-
5/28/2018 Second-Order Sliding-mode Controller Design and Tuning for Grid Synchronisation and Power Control of a Wind Turbine-driven Doubly Fed In
1/12
Published in IET Renewable Power Generation
Received on 26th January 2012
Revised on 10th November 2012
Accepted on 22nd November 2012
doi: 10.1049/iet-rpg.2012.0026
ISSN 1752-1416
Second-order sliding-mode controller design andtuning for grid synchronisation and power control of awind turbine-driven doubly fed induction generatorAna Susperregui1, Miren Itsaso Martinez1, Gerardo Tapia1, Ionel Vechiu2
1Department of Systems Engineering and Control, Polytechnical University College, University of the Basque Country
UPV/EHU, Plaza de Europa, 1, 20018 Donostia-San Sebastin, Spain2
Ecole Suprievre des Technologies Industrielles Avances (ESTIA) Research, Technopole Izarbel, 64210 Bidart, FranceE-mail: [email protected]
Abstract: This study presents a second-order sliding-mode control (2-SMC) scheme for a wind turbine-driven doubly fedinduction generator (DFIG). The tasks of grid synchronisation and power control are undertaken by two different algorithms,designed to command the rotor-side converter at a xed switching frequency. Effective tuning equations for the parameters of
both controllers are derived. A procedure is also provided that guarantees bumpless transfer between the two controllers at theinstant of connecting the DFIG to the grid. The resulting 2-SMC scheme is experimentally validated on a laboratory-scale7 kW DFIG test bench. Experimental results evidence both the high dynamic performance and the superior robustnessachieved with the proposed control scheme.
Nomenclature
cosj power factorir, is rotor and stator current space-vectorsir,is components of rotor and stator current
space-vectorsLlr, Lls rotor and stator leakage inductancesLm,Lr, Ls magnetizing, rotor and stator inductancesLr rotor transient inductancen general turns ratio
P number of pole pairsPr,Ps, Pt rotor-side, stator-side and total active
powersQs stator-side reactive power
Rr,Rs rotor and stator resistancess slipvg, vs grid and stator voltage space-vectorsvg, vr components of grid and rotor voltage
space-vectorss angle between the stator-ux-oriented and the
stationary reference framess angle between the grid-voltage-oriented and
the stationary reference framesr, r rotor electrical position and speedrm rotor mechanical speed
s,sl synchronous and slip angular frequenciess statorux space-vectors component of statorux space-vector
Subscripts
D,Q
direct- and quadrature-axis components, expressedin the stationary reference frame
x, y direct- and quadrature-axis components, expressedin the stator-ux-oriented reference frame
x,y direct- and quadrature-axis components, expressedin the grid-voltage-oriented reference frame
, direct- and quadrature-axis components, expressedin the rotor natural reference frame
Superscripts
R rated value* reference value
1 Introduction
Standard vector control (VC) schemes conceived to commandwind turbine-driven doubly fed induction generators (DFIGs)typically comprise proportional-integral (PI)-based cascadedcurrent and power control loops [13]. However, the systemtransient performance degrades as the actual values of theDFIG resistances and inductances deviate from those basedon which the control system tuning was carried out duringcommissioning [4]. In addition, the tracking of the
maximum power point achieved by adopting classical VCcongurations exhibits the characteristic lags associatedwith PI-based control schemes [5,6].
www.ietdl.org
540 IET Renew. Power Gener., 2013, Vol. 7, Iss. 5, pp. 540551
& The Institution of Engineering and Technology 2013 doi: 10.1049/iet-rpg.2012.0026
-
5/28/2018 Second-Order Sliding-mode Controller Design and Tuning for Grid Synchronisation and Power Control of a Wind Turbine-driven Doubly Fed In
2/12
Overcoming those two drawbacks entails improvingrobustness to DFIG parameter variations, as well asachieving high dynamic performance power control. In thisframework, alternative control schemes for DFIGs are being
proposed, among which a strong research line focuses ondirect power control (DPC) [4, 7]. Several others explorethe option of applying sliding-mode control (SMC) [5,810].
In particular, a rst-order SMC (1-SMC) conguration for
decoupled control of DFIG active and reactive powers isdescribed in [5]. In spite of conferring outstandingrobustness to parameter variations and superior tracking ofa rotor speed-dependent optimum power curve, the 1-SMCstructure put forward leads to a variable switchingfrequency of the rotor-side converter (RSC) transistors. Thismay cause broadband harmonics to be injected into thegrid, hence complicating the design of both the
back-to-back converter and the grid-side AC lter [5,7].This drawback is overcome in [10] through application of
the so-called boundary layer method. By adopting thisapproach, the discontinuous rotor voltage control signals towhich 1-SMC leads are rst smoothed out. The resulting
voltage waveforms are then applied to the DFIG rotor bymeans of a modulation technique, such as pulse-widthmodulation (PWM) or space-vector modulation, whichdrives the RSC transistors at a constant switchingfrequency. Even if the described approach solves the
problem of variable switching frequency, it is only at theexpense of severely compromising the characteristics oftracking accuracy, robustness and disturbance rejectionconferred by SMC. Indeed, within the boundary layer, thefeedback system no longer behaves as dictated by slidingmode, and it is simply reduced to a system with no slidingmode [11].
In this context, with the objective of keeping a constantswitching frequency without renouncing to the robustness
and tracking ability features gained with 1-SMC, aPWM-based second-order SMC (2-SMC) scheme for DFIGcontrol is presented in this paper. This control congurationis not only aimed at accurately tracking time-varyingreference values for the active and reactive powers to beexchanged between the DFIG stator and the grid, but alsoat ensuring the synchronisation required for smoothconnection of the DFIG stator to the grid [1215].In addition, the problem of bumpless transfer between thecontrollers in charge of synchronisation and power control,
at the instant of connecting the DFIG stator to the grid, issolved straightforwardly.
