272 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 1, MARCH 2011
Series Voltage Compensation for DFIG Wind TurbineLow-Voltage Ride-Through Solution
Omar Abdel-Baqi and Adel Nasiri, Senior Member, IEEE
Abstract—This paper introduces a new solution for doubly fedinduction generators to stay connected to the grid during voltagesags. The main idea is to increase the stator voltage to a level thatcreates the required flux to keep the rotor side converter currentbelow its transient rating. To accomplish this goal, a series com-pensator is added to inject voltage in series to the stator side line.The series converter monitors the grid voltage and provides com-pensation accordingly to accomplish this aim. Since the turbineand converter stay connected, the synchronization of operation re-mains established during and after the fault and normal operationcan be resumed immediately after the fault is cleared. To keep thecurrent at its minimum, a control strategy has been developed tokeep the injected voltage and line voltage in phase during and afterthe fault.
Index Terms—Doubly fed induction generator (DFIG), gridfault, low-voltage ride through, series voltage compensation.
NOMENCLATURE�i Current space vector.Lm Magnetizing inductance.Lls , Llr Stator and rotor leakage inductance.Ls , Lr Stator and rotor self-inductance.r Superscript denoting rotor reference frame.Rs , Rr Stator and rotor resistance.s, r Subscript denoting stator and rotor.�v Voltage space vector.⇀vs−n Nominal stator voltage vector.�ψ Flux space vector.�ψs−n Stator flux at normal condition.ωs , ωr , ωm Synchronous, slip, and rotor angular frequen-
cies.τs Stator time constant.σ Leakage factor.
I. INTRODUCTION
AMONG renewable energy sources, wind energy is welladvanced and is expected to play a major role in the future
renewable energy portfolio. Doubly fed induction generators(DFIGs) are the most common type of advanced wind turbine
Manuscript received September 16, 2009; revised May 21, 2010, and August28, 2010; accepted September 27, 2010. Date of publication January 20, 2011;date of current version February 18, 2011. This work was supported by theUniversity of Wisconsin-Milwaukee, Milwaukee, under Research Growth Ini-tiative program. Paper no. TEC-00403-2009.
The authors are with the Departments of Electrical Engineering and ComputerScience, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413 USA(e-mail: [email protected]; [email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TEC.2010.2094620
Fig. 1. Proposed WECC voltage ride-through requirements for all generators.
generators due to their durability, lower cost, simple structure,and ability to adjust reactive power. One of the main drawbacksof using DFIGs is their vulnerability to grid side voltage sags andshort circuits. This type of generator utilizes a power converteron the rotor to adjust the rotor currents in order to regulate theactive and reactive power on the stator side. This converter istypically rated up to 30% of the generator power. When shortcircuit occurs on the grid side, the rotor currents rise and if theconverter is not protected against these high currents, it will bedamaged.
An easy way to protect the converter is to disconnect the gen-erator during low-voltage conditions. But many regulations havebeen developed and are under development to support the gridduring short circuits with reactive power and prevent discon-nection to deliver power when the voltage is restored. Accord-ing to the Western Electricity Coordinating Council regulation,the machine has to remain online if a three-phase short circuitfault occurs at the terminal and lasts for 0.15 s followed by aramp voltage rebuild to 90% of nominal voltage in 2.85 s (seeFig. 1). The wind turbine generator may disconnect from theline transiently outside the no-trip envelope but must reconnectwithin 2 s and rebuild power output at 20% of rated power persecond. This new proposed regulation has been a challengingrequirement for the wind turbine manufacturers and utilities tomeet. Newer types of wind turbine generators are more suscep-tible to short circuit fault due to presence of power electronicscomponents.
