model predictive direct power control of doubly fed
TRANSCRIPT
HAL Id: hal-01813524https://hal.archives-ouvertes.fr/hal-01813524
Submitted on 11 Apr 2020
HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.
Model Predictive Direct Power Control of Doubly FedInduction Generator with Dead-Time Compensation
Binh Quang Van Ngo, Pedro Rodriguez-Ayerbe, Sorin Olaru, Silviu-IulianNiculescu
To cite this version:Binh Quang Van Ngo, Pedro Rodriguez-Ayerbe, Sorin Olaru, Silviu-Iulian Niculescu. Model PredictiveDirect Power Control of Doubly Fed Induction Generator with Dead-Time Compensation. IFAC 2017- 20th World Congress of the International Federation of Automatic Control, Jul 2017, Toulouse,France. hal-01813524
Model Predictive Direct Power Control ofDoubly Fed Induction Generator with
Dead-Time Compensation
Van Quang Binh Ngo, Pedro Rodriguez-Ayerb, Sorin Olaru ∗
and Silviu-Iulian Niculescu ∗∗
∗ Laboratory of Signals and Systems,CentraleSupelec-CNRS-UPS-Paris Saclay University, Gif-sur-Yvette
91192, France (e-mail: [email protected],[email protected], [email protected])
∗∗ Laboratory of Signals and Systems,CNRS-CentraleSupelec-UPS-Paris Saclay University, Gif-sur-Yvette
91192, France (e-mail: [email protected].
Abstract: The paper presents the control of a doubly fed induction generator connected witha three-level neutral point clamped inverter with compensation of dead-time effects. ModelPredictive Direct Power Control is synthesized using a dynamical model of the doubly fedinduction generator and three-level neutral point clamped inverter. The principle of the proposedcontrol scheme is to use the dynamical model to compute predictions of the future values ofthe stator flux, rotor current and DC-link capacitor voltages for all possible configurations ofvoltage vectors. However, the dead-time to avoid the short circuit in the inverter also causesthe modeling errors. Thus, by taking into account the dead-time in the model, it is possiblecompensate the dead-time effect of the switching devices. The active and reactive powers canbe estimated based on the stator flux and the rotor current. The cost function considers theerror between the active, reactive powers and their references, balance the DC-link capacitorvoltage and reduce the switching frequency and common-mode voltage. The optimal switchingstate that minimizes the cost function is selected and applied to the inverter. The simulationresults were carried out with Matlab under different conditions of wind speed and verifying theeffectiveness of the proposed method.
Keywords: Power Plants and Power Systems, Control of renewable energy resources,Application of power electronics, Intelligent control of power systems and Optimal operationand control of power systems.
1. INTRODUCTION
Nowadays, to the best of the author’s knowledge, theglobal wind energy capacity has increased rapidly andbecame one of the fastest developing renewable technolo-gies. Most of the major wind turbine manufactures aredeveloping larger wind turbines in the 1.5-6 MW range.For such an application, doubly fed induction generator(DFIG) represents an attractive solution due to its advan-tages: for instance, it allows the power converter to dealwith approximately 30% of the generator power, reducesconverter cost and power lost (Fig. 1) (Abad et al. (2011)).By using this configuration, it is possible to allow bothbidirectional active and reactive power flow from the rotorside to grid through the rotor side converter (RSC) andgrid side converter (GSC). Furthermore, from the techno-logical point of view, the three-level neutral point-clamped(3L-NPC) inverter structure represents a good solution forhigh power due to its advantages: reduction of the totalharmonic distortion (THD) and increasing the capacity ofthe inverter due to a decreased voltage applied to eachcomponent.
DFIG
RSC GSC
Grid
Tm
From wind turbine
Filter
DFIG
Grid
Gear box
Wind turbine
DC link
Rotor sidecontrol
Sabc_r
Grid sidecontrol
Sabc_g
Wind turbinecontrol
Rotor filter
Grid filter
RSC GSC
DFIG
Grid
Gear box
Wind turbine
Back-to-back converter
Rotor Filter
Grid Filter
3L-NPC 3L-NPC
Ps Pg
PrPr
3L-NPC
3L-NPC
Fig. 1. Schematic diagram of DFIG based wind generationsystems (Abad et al. (2011))
Several approaches have been proposed to control DFIGfor wind energy generation. Most of the existing controlmethods use the classical vector control based on theorientation of the flux stator (stator flux oriented) or statorvoltage (stator voltage oriented). This method allowscontrolling independently the electromagnetic torque oractive power and reactive power by means the componentsof the rotor current (Abad et al. (2011)). However, onedrawback of this method is that its performance dependson accurate machine parameters such as stator and rotor
resistance and mutual inductance. Next, another drawbackof using PI controller is the necessity of tuning of the gainsin the whole operating range of wind speed. In addition,a complex modulation technique along with the DC-linkcapacitor voltages balancing is required to apply thesetechniques to 3L-NPC inverter.