Not only the design and implementation of the resultingglobal control scheme are addressed in detail, but also itsanalytical tuning. As an alternative to the conventionaltrial-and-error method frequently adopted to adjust 2-SMCalgorithms [16], tuning equations for the global 2-SMCsystem put forward are derived based on DFIG parameters
and intuitive specications for the closed-loop timeresponse.
Results of experimental evaluation of the proposed 2-SMCscheme on a 7 kW DFIG prototype are reported.
2 Overview of DFIG models for powercontrol and grid synchronisation
When the DFIG stator is connected to the grid, its rotor-sidemodel, expressed in the stator-ux-oriented xy referenceframe depicted in Fig.1, is given by [17]
irx=
vrx
Lr Rr
Lrirx
Lm
LsLr|cs
| +vsliry (1)
iry=vry
LrRr
Lriryvsl irx+
LmLsL
r
|cs|
(2)
where Lr= Lr L2m
/ Ls
and sl= s r. Regarding theactive and reactive powers owing between the DFIG statorand the grid, they may be expressed as [17]
Ps= 3
2
LmLs
|vg|iry ; Qs=3
2
|vg|Ls
|cs| Lmirx
(3)
Expressions (1)(3) consider that currents owing into the
DFIG stator and rotor are positive, which implies thatgenerated active and reactive powers are represented asnegative.
On the other hand, given that power generation is notprotable for rotor speeds below a given value, the DFIGstator is not connected to the grid until that threshold isexceeded. The connection is not trivial, since the gridvoltage and that induced at the open stator of the DFIGmust coincide both in magnitude and phase to avoidshort-circuits. Therefore, prior to connection, the DFIGmust be commanded to achieve grid synchronisation [18].
Let a new xy reference frame be adopted when thestator is disconnected from the grid, whose y quadrature
axis is collinear with the grid voltage space-vector, asdisplayed in Fig. 2. As proved in [14], the open-stator
Fig. 2 xyreference frame for synchronisation
Fig. 1 Stator-ux-oriented xy reference frame, together with the
stationary DQ reference frame, and the rotor natural frame,
www.ietdl.org
IET Renew. Power Gener., 2013, Vol. 7, Iss. 5, pp. 540551 541
doi: 10.1049/iet-rpg.2012.0026 & The Institution of Engineering and Technology 2013
-
5/28/2018 Second-Order Sliding-mode Controller Design and Tuning for Grid Synchronisation and Power Control of a Wind Turbine-driven Doubly Fed In
3/12
model for the DFIG rotor side, expressed in that referenceframe, is given by
irx=vrx
LrRr
Lrirx+vsliry (4)
iry=vry
LrRr
Lriryvslirx (5)
It turns out that, in steady state, if disconnected from thegrid, the DFIG stator ux and voltage space-vectors are,respectively, collinear with x and y axes [14]. As a result,vss, as depicted in Fig. 2. xy and xyreference framesmust hence be aligned to achieve synchronisation. Yet, fora complete match up, vs must be not only collinear with vg,
but also identical in magnitude. As shown in [14], thosetwo requirements are satised if rotor current regulation iscarried out around set-points
irx= |vg
|Lmvs ; iry=0 (6)
3 Second-order SMC scheme
A global 2-SMC scheme for the DFIG is described in thissection. Owing to the different dynamic behaviours andcontrol targets to be dealt with when its stator isdisconnected from or connected to the grid, the relevantDFIG model is considered to design the control law foreach of those two cases.
3.1 Selection of switching variables
Examination of the set-points in (6) evidences that rotorcurrent regulation must be carried out for gridsynchronisation. Therefore when the DFIG stator isdisconnected from the grid, the switching functions givennext are assumed
sx= irxirx+cx
irxirx
dt (7)
sy= iryiry+cy iryiry dt (8)
where the integral terms, weighted by cx and cy positiveconstants, are added for steady-state response improvement,as suggested in [19].
On the other hand, seeking to achieve close trackingof the maximum power point, Ps , as well as highdynamic performance control of the reactive power, thefollowing switching variables are adopted when connectedto the grid
sP=PsPs+cP
PsPs
dt (9)
sQ=QsQs+cQ QsQs dt (10)where cPand cQ are also positive constants to be tuned.
3.2 SynchronisationDFIG disconnected fromthe grid
3.2.1 Design: Bearing in mind that the irx and iry
set-points in (6) are constant, the following time derivativesof switching functions sxand syresult from combination of(7), (8), (4) and (5)
sx= cx irx+ RrLrcx
irxvsliry 1Lr
vrx (11)
sy= cy iry+RrLr
cy
iry+vslirx1
Lrvry (12)
which reveal that the DFIG is of rst-order relative degreeduring synchronisation. Accordingly, it may be commanded
by applying 1-SMC or 2-SMC [16]. As already mentioned,a structure based on 1-SMC would however lead to avariable switching frequency of the RSC transistors,therefore complicating the design of the power converteritself, as well as that of the grid-side AC lter. Aiming to
overcome that drawback, a PWM 2-SMC realisation,known as the super-twisting algorithm (STA), is adopted [20].Consequently, the voltage to be applied to the rotor is
computed according to control law
vrx= vrxST+vrxeq; vry= vryST+vryeq (13)
where the terms with subscript ST are calculated, throughapplication of the STA, as
vrxST=lx|sx |
sgn sx
+wx sgn sx dt (14)vryST=ly |sy | sgn(sy ) +wy sgn(sy )dt (15)
withx,wx,yandwybeing positive parameters to be tuned.The addends with subscript eqin (13), which correspond toequivalent control terms, are derived by letting sx= sy=0,as dened in [19]. As a result
vrxeq=Lr cx irx+RrLr
cx
irxvsliry
(16)
vryeq=Lr cy iry+RrLr
cy
iry+vslirx
(17)
The sliding regime in manifold sx= sy= sx= sy=0 canalso be attained by applying only the STA control terms in(13). Accordingly, the equivalent control terms in (16) and(17) are not strictly necessary. However, if incorporated, themore accurately they are estimated, the lower is the controleffort let to be done by the STA. In conclusion, althoughuncertainty in Lrand Rrleads to inaccurate vrxeqand vryeq,robustness of the overall control algorithm in (13) is not putin jeopardy, as robustness does actually lie on the STAcontrol terms given by (14) and (15).
