular positionof the space vector of the filtered stator voltage, φs, is obtaineddue to the use of a phase-locked loop (PLL), as shown in Fig. 7.


Equation (10) shows that the high-frequency component of thestator voltage is going to lead the injected high-frequency signal(whose space vector has an angular position of φr) by the rotorangular position, θr, i.e.,

θr = φs − φr. (11)

Nevertheless, if θr < 0 in (11), a wrapping block is imple-mented to keep θr within bounds, i.e., 0 < θr < 2π. Later, aphase compensation block is used to advance (delay) the signalby a value, θcomp, equal to the phase delay (phase advance)introduced by the BPF. According to (10), when measured atthe stator, the frequency of the injected signal will be changedby the rotational speed of the rotor. This is so because θr = ωrt;therefore, it follows from (10) that, at the stator, the frequencyof the injected signal is ωhf + ωr. Nevertheless, since the BPFis centered at ωhf , i.e., there is no delay at such frequency,only ωr is needed in order to determine the amount of phasecompensation.

Finally, as seen in Fig. 7, no machine parameters are neededin order to implement the proposed algorithm. The proposedalgorithm is analogous to phase modulation in the sense thatthe magnitude of the measured high-frequency signal on thestator does not contain any valuable information. The onlyrequirement is that the magnitude has to be high enough tobe properly detected. According to (9), the machine parametersonly influence the magnitude of the high-frequency voltage onthe stator, not the phase. Therefore, it follows that the proposedalgorithm is parameter independent.

B. Selection of the Frequency of the Injected Signal

Since a pulse-width modulation (PWM) converter is utilizedto generate the high-frequency signal injected on the rotor, thefrequency of the injected signal has to be at least an order ofmagnitude below the switching frequency. If this is not the case,the PWM converter will introduce unwanted harmonics. On theother hand, the high-frequency signal on the stator will haveto be properly filtered from the line voltage. Therefore, it isrecommended to place the frequency of the injected signal ata reasonable spectral distance from the grid frequency.

Finally, since the grid voltage normally exhibits a significantharmonic content, the high-frequency signal on the stator hasto be located such that no interference occurs at the locationsat which these harmonics occur. Since the position of the 8thharmonic (480 Hz in the U.S.) is vacant in a three-phase system,this frequency is chosen to be injected on the rotor. As a result,the measured high-frequency signal on the stator will be 540 Hz(the 9th harmonic) at synchronous speed and will be limitedbetween 558 and 522 Hz (assuming that the speed of the DFIMis limited between 0.7 and 1.3 p.u.). This location guaranteesthe least filtering effort since the nearest grid harmonics are at420 and 660 Hz (the 7th and the 11th harmonic, respectively).

V. SIMULATION RESULTS

A Matlab/Simulink simulation model was developed totest the proposed method. The simulation describes a grid-connected four-pole doubly fed induction generator controlled

Fig. 8. Simulation results in which the machine is running at a speed of 30%below synchronous speed. As shown in Fig. 3, a two-phase-to-ground fault isintroduced at t = 0.3 s for 200 ms. The results show (a) the line-to-neutralstator voltage, (b) the stator currents, (c) the actual and the estimated rotorposition, and (d) the error between these two.

by a back-to-back PWM converter. The configuration usedwas shown in Fig. 3. Without any loss of generality, it isassumed that the line reactance has the same order of magnitudeas the stator leakage reactance, i.e., Lg ≈ Lls. The machineparameters used in the simulations are shown in Table I.