Recently, direct torque control (DTC) or direct powercontrol (DPC) (Xu and Cartwright (2006)) have been pro-posed to improve the controller performance. These meth-ods used the hysteresis control and the inverter switchingstates, selected from a look-up table (LUT) based on theerrors between the reference and estimated values, and ro-tor or stator flux position. Therefore, these methods do notrequire the current control loops and space vector modula-tion. Nevertheless, the drawback of LUT is that it has largeactive and reactive power ripple and switching frequencyvariation. In addition, a high-sampling frequency is usedfor DTC/DPC to guarantee acceptable steady-state anddynamic performances. To overcome this problem severaltechniques have been developed such as using DPC withspace vector modulation (SVM) (Kazemi et al. (2010)),predictive control strategy (Sayritupac et al. (2015)) andmodel predictive power control (?). Moreover, the dead-time effect will distort the output voltage, neutral-pointvoltage and current. Thus, a dead-time compensation isnecessary to be added into the control scheme (Irnura et al.(2012); Zhou and Rouaud (1999)). In this context, modelpredictive control is an alternative control technique thathas been recently applied to DFIG due to its advantages,such as easy inclusion of non-linearities in the model, delayand dead-time compensation and no need of current con-trol loops (Errouissi et al. (2016); Sun and Wang (2016)).
The present paper proposes the model predictive directpower control (MPDPC) to control the active and re-active power for DFIG connected to a 3L-NPC inverterwhile maintaining the balance between the DC link ca-pacitor voltage, reducing the switching frequency and thecommon-mode voltage. These objectives are accomplishedthrough the cost function in a predictive control strat-egy. In this paper, we focus on the modelling of errorscaused by dead-time induced by the physical switchingmechanism. With this approach, the model to predict theinverter ouput voltage and neutral-point voltage takes intoaccount the dead-time take of the conveter to compensateits effects. No current loops are considered and the inverterswitches are directly obtained from the cost function min-imization. This control allows improving the quality of thepower regulation and minimizing the switching losses. Inorder to reduce the computational effort, a control horizonof two is used for the prediction, where only combinationof inputs having a difference of one switch in the inverteris considered.
The remaining paper is organized as follow: Section 2presents the mathematical model of direct power controlwith dead-time compensation for a DFIG connected toa 3L-NPC. Next, section 3 details the proposed controlmethod. In section 4, simulation results are representedand analyzed and, finally, section 5 draws the conclusion.
2. MODEL OF DFIG CONNECTED 3L-NPCINVERTER
The doubly fed induction generator (DFIG) can be mod-elled by the equivalent circuit in dq coordinate (see Abadet al. (2011)) based on stator fluxed orientation. The statorand rotor voltage vectors can be described from Fig. 2 asfollows:
udqs = Rsidqs +
dψdqsdt
+ jωsψdqs (1)
udqr = Rridqr +
dψdqrdt
+ jωrψdqr . (2)
where udqs , idqs , ψdqs are the stator voltage, current and fluxvector in dq reference frame while udqr , idqr , ψdqr are therotor counterparts with respect to the stator. Rs, Rr arethe stator resistance and the rotor resistance referred tothe stator, ωs, ωm are the synchronous speed of stator fluxand angular rotor speed (rad/s), ωr = ωs - ωm = sωs isthe rotor angular frequency, with the coefficient s denotingthe slip.
sRdsi rR drisL
mL
rL ~
.r qr
dsddt drd
dtdsu dru
~
.s qs
sRqsi rRsL
mL
rL ~
.r dr
qsddt qrd
dtqsu qru
~
.s ds qri
sRdqsi rRsL
mL
rL
dqsd
dt dq
rddtdq
su
dqri
. dqssj . dq
rrj
~ dqru
~
~ ~
Fig. 2. Equivalent circuit of the DFIG in dq reference frame
The relationship between fluxes and currents is:
ψdqs = Lsidqs + Lmi
dqr , (3)
ψdqr = Lridqr + Lmi
dqs , (4)
with Ls and Lr are the stator and rotor inductances andLm the magnetizing inductance.
By substituting the stator current idqs from equation (3)into equation (1), the stator flux dynamics can be ex-pressed as follows:
dψdqsdt
=1
Ts
(− (1 + jωsTs)ψ
dqs + Lmi
dqr + Tsu
dqs
), (5)
where Ts = Ls
Rsis the time constant of the stator.
By substituting equation (5) and the rotor flux ψdqr fromequations (3) and (4) into equation (2), the dynamics ofthe rotor currents are represented as follows:
didqrdt
=1
σLr
(ψdqs
(LmLsTs
+ jωmLmLs
)+ udqr
)(6)
− 1
σLr
(idqr (Rσ + jωrσLr) +
LmLs
udqs
),
where Rσ = Rr + L2m/LsTs, σ = 1 − Lm
2/LsLr is theleakage coefficient.
