A Neutral-Point Clamped Converter System For

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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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YAZDANI AND IRAVANI: A NEUTRAL-POINT CLAMPED CONVERTER SYSTEM FOR DIRECT-DRIVE VARIABLE-SPEED WIND POWER UNIT 597

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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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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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.



9/12


10/12


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.



11/12


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.

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