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Controlled Operation of Variable Speed Driven Permanent MagnetSynchronous Generator for Wind Energy Conversion Systems

RAJVEER MITTAL* K.S.SANDHU** D.K.JAIN***

Department of Electrical Engineering,

*Guru Gobind Singh Indraprastha University,M.A.I.T, New Delhi, India([email protected] )

**NIT, Kurukshetra(Deemed University),Haryana, India

([email protected] ) ***D.C.R.University of Science & Technology,

Sonepat-131039, Haryana, India(email: [email protected] ).

Abstract: - The introduction of distributed generation through renewable sources of energy has opened a

challenging area for power engineers. As these sources are intermittent in nature, variable speed electric generatorsare employed for harnessing electrical energy from these sources. However, power electronic control is required toconnect these sources to the existing grid. The grid interconnection issues are to be dealt with before connectingthese to the local grid. Power conditioners using self commutating devices are necessary to have grid friendlyinverters. In this paper, the MATLAB based simulation studies have been done to realize a grid friendly invertersystem for harnessing energy from a variable speed wind energy system. The system is designed for low harmonicinjection into the grid and fast control of voltage so as to meet the IEEE standard-1547 requirements.

Index Terms:- Power Conditioners, Power Quality, Variable Speed Generators, Wind Energy, Permanent MagnetSynchronous Generator.

1 IntroductionA wind turbine can be designed for a constant speedor variable speed operation. Variable speed windturbines can produce 8% to 15% more energy outputas compared to their constant speed counterparts,however, they necessitate power electronic convertersto provide a fixed frequency and fixed voltage powerto their loads. The major components of a typicalwind energy conversion system include a windturbine, generator, interconnection apparatus andcontrol systems. Most turbine manufacturers haveopted for reduction gears between the low speedturbine rotor and the high speed three-phasegenerators. Direct drive configuration, where agenerator is coupled to the rotor of a wind turbinedirectly, offers high reliability, low maintenance, and

possibly low cost for certain turbines.At the present time and in the near future, generatorsfor wind turbines will be synchronous generators,

permanent magnet synchronous generators (PMSG),and induction generators (IG),

including the squirrel cage type and wound rotor type.For small to medium power wind turbines, permanent

magnet generators and squirrel cage inductiongenerators are often used because of their reliabilityand cost advantages. Interconnection apparatuses aredevices to achieve power control, soft start andinterconnection functions. Very often, powerelectronic converters are used as such devices. Mostmodern turbine inverters are forced commutatedPWM inverters to provide a fixed voltage and fixedfrequency output with a high power quality. Forcertain high power wind turbines, effective powercontrol can be achieved with double PWM (pulsewidth modulation) converters which provide a bi-

directional power flow between the turbine generatorand the utility grid [7-9].Since wind speed is not constant, a wind farm 'sannual energy production is never as much as the sumof the generator nameplate ratings multiplied by thetotal hours in a year. The ratio of actual productivityin a year to this theoretical maximum is called thecapacity factor . Typical capacity factors are 20-40%,

WSEAS TRANSACTIONS on SYSTEMS Rajveer Mittal, K. S. Sandhu, D. K. Jain

ISSN: 1109-2777 189 Issue 2, Volume 8, February 2009
http://en.wikipedia.org/wiki/Wind_farmhttp://en.wikipedia.org/wiki/Capacity_factorhttp://en.wikipedia.org/wiki/Capacity_factorhttp://en.wikipedia.org/wiki/Wind_farm

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with values at the upper end of the range in particularly favorable sites [9].There are several ways of designing the conversionsystem, depending on power electronics. For full

power conversion, an AC/DC converter connected tothe generator (generator side converter) and a DC/ACconverter connected to the grid (grid side converter),with a DC-link between them is used. The DC linkvaries in an uncontrolled manner and a DC/DCconverter is inserted between the rectifier and theinverter. The grid side inverter is controlled so as tokeep minimum harmonic current injection in the grid.This paper is focused in a PMSG based direct driveturbine, connected to the grid by means of a full

power converter. The variable speed fed PMSG withAC- DC- AC conversion system is modeled andsimulated in MATLAB Simulink so as to verify the

proposed system.[1,8]