Based on equations (5) and (6), the dynamical model ofDFIG can be expressed in matrix form as below:
.x = A(ωs, ωm)x+Bu, (7)
where x =
ψdsψqsidriqr
, u =
udsuqsudruqr
,
D
d
Q
m sr
m
s
sus
q
Coordinate reference frame for control DFIG
D
b
c
x
bx
cxSpace vector
presentation in three-phase (abc)
and stationary reference frame
x
d
Q
q
x
x
ax
Dx
dx
x
Qx
qxm s
r
Space vector presentation in different reference frames
a
Stator
frame
Rotor
frame
Stator flux
frame
Stator frame
Rotor frame
Stator flux frame
m
s
Fig. 3. Vector representation in different reference frame
A(ωs, ωm) =
− 1
Tsωs
LmTs
0
−ωs − 1
Ts0
LmTs
LmLsTsσLr
−ωmLmLsσLr
− RσσLr
ωr
ωmLmσLsLr
LmLsTsσLr
−ωr −RσσLr
, (8)
B =
1 0 0 0
0 1 0 0
− LmσLsLr
01
σLr0
0 − LmσLsLr
01
σLr
.
Since the stator is connected to the grid, the stator flux isa function of the grid voltage in steady state. Neglectingthe small drop in the stator resistance due to its relativelysmall value in comparison with the the stator reactance(Rs << ωsLs), we can obtain:
udqs ≈dψdqsdt≈d(∣∣ψdqs ∣∣ ejωs
)dt
≈ jωsψdqs . (9)
The system being oriented with stator flux (Fig. 3), andtaking into account the equation (9), the component ofstator flux can be derived as follows (Abad et al. (2011)):
uds = ψqs = 0; uqs = Ug ≈ ωsψdqs ≈ ωsψds, (10)
where Ug is the magnitude of the grid voltage.
The active and reactive powers in the stator can beexpressed as below:
Ps =3
2(udsids + uqsiqs) = −3
2ψds
LmLs
ωsiqr
Qs =3
2(uqsids − udsiqs) =
3
2Ug
(ψdsLs− LmLs
idr
).
(11)
Furthermore, by neglecting the coper power losses in thestator and rotor resistance, the active and reactive powersin stator and rotor can be derived (see Abad et al. (2011))as follows:
Pr = −sPs; Qr = sQs. (12)
In addition, the rotor voltage which will be injected intoDFIG, is also the output voltage of 3L-NPC inverter shownin Fig. 4. The inverter output voltage in rotor reference
frame uDQinv is defined as:
uDQinv =2
3
(uAZ + auBZ + a2uCZ
), (13)
with a = ej2π/3 = − 12 + j
√32 .
The inverter output voltage uAZ , uBZ and uCZ of 3L-NPCinverter are calculated (see Ngo et al. (2016)) as a functionof the DC link voltage Udc and switching states Sx:
uAZ = SaUdc2
;uBZ = SbUdc2
;uCZ = ScUdc2, (14)
12S 12D
11D11S
12'S
11ZD
12ZD
22S 22D
21D21S21ZD
22ZD
32S 32D
31D31S31ZD
32ZD
rairau
2Cu2C
1Cu1C
ZdcU
12'D
11'S 11
'D
22'S 22
'D
21'S 21
'D
32'S 32
'D
31'S 31
'D
2Ci
1Ci
1dci AB
C
R rLr
N
Fig. 4. The configuration of the rotor of DFIG connected3L-NPC inverter
where Sx represents the state of a leg and has threepossible values: [-1, 0, 1] or [N, O, P].
Consequently, the rotor voltage referred to the stator in”dq” reference frame (udqr ) can be calculated by usingrotational transformation as (Abad et al. (2011)):
udqr = KuDQinv e−jθr , (15)
where K is the ratio of the stator voltage to the rotorvoltage of the DFIG.
