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Real-time Transient Simulation and Studies ofOffshore Wind Turbines

Thai-Thanh Nguyen, Member, IEEE, Tuyen Vu, Member, IEEE, Thomas Ortmeyer, Fellow, IEEEGeorge Stefopoulos, Member, IEEE, Greg Pedrick, Jason MacDowell, Member, IEEE

Abstract—This paper presents developed real-time simulationmodels for offshore wind turbine generators in compliance withindustry standards. The critical control functions such as negativesequence injection, sequence current limit, voltage ride through,and power curtailments are designed to meet the industryrequirements for future electromagnetic transient (EMT) testingand controls of offshore wind farms. Average-value and switchingdetailed models are developed in the Opal-RT real-time simulator.These models’ real-time capabilities are compared to show theeffectiveness of the average-value model in terms of accuracyand computation efficiency. Studies of balanced and unbalancedfaults illustrate the ability of the proposed turbine models toinject active and reactive currents during fault events. The modelsare validated against the second-generation generic wind turbinemodel proposed by Western Electricity Coordinating Council(WECC). Validation results reveal that the proposed models arealigned with the WECC generic model. In addition, the modelsprovide an extended capability in mitigating the active poweroscillation during unbalanced fault conditions.

Index Terms—Offshore wind turbines, wind farms, directdrives, permanent magnet synchronous generators; negativesequence current control, sequence current limit, turbine modelvalidation.

I. INTRODUCTION

OFFSHORE wind energy systems have received consider-able attention recently due to the need for decarboniza-

tion in conjunction with their potential to produce more windpower with high efficiency than the onshore wind energysystems [1]. The rapid development of offshore wind turbinetechnologies with the direct-drive multi-megawatt turbinesleads offshore wind systems to be a cost-competitive solution.The advanced technology of the direct-drive turbine systemsovercomes the problem of gearbox failure and results in thegrowing usage of high-power 13 MW [2], and 15 MW [3],[4] wind turbines. Offshore wind projects, with the increase indeveloper experience and industry maturity, are getting larger.Modeling of offshore wind turbines, which complies withindustry standards, plays an important role in de-risking off-shore wind projects. Although wind turbine generator (WTG)models have been extensively developed, the majority ofexisting WTG models have not been modeled in compliancewith international standards. A few studies have presented theWTG models that are aligned with international standards [5],[6]; however, those models have not been tested in real-timeenvironments. Additional limitations of those models will bediscussed in the following.

The generic WTG models, also known as standard or sim-plified models, have been developed by international workinggroups such as the Western Electricity Coordinating Coun-cil (WECC) and International Electrotechnical Commission(IEC) [7]–[9]. WECC and IEC models are simple aggre-gated WTG models, which lack detailed converter controllers

such as inner current control loops, torque control, or DC-link voltage control loops, etc. These models are based onpositive-sequence models, which were proposed in accordancewith the original equipment manufacturer to perform dynamicstudies with sufficient accuracy [10]. WECC model aims atminimizing the number of turbine parameters while the IECone focuses on improving the accurate responses [11]. Thesegeneric models are essential for dynamic studies of large-scale wind farm systems since they are simplified and donot require significant computation. However, with the uses ofpower converters integrated with wind turbine generators suchas Types 3 and 4, these generic models might fail to representthe harmonic and control interaction among WTGs since thecurrent control loops of power converters are omitted. Thestudy on harmonic instability of large-scale wind farms wouldbe more challenging [12] and it requires to develop WTGmodels that not only are in accordance with the standards butalso can represent harmonic interactions.

Various studies have introduced detailed electromagnetictransient (EMT) models of wind turbines that have been devel-oped using offline simulation tools like MATLAB/Simulink,PSCAD/EMTDC and EMTP, etc. Although these models allowfor modeling and simulating complex WTG models in thetransient domain, they have not been tested in real-time andare relatively slow when running in offline simulations. A2-MW generic EMT-type model of Type 4 wind turbinehas been introduced in [5], in which the proposed turbinemodel was validated against the field tests of the ENERCONE-82 2.3-MW turbine. Another PMSG wind turbine modelrated at 5-MW with a low-voltage ride-through capability hasbeen introduced in [6], which is evaluated considering theU.S. grid code. However, these proposed models operate inthe phasor domain (positive sequence), which might causeincorrect operation of the protection system during someunbalanced conditions due to the lack of negative sequencecurrent contribution. In addition, the existence of negativesequence voltage during unbalanced faults causes the second-order harmonic oscillation in output active power and DC-link voltage [13]. An asymmetrical component-based 1.5-MW wind turbine model was introduced in [14], which hasthe capability of injecting negative sequence current duringunbalanced faults. Both sequence-based detailed switching(DSW) and averaged-value (AVG) models were evaluated;however, these models were not implemented in real-time. Inaddition, the dynamic responses of the DSW model were notwell-represented by the AVG model. The measurement of CPUusage in [14] indicated that for a 1 s simulation time, the DSWand AVG models required 144.7 s and 28.8 s of CPU time,respectively. Therefore, there is a need to develop and evaluatereal-time turbine models.

