A New Structure Based on Cascaded Multilevel Converter for Variable Speed Wind Turbine Fujin Deng, Zhe Chen, Senior Member, IEEE Institute of Energy Technology, Aalborg University, Aalborg, 9220, Denmark E-mail:
[email protected] [email protected]
Abstract-An alternative structure for variable speed wind turbine, using multiple permanent magnet synchronous generators (PMSGs) drive-train configuration and cascaded multilevel converter is proposed in this paper. This study presents a power electronic solution for the wind turbine. A transformer-less cascaded multilevel converter interface based on PMSGs is developed to synthesize a desired high ac sinusoidal output voltage. The benefits of high power and high ac voltage make this structure possible to be applied in the wind power generation. In addition, the bulky transformer could be omitted. A simulation model of 10 MW variable speed wind turbine based on PMSGs developed in PSCAD/EMTDC is presented. The dynamic performance of grid-connected wind turbine is analyzed. Simulation results shows that the proposed structure may be attractive in wind power generation.
(a)
(b)
I.
INTRODUCTION
Among the renewable energy technologies being vigorously developed, wind turbine technology has being undergoing a dramatic development and now is the world’s fastest growing energy [1]. With large-scale exploration and integration of wind sources, GWEC is predicting the global wind market to grow by over 155% from the current size reaching 240 GW of total installed capacity until 2012. This means a 146 GW increase in just five years [2]. With large-scale exploration and integration of wind sources, variable speed wind turbine generator system (WTGS) is becoming more popular than that of fixed speed [3]. As to the permanent magnet synchronous generator (PMSG) characterized as having large air gaps, which reduce flux linkage even in machines with multi magnetic poles [4], its excitation is provided by permanent magnets instead of field winding. In recent years, with the performance of PMs is improving and cost of PM is decreasing, the use of PMSG is more attractive than before. Besides, the gearbox can be omitted due to low rotational speed in multi-poles PMSG wind generators, resulting in low cost. The trends make PM machines with a full-scale power converter more attractive for wind turbines [5]. Variable speed wind turbines with fullscale power converters present the distinct advantage that the converter totally decouples the generator from the grid shown in Fig. 1(a) [6]. Hence grid disturbances have no direct effect on the generator.
978-1-4244-5226-2/10/$26.00 ©2010 IEEE
Fig. 1. Block diagram of (a) a variable speed wind turbine based on a directdrive PMSG and a full-scale power converter and (b) the proposed wind turbine structure.
In this paper, an alternative structure shown in Fig. 1(b) for variable speed wind turbine is proposed. Compared with Fig. 1(a), the distinct superiority of the proposed structure is that a cascaded multilevel converter is adopted in the wind turbine with multiple generators configuration, which could generate an almost sinusoidal and high ac three-phase voltage [7]. As a result, it is possible for the output side of the multilevel converter to be directly connected into the high voltage ac grid. As a result, the bulky transformer normally placed between the wind turbine and the grid could be omitted in the proposed wind turbine structure. In addition, the multilevel structure leads to an improved output voltage spectrum due to having a greater availability of voltage levels. Hence, the total harmonic distortion (THD) could be easily limited to satisfied harmonic power quality standard [8]. II.