Equivalent control terms are hence included not only toimprove the system transient response [21], but also to easeselection of constants cx and cy, as well as tuning of the
STA x, y, wx and wy gains. Owing to the analogyexisting between the procedures for tuning the algorithmscommanding irx and iry, only that related to irx will be
presented in detail.
www.ietdl.org
542 IET Renew. Power Gener., 2013, Vol. 7, Iss. 5, pp. 540551
& The Institution of Engineering and Technology 2013 doi: 10.1049/iet-rpg.2012.0026
-
5/28/2018 Second-Order Sliding-mode Controller Design and Tuning for Grid Synchronisation and Power Control of a Wind Turbine-driven Doubly Fed In
4/12
3.2.2 Tuning: Substitution of control law (13) into (11)produces
sx= 1
Lrlx
|sx |
sgn sx
+wx sgn sx dt
(18)
Now, given that sgn(sx) =sx/|sx|, taking the time derivativeof (18) leads to
sx= 1
Lr
lx
2|sx | sx+wx
sx
|sx |
(19)
Let us assume that, because of the rst term in the STA, thereaching phase is satisfactorily completed and the slidingregime is entered. From that moment on, |sx| x, with xclose to zero. Considering the most unfavourable case, inwhich |sx| = x, and using the denition of sx in (7), the
following expression can be worked out from (19)
ex+lx
2Lrdx
+cx
a2 cx ,lx( )
ex+1
Lrdx
lx cx2
+ wxdx
a1 cx ,lx ,wx( )
ex
+ wx cxLrdx
a0 cx ,wx( )
ex dt=0 (20)
where ex= irxirx . Taking the time derivative of (20),the following differential equation reecting the ex errordynamics while in sliding regime is obtained
ex+a2ex+a1ex+a0ex=0 (21)
Hence, once x is xed, adequate selection of cx, xand wx allows attaining certain target error dynamics,established through the third-order characteristic equationgiven next
p2 +2jxvnxp+v2nx p+ajxvnx =p3+(2+a)jxvnx
a2t
p2 + 1+2aj2x
v2nxa1t
p+ajxv3nxa0t
=0
(22)
which, provided that is selected high enough 10 gives rise to a pair of dominant poles with respect to a thirdone placed at p= xnx. As a result, it can beconsidered that target error dynamics are entirely denedvia x damping coefcient and nx natural frequency.Those designer-dened error dynamics would theoretically
be achieved just by tuning cx, x and wx so that a2 = a2t,a1 =a1tand a0= a0tare simultaneously fullled.
Considering the expressions fora2, a1and a0provided in(20), as well as those for a2t, a1t and a0t reected in (22),
the latter requirements lead to the following tuning equations
c3
x(2+a)jxvnxa2t
c2
x+ 1+2aj2x
v2nx
a1t
cxajxv3nxa0t
=0
(23)
lx=2Lrdx
(2+a)jxvnxcx
(24)
wx= Lrdxajxv3nx
cx(25)
It is important to note that the coefcients in (23) coincidewith those of target characteristic equation (22), except forthe signs of the squared and independent terms, which arenegative. It therefore turns out that the three possible valuesfor cx are equal to the roots poles of targetcharacteristic equation (22), although their real parts haveopposite signs. The real parts of the desired poles mustnecessarily be negative to ensure stability, which impliesthat the real parts of the three possible values for cx willalways be positive. As a result, since (23) is third-order, it
is guaranteed that at least one of the three solutions for cxwill be both real and positive, as required. If (23) has morethan one feasible solution forcx, then the {cx, x, wx} setleading to the best performance may be identied throughnumerical simulation.
3.2.3 Implementation: The functional diagram providedin Fig. 3 illustrates the procedure for implementing the
proposed synchronisation algorithm. Any variable presentin a given layer of the diagram is also available to thelayers inside, which implies that the algorithm must beimplemented from the outer to the inner layer labelled,respectively, as 1st Step and 3rd Step at their bottom
left-hand corners.In addition to the irx andiry set-points provided in (6), the
actual values ofirxandiryare required to compute switchingfunctions sx and sy, as well as equivalent control terms(16) and (17). Knowledge ofr is also needed to calculatethe sl slip angular frequency present in (16) and (17). In
accordance with Figs. 1 and 2, the Parks ej rsur( )
transform is used to bring rotor current ir and ircomponents to the xy reference frame, where ir and irare derived by applying the Clarkes transform to directlymeasured three-phase rotor current. Based on Fig. 2, anglesis calculated as
arctan
vgQ
vgD 90 (26)
while r, as well as r, can either be measured using anincremental encoder or estimated by an observer, if asensorless scheme is to be implemented.
Similarly, rotor voltage vr and vr natural-framecomponents are obtained through application of the inverseej r
sur( ) Parks transform to vrx and vry control signals. The
inverse Clarkes transform is then applied to vrand vr inorder to achieve the three-phase rotor voltage waveforms to
be supplied as reference signals to the PWM algorithm.