The rotor current referred to the stator in ”dq” referenceframe (idqr ) can be calculated from the rotor current inrotor reference (iDQr ) by using rotational transformation:
idqr =1
KiDQr e−jθr . (16)
In the real implementation of the 3L-NPC inverter, consid-ering a dead-time in the modeling is necessary to preventthe simultaneous conduction of two switching devices ineach leg of the inverter. The dead-time causes outputcurrent waveform distortion and increases the THD, es-pecially with high switching frequency (Kuznietsov et al.(2015); Irnura et al. (2012)). The voltage vector during thedead-time is determined according to the state betweenprevious switching state and present switching state andthe sign of the phase current. For example, in switchingstate [O], switches S11 and S
′
12 are turned ”on”. Theclamping diode DZ11 is turned ”on” by the positve loadcurrent (ira > 0). For ideal case without dead-time, the
switch S′
12 is turned ”off” and S12 is turned ”on” simul-taneously, so that the output voltage changes from zeroto Udc/2 at the same time. If the dead-time is considered,the real gate signals and output voltage approximationare shown in Fig. 5(a). During the dead-time interval,
S′
12 is being turned ”off” and the path of ira remainsunchanged. Thus, the output actual voltage is clampedis zero. After S12 is turned ”on” (switching state [P]), theload current is commutated from DZ11 to S12 and theoutput voltage switches to Udc/2 (Fig. 6(a)). Hence, thereal output voltage is reduced with the mean value Udtand shown with the rectangular pattern in Fig. 5(a). Inbrief, the influence of dead-time on output voltage canbe illustrated in Fig. 5. Thus, in order to compensatethe dead-time, the real voltage applied during a samplingperiod Tsp can be represented by a voltage Udt during thedead-time td and the predicted voltage vector with the resttime Tsp - td (Irnura et al. (2012)). The real output voltageof one phase uxz–real can be expressed as follows:
(i) (Sx(k − 1) = 0) & (Sx(k) = 1),(ii) (Sx(k − 1) = −1) & (Sx(k) = 0),
P
(a) Dead-time for switching state O and P for positive phase current
Udt
0
1td tdTsp - td td Tsp - td
O O P
S12'0
1
uAZ 0
Udc/2Udt
S12
Tsp - td
P
(b) Dead-time for switching state [O] (0) and [P] (1) for negative phase current
Udt
0
1td tdTsp - td td Tsp - td
O O P
S12'0
1
uAZ 0
Udc/2
S12
Tsp - td
k k+1 k+2 k+3
k k+1 k+2 k+3
O
(a) Dead-time for switching state N and O for positive phase current
Udt
0
1td tdTsp - td td Tsp - td
N N O
S11'0
1
uAZ 0
-Udc/2
Udt
S11
Tsp - td
k k+1 k+2 k+3
O
(b) Dead-time for switching state N and O for negative phase current
Udt
0
1td tdTsp - td td Tsp - td
N N O
S11'0
1
0
-Udc/2
S11
Tsp - td
k k+1 k+2 k+3
uAZ
(a) Dead-time effect of switching states O and P with ira > 0
P
(a) Dead-time for switching state O and P for positive phase current
Udt
0
1td tdTsp - td td Tsp - td
O O P
S12'0
1
uAZ 0
Udc/2Udt
S12
Tsp - td
P
(b) Dead-time for switching state [O] (0) and [P] (1) for negative phase current
Udt
0
1td tdTsp - td td Tsp - td
O O P
S12'0
1
uAZ 0
Udc/2
S12
Tsp - td
k k+1 k+2 k+3
k k+1 k+2 k+3
O
(a) Dead-time for switching state N and O for positive phase current
Udt
0
1td tdTsp - td td Tsp - td
N N O
S11'0
1
uAZ 0
-Udc/2
Udt
S11
Tsp - td
k k+1 k+2 k+3
O
(b) Dead-time for switching state N and O for negative phase current
Udt
0
1td tdTsp - td td Tsp - td
N N O
S11'0
1
0
-Udc/2
S11
Tsp - td
k k+1 k+2 k+3
uAZ
(b) Dead-time effect of switching states O and P with ira < 0
P
(a) Dead-time for switching state O and P for positive phase current
Udt
0
1td tdTsp - td td Tsp - td
O O P
S12'0
1
uAZ 0
Udc/2Udt
S12
Tsp - td
P
(b) Dead-time for switching state [O] (0) and [P] (1) for negative phase current
Udt
0
1td tdTsp - td td Tsp - td
O O P
S12'0
1
uAZ 0
Udc/2
S12
Tsp - td
k k+1 k+2 k+3
k k+1 k+2 k+3
O
(a) Dead-time for switching state N and O for positive phase current
Udt
0
1td tdTsp - td td Tsp - td
N N O
S11'0
1
uAZ 0
-Udc/2
Udt
S11
Tsp - td
k k+1 k+2 k+3
O
(b) Dead-time for switching state N and O for negative phase current
Udt
0
1td tdTsp - td td Tsp - td
N N O
S11'0
1
0
-Udc/2
S11
Tsp - td
k k+1 k+2 k+3
uAZ
(c) Dead-time effect of switching states N and O with ira > 0
P
(a) Dead-time for switching state O and P for positive phase current
Udt
0
1td tdTsp - td td Tsp - td
O O P
S12'0
1
uAZ 0
Udc/2Udt
S12
Tsp - td
P
(b) Dead-time for switching state [O] (0) and [P] (1) for negative phase current
Udt
0
1td tdTsp - td td Tsp - td
O O P
S12'0
1
uAZ 0
Udc/2
S12
Tsp - td
k k+1 k+2 k+3
k k+1 k+2 k+3
O
(a) Dead-time for switching state N and O for positive phase current
Udt
0
1td tdTsp - td td Tsp - td
N N O
S11'0
1
uAZ 0
-Udc/2
Udt
S11
Tsp - td
k k+1 k+2 k+3
O
(b) Dead-time for switching state N and O for negative phase current
Udt
0
1td tdTsp - td td Tsp - td
N N O
S11'0
1
0
-Udc/2
S11
Tsp - td
k k+1 k+2 k+3
uAZ
(d) Dead-time effect of switching states N and O with ira < 0
Fig. 5. The effect of dead-time on inverter output voltage
(iii) (Sx(k − 1) = 1) & (Sx(k) = 0),(iv) (Sx(k − 1) = 0) & (Sx(k) = −1),
uxz real(k) =
−Udt + uxz(k)
if satisfy (sign(irx) > 0) & ((i) ∨ (ii)) ,Udt + uxz(k)
if satisfy (sign(irx) < 0) & ((iii) ∨ (iv)) ,uxz(k) otherwise,
(17)where uxz, irx are the inverter output voltage and rotor
current of one phase x = a, b, c; Udt =tdTsp
Udc2
.
