Electric Power Systems Rearch 80 (2010) 46–52
Contents lists available at ScienceDirect
Electric Power Systems
Rearch
j o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /e p s
r
Modeling and control of PMSG-bad variable-speed wind turbine
Hong-Woo Kim a ,Sung-Soo Kim b ,Hee-Sang Ko a ,∗
a Wind Energy Rearch Center,Korea Institute of Energy Rearch,Yuong-gu Jang-Dong 71-2,305-343Daejeon,Republic of Korea b
Chungbuk National University,Republic of Korea
a r t i c l e i n f o Article history:
Received 19July 2008
Received in revid form 1August 2009Accepted 5August 2009
Available online 22 October 2009Keywords:
Permanent-magnetic synchronous generator
Variable speed Wind turbine Wind farm
a b s t r a c t
This paper prents a control scheme of a variable-speed wind turbine with a permanent-magnetic synchronous generator (PMSG)and full-scale back-to-back voltage source converter.A comprehensive dynamical model of the PMSG wind turbine and its control scheme is prented.The control scheme compris both the wind-turbine control itlf and the power-converter control.In addition,since the PMSG wind turbine is able to support actively the grid due to its capability to control independently active and reactive power production to the impod t-values with taking into account its operating state and limits,this paper prents the supervisory reactive power control scheme in order to regulate/contribute the voltage at a remote location.The ability of the control scheme is assd and discusd by means of simulations,bad on a candidate site of the offshore wind farm in Jeju,Korea.
© 2009 Elvier B.V. All rights rerved.
1.Introduction
VARIABLE-SPEED power generation enables the operation of the turbine at its maximum power coefficient over a wide range of wind speeds,obtaining a larger energy capture from the wind with a power converter which allows variable-speed operation.One of the problems associated with variable-speed wind systems today is the prence of the gearbox coupling the wind turbine (WT)to the generator.This mechanical element suffers from considerable faults and increas maintenance expens.To improve reliability of the WT and reduce maintenance expens the gearbox should be eliminated.
Megawatt (MW)class wind turbines equipped with a permanent-magnetic synchronous generator (PMSG)have been announced by Siemens Power Generation and GE Energy.In this concept,the PMSG can be directly driven or have smaller gearboxes or even gearless and is connected to the ac power grid through the power converter.U of the power converter is esntial becau it allows the linkage of the generator operating at variable speed to the ac power grid at a fixed electrical frequency.The converter rating must be similar to or even larger than the rated power of the generator.Permanent-magnetic excitation allows to u a smaller pole pitch than do conventional generators,so the machines can be designed to rotate at rated speeds of 20–200rpm,depending on the generator rated power [1].
∗Corresponding author.Tel.:+825506301670.E-mail address: (H.-S.Ko).
However,the electromagnetic construction of the PMSG is more complex than in the ca of conventional WT concepts such as fixed-speed with squirrel induction generators and variable speed with doubly fed induction generators,etc.Also,the reduced gear ratio may require an increa in the number of generator pole pairs,which complicates the generator construction [1–8].
MW class wind turbines (WTs)have been commissioned in large (offshore)wind farms connected directly to transmission networks.However,incread wind power generation has influ-enced the overall power system operation and planning in terms of power quality,curity,stability,and voltage control [9–14].The local power flow pattern and the system’s dynamic char-acteristics change when large WTs are connected to the utility grid [15].Thus,the compliance with the grid codes of national Transmission System Operators (TSOs)becomes an important issue [16].
Therefore,the interaction between wind farms (WFs)and power systems is a rearch topic that needs more attention.To get a better understanding of how the control systems of the individual WTs and the WFs influence each other,modeling and simulation are esntial.To investigate the interaction between controllers of WTs or WFs and the controllers of the grid is considered a challen
ge.With more advanced control algorithms,WTs and WFs can provide ancillary rvices to the by providing reactive power or participate in voltage/frequency control.To study the impacts of the advanced control strategies on a system level,more modeling efforts are required.
Therefore,this paper prents the detail system modeling and the control design of a PMSG-bad-WT.As well as alternative design and/or control solutions are propod to improve the voltage
0378-7796/$–e front matter © 2009 Elvier B.V. All rights rerved.doi:10.1016/j.epsr.2009.08.003
H.-W.Kim et al./Electric Power Systems Rearch80 (2010) 46–52
47
Fig.1.Grid-connected wind-turbine system.
control at a required location such as a point-of-common coupling (PCC).
This paper is organized as follows:the detail dynamic model including voltage source converter(VSC)control design is pre-nted in Section2;in Section3,the supervisory reactive power control scheme is propod;ca studies are carried out in Section 4;and conclusions are drawn in Section5.
