Sensorless Control of Permanent Magnet Generator in

Sensorless Control of Permanent Magnet Generator in

Wind Turbine ApplicationReza Esmaili, IEEE Student Member

General MotorsAdvanced Technology Center

Torrance, CA 90505

Abstract - This paper discusses a new and simple speedestimator, to be used by a permanent magnet generator, formaximum power tracking in a small size variable speed windturbine. Moreover, a vector control approach is introduced tocontrol the output voltage and current of a single-phase voltagesource inverter, such that the active and reactive power can becontrolled independently. Using the proposed speed estimator,system only needs two measurements to estimate the generatorspeed and implement the maximum power-tracking algorithm.Accuracy of the speed estimator is verified by simulation andexperimental results.

I. INTRODUCTIONToday more than ever small sources of generation, such as

full cells, photovoltaic cells, and small size wind turbines arebecoming economically available to the public at large. Thesesources offer the advantages of load shifting customerdemand, production of power in environmentally friendlierways, and emergency backup power. Distributed Generationsystems allow utility companies to locate small energygenerating or storage units closer to the customer. Thesesources face many hurdles, such as cost, grid interface issues,power electronics design, and control algorithms beforeintegration. The focus in this paper will be on small sizevariable speed wind energy systems.

The generation of electricity from modem wind turbines isnow an established technology, although many developmentsare yet to come. Worldwide there are more than 20000turbines; with the most cost effective for grid integrationbegins at about 400kW capacity and 40m in rotor diameter [1].

Longya Xu, IEEE FellowDepartment of Electrical and Computer Engineering

The Ohio State UniversityColumbus, OH 43210

A typical capacity factor on a good site (wind speedaverage> 6m/s) is 25 to 30°O. Such turbine can be expected tosupply 20 to 4000 of total annual energy into a local grid [2].

Small size variable speed wind turbine systems have beenused in grid connected application as well as remoteapplications, such as water pumping, water heating, andbattery charging. Powers rating of these kinds of turbines areless than 100 kW, typically [3]. In fact, the system based onpermanent magnet generator is one of the most favorable andreliable methods of power generation for small size windturbines. This paper discusses a new and simple speedestimator, to be used by a permanent magnet generator, formaximum power tracking in a variable speed wind turbine.Moreover, a vector control approach is introduced to controlthe output voltage and current of a single-phase voltage sourceinverter, such that the active and reactive power can becontrolled independently.

The paper is organized as follows: in section II structure ofthe wind energy system and speed estimator are discussed.Vector control of independent active and reactive power for asingle phase inverter is introduced in section III. In section IVand V simulation and experimental results are presented.Section VI summarizes the advantages of the overall systemand gives some final remarks.

II. WIND ENERGY CONVERSION SYSTEMFig.1 shows a schematic of the power circuit topology and

control system of a variable speed wind turbine system thatwill be discussed in this paper.

iD iL Ld idc

T1 T2 T3 T4

V + Voltage VaVd,-4e Regulator Vector Control a-VAlgorithm

Vd, Qref Unipolar-PWM Z a

Fig. 1. Power circuit topology and control structure for the wind energy conversion system.

20701-4244-0365-0/06/$20.00 (c) 2006 IEEE

A simple maximum power tracker, which is introduced in[4], is used to extract the maximum power from wind.Moreover, a speed estimator that will be discussed in thefollowing section is used to provide generator speed as inputto the control system and maximum power tracker, as well. Astep-up boost converter is used to control the speed ofpermanent magnet generator, which means turbine speed, bybalancing the input power to the generator from wind turbinewith the output power of the generator in the output terminalsof the diode-rectifier. Detail operation of the ac-to-dcconversion system, including diode-rectifier and boostconverter is given at [4]. Extracted power by turbine fromwind is measured at the output of the diode-rectifier bymeasuring variable dc-bus voltage, Vd, and inductor current, iL.The calculated power is used as the second input to themaximum power tracking controller.

A. Operation ofDiode-Rectifier with CommutatingInductance

Fig.2 shows a simple 3-phase diode-rectifier connected to abalanced three-phase voltage source through a set of inductorsmagnetically coupled in series with resistors.

