three-phase to single-phase generation system …th ree-phase to single-phase generation system...
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Eletrôn. Potên., Fortaleza, v. 25, n. 1, p. 85-95, jan./mar. 2020 85
Th ree-Phase to Single-Phase Generation System Based on Doubly-Fed Induction Ge-nerator
Filipe V. Rocha, Nady Rocha, Victor F. M. B. Melo, Edison R. C. da Silva, Cursino B. Jacobina
THREE-PHASE TO SINGLE-PHASE GENERATION SYSTEM BASED ONDOUBLY-FED INDUCTION GENERATOR
Filipe V. Rocha1, Nady Rocha1, Victor F. M. B. Melo1, Edison R. C. da Silva1, Cursino B. Jacobina21Federal University of Paraíba, João Pessoa – Paraíba, Brazil
2Electrical Engineering Department - Federal University of Campina Grande - UFCG - Campina Grande, Paraíba, Brazile-mail: [email protected], [email protected], [email protected], [email protected],
Abstract – This paper presents a three-phase to single-phase six-leg converter for a wind energy conversionsystem based on Doubly-Fed Induction Generator (DFIG).The converter is composed of six legs and is dividedin three parts: the grid-side converter (GSC), which isresponsible for power factor and DC-link voltage controls,the stator-side converter (SSC), which guarantees thecontrol of the stator voltage, and the rotor-side converter(RSC), which is responsible for vector control of thegenerator. One of the converter’s legs is shared by grid-side and stator-side converters. The main advantages ofthe proposed configuration compared to other topologiespresented in the literature are providing balanced three-phase voltages to the DFIG, simple control system andnot having any limitation with respect to synchronizationbetween grid and stator voltages and DC-link voltage. Thesystem model, pulse-width modulation (PWM) and controlstrategies are discussed and simulation and experimentalresults are presented in order to prove the feasibility of thesystem.
Keywords – DFIG, THREE-PHASE TO SINGLE-PHASE, WECS.
I. INTRODUCTION
Energy demand has increased significantly in the lastdecades and, to ensure the energy security, renewable sourceshave been increasingly explored [1]–[4]. Wind energy is oneof the most competitive among renewable energies. Lowcost generation systems are based on wind turbines with fixedspeed, usually using squirrel cage induction generator (SCIG).The generator is connected to the grid (single-phase or three-phase source) and the reactive power and grid voltage cannotbe controlled [5], [6]. In variable speed systems, the generatoris connected to the grid through an AC-DC-AC converter.Employing either SCIG or permanent magnet synchronousgenerator (PMSG), the generator is connected to a full powerAC-DC-AC converter, meaning that all of the generator poweris processed by the converter [7]–[13].
When only single-phase grid is available (commoncondition in rural or remote areas), the connection betweena three-phase generator and the single-phase grid can beobtained from a three-phase to single-phase converter. In[5] a three-phase SCIG was connected to a single-phase grid
This footnote will be used only by the Editor and Associate Editors. Theedition in this area is not permitted to the authors. This footnote must notbe removed while editing the manuscript.
by means of a five-leg converter, in which the generatorside converter was composed of three legs and the grid sideconverter was composed of two legs, all sharing the same DC-link. In [14], a low-cost system was proposed to connecta three-phase SCIG to a single-phase grid. The generator’sphases were delta-connected and a capacitor was parallel-connected to one of the phases, using the Steimetz connection.In [11], a three-phase SCIG is connected to a single-phasegrid using parallel converters in order to reduce the currentper leg in the grid, reducing, in turn, semiconductor losses andswitches current rating.
On the other hand, very few single-phase to three-phasewind energy systems based on doubly-fed induction generator(DFIG) were discussed in the literature [15]–[17]. A structureof a single-phase grid connected to a three-phase DFIG wasdiscussed in [15], which is illustrated in Figure 1.a. Aninverter is connected to the three-phase rotor of the DFIG,while the three-phase stator is connected to a single-phasegrid. Needless to say, the DFIG stator operates underunbalanced condition, which brings high complexity to thecontrol system in order to adjust speed, stator reactive powerand grid power factor. Besides, the inverter uses a floatingcapacitor, since the system operates employing the singleexternal feeding (SEF) concept, which complicates even morethe control system.
Other possible structure was proposed in [16], in which aDFIG is composed of a three-phase rotor, fed by an inverter,and a single-phase stator, which is connected directly tothe grid. This configuration avoids the unbalanced operationobserved in the topology of Figure 1.a, but single-phaseDFIG with three-phase rotor is not easily found in trade.Atlast, in [17] the authors proposed three single-phase to three-phase converter topologies for DFIG composed of eight,seven and six legs. Pulse-Width Modulation (PWM) andcontrol strategies were presented and a semiconductor lossesanalysis was performed. According to this analysis, thebest performance was achieved with the seven-leg topologyillustrated in Figure 1.b. Note that there is a shared leg betweenthe DFIG stator and the grid. This requires synchronizationbetween the grid voltage and stator voltage, otherwise the levelof DC-link voltage and the power processed by the convertermay increase. However, the six-leg topology is not interestingat all, because the dc-link voltage is bigger than the seven-legtopology. It has to use the double of dc-link voltage.
This paper proposes a single-phase to three-phase topologyin which the DFIG is directly connected to the single-phasegrid and the converter processes only part of the overall outputpower. The converter is divided into three parts as shown in
Eletrôn. Potên., Fortaleza, v. 25, n. 1, p. 85-95, jan./mar. 202086
(a)
DFIG
(b)
Fig. 1. Topologies discussed in (a) [15]. (b) [17].
Figure 2. The grid-side converter (GSC), which is responsiblefor power factor and DC-link voltage controls, the stator-sideconverter (SSC), which guarantees stator voltage control, andthe rotor-side converter (RSC), which is responsible for vectorcontrol of the DFIG. Compared to other topologies presentedin the literature, the proposed system has the advantages ofproviding balanced three-phase voltages to the DFIG, simplecontrol system and does not have any limitation with respectto synchronization between grid and stator voltages and DC-link voltage. The structures illustrated in Figure 1 willbe considered as conventional topologies for benchmarkingpurposes. The proposed system was previously analyzed in[18], but this paper adds information regarding the controllersdesign and new experimental results of the proposed rotorcontrol system.
II. MACHINE MODEL
The induction generator model in d − q generic referenceframe is given by [19]:
vgs = rsigs +
ddt
φ gs + jωgφ g
s (1)
vgr = rrigr +
ddt
φ gr + j (ωg −ωr) φ g
r (2)
φ gs = (lls + lm)igs + lmigr (3)
φ gr = lmigs +(llr + lm)igr (4)
ce = 2Plmℑ(igs ig∗r ) (5)Ps = (vg
sdigsd + vgsqigsq) (6)
Qs = (vgsdigsq − vg
sqigsd) (7)
where j =√−1 is an imaginary number, xg
n = xgnd + jxg
nq isthe vector of variable x in generic reference with n = s,r (s =stator and r = rotor), x = v, i,φ , and ℑ(z) is the imaginary partof z. Furthermore, v, i and φ are vectors of voltage, current andflux, respectively; ωg is the rotation speed generic reference
frame and ωr is the electrical rotor speed; rs and rr are theresistance of the stator and rotor, respectively; lls and llr arethe leakage inductances of stator and rotor, respectively; lm isthe stator-rotor mutual inductance; ce is the electrical torque;P pair of poles; Ps and Qs are the stator active and reactivepowers, respectively.
III. SYSTEM MODEL
The proposed configuration illustrated in Figure 2 consistsin three parts: grid-side, stator-side and the rotor-sideconverters (GSC, SSC and RSC, respectively). Theseconverters depict a single-phase AC-DC-AC converter with ashare leg (leg s). The mathematical model of the system isgiven by:
eg = rai1 + ladi1dt
+ rai2 + ladi2dt
+ vg (8)
vs32 = rai3 + ladi3dt
+ rai2 + ladi2dt
+ v32 (9)
i1 = −is1 + ig (10)i2 = is2 + ig (11)i3 = −is3 (12)vg = vg10 − vs0 (13)
v32 = vs10 − vs0, (14)
where ra and la represent the resistance and inductance ofinductor filter, respectively, vg and v32 are the voltages of theGSC and SSC, respectively, vg10 and vs10 are the pole voltagesof the GSC and SSC, respectively, vs0 is the pole voltage of theshared-leg between the GSC and SSC, ig is the grid current, i1,i2 and i3 are the currents of GSC and SSC and is1, is2 and is3are the generator currents. From (8) the voltage of the grid-side converter (vg = vg10−vs0) can be used to regulate the gridcurrent and from (9) the voltage of the SSC (v32 = vs10 − vs0)can be used to control the line machine voltage vs23 since theline voltage vs12 is already defined by the grid voltage. Themodel of the RSC is similar to that of the conventional three-phase system [19].