3.3 Power controlDFIG connected to the grid
3.3.1 Design: Considering that|cs|in (1) turns out to benegligible when grid connected, combination of (9) and(10) with (1)(3) leads to the time derivatives of switching
www.ietdl.org
IET Renew. Power Gener., 2013, Vol. 7, Iss. 5, pp. 540551 543
doi: 10.1049/iet-rpg.2012.0026 & The Institution of Engineering and Technology 2013
-
5/28/2018 Second-Order Sliding-mode Controller Design and Tuning for Grid Synchronisation and Power Control of a Wind Turbine-driven Doubly Fed In
5/12
variablessPand sQgiven next
sP= Ps
3
2
LmLs
|vg|RrLr
cP
iry+vsl irx+Lm
LsLr
|cs|
+cPPs+3
2
LmLsL
r
|vg|vry(27)
sQ= Qs
3
2
|vg|Ls
cQ|cs| +RrLr
cQ
LmirxvslLmiry
+cQQs+3
2
LmLsL
r
|vg|vrx(28)
which prove that the DFIG is also ofrst-order relative degreewhen connected to the grid. Therefore the design and tuningof power controllers is analogous to that presented inthe preceding section. Thereby, the rotor is fed with the
followingxyaxes-referred voltage
vrx=vrxST+vrxeq; vry=vryST+vryeq (29)
The STA terms are then obtained as
vrxST= lQ|sQ|
sgn(sQ) wQ
sgn(sQ)dt (30)
vryST= lP|sP|
sgn(sP) wP
sgn(sP)dt (31)
whereQ, wQ, Pand wPare positive constants to be tuned.
On the other hand, the equivalent control terms in (29) arecomputed by zeroing (27) and (28), which yields
vrxeq= 2LsL
r
3Lm|vg|Q
s+cQ QsQs
+RrirxLrvsliry(32)
vryeq= 2LsL
r
3Lm|vg|P
s+cP PsPs
+Rriry+vsl Lrirx+
LmLs
|cs| (33)
3.3.2 Tuning: Given that the algorithms governing Psand Qs are adjusted by following the same method, onlytuning of that controlling the active power will be dealt
Fig. 3 Functional diagram of the proposed synchronisation algorithm
www.ietdl.org
544 IET Renew. Power Gener., 2013, Vol. 7, Iss. 5, pp. 540551
& The Institution of Engineering and Technology 2013 doi: 10.1049/iet-rpg.2012.0026
-
5/28/2018 Second-Order Sliding-mode Controller Design and Tuning for Grid Synchronisation and Power Control of a Wind Turbine-driven Doubly Fed In
6/12
with. Substitution of control law (29) in (27) leads to
sP= 3
2
LmLsL
r
|vg| lP|sP|
sgn sP
+wP sgn sP dt
(34)
expression which turns out to be identical to that in (18), once
factor (3Lm|vg|)/(2LsL
r) and subscript
P
are, respectively,replaced by 1/(Lr) and x. Consequently, tuning equations(23)(25) remain valid forcP, Pand wPjust by substituting
Lrand subscript xwith (2LsLr)/(3Lm|vg|) and P. Therefore
c3P(2+a)jPvnPc2P+ 1+2aj2P
v2nPcPajPv3nP=0(35)
lP=4LsL
r
dP
(2+a)jPvnPcP
3Lm|vg|(36)
wP=2LsL
rdPajPv
3nP
3Lm|vg
|cP
(37)
3.3.3 Implementation: Fig. 4 displays the functionaldiagram corresponding to the proposed power controlscheme. Given that it is analogous to that described inSection 3.2, only the main differences will be highlightedhere.
On the one hand, it is essential to note that the actual valuesofPsand Qsare computed as
Ps=3
2 vgDisD+vgQisQ
; Qs=3
2 vgQisDvgDisQ
(38)
hence avoiding the use of the DFIG parameter-dependentexpressions in (3), which are only to be used for controllerdesign. Regarding the reference values for active andreactive powers, a maximum power point tracking (MPPT)strategy provides Ps as a function of r, while Q
s is
established directly or based on Ps and on the demandedcos j* power factor.
On the other hand, anglesis required instead ofsto carryout the Parks transform and inverse transform reected in thediagram of Fig.4. In this case, as evidenced by Fig.1, siscalculated as
rs=arctancsQ
csD(39)
wheresDand sQare in turn estimated as
csD=
vgDRsisD
dt; csQ=
vgQRsisQ
dt
(40)
Fig. 4 Functional diagram of the proposed power control scheme
www.ietdl.org
IET Renew. Power Gener., 2013, Vol. 7, Iss. 5, pp. 540551 545
doi: 10.1049/iet-rpg.2012.0026 & The Institution of Engineering and Technology 2013
-
5/28/2018 Second-Order Sliding-mode Controller Design and Tuning for Grid Synchronisation and Power Control of a Wind Turbine-driven Doubly Fed In
7/12
Aiming at avoiding drift, bandpass lters are used rather thanpure integrators to implement (40) [22]. Accordingly, |s| inequivalent control term (33) is computed from sD and sQas follows
|cs| =c2sD+c2sQ
(41)
3.4 Bumpless transfer
So far, the separate performance of each of the two DFIGoperating states disconnected from and connected to thegrid has only been considered, but an undesirable
phenomenon may appear if the switch between the twocontrollers is not properly carried out. If a direct transfer isaccomplished, discontinuities arise in the control signals atthe instant of connection, owing to the magnitude mismatch
between the rotor voltage components generated by the twocontrollers. This effect produces high stator current values,leading the machine to exchange excessive power with the
grid at the instant of connection. Aiming to attenuate oreven avoid this bump, it is required to apply the samevalues of the control signals previous to and just after thetransfer, that is
vrx=vrx ; vry=vry (42)
Setting the focus on the DFIG rotor voltage components whenconnected to the grid, appropriate combination of (29)(33)
produces
vrx= lQ |sQ| sgn(sQ) wQ sgn(sQ)dt 2LsL
r
3Lm|vg|Q
s+cQ QsQs
+RrirxLrvsliry(43)
vry= lP|sP|
sgn sP
wP sgn(sP)dt 2LsL
r
3Lm|vg|P
s+cP PsPs
+Rriry+vsl Lrirx+LmLs
|cs| (44)
Condition (42) can be satised by carefully selecting theinitial values for integrals
