power generation in the wind energy system may be affected by tripping the wind turbine from utility grid. Hence it is desirable to implement the generator control ...
of Back-to-Back PWM Converters for DFIG Wind Turbine Systems under Unbalanced Grid
Control
Voltage Ahmed G. Abo- Khalil, Dong-Choon Lee
Jeong-Ik Jang, R&D Department KR Group Tower 98-4, Garak-Dong, Songpa-Gu, Seoul, Korea Email: knightO318gyumail.ac.kr
Department of Electrical Engineering Yeungnam University 214-1, Daedong, Gyeongsan, Gyeongbuk, Korea Email: dcleegyu.ac.kr Abstract
This paper presents a new control scheme for minimizing the torque ripple of the generator under unbalanced grid voltage for wind turbine systems using doubly-fed induction generators, where the negative sequence component of the rotor current is utilized. It is found that the generator torque ripples are related with the reactive power component. Increase of stator active power ripples caused by reducing the torque ripple is compensated by controlling the active power ripples of grid-side converter. Simulation results using PSCAD and experimental results show that the conventional vector control of DFIG without considering grid voltage unbalance results in excessive oscillations on the stator active and reactive power, and electromagnetic torque. On the other hand, with the proposed control strategy, improved system control and operation such as reducing oscillations of active power and generator torque can be achieved.
I.
INTRODUCTION
Nowadays, variable speed wind turbines with a DFIG directly connected to the grid are widely used in the field. For the dynamic feature, the DFIG becomes the most popular generator for wind power generation system. Firstly, DFIG can supply power to the grid at constant voltage and constant frequency while the rotor can operate at sub-synchronous mode or super-synchronous mode. Secondly, the rating of the power converter is only about 30% of the rated power of the wind turbine. At third, the generated active and reactive power can be controlled independently. The performance of the DFIG-based wind turbines under the normal condition are now well understood [1]-[4]. For conventional wind farms connected to an electric network, the turbines are disconnected from the grid if voltage unbalance of 6% or more is detected [5]. Then, the continuity of the power generation in the wind energy system may be affected by tripping the wind turbine from utility grid. Hence it is desirable to implement the generator control system to withstand to a certain level of voltage unbalances. If the voltage unbalance is not taken into account in the control system, a highly unbalanced stator current could be produced even with a small unbalanced stator voltage. The unbalanced currents cause unequal heating on the stator winding as well as torque and power pulsation in the generator [6]. The torque ripples can be a source of mechanical stress on the drive train
1-4244-0755-9/07/$20.00 (C2007 IEEE
and gearbox as well as a source of acoustic noise [7]. Control of DFIG systems for network unbalance has been studied in [5], [7], and [8]. In [5], the current reference for compensation was calculated in order to minimize the torque pulsation without using machine parameters. However, the rotor current controller is not easy to design and implement for controlling both dc component in the synchronous reference frame and the compensating rotor current which oscillates at twice the line frequency. Also the paper shows only simulation results without experimental results. In [7] the torque pulsation was used as an input of a lead-lag controller to derive the compensating rotor voltage. Also, these controllers need to be carefully designed for both dc component and the doublefrequency current component. In [9], an efficient dual current control algorithm using positive and negative sequence current components in ac/dc PWM converter systems was proposed. In DFIG control, due to the existence of the double frequency rotor current components, a dual current controller for positive and negative sequence current components has been introduced in [10]. With this method, the generator torque ripple decreases, however, the stator active power ripple appears. So, the power flow into the grid is fluctuated. Applying the same concept in [9] to the control of grid-side converter, the power ripples flow into the grid can be decreased significantly. In this paper, a novel control algorithm is proposed to reduce the active power ripples flowing into the grid as well as the torque ripple of the DFIG by controlling the grid-side converter when the grid voltage is unbalanced. The double frequency components of the stator reactive power are controlled to zero to minimize the torque pulsations. Hence two separate current controllers for the positive and negative sequence components of rotor currents are designed and implemented which allow significant reduction for the torque pulsations. Similarly, the double-frequency components of the grid active power are controlled to zero to minimize the grid power ripples. Another two separate current controllers for the positive and negative sequence components of the grid currents are designed and implemented. Simulation results for a 2[MW] DFIG wind turbine system are provided and experimental result for a 3[kW] wind turbine simulator verifies the validity of the proposed control strategy.