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There are works reported in the literature on the real-timemodels of wind turbines [15]–[18]. However, these WTGmodels have not been developed in compliance with inter-national standards. In addition, these models lack the negativesequence control capability. Existing detailed WTG modelscan be improved to be aligned with international standards,but they are computationally intensive. With high-performancemulti-core processors of real-time simulations such as Opal-RT and RTDS, existing WTG models can be modified to runin real-time. However, those models still need further improve-ments to reduce computation time, making them sufficientfor modeling large-scale wind farms with hundreds of windturbines. To overcome these limitations, this paper proposesreal-time DSW and AVG turbine models of high-power direct-drive PMSG wind turbines for offshore wind studies. Theproposed models are validated against the WECC standardto ensure that they are applicable for practical studies.The main contributions of this paper are as follows:

• Real-time models of high-power direct-drive wind tur-bines, which are in compliance with the internationalstandard, are provided. Compared to existing real-timemodels, the proposed models are optimized and applica-ble for practical studies.

• Both detailed switching and average-value models aredeveloped and tested by real-time simulators. Comparedto AVG model in [14], the proposed AVG model in thispaper well captures dynamic responses of DSW model.

• The real-time WTG models are developed with asymmet-rical components, which are capable of injecting negativesequence current during unbalanced faults.

The rest of this paper is arranged as follows: Section IIpresents the characterization and operational regions of thewind turbines. Detailed wind turbine model and its controlsystem are given in Section III, in which the developed windturbine controls are in accordance with the WECC standard.Section IV describes the real-time modeling and real-timeperformance of both DSW and AVG turbines. The developedturbines are validated against the WECC standard, which isshown in Section V. Section VI shows the evaluation of bothDSW and AVG models under normal and abnormal conditions,including balanced and unbalanced dynamic studies. Finally,the main findings of this paper is summarized in Section VII.

II. WIND TURBINE CHARACTERISTIC AND OPERATION

The steady-state power characteristic of a wind turbine ispresented in this section. Four operating regions and theircorresponding control strategies are discussed. The character-ization of WTGs shows the turbine output power under fourcontrol regions.

A. Wind Turbine Characteristic

The wind turbine blades are used to capture the wind energy.The aerodynamic power extracted from wind is given by (1).

Pm =1

2ρπR2Cp(λ, β)v

3w, (1)

where ρ is the air density; R is the turbine rotor radius;Cp(λ, β) is the rotor power coefficient depending on tip-speedratio λ and pitch angle β; and vw is the wind speed.

Fig. 1. Regions of control. Note that regions 1 and 4 are not shown in thefigure.

The tip-speed ratio determines the fraction of available windpower extracted by the wind turbine rotor, which is calculatedby (2).

λ =ωrR

vw, (2)

where ωr is the rotor angular speed.Rotor power coefficient Cp represents the characteristic of

the wind turbine, which is depended on the tip-speed ratio andthe pitch angle, as given by (3).

Cp(λ, β) =

4∑i=0

4∑j=0

aijλjβi, (3)

where coefficients aij is given in [19].

B. Wind Turbine OperationTypically, there are four primary regions (RG) of wind

turbine operation. In region 1, the generator is in an idle modesince the wind speed is too low to rotate the turbine rotor.The generator is turned on and starts producing power whenthe wind speed surpasses the cut-in speed. The wind turbineoperates on region 2 when the wind speed is above the cut-in speed but still too low to generate rated power. The mainobjective of wind turbine control in this region is to maximizepower captured from wind energy, which is achieved by theoptimal torque control. The wind turbine is in region 3 whenthe wind speed is high enough to produce the rated poweroutput. In this case, the pitch controller is activated to safelyregulate the generator speed and power at rated levels. Region4 occurs when the wind speed is too high. The wind turbinegenerator is shut down in this region to prevent damage tothe turbine. Fig. 1 shows regions 2 and 3 of wind turbineoperation, in which region 1.5 indicates the transition betweenregions 1 and 2 [3].