sgn(sQ)dt and
sgn(sP)dt at
the instant of connection. Thus, substitution of (43) and(44) into (42) allows deriving those initial values as
sgn(sQ)dtt=0=
RrirxLrvslirylQ|sQ| sgn(sQ) vrx
wQ
2LsLrQ
s+cQ QsQs 3Lm|vg|wQ
(45)
sgn(sP)dtt=0=
Rriry+LrvslirxlP|sP| sgn sP vry
wP
2LsLr P
s+cP PsPs
3Lm|vg|wP
+Lmvsl|cs|LswP
(46)
4 Experimental validation
4.1 Description of the experimental rig
Experimental validation of the global control schemepresented throughout Section 3 is carried out on the 7 kWDFIG test bench shown in Fig. 5. The electric parametersof the DFIG under consideration are collected in Table 1.The values of resistances and inductances were identied ina recent study reported in [23]. The DFIG is driven by a15 kW armature-controlled dc motor, whose rotationalspeed can be commanded at will via a commerciallyavailable controller. The eMEGAsim OP4500 F11-13
platform by Opal-RT is used to perform rapid controlprototyping of the synchronisation and power controlalgorithms reected, respectively, in the functional diagramsof Figs. 3 and 4. The state of the synchronisation stage isdisplayed by means of a conventional lamp synchronoscope.
The sample rate for the global control algorithm, as wellas the frequency for the triangular carrier of the PWM
Table 1 7 kW DFIG electric parameters
Parameter Value
|vg| 4002/3
V
|is|R 16
2
A
|ir|R 24
2
A
Rs 370 mRr 145.8541 mLls 4.86 mHLlr 1.2138 mHLm 37.6812 mH
N 2.001Ls = Lls + nLm 80.2601 mHLr = Llr + Lm/n 20.045 mHP 2
Fig. 5 Experimental setup
www.ietdl.org
546 IET Renew. Power Gener., 2013, Vol. 7, Iss. 5, pp. 540551
& The Institution of Engineering and Technology 2013 doi: 10.1049/iet-rpg.2012.0026
-
5/28/2018 Second-Order Sliding-mode Controller Design and Tuning for Grid Synchronisation and Power Control of a Wind Turbine-driven Doubly Fed In
8/12
modulator, are xed to 5 kHz. In addition, the techniqueproposed in [24] is implemented in order to compensate the2.3s dead time inherent to the RSC. The integral termsincluded in both the switching functions and the STA itselfare digitally implemented based on Tustins trapezoidalmethod. Yet, with the aim of avoiding derivative ringing
[25], Eulers rectangular method is adopted to discretise thetime derivatives of Qs and P
s included in equivalent
control terms (32) and (33).Tuning equations (23)(25) and (35)(37) have been
directly applied to derive the values of the global 2-SMCalgorithm parameters reected in Table2. x, y and nx, yhave been selected so as to achieve synchronisation ofstator voltage to that of the grid in 105 ms, showing noovershoots. Given thatx, y = 1, two values are possible forcx, y; namely, nx, y and nx, y. However, numericalsimulation revealed that the {cx, y, x, y, wx, y} parameterset leading to the best performance was that resulting fromselecting cx, y = nx, y. Similarly, as a result of the valuesxed for
P, Qand
nP, Q, possible errors arising in active
and reactive powers would theoretically vanish in 50 ms,with no overshoots. As for the previous case, cP, Q arechosen to be equal to nP, Q.
For simplicity, the power signal feedback method isapplied in this case to dene the maximum power point to
be attained, Ps . Nevertheless, it is to be noted that theproposed 2-SMC power control algorithm is independent ofthe MPPT strategy adopted to establish the time-varyingreference value for Ps. As a consequence, tip-speed ratio orhill-climb searching strategies could equally be used todenePs [26].
In particular, the optimum power curve of a high-powerDFIG installed in an actual wind turbine is taken as starting
point. It was obtained by the manufacturer via off-lineexperimentation and consists in an empirical functionexpressing the total output power to be generated, Pt, as acubic function of the rotor speed, rm. That function is thenscaled in power level to derive a plausible optimum powercurve for the 7 kW DFIG under consideration.
Bearing in mind that the following relation holds for aDFIG
Pt=Ps+Pr (47)
where [18]
Pr sPs= vsvr
vsPs=
vsPvrmvs
Ps (48)
it turns out that
Psvs
PvrmPt (49)
Accordingly, based on the optimum power curve providingP
t, the rotor speed-dependent reference value for the
stator-side active power is computed as
Ps=
vsP
Ptvrm
(50)
thus evidencing that the resultingPs is a quadratic function ofthe rotor speed, asPtis, in turn, described as a cubic functionofrm.
In order to avoid setting unachievable reference values forPsandQs, it is required to observe the feasibility region of theDFIG, represented by the shaded area of Fig. 6. The DFIGfeasibility region is obtained by intersection of twosemicircles. The dashed line delimiting one of those
semicircles displays the restriction because of the rated rotorcurrent, and its analytical expression is found to be [2]
P2s+ Qs
3|vg|22Lsvs
2= 3
2
LmLs
|vg||ir|R 2
(51)
On the other hand, the analytical expression for thesemicircumference in solid line is given by
P2s+Q2s=3
2|vg||is|R
2(52)
which corresponds to the constraint imposed by the ratedvalue of the stator current. Examination of the feasibilityregion reveals the limited ability of this particular DFIG togenerate reactive power. In effect, Qs can be injected intothe grid only when generated Psis below 4.547 kW.