Fd Id

ioL Rectifier.

e_n L R t , "rP

D4, D62 D22

Fig.2. Three- phase voltage source connected to line commutateddiode-rectifier.

Because of the inductor there is a finite commutationinterval that affects the average output voltage of the rectifier.To formulate the average output voltage, we assume that theoutput current of the converter, id, is constant and is equal toits average value Id- Moreover, we initially ignore the resistivepart of the inductor to simplify the output voltage equation.The instantaneous output voltage of the rectifier duringcommutation interval can be derived as:

equal to Ex, as shown in Fig.3. Ex, can be calculated asfollow:

Ex = f(ebC-Vd)dO= 2;feabdO

Ex = 3,'3E. (1-cosy)2IT

eab

(3)

(4)

ebc f ela

Fig.3. Commutation effect on the output voltage of the three-phasediode-rectifier under operation with L.

On the other hand after simplification:

d.a ean - ebnf dia eabdt 2(L-M) dt =2(L-M) (5)

Let us to assume: ean(t)=Emsin(cot+150') that results in:eab(t)= \3 Emsin(cwt+1800). Solving (5) under initial conditionia(t=0)=Id concludes:

(6)2a (t) = Id + -1 EM)o(cosa t-1)

To calculate the commutation angle "Y", which is neededfor calculation EX, this reality can be use that in the end ofcommutation process ia()=0.

2(L-M)co9ia(y) = 0 > 1-Cosy= )Id

-[3EmVd = (eac +ebc)+ (M-L) a(i, 6) +(L-M) dc

2 2 dt dt(1)

Since "id" is assumed to be constant, equal to its averagevalue ld, during the commutation interval:

'a + ib = id ~Z_ Id> vd = eac + ebc (2)

ic =-id Z Id

Let us to consider the mean voltage reduction in the outputvoltage of the diode-rectifier due to commutation interval is

Substituting from (7) into (4):

3oi(L-M)Ex =- Id

/Z(8)

Finally, the average output voltage of the diode-rectifierconsidering the resistive part of the inductor can be simplywritten as:

Vd= 3[3Em 3co(L-M) I -2RIdif if

(9)

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e

"I,\

E-1, 11

eea "I,

7 i*-* b

(7)

B. Speed EstimatorMachine notations and prototype parameters of the surface-

mounted permanent magnet generator are given in Table.l.TABLE I

MACHINE NOTATION AND PARAMETER

Pr Rated out put power in kW 20Nr Rated mechanical speed in rpm 211Pole Number of poles 36ENL Peak line-to- neutral back emf in no-load 295.6Rs Stator winding resistance in Q 1.764Lis Stator leakage inductance in mH 0.28Lms Stator magnetizing inductance in mH 2.8Km Peak line-to-neutral back emf constant in V/rpm 1.4J Moment of inertia in kg/m2 10

Fig.4 shows the permanent magnet generator connected tothe three-phase diode-rectifier.

'd Id

Vd3Em 3a)( +L+)Id-2 ()R+ Rs) Id

where:

Em = Km()m

(1 1)

(12)

P 2;T Pira-) =2 60 )m =60m (13)

Ls = Lls +3

Lmns (14)

Where, w11 is the mechanical speed of the generator in rpm;Em is the maximum of the phase voltage induced into thestator windings; and Ls is called the synchronous inductanceof the generator. Substituting from (12) and (13) into (11) andsolve it for Wm results in:

Vd +2(R+Rs)Id

Km 2 (Ls +L)Id(15)

Vd

Equation (15) can be used to estimate the generator speedjust by measuring the average output voltage and current ofthe diode-rectifier.

Fig.4. Direct-drive permanent magnet generator connected to the rectifier.

The permanent magnet generator can be modeled by itsphase voltage equations as follows:

e V RS ° ]° ]

ebnl= Vbn +~0 Rs i

_ecn_ _Vcn_ ° ° RS- icLls + Lms -0.5Lms -0.5Lsm1 Fa]-0.5Lms Lls +Lns -0°5Lrs dt lb (10)-0.5LMS -0.5Lms Ls + Lmsj ic

The equivalent circuit of the permanent magnet generator,based on (10), connected to the rectifier is depicted in Fig.5.