C. Wind Turbine CharacterizationThe characterization of three wind turbine models (8 MW,

12 MW, and 15 MW models) is shown in Fig. 2, whichindicates the turbine output power at different wind speeds.The wind turbine starts producing power when the wind speedis higher than the cut-in speed of 3 m/s. When the wind speedis larger than the cut-in speed but smaller than the rated windspeed of 12 m/s, the wind turbine adjusts the rotor speed tomaximally capture the wind power. The output turbine poweris kept constantly at the rated power when the wind speed ishigher than the rated speed.

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Fig. 2. Power curve characterization of wind turbine models.

Fig. 3. Direct-drive PMSG with control functions.

III. WIND TURBINE MODELING

The typical structure of the direct-drive PMSG wind turbineis shown in Fig. 3, in which the wind turbine is directlycoupled with the rotor of the synchronous generator. The statorwinding of PMSG is connected to the back-to-back (BTB)converter that comprises a machine-side converter (MSC), agrid-side converter (GSC), and a DC chopper. The MSC isresponsible for the torque control of PMSG, whereas the GSCmaintains the DC-link voltage and reactive power exchangewith the grid. The DC chopper is connected in parallel withthe DC link to maintain a stable DC-link voltage duringtransient conditions. The grid filter is used for the grid-sideconverter to reduce the harmonics caused by switching ofpower converters. The step-up transformers are used to boostthe turbine generator voltage to the collector system levels. Themain control functions of the direct-drive PMSG wind turbineinclude the pitch angle control, machine-side and grid-sidecontrollers, which will be discussed in the following.

A. Pitch Angle ControllerThe pitch angle control, which is shown in Fig. 4 is used

to adjust the aerodynamic power captured from wind energy.A lookup table with the input of wind speed (vw) is usedto generate the pitch angle reference in region 1.5 (βR1). Thepitch angle reference (β∗) is equal to zero when the wind speed(vw) is higher than the cut-in speed (vcin) and smaller than therated wind speed (vrated). When the wind speed is above therated wind speed or the turbine power reference (P ∗) is lessthan the rated power (Prated), the pitch angle is controlled bythe proportional-integral (PI) regulator with limitation of bothmagnitude and rate-of-change to manage the turbine outputpower.

B. Machine-side ControllerThe MSC controller shown in Fig. 5 includes an inner

current control loop and an outer torque control loop. Thetorque controller generates the current reference (i∗Md) for the

Fig. 4. Schematic diagram of the pitch controller.

Fig. 5. Control diagram of the machine-side converter: (a) Torque controlloop; (b) Inner current control loop.

inner current loop. The PI regulator with the rated limiter isused to compensate for the torque error. The torque referenceis provided by the speed control or optimal torque controldepending on the wind speed. Region 1.5 is an operationmode where the wind speed is higher than the cut-in speedbut smaller than 7 m/s. In this region, the rotor speed iscontrolled at 0.6 pu and the wind turbine generator begins toproduce power. When the wind speed is lower than the ratedspeed, the wind turbine operates in region 2 where the optimaltorque in (4) is used to maximize the wind power. The windturbine operates in region 3 when the wind speed is higherthan the rated wind speed. In this region, the generator torqueis regulated by an additional rotor speed control to maintainrotor speed constantly at 1 pu. The wind turbine is turned offin region 4 where the wind speed is higher than the cut-outspeed.

Topt = koptω2r , (4)

kopt = 0.5ρπR2Cmaxp (R/λopt)

3, (5)

where λopt is the optimal tip-speed ratio.

C. Grid-side ControllerThe grid-side controller is responsible for DC-link voltage

regulation under normal conditions. When a fault occurs in thegrid side, the suddenly drop in WTG’s terminal voltage resultsin the rapid rise in DC link voltage. The DC chopper withthe hysteresis control is activated to protect the DC system.Under fault conditions, the DC-link control loop in the grid-side controller is frozen and the current control loop regulatesthe active and reactive currents injecting into grids.

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Fig. 6. Control diagram of the grid-side converter: (a) Overal control diagram; (b) SOGI-PLL and sequence current and voltage extractor; (c) Active andreactive current injection; (d) Sequence current control loop.