2 Wind Turbine GenerationTechnologies

2. 1 Fixed Speed Induction Generators (FSIG)Wind Turbines

The FSIG wind turbine is a simple squirrel cageinduction generator, which can be directly coupled tothe electricity supply network. The frequency of thenetwork determines the rotational speed of the statorsmagnetic field, while the generators rotor speedchanges as its electrical output changes. However,

because of the well known hard torque- slipcharacteristic of the induction machine, the operatingrange of the generator is very limited. The windturbine is therefore effectively fixed speed. FSIGs donot have the capability of independent control ofactive and reactive power, which is their maindisadvantage. Their great advantage is their simpleand robust construction, which leads to lower capitalcost. In contrast to other generator topologies, FSIGsoffer no inherent means of torque oscillation dampingwhich places greater burden and cost on their gearbox[2,8]. The wind energy system and power qualityaspects are discussed in detail in the literature [5, 18,21-23].

2.2 Doubly Fed Induction Generators (DFIG)Wind TurbinesThe DFIG is a wound rotor induction generator whoserotor is fed via slip rings by a frequency converter.The stator is directly coupled to the electrical powersupply network. As a result of the use of thefrequency converter, the network frequency isdecoupled from the mechanical speed of the machine

and variable speed operation is possible, permittingmaximum absorption of wind power. Since powerratings are a function of slip, DFIGs operate over arange of speeds between about 0.75 and 1.25 pu ofsynchronous frequency, which requires converter

power ratings of approximately 25%. A greatadvantage of the DFIG wind turbine is that it has thecapability to independently control active and reactive

power. Moreover, the mechanical stresses on a DFIGwind turbine are reduced in comparison to a FSIG.Due to the decoupling between mechanical speed andelectrical frequency that results from DFIG operation,the rotor can act as an energy storage system,absorbing torque pulsations caused by wind gusts [3,10, 11 , 19]. Other advantages of the DFIG includereduced flicker and acoustic noise in comparison toFSIGs. The main disadvantages of DFIG windturbines in comparison to FSIGs are their increasedcapital cost and the need for periodic slip ringmaintenance [4].

2.3 Direct Drive Synchronous Generator WindTurbine

An alternative to the much-used induction machinegenerator is the use of a multipole synchronousgenerator, fed through a power electronic AC/DC/ACstage. The excitation of the synchronous generatorcan be given either by an electrical excitation systemor by permanent magnets. The AC/DC/AC converteracts as a frequency converter and decouples thegenerator from the Grid. It consists of two back-to-

back voltage source converters, usually with IGBTswitches, which can independently control the active

power transfer through the DC link and the reactive power output at each converter terminal .The speedrange is generally similar to that of DFIGs. Themultipole construction of the synchronous generatorleads to a low mechanical rotational speed of thegenerator rotor and can permit direct coupling to thewind turbine. The possibility of reducing the numberof stages in the gearbox or eliminating it completelyis often quoted as an advantage of direct drivesynchronous generator wind turbines. However setagainst this is the greater VA rating of the powerelectronic converter compared with DFIGs and thelarger physical generator size. As a result of theincreased mechanical stresses experienced by FSIGwind turbines at present there is a practical limit to therating of commercial models of this technology. All

present commercial models for multi-MW windturbines in the range above 3MW are either DFIGs, orsynchronous generators coupled to the networkthrough back-to-back converters.A comparison between the variable speed wind



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turbine and the constant speed wind turbine showsthat variable speed reduce mechanical stresses: gustsof wind can be absorbed, dynamically compensate fortorque and power pulsations caused by back pressureof the tower. This backpressure causes noticeabletorque pulsations at a rate equal to the turbine rotorspeed times the number of rotor blades. The used of adoubly fed induction generator in WECS with therotor connected to the electric grid through an AC-ACconverter offers the following advantages:

only the electric power injected by the rotorneeds to be handled by the convert , implying aless cost AC-AC converter;

Improved system efficiency and power factorcontrol can be implemented at lower cost; theconverter has to provide only excitationenergy.

Hence, taking advantage of power electronic advancesin recent years, WECS equipped with doubly fedinduction generator systems for variable speed windturbine are one of the most efficient configurations forwind energy conversion[12].

2.4 Permanent Magnet SynchronousThe scheme of a grid-connected PMSG for direct-drive wind turbines is shown in Fig. 2. Theadvantages of PM machines over electrically excitedmachines can be summarized as follows according toliteratures:

higher efficiency and energy yield, no additional power supply for the magnet

field excitation, improvement in the thermal characteristics ofthe PM machine due to the absence of the fieldlosses,

higher reliability due to the absence ofmechanical components such as slip rings,

lighter and therefore higher power to weightratio.

