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596 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 2, JUNE 2006
A Neutral-Point Clamped Converter System forDirect-Drive Variable-Speed Wind Power Unit
Amirnaser Yazdani,Member, IEEE,and Reza Iravani,Fellow, IEEE
AbstractRecent and ongoing developments in wind turbinetechnology indicate a trend towards utilization of high capacity(e.g., up to 5 MW) wind power units in large wind farms. Highercapacity of the wind turbine necessitates operation of the corre-sponding electric machine and thestatic converter systemat highervoltages. This paper presents a neutral point diode clamped (NPC)converter system that inherently accommodates higher voltage andpower ratings of a high capacity wind power unit. The overall con-trol strategy of an NPC-based wind power unit and the detailsof the ac side and the dc side controls of the NPC converter sys-tem are also described. The generator-side NPC converter providestorque-speed control of the turbine-generator unit. The network-side NPC converter controls real and reactive power flow to the
network and thus regulates the dc bus voltage and the ac sidepower-factor (or voltage) respectively. The paper also presents anew control approach to balance the dc capacitor voltages. TheNPC converter system is augmented with a dc chopper that con-trols the synchronous generator field current. The NPC-based con-verter system is used to interface a 3 MW, direct-drive (gearless),synchronous machine based wind power unit to the utility grid.Performance of the overall NPC-based wind power unit, under theproposed controls, is evaluated based on time domain simulationsin the power systems computer aided design (PSCAD) electromag-netic transient for DC (EMTDC) environment.
IndexTermsCurrent control, dc-side voltage balancer, electro-magnetic transients, neutral-point diode clamped (NPC) converter,variable-speed wind-power system.
I. INTRODUCTION
WORLDWIDE, wind energy has been the fastest growing
energy technology within the last several years, and all
factors indicate that the growth will continue for many years in
the future [1]. The technological trend of large wind turbines,
for wind farm applications, is toward large capacity units. For
example, a 5 MW prototype wind power unit was recently in-
stalled and is currently being tested [2]. The high capacity of a
wind turbine indicates that the corresponding electric machine
and static power converter system must operate at higher voltage
levels to achieve 1) maximum efficiency and 2) optimum size,
volume, and form-factor.
The back-to-back connected, two-level voltage-sourced con-verter (VSC) system is the most widely used static converter
configuration for variable-speed wind power units [3], [4]. Op-
eration of the two level converter system at high voltage levels
requires valves with high voltage ratings. This can be achieved
through either by using the state-of-the-art switches available at
Manuscript received December 29, 2004, revised June 06, 2005. Paper no.TEC-00369-2004.
The authors are with the Center for Applied Power Electronics (CAPE)at the Department of Electrical and Computer Engineering, University ofToronto, Toronto, ON M5S 3G4, Canada (e-mail: [email protected];[email protected]).
Digital Object Identifier 10.1109/TEC.2005.860392
high voltage ratings, or cascading switches with lower-voltage
ratings. The former option imposes excessive switch cost which
may render the converter unit economically unattractive or even
unacceptable. The latter approach imposes its own technical
challenges; e.g., equal voltage sharing and simultaneous gating
requirements.
Another approach that avoids the previously described
problems is use of the multilevel VSC instead of the two-level
VSC [5], [6]. This paper proposes the application of the
three-level neutral point diode clamped (NPC) converter [7]
for a high-power variable-speed wind power unit. Applications
of the NPC converter for back-to-back HVDC links [8] and
high-power drives [9] have been reported in the technical
literature, but has neither been proposed nor investigated for
wind power applications.
This paper provides a detailed formulation and evaluation of
the control system of a back-to-back NPC converter system for
a direct-drive (gearless) variable-speed synchronous machine
based wind-power system. The proposed direct drive, variable
speed, NPC-based wind power configuration has the following
salient features when compared with fixed-speed, squirrel-cage
induction machine based and doubly-fed induction machine
based wind power unit.
1) Eliminationof the gearbox significantly reduces scheduledand unscheduled maintenance;
2) Mechanical speed of the turbine-generator is controlled
in a noticeably wider range and thus the captured wind
energy is higher;
3) The configuration can naturally accommodate low-speed
(high-pole) permanent magnet synchronous machines,
which translates in significant reduction in size, volume,
and weight; and
4) The converter systemacts as a buffer between theelectrical
grid and the turbine-generator, and thus minimizes unde-
sirable dynamic interactions between the two subsystems,
e.g., due to wind speed fluctuations and electrical faults.The control model is developed based on a generalized state-
space model of the NPC converter [10] and includes 1) torque-
speed control of the synchronous machine, 2) grid-side power-
factor (voltage) control, 3) net dc bus voltage control, and 4)
dc capacitor voltage equalizer. The NPC converter system is
augmented by a dc-dc chopper that is supplied from the dc-
bus, and controls the synchronous machine field current. The
chopper controls are also described in detail. This paper also
presents the control strategy of the overall wind-power unit.