IV. CONTROL STRATEGY
Figure 3 shows the control block diagram of the proposedsystem. The control block is divided in the DC-link voltageand power factor control (realized by means of the GSC),the line voltage control (realized by means of the SSC) andthe active and reactive power control (realized by means ofthe RSC). The grid-side converter control consists of twocascaded control loops. In the outer loop, the capacitor DC-link voltage vC is adjusted to its reference value v∗C utilizinga PI type controller, represented by block RC. The output ofthe DC-link voltage control is the amplitude of the referencecurrent of the single-phase grid (I∗g ). The instantaneousreference current (i∗g) is synchronized with the grid voltage bymeans of a Phase Locked Loop (PLL) scheme [20] representedin Figure 3 by block Gir. In the inner current loop, the gridcurrent control is implemented using a resonant controllerdescribed in [21]. This controller is represented by block Rg.The output of the current control defines the reference voltagev∗g.
Eletrôn. Potên., Fortaleza, v. 25, n. 1, p. 85-95, jan./mar. 2020 87
AC-DC-AC
2vc
2vcra
ra
ra
l
l
l vg
v32
Fig. 2. Proposed topology.
Fig. 3. Control block diagram converters GSC and SSC.
At the stator-side converter, the line voltage control isrealized also using a resonant controller, represented by blockRs. As the voltage vs12 is already defined by the grid voltage,because the grid source is directly connected to the generator,the amplitude of grid voltage is estimated by block Gamp toensure the balanced three-phase voltages. As presented inFigure 3, the Gamp block extracts the amplitude of the eg(i.e., Vg) multiplying the grid voltage eg by an unity sinusoidalsignal. The angle of the sinusoidal signal is obtained usinga PLL scheme and it is approximately equal to the angle ofthe grid voltage. Thus, with a Low Pass Filter (block LPF),the amplitude of the grid voltage is extracted (Vg). Then, thereference line voltage v∗s32 is determined by the block Gvs andit is compared to the measured line voltage vs32. Thereafter,the controller (Rs) determines the reference voltage v∗32.
A. DFIG Vector ControlThere are two main DFIG control strategies: the Direct
Power Control (DPC), where the reference voltages areobtained from the direct control of active and reactivepower [22]; and Voltage Oriented Control (VOC), where thereference voltages are obtained from the cascade control ofthe active and reactive power with the dq components of therotor current in the stator voltage reference [23].
The VOC was the strategy used in this work. Block diagramof the control RSC is shown in Figure 4. The reference d-axisis chosen to align with the stator voltage, resulting in null value
for the stator voltage component q-axis (vvsq = 0). Thus, from
(3), (6) and (7) it is possible to write the equations of active andreactive power of the stator as functions of the rotor currentsas:
Ps =−lmvv
sdls
ivrd (15)
Qs =lmvv
sdls
ivrq. (16)
In (15) and (16) it is noted that the active and reactive powerare decoupled in terms of the dq currents of rotor. In thisway, the method of control is based on decoupled control ofactive and reactive power. The reference dq rotor currentsare obtained using two PI controllers, where the active powerloop defines the iv∗rd component and the reactive power loopdetermines the iv∗rq component. The current control is realizedin the stationary reference frame. Then, the currents is∗rd andis∗rq are obtained from coordinate transform e jθ , where θ is theangle between the stator voltage reference frame and the statorreference frame. They are compoared to the measured valuesand controlled by resonant PI controllers (PI-R), obtaining therotor voltages in the stator reference frame. From the rotorposition and coordinate transform e− jε , where ε is the anglebetween the stator reference frame and the rotor referenceframe. The rotor reference voltages are determined in therotor reference frame, and then the voltages v∗r1, v∗r2 and v∗r3are obtained from dq-123 block, based on Park’s transform.The rotor voltages are used in the PWM strategy.
PI
Q s
−
Qs + ivrq
PI
Ps
−
Ps + ivrd
ejθ
sen θ cos θ
PI-Risrq
isrq
−
PI-Risrd
isrd
−
e−jε
sen ε cos ε
dq
123
vr2
vr1
vr3
*
*
*
*
*
*
*
*
*
Σ
Σ
Σ
Σ
Fig. 4. Block diagram of power system.
(a)
DFIG
(b)
Fig. 1. Topologies discussed in (a) [15]. (b) [17].
Figure 2. The grid-side converter (GSC), which is responsiblefor power factor and DC-link voltage controls, the stator-sideconverter (SSC), which guarantees stator voltage control, andthe rotor-side converter (RSC), which is responsible for vectorcontrol of the DFIG. Compared to other topologies presentedin the literature, the proposed system has the advantages ofproviding balanced three-phase voltages to the DFIG, simplecontrol system and does not have any limitation with respectto synchronization between grid and stator voltages and DC-link voltage. The structures illustrated in Figure 1 willbe considered as conventional topologies for benchmarkingpurposes. The proposed system was previously analyzed in[18], but this paper adds information regarding the controllers
design and new experimental results of the proposed rotorcontrol system.
II. MACHINE MODEL
The induction generator model in d − q generic referenceframe is given by [19]:
vgs = rsigs +
ddt
φ gs + jωgφ g
s (1)
vgr = rrigr +
ddt
φ gr + j (ωg −ωr) φ g
r (2)
φ gs = (lls + lm)igs + lmigr (3)
φ gr = lmigs +(llr + lm)igr (4)
ce = 2Plmℑ(igs ig∗r ) (5)Ps = (vg
sdigsd + vgsqigsq) (6)
Qs = (vgsdigsq − vg
sqigsd) (7)
where j =√−1 is an imaginary number, xg
n = xgnd + jxg
nq isthe vector of variable x in generic reference with n = s,r (s =stator and r = rotor), x = v, i,φ , and ℑ(z) is the imaginary partof z. Furthermore, v, i and φ are vectors of voltage, current andflux, respectively; ωg is the rotation speed generic reference
frame and ωr is the electrical rotor speed; rs and rr are theresistance of the stator and rotor, respectively; lls and llr arethe leakage inductances of stator and rotor, respectively; lm isthe stator-rotor mutual inductance; ce is the electrical torque;P pair of poles; Ps and Qs are the stator active and reactivepowers, respectively.
III. SYSTEM MODEL
The proposed configuration illustrated in Figure 2 consistsin three parts: grid-side, stator-side and the rotor-sideconverters (GSC, SSC and RSC, respectively). Theseconverters depict a single-phase AC-DC-AC converter with ashare leg (leg s). The mathematical model of the system isgiven by:
eg = rai1 + ladi1dt
+ rai2 + ladi2dt
+ vg (8)
vs32 = rai3 + ladi3dt
+ rai2 + ladi2dt
+ v32 (9)
i1 = −is1 + ig (10)i2 = is2 + ig (11)i3 = −is3 (12)vg = vg10 − vs0 (13)
v32 = vs10 − vs0, (14)
where ra and la represent the resistance and inductance ofinductor filter, respectively, vg and v32 are the voltages of theGSC and SSC, respectively, vg10 and vs10 are the pole voltagesof the GSC and SSC, respectively, vs0 is the pole voltage of theshared-leg between the GSC and SSC, ig is the grid current, i1,i2 and i3 are the currents of GSC and SSC and is1, is2 and is3are the generator currents. From (8) the voltage of the grid-side converter (vg = vg10−vs0) can be used to regulate the gridcurrent and from (9) the voltage of the SSC (v32 = vs10 − vs0)can be used to control the line machine voltage vs23 since theline voltage vs12 is already defined by the grid voltage. Themodel of the RSC is similar to that of the conventional three-phase system [19].