III. VECTOR CONTROL OF SINGLE-PHASE VOLTAGE SOURCEINVERTER

In vector control approach for three-phase inverters [5],time varying variable, such as phase voltages and currents willbe transferred to the synchronous frame, which causes to dealwith dc values instead of time varying variables. However, d-qtransformations are defined for two-phase and three-phasesystems [6]. Therefore, to use this method for a single-phaseinverter we need to build a two-phase balance system. Animaginary phase, in which is orthogonal to the original system,can be considered such that, it has the same structure with thereal circuit except there is 90° phase difference betweenvoltages and currents in this circuit and the real one [7]. A fullbridge single-phase inverter and its imaginary circuit areshown in Fig.6.

Using transformation matrix defines based on Fig.7; phasordiagram shown in Fig.8; and q-axis aligned with the phasevoltage vector of the real circuit, Vd=0 and vq=IvI, active andreactive power can be simplified as:

vd P = |V| iq

Q = -|v| id

(16)

(17)

Fig.5. Equivalent circuit of permanent magnet generator connected to thediode-rectifier.

The average output voltage of the rectifier based on (9) andFig.5 can be formulated as below:

Considering grid voltage, lvl, is constant; therefore, activeand reactive power can be controlled, using iq and idrespectively. Transforming phase voltage equations into thesynchronous frame, and considering Vd=0 and vq=lvl results in:

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L] (18)

To provide decoupled control of active and reactive power

based on (18), the output voltages of the inverter in the d-qframe should be chosen as:

eq = L(xl - oid)+ |v| (19)

ed =L(x2 +coiq) (20)

Vd, -

(21)

(22)

Fig.9 shows the control block diagram of the single-phaseinverter based on the vector-control algorithm. To turn on andoff the switches in the inverter a unipolar switching scheme isused for pulse-width modulation [8]. With unipolar switchingscheme introduced in Fig.9, harmonics in the output voltage ofthe inverter begin at around 2mf, where mf is modulationfrequency ratio. Note that, the commanded active and reactivepower should be chosen two times the desired values; becausethe imaginary circuit will not deliver (absorb) any active andreactive power to (from) the grid.

1M

T

T2

Fig.6. Single-phase inverter and its imaginary circuit.Fig.9. Vector control structure with unipolar switching scheme for

the single-phase inverter.

Fig.7. Definition of rotating reference frame.

fd

Vd _Vtd

'+. ~~~fqq q

Fig.8. Voltage and current vectors in d-q frame.

Control rules of (19) and (209) can be completed throughdefining current feedback loops as follows:

IV. SIMULATION RESULTSTo validate the speed estimator introduced in (15), a simple

RL load is connected to the output of the diode-rectifier shownin Fig.4. The actual and estimated generator speeds aredepicted in Fig.10. The estimated speed is calculated based onequation (15). After one second the mechanical input torquechanges form lOON.m to 200N.m, which causes to changegenerator speed. As can be seen from Fig.10, the estimatedspeed is in a good accuracy with the actual speed of thegenerator.

WM0m()Est

so L

20 I20

0.0 05 1.0 15 2.0 2.5

Time(Sec)Fig. 1O. Real and estimated speed of the permanent magnet generator.

Simulation results of independent active and reactive powercontrol of the single-phase inverter based on vector controlmethod are shown in Fig.11. As mentioned previously and is

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k2x, = k, +iq-iqs

k2X2 = k, +- 'd-'d

s

shown in Fig 1-a & b, active and reactive powers arecontrolled through the q-axis and d-axis current components.

To examine the dynamic of the control algorithm, the inputpower to the dc-bus of the inverter is changed, which can bebecause of wind speed variation in the real system. As can beseen from Fig. 11-a, controller changes the set value of the q-axis current to maintain the dc-link voltage fixed at 420 volts,shown in Fig. 11-c. Furthermore, after 2 seconds the reactivepower command changes from zero to 8kvar, this means theset value of d-axis current changes from zero to -50 amps.Likewise, dynamic response of the d-axis current regulator isshown in Fig.1 1-a.