The grid-side converter of the wind turbine in this paperis designed based on the asymmetrical components of turbinevoltage and current. The unbalanced three-phase voltage canbe represented by the positive and negative sequence compo-nents that are transformed into the synchronous rotating frame,as given by (6), in which v+Gdq is the positive dq componentwhile v−Gdq is the negative dq component [20].

vGdqs = v+Gdqejωt + v−Gdqe

−jωt

=2

3(vGa + avGb + a2vGc), (6)

v+Gdq =2

3(v+Ga + av+Gb + a2v+Gc)e

−jωt = v+Gd + jv+Gq, (7)

v−Gdq =2

3(v−Ga + av−Gb + a2v−Gc)e

jωt = v−Gd + jv−Gq, (8)

where a = ej2π3 ; vG is the terminal voltage of converter.

The positive and negative sequence currents, i+Godq andi−Godq , can be defined in the same manner. The complexpower is calculated by the sequence components of voltageand current, as given by (9), which includes the second-orderharmonic oscillations of power.

S = p(t) + jq(t) = vGdqsi∗Godqs, (9)

p(t) = P + Pc2 cos(2ωt) + Ps2 sin(2ωt), (10)q(t) = Q+Qc2 cos(2ωt) +Qs2 sin(2ωt), (11)

where

P =3

2(v+Gd · i

+God + v+Gq · i

+Goq + v−Gd · i

−God + v−Gq · i

−Goq),

Pc2 =3

2(v−Gd · i

+God + v−Gq · i

+Goq + v+Gd · i

−God + v+Gq · i

−Goq),

Ps2 =3

2(v−Gq · i

+God − v−Gd · i

+Goq − v+Gq · i

−God + v+Gd · i

−Goq),

Q =3

2(v+Gq · i

+God − v+Gd · i

+Goq + v−Gq · i

−God − v−Gd · i

−Goq),

Qc2 =3

2(v−Gq · i

+God − v−Gd · i

+Goq + v+Gq · i

−God − v+Gd · i

−Goq),

Qs2 =3

2(−v−Gd · i

+God − v−Gq · i

+Goq + v+Gd · i

−God + v+Gq · i

−Goq).

The second-order oscillations of reactive power are not con-sidered for the control design [21]. However, the oscillationsof active power cause the fluctuation of the DC-link voltageat a frequency twice the nominal frequency. To cancel thefluctuation in DC-link voltage, the oscillatory terms of activepower (Pc2 and Ps2) are set to zero. Thus, the reference valuesof positive and negative sequence currents can be obtainedfrom (12).

i+∗God

i+∗Goq

i−∗God

i−∗Goq

=2

3

v+Gd v+Gq v−Gd v−Gq

v+Gq −v+Gd v−Gq −v−Gd

v−Gq −v−Gd −v+Gq v+Gd

v−Gd v−Gq v+Gd v+Gq

−1 PQPs2

Pc2

(12)

The overall control scheme of the grid-side converter isshown in Fig. 6(a), which has the main functions of regulatingDC-link voltage and output reactive power. The active powerreference (P ∗) is generated by the DC-link voltage controller,while the reactive power reference (Q∗) is received directly

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Fig. 7. Look-up table of limit logic VDL1 and VDL2.

Fig. 8. Schematic diagram of the sequence current limit.

from the upper control layer, such as the wind power plantlevel controller. Under abnormal conditions, outer DC-link andreactive power controls are frozen and the active and reactivecurrents injected into grid are defined following WECC currentlimit logic. The sequence current generator based on (12) usesthe active and reactive power references as inputs to calculatethe sequence current references for the inner sequence currentcontrol loop. The phase angle of terminal voltage (θ) iscalculated by the second-order generalized integrator (SOGI)phase-locked loop (PLL), which can achieve accurate phase-locking under unbalanced conditions, then it is used to extractthe sequence components of current and voltage, as shown inFig. 6(b).

The low-voltage ride-through requirement of the wind tur-bine is fulfilled by the current injection function that is usedto manage the active and reactive current injected into thegrid during low-voltage conditions, as shown in Fig. 6(c). Thiscurrent injection function is proposed with the considerationof the WECC generic turbine model [22]. Two lookup tables(VDL1 and VDL2) in Fig. 7 are defined by four pairs ofnumbers, which determines the limits on the total reactiveand active currents injected into the grid during low voltageconditions. The VDL1 and VDL2 curves allow the reductionof active and reactive currents to zero at very low voltages.The WECC current limit logic defined in [22] is modifiedin this paper for the positive sequence currents, as givenby Algorithm 1. The modified WECC current limit logic isdifferent from the original in terms of the lower limit of activecurrent injection (Ipmin) as the active current of the grid-sideconverter could be negative to maintain the DC-link voltage.