PROPOSED WIND TURBINE STRUCTURE
A. Proposed Wind Turbine Configuration The proposed variable speed wind turbine structure is shown in Fig. 2. The multiple-generator drive train configuration is adopted here, where a few six-phase PMSGs are placed in one nacelle. These six-phase PMSGs are driven by the same wind turbine, and controlled by cascaded
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Converter unit
PMSG_j C
iL
+
LC
uc
-
O
-
-
ua
+
p L
A
LA
C
+ sw Cr
Vdc + Cb
s11 s13 1 2 s12 s14
LB
ub 2K6 2K5 2K4 2K3 2K2 2K1
(2K-1)6 (2K-1)5 (2K-1)4
(2K-1)3 (2K-1)2 (2K-1)1
46 45 44 43 42 41
36 35 34 33 32 31
26 25 24 23 22 21
16 15 14 13 12 11
L
B C
+ Cr
C
+ Cr
s21 s23 + Cb
3
s22 s24
4
s31 s33 + Cb
5
s32 s34
6
L
Converter module
multilevel converter so as to capture the optimal energy from the wind. The cascaded multilevel converter is competent to transfer the low ac voltage to a high ac level. The six-phase PMSG is adopted here, which consists of two sets of the three-phase stator windings without direct connection. Since two sets of three-phase stator windings are spatially shifted by 30 electrical degrees, the system can cancel out some dominant harmonics produced by the diode rectifiers [9], [10]. The model of the six-phase electrical machine refers to [11], which is not detailed described here. In this structure wind turbine, the three-phase windings of PMSG are separated with each other without connection, which is used to isolate the electrical interface among converter modules in the cascaded converter shown in Fig. 3. The converter unit is shown in Fig. 3, where the power output of the generator is restricted by the inductance of the coils. Herein, a capacitor is connected in parallel with the coil so as to cancel part of the inductance [12], [13]. In each converter module, the ac output from the generator is converted to dc through diode rectifier. The boost converter with the characteristics referring to [14] is adopted here to stabilize the dc-links, which provides a stable dc voltage for the single-phase H-bridge converter. The configuration to electrically stack K numbers of PMSGs is depicted by Fig. 2, where a particular phase of each set of three-phase stator windings is stacked to the same phase of the other sets of stator windings through the converter modules which are connected in series at the output sides. Since each series connected H-bridge converter unit is electrically isolated, this cascaded multilevel converter configuration provides that the load voltage is the sum of each H-bridge outputs. It effectively increases the ac output voltage of this structure wind turbine. It is possible for the variable speed wind turbine with this structure to be directly connected into a ac grid. Hence, the bulky transformer could be omitted in this structure. B. Phase-shifted Unipolar SPWM A phase-shifted unipolar sinusoidal PWM (SPWM) switching scheme referring to [15], [16] is used for the cascaded multi-level converter including K numbers of H-
2
Va_j
n
+
Fig. 2. Block diagram of the proposed structure with the internal interface.
1
Generator side converter
Vb_j
Vc_j
Grid side converter
Fig. 3. Circuit configuration of single PMSG with a detailed, three-phase windings converter unit.
Fig. 4. Block diagram of the generator side controller.
bridge converters. The phase shift time Tps for jth H-bridge converter could be calculated with the following equation. TPS = ( j − 1)Ts 2 K
(1)
where Ts is the triangle carrier signal cycle. One of the main advantages of this switching scheme is that the harmonics of the resultant cascaded multilevel converter output voltage only appear as sidebands centered around the frequency of 2kfs and its multiples, provided that the voltage across the dc capacitor of each inverter is the same (fs = 1/Ts, is the frequency of triangle carrier signal). III.
CONTROL OF THE WIND TURBINE
The collected power of all PMSGs is directly feed into the ac grid by the cascaded multilevel converter, which could be divided into generator side converter and grid side converter shown in Fig. 3. A. Generator Side Converter (Diode Rectifier & Boost Converter) The generator side converter (diode rectifier and boost converter) connected to the stator of the PMSG effectively decouples the generator from the network. Hence, the generator rotor and the wind turbine rotor can rotate freely depending on the wind condition. The control block for generator side converter is shown in Fig. 4, which is used to keep the dc-link voltage constant in each converter module with the switch frequency for boost converter as 1 kHz. It adopts double control loops. The dclink voltage Vdc is controlled in the outside loop by a voltage controller, and produces corresponding current command iL*. In inside loop, a current controller is adopted to regulate the inductance current iL to track the command value.
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1
θu
C
D
1
1.1
θu
θu ωL ωL
B
0.09 0
0
A 0.42 0.47
Rotor speed [p.u.]
Fig. 6. Optimal rotor speed versus power characteristic.
C p = 0.73(
ω
151
λi
− 0.58θ − 0.002θ 2.14 − 13.2)e −18.4 / λi
(3)
with Fig. 5. Block diagram of grid side controller
B. Grid Side Converter (Cascaded Multilevel Converter) The aim of the grid side converter is to regulate the active power and reactive power fed to the grid. Vector control technique has been developed for the grid side cascaded multilevel converter with the switch frequency as 1 kHz. The block diagram of the control system for the grid converter is illustrated in Fig. 5, where the subscripts d and q refer to the d, q-axis quantities. The grid side converter is controlled in a synchronously rotating d, q-axis frame with the d-axis oriented along the grid voltage vector position, which ensures decoupling control of grid-side active and reactive powers fed to the grid. The grid side converter adopts double control loops as well. Based on the measured generator speed ω, the MPPT method calculates the optimal power command P* using the rotor speed versus power characteristic [6], [17]. In the outside loop, the wind turbine is controlled by the power controller Gp(s) to track the power command P* and Q*, and generates corresponding current command id* and iq*. The inside loop is controlled by the current controller Gi(s) to follow the current command. IV. A.