Performance of the overall wind power unit, including the NPC
converter system and the controllers, is evaluated based on time
domain simulationstudies in the PSCAD/EMTDCenvironment.
0885-8969/$20.00 2006 IEEE
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Fig. 1. Single-line schematic diagram of a three-level VSC-based power conversion system.
This paper is organized as follows: Section II introduces
the wind power system. Section III deals with the models ofthe synchronous machine, the machine side NPC converter,
and the machine torque-speed control. Section IV develops
the models for the grid side NPC converter, the grid side
current controllers, the net dc bus voltage controller, and the
dc-side voltage equalizer. The wind power system control strat-
egy is described in Section V. Section VI presents the sys-
tem performance in response to the startup, a wind gust, and
a line-to-neutral fault in the grid. Section VII concludes the
paper.
II. SYSTEMSTRUCTURE ANDMODEL
Fig. 1 shows a schematic representation of a three-level NPC-
based wind power system. The system is comprised of a wind
turbine that is directly coupled to a high pole synchronous ma-
chine. The synchronous machine is field-controlled. The ma-
chine is vector-controlled by NPC1. The second three-level NPC
converter, NPC2, interfaces the wind power system to the utility
grid.
The dc bus is composed of twonominally identicalcapacitors.
The clamped points of the two NPC converters are connected to
the capacitors at midpoint 0, Fig. 1. The midpoint is assumed to
be the circuit voltage reference, but is not necessarily grounded.
Grounding midpoint or any other node in the converter sys-
tem must take into account protection requirements and other
unit dependent factors; e.g., configuration of the interface trans-
former.
A current-controlled buck converter, supplied from the DC-
bus, is used to regulate the machine field current if. The buck
converter is a diode clamped converter and thus can withstand
high dc bus voltages. Therefore, the clamped point of the buck
converter is also connected to the midpoint 0. ResistorRp rep-
resents the total switching losses of the NPC converters, and is
not a physical component.
NPC2 equalizes the voltages of the dc side capacitors and
regulates the dc bus voltage, [10], [14]. The ac side terminals of
NPC2 are connected to the utility grid through series connected
TABLE ISYSTEMPARAMETERS
inductors and a three-phase transformer. R represents the on-
state loss of NPC2 switches and the internal resistance of series
inductorL. Two three-phase shunt filters are installed at the low
voltage side of the transformer as shown in Fig. 1. The shunt
filters trap dominant switching harmonics and prevent voltage
distortion at the point of common coupling (PCC).
A sinusoidal PWM switching is adopted for the NPC con-
verters. The PWM carrier signals of both NPC converters and
the buck converter are synchronized to the grid voltage Vsabcat the low voltage side of the interface transformer, see Fig. 1.
Therefore, the converters operate at constant switching frequen-cies, and high frequency jitters and EMI phenomenon are mini-
mized.Pextdenotes the power delivered to the dc bus from the
machine side through NPC1. The system parameters are given
in Tables IIII.
III. SYNCHRONOUSMACHINEVECTORCONTROL
A. Machine Dynamic Model
The machine model, in its rotordq-frame; is adopted from
[11]. The voltage and current vectors of the machine stator in
the dq-frame, i.e., Vstdqand Istdq, are related to the correspond-
ing abc-frame values; i.e., the vector of fundamental voltage
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598 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 2, JUNE 2006
TABLE IISYNCHRONOUSMACHINEPARAMETERS
TABLE IIIWINDTURBINEPARAMETERS
components at the machine-NPC1 terminalsVstabc(t), and thecurrent vectoristabc(t) (see Fig. 1) by the following transfor-mations
Vstdqo= T(Pr )Vstabc(t) (1)
Istdqo= T(Pr )istabc(t) (2)
wherer andPare the rotor mechanical angle and the number
of pole-pairs. The transformation matrixTis defined by
T() = 2
3
cos() cos 2
3
cos
4
3
sin() sin
2
3
sin
4
3
12
12
12
.(3)
Vstdqis related to the dcbusvoltageVdc through the amplitude
and phase angle: i.e., m1 and 1, of the PWM modulation
waveform of NPC1, as given by (4) and (5)
Vstd=m1
2 Vdc cos 1 (4)
Vstq=m1
2 Vdc sin 1. (5)
Based on (4) and (5):
1= tan1
Vstq
Vstd
(6)
m1=
2
V2std+ V
2stq
Vdc . (7)
TABLE IVGLOSSARY OFTERMS
The dynamic model of the machine, in thedq-frame is [11]
Lfdif
dt = Rfif + Vf + Lmd
dIstd
dt (8)
LddIstd
dt = RsIstd+ LqIstqPr Vstd+ Lmd
dif
dt (9)
LqdIstq
dt = RsIstq LdIstdPr Vstq+ Lmd ifPr
(10)
where r = d rdt
, and the other terms are defined in Table IV.
