ORIGINAL RESEARCH Open Access

Modified vector controlled DFIG windenergy system based on barrier functionadaptive sliding mode controlTummala S. L. V. Ayyarao

Abstract

Increased penetration of wind energy systems has serious concerns on power system stability. In spite ofseveral advantages, doubly fed induction generator (DFIG) based wind energy systems are very sensitive togrid disturbances. DFIG system with conventional vector control is not robust to disturbances as it is basedon PI controllers. The objective of this paper is to design a new vector control that is robust to externaldisturbances. To achieve this, inner current loop of the conventional vector control is replaced with slidingmode control. In order to avoid chattering effect and achieve finite time convergence, the control gains areselected based on positive semi-definite barrier function. The proposed barrier function adaptive slidingmode (BFASMC) is evaluated by testing it on a benchmark multi-machine power system model under variousoperating conditions. The simulated results show that the proposed method is robust to various disturbances.

Keywords: Doubly fed induction generator (DFIG), Wind power generation, Sliding mode control, Robust control

1 IntroductionIncreased population, global warming, change in gov-ernments green policies, increased flow of funds, anddecreased installation costs paved a path for Renew-able energy systems. Wind energy is one of the prom-inent renewable systems and is consistently expandingthroughout the world. More than 51 GW of wind en-ergy is installed in 2017 only [18] and this shows thatwind energy is slowly capturing the energy market.DFIG is the most popular generator compared toothers in wind energy systems. It consists of a windturbine coupled to the shaft of the induction machine.The stator of the DFIG system is directly connected tothe grid while the rotor is connected to the grid via aback to back converter which regulates the slip power.This greatly reduces the converter rating. Highly effi-cient independent active and reactive power control isanother advantage of the DFIG system. Because of theabove advantages, DFIG dominated the entire variablespeed wind energy systems. But the performance ofthe DFIG system during grid perturbations is drastic-ally affected [12].

In the conventional vector control, the converterconnected on the rotor side commonly named asRotor side converter (RSC) regulates the active andreactive power and Grid side converter (GSC)regulates the DC link voltage. The performance of theconventional vector controlled DFIG system highlydepends on the PI controller parameters. Several PIcontrollers tuning techniques like particle swarmoptimization, Differential evolution, Bacteria foragingare proposed in the literature [11, 16, 17]. Thesemethods are based on linearized model of DFIG aroundan operating point. However, DFIG system is a highlynonlinear system and thus performance of the conven-tional vector controlled DFIG system is compromisedfor large disturbances like three-phase faults. Nonlinearcontrollers are proposed in the literature as an alterna-tive to overcome the nonlinearity behavior of DFIGsystem [3, 6, 14].As wind speed is stochastic in nature [5, 8] variable

power generation has drastic effect in multi-machinepower systems and therefore robust control is themost effective way in dealing with DFIG system.Sliding mode control is one of the robust control tech-niques [15] and therefore has been implemented forCorrespondence: ayyarao.tslv@gmrit.org; ayyarao.tummala@gmail.com

Department of EEE, GMR Institute of Technology, Rajam 532127, India

Protection and Control ofModern Power Systems

© The Author(s). 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, andreproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link tothe Creative Commons license, and indicate if changes were made.

Ayyarao Protection and Control of Modern Power Systems (2019) 4:4 https://doi.org/10.1186/s41601-019-0119-3

controlling the DFIG system [4]. Nevertheless, firstorder sliding mode control introduces controlchattering and the hardware realization requires high-frequency switching converters. To overcome thisissue, second order sliding mode control techniquesare applied for DFIG system [1, 2, 9]. Some of theconcerns are the design of the controller assumes thatthe bound of the disturbance is known which may notbe possible in practice and the control parametersmay be overestimated. Perturbation estimation basedsliding mode control is proposed in [10].Barrier function based adaptive sliding mode control

is introduced in [13]. To achieve finite time conver-gence, chattering free and improved robustness to vari-ous disturbances, the conventional vector controlledDFIG system is modified and the current control loopis implemented with BFASMC. BFASMC is introducedin the inner current loop to achieve faster convergencethan outer control loop.The major contributions of the paper are as follows:

1. This paper proposes a modified vector controlledDFIG based wind energy system. The proposedcomposite sliding mode control is a combinationof PI control for outer loop and BFASMC forinner current loop dynamics. The inner currentloops of both rotor side control and grid sidecontrol are designed based on BFASMC.