Recently, many researchers have focused on different tech-niques to overcome the low-voltage ride-through (LVRT) issue.Majority of these solutions rely on a rotor clamp circuit that cre-ates a short circuit on the rotor to divert the high rotor currentsfrom the power electronics converters [1]. Some of the newertypes place a definite resistance across the rotor terminal thathelps in accelerating rotor current decay. These clamp circuitschange the effective resistance across the rotor terminals usingforce commutation, PWM modulation, or actively changing the
ABDEL-BAQI AND NASIRI: SERIES VOLTAGE COMPENSATION FOR DFIG WIND TURBINE LOW-VOLTAGE RIDE-THROUGH SOLUTION 273
Fig. 2. Configuration of the series converter for the proposed LVRT solution.
resistor clamp [1], [2]. In addition to the rotor clamp circuit,to meet the requirements, a commutated semiconductor switchon the stator may be used to control the phase of the voltageapplied to the machine. The major drawback of these methodsis that they are only aimed at protecting the rotor converter dur-ing fault. They convert the DFIG to a simple induction machineduring fault since they create short circuit on the rotor [2]. Theinduction machine draws a lot of reactive power from the gridduring fault and voltage build up. This exactly happens when thegrid needs reactive power to resume normal operation. There-fore, using a rotor clamp circuit will further complicate the faultsituation for the grid. In addition, when the wind turbine is work-ing in supersynchronous mode, the voltage on dc-link capacitordramatically increases. The rotor clamp circuits do not offer anysolution to protect this capacitor. An additional circuit is neededto lower the capacitor voltage [3].
Utilization of voltage compensation using series convertershas been introduced and applied for many applications such asdynamic voltage restorer [5], static compensators [12], and har-monic compensations [13]. In this paper, we present a solutionto use a series converter on the stator terminal of a DFIG tomitigate the effect of the short circuit on the wind turbine. Thisconverter, as shown in Fig. 2, acts the same as a series activefilter for voltage compensation. The converter consists of threeinsulated gate bipolar transistor switching legs with a capacitor(C) as energy storage. Each switching leg can be controlled inde-pendently. Therefore, effects of unbalanced short circuit faultson the turbine can also be mitigated. The converter delivers ac-tive power for a very short period. Therefore, a proper sizingof the capacitor is required. The converter continuously moni-tors the grid side voltage. When this voltage dips, the converterapplies a voltage through series transformer to compensate forthe voltage dip. The level of voltage compensation depends onthe rating of the converter. Since the converter is considered toapply voltage for a very short period of time, the rating can behigh for a compact size converter. The converter does not need tocompensate for 100% of line voltage during short circuit. It onlyneeds to compensate the voltage to a level that limits the shortcircuit fault current. Typically, the converters on the rotor cantolerate up to 300% of its rated current in transient conditions.Therefore, the series converter can be designed at an apparentpower rating well below the power rating of the turbine.
Fig. 3. Configuration of a DFIG wind turbine system.
II. DFIG DURING GRID FAULT
Many references have discussed the modeling of DFIG windturbines [8], [9]. Fig. 3 shows the block diagram of a DFIGwind turbine system. The generator has a three-phase woundrotor supplied, via slip rings, from a four-quadrant, pulse widthmodulation (PWM) converter with voltage of controllable am-plitude and frequency [4].
A Park model in the stationary stator-orientated referenceframe, developed for DFIG in [10], is used to analyze the effectof grid fault on the generator. In this model, the rotor variablesare referred to the stator side for simplicity. Using motor conven-tion, the stator and rotor voltages in abc frame can be expressedas
�vs = Rs�is +
d
dt�ψs (1)
�vr = Rr�ir +
d
dt�ψr − jωm
�ψr . (2)
The stator and rotor fluxes are given by
�ψs = Ls�is + Lm
�ir (3)
�ψr = Lr�ir + Lm
�is (4)
where Ls = (Lls + Lm ) and Lr = (Llr + Lm ).
274 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 1, MARCH 2011
Fig. 4. DFIG-equivalent circuit for short circuit analysis.
Fig. 4 shows the equivalent circuit corresponding to the afore-mentioned equations.
For the purpose of the rotor over-current analysis during theshort circuit, the rotor voltage from converter point of view isthe most important variable in the analysis [10]. This voltageis induced by the variation of the stator flux, which can becalculated by deriving�is from (3) and substituting into (4):
�ψr =Lm
Ls
�ψs − σLr .�ir , σ = 1 − L2m
Ls.Lr. (5)
Thus, the rotor voltage can be found by combing (2) and (5)
�vr =Lm
Ls
(d
dt− jωm
)�ψs︸ ︷︷ ︸
vr o
+(
Rr + σLr
(d
dt− jωm
))�ir .