The d-component of positive sequence voltage (v+Gd) isused to detect the normal and abnormal conditions, as givenby (13). When the Vdip signal is equal to one, the currentinjection function manages the amount of injected active andreactive current into the grid during low voltage conditions.The states of the reactive current switch and active currentswitch are changed from 0 to 1 when the voltage-dip conditionis detected. The injected reactive current is proportional tothe voltage drop, while the injected active power is calculatedfrom the mechanical power. A deadband is used to managethe injected reactive current with respect to the voltage-dip

Algorithm 1 Modified WECC current limit logic.1: if Pqflag = 0 %Q-priority then2: Iqmax = min(VDL1, Imax)3: Iqmin = −Iqmax

4: Ipmax = min(VDL2,√I2max − I2qcmd)

5: Ipmin = −0.5Ipmax %For DC-link control6: else7: Iqmax = min(VDL1,

√I2max − I2pcmd)

8: Iqmin = −Iqmax

9: Ipmax = min(VDL2, Imax)10: Ipmin = −0.5Ipmax %For DC-link control11: end if

conditions.

Vdip =

1 if Vt ≤ vdip or Vt ≥ vup0 otherwise

(13)

Vt = v+Gd (14)

where vdip and vup are the pre-defined values that are used todetect low-voltage and high-voltage conditions, respectively.

Once the injected amounts of positive sequence activeand reactive currents are obtained, the positive and negativesequence currents are calculated as follows:

i+∗∗God =Ipcmd (15)i+∗∗Goq =Iqcmd (16)

i−∗∗God =

1

v+Gd

2+ v+Gq

2

(− (Ipcmdv

−Gdv

+Gd − Ipcmdv

−Gqv

+Gq

+ Iqcmdv−Gdv

+Gq + Iqcmdv

−Gqv

+Gd)), (17)

i−∗∗Goq =

1

v+Gd

2+ v+Gq

2

(− (Ipcmdv

−Gdv

+Gq + Ipcmdv

−Gqv

+Gd

− Iqcmdv−Gdv

+Gd + Iqcmdv

−Gqv

+Gq). (18)

The sequence current limit function is additionally used toensure that the RMS value of each phase current is limited. Theschematic diagram of the sequence current limit function isillustrated in Fig. 8. The asymmetrical components of currentreferences are converted back into phasor components. TheRMS value of each phase is calculated accordingly. Duringnormal operation, where the converter current is smaller thanthe limited value, the current limit gain (kCL) is equal to one.In case of disturbance, if the largest RMS value among threephases exceeds the limited value, the current limit functionstarts working to reduce the current references by adjustingkCL.

The current compensator block is used to convert the limitedpositive and negative output load current references i∗LGodq intothe inductor filter current references i∗Gdq , as given by (19) and(20). The sequence current control, which consists of positivesequence and negative sequence current controllers, uses theinductor filter current references as inputs. Fig. 6(d) showsthe sequence current control diagram, in which L is the filterinductance, ω0 is the grid angular frequency, and vdc is theDC-link voltage.

i+∗Gdq = i+∗L

Godq − (i+Godq − i+Gdq), (19)

i−∗Gdq = i−∗L

Godq − (i−Godq − i−Gdq). (20)

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IV. REAL-TIME MODELLING OF DETAILED SWITCHINGAND AVERAGE TURBINE MODELS