4.2 Experimental results
Aiming at showing some of the most illustrative results of theglobal 2-SMC scheme put forward, a test is conducted wherethe DFIG is subjected to the sequence of operation modesreected in Table 3. Additionally, the 15 kW dc motor iscommanded so that, during the test, the DFIG rotor speed
evolves with time as shown in Fig.7.The time progress of the DFIG rotor speed has been
conceived with the aim of evaluating the proposedsynchronisation and power control algorithms under
Table 2 Specifications set to tune the 2-SMC arrangement,and resulting parameter values
Specification Value Parameter Value
x, y 0.05 A cx,cy 55.2381x, y 1 x, y 5.4469nx, ny 55.2381 rad/s wx,wy 30.5811 10
P 35 W cP,cQ 116Q 15 VAr P 1.5453 10
1
P,Q 1 Q 1.0116 10 1
nP,nQ 116 rad/s wP 48.2032 10 wQ 20.6585 Fig. 6 Feasibility region for the 7 kW DFIG
www.ietdl.org
IET Renew. Power Gener., 2013, Vol. 7, Iss. 5, pp. 540551 547
doi: 10.1049/iet-rpg.2012.0026 & The Institution of Engineering and Technology 2013
-
5/28/2018 Second-Order Sliding-mode Controller Design and Tuning for Grid Synchronisation and Power Control of a Wind Turbine-driven Doubly Fed In
9/12
realistic conditions. In an actual wind turbine, rotor speedvariations are expected to be inappreciable duringsynchronisation, as it only takes a few cycles 105 ms inthis particular case. Considering this, rotor speed isregulated around 1220 rpm when testing the synchronisationscheme. However, it should be noted that thesynchronisation algorithm described in Section 3.2.1 isdesigned to operate with no restriction on rotor speed.
Regarding the second part of the test, devoted to analyse
the presented power control algorithm, rotor speed is variedin order that a signicant part of the optimum power curveis to be tracked both up and downwards. For that purpose,starting at second 9, rotational speed is accelerated from1220 to 1620 rpm, and subsequently decelerated back to1220 rpm from second 16 onwards. The acceleration anddeceleration displayed in Fig. 7emulate, respectively, thoseexperienced by a DFIG installed in a real wind turbine of
H= 0.9346 s inertia constant while undergoing a suddenincrease followed by a sudden decrease of wind speed.
The initial rotor positioning stage is activated manually atinstant p, and it lasts 0.5 s, until instant s. The purpose ofthis operation mode is to obtain an accurate estimate of the
rotor position at instant s, r0. From instant s on, theencoder measures the increment of the rotor electrical anglewith respect to r0, r. Thus, the absolute rotor positionrequired for synchronisation and power control is derived asr= r0 + r. The procedure described in [14] is followedfor initial rotor positioning.
Grid synchronisation is automatically launched at instants.Fig.8zooms at the beginning of the synchronisation process.In particular, Fig. 8a displays the transient response of thevoltage induced at the terminals of the DFIG open stator,showing that synchronisation with grid voltage isaccomplished at approximately the specied settling time of105 ms. For clarity, only voltages corresponding to phaseAare represented. The vra, vrb and vrc voltage components
shown in Fig. 8b are those supplied as inputs to thePWM modulator driving the RSC transistors duringsynchronisation. The resulting three-phase rotor current isdisplayed in Fig.8c.
After the lamps of the synchronoscope turn off, indicatingthat grid synchronisation has been achieved, the DFIG statoris manually connected to the grid at instantc. As a result ofthe bumpless transfer between the 2-SMC algorithms incharge of synchronisation and power control, gridconnection at zero power turns out to be smooth. This issubstantiated by Figs. 9a and b, which zoom, respectively,at the active and reactive powers interchanged between theDFIG stator and the grid around instant c. As expected,
they are both equal to zero prior to connection, and they arekept within the ranges of 80100 W and 200250 VAjust after connecting the DFIG stator to the grid. Thethree-phase rotor voltage and current leading to such a
Table 3 Operation modes of the DFIG during the test
Operation mode Time range, s
global control algorithm is idle 0pinitial rotor positioning ps;s= p+ 0.5grid synchronisation scconnected to the grid with no power exchange c5linear increase of generated power up to3.752 kW
56
generation according to optimum power curve 923
Fig. 8 Grid synchronisation
aGrid and DFIG open-stator voltagesb Reference values of the three-phase rotor voltage fed into the PWMmodulatorcThree-phase rotor currentFig. 7 DFIG rotational speed
Fig. 9 Smooth connection at zero power
aActive powerbReactive powerc Reference values of the three-phase rotor voltage fed into the PWMmodulatordThree-phase rotor current
www.ietdl.org
548 IET Renew. Power Gener., 2013, Vol. 7, Iss. 5, pp. 540551
& The Institution of Engineering and Technology 2013 doi: 10.1049/iet-rpg.2012.0026
-
5/28/2018 Second-Order Sliding-mode Controller Design and Tuning for Grid Synchronisation and Power Control of a Wind Turbine-driven Doubly Fed In
10/12
smooth connection are those shown in Figs. 9c and d,respectively. If the manoeuvre of connecting the DFIGstator to the grid at zero power was ideal, both the rotorvoltage and current previous to instant c would remainunchanged after connection.