Based on the configuration in Fig. 4, the dynamic ofneutral-point voltage (Z) is obtained based on the rotorcurrents and the switching states of 3L-NPC inverter (Ngoet al. (2016)):
duzdt
= − 1
2Cidc1 (18)
= − 1
2C
((1− |Sa|)ira + (1− |Sb|)irb + (1− |Sc|)irc
)
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zdc1ai rai
12'S 12
'D
11'S 11
'D
Switching state O
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zdc1ai rai
12'S 12
'D
11'S 11
'D
Dead-time interval
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zdc1ai rai
12'S 12
'D
11'S 11
'D
Switching state P
(a) Commutation with positive current
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zdc1ai rai
12'S 12
'D
11'S 11
'D
Switching state O
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zrai
12'S 12
'D
11'S 11
'D
Dead-time interval
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zrai
12'S 12
'D
11'S 11
'D
Switching state P
(a) Commutation with negative current
(a) Commutation from swiching state O to P with ira > 0
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zdc1ai rai
12'S 12
'D
11'S 11
'D
Switching state O
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zdc1ai rai
12'S 12
'D
11'S 11
'D
Dead-time interval
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zdc1ai rai
12'S 12
'D
11'S 11
'D
Switching state P
(a) Commutation with positive current
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zdc1ai rai
12'S 12
'D
11'S 11
'D
Switching state O
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zrai
12'S 12
'D
11'S 11
'D
Dead-time interval
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zrai
12'S 12
'D
11'S 11
'D
Switching state P
(a) Commutation with negative current(b) Commutation from swiching state O to P with ira < 0
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zdc1ai rai
12'S 12
'D
11'S 11
'D
Switching state N
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zdc1ai rai
12'S 12
'D
11'S 11
'D
Dead-time interval
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zdc1ai rai
12'S 12
'D
11'S 11
'D
Switching state O
(a) Commutation with positive current
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zdc1ai rai
12'S 12
'D
11'S 11
'D
Switching state N
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zrai
12'S 12
'D
11'S 11
'D
Dead-time interval
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zrai
12'S 12
'D
11'S 11
'D
Switching state O
(a) Commutation with negative current
(c) Commutation from swiching state N to O with ira > 0
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zdc1ai rai
12'S 12
'D
11'S 11
'D
Switching state N
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zdc1ai rai
12'S 12
'D
11'S 11
'D
Dead-time interval
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zdc1ai rai
12'S 12
'D
11'S 11
'D
Switching state O
(a) Commutation with positive current
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zdc1ai rai
12'S 12
'D
11'S 11
'D
Switching state N
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zrai
12'S 12
'D
11'S 11
'D
Dead-time interval
12S 12D
11D11S11ZD
12ZD
2Cu2dC
1Cu1dC
Zrai
12'S 12
'D
11'S 11
'D
Switching state O
(a) Commutation with negative current(d) Commutation from swiching state N to O with ira < 0
Fig. 6. Commutation during the dead-time
Furthermore, the dead-time can also affect the neutral-point voltage because of the different neutral-point currentas shown in Fig. 6 (Sprenger et al. (2013)). Summarizing,the neutral-point curent during the dead-time only existswhen there are transitions between switching states [O]and [P] with positive load current or between switchingstates [N] and [O] with negative load current or remainthe switching state [O]. Thus, the neutral-point current ofone phase during the dead-time can be described:
(v) (sign(irx) > 0) & ((i) ∨ (ii)),(vi) (sign(irx) < 0) & ((iii) ∨ (iv)),(vii) (Sx(k − 1) = 0) & (Sx(k) = 0),
idc1x dt =
tdTsp
irx, if satisfy ((v) ∨ (vi) ∨ (vii)) ,
0, otherwise,(19)
where idc1x–dt is the neutral-point current during the dead-time of one phase x = a, b, c.
Similarly, the real neutral-point current during a samplingperiod is expressed by the neutral-point current during thedead-time td and the predicted current with the rest timeTsp − td:idc1–real = idc1a–dt+idc1b–dt+idc1c–dt+
Tsp − tdTsp
idc1. (20)
By using the equation (18), the neutral-point voltage forcompensate the dead-time can be rewritten:
duz–realdt
= − 1
2Cidc1–real. (21)
In an inverter driven system, the common-mode voltage(ucm) is defined as the voltage between the rotor neutral(N) and the neutral-point voltage (Z). Thus, the common-mode voltage (CMV) can be expressed as follows (Ro-driguez and Cortes (2012)):
ucm =uAZ + uBZ + uCZ
3. (22)
Therefore, a compensation for the dead-time can be es-tablished for MPDPC. By using modified voltage vectorin equation (17), (21) and (22), we can predict the powertaking into account the dead-time voltage at switchingstate.