2. The proposed idea is simple to design and reducescontrol chattering as well.

3. Active power and terminal voltage deviationsconverge to zero in finite time post disturbance.

4. The controller is robust to various perturbationslike three-phase faults on transmission lines,parametric variations, and variable wind speeds.

5. The proposed controller does not require the upperbounds of the disturbance.

The rest of the paper is organized as follows: Section 2briefs the dynamic model of the DFIG system; Section 3introduces BFASMC. The design of the proposed compos-ite sliding mode control is detailed in Section 4. Theproposed control technique is evaluated and tested on abenchmark multi-machine power system and the simu-lated results are analyzed in Section 5. Finally, concludingremarks are given in the last section.

2 Dynamic model of DFIG based wind energysystemThe dynamics of the DFIG system are given by(1)–(3) [7]

dψdr

dt¼ Vdr−Rridr þ sωsψqr ð1Þ

dψqr

dt¼ Vqr−Rriqr−sωsψdr ð2Þ

dωdt

¼ 1JTm−Teð Þ ð3Þ

where ψdris rotor d-axis flux linkage; ψqris rotor q-axisflux linkage; Vdris rotor d-axis voltage; Vqris rotor q-axisvoltage; idris rotor d-axis current; iqris rotor q-axiscurrent; s is the slip; Rris the rotor resistance; ωis therotor speed; J is the moment of inertia; Tm is mechanicaltorque acting on the rotor; Te is the electromagnetictorque developed by the rotor.The flux linkages are given by:

ψdr ¼ −Lmids þ Lrridr ð4Þψqr ¼ −Lmiqs þ Lrriqr ð5Þ

where idsis stator d-axis current; iqsis stator q-axiscurrent.The electromagnetic torque developed by the rotor is

given by:

Te ¼ ψqridr−ψdriqr ð6Þ

The mechanical output of the wind turbine is givenby:

Tm ¼ 12σAv3wcp λ; βð Þ ð7Þ

where σ is the air density; Ais the area swept by theturbines; vwis the wind speed; cpis the Performancecoefficient of the turbine; λis the tip speed ratio; βis thepitch angle.

cp ¼ c1c2λi

−c1c3β−c1c4

� �e−c6λ þ c6λ ð8Þ

c1, c2, c3, c4, c5, c6 are constants and λiis a function ofλ, β.The wind turbine operates with maximum power

point tracking (Fig. 1).

3 An introduction to barrier function adaptivesliding mode controlLet us consider a system whose dynamics are given by:

_x ¼ uþ d ð9Þwhere x ∈ℜis the state of the system, u ∈ℜ is thecontrol input to the plant, d is the unknown boundeddisturbance acting on the system i.e., |d| ≤ dm where dmis a finite positive value. Let us assume that the boundsof the disturbance acting on the system are unknown.A First order sliding mode control (FOSMC) input

required to stabilize the system is given by:

Ayyarao Protection and Control of Modern Power Systems (2019) 4:4 Page 2 of 8

u ¼ −Κ sign xð Þ ð10ÞThere are two major issues with the first order

sliding mode control. The first one is a selection ofoptimum control gain and the second one is controlchattering. For optimum control parameter selection,adaptive sliding mode control techniques are proposedin the literature. In order to minimize the controlchattering, higher order sliding mode control tech-niques are introduced. The above two issues can betackled using the recently proposed Barrier functionbased adaptive sliding mode control. The controlinput in (10) is modified as:

u ¼ −Κ̂ xð Þ sign xð Þ ð11ÞNow the control parameter is a function of system

state and this control parameter is updated at every in-stant based on the positive semi-definite barrier functiongiven by (12)

