modeling, control and analysis of doubly fed … · modeling, control and analysis of doubly fed...

MODELING, CONTROL ANDANALYSIS OF DOUBLY FED

INDUCTION GENERATOR DURINGSTEADY STATE AND TRANSIENT

STATE

Maheswari Muthusamy1, Parvathy Ayalur Krishnamoorthy2,Department of Electrical and Electronics Engineering,

Hindustan Institute of Technology and Science,Chennai, India.

[email protected],[email protected]

June 25, 2018

Abstract

Electrical power genertaion from renewable sources in-creased rapidly due to concern on environmental pollution,depletion of fossil fuels and energy shortage .To meet theincreased power demand Doubly Fed Induction Generatorsare mostly used in variable speed wind turbines because ofits economic factors such as Low cost, Size, and low losses.Due to increased penetration of wind power generation topower system grid, it is essential to analyze the influence ofDFIG wind turbines on power system network. The maindrawback of DFIG is that it is very delicate to grid instabil-ities such as voltage dips. Hence in this paper the operationof DFIG under steady state and transient state has beenstudied with MATLAB/SIMULINK. Extensive simulationstudy investigates the transient overshoots and ripples that

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International Journal of Pure and Applied MathematicsVolume 120 No. 6 2018, 1517-1535ISSN: 1314-3395 (on-line version)url: http://www.acadpubl.eu/hub/Special Issue http://www.acadpubl.eu/hub/

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present in rotor current, DC link voltage and Electromag-netic Torque. This paper also gives theoretical analysis onhow asymmetrical voltage dip is severe than the symmetri-cal voltage dip.

Key Words:Doubly Fed Induction Generator, Sym-metrical Voltage dip, Asymmetrical Voltage dip.

1 INTRODUCTION

Generating electricity from wind turbines has increased tremen-dously considering the developments in last few decades. Doublyfed induction generators (DFIGs) are the widely used technologyin variable speed wind energy conversion systems with the advan-tages of partial active power and reactive power control capabili-ties at Sub synchronous and Super synchronous generator operationmode, lower converter costs and less power losses. In addition, thistechnology is cost effective than the PMSG concept since it em-ploys back to back Voltage Source Converters with rating of 30%of the generator size [1],[2] .Commonly, the DFIG is directly con-nected to the electrical network by the stator windings and througha bidirectional converter in the rotor windings. DFIG concept suf-fers from some problem especially during grid faults. When voltagesag occurs, the stator current increases and consequently the rotorcurrent also increases. Also, it results in DC link overvoltage andtorque oscillations in the machine and voltage dip at DFIG termi-nals. Proper measures must be taken to protect the converter andturbine against various voltage sag conditions.This manuscript is organized as follows: The second section presentsthe Analytical modeling of DFIG. Wind turbine model with max-imum power point tracking is presented in section 3. Modeling ofBack to Back Converter control is presented in fourth section. Infifth section, Steady State Analysis and Transient analysis of DFIGduring Symmetrical and Asymmetrical fault condition is discussed.Simulation results are presented in section six and conclusions aregiven.

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2 ANALYTICAL MODELING OF DFIM

The model of the DFIM are represented with differential equationswhich can be obtained using the space vector representation in sta-tionary reference frame [3].Voltage equations of DFIG in space vec-tor form can be expressed as

Where vs,Ψs, Rs, is, Ls are Stator Voltage, flux, resistance, currentand Inductance. vr,Ψr, Rr, ir, Lr are Rotor quantities. Subscriptsand m are leakage and mutual quantities respectively. Taking intoaccount the Coordinate transformation, by denoting the analogousspace vector to the stationary reference frame the model of theDFIM is obtained. Rotor voltage and rotor flux on stationary ref-erence frame is given by

Figure 1 shows the αβ electrical model of the DFIM in statorcoordinates.

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Figure 1.Equivalent circuit of DFIM in stationary reference frame(αβ)

Continuing with the model electric power and torque can becalculated as,

3 MODELING OF WIND TURBINE

AND IMPLEMENTATION OFMPPT

CONTROLLER

Wind turbine model

Power extraction from the wind is obtained by AerodynamicTheory. Calculating the mechanical torque in terms of wind veloc-ity, the torque produced by the rotor can be denoted as,

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where ρ is air density, R is the radius of the wind turbine rotorand t is the angular speed of the rotor. Based on the above equa-tions wind turbine is modeled in MATLAB/SIMULINK. Figure 2.Displays the model of Wind Turbine.