2.Dynamic model of PMSG-WT-bad power system
The system considered in this paper is shown in Fig.1.The WF consists of5unit of WT.Each WT is equipped with a0.69/22.9kV step-up transformer(TR).The WF is connected to the grid using a2km submarine cable(Ca)and a14km overhead transmission line(TL).The considered operating condition is as follows:the WF supplies7MW of active power and0.3MVar of reactive power to the local load,which consumes8MW and1.9MVar.The remain-ing active power comes through the154kV utility grid,which is reprented by an infinite bus(Table1).
Although the fundamental principle of a WT is straightforward, modern WTs are very complex syste
ms.The design and optimiza-tion of the WT’s blades,drive train,and tower require extensive knowledge of aerodynamics,mechanical and structural engineer-ing,control and protection of electrical subsystems,etc.
The details of the WT considered in the model are shown in Fig.2.The WT consists of the following components:a three-bladed rotor with the corresponding pitch controller[17];a PMSG with two converters,a dc-link capacitor,and a gridfilter;and converter controllers.
Although personal computers are becoming increasingly faster, computational speed is still one of the limiting factors in dynamic simulation of power systems[18,19].Electrical transients have very small time constants that require small integration time steps and result in long computation time.To keep the simulation speed rea-
Table1
Operating conditions.
p(pu)q(pu)
IB
0.4190.8039
WF 3.5620.1687
Total 3.9810.9725
Resistance Reactance Load0.30990.0757 Bus:4(PCC);v(pu):1.1435.Fig.2.Permanent-magnetic synchronous generator wind turbine(PMSG-WT). sonable,special attention should be given to model
development.In particular,in this paper,to increa the simulation speed of various electrical components,the components are modeled in the dq-synchronous reference frame[20].Wherein,the d-axis is assumed to be aligned to the statorflux,and the current coming out of the machine is considered positive.The PMSG controllers utilize the concept of disconnection of the active and reactive power controls by transformation of the machine parameters into the dq-reference frame and by parating forming of the stator voltages.Then,the active power can be controlled by influencing the d-axis component of the stator current while the reactive power can be controlled by influencing the q-axis components of the stator current.The system parameters and control gains,etc.,are summarized in Appendix A.
2.1.Permanent-magnetic synchronous-generator(PMSG)
The PMSG was reprented by the following equations[1]:
1
ωb
d ds
d t
=v d1+R s i ds+ωe qs,
1
ωb
d qs
d t
=v q1+R s i qs−ωe ds(1) with
ds
兄弟成双
=−L ds i ds−m,qs=−L qs i qs(2) where v is the voltage,R is the resistance,i is the current,ωe is the stator electrical angular speed,ωb is the ba angular speed in rad/s,L s is the stator leakage inductance,m is the exciterflux of the PMSG,and is theflux linkage.The subscripts d and q indi-cate the direct and quadrature axis components,respectively.The subscripts s indicates stator quantities.The electrical active and reactive power delivered by the stator are given by有梦不觉人生寒
P s=v d1i ds+v q1i qs,Q s=v d1i qs−v q1i ds(3) The mathematical model of a TL,a TR,a cable,and a load can be obtained from the description of the R,L,C gment[20]into the dq-synchronous reference frame.The equations of the TL,the TR, the cable,and the RL
load are given in(4)–(7)bad on Fig.3where superscript s and e stand for the nding-end and the receiving-end.
Fig.3.Lumped-parameter equivalent-circuit description in the dq-domain.
48H.-W.Kim et al./Electric Power Systems Rearch80 (2010) 46–52
For example,in the TL model(e.Eq.(4))v s
d corresponds to v d3at
bus3and v e
d
corresponds to v d4at bus4.
2.2.Transmission line(TL)
L TL ωb d i dl
d t
=v d4−v d3−R TL i dl+ωe L TL i ql,
L TL ωb d i ql
d t
=v q4−v q3−R TL i ql−ωe L TL i dl,煮虾用什么调料
C TL ωb d v d3
d t
=i s
dc
+ωe C TL v q1,C TL
ωb
d v q3
d t
=i s qc−ωe C TL v d3,
C TL ωb d v d4
d t
=i e
dc
+ωe C TL v q4,C TL
ωb
d v q4
d t
=i e qc−ωe C TL v d4(4)
2.3.Transformer(TR)
L tr ωb d i dl
d t
=v d2−v d1−R tr i dl+ωe L tr i ql,
向前奔跑L tr ωb d i ql
d t
=v q2−v q1−R tr i ql−ωe L tr i dl,
C o ωb d v d1
dt胡萝卜土豆炖牛肉
=i dl+ωe C o v q1,C o
ωb
d v q1
d t
=i ql−ωe C o v d1(5)
where C o is the dummy capacitor to obtain voltage for modeling purpo.