K̂ xð Þ ¼ xj jΓ− xj j ð12Þ

where, Γ > 0 is a control parameter.Therefore when x→ 0, K̂→0 . If the state x is in the

neighborhood of origin i.e., jxjΓ is very much less than

one, then K̂≃ jxjΓ . This clearly shows that the state x

converges to zero with the BFASMC. For more detailswith stability proof refer [13].

4 Control of DFIG wind energy systemDFIG based wind energy system is a nonlinearstochastic system and is subjected to many distur-bances like faults on the transmission line, parameterperturbations, and variable wind speeds. However, theconventional vector controlled DFIG system is notrobust. In order to improve the robustness of conven-tional vector control, sliding mode control is introduced

in the current control loop and accordingly, the controlobjectives are chosen as:

Ltt→t F

idr−idr ref� �

→0 ð13Þ

Ltt→t F

iqr−iqr ref� �

→0 ð14Þ

Ltt→t F

idg−idg ref� �

→0 ð15Þ

Ltt→t F

iqg−iqg ref� �

→0 ð16Þ

where tF is a finite time value and idr_ref and iqr_ref arethe reference d-axis and q-axis currents.In the vector controlled DFIG system with stator flux

orientation,ψqs = 0and ψds = ψs. Modifying the dynamicsgiven in (1–2) in terms of rotor currents:

diqrdt

¼ 1σLr

V qr−Rriqr−sωsψdr

� � ð17Þ

didrdt

¼ 1σLr

V dr−Rridr þ sωsψqr

� �ð18Þ

Fig. 1 DFIG based wind energy system connected to the grid

Fig. 2 Modified rotor side controller

Ayyarao Protection and Control of Modern Power Systems (2019) 4:4 Page 3 of 8

The reference rotor current idr_ref is generated usingPI controller by comparing reference and actual activepowers while the reference current iqr_ref is generatedusing another PI controller using terminal voltageerror. Now these currents are compared with theactual currents and current errors are generated asgiven (19) & (20).

ed ¼ idr−idr ref ð19Þeq ¼ iqr−iqr ref ð20Þ

Because of the features like chattering free, finite timeconvergence and simplicity in design, current controllersare designed with BFASMC.For the design of control input in d-axis loop, the

sliding surface is selected as:

ρd ¼ ed ð21ÞTaking the derivative of (21) and from (17), the error

dynamics ofρdare given as:

_ρd ¼ 1σLr

Vdr−Rridr þ sωsψqr

� �−_idr ref þ φd ð22Þ

where φd represents unmodelled dynamics and paramet-ric variations.Now modifying the error dynamics in (22) as:

_ρd ¼ ud þ ϕd ð23Þ

where

ud ¼ 1σLr

Vdr−Rridr þ sωsψqr

� �ð24Þ

and ϕd is the cumulative disturbance.From (11), the control input required to stabilize the

error in fixed time is given by (25)

ud ¼ −K̂dr ρd�� �� sign ρd

� � ð25Þ

Fig. 3 Modified grid side controller

c

2KV/25KV

2KV/25KV

2KV/25KV

575V/25KV

9MVA2KV

9MVA2KV

9MVA2KV

9MVA 575V1

2

3

4 5 67

8

c

Area-1 Area-2

Fig. 4 Benchmark multi-machine power system

0

10

20

−0.5

0

0.5

−1

−0.5

0

0.5

1

time in sψqs

ψds

Fig. 5 3-D plot of flux linkages w.r.t time for a three-phasefault at bus 4

0.8 1 1.2 1.4 1.6 1.8

0.8

1

1.2

Ter

min

al v

olta

ge in

p.u

.