IV. CONTROL STRATEGY
Figure 3 shows the control block diagram of the proposedsystem. The control block is divided in the DC-link voltageand power factor control (realized by means of the GSC),the line voltage control (realized by means of the SSC) andthe active and reactive power control (realized by means ofthe RSC). The grid-side converter control consists of twocascaded control loops. In the outer loop, the capacitor DC-link voltage vC is adjusted to its reference value v∗C utilizinga PI type controller, represented by block RC. The output ofthe DC-link voltage control is the amplitude of the referencecurrent of the single-phase grid (I∗g ). The instantaneousreference current (i∗g) is synchronized with the grid voltage bymeans of a Phase Locked Loop (PLL) scheme [20] representedin Figure 3 by block Gir. In the inner current loop, the gridcurrent control is implemented using a resonant controllerdescribed in [21]. This controller is represented by block Rg.The output of the current control defines the reference voltagev∗g.
Eletrôn. Potên., Fortaleza, v. 25, n. 1, p. 85-95, jan./mar. 202088
Gci(s) Gv (s) Gi(s)*Ird(s)s *Vrd(s)
sVrd(s)s
Ird(s)s
Gci(s) Gv (s) Gi(s)*Irq(s)s *Vrq(s)
sVrq(s)s
Irq(s)s
Fig. 5. Block diagram of current control system.
1) Design of Current Controllers: From the equations ofthe dynamic modeling of the DFIG, a current control loop isdefined, as illustrated in Figure 5. Gi(s) is the transfer functionof the current plant, Gv(s) is the voltage source represented bya first order transfer function with time constant Tv and Gci(s)the transfer function of the PI controller.
Gi(s) =Isrd(s)
V srd(s)
=Isrq(s)
V srq(s)
=
1rsr
σ lrrsr
s+1(17)
Gv(s) =V s∗
rd (s)V s
rd(s)=
V s∗rq (s)
V srq(s)
=1
Tvs+1(18)
Gci =Kii
s(
Kpi
Kiis+1) (19)
σ = 1− l2m
lslr(20)
rsr =(ls −σ ls)rr
lr(21)
where σ is leakage coefficient, ls (ls = lls + lm) and lr (lr =llr + lm) are the inductances of stator and rotor, respectively.The closed loop transfer function shown in (22) is obtained bycanceling the current plant pole (s=− rsr
σ lr) with the zero of the
PI controller (s = − KiiKpi
). The gains Kii and Kpi are calculatedin order to obtain real and identical poles of the closed-looptransfer function G f I .
G f I(s) =Kii/rsr
Tvs2 + s+(Kii/rsr)(22)
Kii =rsr
4Tv(23)
Kpi =σ lr4Tv
. (24)
2) Design of Power Controllers: The power control loop isshown in Figure 6, in which Gcp(s) and Gcq(s) are the transferfunctions of the active and reactive PI controllers, respectively;Gp(s) and Gq(s) are the transfer functions obtained from (15)and (16) and G f I(s) is the internal loop of the current control,which is approximated to a first-order function.
Gp(s) = Gq(s) =Ps(s)Isrq(s)
=Qs(s)Isrd(s)
=lmVs
ls(25)
Gcp = Gcq =Kipq
s(
Kppq
Kipqs+1) (26)
G f I =1
(2Tvs+1)2 ≈ 14Tvs+1
(27)
From (25)-(27) closed-loop transfer function is defined by:
G f p(s) = G f q(s) =lmVsKppqs+lmVsKipq
4lsTv
s2 +lmVsKppq+ls
4lsTvs+ lmVsKipq
4lsTv
. (28)
The denominator can be represented by polynomialcharacteristic of a second-order system s2 + 2ξ ωns + ω2
n ,where ωn is natural frequency and ξ is damping factor. Thenthe gain is given by:
Kipq(s) =4lsTvωn
2
lmVs(29)
Kppq(s) =1
lmVs(8lsTvξ ωn − ls) (30)
where the values of the damping factor, natural frequency andTv are ξ = 0.8, ωn = 9.5 rad/s and Tv = 0.01s, respectively.
Gcp(s) Gfi (s) Gp (s)*Ps (s)
*Ird(s)s
Ird(s)s Ps(s)
Gcq(s) Gfi (s) Gq (s)*Qs(s)
*Irq(s)s
Irq(s)s Qs(s)
Fig. 6. Block diagram of power control system.
V. PWM STRATEGY
The RSC can be commanded by using an adequate PWMstrategy for three-phase voltage source inverter [24]–[26].Only the PWM implementation of grid and stator sideconverters is highlighted in this paper.
In Sinusoidal PWM (SPWM) the reference pole voltagesare compared with a high frequency triangular signal todetermine the switch states. Considering that v∗g is the GSCreference voltage and v∗32 is the SSC reference voltage, theycan be defined based on the reference pole voltages by
v∗g = v∗g10 − v∗s0 (31)v∗32 = v∗s10 − v∗s0. (32)
In order to determine the three pole voltages, an auxiliaryvariable v∗x must be added. By making v∗x = v∗s0, the referencepole voltages v∗g10, v∗s0 and v∗s10 are determined by:
v∗g10 = v∗g + v∗x (33)v∗s0 = v∗x (34)
v∗s10 = v∗32 + v∗x . (35)
The choice of the auxiliary variable v∗x is free in a rangedefined by the limits of the pole voltages ±v∗C/2.
The voltage v∗x must be chosen such that:
v∗xmin ≤ v∗x ≤ v∗xmax (36)
v∗xmin = −v∗C2−minv∗g,v
∗32,0 (37)
v∗xmax =v∗C2−maxv∗g,v
∗32,0, (38)
Eletrôn. Potên., Fortaleza, v. 25, n. 1, p. 85-95, jan./mar. 2020 89
where v∗C is the reference DC-link voltage. Once v∗x isdetermined, the reference pole voltages v∗g10, v∗s0 and v∗s10 areobtained from (33) to (35).
VI. ANALYSIS OF GSC AND SSC
A. Normalized Currents Processed by GSC and SSCThe currents of the GSC and SSC are defined as i1, i2 and
i3 and are determined by (10)-(12). Figure 7 shows currentsRMS values normalized by nominal generator current (isn).The curves shown in Figure 7 were obtained considering fourdifferent mechanical torques [100%, 75%, 50% and 25% ofthe nominal (rated) mechanical torque] with the range of therotor speed being from 0.7 to 1.3 of the synchronous speed.
Rotor Speed (PU)
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
Curr
ent
Leg
- g
1(P
U)
0
0.2
0.4
0.6
0.8
1
1.2
1.4100%
75%
50%
25%
(a)
Rotor Speed (PU)
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
Cu
rren
t L
eg -
s(P
U)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
100%
75%
50%
25%
(b)
Rotor Speed (PU)
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
Cu
rren
t L
eg -
s1
(PU
)
0
0.2
0.4
0.6
0.8
1 100%
75%
50%
25%
(c)
Fig. 7. Normalized currents. (a) Current of the leg g1. (b) Current ofthe leg s. (c) Current of the leg s1.
Figures 7.a and 7.b show that currents of the GSC (legs g1and s, respectively) depend on the rotor speed of the DFIG.In subsynchronous operation, the rotor absorbs power fromthe grid. Because of this, the currents i1 and i2 present lowervalues than those observed in the case of supersynchronousoperation. In addition, in supersynchronous operation, thesecurrents are greater than the stator current of the leg s1, shownin Figure 7.c. As can be seen, currents i1 and i2 can be upto 30% higher than the currents of the generator. From thisanalysis, it is noted that the higher effort in the switch occursin supersynchronous operation with rotor speed of 1.3 pu, in
which the device must handle 1.3 of the nominal current of theDFIG.
B. Normalized Apparent and Active Power Processed by GSCand SSCThe apparent powers of the GSC and SSC are defined as
Sgsc and Sssc, respectively. In this analysis, the stator reactivepower is null, then the stator active power is equal to apparentpower (Ss = Ps). The nominal (rated) apparent power of themachine is defined as Ssn. Figure 8 shows the normalizedapparent power curves |Sgsc/Ssn| and |Sssc/Ssn|. The apparentpowers Sgsc, Sssc, are defined by:
Sgsc =12
vgi∗1 (39)
Sssc =12
v32 i∗3 (40)
where i∗1 and i∗3 are the complex conjugate of the vectorcurrents i1 and i3, respectively. These results were obtainedconsidering four different values for the mechanical torque[100%, 75%, 50% and 25% of the nominal (rated) mechanicaltorque] with the range of the rotor speed being from 0.7 to 1.3of the synchronous speed. From Figure 8.a, it is possible tosee that the normalized apparent power processed by the SSCrepresents only a fraction of the apparent generator power. Forexample, when rated torque is applied, the power handled bythe SSC is approximately 60% of the DFIG’s rated power.