2.4.Cable
L ca ωb d i dl
d t
=v d3−v d2−R ca i dl+ωe L ca i ql,
L ca ωb d i ql
d t
=v q3−v q2−R ca i ql−ωe L ca i dl,
C ca ωb d v d2
d t
=i s
dc
+ωe C ca v q2,C ca
ωb
d v q2
d t
=i s qc−ωe C ca v d2(6)
2.5.RL load
The RL load in the dq-domain can be described as
L load ωb d i dL
d t
=v d4−R load i dL+ωe L load i qL,
L load ωb d i qL
d t
=v q4−R load i qL−ωe L load i dL,
C o ωb d v d4
d t
=i dL+ωe C o v q4,C o
ωb
d v q4
d t
=i qL−ωe C o v d4(7)
As shown in Fig.2,the grid-side converter is connected to the grid through thefilter.The voltage equations for thefilter in the dq-synchronous reference frame are as follows.
2.6.RL-filter on the grid-side converter
Lfilt ωb d i dg
d t
=v d1−Rfilt i dg+ωe Lfilt i qg,
Lfilt ωb d i qg
d t
=v q1−Rfilt i qg−ωe Lfilt i dg(8)
where subscriptfilt stands for
filter.
Fig.4.Block diagram of the VSC controller showing the input/output孢子粉的副作用
variables.
Fig.5.WT maximum energy-harvesting curve.
2.7.Voltage source converter controller
Fig.4prents the detailed block diagram of the VSC controller
depicting the respective input and output variables.Here,P t
g
中学一级教师
is
the t-value for the active power for the WT terminal.The value
of P t
g
is determined from the WT energy-harvesting character-
istic as shown in Fig.5,which is reprented here as a look-up
table P t
g
(ωr)determined in terms of generator rotational-speedωr.
Since variable-speed WTs are traditionally operated in the power
factor control(PFC)mode to achieve the unity power factor at the
terminal of the WT,the reactive power t-points Q t
g
is t to zero.
The VSC control module consists of the generator-side,the dc-
link,and the grid-side converter controller.The controllers utilize
proportional-integral(PI)controllers.The PI controllers are tuned
using the Nyquist constraint technique to deal with model uncer-
tainties[21,22].Each of the controllers is briefly described below.
Generator-side converter controller:Fig.6shows a block diagram
of the generator-side converter controller module,which includes
four internal PI controllers,PI1through PI4.The controller is imple-
mented as two branches,one for the active power(PI1and PI2)and
one for the reactive power(PI3and PI4)with the corresponding
de-coupling terms between the d and q axes,
respectively.
Fig.6.Block diagram of the generator-side converter controller.
H.-W.Kim et al./Electric Power Systems Rearch 80 (2010) 46–52
49
Fig.7.Block diagram of the grid-side converter controller.
The transfer function from the stator voltage to the stator cur-rent is approximated as
I ds (s )V ds
(s )I qs (s )
V qs
(s ) T
=
1
R s +s (L ds /ωb )1
R s +s (L qs /ωb )
T
(9)
Similarly,the transfer function from the stator current to reac-tive and active power is approximated as
P s (s )I ds (s )Q g (s )I qs (s )
T就字的笔顺
=
R s +s
L ds ωb
R s +s
L qs ωb
T
(10)
Then,(9)is ud to tune PI2and PI4,and (10)is ud to tune PI1
and PI3.
Grid-side converter controller :Fig.7shows a block diagram of the grid-side converter controller modu
le,which also includes two internal PI controllers PI5and PI6,with corresponding de-coupling terms between the d and q axes.
The voltage equation for the grid-side converter RL-filter can be expresd as
L filt ωb
d i
dg d t
=v d1−R filt i dg +ωe L filt i qg , L filt
ωb
d i qg d t
=v q1−R filt i qg −ωe L filt i dg
(11)
from which the transfer function from the filter voltage to current
is
I dg (s )V d1(s )
I qg (s )
V q1(s )
T =
1
R filt filt /ωb )1
R filt filt /ωb )
T
(12)
The inputs to the grid-side controller are the t-values for the currents,which flows to the grid through the VSC.The t-values of the input currents are calculated by the active and reactive power
commands P t s and Q t g
as follows:
i t qg i t dg
=
v q1
v d1−v d1
v q1
−1
P t s Q t g
(13)
where P t s and Q t g
are the t-point of the active and reactive power commands.The value for P t s
is provided by the dc-link con-troller,which determines the flow of active power and regulates the dc-link voltage by driving it to a constant reference value.