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'ds
Turbine
L
L
R
IbX s
Wind
r
vde
( )r R(e
(Sj, jr
VdsL
Lm
dr
+
Vdr
Fig. 1. Configuration of DFIG wind power systems.
Fig. 2. Equivalent circuit of DFIG.
II. DFIG MODEL AND CONTROL
Configuration of the overall wind generation system is shown in Fig. 1. The stator of DFIG is directly connected to the grid and the rotor is connected through back-to-back PWM converters. The DFIG is controlled in a rotating d-q reference frame, with the d-axis aligned with the stator flux vector. The stator active and reactive power is controlled by regulating the current and voltage of the rotor. Therefore the current and voltage of the rotor needs to be decomposed into the component related to stator active and reactive power. A. DFIG model Figure 2 shows the d-q equivalent circuits of DFIG. Under stator flux-oriented control, the fluxes, currents and voltages can be expressed as [11 ] 'dqs =Lsidqs + LmIdqr
(1)
kdqr = Lridqr + Lmidqs
(2)
Vds=Ri vdqs Rsdqs+
vdqr
d dt
dqs + jO)e2dqs
r1dqr++d ddqr + j(0)e O)r)Adqr
-Ri
-
(3) (4)
B. Power control Stator-flux oriented control is adopted in this control scheme where the d-axis is aligned with the stator flux space vector. The q-axis component of the rotor current can control either the generator torque or the stator active power. On the other hand, the rotor d-axis current component can control directly the stator reactive power. Using (1)-(6), the stator active and reactive power can be expressed as
2 2LL5
3
QS
Ls
2L
III. DFIG CONTROL UNDER UNBALANCED GRID VOLTAGE
A.
Generator torque For unbalanced grid voltage, (1)-(4) are not sufficient to derive the generator torque equation. Expressing the negative sequence components for the fluxes and voltages,
'dqs =sidqs +Lmidqr
Ls
'dqr =r
Ad,qs
vn Vdqs
Stator self-inductance; Lr Rotor self-inductance; Stator d-q axis flux linkage; dqs otor d-q axis flux linkage; lds, ldq: Stator and rotor d-q axis currents. Oe X jr: Source and rotor angular frequencies
d =RJidqs ++dt s
(10)
+Lm dqs
eL)A+ dqs i(We)dqs
(1 1)
J
+
rd )rdqr
(12)
where, the superscripts 'p' and 'n' indicate the positive and negative sequence components, respectively. The total apparent power of the generator can be expressed
(5)
as
(6)
where the superscript '"' means the complex conjugate and
S*) ST=1.5(vsi-s* Vdqs ldqs +s Vdqr6dqr
s
qs
dr
(9)
- RPidqr + d idqA vaqr dqr -rdqr dt dqr + j( O)
The phase angle of the stator flux vector is calculated as follows;
6 =tan-1
(8)
-dr)
'rm
Lm Magnetizing inductance;
J(VdqRsidqs)dt
Vj(lms
7
where is the magnetizing current. It is noticeable that the stator active and reactive power components are proportional to iqr and idr, respectively.
where
dqs
Vqslqr
ds
where the superscript 's' indicates quantities in the stationary reference frame.
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VcqVdqr id
dqr
ei9'-C9w)tvpdqr + ej.( -=e
te)tiPdqr + ej
(13)
C9C)t ndqr W),- trin
dqr
=s 1 .5(vqpsidps
-v
iqps + vqnsids-vdnsiqns)
svi +dsf *5(VqsidsVdpsiqn Vqnsidp svi$) _VniqpS QSc2 =1.5(vqpdJ +
Qsc21
Qss 2
converter
Q.a
SVPWM
Fig. 3. Power control of DFIG system under unbalance grid voltage.