3. MODEL PREDICTIVE DIRECT POWERCONTROL APPLIED TO DFIG CONNECTED
3L-NPC
The aim of the predictive direct power control schemeis to minimize the error between the predicted activeand reactive powers and their reference values, to main-tain voltage balance of the capacitor and to reduce theswitching frequency and common-mode voltage. In orderto achieve these objectives, the cost function for the DFIGconnected 3L-NPC inverter with two-step prediction canbe expressed as follows (Rodriguez and Cortes (2012)):
g = |P ∗s (k + 2)− P ps (k + 2)|+ |Q∗s(k + 2)−Qps(k + 2)|+ λdc |upz(k + 2)|+ λcm |ucm|+ λnnc (23)
where λdc, λn and λcm are the weighting factors of thecapacitor voltage balancing, the reduction of commutationand CMV. nc penalizes the number of switching changeswhen the switching state S(k) is applied compared withprevious state S(k − 1). It can be expressed as:
nc = |Sa(k)− Sa(k − 1)| + |Sb(k)− Sb(k − 1)|+ |Sc(k)− Sc(k − 1)|. (24)
In the real-time implementation of the control scheme,the calculation time of the control law will induce somesample time delay in the actuation (Sun and Wang (2016);Errouissi et al. (2016)). Several studies to address thedelay compensation, but this particular aspect is not thefocus of this paper. A simple solution to compensatethe computational delay is to compute at time instantk the cost function corresponding to time instant k + 1using an estimation of the state at time k + 1 and thenthe optimal switching state is applied at time k + 1. Inthis paper, we used the method proposed by Ngo et al.(2016) to reduce the computational effort and allow astraightforward implementation.
The equation (7) can be discretized considering Tsp as asampling period and k as the sampling time by using zero-order hold (ZOH) with no delay:
x(k + 1) = Adx(k) +Bdu(k) (25)
where
Ad = eATsp , Bd =
∫ Tsp
0
eA(Tsp−dτ)Bdτ ' BTsp. (26)
Since the active and reactive powers references are DCquantities, to reduce the computational time and theoscillations in the reference powers when a sudden changeoccurs, the extrapolation can be simplified as follows:
P ∗s (k + 2) = P ∗s (k);Q∗s(k + 2) = Q∗s(k). (27)
Finally, the objective of proposed predictive control canbe obtained by evaluating some appropriate cost functionfor all considered input combinations (see algorithm 1).
Algorithm 1 Algorithm of model predictive direct powercontrol for DFIG connected 3L-NPC inverter
Measure is(k), ir(k), uz(k), us(k), ωm and Udc; Readthe reference values P ∗s (k) and Q∗s(k)Estimation of stator flux ψds(k); Extrapolation of refer-ences P ∗s (k + 2), Q∗s(k + 2) and udqs (k + 1)%comment: xopt, gopt are the optimal values of theswitching states and cost function%Initialize optimal values: xopt, goptPredict stator flux: ψpds(k + 1)for i = 1 to 27 do
Compute predictions with dead-time compensation:ipdr(k + 1), ipqr(k + 1) and upz(k + 1)
Estimate the values: nc and ucmPredict corresponding switching transitions
%comment: m = length(corresponding switching tran-sitions)
for j = 1 to m doPredict: ipdr(k + 2), ipqr(k + 2), ψpds(k + 2) and
upz(k + 2)Estimation of power: P ps (k + 2) and Qps(k + 2)Compute the cost function gif g < gopt then
gopt = g;xopt = iend if
end forend forStore the present value of xopt and apply Sa, Sb, Scconsidering the dead-time
4. SIMULATION RESULTS
In order to validate the effectiveness of the model predic-tive direct power control (MPDPC) strategy with dead-time compensation for DFIG under different modes ofspeed operation, the whole control scheme has been simu-lated using MATLAB/Simulink and the SimPowerSystemstoolbox with the parameters as indicated in Table A.1.
With the aim to evaluate the steady state performance,the mean absolute percentage error (MAPE) is used. Thisquantity can be expressed as follows:
MAPE =1
n
n∑i=1
∣∣∣∣ y∗i − yiy∗i
∣∣∣∣, (28)
where y∗i is the reference vector and yi is the measurementvector.