0.8 1 1.2 1.4 1.6 1.8

2

4

6

time in s

Act

ive

pow

er in

MW

ProposedPI control

Fig. 6 Terminal voltage and active power deviations for athree-phase fault at bus 4

Ayyarao Protection and Control of Modern Power Systems (2019) 4:4 Page 4 of 8

where

K̂dr ¼ρd�� ��Γd−ρd

ð26Þ

From (24),

Vdr ¼ σLrud þ Rridr−ωslψqr ð27Þ

For the design of control input in q-axis loop, thesliding surface is chosen as:

ρq ¼ eq ð28Þ

Taking the derivative of (28) and from (18),

_ρq ¼1σLr

V qr−Rriqr−ωslψdr

� �−_iqr ref þ φq ð29Þ

where φq represents unmodelled dynamics and paramet-ric variations.Let

uq ¼ 1σLr

V qr−Rriqr−ωslψdr

� � ð30Þ

Modifying error dynamics in (30) as:

_ρq ¼ uq þ ϕq ð31Þ

From (31), the control input required to stabilize theerror in fixed time is:

uq ¼ −K̂ qr ρq

��� ��� sign ρq� �

ð32Þ

0.8 1 1.2 1.4 1.6 1.8 21160

1180

1200

1220

1240

1260

1280

1300

time in s

DC

link

vol

tage

in V

Proposed methodPI Control

Fig. 7 DC voltage for a three-phase fault at bus 4

1 1.1 1.2 1.3 1.4 1.50.8

1

1.2

Ter

min

al v

olta

ge in

p.u

.

1 1.1 1.2 1.3 1.4 1.50

2

4

6

time in s

Act

ive

pow

er in

MW

ProposedFOSMC

Fig. 8 Comparison of the proposed method with FOSMC

0.2 0.2005 0.201 0.2015 0.202 0.2025 0.203

−0.5

0

0.5

time in s

cont

rol i

nput

udd

Fig. 9 Control chattering with FOSMC. Red color lineindicates FOSMC and the blue one indicates theproposed method

−1.5 −1 −0.5 0 0.5 1 1.5−1.5

−1

−0.5

0

0.5

1

1.5

ψds

ψqs

Fig. 10 Stator flux linkages

Ayyarao Protection and Control of Modern Power Systems (2019) 4:4 Page 5 of 8

where

K̂ qr ¼ρq

��� ���Γq−ρq

ð33Þ

From (32),

Vqr ¼ σLruq þ Rriqr þ ωslψdr ð34ÞThe proposed idea of rotor side converter control can

be viewed from Fig. 2.A similar procedure is followed for the design of

grid side control as shown in Fig. 3. DC link voltage

is compared with the reference voltage and voltageerror is given to PI controller which generates thereference current idg_ref. BFASMC is used in the de-sign of the current control.Remarks: The control parametersΓq,Γdare selected

based on the maximum possible current errors eq and edrespectively.

5 Results and discussionThe proposed composite sliding mode control is evalu-ated by testing in a simulated environment MATLAB/Simulink. In order to observe the robustness of theproposed control idea, it is tested for various testconditions for a benchmark multi-machine power sys-tem model. This benchmark system is a modified two

0.8 1 1.2 1.4 1.6 1.80

0.5

1

1.5

Ter

min

al v

olta

ge in

p.u

.