Both detailed switching (DSW) and average (AVG) tur-bine models are implemented by the OPAL-RT eMEGASIMsimulator. Opal-RT is widely used by international industriesfor real-time applications. The differences between real-timemodels and conventional models in MATLAB/Simulink arethe converter, pulse width modulation, and the decouplingmodels. On the other hand, the difference between DSW andAVG models lies in the converter modeling while the turbinecontrollers are alike, except for the pulse width modulationblock, as shown in Fig. 9. In the real-time DSW model, thetwo-level time-stamped bridges (TSB) with high-impedancecapability from the RT-events library are used to modelthe detailed switching converter while the Universal Bridgemodules are used in the conventional models. The three-phase two-level converter model is considered in this paperas its main focus is on the converter controller. For the multi-MW WTGs, different converter models such as multi-levelconverters or parallel structures can be retrofitted with a slightmodification in the converter models and the pulse widthmodulation techniques. The real-time event (RTE) space-vector pulse width modulation (SPWM) is used to generate thepulse-width modulated signals for the DSW converter whilethe PWM generator modules are required in the conventionalmodels. The AVG model, which uses the ideal voltage andcurrent sources to model the converter, is built using theUniversal Bridge block from the SimPowerSystems library.Since the DC link voltage of the back-to-back (BTB) converterdoes not change significantly for a time-step simulation, theDC-bus decoupling method provided by the ARTEMiS libraryis used to accelerate the real-time simulation, which is notavailable in the conventional models. The DC-bus decouplingblock also includes the DC chopper, which is used to protectthe DC system from overvoltage conditions. Both DSW andAVG models use the DC-bus decoupling block for efficientreal-time computation.

The real-time simulator OP5700, which is equipped with an8-core Intel Xeon processor E5 3.2 GHz, is used to evaluate

(a) DSW model

(b) AVG model

Fig. 9. Real-time modelling of DSW and AVG turbines.

TABLE IREAL-TIME CAPABILITY OF DSW AND AVG MODELS.

Model type Samplingtime (µs)

CPU usage(%)

Total CPUtime (µs)

DSW 50 14.43 7.17AVG 50 11.04 5.52

Fig. 10. Real-time capability with different number of turbines (TBs) and thereduction of CPU usage with the use of AVG model.

the real-time performance of the proposed turbine models. Thereal-time capability of the DSW and AVG models is monitoredby monitoring models provided by RT-Lab, which is shownin Table I. The percentage of CPU usage indicates the CPUcapacity that is in use to execute the turbine models. Thetotal CPU time includes all time spent by RT-Lab servicesto execute the model. Both DSW and AVG models areimplemented in RT-Lab with the sampling time of 50 µs. Itcan be seen in Table I that the CPU usage and total CPU timefor the AVG model are smaller than that of the DSW model.The impact of turbine numbers on the real-time capability ofboth models is shown in Fig. 10, which indicates that the CPUusage is 48.09% for the case of three DSW turbines, whereasit is 32.82% for the same number of AVG models. Fig. 10also shows the reduction of CPU usage when the AVG modelis used in place of the DSW model. Although the percentageof CPU reduction is trivial in the case of a single turbine, itis significant in the case of multiple turbines. It can be seenwhen modeling three turbines that use the AVG model canreduce 15% of CPU usage compared to the DSW model. TheCPU reduction is an important factor that should be consideredfor modeling the wind farm system when considering a largenumber of turbines.

V. MODEL VALIDATION

The detailed 15MW real-time model is validated againstthe WECC generic model in the paper to ensure that theproposed model is suitable for practical interconnected studies.The model validation is conducted with different operationregions of WTGs.

A. Test SystemThe validation setup is shown in Fig. 11, in which the

controlled voltage source is used to represent the voltage dipthat occurs on the utility side. The measured voltage dip atthe terminal of the wind turbine generator (WTG) is shown inFig. 12, for four different cases. Each case is used to validatethe wind turbine models under different wind speed conditions.These voltage cases are used as the inputs of the WECC modelfor validation. The active and reactive power responses of

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Fig. 11. Setup for model validation.

Fig. 12. Voltage dip measured at the WTG terminal.

TABLE IIPARAMETERS OF 15MW WIND TURBINE MODEL.

Components Parameters

Step-up transformerRated power: 18 MVA

Rated voltage (RMS line): 4 | 66 kVLeakage reactance: 0.1 pu

BTB converter

Rated power: 15 MWDC link voltage: 10 kV

DC link capacitance: 4000 µFOutput LC filter: 0.275 mH; 1024 µF

Switching frequency: 3 kHz

PMSG

Rated power, Prated: 15 MVANumber of pole pairs, p: 162

Stator resistance, Rs: 0.0368 Ω

Stator d-axis inductance, Ld: 0.0087 HStator q-axis inductance, Lq : 0.0058 H

Rated speed, ωr : 0.8 rad/sTotal reflected inertia, J : 3.16× 108 kgm2

Wind turbineRated wind speed, vrated: 12 m/sTurbine rotor diameter, D: 236 m

detailed models during these voltage cases are recorded tocompare with the WECC model. Detailed parameters of thewind turbine generator are shown in Table II.