Taking the real part of (13) and dividing it by the mechanical speed, the instantaneous torque is obtained as [12] (14) + sin(2 oet) Te(t) = TeO + where TO =1 .5Lm (iqs idr + iqns idn
.5Vids
+Vqsiq
-dsid-qiP
The d-axis of both positive and negative sequence components are aligned with the positive and negative components of the stator flux. Hence the positive and negative sequence components of the stator d-axis voltage are zeros. The generator torque and stator active and reactive power are expressed in terms of the stator and rotor currents, which was derived in [10]. It is found that the stator reactive power ripple is related with the generator torque ripple. So, to reduce the generator torque ripple, an additional controller for reactive power ripples is added, which is shown in Fig. 3. IV. CONTROL OF GRID-SIDE CONVERTER
T12 cos(2?),t) T'2
It is known from the stator active and reactive power equations that stator active power ripples are increased by applying the power control for torque ripple reduction. This means that active power ripple flows into the grid since the Te2 =1. 5Lm (iqP idr +iq- idr ) stator terminal is connected to the grid directly. Since this situation is not desirable, the active power ripple component = Te 2 1 .5Lm (iqpsiqnr-iqnsiqpr ) should be reduced. This can be achieved by controlling the It is shown from (14) that the generator torque due to the grid-side converter to compensate for the active power ripples. Just as it was derived in case of the generator control in the source voltage unbalance includes the dc component( TO) and previous section, the active and reactive power equations can ac components( Tec2 X Ts2 ) which have the double frequency of be expressed as the source. The torque pulsation can be decreased by (18) p(t) = Po + 'c2 cos(2wet) + 's2 sin(2 Wet) controlling the negative-sequence component of the rotor current.
B. Control ofgenerator-side converter Next, the relationship of the stator power and the torque is investigated. The stator-side apparent power under unbalanced grid voltage can be expressed in terms of the positive and negative sequence components as [10]
q(t) = Qo + Qc2 CoS(2Cw)et) + Qs2 sin(2ct) where
Po=1.5(vp idp + vqps iqp + vds id + vqs iqn) =12 1.5(vdsid + vqsiq + vdsid + vqsiq ) =
ei c,vdqs + e
e dqs + dqs. From (15), instantaneous active power ps(t) and reactive power qs (t) are obtained as
PsO + Psc2 CoS(2o(et) + Pss2 sin(2o(et) qs (t) = Qso + Qsc2 CoS(2cWet) + Qss2 sin(2cWet) Ps (t)=
~1.s(dds .5(vPidPss +v46qsP~qs+vP dsn(lds +
PSs2= 1 . (qs is
n
=qs
Vs iqs
+v
iqn -V nidp _Vqnsiqp ) The current reference of the grid-side converter compensating for the stator active power ripple can be derived Q2=
vaq
dlqs dewqsJ~ +'
]1~c2=1 .5(vdpidns +pv'qcs
Vdnsiqp _Vqpidn + Vdp in )
Qc 2= 1.*5(vqps idn-vdps iqn + vqns idp -vdns iqp )
idqs
where
1 . 5(Vn idp
Qo =1.5(vqpsidp-vdpiqp +vqsidn -vdsiq)
Ss=1*5dqs dqs(15 where vaq
(19)
qs qs)
ip +nvVqs iqspj~
+ Vds cds
-Vqs ids + VdPs iqs)
nd
+
Vp
as
dP* (t)
(16)
qP* (t)
id(t
(17)
_q* (t) +
1.*5(vdp
Vdcs _
Vqns VdS
vP
qs
-Vds
Vdn qs
-Vds
n
-VPqs
vn
Vds
qs
Vqs
PV
ns
.PO 0
(20)
-P* _i
sc~2
_j
where, PO0 means the power reference for the constant dc voltage which is the product of the dc voltage controller output and the dc voltage reference. Fig. 4 shows the control block
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Fig. 4. Control diagram of grid side converter under unbalance grid voltage.