Vfis the average ofVfover one switching period.
No damper winding is considered in the model. The reason is
that the machine is current-controlled and the flux is regulated
at a constant value. Thus, the impact of damper windings is in-
significant [11], and practically, damper bars are removed from
a vector-controlled machine. Similarly, the magnetic saturationis not included in the model, since the flux is tightly regulated
in a vector-controlled machine.
The machine electrical torque is given by [11]
Te =
3
2
P(LmdifIstq LdIstdIstq+ LqIstdIstq). (11)
B. Machine Vector Control
Te is a nonlinear function of machine currents. Based on a
vector control strategy, the nonlinearity can be avoided and the
current coupling minimized. One optimal approach is to impose
Istd= 0[11] and [12]. This reduces (11) to
Te =
3
2
PLmd ifIstq. (12)
Equation (12) shows that Teis a linear function ofIstq, provided
that field currentif is regulated at a constant value; e.g., at the
rated field current. Moreover, imposing Istd= 0 ensures that thestator currents are minimum for a pre specified torque and, thus,
the machine efficiency is enhanced [12]. Furthermore, regulat-
ingIstd at zero eliminates the transient impact of the machine
damper windings (if they exist) on the torque [11]. The struc-
tures of the machine current regulators, based on the availability
of the rotor angle r and speed r via either measurement or
estimation [13], is as follows:
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1) Rotor Current Regulator: In (8),if is the state variable,
Vfis the control input, and LmddIstddt
is the coupling term be-
tween if andIstd. Istd is to be regulated at zero. Thus, if the
closed loop system is stable, LmddIstddt
becomes zero after tran-
sients. Hence, (8) can be approximated as
Lf
dif
dt =
Rfif+ Vf. (13)The output voltage of the buck converter is
Vf =d.Vdc (14)
wheredis the duty ratio.dis provided by the following control
law
d= 1
Vdc
Kf pef + Kf i
t0
efdt
(15)
where, ef =ifref ifand ifrefis set at the rated value. Choos-
ing Kf p = L ff
and Kf i = Rff
, we deduce the closed loop trans-
fer function as
if(s)
ifref(s) =
1
fs + 1, (16)
wherefis the time constant of the closed loop response.
2) Stator Current Regulators: In (9), Istd is the state vari-
able,Vstdis the control input, and Lmddi fdt
is the coupling term
between Istdand if. If the closed loop system is stable, Lmddi fdt
becomes zero after transients and (9) can be approximated as
LddIstd
dt = RsIstd+ LqIstqPr Vstd. (17)
Let us define the following change of variable
Vstd= ustd+ LqIstqPr (18)
where ustdis the control variable. ustdis given by the following
PI controller
ustd= Kdp estd+ Kdi
t0
estddt (19)
whereestd= IstdrefIstd, and referenceIstdrefis set to zero.Istdand Istqare filtered Istdand Istq, respectively. The filteringis to reduce the impact of current harmonics on the closed loop
system. The transfer function of each filter is
Fi(s) =IstdIstd
=IstqIstq
= 1is + 1
. (20)
To provide adequate attenuation of harmonics, i must be large,
but considerably smaller than the smallest desired time-constant
of the closed loop system. These constraints can be readily
satisfied, since the PWM generated harmonics are of high order.