B. Model Validation

Fig. 13 shows the validation results in a case where thewind turbine is operated in region 2 as the wind speed is10 m/s. The validation results in cases where the wind turbinehas a rated power output, shown in Fig. 14. As shown inthese figures, the detailed wind turbine has the capability ofinjecting power during voltage dip conditions, which is thesame as the WECC generic model. In the first validation, at10 m/s wind speed, when the voltage dips to zeros (case 1),the power is forced to zero, as shown in Fig. 13(a). However,in cases 3 and 4, where the voltage dips to 0.6 and 0.8 pu,respectively, the turbine can maintain active power stably at thesame value as in the pre-fault condition. The reactive powerof 0.32 and 0.18 pu are injected into the grid supporting forthe grid during voltage-dip conditions. The injected amount

(a) Case 1 (b) Case 2

(c) Case 3 (d) Case 4

Fig. 13. Model validation with wind speed of 10 m/s.

(a) Case 1 (b) Case 2

(c) Case 3 (d) Case 4

Fig. 14. Model validation with wind speed of 15 m/s.

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Fig. 15. 15MW wind turbine performance under varying wind speeds: (a)wind speed; (b) pitch angle; (c) rotor speed; (d) DC-link voltage; (e) outputactive power; (f) output reactive power.

Fig. 16. Three-phase voltage and current of 15MW model: (a) and (b) are thevoltage and current respectively in DSW model; (c) and (d) are the voltageand current respectively in AVG model. Note: Blue line represents phase a,orange line represents phase b, and yellow line represents phase c.

of power is different, depending on the voltage-dip levels andoperation modes of turbines. In the second validation with thewind speed of 15 m/s where the turbine is operated underthe rated condition, the amount of injected active power isdifferent from the first validation as the turbine is able toproduce more power during some low voltage conditions. Itcan be seen that the performances of the detailed model havecomplied with the WECC generic model.

VI. EVALUATION OF DSW AND AVG MODELS

The DSW and AVG models are evaluated in this sectionunder different scenarios such as wind dynamic, power cur-tailment, balanced and unbalanced fault conditions. The winddynamic scenario is performed to validate the region operationof WTGs. The power curtailment scenario is used to verify theoperation of WTGs when they receive power commands fromwind plant control system. Finally, the balanced and unbal-anced fault studies are conducted to evaluate the effectivenessof the proposed models under abnormal conditions.

A. Turbine Performance under Wind DynamicsThe performances of both DSW and AVG wind turbine

models are evaluated in the dynamic wind condition, as

Fig. 17. Power curtailment performance of wind turbine models: (a) windspeed; (b) pitch angle; (c) rotor speed; (d) DC-link voltage; (e) output activepower; (f) output reactive power.

shown in Fig. 15. The wind speed is changed from 6 m/sto 25 m/s. The rotor speed is controlled at 0.6 pu in region1.5 when the wind speed is 6 m/s. When the wind speedis increased to 10 m/s, the turbine is operated in region 2where the optimal torque control is used. The pitch controlleris activated in region 3, when the wind speed is higher thanthe rated wind speed of 12 m/s, which is indicated by theincrease in the pitch angle in Fig. 15(b). The rotor speed iscontrolled constantly at 1 pu in this region. The wind turbine’soutput active power changes along with the wind speed and ismaintained constantly at the rated value when the wind speedis higher than the rated wind speed. The DC-link voltage andoutput reactive power is maintained stably during the windspeed variations. Three-phase voltage and current measured atterminal DSW and AVG turbine models are shown in Fig. 16,which indicate that a low total harmonic distortion is achievedby the DSW model. It is observed in Figs. 15 and 16 thatthe AVG model can represent the same dynamic responseas the DSW model, except for the high-frequency harmonicdistortion.

B. Active and Reactive Power RegulationThe wind turbines are capable of regulating power as

required by the transmission system operator. The performanceof active and reactive power regulation of both DSW andAVG models is shown in Fig. 17. The active power referencedecreases from 1 pu to 0.8 pu then 0.5 pu and then it increasesto 0.8 pu and 1 pu. The reactive power reference changes from+0.5 pu to -0.5 pu, in which the positive sequence reactivepower reference indicates the wind turbine supplying reactivepower for the grid and vice versa. The pitch angle changesto regulate the output active power of turbines, as shown inFig. 17(b). Figs. 17(e) and (f) indicate that the output power ofthe turbines follows the references. It is also observed in thiscase that the dynamic response of the AVG model is consistentwith the DSW model.