(6)The rotor voltage given by (6) can be divided into two terms.
The first term is the open circuit voltage (�vr0) and it depends onthe stator flux. The second term is smaller and it is caused bythe voltage drop on both the rotor resistance Rr and the rotortransient inductance σLr . From (6), when there is no current inthe rotor circuit, the rotor voltage due to the stator flux is (�vr0):
�vr0 =Lm
Ls
(d
dt− jωm
)�ψs. (7)
A. Analysis Under Normal Operation
Under the normal condition, rotor current control techniqueis utilized to adjust the active and reactive power at the generatorterminal. The rotor current phase and magnitude are controlledto regulate the reactive power at zero and keep the generatorrunning at unity power factor. Sensed wind speed is used to de-termine the reference active power of the turbine. Under normaloperation, the rotor voltage can be described as
�vr = �vsLm
Lss︸ ︷︷ ︸
Vr 0
+(
Rr + σLr
(d
dt− jωm
))�ir︸ ︷︷ ︸
Vr i
(8)
where s is the slip (s = ωr/ωs, ωr = ωs − ωm ).The rotor resistance and the transient reactance are typically
small. In addition, since the generator slip is limited to ±30%,the rotor current frequency is fr < 18 Hz [10]. As a result, themagnitude of Vri in (8) is smaller than Vr 0 . The rotor voltagedue to the stator flux can be written as [10]
�vr0 = jωrLm
Ls
�ψs =ωr
ωs
Lm
LsVse
jωs t . (9)
Fig. 5. Rotor voltage with −0.2 slip and 1 s stator time constant.
The amplitude of the voltage �vr0 can be described as a functionof the amplitude of the stator voltage as follows:
Vr0 = VsLm
Lss. (10)
During the normal operation, the rotor voltage �vr0 depends onthe magnitude of the stator voltage and the slip.
B. Analysis During Short Circuit
At the moment of the short circuit (t0 = 0), the open circuitrotor voltage due to the stator flux is given by
�vr0 = −Lm
Ls
(1τs
+ jωm
)· �Ψ0 · e−t/τs , �Ψ0 =
Vs
jωsejωs t0
(11)where Ψ0 is the stator flux just before the short circuit.
The voltage is a space vector fixed to the stator. Its amplitudedecreases exponentially to zero. With respect to the rotor, thisvoltage rotates reversely with rotor angular frequency of ωm
�vrr0 = −Lm
Ls
(1τs
+ jωm
)· �Ψ0 · e−t/τs e−jωm t . (12)
Fig. 5 shows the rotor voltage behavior during three-phase shortcircuit with a slip of –20%. As can be seen, the magnitude ofthe rotor voltage vr0 reaches its maximum value at the momentof the short circuit. Using (12) and neglecting the term 1/τs
due to its small value (τS ≈ 1s − 3s) for a 1-MW machine andlarger [7], [11], we have
Vr0 =Lm
Ls
ωm
ωsVs =
Lm
Ls(1 − s)Vs. (13)
According to (13), Vr0 is proportional to 1 – s. On the contrary,the steady-state voltage is proportional to the slip, as given in(10). Since the slip is in the range of –0.3 to 0.3 [10], it canbe concluded that the amplitude of the voltage induced on therotor winding during short circuit is closer to stator voltage.
ABDEL-BAQI AND NASIRI: SERIES VOLTAGE COMPENSATION FOR DFIG WIND TURBINE LOW-VOLTAGE RIDE-THROUGH SOLUTION 275
The ratio of rotor open-circuit voltage to rotor voltage causedby rotor impedance is larger in this case compared with steady-state situation. It can even be higher if the machine operates atlower slips or at supersynchronous speed.