DC-link dynamic model and its controller :The capacitor in the dc-link is an energy storage device.Neglecting loss,the time derivative of the energy in this capacitor depends on the differenc
e of the power delivered to the grid filter,P g ,and the power provided by the stator circuit of the PMSG,P s ,which can be expresd as 12C dc ωb d v 2
dc
d t
=P g −P s
(14)
The dc-link controller regulates the capacitor voltage by driving it to the reference value v ref dc
,and outputs the t-point for the active power P t s needed in (13).Fig.8shows the dc-link model with
its
Fig.8.DC-link model and its
controller.
Fig.9.Schematic diagram of the supervisory reactive power control.
controller PI7.The t-point for the output active power by P t s
=v dc i t dc ,s
.3.The supervisory reactive power control
The purpo of the supervisory reactive power control pre-nted in this ction is to regulate the voltage at the specified remote PCC (e Fig.1)by adjusting the reactive power produced by the grid-side converter,taking into account its operating state and limits.As shown in Fig.9,the control objective is to utilize Q j from the grid-side VSC to control the voltage at the PCC to the predefined value by the reactive power t-point control signal Q t j .
When controlling WT,it is important that the operating limit of WT is not exceeded.The reactive power required from an individual grid-side converter of the VSC can be computed as
Q t j =min
Q max j ,
Q max
j Q max 1
+···+Q max 5
Q pcc
(15)
where j =1,...,5,Q max j is the maximum reactive power (limit)
that the j th grid-side converter can provide,and Q pcc is the total reactive power required to support the voltage at the PCC.
Fig.10shows the active and reactive power operating lim-its,wherein it is assumed that the grid-side converter should not exceed its apparent power limit S max j depicted by the half-circle.Suppo that at a given time each grid-side converter is delivering the active power denoted herein by P j .Then,in addition to the active power,the converter can supply or absorb a maximum of Q max j of the reactive power.Therefore,the reactive power available from the grid-side converter lies within the limits [−Q max j ;+Q max j ],which are operating-condition
dependent.
Fig.10.VSC active and reactive power operating limits.
50H.-W.Kim et al./Electric Power Systems Rearch
80 (2010) 46–52
Fig.11.Implementation of PI controller with the distributed anti-windup.
Thus,the maximum available reactive power from the each grid-side converter can be expresd as Q max
j =
(S max j )2−P 2
j (16)
where it is assumed that the nominal apparent power of the each converter is S max j ,defined here as the WT rating.Bad on Fig.10,it also follows that −S max j ≤P j ≤S max j .Thus,the maximum reactive
power t-point of Q t j (e Fig.4)can be determined by (15)and (16).
Finally,a proportional-integral (PI)controller is designed for a controller shown in Fig.9.The PI gains are summarized in Appendix A .Since limiting control action should be implemented together with the integrator-anti-windup scheme that would stop inte-grating the error when the limit is being reached,a PI controller with the propod distributed anti-windup is implemented in Mat-lab/Simulink [23]as shown in Fig.11for ca studies.4.Ca studies
The system depicted in Fig.1was implemented in detail using the Matlab/Simulink [21].Computer studies considering the wind-speed variations,the local-load variations,and the voltage sag due to the fault were conducted to compare the dynamic respons of the system with different controls.In comparison,Mode 1indi-cates the PFC-mode operation of the grid-side converter of the WT,
which Q t g
is t to zero.As the propod operation,Mode 2actively utilizes Q t g
from the grid-side converter for voltage control at the PCC.
4.1.Wind-speed variation
In this study,the wind speed shown in Fig.12was considered for the WTs.Fig.13shows the voltage at the PCC,predicted by the model with different controls,respectively.As shown in Fig.13,Mode 1operation caud the voltage deviation about 3%,which is much higher than the permissible voltage range of HV
power
Fig.12.Wind speed
(m/s).Fig.13.Voltage obrved at the PCC due to the wind-speed
variation.
Fig.14.Active and reactive power from WF to PCC for wind-speed variation.
system network ±2%while Mode 2operation achieved the voltage regulation at the PCC.Fig.14shows the measured data of the active power and the reactive power from the WF to the PCC (e Fig.1).The reactive power contribution from the WTs is the difference between Mode 2and Mode 1.4.2.Local-load variation
For this study,the local-load impedance is decread by 20%with wind speed 12m/s.The comparison of the voltage transients obrved at the PCC was showed in Fig.15.As can be noticed,
when
Fig.15.Voltage obrved at the PCC due to the 20%impedance decrea.