The frequency and voltage of the injected high-frequencysignal are 480 Hz and 10% of the magnitude of the rotorvoltage, respectively. The description given in Section II alsoapplies. Fig. 8 shows the simulation results when a 5-hp DFIMis running at a speed of 30% below synchronous speed and atwo-phase-to-ground fault (in phases b and c) is introduced att = 0.3 s, as shown in Fig. 3. The fault is removed at t = 0.5 s.Before the fault is removed, the voltages and currents of themachine are greatly distorted due to the now appearing negativeand zero sequences. Phase a of the stator voltage goes from170 V peak to 90 V peak, whereas the other two phases decreaseto 45 V peak each. If any of these quantities is used as areference in an adaptive system, they would be very difficultto track by the conventional technique of a PI controller in asynchronously rotating reference frame if an acceptable degreeof accuracy is desired. Nevertheless, the result obtained withthe proposed observer shows its great degree of immunity tothis kind of disturbances since, as shown in Fig. 8(d), the errorbetween the actual and the estimated rotor position is boundedto 25◦. This error happens due to two reasons. First, the outputof the BPF will change in magnitude during the transient state.Second, during a transient state, the PLL output is also afunction of the magnitude of the input signal, as opposed to onlythe phase. Nevertheless, if more advanced filtering techniquesare utilized for the high-frequency voltage on the stator, thiserror can be greatly reduced.

Fig. 9 is similar to Fig. 8, but a three-phase-to-ground fault,rather than a two-phase-to-ground fault, is simulated instead.


Fig. 9. Simulation results in which the machine is running at a speed of 30%below synchronous speed. As shown in Fig. 3, a three-phase-to-ground faultis introduced at t = 0.3 s for 200 ms. The results show (a) the line-to-neutralstator voltage, (b) the stator currents, (c) the actual and the estimated rotorposition, and (d) the error between these two.

Fig. 10. Experimental setup used to test the proposed algorithm. The mechan-ical encoder is used for verification purposes.

VI. EXPERIMENTAL RESULTS

Experimental results have been pursued to verify the feasibil-ity of the proposed method during synchronous speed, changesin the speed command, and FRT conditions.

A. Experimental Setup

The system setup for experimental testing is shown inFig. 10, and its block diagram is shown in Fig. 3. TwoPWM back-to-back inverters are connected to the rotor of themachine. The rotor-side PWM inverter is controlled using afrequency of 10 kHz, which is also the sampling frequency ofthe sensors and of the interrupt subroutine. Current transducersare used to measure the rotor currents. Two voltage transducersare used to measure the stator voltage. A second-order analoglow-pass filter with a cutoff frequency of 863 Hz filters out theswitching noise but not the high frequency injected for sensingpurposes. The BPF of Fig. 7 is implemented as a digital filter. A

Fig. 11. Experimental results showing the dynamic response of the proposedalgorithm to changes in the speed command. The results show (a) the measured,the command, and the estimated rotor speed and (b) the error between themeasured and the estimated speed.

Fig. 12. Rotor phase currents when the machine under test goes from 0.8 p.u.to synchronous speed. It is shown that the machine remains at synchronousspeed for 18 s. Time/div equals 4 s.

speed encoder of 1024 pulses per revolution is used to measurethe rotational speed and rotor angle. The mechanical encoder isused only for comparison purposes.

Since a new control technique during FRT conditions isoutside the focus of this paper, the conventional stator field-oriented control technique is used to control the DFIM [20].However, the current loop bandwidth has to be lower thanthe frequency of the injected signal; otherwise, the currentcontrollers will disturb the injected signal. A low-pass filter forthe measured currents could be used which would serve the dualpurpose of filtering out the injected high-frequency signal aswell as the PWM noise. Low-pass filters with a cutoff frequencyof 100 Hz have been implemented in this experimental setup.


Fig. 13. Experimental results for a symmetrical three-phase-to-ground fault. The rotor speed is initially running at 0.9 p.u. At t = 0.43 s, a three-phase-to-ground fault is produced, decreasing the stator voltage to 0.3 p.u. The fault is removed at t = 1.47 s. The results show (a) the stator voltage of phase a and (b) themeasured and the estimated rotor position for the time range enclosed by the blue square in (a), i.e., few milliseconds before and after the fault. The error betweenthe measured and the estimated rotor position for the same time range as (b) is shown in (d). Results analogous to (b) and (d) are shown in (c) and (e), but focusingon the instant of the recovery from the fault, which is the time range enclosed by the red square in (a).