However, PM machines have some disadvantages,which can be summarized as follows:

high cost of PM material, difficulties to handle in manufacture, Demagnetization of PM at high temperature.

In recent years, the use of PMs is more attractive than before, because the performance of PMs is improvingand the cost of PM is decreasing. The trends makePM machines with a full-scale power converter moreattractive for direct-drive wind turbines. Consideringthe performance of PMs is improving and the cost ofPM is decreasing in recent years, in addition to thatthe cost of power electronics is decreasing, variablespeed direct-drive PM machines with a full-scale

power converter become more attractive for offshorewind powers.[2-5] On the other hand, variable speedconcepts with a full-scale power converter and asingle- or multiple-stage gearbox drive train may beinteresting solutions not only in respect to the annualenergy yield per cost but also in respect to the totalweight. For example, the market interest of PMSGsystem with a multiple-stage gearbox or a single-stagegearbox is increasing [10-12, 20].

3 IEEE STD. 1547IEEE std. 1547[7] defines distributed generation (DG)as: Electric generation facilities connected to an AreaEPS through a point of common coupling (PCC); asubset of DR. And, distributed resources (DR) as:Sources of electric power that are not directlyconnected to a bulk power transmission system. Fig.1shows the various forms of distributed generation.

The power quality issues related to distributed

resources are: The DR and its interconnection system shallnot inject DC current greater than 0.5% of thefull rated output current at the point of DRconnection.

The DR shall not create objectionable flickerfor other customers on the area energy powersystem (EPS).

When the DR is serving balanced linearloads, harmonic current injection into theArea EPS at the point of common coupling(PCC) shall not exceed the limits stated. Theharmonic current injections shall be exclusiveof any harmonic currents due to harmonicvoltage distortion present in the Area EPSwithout the DR connected.

For an unintentional island in which the DRenergizes a portion of the Area EPS throughthe PCC, the DR interconnection system shalldetect the island and cease to energize theArea EPS within two seconds of theformation of an island.



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Fig .1. Distributed Generation

4 Grid Requirements4.1 Voltage Regulation A DR shall not cause the voltage at the Point ofCommon Coupling (PCC, see Figure 1) to go outsideof Range A specified by Standard ANSI C84.1(orCSA CAN3-C235-83) [6]. For a 120/240V system,this specifies a maximum voltage of 126/252V and aminimum voltage of 114/226V.

4.1.1 Synchronization When synchronizing, a DR shall not cause more than

+/-5% of voltage fluctuation at the PCC.

4.1.2 MonitoringA DR of 250 kW or larger shall have provisions formonitoring connection status and real and reactive

power output at the DR connection.

4.1.4 Isolation Device A readily accessible, lockable, visible-break isolationdevice shall be located between the DR and the EPS.

4.2 Safety and Protection Requirements

4.2.1 Voltage DisturbancesAt abnormal voltages, a DR shall cease to energizethe EPS within the specified clearing time.

4.2.2Frequency DisturbancesA DR shall cease to energize the EPS if the frequencyis outside the range 59.3 - 60.5 Hz.Loss of Synchronism: A DR of 250 kW or larger shallhave loss of synchronism protection function.

4.2.3Reconnection:A DR may reconnect to the power system 5 min. afterthe EPS voltage and frequency return to normal.

4.2.4 Unintentional IslandingA DR shall cease to energize the EPS within 2 sec. ofthe formation of an island.

4.3 Power Quality Requirements4.3.1 HarmonicsThe total demand distortion of a DR, which is definedas the total rms harmonic current divided by themaximum demand load current, shall be less than 5%.Each individual harmonic shall be less than thespecified level.

4.3.2 DC Current InjectionA DR shall have a dc current injection of less than0.5% of its rated output current.

Flicker: A DR shall not create objectionable flickerfor other customers on the area EPS.

5 Abnormal Grid ProblemsIn Europe, substantial wind penetration exists todayand will only increase over time. The impacts on thetransmission network are viewed not as an obstacle todevelopment, but rather as obstacles that must beovercome. High penetration of intermittent wind

power (greater than 20 percent of generation meetingload) and may affect the network in the following

ways and has to be studied in detail:

5.1 Poor grid stabilityFor economic exploitation of wind energy, a reliablegrid is as important as availability of strong winds.The loss of generation for want of stable grid can be10% to 20% and this deficiency may perhaps be themain reasons for low actual energy output of WEGscompared to the predicted output in known windyareas with adequate wind data.