C. Analysis Under Partial Voltage Sag
For this analysis, we assume that the generator is running atthe nominal stator voltage, when at t = 0 the stator voltage dipsfrom ⇀
vs−n to ⇀vs , where ⇀
vs−n is the nominal stator voltage:
�vs ={
�vs−n , for t < 0�vs, for t ≥ 0 (14)
⇀vs = rs
�is +d�ψs
dt. (15)
Solving for�is from (3) and substituting into (15) yields
d�ψs
dt= �vs −
rs
Ls
�ψs. (16)
Neglecting the stator resistant, the stator flux can be written as
�ψs−n (t < 0) =�vs−n
jωs. (17)
Replacing phasor of �vs−n with Vs−nejωs t , we achieve
�ψs−n (t < 0) =Vs−n
jωsejωs t . (18)
A balanced voltage sag at the stator terminal is assumed to bea step change of the stator voltage. We define h as the ratio ofthe stator voltage before and after the sage as follows:
h =|�vs |
|�vs−n |. (19)
Neglecting the stator resistant, stator flux response to a voltagesag occurring at t = 0 is explained as follows:
�ψs(t) =vs
jωsejωs t +
(vs−n − vs
jωs
)e−(t/τs ) . (20)
Combining (19) and (20), the stator flux can be described as
The second component of (21), which describes stator flux,“freezes” according to Faraday’s law (apart from the slow expo-nential decay). This “frozen” part appears to produce a transientoscillatory stator flux that decays with the stator time constant.
By substituting (21) into (7), the rotor voltage caused by thestator flux, in stationary reference frame, is achieved as follows:
�vr0 = |�vs−n |Lm
Ls(h.s.ejωs t − (1 − h)(1 − s)e−t/τs ). (22)
The two terms in (22) are different in nature. The first part isgenerated by the new grid voltage and its amplitude is small
because it is proportional to the slip. The second voltage is thetransient term and its amplitude is proportional to the depth ofthe voltage dip and to 1 – s. This voltage causes huge rise in therotor current. Equation (22) is the rotor voltage when there is norotor current. However, during the normal operation, the rotorconverter controls the rotor current in order to achieve the activeand reactive reference power. The voltage in the rotor terminalsthat has to be generated by the converter is provided by
�vr = |�vs−normal|Lm
Ls(h.sejωs t − (1 − h)(1 − s)e−t/τs )
+(
Rr + σLr
(d
dt− jωm
))�ir . (23)
For a short circuit at turbine terminal, the aforementioned anal-ysis is applied by setting h to 0.
III. PROPOSED SOLUTION
To start analyzing the proposed solution, it is assumed thatthe generator is operating under normal condition when at timet0 a three-phase short circuit occurs:
�vs ={
Vsejωs t , for t < 0
0, for t ≥ 0.(24)
As soon as the short circuit is detected, we apply a voltage vectorof �vc via the series converter on the stator, where |�vc | = |�vs | att = 0, and τ 1 is the time constant to be quantified later fromenergy equations of the system. Vector ⇀
vc is rotating with thespeed of ωs and its magnitude is declining with the time constantof τ 1 :
�vc ={
0, for t < t0Vce
jωs te−t/τ1 , for t >= t0 .(25)
Under this condition, the expression for the stator flux can beobtained from (1) and (3) as follows:
d�ψs
dt= �vs −
Rs
Ls
�ψs. (26)
Substituting�vs = �vc , the solution to this nonhomogeneous first-order differential equation can be found. Assuming zero delayfor the compensation, the homogeneous part of (26) can beeliminated. This part corresponds to the transient flux. Solving(26) for the stator flux, we get
�ψs =Vc
jωs − (1/τ1) + (1/τs)ejωs te−t/τ1 . (27)
Substituting (27) into (7), the rotor voltage induced from thestator flux is obtained as follows:
�vr0 =Lm
Ls
(d
dt− jωm
)Vc
jωs − (1/τ1) + (1/τs)ejωs te−t/τ1
(28)
276 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 1, MARCH 2011
Fig. 6. Open circuit rotor voltage during short circuit with slip of –0.2 and τ 1of 0.1 s at t ≥ t0 .