Figure 2 Wind Turbine Model

Implementation of MPPT control

In this paper indirect speed controller is considered for Maxi-mum Power Point Tracking (MPPT). Controller circuit is given inFigure 3. Maximum power is extracted by indirect speed control.For any rotational speed deviation around a point in the maximumpower curve, Variable speed wind turbine goes back to its operatingpoint.

Figure 3 Indirect speed control method of MPPT controller

From this optimal torque can be derived as the quadratic func-tion of the wind turbine speed.

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4 MODELING OF ROTOR SIDE AND

GRID SIDE CONVERTER CONTROL

Schematic diagram of DFIG is shown in Figure 4. The stator is di-rectly connected to the Grid and the supply voltage to stator will behaving the constant Amplitude and Frequency of Grid. The rotor isalso Connected to the grid through Back to Back power electronicconverters. (shown in schematic diagram Figure 4).Hence supplyvoltage of the rotor will be at different Magnitude and frequencyso as to obtain various speed and torque operational circumstancesof the machine. This PWM converter with the suitable controllergives the mandatory rotor AC voltages to regulatel the operatingpoint of DFIG and to achieve the real and reactive power exchangeto the grid via rotor.

Figure 4 Schematic diagram of Grid connected DFIG WT

Rotor Side converter controlStator active and reactive power is controlled by RSC through

rotor current vector control [4]. complete vector control diagramis shown in Figure 5. Three phase rotor current is converted intodirect and quadrature axis rotor current in dq frame. PLL is usedfor angle calculation. d-axis current is aligned with the stator flux.idr is proportional to the stator reactive power, and that the iqris proportional to the torque or active stator power. Therefore,from synchronous reference frame model of DFIG the rotor voltage

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equations are obtained as a function of the rotor currents and statorflux .

Figure 5 Vector control of Rotor Side Converter

Grid side converter control

Grid side converter regulates the DC link voltage and indepen-dently controls the reactive power injected in to Grid. From theVbus and Qg references PWM pulses are created to control theswitches Sa g, Sb g, and Sc g. Thus, the modulator generates thegrid side converter pulses Sa g, Sb g, Sc g from the three phasevoltage references V ∗

af , V∗bf and V ∗

cf . First the three phase grid cur-rent is converterd to stator reference frame which is again convertedinto dq reference frame which gives direct and quadrature axis gridcurrent. It must be noted that the current references (I∗dg, i

∗qg) are

decoupled from the reactive and active powers.Thus, I∗dg controlimplies Pg control, while I∗qg control implies Qg control. The dqvoltage references (V ∗

df , V∗qf ) are autonomously produced by the dq

current (I∗dg, I∗qg) controllers. Hence reference three phase voltages

are created in synchronously rotating coordinates(V ∗df , V

∗qf ), then

transformed to stationary reference (αβ)coordinates (V ∗αf , V

∗βf ), and

nally the abc votage references are generated. Grid side converter

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Vector control strategy shown in Figure 6. GSC control fullls thetwo main objectives of the grid side converter: It controls the DClink bus voltage and also the real and reactive power between therotor and the grid.

Figure 6 Vector control of Grid Side Converter.

5 STEADY STATE ANALYSIS AND

TRANSIENT ANALYSIS

Steady State Analysis:

ωr depends on the electrical speed of the shaft ωm , which leads tothree modes such as Subsynchronus operation when slip Positive,

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Supersynchronus operation when slip negative and synchronous op-eration when slip is zero. Steady state equivalent circuit of DFIGis shown in Figure 7.

Figure 7 Steady State Equivalent circuit of DFIG

For practical analysis, the rotor circuit is ”converted” to thestator frequency s, simply by doing:

Figure 8 Modified Equivalent circuit referred to stator

In modified equivalent circuit rotor parameters are presented at thesame stator frequency.