Substituting forVstdfrom (18) into (17), we obtain
LddIstd
dt = RsIstd+ LqPr (Istq Istq) + ustd. (21)
Based on (21), Istdcannot be decoupled fromIstq, since (Istq
Istq)is not zero during transients. However, since the filter time
constanti is small,(Istq Istq)rapidly approaches zero, and
Fig. 2. Block diagram of machine current controllers.
the coupling is weakened. Consequently, the following SISO
model is obtained for the machined-axis current dynamics
LddI
stddt = R
sIstd+ ustd. (22)
Similarly, theq-axis stator current controller is defined by
ustq = Kqp estq+ Kq i
t0
estqdt (23)
Vstq = ustq LdIstdPr + Lmd ifPr (24)
where, estq= Istqref Istq. Istqrefis the q-axis reference value,which is determined based on the desired torque. Substituting
forVstq from (24) into (10) and ignoring the transient impact
of(Istd Istd), we deduce the following SISO model for themachineq-axis current dynamics
LqdIstq
dt = RsIstq+ ustq. (25)
The PI-controller gains Kdp , Kdi ,Kqp , and Kqi can be deter-
mined from pole placement, based on the desired performance.
Fig. 2 shows block representations of the machined-andq-axis
current controllers.
IV. CONTROL OFGRID-SIDECONVERTER, NPC2
A. Dq-Frame Synchronization
The dynamic model of NPC2 is developed in the grid syn-
chronously rotating dq-frame. The dq quantities are related tothe correspondingabcquantities through
fdqo= T(t)fab c(t) (26)
where is the grid frequency, and the transformation matrix T
is given by (3). The dq-frame is synchronized to the three-phase
ac side voltagesVsabc , (see Fig. 1) such thatVsq = 0. Thus,
Vsa (t) =Vsd cos(t) (27)
Vsb (t) =Vsd cos
t
2
3
(28)
Vsc
(t) =Vsd
cost 43 . (29)
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Fig. 3. Block representation of (a) three-phase space-vector PLL, (b)dq-frame current controllers.
The synchronization is achieved by a space-vector PLL[15]. The block diagram of the space-vector PLL is shown in
Fig. 3(a). The feedback loop with compensatorH(s)adjust an-gle such that Vsq is forced to zero. The PLL compensator
H(s)must include an integral term for zero steady state error.Moreover, H(s) should include a band-stop characteristic toeliminate distortions ofVsq, and provide a distortion free angle.
Similarly, notch filters Fn (s) are required for conditioningVsd andVsq.
B. Dynamic Model
A dynamic model of NPC2 in thedq-frame is [10]
dId
dt =
R
LId + Iq
1
LVsd +
1
LVtd (30)
dIq
dt = Id
R
LIq
1
LVsq+
1
LVtq (31)
d
dt(V1 V2) =
3
C(Idcos2+ Iqsin2)(0 0) (32)
dVdc
dt =
2
Ciext
3
2Cm2(Idcos 2+ Iqsin 2)
3
C(0+ 0)(Idcos 2+ Iqsin 2) (33)
where
Vtd =
V1
m2
2 +
20
+ V2
m2
2 +
20
cos2 (34)
Vtq =
V1
m2
2 +
20
+ V2
m2
2 +
20
sin 2. (35)
m2 and 2 are the amplitude and phase angle of the PWM
modulation signals, V1 and V2 are the dc components of the dcside voltagesV1 and V2, and0 and 0 are small offsets added
to the PWM modulating waveforms, in consecutive half-cycles,
to equalize V1and V2[10]. Since0and 0are small, (34) and
(35) can be approximated as
Vtd m2
2 Vdc cos 2 (36)
Vtq m2
2 Vdc sin 2. (37)
m2and 2are calculated from (34) and (35) as
2= tan1
Vtq
Vtd
(38)
m2=2
V2td + V2tq
4(0V1+ 0V2)
Vdc
2V2td + V2tqVdc
. (39)
Equations (30) and (31) are used for the ac side current control,
(32) is used for the dc side voltage equalization, and (33) is used
for the net dc bus voltage control.
C. AC Side Current Control
The objectives of the ac side current controls are 1) dc bus
voltage control and 2) reactive power control. Principles of
current control are given in detail in [10]. Fig. 3(b) shows a
block representations of the d- and q-axis current controllers.
As shown in Fig. 3(b),Id andIqare passed through the corre-
sponding notch filters to eliminate distortions.