5.2 Low-frequency operationLow frequency operation affects the output of WEGsin two ways. Many WEGs do not get cut-in, when thefrequency is less than 48 Hz (for standard frequencyof 50 Hz) through wind conditions are favorable, withconsequent loss in output. This deficiency apart, theoutput of WEGs at low frequency operation isconsiderably reduced, due to reduced speed of therotor. The loss in output could be about 5 to 10% onthe account of low frequency operation.



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5.3 Impact of low power factorWEGs fitted with induction generators need reactive

power for magnetizing. Normally in conventionalenergy systems, generators apart from supplyingactive power will be supplying a reactive power. Butin case of WEGs fitted with induction generators,

instead of supplying reactive power to the grid, theyabsorb reactive power from grid, which undoubtedlyis a strain on the grid. Suitable reactive powercompensation may be required to reduce the reactive

power burden on the grid.

5.4 Power flowIt is to be ensured that the interconnectingtransmission or distribution lines will not be over-loaded. This type of analysis is needed to ensure thatthe introduction of additional generation will not

overload the lines and other electrical equipment.Both active and reactive power requirements should be investigated.

5.5 Short circuitIt is required to determine the impact of additionalgeneration sources to the short circuit current ratingsof existing electrical equipment on the network.

5.6 Power QualityFluctuations in the wind power may have direct

impact on the quality of power supply. As a result,large voltage fluctuations may result in voltagevariations outside the regulation limits, as well asviolations on flicker and other power qualitystandards.

6. Various Topologies for GridConnected Variable Speed PMSG

Variable speed use is good for extracting more primemover power as in wind turbine or for providingoptimum efficiency for the prime mover by increasing

its speed with power. Variable speed also allows for amore flexible generator system. For wind turbines, a battery may be added to store the extra wind energythat is not momentarily needed for the existing loadsor local power grids [13-17]. There are two mainways to handle the necessity of constant DC linkvoltage at variable speed:

PMSG with diode rectifier and DC-DCchopper as shown in Fig. 2.

PMSG with rectifier and DC-DC boost

convertor as shown in Fig. 3. PMSG with PWM rectifier with battery for

storing the extra wind energy as shown in Fig.4.

Fig.2.PMSG with diode rectifier and DC-DC chopper

Fig .3. PMSG with rectifier and DC-DC Boostconvertor

Fig .4. PMSG with PWM rectifier with battery forstoring the extra wind energy

7 Proposed System and ModellingA Permanent Magnet Synchronous Generator isdriven by a variable speed wind energy conversionsystem. The PMSG block is fed from the speedcontroller. The speed fed is 94 rad/sec correspondingto 60 Hz supply system for four pair of poles. The ACoutput of PMSG is rectified with the help ofuncontrolled rectifier. The DC-DC boost converter is



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used to keep the DC-link voltage constant at the VSIinverter input. The inverter output is fed to the grid.The inverter is controlled so that the injected currentis near to sinusoidal.The supply system consists of wind turbine, three-

phase PMSG, DC- AC-DC converter and voltagesource inverter system.

7.1 Wind Turbine ModelingThis block implements a wind energy conversionsystem. The inputs are actual and desired speed andthe output of the block is mechanical power (P ). Theamount of power harnessed from the wind of velocityv is as follows.P=1/2 AC p 3WhereP = wind power in watts = air density in kg/m 3A= swept area in m 2

C p=power coefficient of wind turbine

= wind speed in m/s7.2 Modeling of Permanent Magnet

Synchronous MachineThe permanent magnet synchronous machine blockoperates in generating or motoring modes. Theoperating mode is dictated by the sign of themechanical power (positive for generating, negativefor motoring). The electrical part of the machine isrepresented by a sixth-order state-space model. Themodel takes into account the dynamics of the statorand damper windings. The equivalent circuit of the

model is represented in the rotor reference frame (d-qframe). The following equations are used to expressthe model of the PMSG as:Vd = R sid + p d - w r q (1)Vq = R siq + p q + w r d (2)V fd = R fdi fd + p fd (3)V kd = R kdikd + p kd (4)V kq1 = R kq1ikq1 + p kq1 (5)V kq2 = R kq2ikq2 + p kq2 (6)where d = Ld id + Lmd ( i fd + ikd) (7)