The DFIM is speed controlled as a motor (no prime moveris used), with the stator flux being obtained from the statorvoltages and currents.

The machine parameters used for the experimental testingare shown in Table I. A high-frequency signal of 480 Hz isinjected to the rotor-side windings while the stator-side voltagesare measured. An estimate of the rotor angular position, whichis used to control the machine, is obtained by applying thealgorithm described in Section IV and Fig. 7. A microcontrollerboard, based on the TMS320F2812 from Texas Instruments,is used to implement the proposed observer and the wholesensorless vector-control system. Since the microcontroller uti-lized does not have digital-to-analog converters, the results ofthe proposed algorithm (like rotor angular position and speed)are saved in the microcontroller memory and then exported toMatlab for display.

B. Dynamic Response and Performance at Synchronous Speed

The performance of the proposed algorithm has been testedfor changes in the speed command. Fig. 11 shows the measured,the command, and the estimated speed as well as the estimationerror.

Initially, the machine is running at 1.2 p.u. After 1.8 s, thespeed command starts to change until it reaches 0.8 p.u. at t =5.5 s. This speed command is kept for 4 s, until it is changedagain to 1.2 p.u. These values were chosen since a DFIM usedfor wind power generation normally works in this speed range.As seen in Fig. 11(a), the proposed algorithm follows the realspeed very closely, with an error, shown in Fig. 11(b), of lessthan 2%.

Fig. 12 shows the rotor currents for phases a and b when themachine under test is accelerated from 0.8 p.u. to synchronousspeed. After running at 0.8 p.u. for 6 s, the speed commandchanges to 1.0 p.u. At that point, the current controller com-mands an increase in current magnitude in order to boost themachine torque. After the transient, the rotor phase currentsbecome dc values and remain as such for 18 s. Note that thetime/div is 4 s. Therefore, unlike previous publications basedon rotor-flux estimation [21], the proposed observer has goodperformance at synchronous speed.

C. Test Under Symmetrical 3− ϕ-to-Ground Fault

As shown in the block diagram of Fig. 3, a symmetrical three-phase-to-ground fault is produced manually by the closing of abreaker. Fault impedances limit the maximum fault current; asa consequence, the stator voltage decreases to 0.3 p.u. duringthe fault rather than to zero. No new control algorithm forFRT conditions is used, but the rotor currents remain limitedbecause a sufficiently high dc-bus voltage is used. The machineis initially running at 0.9 p.u. when the fault condition isproduced, at t = 0.43 s. Fig. 13(a) shows the voltage of phasea in p.u. during the instance of the fault, during the recovery,and in between. Fig. 13(b) shows the measured and the esti-mated rotor-position information for the time range of the firstenclosed area of Fig. 13(a), i.e., at the fault. Fig. 13(d) showsthe error, in degrees, between the estimated and the measuredrotor position. Fig. 13(c) and (e) presents similar informationto Fig. 13(b) and (d) but focuses on the instant of the recovery,which is the second enclosed area of Fig. 13(a).


Fig. 13(d) shows that, during the instant of the fault, the errorremains limited to ±15◦, whereas at the instant of the recovery,at t = 1.48 s, the error reaches a maximum value of 25◦. Theseresults are in good agreement with the simulation results shownin Fig. 9.

It has been observed that the error is inversely proportionalto the magnitude of the injected high-frequency signal. Nev-ertheless, since the higher the magnitude of such signal, thehigher the harmonic distortion being injected to the grid, themagnitude of the injected high-frequency signal has to belimited.

Intuitively, better accuracy without sacrificing harmonic dis-tortion can be achieved owing to the utilization of better detec-tion and filtering mechanisms for the high-frequency signal atthe stator.

VII. CONCLUSION AND FUTURE WORK

A new method of rotor-position identification for the sensor-less control of grid-connected DFIMs has been proposed. Themathematical foundations of the proposed method, as well asan algorithm for its implementation, were presented. Computersimulation and experimental results were shown in order toconfirm the high accuracy of the proposed technique under FRTconditions and synchronous speed, respectively. The analysisand experimental results show that knowledge of the machineparameters, with the exception of the number of poles, isunnecessary in order to apply the proposed sensorless method.