Transient Analysis

Sudden drop of grid voltage is known as Voltage dip which iscaused by incidents of faults arising in the power system grid. Thissection emphasis on both symmetric fault and asymmetric fault.Since Stator is directly connected with the grid,any grid disturbancewill affect the stator of the DFIG, it is essential to investigate thebehaviour of the stator flux in order to realize the complications

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resulting from the disturbance caused by the dip.hence stator fluxcan be represented as

From equation it can be noticed that stator flux depends onstator voltage and rotor current . when unexpected voltage diphappens, the stator flux cannot reach the steady state as rapidly asthe stator voltage.The term of the rotor current can make the fluxfalloff more fast . But the rotor current is controlled by means ofthe rotor-side converter if it remains connected. Equivalent circuitof DFIG for voltage dip analysis and space vector diagram is shownin Figure 9.a) and 9.b)

where ω is angular frequency and V represent voltage magnitude.Superscripts p denotes positive sequence, n denotes negative se-quence and 0 denotes zero sequence quantities.The stator ux canbe stated as,

where s = Ls/Rs is the time constant of ψ and ψn0 is the initialnatural ux. Transferring (23) into rotor reference frame, we have

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Symmetrical Voltage dip analysis:

Symmetrical faults are type of faults in which all the phases areshort circuited to each other and frequently to ground..

Asymmetrical Voltage dip analysis

Asymmetrical faults contain only one or two phases. In Asym-metrical faults the three phase lines become unbalanced. Such typesof faults occur between line-to-line or between line to-ground. outof different faults line to line fault is the utmost severe situation.The positive and negative component for Asymmetrical faults are

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By comparing the above equations , it is clear that the Line-to-Linegrid aymmetrical fault is more adverse than the symmetrical gridfault.

6 SIMULATION RESULTS ANDDIS-

CUSSION

In this section broad simulation study is carried out to to ob-serve the behaviour of DFIG during Steady state and transientstate includes both Symmetrical and Asymmetrical grid fault con-ditions.The simulation is carried out using MATLAB/Simulink for2MW DFIG wind turbine with rated voltage of 690V and ratedcurrent of 1760 A with rated speed of 1500 rpm .The vector con-trol strategy oriented with stator flux is implemented in the RSCto regulate the active and reactive powers of the DFIG, while thegrid-side converter (GSC) is designed to maintain constant dc-linkvoltage.Also, a programmable three phase voltage source is em-ployed to simulate several dip circumstances that can happened atthe generator terminals.

Steady State Analysis Results

Performance of DFIG wind turbine in steady state is anal-ysed for subsynchronous speed (wind speed 8m/s) and Super Syn-

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chronous speed (10 m/s) and the results are given in Figure 10. Inorder to validate the results three blade wind turbine characteris-tics (shown in Figure 11) are emulated with MATLAB coding andthe steady state results are compared with it and proved that boththe results are similar.

Figure 10 Simulink results Steady State analysis with wind speed8m/s and 10m/s

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Figure 11 Emulated Power Characteristic of 3 blade wind turbine

From Figure 11 it is shown that at 10m/s the approximatepower generation is of 1.5 MW. The same can be verified by mul-tiplying steady state Torque and speed from Figure 10. For thewind speed of 8m/s (sub synchronous speed) the machine reachesthe steady state between 2second to 3seconds and for 10m/s (Su-per Synchronous) ,steady state is reached between 5 and 6 sec-onds.between 3second to 4 second ,the machine runs at synchronousspeed. From the graph at 10m/s wind speed the torque at steadystate is noted as -9000N/m and the speed is about 170 rpm. Hencethe Power (Torque * Speed) is approximately 1.53MW. Negativesign on the torque indicates that the machine is operated as a Gen-erator. It can also be noted from figure 10.c) that during the sub-synchronous mode the rotor current is having the phase sequenceof RYB and for Super synchronous mode the sequence is changedto RBY and also during Synchronous speed range the rotor currentis constant.

Symmetrical Voltage Dip Analysis:

Behaviour of DFIG during Symmetrical Voltage dip is shown inFigure 12a),12 b) and 12 c).