q = Lq iq + Lmq ikq (8)fd = L fd i fd + Lmd ( id + ikd) (9)kd = L kd ikd + Lmd ( id + i fd) (10)kq2 = L kq2 i kq2 + Lmq iq (11)

where the subscripts used are defined as: d, q: d and qaxis quantity, r, s: Rotor and stator quantity, l, m:Leakage and magnetizing inductance, f, k: Field anddamper winding quantity. R s represents statorresistance, L ls stator leakage inductance, L md and L mq represent d-axis and q-axis magnetizing inductances.R f ' denotes field resistance and L lfd ' leakageinductance, both referred to the stator. Damper d-axis

resistance R kd ' and leakage inductance L lkd ', Damperq-axis resistance R kq1' and leakage inductance L lkq1 'and the q-axis resistance R kq2 ' and leakage inductanceL lkq2 ' All these values are referred to the stator. Allrotor parameters and electrical quantities are viewedfrom the stator and are identified by primed variables.The simplified synchronous machine blockimplements the mechanical system described by:w(t)= (Tm Te)dt / (2H) K dw(t) (12)w(t) = w(t) + w o (13)

7.3 Excitation SystemFor simulation of PMSG, the excitation is kept

constant at 1.0 p.u. in this model of synchronousgenerator.

7.4 Modeling of Control SchemeThe control scheme is mainly used to derive

reference source currents, which are used in PWMcurrent controller of VSI of BESS. These are derived

in following section.The reference source currents are having twocomponents, in-phase component and a quadraturecomponent. They are estimated in sequence asfollows:The unit vectors in-phase with v a, v b and v c arederived as:ua = v a / V m; u b = v b / V m; u c = v c / V m (14)where V m is the amplitude of the AC terminal voltageat the PCC and can be computed as:Vm = 2/3 (v a2+v b2+v c2) (15)where v a, v b, and v c are the instantaneous voltages at

PCC and can be calculated as:va = v san - R s isa - Ls pi sa (16)v b = v sbn - R s isb - Ls pi sb (17)vc = vscn - R s isc - Ls pi sc (18)where L s and R s are per phase source inductance andresistance respectively. v san , v sbn , and v scn are the three

phase instantaneous input supply voltages at PCCand are expressed as:vsan=v smsin( t)vsbn=v smsin( t-2/3) (19)vscn=v smsin( t+2/3)

where v sm is the peak value and = 2 f is thefrequency of the supply.The unit vectors in-quadrature with v a v b and v c may

be derived by taking a quadrature transformation ofthe in-phase unit vectors u a, u b and u c as:wa = - u b/ 3 + u c/ 3 (20)w b = 3 u a/ 2 + (u b -u c)/(2 3) (21)wa = -3 u a/ 2 + (u b -u c)/(2 3) (22)The quadrature component of the reference sourcecurrents is computed as:The voltage error V er at PCC at the nth sampling



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instant is as:Ver(n) = V ref(n) V m(n) (23)The output of the PI controller at the nth samplinginstant is expressed as:I* smq(n) = I* smq(n-1) +K p{V er(n) - V er(n-1) }+K iVer(n) (24)where K p and K i are the proportional and integralconstants, respectively of the proportional integral(PI) controller and the superscript represents thereference quantity.The quadrature components of the reference sourcecurrents are estimates as:i*saq = I* smq wa; i*sbq = I* smq w b; I*scq = I* smq wc (25)The in-phase component of the reference sourcecurrents is computed as:i*sad= I* smd ua; i* sbd = I* smd u b; i*scd = I* smd uc (26)where I*smd is considered fixed value corresponding tothe constant source current for load leveling.

Reference source currents are computed as the sumof the in-phase components of the reference sourcecurrents and the quadrature components of the

reference source currents given as:i*sa= i* saq+i* sad; i* sb=i* sbq+i* sbd ; i*sc=i* scq+i* scd (27)These source reference currents are compared withthe sensed source currents in PWM current controller.The current errors of all the three phases areamplified. If the amplified reference source currenterror signal, i saerr , is greater than the triangular wavecarrier signal, switch S 1 is ON and switch S 4 is OFF,and the value of SA is 1. When the amplifiedreference source current error signal is less than thetriangular wave carrier signal switch S 1 is OFF andswitch S 4 is ON, and the value of SA is 0. Similarlogic applies to other phases.

8 MATLAB Simulation of theProposed Topology

The MATLAB simulation of the PMSG and the DC-DC boost converter is shown in the Fig. 5. Theinverter and the grid system is shown in Fig. 6.