�vr0 =(
Lm
LsVc
(jωs − jωm ) − (1/τ1)jωs − (1/τ1) + (1/τs)
)ejωs te−t/τ1 . (29)
This voltage is a space vector that rotates at synchronous fre-quency. Its amplitude decreases exponentially with the timeconstant of τ 1 . With respect to the rotor, this voltage rotatesreversely at the slip frequency. Since the time constant for largemachines is much greater than 200 ms, if we set τ1 � τs , therotor open circuit voltage can be written in terms of the slip asfollows:
�vr0 =(
Lm
LsVcs
)e−t/τ1 ej (ωs −ωm )t . (30)
Substituting (30) into (8), the rotor voltage connected to theconverter can be found
�vr = �vce−t/τ1
Lm
Lss +
(Rr + σLr
(d
dt− jωm
))�ir . (31)
The initial magnitude of the new rotor voltage at the momentof the short circuit (t ≥ t0) due to the stator flux equals to themagnitude of the stator voltage under normal condition and itexponentially decreases to zero with the stator time constant, asshown in Fig. 6. According to (30), the time constant of rotorvoltage due to the stator flux no longer depends on the statortime constant or stator voltage. The time constant has changedto the new time constant of τ 1 . The “frozen” component of thestator flux that causes the second term of (22) is removed. Therotor current will not rise due to a step change in stator voltage.As can be seen in (30) and (31), this could have been performedwithout adding the time constant of τ 1 . However, adding thetime constant reduces the requirement for energy storage sizefor the series converter while keeping the rotor side invertercurrent within the acceptable limits.
Fig. 7 shows the transient of the stator flux trajectory due to athree-phase short circuit when the compensation is applied. Atthe moment of short circuit, the compensator injects a voltage to
Fig. 7. Stator flux trajectory transients with compensation.
the stator circuit to keep the stator flux rotating at synchronousspeed but its magnitude decreases exponentially with the timeconstant of τ 1 . Since the stator flux keeps rotating during theshort circuit transient at stator frequency, the induced voltage inthe rotor due the stator flux does not exceed its nominal value.
Fig. 8 shows the simulation results for the system behav-ior during a symmetrical three-phase short circuit at t = 0.3 s.The rotor current rises to 5 p.u. and the dc-bus voltage risesapproximately to 1.6 p.u. as well. During the short circuit, theelectromagnetic torque spikes approximately to 2.5 p.u. Ac-tive power, reactive power, and torque reduce to zero after atransient. These short circuit characteristics are what make thesystem very venerable to short circuit.
Fig. 9 shows the system behavior with voltage compensation.The simulation result reveals the effectiveness of the proposedsolution for keeping the rotor current under rated value at themoment of short circuit.
The series converter does not need to compensate with a 100%magnitude decaying voltage. The initial converter voltage canbe less than 100%. However, this will cause the rotor currentto rise. Fig. 10 shows the simulation results for a partial volt-age compensation with time constant τ 1 . The results show thatwith τ 1 set to 0.05 s and voltage compensation with an initialmagnitude of 50%, the rotor current is approximately rises to2.5 p.u. As the converter can tolerate transient currents of up tothree times its rated current, the partial voltage compensationguarantees successful voltage ride though with a smaller energystorage requirements and smaller series converter rating.
IV. CONTROL TECHNIQUE
In this section, the control technique for the series converteris described. The measured grid voltages (Vsa , Vsb , and Vsc ) areconverted into the stationary reference frame voltage quantities(Vsα and Vsβ ) using the following transformation [6]:
ABDEL-BAQI AND NASIRI: SERIES VOLTAGE COMPENSATION FOR DFIG WIND TURBINE LOW-VOLTAGE RIDE-THROUGH SOLUTION 277
Fig. 8. Simulation results for a three-phase short circuit on the terminal of a1.5-MW DFIG wind turbine.
Fig. 9. Simulation results for a three-phase short circuit on the terminal of a1.5-MW DFIG wind turbine when a full compensation is applied.
[Vsα
Vsβ
]=
√23
[1 −1/2 −1/20
√3/2 −
√3/2
] ⎡⎣Vsa
Vsb
Vsc
⎤⎦ . (32)
Then, the stationary reference frame voltage quantities are con-verted into the synchronous rotating reference frame voltagequantities (Vsd and Vsq ) rotating by the grid voltage angle of
Fig. 10. Simulation response of a 1.5-MW DFIG wind turbine to a three-phasevoltage sag with h = 0.15, 50% stator voltage compensation, and τ 1 = 0.05 s.