As evidenced by Fig. 10, power generation is started atsecond 5. Between seconds 5 and 6, Ps is raised linearlyfrom 0 to 3.752 kW value which, according to (50),
corresponds to the optimum stator-side power for a 1220rpm rotational speed and established as dictated by (50)for the remaining time. In view of the feasibility regiondepicted in Fig.6, Qs is set in order that the DFIG operateswith a 0.81 lagging inductive power factor allthrough the test. Figs. 10a and b evidence the excellent
performances of Ps and Qs when tracking their respectivetime-varying reference values. In the worst case, whileoperating at supersynchronous speeds, chatter in reactive
power approximately reaches 3% of the 7 kW ratedpower. However, during the rest of the experiment, chatterpresent inPsand Qs represents < 1.5%.
Aiming at further assessing the dynamic performance ofthe proposed power control scheme, the experimentdiscussed above is repeated, but dening Qs as thesuccession of 1 kVAr steps displayed in Fig. 11b. Thedifferent set-points for Qs are carefully selected so thatthe resulting (Ps, Qs) operating points fall inside the DFIGfeasibility region shaded in Fig. 6. Fig. 11b conrms theoutstanding dynamic response of Qs when reacting to
sudden set-point changes. Moreover, as shown by Fig.11a,tracking ofPs is not affected by the steps in reactive power.The reection of those reactive power steps as abruptvariations in rotor current is clearly observable byexamining Figs.11band d.
In order to evaluate the robustness of the proposed globalcontrol scheme, the two tests above are repeated once x, y,wx, y, P, Qand wP, Qare re-tuned by deliberately assumingincorrect values for Lm, Ls and Lr. In particular, Lm isconsidered to be a 50% higher than its actual value inTable 1, which in turn leads to adopt incorrect values for
Fig. 10 Tracking of optimum stator-side power and Qs
aActive powerbReactive powerc Reference values of the three-phase rotor voltage fed into the PWMmodulatordThree-phase rotor current
Fig. 11 Tracking of optimum stator-side power and reactive power
steps
aActive powerbReactive powerc Reference values of the three-phase rotor voltage fed into the PWMmodulatordThree-phase rotor current
www.ietdl.org
IET Renew. Power Gener., 2013, Vol. 7, Iss. 5, pp. 540551 549
doi: 10.1049/iet-rpg.2012.0026 & The Institution of Engineering and Technology 2013
-
5/28/2018 Second-Order Sliding-mode Controller Design and Tuning for Grid Synchronisation and Power Control of a Wind Turbine-driven Doubly Fed In
11/12
both Ls and Lr see their Lm-dependent expressions inTable 1. Moreover, not only those inductances but also Rris deliberately assumed to be incorrect a 50% lower thanits actual value when computing equivalent control terms(16), (17), (32) and (33).
The main results of the rst robustness experiment areshown in Figs.12 and 13. The grid synchronisation detailed
by Fig. 12a, as well as the active and reactive power
tracking displayed in Figs. 13a and b, remain highlysatisfactory in spite of the aforementioned 50% mismatchesin Lm and Rr, hence supporting the robustness of the
proposed global 2-SMC scheme. In addition, the low-powerow between the DFIG stator and the grid reected byFigs.12b and c at instantc corroborates that smoothness of
connection is also preserved. Rotor voltage and currentsignals have not been provided to avoid reiteration with nosignicant added information.
To conclude, the second robustness experiment consists inrepeating the test whose results are provided in Fig.11underthe afore-cited parameter mismatches. Its most representativeresults are shown in Fig.14, where a still excellent tracking of
both the optimum stator-side power and the reactive powersteps can be observed.
5 Conclusions
A PWM-based 2-SMC scheme both for grid synchronisationand power control of a DFIG has been presented. Itallows keeping the tracking accuracy and robustnessfeatures characteristic of standard SMC, while leading to axed switching frequency of the RSC transistors.Experimentation conducted on a 7 kW DFIG test bench
proves that high dynamic performance control and superiorrobustness against DFIG parameter variations are achievedwhen applying the proposed global 2-SMC scheme. Inaddition, bumpless transfer between the gridsynchronisation and power control operating regimes isguaranteed, which results in smooth connection of theDFIG stator to the grid.
A systematic methodology to tune all the parametersinvolved in the presented 2-SMC realisation is also
provided. Its main benet lies in deriving the values ofthose parameters via direct application of tuning equations,hence eluding the generally time-consuming task oftrial-and-error adjustment suggested in [16], which is stillthe most usual practice. The satisfactory experimentalresults obtained support the effectiveness of the proposedtuning method.
6 Acknowledgments
The authors thank Giovanna Santamara, from Jema Energy,for her helpful advice. We are also grateful to ManuLarramendi and J. Ignacio Susperregui for their help in
Fig. 12 Synchronisation and grid connection under 50%
mismatches in Lmand Rr
aSynchronisationbActive powercReactive power
Fig. 13 Tracking of optimum stator-side power and Qs under 50%mismatches in Lmand Rr
aActive powerbReactive power
Fig. 14 Tracking of optimum stator-side power and reactive power
steps under 50% mismatches in Lmand Rr
aActive powerbReactive power
www.ietdl.org
550 IET Renew. Power Gener., 2013, Vol. 7, Iss. 5, pp. 540551
& The Institution of Engineering and Technology 2013 doi: 10.1049/iet-rpg.2012.0026
-
5/28/2018 Second-Order Sliding-mode Controller Design and Tuning for Grid Synchronisation and Power Control of a Wind Turbine-driven Doubly Fed In
12/12
modifying the 7 kW DFIG test bench. This work has beendeveloped within the Intelligent Systems and Energy (SI+E)research group of the University of the Basque Country UPV/EHU, and has been funded by the Spanish Ministry ofEconomy and Competitiveness, under project codeDPI2012-37363-C02-01 and grant code BES-2008-002563,as well as by the Basque Government (Spain), under researchgrant IT677-13, and the UPV/EHU, under unit of formation
and research UFI11/28.