Id,l Idrefb Wxf I~~~~~~a)la,,L. 4I4I1so1 ..........

typical wind turbine characteristics given in [4], the optimumoperating points of the turbine are, (203r/min, 13kW), and(220r/min, 21kW) for two different wind speeds. In Fig.12 isassumed the wind speed changes after 30 seconds which causeto change the maximum power generation from 13kW to21kW.

V. EXPERIMENTAL RESULTS

Fig.13 shows the experimental test setup which is used toverify the speed estimator. In the setup a dc motor is usedinstead of the wind turbine. Furthermore, as shown in Fig.4,output terminals of the PMG are connected to the three phasediode-rectifier. Parameters of the PMG used in theexperimental test setup are given in Table II.

0

.100

20K

15K

=5 K 1.

5K0

47's4504254007

36 L

(h)

(C)

00 0.50 1 00 1.50Tine (s

Fig. 11. Independent active and reactive power control using iq and id.

Fig.13. Experimental test setup at OSU.

TABLE IIPARAMETERS OF PMG USED IN THE TEST SETUP

Rated out put power inW 746

Rated mechanical speed in rpm 1800

Number of poles 4

Peak line-to- neutral back emf in no-load in volt 212.3

Stator winding resistance in Q 2.84

Synchronous inductance in mH 82

0 10 20 30x 10o Time(sec)

50 100 150Shaft Speed (rpm)

Fig. 12. Maximum power tracking

200 250

Finally Fig. 12 shows the maximum power tracking resultusing the speed estimator. The simulation program uses the

Estimated speed and actual speed of the generator areshown in Fig. 14-a. For better comparison, percentage of speederror between actual and estimated one is depicted in Fig. 14-b.Speed error is defined as below:

|Estimated Speed-Actual Speed|Speed Error=x10

Actual Speed

As can be seen from the Fig. 14-b, speed estimator tracks thegenerator speed with an error of less than 0o5, which is a verygood estimation for wind turbine application.

VI. CONCLUSIONThis paper introduces a simple speed estimator for a

permanent magnet generator that could be used to implementmaximum power tracking in wind turbine application.

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h- 1.5 =:

ol

1-

0

Furthermore, a vector control approach is introduced tocontrol the output voltage and current of the single-phasevoltage source inverter, such that the active and reactivepower can be controlled independently. Simulation andexperimental results confirm that speed estimator and vectorcontrol algorithm work efficiently in the close loop controlsystem to estimate generator speed for maximum powertracking from wind; and control active and reactive powerindependently.

200

800 .- ..-. .-. ..-.-.-.--.--.-- .-.--

2000 2 3 4 65 7 8 9 0

10

e...............................

St ........ .. .. ..._...

0 2 3 4 6 6 7 8 9 D

Tme (seC)

Fig. 14. Percentage of speed error using the speed estimator.

REFERENCES[1] H. P. Klein, J. Schmid, "Eurowin- the European Wind Turbine Data

Base," Annual reports from 1990 and 1991, EC DG XII. Brussels, 1992.[2] J. Twidell, "Renewable Energy: Implementation and Benefits,"

Advances in Power System Control, Operation and Management, 1993,pp. 418-424, vol. 1.

[3] E. Muljadi, and J. Green, "Battery Charging Using a Soft-StallControlled Wind Turbine," National Renewable Energy Laboratory,December 2001, Denver, Colorado.

[4] R. Esmaili, L. Xu, and D. K. Nichols, "A New Control Method ofPermanent Magnet Generator for Maximum Power Tracking in WindTurbine Application," Power Engineering Society General Meeting June2005.

[5] C. Schauder and H. Mehta, "Vector analysis and control of advancedstatic VAr compensators," in Proc. 1993 IEE Generation, Transmissionand Distribution Conference, pp.299-306, vol. 140.

[6] P. C. Krause, 0. Wasynzuk, and S. D. Sudhoff, "Analysis of ElectricMachinery and Drive Systems," John Wiley & Sons, New York, 2002

[7] R. Zhang, M. Cardinal, P. Szczesny, M. Dame, "A grid simulator withcontrol of single-phase power converters in D-Q rotating frame," PowerElectronics Specialists Conference, 23-27 June 2002, pp.1431 - 1436,vol.3.

[8] D. W. Hart, "Introduction to Power Electronics," Prentice Hall PTR,1999.

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