C. Balanced Fault StudiesThe wind turbine models are evaluated in the condition of

balanced fault on the high side of the step-up transformer from

9

Fig. 18. Transient three-phase voltage and current of DSW model measuredat turbine terminal: (a) Voltage; (b) Current. Note: Blue line represents phasea, orange line represents phase b, and yellow line represents phase c.

Fig. 19. Transient three-phase voltage and current of AVG model measuredat turbine terminal: (a) Voltage; (b) Current. Note: Blue line represents phasea, orange line represents phase b, and yellow line represents phase c.

Fig. 20. Balanced fault performance of 15MW model: (a) wind speed; (b)pitch angle; (c) rotor speed; (d) DC-link voltage; (e) output active power; (f)output reactive power.

Fig. 11. The evaluation results are shown in Figs. 18, 19, and20. The three-phase-to-ground fault occurs at 500 s and iscleared after 0.15 s. The three-phase-to-ground fault results inthe voltage drop to zero, as shown in Figs. 18 and 19. Theterminal voltage dip is sensed, and the current limit functionsin the grid-side controller start limiting the injected active andreactive current during the fault. The output power during thisfault, dropped to zero, as shown in Fig. 20. Since the windturbine still captures wind power, the DC link power increases

Fig. 21. Transient voltage and current of typical control of DSW model underunbalanced fault: (a) Voltage; (b) Current. Note: Blue line represents phasea, orange line represents phase b, and yellow line represents phase c.

Fig. 22. Transient voltage and current of proposed sequence-control ofDSW model under unbalanced fault: (a) Voltage; (b) Current. Note: Blue linerepresents phase a, orange line represents phase b, and yellow line representsphase c.

Fig. 23. Comparison of transient power under unbalanced fault: (a) Activepower; (b) Reactive power.

significantly, resulting in the rise in DC link voltage. The DCchopper is activated in this case to prevent the damage causedby overvoltage in the DC link, as shown in Fig. 20(d). Whileclearing the fault, the DC chopper is disabled and the DClink controller is activated to regulate the DC link voltage,resulting in the oscillations in DC link voltage and activepower. When the fault is cleared, the DC link voltage, outputpower is recovered to the nominal values. It can be seen thatthe high-frequency harmonic distortion can be observed in theDSW model whereas the AVG model can represent the samedynamic response as the DSW model.

D. Unbalanced Fault StudiesThe proposed turbine model is evaluated in the unbalanced

fault condition and its performance is compared with the typ-

10

ical turbine model that is designed without negative sequencecontrol capability. The phase-a-to-ground fault is applied onthe high side of the step-up transformer from Fig. 11. It shouldbe noted that although only the DSW models are compared inthis section, the performances of AVG models are the same.The transient voltage and current measured at turbine terminalsare shown in Figs. 21 and 22. Since the proposed model hascapability of negative sequence current injection, the outputcurrent of turbine under proposed controller is different to thetypical control model, as shown in Figs. 21(b) and 22(b). Thecomparison of power during an unbalanced fault shown inFig. 23, indicates that the second-order harmonic oscillation inthe active power component is damped out with the proposedsequence control. This is an advantage of the proposed turbinemodels.

VII. CONCLUSION

The real-time models of offshore wind turbines, which wereproposed in this paper, provide the capabilities of limitingsequence currents and injecting negative sequence currents.The proposed models developed in compliance with the stan-dardized turbine models are suitable for practical studies oninterconnected wind farm systems. The turbine model valida-tion studies reveal that the proposed models were aligned withthe WECC generic turbine model. Both detailed switching andaverage turbine models were presented, and their real-timeperformances were evaluated under normal and abnormal con-ditions. Real-time simulation results reveal that the dynamicresponses of the detailed switching model and the averagemodel are the same, except for the high-frequency harmonicsin the detailed model due to the converter switching. Thanksto the capability of injecting negative sequence currents duringunbalanced conditions, the proposed models demonstrate thesuperior performance of damping the second-order harmonicoscillation from active power, compared to the typical turbinemodel. Compared to existing models, real-time models inthis paper offers the advantages of computational efficiencyand standards compliance. Combining DSW and AVG modelsenables the modeling of large-scale offshore wind farms inreal-time environments, which will be considered in our futureworks.

ACKNOWLEDGMENT

This material is based upon research supported by, or in partby, the New York State Energy Research and DevelopmentAuthority (NYSERDA) under award number 148516.

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