The transfer function of each notch filter is:
Fn (s) =fdq
fdq=
1 + s2
21 +
m=2m=1 ams
m. (40)
Then, the closed loop current dynamics are expressed by
Gi(s) = Id(s)
Idref(s) =
Iq(s)
Iqref(s)
1 +
k i ps
k i i 1 +
m=2m=1 ams
m
1 + n=4n=1 bnsn (41)
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where kip and kii are the proportional and the integral gains
of the current controllers, respectively. The poles of the notch
filters, Fn (s), given by 1 +m=2
m=1 amsm = 0, appear as the ze-
ros ofGi(s). Based on the adopted control strategy, the reactiveand real power components supplied by NPC2 to the grid can
be expressed as
Qg = 3
2Vsd Iq (42)
Pg = 3
2Vsd Id . (43)
In Fig. 3(b),Iqrefis set at zero for operation at unity power-
factor. Based on the power balance principle, Idrefis determined
by the dc bus voltage controller to keep the dc bus voltage
regulated, as discussed in the following section.
D. DC-Bus Voltage Dynamics and Control
The dynamics of the dc bus voltage are described by (33).Since (33) contains m2Idcos2and m2Iqsin 2, which includemultiplications of the state variables and the control inputs, con-
trol ofVdc based on (33) is not straightforward. A modified form
of (33), based on the principle of power balance, is presented
in [14]; (33) can be rewritten as:
dV2dcdt
= 2
RpCeqV2dc +
2
CeqPext
3L
2Ceq
dI2ddt
+dI2q
dt
3
CeqVsd Id . (44)
In (44),V2dc is the output variable, Id is the input signal,Iqand
Pex t are the disturbance signals. Equation (44) is linear with
respect to V2dc and Pext, but nonlinear with respect to Id and
Iq. Based on (44),Id andPextaffectV2dc during transients, and
the steady state.Iqhas an insignificant transient impact on V2dc .
Hence, in the following analysis, for simplicity and without the
loss of generality, we do not consider the impact ofIq. Equation
(44) is linearized as
dV2dcdt
= 2
RpCeqV2dc
+ 2Ceq
Pext 3LIdssCeq
dIddt
+ VsdLIdss
Id . (45)where ss and represent the steady state value and the
small signal perturbation of a variable, respectively. Since Rp is
large, the following equality holds
Pextss 3
2Vsd Idss. (46)
Expressing (45) in the Laplace domain and substituting forIdssfrom (46), we deduce
V2dc (s) =Gv (s)Id+ Gp(s)Pext (47)
Fig. 4. Block representation of the dc bus voltage controller.
where transfer functionsGv (s)and Gp(s)are
Gv (s) =V2dc (s)
Id(s)=
2LPextssVsdCeq
s + 1.5V 2s dLPextss
s + 2
RpCe q (48)
Gp(s) =Vdc (s)
Pext(s)= 2Ceq
1s + 2
RpCe q
. (49)Equation (48) shows that transfer functionGv (s)has a pole at
P = 2RpCe q
and a zero at Z= 1.5V 2
s d
LPextss. Since Rp is large,
the pole is constant and fairly close to the origin. However, the
location of zero is highly dependent onPextssand can vary from
to + depending on the mode of operation and the amountof steady state real power flowPextss. IfPextss is negative, the
system is nonminimum-phase. This is the case when the wind
power system is in the standby mode of operation and a smallamount of power is drawn from the grid to compensate for the
losses. However, in this case, the nonminimum-phase zero is
far from the origin and has no significant impact on the system
stability.
Fig. 4 shows a block representation of the dc bus voltage
control system. The dc bus voltage is controlled by Id ; the
controller is designed based on (48) and at the rated power.
To mitigate the transient impact of the disturbance signal Pext,
a feed-forward action is included in the control scheme. The
following methods can be considered to obtain Pext for the
feed-forward:
1) Direct measurement of iext, and calculation of power
based onPext= iextVdc ;2) Torque estimation based on (12), and calculation of power
based onPext Pm Ter .
Method 1) needs an instantaneous Hall effect current sen-
sor for the dc current measurement. Moreover, since iext is a
switched waveform, additional low pass filtering is necessary
to provide a smooth measurement ofPext. This results in a
slow feed-forward process. Method 2) utilizes the machine pa-
rameters andIstq, which is available from the machine vector
control. Therefore, Method 2) is adopted in this study.Pextis a
few percent less than the machine mechanical powerPm , due to
the machine and converter losses. Thus, the feed-forward action
is less accurate at lower power levels.