On the other hand, the average switching frequency persemiconductor (fsw) = 1 kHz is calculated according to the
Rotorspeed[rpm]
0 0.5 1 1.5 2 2.51100
1200
1300
1400
1500
1600
1700
1800
1900
Sub-synchronous speeds > 0, Pr > 0
Hyper-synchronous speeds < 0, Pr < 0
Time [s]
Fig. 7. Rotor angular speed time response
following expression proposed in (Rodriguez and Cortes(2012)):
fsw =∑
x=a,b,c
fsw1x+ fsw2x
6, (29)
where fsw1x, fsw2x
are the switching frequencies of eachupper switch.
With the purpose of control the power factor (PF), thereactive power reference is given by:
Qs ref = Ps ref
√1− PF 2
PF. (30)
In our comparison, the DFIG was assumed to be in speedcontrol, i.e., the rotor speed is set externally, and has slowchanges because of the large inertia of the wind turbine.In order to observe the dynamics response of the DFIG,various active and reactive power steps with rotor speedvarying from 1200 to 1800 rpm (Fig. 7) were carried out.The active power reference is changed from -2 MW to -1 MW at 1.5 s and from -1 MW to -1.5 MW at 2 s(Fig. 8(a)). While the reactive power reference is changedfrom -1.24 MVar to 0.62 MVar at 1.5 s and from 0.62MVar to 0 Var at 2 s, corresponding with the changeof power factor from 1 to a leading (0.85) or lagging (-0.85). When the rotor speed of the generator is greaterthan synchronous speed, the slip is negative (s = -0.2),thus, the rotor power Pr will be transferred from thegenerator rotor to the grid through the rotor converters ofthe DFIG, whereas the RSC operates as a rectifier and theGSC as an inverter. The powers delivered to the grid Pgand Qg which are the sum of the stator and rotor powersare illustrated in Figs. 8(a) and 8(b). On the contrary,the slip is positive (s = 0.2) with sub-synchronous speed.This positive slip means that the rotor power Pr willbe positive and will be received from the grid throughthe converters in which the RSC operates as an inverterand the GSC as a rectifier (Fig. 8). In addition, Figs.8(a) and 8(b) indicate that the active power is trackingtheir references with fast dynamics and without affectingthe reactive power. The mean absolute percentage errorof active and reactive power for uncompensated case are1.68% and 2.25%, whereas, for the proposed method theyare 1.65%, and 2.22%, respectively.
For further verification of the dead-time compensationmethod, the spectrum of the stator current is analyzedand compared for the uncompensated and compensatedcase in Fig. 9. For the uncompensated case in Fig. 9(a), theamplitude of the order harmonic is larger, which is causedby the dead-time effect. The THD for the uncompensatedstator current is around 4.3%. But for the compensatedcurrent in Fig. 9(b), the order harmonic components havebeen largely reduced, especially the 21th, 22th and 23th
order harmonic. Also the THD for the stator current is
0.5 1 1.5 2 2.5−2.5
−2
−1.5
−1
−0.5
0
0.5x 10
6
Time [s]
Activepower[W] Ps_ref
PrPs
Pg= Ps + Pr
(a) Generated active power
Time [s]0.5 1 1.5 2 2.5
−1.5
−1
−0.5
0
0.5
1
1.5x 10
6
Reactivepower[Var]
Sub-synchronousspeed with PF=1
Approximately synchronousspeed with PF=0.85
Hyper-synchronousspeed with PF=-0.85
Hyper-synchronousspeed with PF=1
Qs_ref
QrQs
Qg= Qs + Qr
(b) Generated reactive power
0.5 1 1.5 2 2.5−3000
−2000
−1000
0
1000
2000
3000
Time [s]
Current[A]
i saisbisc
(c) Stator current
0.5 1 1.5 2 2.5−1500
−1000
−500
0
500
1000
1500
Time [s]
Current[A]
Sub-synchronousspeed
Approximatelysynchronous speed
Hyper-synchronousspeed
irairbirc
(d) Rotor current
Fig. 8. The dynamic response of the power and currentwith rotor speed variation
reduced from 4.3 % to 3.03 % which is under the 5% limitrequired by the IEEE 519 standards.
5. CONCLUSIONS
In this paper, a new direct power control with dead-timecompensation method for DFIG system has been proposedto control the active and reactive powers directly. First,the mathematical model including the dead-time errors isestablished, and then the cost function, which containsthe power errors, the capacitor voltage balancing and thereduction of the switching frequency, is proposed. In orderto verify the performance of control scheme, there is a
0 500 1000 1500 20000
0.5
1
1.5
2
2.5
3
3.5
Frequency [Hz]
Currentmagnitudeh.offundamental) Fundamental h50 Hz) = 1784 A, THD = 4.3 .
21th
22th
23th
17th
3th
(a) Without compensation
0 500 1000 1500 20000
0.5
1
1.5
2
2.5
3
3.5
Frequency [Hz]
Currentmagnitude(.offundamental) Fundamental (50 Hz) = 1787 A, THD = 3.03 .