Figure 12 i) RSC control during Symmetrical Voltage Dip

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Figure 12 ii) GSC control during Symmetrical Voltage Dip

Figure 12 iii) Symmetrical Fault Analysis

Symmetrical fault is created by the programmable voltage sourceat time 3 seconds and the fault is cleared at t=3.1second. From thefigure 12.i) c) it is noted that the stator Voltage Vs is reduced to10% of Vs, Hence Stator current (Is) and Rotor current (Ir ) areincreased to very high value during Fault period shown in figure12.i)f) and 12.i)h). Stator Voltage Starts increasing at 3.5 secondsand reaches steady state at 4seconds.12.i) b) shows Torque Oscil-lations also high during fault period.In order to control the torqueoscillations Quadrature axis rotor current and Quadrature axis ro-tor voltage also varied shown in 12.i)d and 12.i)h.Figure 12.ii) shows the Grid side converter control during Symmet-rical fault.12.ii)a) shows the variation in DC bus voltage at fault

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duration and Reactive power requirement is compensated by con-trolling quadrature axis grid current shown in figure 12.ii) b and e.Figure 12.iii) shows fault analysis during symmetrical Voltage dip.Asdiscussed already stator voltage is reduced and stator and rotor cur-rent is increased to high value.inorder to reach steady state statorflux has to be reduced. It won’t evolve quickly.Hence some externalcircuit like crowbar has to be implemented to damp the stator fluxquicky.Figure 12.iii)d)shows the Flux variation during symmetricalfault.

Asymmetrical Voltage dip analysis:

Asymmetrical fault is created at 3seconds and cleared at 3.9 sec-onds. As analysed in section 5 Asymmetrical phase to phase faultis severe than the symmetrical fault. For asymmetrical voltage dipwe need to consider both positive and negative sequence componentalso. DFIG is modeled with asymmetrical fault and the simulationresults are shown in following figure 13.i) and 13.ii)Figure 13.i) Shows the Control of rotor side converter during Asym-metrical fault.At t=3s each phase is having Unsymmetrical voltagesas shown in figure 13.i)c).Due to unsymmetrical reduction in sta-tor voltage there is unsymmetrical Variation in stator and rotorcurrents shown in figure 13.i)f) and 13.i)i).Due to Asymmetricalvoltage there is a torque oscillation and the torque cannot reachthe steady state value as shown in figure 13.i.b). There is a varia-tion in positive and negative sequence quadrature and Direct axisrotor current according to torque oscillations shown in Figure 13.i)dand 13.i)e.In Figure 13.ii) Grid side converter control during Asymmetricalfault is discussed. Small variation in DC bus voltage is shown. Thereactive power requirement is compensated by Positive and nega-tive sequence quadrature axis grid current shown in figure 13.ii) band 13.ii)e.

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Figure 13.i) RSC control during Asymmetrical Voltage dip

Figure 13.ii) GSC control during Asymmetrical Voltage dip

7 CONCLUSION

This paper analyzes the steady state performance and transientperformance of DFIG wind turbine generator. As seen from thesimulation results voltage dip causes large variation in stator as wellas rotor current. Proper measures need to be taken to limit thesecurrents in order to protect the back to back converters therebyprotection of wind turbine. Several methods have been discussedin the literature. But all the methods requires additional hardware

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circuit which increases the size and cost of the turbine. Thereforemore focus is required to implement soft computing based convertercontrol techniques during symmetrical and Asymmetrical Voltage.

References

[1] T. Ackermann. Wind Power in Power Systems. Hoboken, NJ:Wiley, 2005.

[2] Z. Chen, J. M. Guerrero, and F. Blaabjerg.A review of thestate of the art of power electronics for wind turbines. IEEETrans. PowerElectron., Aug. 2009.

[3] Abad. G, Lopez. J, Rodri guez. M, Marroyo. L, Iwanski.G. Doubly Fed Induction Machine: Modeling and Controlfor Wind Energy Generation Applications. Wiley-IEEEPress,2011.

[4] Abad. G, Iwanski. G. Properties and control of a Doubly FedInduction Machine. Power Electronics for Renewable EnergySystems, Transportation and Industrial Applications, 2014.

[5] Wenyong Guo, Liye Xiao, Shaotao Dai, Yuanhe Li, Xi Xu,Weiwei Zhou, and Luo Li. LVRT Capability Enhancement ofDFIG with Switch-Type Fault Current Limiter. IEEE Trans-actions on Industrial Electronics, 2015.

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