θ. A phase lock loop (PLL) is used to generate the grid voltageangle
[Vsd
Vsq
]=
√23
[cos θ sin θ− sin θ cos θ
] [Vsα
Vβ
]. (33)
The synchronous rotating reference frame voltage components(Vsd and Vsq ) are compared with the desired voltage to producethe reference voltage for voltage regulator as shown in Fig. 11.During normal operation, the compensator is not injecting anyvoltage. In this case, if the capacitor is charged at its prede-termined voltage, the compensator operates at standby mode.Otherwise, it will charge the capacitor from the line.
V. ENERGY CALCULATIONS FOR DC CAPACITOR
During short circuit on the stator, the wind turbine cannotexport any power to the grid. However, when the compensationis applied, the series converter absorbs all the turbine energyand charges the capacitor. If a decaying time constant is appliedto the compensation voltage, the absorbed power and capacitorsize can be greatly reduced.
A. Case 1
In this case, no time constant (τ 1) is introduced for the voltagecompensation and the series converter provides 100% compen-sation during short circuit. We will have
E =
0.2∫0
√3.Vc .I (34)
278 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 1, MARCH 2011
Fig. 11. Block diagram of the converter control technique.
where E is the energy delivered from 0 to 0.2 s. VC is thecapacitor voltage and I is the generator current. 0.2 s is themaximum three-phase short circuit duration that the turbinemust withstand. The capacitor size for this case the can becalculated as
C =2
0.2∫0
√3VC .I
ΔV 2 (35)
where ΔV is the maximum allowable voltage variation of thecapacitor. In fact, the wind turbine delivers the same powerbefore, during, and after the short circuit since the generatordoes not see the short circuit in this case. Therefore, a largecapacitor bank is required to absorb the energy.
B. Case 2
In this case, time constant τ 1 is introduced for the voltagecompensation. Substituting Vc = Vce
−t/τ1 into (35), we get
C =2E
V 2 =2∫ 0.2
0
√3 · Vce
−t/τ1 · IV 2 . (36)
From the aforementioned equation, it can be found that theenergy delivered is a function of the time constant τ 1 and can becontrolled by adjusting it. In addition, the capacitor size can alsobe significantly reduced. Fig. 12 shows the active and reactivepower of the turbine during short circuit with compensation.Both power decline to zero after a fast transient.
VI. TEST RESULTS
In order to validate the analytical and simulation analyses, anexperimental setup was built and tested. The block diagram ofthe test setup is shown in Fig. 2. A picture of the test setup inthe laboratory is also shown in Fig. 17. It includes the followingcomponents:
1) dSPACE DS1104 DSP controller board: the control pro-gram is written in Simulink environment combined withthe real-time interface of the DS1104 board;
2) a dc motor driving the induction motor at desired speed toemulate mechanical wind power;
Fig. 12. Active and reactive power delivered with exponentially decayingvoltage compensation (Vc = Vc e−t/ τ 1 ).
Fig. 13. System behavior during the short circuit without compensation.
3) a voltage source inverter (VSI) operating at 40-kHzswitching frequency connected to the series transformer.This VSI is used to control the amplitude and the phase ofthe injected voltage;
ABDEL-BAQI AND NASIRI: SERIES VOLTAGE COMPENSATION FOR DFIG WIND TURBINE LOW-VOLTAGE RIDE-THROUGH SOLUTION 279
Fig. 14. System behavior during the short circuit with τ 1 = infinity.
Fig. 15. System behavior during the short circuit with τ 1 = 0.1 s.
4) a 1 hp wound rotor induction machine simulating a windturbine generator;
5) a three-phase transformer (240 V:240 V) for series voltageinjection;
6) sensors for grid voltage, short circuit indicator, rotor cur-rents, and stator voltage.
The phase voltages of the grid side is sensed and fed to a PLLimplemented in the controller to generate the reference voltages.The actual grid voltage and reference voltages are comparedto generate the reference voltage and gate commands for theseries converter. The output voltage of the converter is appliedto the stator side using three single-phase transformers. Thisconfiguration allows for independent compensation of phasevoltages. Inductor L1 and capacitor C1 form a low-pass filterto remove the switching frequency harmonics from the outputof the converter. The controller also adjusts the voltage of thedc-bus capacitor with very slow dynamic.
A. Behavior Under Symmetrical Short Circuit WithoutVoltage Compensation
Fig. 13 shows the measured grid voltage, short circuit indi-cator, rotor current, and stator voltage. The experimental results
Fig. 16. System behavior during the short circuit with τ 1 = 0.05 s.