The results presented dealt with the implementation, steady-state analysis, experimental dynamic performance, and feasibil-ity during FRT conditions of the proposed sensorless observer;its small-signal modeling will be covered in a future paper. Theimpact and possible cross-interference resulting from utilizingthe proposed sensorless control method in a set of DFIMsconnected in parallel, like the ones found in wind farms, is animportant aspect that will be considered further.

REFERENCES

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Longya Xu (S’89–M’90–SM’93–F’04) received theM.S. and Ph.D. degrees in electrical engineeringfrom the University of Wisconsin, Madison, in 1986and 1990, respectively.

In 1990, he joined the Department of Electricaland Computer Engineering, The Ohio State Uni-versity (OSU), Columbus, where he is currently aProfessor. He has served as a Consultant to severalindustrial companies, including Raytheon Company,Boeing, Honeywell, GE Aviation, U.S. Wind PowerCompany, General Motors, Ford, and Unique Mobil-

ity Inc., for various industrial concerns. He is currently the Director of the newlyestablished Center of High Performance Power Electronics, OSU, which issupported by the Ohio Third Frontier Program. His research and teaching inter-ests include the dynamics and optimized design of special electrical machinesand power converters for variable-speed systems, the application of advancedcontrol theory and digital signal processors for motion control, and distributedpower systems in super-high-speed operations. Over the past 20 years, he hasconducted several research projects on electrical and hybrid electrical vehiclesand variable-speed constant-frequency wind power generation systems.

Dr. Xu is currently a Member-at-Large of the IEEE Industry ApplicationsSociety (IAS) Executive Board. He has served as the Chair of the ElectricMachines Committee of the IEEE IAS and an Associate Editor for the IEEETRANSACTIONS ON POWER ELECTRONICS. He was the recipient of the FirstPrize Paper Award from the Industrial Drives Committee of the IEEE IAS in1990, the Research Initiation Award from the National Science Foundationin 1991 for his work on wind power generation, and the Lumley ResearchAward from the College of Engineering, OSU, in 1995, 1999, and 2004, forhis outstanding research accomplishments.


Ernesto Inoa (S’10) was born in the DominicanRepublic. He received the B.S. degree (magna cumlaude) in electronics engineering from the PontificiaUniversidad Católica Madre y Maestra, Santiago delos Caballeros, Dominican Republic, in 2000, andthe M.S. degree in electrical and computer engineer-ing from the University of Central Florida, Orlando,in 2005. He is currently working toward the Ph.D.degree at The Ohio State University, Columbus.

From 2000 to 2002, he was an Automation En-gineer with CND, a Dominican brewing company,

where he helped to automate several bottling lines with the use of pro-grammable logic controllers. His major research interests are related to theapplication of advanced control theory and digital signal processing techniquesto power electronics, motor drives, and energy conversion systems.

Mr. Inoa was the recipient of the Best Student Presentation Award at the 2011IEEE Energy Conversion Congress and Exposition held in Phoenix, AZ.

Yu Liu (S’10) received the B.S. degree in electri-cal engineering from Southeast University, Nanjing,China, in 2008. He is currently working toward thePh.D. degree in electrical engineering at The OhioState University, Columbus.

His research interests include variable-speed drivecontrol and power electronics for electric drivetrains.

Bo Guan (S’07) received the B.S. and M.S. degreesin electrical engineering from Shanghai University,Shanghai, China, in 2003 and 2006, respectively.Since September 2006, he has been with the De-partment of Electrical Engineering, The Ohio StateUniversity, Columbus, where he is currently workingtoward the Ph.D. degree.

From 2004 to 2006, he was an R&D Engineer withShanghai KINWAY Technology, Inc. (a high tech-nology company specializing in power electronicsproducts for industrial and automotive applications),

Shanghai. His present research interests include the analysis, design, andcontrol of high-performance electric machine drives, power electronics circuits,and microprocessor-based control systems.

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