0.8 1 1.2 1.4 1.6 1.8−2

0

2

4

6

8

time in s

Act

ive

pow

er in

MW

ProposedPI Control

Fig. 11 Response of DFIG for a fault at bus 5

0.8 1 1.2 1.4 1.6 1.8800

900

1000

1100

1200

1300

1400

1500

1600

time in s

DC

link

vol

tage

in V

ProposedPI Control

Fig. 12 DC link voltage for a three-phase fault at bus 5

20 25 30 35 405

10

15

Win

d sp

eed

in m

/s

20 25 30 35 403.4

3.6

3.8

4

4.2

time in s

Act

ive

pow

er

Fig. 13 Response of DFIG system for variable wind speed

26 26.5 27 27.5 28−4

−3

−2

−1

0

1

2

3x 10

−3

time in s

Act

ive

pow

er e

rror

in M

W

PI ControlProposed

Fig. 14 Active power error for variable wind speed

Ayyarao Protection and Control of Modern Power Systems (2019) 4:4 Page 6 of 8

area Kundur’s model [16, 17], (Feng [3]) with one ofthe synchronous generator replaced with DFIG basedwind energy system as shown in Fig. 4. The detailedreport of the benchmark system is given in [19].

5.1 A three-phase fault on bus 4As the power system is a large distributed system,three phase faults on transmission lines are common.A three-phase is applied at bus 4 at 1 s with a faultresistance of 1Ω. The fault is cleared after 0.2 s. The windspeed is assumed constant at 10m/s. The functioning ofthe composite control can be visualized by observing theflux linkages as shown in Fig. 5. Under the pre-fault condi-tion, flux linkages are distortion free. The flux distortionsare present during the transients and the controller bringsthe system to the steady state.The proposed idea is compared to conventional PI

control. The active power deviations and terminal volt-age deviations are captured in Fig. 6. With PI control,the active power and terminal voltage oscillates and set-tles after 1.8 s. Yet, with the proposed composite slidingmode control, the active power and terminal voltageoscillations are less and settles faster with less peakovershoot. The peak overshoot and settling time of DClink voltage with the proposed method are improved con-siderably when compared with the conventional PI controlas shown in Fig. 7. One of the major drawback withFOSMC is the selection of optimum control gain value.The performance of the DFIG system with FOSMC withhigh control gain is depicted in Fig. 8 and the same iscompared with the proposed method. Control chattering isanother concern with FOSMC, but with the proposedapproach, control chattering is minimized. This is because,when the sliding surface ρ is approaching zero, controlinput tends to zero. The control input ud with FOSMC hasundesirable oscillations and this can be visualized in Fig. 9.

5.2 A three-phase fault at bus 5A three-phase fault is applied at bus 5 with fault resistanceof 1Ω. The flux linkage deviations are plotted in Fig. 10. Asthe fault is closer to the wind generation system, the distor-tions are enormous. After the fault, the active power andterminal voltage deviations are less with the proposed ap-proach compared with the conventional approach. This canbe visualized in Fig. 11. A similar result can be observedwith the DC link voltage as shown in Fig. 12.

5.3 Variable wind speedThe power output of the wind energy system varies con-tinuously with time because of the stochastic nature ofwind. Hence, the DFIG system is simulated with variablewind speed profile and the corresponding active power isshown in Fig. 13. The zoomed plot of active power error is

shown in Fig. 14 and it shows the efficacy of the proposedapproach.

6 ConclusionsThis paper presents a modified vector controlled DFIGsystem. The inner current loop with PI control in theconventional system is replaced with adaptive sliding modecontrol where the control gains are updated based onsemi-definite barrier function. The proposed compositecontrol is evaluated for a benchmark multi-machine powersystem model for various operating conditions. The pro-posed method has shown a considerable effect on thepower system stability when compared to the conventionalPI controller. The proposed method is robust to large dis-turbances like a three-phase fault.

AcknowledgementsNot applicable.

FundingThe authors declare that the research is not funded by any Government/Private institution/agency.

Availability of data and materialsAll the data is given in the paper or properly cited wherever necessary.

Authors’ contributionsTSLVAR contributed to analysis, modelling, manuscript preparation, revisionand typesetting of the manuscript. TSLVAR read and approved the finalmanuscript.

Competing interestsThe authors declare that they have no competing interests.

Received: 22 August 2018 Accepted: 17 February 2019

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