diagram of the grid-side converter under unbalanced grid voltage. The dual current controller is employed as in the generator-side converter. V. SIMULATION RESULTS
Simulations of the proposed control scheme for a DFIGbased generation system were performed using PSCAD software. The DFIG used for simulation is rated at 2[MW] and the wind speed is constant at 10[m/s]. The grid voltage is Fig. 5. Power control without controlling the unbalanced grid voltage. 690[V] and 60[Hz]. For 2 [MW] DFIG system, 20% unbalance voltages are applied at the grid side. Initially, the system runs under balanced condition and then the grid voltage is disturbed at 1.5[sec] and then the voltage balance is recovered at 3.5[sec]. Fig. 5 shows the DFIG performance with the conventional stator-flux oriented control without considering the unbalanced condition. It is shown that the positive and negative sequence components of the rotor current include 120[Hz] components, which means the stator current highly unbalanced. Similarly, the stator active and reactive powers, and the electromagnetic torque all contain significant pulsations at 120[Hz]. The magnitude of the torque and speed ripples is 0.12[pu] and 13[rpm], respectively. Fig. 6 shows the DFIG performance only with control of the generator-side converter considering unbalanced condition. Due to dual current control, the rotor current ripple is suppressed. Accordingly, the generator torque and speed ripples almost disappear. However, it is shown that the stator active power ripples increase, of which magnitude are 0.02[pu] and 1 [rpm], respectively. Next, consider the case that the gridside converter is controlled together with the generator-side converter by the dual current control mode. Fig. 7 shows the DFIG power control performance is not changed with the additional dual current control of the grid-side converter. Figure 8 shows the active and reactive power of the stator, the grid-side converter, and the grid. The ripple component of the stator active power appears due to suppression control of the shown in Fig. 8. Instead, the stator active power ripple is DFIG torque ripple. To get rid of the power ripple, the grid- increased a little higher, however, it is insignificant since it has side converter injects the compensating power into the grid. So, no effect on the power factor. the grid active power ripple has been reduced to the level as
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Fig. r
(a),-,
1
hVc
1
T
-Vt
-V-a DD ;,t AnAjj
iov
, 1i
Fig. 7.
ia abC'C
75[M/d iv
.
(b),
O[A]
~ 5[A]/div I Fig. 10 The grid phase voltages and stator currents under unbalanced conditions
Fig. 8. Active and reactive power at the grid power smoothing control.
VI. EXPERIMENTAL RESULTS
To verify the feasibility of the proposed control scheme, a small scale 3[kW] laboratory prototype is used to verify the control scheme, which is shown in Fig. 9. The stator of the DFIG is connected to the utility grid. The rotor is connected to the grid through the back-to-back PWM converters to provide bidirectional power flow. The converter switching frequency is
5 [kHz], and the current and the speed control sampling periods are 100 [,Ls] and 1 [ms], respectively. For the experiments, the amplitude of the a-phase voltage Va is reduced to produce the unbalance as shown in Fig. 1 0(a). Fig. 10(b) shows the stator currents which are also unbalanced. Without regulating the stator and grid ripples, the stator active power is fluctuated around the reference value, which is 2000[W], with a frequency of 120[Hz]. The stator reactive power also oscillates around the 0[VAR] reference value with the same frequency. As a result of the unbalanced stator voltages and currents, the generator torque pulsates around the average value as shown in Fig. 11. The oscillations of the stator active power and electromagnetic torque are 20% and 22% of their rated values, respectively. The grid active and reactive power is fluctuated at the same frequency as shown in Fig. 12. With regulating the ripple components of the stator reactive power and grid active power, the stator reactive power and generator torque ripples have been decreased significantly as shown in Fig. 13. On the other hand, the reduction of the stator active power ripples is lower than the reactive power. The grid active and reactive power ripples have been decreased significantly as shown in Fig. 14. The controller performance is shown to be effective in reducing the stator reactive power ripples and the grid active power ripples.
2641
r)
St
(a)