On the other hand, with respect to the power of the GSC,as can be seen in Figure 8.b, it depends on the rotor speedand therefore on the rotor power flow. In subsynchronousoperation, the power is delivered to the rotor by the RSC.Therefore, part of the power delivered by the stator istransferred to the rotor by means of SSC and RSC, whileGSC delivers just a small part of power to the grid. Forexample, with rated torque and rotor speed of 0.7 pu, thepower processed by the GSC is approximately of 30% of therated power (see Figure 8.b).
Now considering supersynchronous operation, the rotormust deliver power. Therefore, all power processed by SSCand RSC is delivered to the grid by means of the GSC.Therefore, power processed by GSC increases. For example,with rated torque and rotor speed of 1.3 pu, the powerprocessed by the GSC is approximately of 80% of the ratedpower (see Figure 8.b). It is worth to point out that in allcases neither the SSC nor the GSC process the total powerof the generator. It represents an advantage when comparedto full-rated systems, like the one illustrated in Figure 1.b.From this analysis, it is possible to see that, in the worst case(supersynchronous operation with rotor speed of 1.3 pu), theSSC and GSC converters processed power of approximately60% and 80% of nominal, respectively. This implies the useof lower rated and cheaper devices.
For power flow analysis of SSC and GSC converters anactive power study was performed in Figure 9. Figure 9.ashows the active power in the SSC. It is observed that at alloperating points the power is negative. This shows that theactive power flows from DFIG stator to SSC at all points.Note that the highest power processing happens at the 1.3pu rotor speed. This is because the generator works in
Gci(s) Gv (s) Gi(s)*Ird(s)s *Vrd(s)
sVrd(s)s
Ird(s)s
Gci(s) Gv (s) Gi(s)*Irq(s)s *Vrq(s)
sVrq(s)s
Irq(s)s
Fig. 5. Block diagram of current control system.
1) Design of Current Controllers: From the equations ofthe dynamic modeling of the DFIG, a current control loop isdefined, as illustrated in Figure 5. Gi(s) is the transfer functionof the current plant, Gv(s) is the voltage source represented bya first order transfer function with time constant Tv and Gci(s)the transfer function of the PI controller.
Gi(s) =Isrd(s)
V srd(s)
=Isrq(s)
V srq(s)
=
1rsr
σ lrrsr
s+1(17)
Gv(s) =V s∗
rd (s)V s
rd(s)=
V s∗rq (s)
V srq(s)
=1
Tvs+1(18)
Gci =Kii
s(
Kpi
Kiis+1) (19)
σ = 1− l2m
lslr(20)
rsr =(ls −σ ls)rr
lr(21)
where σ is leakage coefficient, ls (ls = lls + lm) and lr (lr =llr + lm) are the inductances of stator and rotor, respectively.The closed loop transfer function shown in (22) is obtained bycanceling the current plant pole (s=− rsr
σ lr) with the zero of the
PI controller (s = − KiiKpi
). The gains Kii and Kpi are calculatedin order to obtain real and identical poles of the closed-looptransfer function G f I .
G f I(s) =Kii/rsr
Tvs2 + s+(Kii/rsr)(22)
Kii =rsr
4Tv(23)
Kpi =σ lr4Tv
. (24)
2) Design of Power Controllers: The power control loop isshown in Figure 6, in which Gcp(s) and Gcq(s) are the transferfunctions of the active and reactive PI controllers, respectively;Gp(s) and Gq(s) are the transfer functions obtained from (15)and (16) and G f I(s) is the internal loop of the current control,which is approximated to a first-order function.
Gp(s) = Gq(s) =Ps(s)Isrq(s)
=Qs(s)Isrd(s)
=lmVs
ls(25)
Gcp = Gcq =Kipq
s(
Kppq
Kipqs+1) (26)
G f I =1
(2Tvs+1)2 ≈ 14Tvs+1
(27)
From (25)-(27) closed-loop transfer function is defined by:
G f p(s) = G f q(s) =lmVsKppqs+lmVsKipq
4lsTv
s2 +lmVsKppq+ls
4lsTvs+ lmVsKipq
4lsTv
. (28)
The denominator can be represented by polynomialcharacteristic of a second-order system s2 + 2ξ ωns + ω2
n ,where ωn is natural frequency and ξ is damping factor. Thenthe gain is given by:
Kipq(s) =4lsTvωn
2
lmVs(29)
Kppq(s) =1
lmVs(8lsTvξ ωn − ls) (30)
where the values of the damping factor, natural frequency andTv are ξ = 0.8, ωn = 9.5 rad/s and Tv = 0.01s, respectively.
Gcp(s) Gfi (s) Gp (s)*Ps (s)
*Ird(s)s
Ird(s)s Ps(s)
Gcq(s) Gfi (s) Gq (s)*Qs(s)
*Irq(s)s
Irq(s)s Qs(s)
Fig. 6. Block diagram of power control system.
V. PWM STRATEGY
The RSC can be commanded by using an adequate PWMstrategy for three-phase voltage source inverter [24]–[26].Only the PWM implementation of grid and stator sideconverters is highlighted in this paper.
In Sinusoidal PWM (SPWM) the reference pole voltagesare compared with a high frequency triangular signal todetermine the switch states. Considering that v∗g is the GSCreference voltage and v∗32 is the SSC reference voltage, theycan be defined based on the reference pole voltages by
v∗g = v∗g10 − v∗s0 (31)v∗32 = v∗s10 − v∗s0. (32)
In order to determine the three pole voltages, an auxiliaryvariable v∗x must be added. By making v∗x = v∗s0, the referencepole voltages v∗g10, v∗s0 and v∗s10 are determined by:
v∗g10 = v∗g + v∗x (33)v∗s0 = v∗x (34)
v∗s10 = v∗32 + v∗x . (35)
The choice of the auxiliary variable v∗x is free in a rangedefined by the limits of the pole voltages ±v∗C/2.
The voltage v∗x must be chosen such that:
v∗xmin ≤ v∗x ≤ v∗xmax (36)
v∗xmin = −v∗C2−minv∗g,v
∗32,0 (37)
v∗xmax =v∗C2−maxv∗g,v
∗32,0, (38)
Eletrôn. Potên., Fortaleza, v. 25, n. 1, p. 85-95, jan./mar. 202090
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
Rotor Speed (PU)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Po
we
r o
f th
e S
SC
(P
U)
100%
75%
50%
25%
(a)
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
Rotor Speed (PU)
0
0.2
0.4
0.6
0.8
Po
we
r o
f th
e G
SC
(P
U)
75%
50%
25%
100%
(b)
Fig. 8. Normalized Power. (a) Apparent power of SSC. (b) Apparent power of the GSC.
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
Rotor Speed (PU)
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
Ac
tiv
e P
ow
er
SS
C (
PU
)
100%
75%
50%
25%
(a)
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
0
0.2
0.4
0.6
0.8
1
Ac
tiv
e P
ow
er
GS
C (
PU
)
Rotor Speed (PU)
100%
75%
50%
25%
(b)
Fig. 9. Normalized Power. (a) Active power of SSC. (b) Active power of GSC.
supersynchronous mode, so the rotor provides power to theRSC and increases the energy processed by the SSC. Figure9.b shows the active power in the GSC. Unlike the SSCconverter, the GSC has positive active power at all operatingpoints, which means that the power flows from GSC to thegrid. For subsynchronous mode the power processed bythe GSC is low because the rotor absorbs a portion of theSSC power flow, while for supersynchronous mode the rotorprovides power, so the GSC processes the rotor power flowplus the SSC power flow.
VII. DC-LINK CAPACITOR
The methodology employed for the capacitors design canbe found in [27]. By means of harmonic spectrum analysisof the DC-link current, the presence of dominant high orlow frequency components are determined. In single-phaseto three-phase systems the predominant component in thecapacitor current is twice the grid frequency, so according to[27], the capacitance can be determined by:
C =Pload
240Vs fgridVripple(41)
where C is the capacitance of DC-link voltage, Pload power ofDFIG, fgrid is the grid frequency, Vs is the stator voltage inRMS value and Vripple is the ripple voltage of DC-link. Forthe system parameters with a capacitance of 2200µF a rippleof less than 1% was obtained.