WIND TURBINE MODELING
Aerodynamic Model The mechanical power extracted from the wind can be expressed as follows [6], 1 Pw = ρπR 2 v 3C p (θ , λ ) (2) 2 where Pw is the extracted power from the wind, ρ is the air density (kg/m3), R is the blade radius (m), v is the wind speed (m/s) and CP is the power coefficient which is a function of the pitch angle of rotor blades θ (deg) and of the tip speed ratio λ. The term λ is defined as λ= ωwR/v, with ωw the wind turbine speed. The power coefficient may be calculated as [18]
1
1 0.003 − (4) (λ − 0.02θ ) (θ 3 + 1) The wind turbine power coefficient is maximized Cp_max=0.44 for the optimal tip-speed ratio value λopt = 6.9 when the blades pitch angle is θ = 0o. For each wind speed, there exists a specific point in the wind turbine output power versus rotating-speed characteristic where the output power is maximized. The control of the wind turbine results in a variable-speed wind turbine operation, such that maximum power is extracted continuously from the wind below the rated wind speed. In addition, the wind turbine operates at the rated power during the period of high wind speed by the variable-pitch regulation [19], [20]. In this paper, the pitch angle control system is modeled referring to [21], which is not described here. Based on (2) ~ (4), the relation between the optimal power and the wind turbine speed below the rated wind speed can be obtained below. C p_ max 3 1 Pw _ max = ρπR 5 ⋅ ωw (5) 3 2 λopt
λi
=
Combing the wind turbine characteristic in Appendix and the maximum power point tracking (MPPT) method [17], the rotor speed versus power characteristic that leads to optimal energy capture is developed as Fig. 6. In order to avoid large power fluctuations when rotor speed changes near the minimum rotor speed, a control characteristic similar to that leads to optimal energy capture are adopted [18]. The control characteristic is depicted by the curves AB in Fig. 6. B.
Mechanical Drive Train According to [22], it has been shown that the two-mass drive-train model is suitable for transient stability analysis. Fig. 7 shows the drive train model for the multiple-generator configuration wind turbine. Owing the mass of wind turbine is much bigger than that of generator, the interface among generators could be considered as rigid connection. Referring to [21] and [22], the drive-train mode for Fig. 7 could be obtained below.
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Wind turbine
K
Tw ωw
D
ωg
G1
Tg1
J g1
G2
GK
Tg 2
J g2
TgK
JgK
Jw
Fig. 7. Block diagram of the drive train model.
⎧ dω w ⎪ J w dt = Tw − D(ω w − ω g ) − Kθ wg ⎪ ⎨ i =1 dω g ⎪ J gi = D (ω w − ω g ) + Kθ wg − ⎪⎩ K dt
∑
(6)
i =1
∑
Tgi
Fig. 8(a). Wind speed
K
where Jw and Jg are the equivalent wind turbine inertia and generator inertia respectively. Torque Tw and Tg represent the aerodynamic torque of the wind turbine and the generator loading torque, respectively. ωw and ωg are the wind turbine and generator rotor speed respectively. θwg is the angle between the turbine rotor and the generator rotor. K is the elastic characteristic of the shaft. D is the mutual damping. V.