Out22Out11

Conn 22

Conn 11

v+-

v+-

v+-

Vdc_ref (V)

94

A

B

C

+

-

Three -Phase Breaker

A

B

C

a

b

c

Three -PhaseSeries RLC Load

A B C

Scope2

Scope1

Permanent MagnetSynchronous Machine

w

mA

B

C

1+

1

+2

2

g

m

C

E

g

m

C

E

[Ic]

Vdcin]

[VdcO]

[Iabc _Source ]

[Vabc_Source]

lse lse

Display

300

i +-

Fig. 5. MATLAB simulation of PMSG and DC-DC converter



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vbc2

v+-

powergui

Discrete,s = 1e-005 s

Three -Phase So

A

B

C

Three -PhaseParallel RLC Load 1

A B

Subsystem

Out1

Out2

Conn1

Conn2

IGBT Inverter 1

g

A

B

C

+

-

[Iabc _grid]

[Vabc_grid][Vabc_source]

[Vdc]

[Iabc _source]

[Pulsesg]

I

c

I

c

Fig. 6. MATLAB simulation of inverter and the grid

9. Simulation ResultsThe figures 7-9 show the source voltages (V abc),source currents (I abc), grid voltages (V grid), gridcurrents (I grid) and the DC- link voltage (V dc). Therating of the PMSG is given in the Appendix.

9.1 Performance of the proposed system atrated wind speed :

The PMSG is run at 31.6 rad/sec. The PMSGgenerator voltage builds up to 100 volts. Once the

steady state is reached, the generator output isconnected to the uncontrolled rectifier. Theuncontrolled DC is kept constant to 250 volts at theDC link with the help of DC-DC Boost Convertor as

shown in Fig. 7. The inverter output I grid is sinusoidalas shown in the Fig. 8 indicating the low harmonics

9.2 Performance of the proposed system atreduced wind speed :

The PMSG is now run at half of the rated speed at15.8 rad/sec. The PMSG generator voltage builds upto 50 volts. Once the steady state is reached, thegenerator output is connected to the uncontrolledrectifier. The uncontrolled DC is again kept constantto 250 volts at the DC link as shown in Fig. 9. Theinverter output V grid and I grid are sinusoidal as shownin the figure indicating the low harmonics. The powergenerated by PMSG is absorbed by the grid.



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-200

0

200

V a

b c

-20

0

20

I a

b c

-200

0

200

V g r

i d

-10

0

10

I g r

i d

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0

240

250

260

270

time(s)

V d c

Fig. 7. Performance of PMSG system at rated speed

1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1-4

-3

-2

-1

0

1

2

3

4

time(sec.)

i n j e c t e d c u r r e n t

( A )

Fig. 8. Injected current at rated speed



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-200

0

200

V a

b c

-20

0

20

I a

b c

-200

0

200

V g r

i d

-10

0

10

I g r

i d

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0240

250

260

270

time(s)

V d c

Fig .9. Performance of PMSG system at half of the rated speed

10 ConclusionIn this paper the power conditioning of variable speeddriven PMSG fed AC-DC-AC system has beenstudied for reduced harmonics injection into the grid.The inverter is controlled so as to meet IEEE standard1547 requirements for connection of distributed

generation to the local grid. The simulated resultsvalidate the proposed topology.

Appendi x:

Permanent Magnet Synchronous Generator:3-Phase , 300 V, 60 Hz, 3000 rpm, 4-poleElectromagnetic Torque : 0.8 NmStator Resistance(R S) : 18.7 Inductance : Ld(H) = Lq(H) : 0.02682 HFlux induce by magnets : 0.1717 wb

References:

[1] Ghosh and G. Ledwich, Power QualityEnhancement Using Custom Power Devices.Kulwer Academic, 2002.

[2] Gipe, P. (1995) Wind power, Chelsea GreenPublishing Company, Post Mills, Vermount,

USA.[3] S. Santoso, H. W. Beaty, R. C. Dugan, and M. F.McGranaghan, "Electrical Power SystemsQuality," 2d ed: McGraw Hill, 2002.

[4] Singh, B. (1995) Induction generator-a prospective, Electric Machines and PowerSystems , Vol. 23, pp. 163-177.

[5] C. Ong "Dynamic Simulation of ElectricMachines Using MATLAB/Simulink" Editorial"Prentice Hall", 1998.



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