VIII. SIMULATION RESULTS
In order to demonstrate the validity of the model andPWM and control strategies for the proposed topology, digitalsimulations have been performed. Current and power control
gains are Kii = 350.5, Kpi = 1.44, Kipq = 0.07 and Kppq =0.002. DFIG parameters used in simulation are shown in TableI, while the setup parameters are shown in Table II.
Figures 10 and 11 illustrate the steady-state curves obtainedfor the proposed topology. Stator active and reactive powerreferences were -500 W and 0 VA, respectively. The system isworking in supersynchronous mode with a speed of 477rad/s.Power waveforms are illustrated in Figure 10.a, which showsthat both active and reactive powers assume their referencevalues. And using Park’s transformation with stator voltagereference frame [23], the obtained rotor current componentsivrd and ivrq are illustrated in Figure 10.b. From Figures 10.a and10.b, it is possible to see that RSC control operated adequately.Also, as shown in Figures 10.c and 10.d, stator line voltagesprovided by PWM and control strategies are sinusoidal andbalanced, producing balanced currents, which is an advantagewhen compared to topology of Figure 1.a.
On the other hand, PWM and control strategies operatedadequately providing sinusoidal grid current with high powerfactor, as illustrated in Figure 11.a. The phase oppositionbetween the grid voltage and grid current shows that thesingle-phase grid was receiving power of GSC. Also, DC-link voltage is well adjusted to its reference value, as seen inFigures 11.b and 11.c illustrates the converter currents, it isobserved that current i3 is equal to −is3 and i1 and i2 are alinear combination of ig, is1 and is2.
Figure 12 shows the transient performance of the system,when the reference of the stator power was changed from -250W to -500 W at the time of 4.5 s. The reactive power referencewas kept null and DC-link voltage reference was maintained400 V [see Figure 12.a and 12.b]. With the increase of thepower provided by the generator, the grid current increased asshown in Figure 12.d.
Eletrôn. Potên., Fortaleza, v. 25, n. 1, p. 85-95, jan./mar. 2020 91
Time (s)
3 3.01 3.02 3.03 3.04 3.05
Po
we
rs (
W)
an
d (
Va
r)
-600
-400
-200
0
Qs
Ps
(a)
Time (s)
3 3.01 3.02 3.03 3.04 3.05
Cu
rre
nt
(A)
-10
-8
-6
-4
-2
0
2
ird
irq
(b)
Time (s)
3 3.01 3.02 3.03 3.04 3.05
Vo
lta
ge
s (V
)
-400
-200
0
200
400Vs12 Vs23 Vs31
(c)
Time (s)
3 3.01 3.02 3.03 3.04 3.05
Cu
rre
nts
(A
)
-3
-2
-1
0
1
2
3
is1 is2 is3
(d)
Fig. 10. Simulation results - steady-state. (a) Stator active andreactive power (Ps, Qs). (b) d − q rotor currents (ivrd and ivrq). (c)Stator line voltages (vs12, vs23 and vs31). (d) Stator currents (is1, is2and is3).
Time (s)
3 3.01 3.02 3.03 3.04 3.05
Cu
rre
nt
(A)
an
d V
olt
ag
e (
V)
-400
-200
0
200
400
eg
10ig
(a)
Time (s)
3 3.01 3.02 3.03 3.04 3.05
Vo
lta
ge
(V
)
100
200
300
400
500
(b)
Time (s)
3 3.01 3.02 3.03 3.04 3.05
Cu
rre
nts
(A
)
-10
-5
0
5
10
i1 i2i3
(c)
Fig. 11. Simulation results - steady-state. (a) Current and voltageof the grid (ig and eg). (b) DC-link voltage (vC). (c) SSC and GSCcurrents (i1, i2 and i3).
TABLE IDFIG Parameters
Parameter Valuers 15.1 Ωlls 39.9 mHrr 6.22 Ωllr 19.9 mHlm 0.5238 HP 1
Rated line voltage 220 VrmsRated power 0.55 kWFrequency 60 Hz
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
Rotor Speed (PU)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Po
we
r o
f th
e S
SC
(P
U)
100%
75%
50%
25%
(a)
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
Rotor Speed (PU)
0
0.2
0.4
0.6
0.8
Po
we
r o
f th
e G
SC
(P
U)
75%
50%
25%
100%
(b)
Fig. 8. Normalized Power. (a) Apparent power of SSC. (b) Apparent power of the GSC.
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
Rotor Speed (PU)
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
Ac
tiv
e P
ow
er
SS
C (
PU
)
100%
75%
50%
25%
(a)
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
0
0.2
0.4
0.6
0.8
1
Ac
tiv
e P
ow
er
GS
C (
PU
)
Rotor Speed (PU)
100%
75%
50%
25%
(b)
Fig. 9. Normalized Power. (a) Active power of SSC. (b) Active power of GSC.
supersynchronous mode, so the rotor provides power to theRSC and increases the energy processed by the SSC. Figure9.b shows the active power in the GSC. Unlike the SSCconverter, the GSC has positive active power at all operatingpoints, which means that the power flows from GSC to thegrid. For subsynchronous mode the power processed bythe GSC is low because the rotor absorbs a portion of theSSC power flow, while for supersynchronous mode the rotorprovides power, so the GSC processes the rotor power flowplus the SSC power flow.
VII. DC-LINK CAPACITOR
The methodology employed for the capacitors design canbe found in [27]. By means of harmonic spectrum analysisof the DC-link current, the presence of dominant high orlow frequency components are determined. In single-phaseto three-phase systems the predominant component in thecapacitor current is twice the grid frequency, so according to[27], the capacitance can be determined by:
C =Pload
240Vs fgridVripple(41)
where C is the capacitance of DC-link voltage, Pload power ofDFIG, fgrid is the grid frequency, Vs is the stator voltage inRMS value and Vripple is the ripple voltage of DC-link. Forthe system parameters with a capacitance of 2200µF a rippleof less than 1% was obtained.
VIII. SIMULATION RESULTS
In order to demonstrate the validity of the model andPWM and control strategies for the proposed topology, digitalsimulations have been performed. Current and power control
gains are Kii = 350.5, Kpi = 1.44, Kipq = 0.07 and Kppq =0.002. DFIG parameters used in simulation are shown in TableI, while the setup parameters are shown in Table II.
Figures 10 and 11 illustrate the steady-state curves obtainedfor the proposed topology. Stator active and reactive powerreferences were -500 W and 0 VA, respectively. The system isworking in supersynchronous mode with a speed of 477rad/s.Power waveforms are illustrated in Figure 10.a, which showsthat both active and reactive powers assume their referencevalues. And using Park’s transformation with stator voltagereference frame [23], the obtained rotor current componentsivrd and ivrq are illustrated in Figure 10.b. From Figures 10.a and10.b, it is possible to see that RSC control operated adequately.Also, as shown in Figures 10.c and 10.d, stator line voltagesprovided by PWM and control strategies are sinusoidal andbalanced, producing balanced currents, which is an advantagewhen compared to topology of Figure 1.a.
On the other hand, PWM and control strategies operatedadequately providing sinusoidal grid current with high powerfactor, as illustrated in Figure 11.a. The phase oppositionbetween the grid voltage and grid current shows that thesingle-phase grid was receiving power of GSC. Also, DC-link voltage is well adjusted to its reference value, as seen inFigures 11.b and 11.c illustrates the converter currents, it isobserved that current i3 is equal to −is3 and i1 and i2 are alinear combination of ig, is1 and is2.
Figure 12 shows the transient performance of the system,when the reference of the stator power was changed from -250W to -500 W at the time of 4.5 s. The reactive power referencewas kept null and DC-link voltage reference was maintained400 V [see Figure 12.a and 12.b]. With the increase of thepower provided by the generator, the grid current increased asshown in Figure 12.d.