SYSTEM SIMULATION
A 10 MW variable speed wind turbine with the proposed configuration shown in Fig. 2 is modeled. The wind turbine is composed with five 2 MW six-phase PMSGs. Here, the 10 converter modules are connected in series with each other to make up one 21-level cascaded multilevel converter. There are three cascaded multilevel converters in the wind turbine to construct three phases to be interfaced with the ac grid. The wind model is the standard component model from the PSCAD library referring to [23]. As to the converter module unit, the reference command for the dc-link voltage Vdc is set as 1.2 kV. The RMS value of the line-to-line voltage in the grid is given as 11 kV. In this case study the transmission distance is assumed to be 5 km. Here, the transmission cable with a cross section area of 800mm2 is adopted. The resistance and the inductance of this cable are approximately 0.0221 Ω/km and 0.00031 H/km respectively. A variable wind speed in average as rated value shown in Fig. 8(a) is used to evaluate the performance of this structure wind turbine. The wind turbine speed is around the rated speed shown in Fig. 8(b). At 22s, the generator speed is over the rated value, which results in the action of the pitch angle control system shown in Fig. 8 (c). The sum of the generator torque is shown in Fig.10(d), which regulate the wind turbine speed so as to capture the optimal wind energy. Besides, the wind turbine torque is given in Fig. 8(d). Here, only the 6 numbers of dc-link voltage Vdc for sixphase PMSG 1 is given in Fig. 8(e). All of them are kept constant as 1.2 kV by the corresponding boost converter. The other 24 dc-link voltage for the other four PMSGs is also stabilized as 1.2 kV, which are not plot.
Fig. 8(b). Wind turbine speed
Fig. 8(c). Pitch angle
Fig. 8(d). Wind turbine torque and the sum of generator torque
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Fig. 8(e). Vdc11, Vdc12, Vdc13, Vdc14, Vdc15 and Vdc16
Fig. 8(f). Windings power
Fig. 8(g). Reference power and grid power
Fig. 8(h). Windings 1 voltage Uabc
Fig. 8(i). Windings 1 current Iabc
Fig. 8(j). Windings 1 and windings 2 voltage Ua and Ux
The 10 numbers of windings power is shown in Fig. 8(f). It can be seen that, the power share for each converter module in the cascaded multilevel converter is equalized. Fig. 8(g) shows the power sent into the grid by this structure wind turbine. It is easy to recognize that this variable speed wind turbine could track the power command and capture the optimal power. Besides, the windings 1 voltage Uabc and current Iabc is shown in Fig. 8(h) and (i). Both of them are nearly symmetrical three-phase voltage and current. Fig. 8(j) shows that the two sets of three-phase stator windings in PMSG 1 are spatially shifted by 30 electrical degrees VI.
CONCLUSION
This paper illustrates a new structure based on cascaded multilevel converter for variable speed wind turbine. The multiple-generator driven train configuration is adopted here. A few permanent magnet synchronous generators are placed in one nacelle and driven by the same wind turbine, which increases the wind turbine capacity. The cascaded multilevel converter technology is applied in the wind turbine, which could step up the output ac voltage. Hence, this structure wind turbine could be directly connected into the high voltage ac grid. In addition, the bulky transformer could be omitted. A 10 MW variable speed wind turbine with this structure is modeled, and the simulation results show the proposed structure has good potential for wind generation.
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APPENDIX TABLE I WIND TURBINE AND GENERATOR CHARACTERISTIC Wind turbine rated power (MW)
10
Rotor diameter (m)
160
Rotating speed (r/m)
4.2~11
Nominal wind speed (m/s)
12
Generator Rated power (MW)
2
Phases
6
Stator rated line voltage (V)
690
Rated frequency (Hz)
50
Number of pole pairs
299
Stator winding resistance (p.u.)
0.001
Windings 1 leakage reactance Xl1 (p.u.)
0.036
Windings 2 leakage reactance Xl2 (p.u.)
0.036
Inter-phase mutual reactance Xmd (p.u.)
0.66
Inter-phase mutual reactance Xmq (p.u.)
0.4
stator windings mutual leakage Xlqd (p.u.)
0
Magnetic strength (p.u.)
1.2
Generator inertia (s)
1
Equivalent wind turbine inertia (s)
25
Shaft stiffness K (p.u.)
0.68
Shaft damping D (p.u.)
0.02
TABLE II CASCADED MULTILEVEL CONVERTER CHARACTERISTIC Capacitor Cr (F)
0.035
Induction L (H)
0.001
Capacitor Cb (F)
0.035
Resistance Rf (Ω)
0.00157
Induction Lf (H)
0.0005
[2]
[3]
[4]
[5] [6] [7]
[8]
[10]
[11] [12]
[13] [14] [15]
[16] [17] [18]
[19]
[20]
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