21th
17th
22th23th
3th
(b) With compensation
Fig. 9. Stator current spectrum with and without compen-sation
comparison between the case without compensation andthe proposed method. The simulation results show thatthis method can successfully track the active and reactivepowers, maintain their balanced capacitor voltages, reducethe switching frequency and common-mode voltage. Fur-thermore, by using the proposed method we can reducethe voltage error due to switching dead-time while main-taining an acceptable quality of current and power. Thelinear PI controllers for the power, current loops and themodulation block are further eliminated. In addition, bymaintaining the device switching frequency below 1 kHz,the proposed method is an interesting alternative to con-trol the DFIG connected 3L-NPC inverter for megawattrange wind power applications.
REFERENCES
Abad, G., Lopez, J., Rodriguez, M.A., Marroyo, L., andIwanski, G. (2011). Doubly fed induction machine-Modelling and control for wind energy generation. JohnWiley and Sons.
Errouissi, R., Al-Durra, A., Muyeen, S.M., Leng, S., andBlaabjerg, F. (2016). Offset-free direct power control ofDFIG under continuous-time model predictive control.IEEE Transaction On Power Electronics.
Filho, A.J.S. and Ruppert, E. (2010). A deadbeat activeand reactive power control for doubly fed inductiongenerator. Electric Power Components and Systems,38(5), 592–602.
Hu, J. and Yuan, X. (2012). Vsc-based direct torque andreactive power control of doubly fed induction generator.Journal Renewable Energy, 40, 13–23.
Irnura, A., Takahashi, T., Fujitsuna, M., Zanma, T., andDoki, S. (2012). Dead-time compensation in model pre-dictive instantaneous-current control. In Proceeding of38th Annual Conference of IEEE Industrial ElectronicsSociety (IECON 2012), 5037–5042.
Kazemi, M.V., Yazdankhah, A.S., and Kojabadi, H.M.(2010). Direct power control of DFIG based on discretespace vector modulation. Journal Renewable Energy,35, 1033–1042.
Kuznietsov, A., Wolf, S., and Happek, T. (2015). Modelpredictive control of a voltage source inverter with com-pensation of deadtime effects. In Proceeding of 2015IEEE International Conference on Industrial Technol-ogy (ICIT), 2532–2536.
Ngo, B.Q.V., Rodriguez-Ayerbe, P., and Olaru, S. (2016).Model predictive direct power control for doubly fedinduction generator based wind turbines with three-levelneutral-point clamped inverter. In 42nd Annual Confer-ence on IEEE Industrial Electronics Society IECON.
Rodriguez, J. and Cortes, P. (2012). Predictive Control ofPower Converters and Electrical Drives. John Wiley.
Sayritupac, J., Albanez, E., Rengifo, J., Aller, J.M., andRestrepo, J. (2015). Predictive control strategy forDFIG wind turbines with maximum power point track-ing using multilevel converters. In Proceeding of work-shop on Power Electronics and Power Quality Applica-tions (PEPQA), 1–6. Bogota.
Sprenger, M., Barth, T., Alvarez, R., Tannhaeuser, M.,and Bernet, S. (2013). Experimental verification ofdirect dead-time control and DC-link neutral-point bal-ancing of a three level neutral-point-clamped (3l-npc)vsc. In Proc. IEEE Energy Conversion Congress andExposition, 409–413.
Sun, D. and Wang, X. (2016). Low-complexity modelpredictive direct power control for DFIG under bothbalanced and unbalanced grid conditions. IEEE Trans-actions on Industrial Electronics, 63(8), 5186–5196.
Xu, L. and Cartwright, P. (2006). Direct active and reac-tive power control of DFIG for wind energy generation.IEEE Transactions on Energy Conversion, 21(3), 750–758.
Zhou, D. and Rouaud, D.G. (1999). Dead-time effectand compensations of three-level neutral point clampinverters for high-performance drive applications. IEEETransactions on Power Electronics, 14(4), 782–788.
Appendix A. PARAMETERS FOR DFIG,CONTROLLER AND SWITCHING DEVICES
Table A.1. Simulation parameters
Parameter Value Description
Prated 2 [MW] Rated stator three phase active powerUs−rated 690 [V] Line to line nominal stator voltageUr−rated 2070 [V] Line to line nominal rotor voltageIs−rated 1760 [A] Each phase nominal stator currentns−rated 1500 [rpm] Synchronous speed
p 2 The number pairs of polesRs 2.6 [mΩ] Stator resistanceRr 2.9 [mΩ] Rotor resistanceLσs 87 [µH] Stator leakage inductanceLσr 87 [µH] Rotor leakage inductanceLm 2.5 [mH] Mutual inductanceJ 0.314 [kg.m2] Moment of inertiafs 50 [Hz] Frequency of the gridfsp 10 [kHz] Sampling frequency of MPDPCUdc 1200 [V] DC link voltageC 16000 [µ F] DC link capacitortd 5 [µs] Dead-time of IGBT
Vf , Vfd 0.8; 0.1 [V] Forward voltage of IGBT and diodeλdc 200 Weighting factor of the voltage balancingλn 35000 Switching frequency reduction factorλcm 200 Weighting factor of the reduction of CMV