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E. DC-Side Voltage Equalization
The dc side voltage balancer maintains the dc components of
voltagesV1 and V2 (see Fig. 1) equal at a pre-specified value
[10]. In view of (32), we define
0= sgn() (50)
0= sgn() (51)
e= V1 V2 (52)
where the sign functionsgn( )is unity for a positive argument,and zero otherwise. Substituting for0from (50), 0from (51),
ande from (52), in (32) we obtain
de
dt =
3
C(Idcos 2+ Iqsin 2). (53)
Based on (53), can be adjusted to equalize the voltages of
the two dc side capacitors. The plant modeled by (53) is re-
garded as an integrator with a variable gain. The integral gain,3
C(Idcos 2+ Iqsin 2), is a function of the system operatingpoint. To optimize the control design, the range of gain varia-tions should be known. The ranges over which Id and Iqchange
are known from the operational specifications. However, angle
2and consequently cos2and sin 2are functions of the oper-ating point. Therefore, the range of2cannot be predetermined
from the converter specifications, and must be deduced based
on intermediate calculations. Thus, we manipulate (53) to tailor
it for control design.
Multiplying and dividing the right hand side of (53) by
m2Vd c2
, and substituting form2cos2and m2sin 2from (36)and (37) in the resultant, we obtain
dedt
= 6Cm2Vdc
(Vtd Id+ VtqIq). (54)
Since in the steady state, Vtd Id + VtqIq Vsd Id , (54) can berewritten as
de
dt =
6
C
Vsd
Vdc
Id
m2
. (55)
m2 typically assumes values from 0.5 to 0.9 over the whole
operating range. Therefore, (54) can be approximated as
de
dt =
6
C
Vsd
Vdc
Idss
mtyp.
. (56)
In (56),Vsd is a constant value, Vdc is regulated at its nominalvalue, and the rated value ofIdss is known from the converter
specifications. In (56), is thecontrol variableand e is theoutput
to be regulated at zero. SinceV1and V2contain high amplitude
triple line frequency components, a low pass or a notch filter is
required in the loop, to provide V1 and V2 as required by (52).Fig. 5 shows a block diagram of the dc side voltage balancer.
V. CONTROLSTRATEGY OFWIND-POWERSYSTEM
The wind turbine is characterized by its mechanical power,
which is given by [16], [17]
Ptur= 0.5r2
Cp(, )V3w (57)
Fig. 5. Block diagram of the dc side voltage balancer.
where is the air mass density, r is theblade length, andVw isthe
wind velocity.Cp(, ) is called Power Performance Coefficientand varies within the range of zero to 0.59 (Betz limit) [17].
Cp(, )is a static nonlinear function of the blade pitch angleand tip speed ratio . The analytical formula forCp(, )areavailable in [16] and [18]. The blade tip speed ratio is given as
= VtipVw
= rrVw
(58)
where Vtip is the blade tip speed and is the turbine speed.
Based on (57), the turbine power is a nonlinear function of
the wind speed and the turbine speed. The maximum power is
captured at an optimum turbine speed and the corresponding
optimum turbine torque.
To obtain the maximum power at wind speeds below a cer-
tain wind speed, the pitch angle is set to a small value; e.g.,
5, andCp(, )is maximized. Since the pitch angle is a con-stant value in this mode, Cp(, )is a single-valued function of; i.e., Cp(). The peak ofCp() corresponds to = op t .
Therefore, the turbine speed must be changed according tothe wind speed to keep at opt. This is achieved through
the machine torque control. The optimum operating point can
be reached if the following reference is commanded to the ma-
chine torque controller [3]
Teref=Kopt2r . (59)
Based on Teref, the corresponding Istqref is determined from
(12), and commanded to the machineq-axis current controller.
Koptis given by
Kopt= 0.5r5Cp(opt)
3opt. (60)
Koptcan be calculated based on the turbine manufacturer data
or measurements.
VI. CASESTUDIES ANDSIMULATIONRESULTS
A detailed switching model of the wind power system of
Fig. 1 and the controllers are developed in the PSCAD/EMTDC
[19] environment. Based on the system parameters in
Tables IIII, the designed controllers are given in the Appendix.
The following case studies illustrate typical time responses of
the proposed wind power unit from the startup to t= 30 s.To simulate more realistic operating conditions, actual mea-
sured wind speed [20] is imposed on the turbine. However, to
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YAZDANI AND IRAVANI: A NEUTRAL-POINT CLAMPED CONVERTER SYSTEM FOR DIRECT-DRIVE VARIABLE-SPEED WIND POWER UNIT 603
Fig. 6. dc bus voltage during startup.
demonstrate the performance of the wind power unit under the
most severe operating conditions, we add a 2.5 m/s step change
to the wind speed waveform at t= 11 s; and at t= 21 s, weremove the step function.