Eletrôn. Potên., Fortaleza, v. 25, n. 1, p. 85-95, jan./mar. 202092
Time (s)
4 4.5 5 5.5 6
Po
we
rs (
W)
an
d (
Va
r)
-600
-400
-200
0
Qs
Ps
(a)
Time (s)
4 4.5 5 5.5 6
Vo
lta
ge
(V
)
100
200
300
400
500
(b)
4 4.5 5 5.5 6Time (s)
400
420
440
460
480
500
Roto
r Spe
ed (r
ad/s
)
(c)
4.3 4.4 4.5 4.6 4.7 4.8 4.9
Time (s)
-400
-200
0
200
400
Cu
rre
nt
(A)
an
d V
olt
ag
e (
V) 25ig
eg
(d)
Fig. 12. Simulation results - transient-state. (a) Stator active andreactive powers (Ps and Qs). (b) DC-link voltage (vC). (c) rotorspeed (ωr). (d) Current and voltage of the grid (ig and eg).
TABLE IISetup Parameters
Parameter ValueInductance of inductor filter la 12 mHResistance of inductor filter ra 0.55 Ω
Capacitance of the filter Ca 5µFCapacitance equivalent of the DC-link 2200 µF
DC-link reference voltage vC 400 VGrid phase voltage 220 Vrms
Switching frequency 10 kHz
IX. EXPERIMENTAL RESULTS
The topology presented in Figure 2 has been implementedexperimentally in laboratory. DFIG parameters are shownin Table I and the setup parameters are shown in Table II.The experimental setup is based on a Digital Signal Processor(DSP) TMS320F28335 with a microcomputer equipped withappropriate plug-in boards and sensors. Results were obtainedby oscilloscope Agilent DSO-X 3014A 100MHZ. The inputmechanical torque was provided by a squirrel-cage inductionmotor (SCIM) of 0.55 kW fed by a WEG inverter. A photo ofthe experimental setup is shown in Figure 13.
(a)
(b)
Fig. 13. Experimental setup. (a) Power converter. (b) SCIM plusDFIG.
Figures 14 and 15 illustrate steady-state experimentalresults, with a stator active and reactive power referencesof -500 W and 0 VA, respectively. By measuring statorvoltages and currents, Park’s transformation is applied andstator active and reactive powers are calculated according to(6) and (7), respectively. Figure 14.a shows that the controlsystem adequately adjusts both active and reactive powers totheir reference values. Also, by measuring the rotor currentsand applying Park’s Transformation, current components ivrdand ivrq are the ones shown in Figure 14.b. PWM and controlstrategies assure balanced stator line voltages, producingbalanced stator currents, as illustrated in Figures 14.c and 14.d.
Figure 15.a shows the rotor currents ir1, ir2 and ir3. Theyare sinusoidal and oscillate at low frequency (slip frequency).Grid current and voltage are illustrated in Figure 15.b. Notethat high power factor and sinusoidal current are provided bythe control system. It is possible to see the power flow fromthe GSC to the grid. DC-link voltage is shown in Figure 15.c,which is correctly adjusted to the value of 400 V.
Eletrôn. Potên., Fortaleza, v. 25, n. 1, p. 85-95, jan./mar. 2020 93
Time (10 ms/div)
Pow
er. (
500
W/d
iv)
DSP - 100 points/div
Ps
Qs
(a)
Time (10 ms/div)
Pow
er. (
2 A
/div
)
DSP - 100 points/div
irq
ird
(b)
Time (10 ms/div)
(c)
Time (10 ms/div)
(d)
Fig. 14. Experimental results - steady-state. (a) Stator active andreactive powers (Ps and Qs). (b) d −q rotor currents (ivrd and ivrq). (c)Stator line voltages (vs12, vs23 and vs31). (d) Stator currents (is1, is2and is3).
Time (100 ms/div)
(a)
Time (10 ms/div)
(b)
Time (10 ms/div)
(c)
Fig. 15. Experimental results - steady-state. (a) Rotor currents (ir1,ir2 and ir3). (b) Current and voltage of the grid (ig and eg). (c) DC-link voltage (vc).
X. CONCLUSION
This paper presented a three-phase to single-phase to windenergy conversion system based on Doubly-Fed InductionGenerator. The generator is directly connected to thesingle-phase source and the system has the advantages ofreduced cost of the power converter (because the converterprocess only part of the overall output power). In thesupersynchronous mode with rotor speed 1.3 times the
Time (s)
4 4.5 5 5.5 6
Po
we
rs (
W)
an
d (
Va
r)
-600
-400
-200
0
Qs
Ps
(a)
Time (s)
4 4.5 5 5.5 6
Vo
lta
ge
(V
)
100
200
300
400
500
(b)
4 4.5 5 5.5 6Time (s)
400
420
440
460
480
500
Roto
r Spe
ed (r
ad/s
)
(c)
4.3 4.4 4.5 4.6 4.7 4.8 4.9
Time (s)
-400
-200
0
200
400
Cu
rre
nt
(A)
an
d V
olt
ag
e (
V) 25ig
eg
(d)
Fig. 12. Simulation results - transient-state. (a) Stator active andreactive powers (Ps and Qs). (b) DC-link voltage (vC). (c) rotorspeed (ωr). (d) Current and voltage of the grid (ig and eg).
TABLE IISetup Parameters
Parameter ValueInductance of inductor filter la 12 mHResistance of inductor filter ra 0.55 Ω
Capacitance of the filter Ca 5µFCapacitance equivalent of the DC-link 2200 µF
DC-link reference voltage vC 400 VGrid phase voltage 220 Vrms
Switching frequency 10 kHz
IX. EXPERIMENTAL RESULTS
The topology presented in Figure 2 has been implementedexperimentally in laboratory. DFIG parameters are shownin Table I and the setup parameters are shown in Table II.The experimental setup is based on a Digital Signal Processor(DSP) TMS320F28335 with a microcomputer equipped withappropriate plug-in boards and sensors. Results were obtainedby oscilloscope Agilent DSO-X 3014A 100MHZ. The inputmechanical torque was provided by a squirrel-cage inductionmotor (SCIM) of 0.55 kW fed by a WEG inverter. A photo ofthe experimental setup is shown in Figure 13.
(a)
(b)
Fig. 13. Experimental setup. (a) Power converter. (b) SCIM plusDFIG.
Figures 14 and 15 illustrate steady-state experimentalresults, with a stator active and reactive power referencesof -500 W and 0 VA, respectively. By measuring statorvoltages and currents, Park’s transformation is applied andstator active and reactive powers are calculated according to(6) and (7), respectively. Figure 14.a shows that the controlsystem adequately adjusts both active and reactive powers totheir reference values. Also, by measuring the rotor currentsand applying Park’s Transformation, current components ivrdand ivrq are the ones shown in Figure 14.b. PWM and controlstrategies assure balanced stator line voltages, producingbalanced stator currents, as illustrated in Figures 14.c and 14.d.
Figure 15.a shows the rotor currents ir1, ir2 and ir3. Theyare sinusoidal and oscillate at low frequency (slip frequency).Grid current and voltage are illustrated in Figure 15.b. Notethat high power factor and sinusoidal current are provided bythe control system. It is possible to see the power flow fromthe GSC to the grid. DC-link voltage is shown in Figure 15.c,which is correctly adjusted to the value of 400 V.
Eletrôn. Potên., Fortaleza, v. 25, n. 1, p. 85-95, jan./mar. 202094
synchronous speed, which is the worst case scenario, theprocessed power by SSC and GSC was approximately 60%and 80%, respectively. In all analyzed cases, the powerprocessed by the converters is less than the generator ratedpower, implying in the use of lower rated and cheaper devices.Control and PWM strategies assured balanced stator three-phase voltages. Simulation and experimental results showedtheir validity and the feasibility of the conversion system.
REFERENCES
[1] N. Swami Naidu, B. Singh, “Doubly Fed InductionGenerator for Wind Energy Conversion Systems WithIntegrated Active Filter Capabilities”, IEEE Trans IndInformatics, vol. 11, no. 4, p. 923–933, Aug 2015.
[2] X. Liang, “Emerging power quality challenges dueto integration of renewable energy sources”, in 2016IEEE Industry Applications Society Annual Meeting,p. 1–9, Oct 2016.
[3] D. Zhou, G. Zhang, F. Blaabjerg, “OptimalSelection of Power Converter in DFIG WindTurbine With Enhanced System-Level Reliability”,IEEE Transactions on Industry Applications,vol. 54, no. 4, p. 3637–3644, July 2018, doi:10.1109/TIA.2018.2822239.