Fig. 17. Hardware setup in the laboratory for testing.
show that the rotor current jumps to approximately five timesof the nominal current during short circuit and exponentiallydecays to zero with the stator time constant.
B. Behavior Under Symmetrical Short Circuit With SeriesVoltage Compensation
In this section, the rotor current behavior is analyzed underdifferent conditions for the injected voltage as follows:
1) 100% stator voltage compensation with nondecaying in-jected voltage. Fig. 14 shows the system behavior duringthe short circuit with full stator voltage compensation. Itshows that the short circuit does not have any significantimpact on the rotor current. The rotor current stays withinits normal value with small transient due to delay in volt-age injection;
2) 100% stator voltage compensation with decaying voltagewith time constant τ 1 . The results of this case for twovalues of τ 1 are shown in Figs. 15 and 16. It can be seenthat the rotor current decreases exponentially according tothe compensated voltage time constant of τ 1 . The rotorcurrent starts decaying after the short circuit from its ini-tial value without experiencing any over current. Since the
280 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 1, MARCH 2011
energy that is being delivered during the short circuit isproportional to the stator voltage, the required size of theenergy storage capacitor is decreased due to a smaller sta-tor voltage. In fact, it is not necessary to compensate 100%of the stator voltage during the short circuit to eliminatethe rotor circuit over current. The most important point isto keep the frequency of the exponentially decaying com-pensated voltage the same as the grid frequency duringthe short circuit. This allows for the stator flux to rotatewith its initial speed during the short circuit and results inkeeping the rotor circuit voltage due to the stator flux thesame as its value during normal operation.
VII. CONCLUSION
DFIG is subject to intense stress during considerable gridvoltage sag. Additional measures must be taken to protect theturbine and provide LVRT even at zero grid voltage in accor-dance with utility requirements. Wind turbine equipped withseries voltage compensator described in this paper is able tostay connected to the grid and limit the rotor currents within anacceptable range. This LVRT solution for the DFIG also allowsfor reactive power support to the grid during grid fault. The aimof the proposed technique is to limit the rotor side converter highcurrents and to provide the stator circuit with the necessary volt-age via a series transformer without disconnecting the converterfrom the rotor or from the grid. The wind turbine can resumenormal operation within a few hundred milliseconds after thefault has been cleared. For longer voltage dips, the generatorcan even supply reactive power to the grid. Simulation and ex-perimental results verify the effectiveness and viability of theproposed technique. According to analyses presented, the sizeof the energy storage capacitor does not need to be excessivelylarge for the system to operate.
APPENDIX
The parameters of the machine and controller that have beenused for modeling and simulations are given as follows.
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Omar Abel-baqi was born in Al-Zawi, Palestine. Hereceived the B.S. degree from Palestine PolytechnicUniversity, Hebron, West Bank, and the M.S. degreefrom the University of Detroit Mercy, Detroit, MI,in 2000 and 2004, respectively, and the Ph.D. degreefrom the University of Wisconsin-Milwaukee, Mil-waukee, in 2010, all in electrical engineering.
He is currently an R&D Principle Engineer atBucyrus International, South Milwaukee, WI.
Adel Nasiri (M’04–SM’06) was born in Sari, Iran,in 1974. He received the B.S. and M.S. degrees fromthe Sharif University of Technology, Tehran, Iran, in1996 and 1998, respectively, and the Ph.D. degreefrom the Illinois Institute of Technology, Chicago, in2004, all in electrical engineering.
He was with Moshanir Power Engineering Com-pany, Tehran, from 1998 to 2001. He also worked forForHealth Technologies, Inc., Daytona Beach, FL,from 2004 to 2005 on an automated syringe fillingdevice. He is currently an Associate Professor in the
Department of Electrical Engineering and Computer Science, University ofWisconsin–Milwaukee, Milwaukee. He is a coauthor of a book entitled Unin-terruptible Power Supplies and Active Filters (CRC Press, 2003), and the authorof numerous journal papers and conference presentations. His research interestsinclude power electronics converters, renewable energy systems, energy stor-age, and electric motor drives.