A. System StartUp
Initially, the pitch angle is set at 5, and the turbine speed
is zero. Figs. 68 illustrate the system behavior during startup.Until t= 0.05s, gating signals of NPC1 and NPC2 are blockedand the dc bus capacitors are charged to about 1000 V through
the antiparallel diodes of NPC2, see the Fig. 6. At t = 0.05s,gating signals of NPC2 are released, the reference of the dc
bus voltage is ramped up, and the dc bus voltage reaches its
prespecified value of 2000 V. At t= 0.4 s, gating signals ofNPC1 are also released, and the machine vector controller takes
over; the dc bus voltage experiences a transient disturbance as
shown in Fig. 6.
Fig. 7(a) and (b) shows that the field current and Istdare regu-
lated at 1.0 p.u. and zero, respectively. Since the turbine speed is
low (less than 3.5 rpm), the turbine torque is very small. Hence,the control system sets Istqat 3.55kA, corresponding to 1.0p.u., to accelerate the turbine Fig. 7(c). During acceleration,
power is drawn from the grid. Fig. 7(a)(c) illustrates that, ifis well decoupled from Istd and Istq. However, Istd and Istqare not entirely decoupled during transients. This is due to the
effect of current measurement filters.
Fig. 7(d) indicates that, corresponding to a change in Istq, the
dc bus voltage controller with its feed-forward action changes
thed-axis current component of NPC2, Id . The change ofId is
to ensure the balance of power. Fig. 7(d) and (e) shows that due
to the notch filters,Id andIqare not entirely decoupled.
Fig. 7(f) shows that duringthe time interval that themachine is
supplied from the system and is accelerating, capacitor voltages
V1 and V2 significantly deviate from their nominal values of
1000 V. The reason is that during this time interval, the machine
speed (and its stator frequency) is very low while the machine
currents are large; and the midpoint current of NPC1, inp 1, has
a dominant third harmonic component [21] with an amplitude
proportional to the amplitude of machine current. Therefore,
inp1 has a large magnitude at a fairly low frequency. At this
low frequency, the impedances of the dc capacitors are large
and therefore, the third harmonic ofinp 1 imposes large ripple
components on V1 and V2. Fig. 7(g) shows that despite large
deviations ofV1 and V2, the net dc bus voltage Vdc is tightly
regulated at its nominal value. Fig. 7. System response during startup.
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YAZDANI AND IRAVANI: A NEUTRAL-POINT CLAMPED CONVERTER SYSTEM FOR DIRECT-DRIVE VARIABLE-SPEED WIND POWER UNIT 605
Fig. 10. System response to a sudden wind speed increase.
However, a step change in the wind speed is artificially in-
troduced to subject the system to the most severe conditions
and evaluate the system performance under the worst case
scenario.
Fig. 9(b) and (d) shows that the turbine torque Ttur andpower Ptur increase rapidly due to the wind speed change.
However, the machine torque Te and power Pm do not in-
stantly react to the disturbance. The reason is that Te is
proportional to the square of the turbine speed, and due to
the turbine inertia, the turbine speed cannot have a sudden
change.
Fig. 9(b) indicates that due to the change in the wind speed,
the turbine torque becomes higher than that of the machine.
Consequently, the turbine accelerates (Fig. 9(c)). Fig. 9(d) and
(e) shows thatPm andPg smoothly followPtur.
Att = 18.5s, phase (c) of the PCC is subjected to a line-to-ground fault. Therefore, the grid power is disturbed (Fig. 9(e)).
The fault is self-cleared after 1.0 second. Fig. 9(b) and (c) shows
that during the fault, the machine torque and the turbine speed
are not affected. This is because of the decoupling property of
the back-to-back converter configuration via the dc link.
When the ground fault occurs, the amplitude of the positive-
sequence component of Vsabc becomes 0.67 times its rated
value. Therefore, the dc bus voltage controller increases Id by
1.5 times, to maintain the balance of power and the dc bus volt-
age (Fig. 10(a)). Fig. 10(b) shows that Iq is fairly decoupled
fromId , despite the fault.
Fig. 10(c) illustrates that during the fault, the system is stable
and the average of the dc bus voltage remains tightly regulated.
However, a 120 Hz ripple component is experienced by the dc
Fig. 11. System response to line-to-ground fault.
bus voltage. This is a result of the ac side voltage and current
imbalance due to the fault.
Fig. 11(a) and (c) provides a closeup of the NPC2 currents,
the DC-bus voltage, and the capacitors voltages, during thefault. Fig. 11(a) shows the unbalanced NPC2 line currents.