7 References
1 Hopfensperger, B., Atkinson, D.J., Lakin, R.A.: Stator-ux orientedcontrol of a doubly-fed induction machine without position encoder,IEE Proc. Electr. Power Appl., 2000, 147, (4), pp. 241250
2 Tapia, A., Tapia, G., Ostolaza, J.X., Senz, J.R.:Modeling and controlof a wind turbine driven doubly fed induction generator, IEEE Trans.Energy Convers., 2003, 18, (2), pp. 194204
3 Pea, R., Clare, J.C., Asher, G.M.: Doubly fed induction generatorusing back-to-back PWM converters and its application tovariable-speed wind-energy generation, IEE Proc. Electr. PowerAppl., 1996, 143, (3), pp. 231241
4 Xu, L., Cartwright, P.:Direct active and reactive power control of DFIG
for wind energy generation
, IEEE Trans. Energy Convers., 2006, 21
,(3), pp. 7507585 Susperregui, A., Tapia, G., Zubia, I., Ostolaza, J.X.: Sliding-mode
control of doubly-fed generator for optimum power curve tracking,Electron. Lett., 2010, 46, (2), pp. 126127
6 Tapia, G., Tapia, A.: Wind generation optimisation algorithm for adoubly fed induction generator, IEE Proc. Gener. Transm. Distrib.,2005, 152, (2), pp. 253263
7 Zhi, D., Xu, L.: Direct power control of DFIG with constant switchingfrequency and improved transient performance, IEEE Trans. EnergyConvers., 2007, 22, (1), pp. 110118
8 Beltran, B., Ahmed-Ali, T., Benbouzid, M.E.H.: High-ordersliding-mode control of variable-speed wind turbines, IEEE Trans.Ind. Electron., 2009, 56 , (9), pp. 33143321
9 Ben Elghali, S.E., Benbouzid, M.E.H., Ahmed-Ali, T., Charpentier, J.F.,Mekri, F.: High-order sliding mode control of DFIG-based marinecurrent turbine. Proc. 34th Annual Conf. on IEEE Industrial
Electronics (IECON 2008), Orlando, USA, November 2008, pp.12281233
10 Hu, J., Nian, H., Hu, B., He, Y., Zhu, Z.Q.: Direct active and reactivepower regulation of DFIG using sliding-mode control approach, IEEETrans. Energy Convers., 2010, 25 , (4), pp. 10281039
11 Young, K.D., Utkin, V.I., zgner, .: A control engineers guide tosliding mode control, IEEE Trans. Control Syst. Technol., 1999, 7,(3), pp. 328341
12 Blaabjerg, F., Teodorescu, R., Liserre, M., Timbus, A.V.: Overview ofcontrol and grid synchronization for distributed power generationsystems, IEEE Trans. Ind. Electron., 2006, 53 , (5), pp. 13981409
13 Arbi, J., Ghorbal, M.J.B., Slama-Belkhodja, I., Charaabi, L.: Directvirtual torque control for doubly fed induction generator gridconnection,IEEE Trans. Ind. Electron., 2009, 56, (10), pp. 41634173
14 Tapia, G., Santamara, G., Telleria, M., Susperregui, A.: Methodology
for smooth connection of doubly fed induction generators to the grid,IEEE Trans. Energy Convers., 2009, 24, (4), pp. 959971
15 Peresada, S., Tilli, A., Tonielli, A.: Power control of a doubly fedinduction machine via output feedback, Control Eng. Pract., 2004,12, (1), pp. 4157
16 Bartolini, G., Ferrara, A., Levant, A., Usai, E.:On second order slidingmode controllers, in Young, K.D., zgner, . (Eds.): Variablestructure systems, sliding mode and nonlinear control (SpringerVerlag, 1999, 1st edn.), pp. 329350
17 Vas, P.:Sensorless vector and direct torque control(Oxford UniversityPress, 1998, 1st edn.)
18 Tazil, M., Kumar, V., Bansal, R.C., et al.: Three-phase doubly fedinduction generators: an overview, IET Electr. Power Appl., 2010, 4,(2), pp. 7589
19 Utkin, V., Guldner, J., Shi, J.: Sliding mode control inelectromechanical systems(Taylor & Francis, 1999, 2nd edn.)
20 Levant, A.:
Sliding order and sliding accuracy in sliding mode control
,Int. J. Control, 1993, 58 , (6), pp. 1247126321 Rashed, M., Goh, K.B., Dunnigan, M.W., MacConnell, P.F.A.,
Stronach, A.F., Williams, B.W.: Sensorless second-ordersliding-mode speed control of a voltage-fed induction-motor driveusing nonlinear state feedback, IEE Proc. Electr. Power Appl., 2005,152, (5), pp. 11271136
22 Pea, R., Crdenas, R., Proboste, J., Asher, G., Clare, J.: Sensorlesscontrol of doubly-fed induction generators using a rotor-current-basedMRAS observer, IEEE Trans. Ind. Electron., 2008, 55, (1),
pp. 33033923 Zubia, I., Zatarain, A., Alcalde, C., Ostolaza, X.: In situ electrical
parameter identication method for induction wind generators, IETElectr. Power Appl., 2011, 5 , (7), pp. 549557
24 Lin, J.L.:A new approach of dead-time compensation for PWM voltageinverters, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 2002,49, (4), pp. 476483
25 strm, K.J., Hgglund, T.: PID controllers: Theory, design andtuning(Instrument Society America, 1995, 2nd edn.)
26 Wang, Q., Chang, L.: An intelligent maximum power extractionalgorithm for inverter-based variable speed wind turbine systems,IEEE Trans. Power Electron., 2004, 19, (5), pp. 12421249
www.ietdl.org
IET Renew. Power Gener., 2013, Vol. 7, Iss. 5, pp. 540551 551
doi: 10.1049/iet-rpg.2012.0026 & The Institution of Engineering and Technology 2013