[4] A. S. Bubshait, A. Mortezaei, M. G. Simoes, T. D. C.Busarello, “Power Quality Enhancement for a GridConnected Wind Turbine Energy System”, IEEETransactions on Industry Applications, vol. 53, no. 3,p. 2495–2505, May 2017.
[5] R. Machado, J. Pomilio, E. Goncalves Marra,“Electronically controlled bi-directional connectionof induction generator with a single-phase grid”, inIndustrial Electronics Society, 2001. . The 27th AnnualConference of the IEEE, vol. 3, p. 1982–1987 vol.3,Nov 2001.
[6] T. Chan, L. Lai, “Phase balancing for an inductiongenerator operating on a single-phase power system”,in Power Engineering Society Winter Meeting, vol. 1,p. 165–170 vol.1, Jan 2000.
[7] E. Marra, J. Pomilio, “Induction-generator-basedsystem providing regulated voltage with constantfrequency”, IEEE Trans Ind Electron, vol. 47, no. 4,p. 908–914, Aug 2000.
[8] C. Xia, Z. Wang, T. Shi, Z. Song, “A Novel CascadedBoost Chopper for the Wind Energy ConversionSystem Based on the Permanent Magnet SynchronousGenerator”, IEEE Trans Energy Conversion, vol. 28,no. 3, p. 512–522, Sept 2013.
[9] H. Nian, R. Zeng, J. Liu, W. Zhang, “Complementaryhalf controlled converter for directly-driven PMsynchronous generator in wind power generationapplication”, in Energy Conversion Congress andExposition (ECCE), p. 358–362, Sept 2009.
[10] E. dos Santos, C. Jacobina, M. Correa, N. Rocha,“Distributed generation system based on single-phase grid, induction generator and solar photovoltaicpanel”, in Applied Power Electronics Conference andExposition (APEC), p. 1290–1295, Feb 2008.
[11] N. Rocha, E. de Menezes, I. de Oliveira, C. Jacobina,“Single-phase to three-phase induction generationsystem with two parallel single-phase half-bridgeconverters”, in Power Electronics Conference(COBEP), p. 678–685, Oct 2013.
[12] Z. Zhang, Y. Zhao, W. Qiao, L. Qu, “A Discrete-Time Direct Torque Control for Direct-Drive PMSG-Based Wind Energy Conversion Systems”, IEEETransactions on Industry Applications, vol. 51, no. 4,p. 3504–3514, July 2015.
[13] M. Ashourianjozdani, L. A. C. Lopes, P. Pillay,“Power Electronic Converter Based PMSG Emulator:A Testbed for Renewable Energy Experiments”, IEEETransactions on Industry Applications, vol. 54, no. 4,p. 3626–3636, July 2018.
[14] J. Dias, J. Diniz N, A. Almeida, E. dos Santos Junior,N. Rocha, “Low cost single-phase grid-tie generator”,in Industry Applications Society Annual Meeting (IAS),p. 1–6, Oct 2013.
[15] Y. Han, J. Ha, “Wound Rotor Machine Fed bya Single-Phase Grid and Controlled by an IsolatedInverter”, IEEE Transactions on Power Electronics,vol. 29, no. 9, p. 4843–4854, Sep. 2014, doi:10.1109/TPEL.2013.2283738.
[16] K. Lee, Y. Han, J. Ha, “Wound Rotor Machine WithSingle-Phase Stator and Three-Phase Rotor WindingsControlled by Isolated Three-Phase Inverter”, IEEETransactions on Energy Conversion, vol. 30, no. 2, p.558–568, June 2015, doi:10.1109/TEC.2015.2394807.
[17] G. C. Leandro, E. L. Soares, N. Rocha, “Single-phase to three-phase reduced-switch-count convertersapplied to wind energy conversion systems usingdoubly-fed induction generator”, in 2017 BrazilianPower Electronics Conference (COBEP), p. 1–6, Nov2017.
[18] N. Rocha, I. A. C. de Oliveira, E. R. C. da Silva, C. B.Jacobina, “Single-phase to three-phase generationsystem based on doubly-fed induction generator”,in 2017 IEEE Energy Conversion Congress andExposition (ECCE), p. 3274–3280, Oct 2017.
[19] R. Pena, J. Clare, G. Asher, “Doubly fed inductiongenerator using back-to-back PWM converters and itsapplication to variable-speed wind-energy generation”,Electric Power Applications, IEE Proceedings -, vol.143, no. 3, p. 231–241, May 1996.
[20] S. M. Shahruz, “Novel phase-locked loops withenhanced locking capabilities”, in American ControlConference, p. 4086–4091, May 2002.
[21] C. B. Jacobina, M. B. de R. Correa, R. F. Pinheiro,E. R. C. da Silva, A. M. N. Lima, “Modelingand Control of Unbalanced Three-phase SystemsContaining PWM Converters”, IEEE Trans Ind Appl,vol. 37, no. 6, p. 1807–1816, Nov./Dec. 2001.
[22] Lie Xu, P. Cartwright, “Direct active and reactivepower control of DFIG for wind energy generation”,IEEE Transactions on Energy Conversion,vol. 21, no. 3, p. 750–758, Sep. 2006, doi:10.1109/TEC.2006.875472.
Eletrôn. Potên., Fortaleza, v. 25, n. 1, p. 85-95, jan./mar. 2020 95
[23] A. R. Kumhar, “Vector Control Strategy to ControlActive and Reactive Power of Doubly Fed InductionGenerator Based Wind Energy Conversion System”,in 2018 2nd International Conference on Trends inElectronics and Informatics (ICOEI), p. 1–9, May2018, doi:10.1109/ICOEI.2018.8553761.
[24] V. Blasko, “Analysis of a Hybrid PWM Basedon Modified Space-Vector and Triangle-ComparisonMethods”, IEEE Trans Ind Appl, vol. 33, no. 3, p. 756–764, May/June 1996.
[25] H. W. van der Broeck, H. C. Skudelny, G. V. Stanke,“Analysis and Realization of a Pulsewidth ModulatorBased on Voltage Space Vectors”, IEEE Trans on IndAppl, vol. 24, no. 2, p. 142–150, Jan./Feb. 1988.
[26] J. Holtz, “Pulsewidth modulation for electronic powerconversion”, Proceedings of the IEEE, vol. 82, no. 8,p. 1194–1214, Aug. 1994.
[27] A. M. Hava, U. Ayhan, V. V. Aban, “A DCbus capacitor design method for various inverterapplications”, in 2012 IEEE Energy ConversionCongress and Exposition (ECCE), p. 4592–4599, Sep.2012, doi:10.1109/ECCE.2012.6342196.
BIOGRAPHIES
Filipe Vieira Rocha, was born in Ribeirão Preto, São Paulo,Brazil, in 1993. He received the B.S. degree in electricalengineering from the Federal University of Campina Grande,Campina Grande, Brazil, in 2017. Since 2017, he is workingin M.S. degreeing electrical engineering in Federal Universityof Paraíba, João Pessoa, Brazil. His research interests includepower electronics, electrical drives and renewable energysource.
Nady Rocha, was born in São Gabriel, Bahia, Brazil, in1982. He received the B.S., M.S., and Ph.D. degrees inelectrical engineering from the Federal University of CampinaGrande, Campina Grande, Brazil, in 2006, 2008, and 2010,respectively. Since 2011, he has been with the Departmentof Electrical Engineering, Federal University of Paraíba,João Pessoa, where he is currently an Associate Professor ofElectrical Engineering. His research interests include powerelectronics, renewable energy sources and electrical drives.
Victor Felipe Moura Bezerra Melo, was born in Pesqueira,Brazil, in 1988. He received the B.S., M.S. and Ph.D. degreesin electrical engineering from the Federal University ofCampina Grande, Campina Grande, Brazil, in 2012, 2013,
and 2017, respectively. From October 2014 to June 2018he was with Federal Institute of Technology of Pernambuco(IFPE), Afogados da Ingazeira, Brazil, where he was aProfessor. Since June 2018 he has been with FederalUniversity of Paraíba, where he is currently a Professor. Hiscurrent research interests include power electronics, staticconverters, electrical drives, and active power filters.