Fig. 11(b) shows that the dc bus voltage is polluted with the
120 Hz ripple component. However, the dc bus voltage is well
regulated within 2.5% of its rated value. Fig. 11(c) indicatesthat the dc side voltage balancer maintainsV1and V2despite the
fault.
C. Sudden Wind Speed Drop
Fig. 12 shows the system response to an artificial step change
of2.5 m/s in the wind speed at the pitch angle of 5 . Priorto the step change, the wind speed, the turbine speed, and
the grid power are at 9.5 m/s, 17 rpm, and 1250 kW, respec-
tively. Att = 21the wind speed drops by 2.5 m/s (Fig. 12(a)).Fig. 12(b) and (d) shows that the turbine torque Tturand power
Ptur drop rapidly due to the wind speed drop. However, the
machine torque Te and power Pm do not instantly react to
the disturbance, since the turbine speed cannot have a sudden
change.
Fig. 12(b) indicates that due to the change in the wind speed,
the turbine torque becomes smaller than that of the machine.
Consequently, the turbine decelerates and its speed reduces
(Fig. 12(c)). Fig. 12(d) and (e) shows thatPm andPg smoothly
follow Ptur. Fig. 12(f) shows that the dc bus voltage is regulated
at the rated voltage of 2 kV.
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606 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 2, JUNE 2006
Fig. 12. System response to a sudden wind speed drop.
VII. CONCLUSION
This paper presents a new application of a back-to-back con-
nected, three-level NPC converter as the conversion system for
a gearless, synchronous-machine based wind power unit. The
NPC converter provides an economically attractive and techni-
cally viable alternative to the two-level VSC, where operation
at higher voltage levels is desired to meet the requirements for
higher efficiency.
This paper introduces detailed models of the ac side and dc
side controls of the NPC-based back-to-back converter system.
The machine-side NPC converter provides torque-speed control
of the synchronous generator, based on a vector-control strat-egy. The generator field current is regulated by a dc-dc chopper
which is supplied from the dc bus of the back-to-back NPC con-
verter system. The grid-side NPC converter controls real- and
reactive-power flow to the network, and regulates the DC-bus
voltage and ac side power-factor, respectively. The paper also
adopts a newly introduced control approach for dc side partial
voltage equalization. Performance of the overall wind power
unit, including the NPC converter system and its controllers,
is evaluated based on time domain simulation studies in the
PSCAD/EMTDC environment. Time domain responses of the
system under startup, variations in the wind speed, and grid
faults, show sound operation of the proposed converter system
and controls.
APPENDIX
WINDPOWERUNITCONTROLLERS
Fn (s) =fdq(s)
fdq(s) =
s2 + (754)2
s2 + 602s + (754)2
Ki(s) =udq(s)
edq=
0.09s + 1.05
s
H(s) = 16.4 s2 + (754)2s2 + 452s + (444)2
s + 92.4s
Kv (s) =
uv (s)
ev (s) = 5.2
s + 314
s + 2600
s + 50
s
F(s) =
s2 + (2 180)2
s + 600s + (300)2
K(s) = 4.5
s + 300
Fi(s) = 500
s + 500
Kd(s) = ustd(s)estd(s)
= 0.406s + 0.652s
Kq(s) =ustq(s)
estq(s) =
0.308s + 0.652
s
Kf(s) =uf(s)
ef(s) =
0.414s + 0.199
s .
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Amirnaser Yazdani (M05) received the B.Sc. de-gree in 1995,(with honors) from Sharif University ofTechnology, Tehran, Iran, the M.Sc. degree in 2001,from the University of Tehran, and the Ph.D. degreein 2005, fromthe University of Toronto, Toronto, ON,Canada, all in electrical engineering.
From 1995 to 2002, he was with Maharan Engi-neering Corporation, Tehran, Iran, where he workedon the design of switching power supplies and UPS
systems. His research interests include design, dy-namic modelling and control of switching powerconverters.
Currently, he is with Digital Predictive Systems (DPS) Inc., Mississauga,Ontario, Canada, as an Industrial Research and Development Post-DoctoralFellow.
Reza Iravani (M85SM00F03) received theB.Sc. degree from Tehran Polytechnic University,Tehran, Iran, in 1976, and the M.Sc. and the Ph.D.degrees from the University of Manitoba, Winnipeg,MB, Canada, in 1981 and 1985, respectively, all inelectrical engineering.
He is currently a Professor at the University ofToronto, Toronto, ON, Canada. His research interestsinclude power electronics and power system dynam-ics and control.