Edison Roberto Cabral received the B.S.E.E. degree fromthe Polytechnic School of Pernambuco, Recife, Brazil, in1965, the M.S.E.E. degree from the University of Rio deJaneiro, Rio de Janeiro, Brazil, in 1968, and the Dr.Eng.degree from the Universite Paul Sabatier, Toulouse, France,in 1972. From 1967 to 2002, he was with the Departmentof Electrical Engineering, Federal University of Paraíba,João Pessoa, Brazil, where he was a National Senior VisitingProfessor till the beginning of 2018. In 1990, he was withthe Federal University of Rio de Janeiro, Rio de Janeiro,and from 1990 to 1991, he was with the University ofWisconsin Madison, Madison, WI, USA, as a VisitingProfessor. From 2002 to 2012, he was with the Departmentof Electrical Engineering, Federal University of CampinaGrande, Campina Grande, Brazil, where he is currently aProfessor Emeritus, still acting. He was the Director of theResearch Laboratory on Industrial Electronics and MachineDrives for 30 years. His current research interests includepower electronics and motor drives. Dr. da Silva was theGeneral Chairman of the 1984 Joint Brazilian and Latin-American Conference on Automatic Control, sponsored bythe Brazilian Automatic Control Society (SBA), the IEEEPower Electronics Specialists Conference in 2005, and theBrazilian Conference on Automatic Control in 2012 and2018. He is a Past-President of the SBA.
Cursino Brandão Jacobina, was born in Correntes, Brazil, in1955. He received the B.S. degree in electrical engineeringfrom the Federal University of Paraíba, Campina Grande,Brazil, in 1978, and the Diplôme d?Etudes Approfondies andthe Ph.D. degrees in electrical engineering from the InstitutNational Polytechnique de Toulouse, Toulouse, France, in1980 and 1983, respectively. From 1978 to March 2002, hewas with the Department of Electrical Engineering, FederalUniversity of Paraíba, João Pessoa, Brazil. Since April 2002,he has been with the Department of Electrical Engineering,Federal University of Campina Grande, Campina Grande,Brazil, where he is currently a Professor of ElectricalEngineering. His research interests include electrical drives,power electronics and energy systems
synchronous speed, which is the worst case scenario, theprocessed power by SSC and GSC was approximately 60%and 80%, respectively. In all analyzed cases, the powerprocessed by the converters is less than the generator ratedpower, implying in the use of lower rated and cheaper devices.Control and PWM strategies assured balanced stator three-phase voltages. Simulation and experimental results showedtheir validity and the feasibility of the conversion system.
REFERENCES
[1] N. Swami Naidu, B. Singh, “Doubly Fed InductionGenerator for Wind Energy Conversion Systems WithIntegrated Active Filter Capabilities”, IEEE Trans IndInformatics, vol. 11, no. 4, p. 923–933, Aug 2015.
[2] X. Liang, “Emerging power quality challenges dueto integration of renewable energy sources”, in 2016IEEE Industry Applications Society Annual Meeting,p. 1–9, Oct 2016.
[3] D. Zhou, G. Zhang, F. Blaabjerg, “OptimalSelection of Power Converter in DFIG WindTurbine With Enhanced System-Level Reliability”,IEEE Transactions on Industry Applications,vol. 54, no. 4, p. 3637–3644, July 2018, doi:10.1109/TIA.2018.2822239.
[4] A. S. Bubshait, A. Mortezaei, M. G. Simoes, T. D. C.Busarello, “Power Quality Enhancement for a GridConnected Wind Turbine Energy System”, IEEETransactions on Industry Applications, vol. 53, no. 3,p. 2495–2505, May 2017.
[5] R. Machado, J. Pomilio, E. Goncalves Marra,“Electronically controlled bi-directional connectionof induction generator with a single-phase grid”, inIndustrial Electronics Society, 2001. . The 27th AnnualConference of the IEEE, vol. 3, p. 1982–1987 vol.3,Nov 2001.
[6] T. Chan, L. Lai, “Phase balancing for an inductiongenerator operating on a single-phase power system”,in Power Engineering Society Winter Meeting, vol. 1,p. 165–170 vol.1, Jan 2000.
[7] E. Marra, J. Pomilio, “Induction-generator-basedsystem providing regulated voltage with constantfrequency”, IEEE Trans Ind Electron, vol. 47, no. 4,p. 908–914, Aug 2000.
[8] C. Xia, Z. Wang, T. Shi, Z. Song, “A Novel CascadedBoost Chopper for the Wind Energy ConversionSystem Based on the Permanent Magnet SynchronousGenerator”, IEEE Trans Energy Conversion, vol. 28,no. 3, p. 512–522, Sept 2013.
[9] H. Nian, R. Zeng, J. Liu, W. Zhang, “Complementaryhalf controlled converter for directly-driven PMsynchronous generator in wind power generationapplication”, in Energy Conversion Congress andExposition (ECCE), p. 358–362, Sept 2009.
[10] E. dos Santos, C. Jacobina, M. Correa, N. Rocha,“Distributed generation system based on single-phase grid, induction generator and solar photovoltaicpanel”, in Applied Power Electronics Conference andExposition (APEC), p. 1290–1295, Feb 2008.
[11] N. Rocha, E. de Menezes, I. de Oliveira, C. Jacobina,“Single-phase to three-phase induction generationsystem with two parallel single-phase half-bridgeconverters”, in Power Electronics Conference(COBEP), p. 678–685, Oct 2013.
[12] Z. Zhang, Y. Zhao, W. Qiao, L. Qu, “A Discrete-Time Direct Torque Control for Direct-Drive PMSG-Based Wind Energy Conversion Systems”, IEEETransactions on Industry Applications, vol. 51, no. 4,p. 3504–3514, July 2015.
[13] M. Ashourianjozdani, L. A. C. Lopes, P. Pillay,“Power Electronic Converter Based PMSG Emulator:A Testbed for Renewable Energy Experiments”, IEEETransactions on Industry Applications, vol. 54, no. 4,p. 3626–3636, July 2018.
[14] J. Dias, J. Diniz N, A. Almeida, E. dos Santos Junior,N. Rocha, “Low cost single-phase grid-tie generator”,in Industry Applications Society Annual Meeting (IAS),p. 1–6, Oct 2013.
[15] Y. Han, J. Ha, “Wound Rotor Machine Fed bya Single-Phase Grid and Controlled by an IsolatedInverter”, IEEE Transactions on Power Electronics,vol. 29, no. 9, p. 4843–4854, Sep. 2014, doi:10.1109/TPEL.2013.2283738.
[16] K. Lee, Y. Han, J. Ha, “Wound Rotor Machine WithSingle-Phase Stator and Three-Phase Rotor WindingsControlled by Isolated Three-Phase Inverter”, IEEETransactions on Energy Conversion, vol. 30, no. 2, p.558–568, June 2015, doi:10.1109/TEC.2015.2394807.
[17] G. C. Leandro, E. L. Soares, N. Rocha, “Single-phase to three-phase reduced-switch-count convertersapplied to wind energy conversion systems usingdoubly-fed induction generator”, in 2017 BrazilianPower Electronics Conference (COBEP), p. 1–6, Nov2017.
[18] N. Rocha, I. A. C. de Oliveira, E. R. C. da Silva, C. B.Jacobina, “Single-phase to three-phase generationsystem based on doubly-fed induction generator”,in 2017 IEEE Energy Conversion Congress andExposition (ECCE), p. 3274–3280, Oct 2017.
[19] R. Pena, J. Clare, G. Asher, “Doubly fed inductiongenerator using back-to-back PWM converters and itsapplication to variable-speed wind-energy generation”,Electric Power Applications, IEE Proceedings -, vol.143, no. 3, p. 231–241, May 1996.
[20] S. M. Shahruz, “Novel phase-locked loops withenhanced locking capabilities”, in American ControlConference, p. 4086–4091, May 2002.
[21] C. B. Jacobina, M. B. de R. Correa, R. F. Pinheiro,E. R. C. da Silva, A. M. N. Lima, “Modelingand Control of Unbalanced Three-phase SystemsContaining PWM Converters”, IEEE Trans Ind Appl,vol. 37, no. 6, p. 1807–1816, Nov./Dec. 2001.
[22] Lie Xu, P. Cartwright, “Direct active and reactivepower control of DFIG for wind energy generation”,IEEE Transactions on Energy Conversion,vol. 21, no. 3, p. 750–758, Sep. 2006, doi:10.1109/TEC.2006.875472.