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Synchronverter-based Control Strategy for Back-to-back Converters in Wind Power Applications
Synchronverter-based Control Strategy for Back-to-back Converters in Wind Power Applications Zhenyu Ma ∗ and Qing-Chang Zhong ∗∗ ∗
Loughborough University, Leicestershire, LE11 3TU, United Kingdom Email: [email protected]. ∗∗ The University of Sheffield, Sheffield, S1 3JD, United Kingdom Tel: +44-114 22 25630, fax: +44-114 22 25683, Email: Q.Zhong@Sheffield.ac.uk.
Abstract Back-to-back PWM converters are becoming a realistic alternative to the conventional converters in high-power wind-energy applications. In this paper, a control strategy based on the synchronverter technology is proposed for back-to-back PWM converters. Both converters are run as synchronverters, which are mathematically equivalent to the conventional synchronous generators. The rotor-side converter is responsible for maintaining the DC link voltage and the grid-side converter is responsible for the maximum power point tracking (MPPT). Simulation results show that the proposed method operates properly. Keywords: Synchronverter, virtual synchronous generators, back-to-back converter, wind turbine, maximum power point tracking (MPPT), voltage sags 1. INTRODUCTION During the last decade, more and more attention has been paid to utilising renewable energy sources to tackle the energy crisis we are facing. Wind power has been regarded as one of the main renewable power sources to replace/complement fossil fuels. Wind energy has many advantages such as no pollution, relatively low capital cost involved and the short gestation period. Many countries have set strategic plans to develop technologies for utilising wind power and a lot of researchers have shifted into this area. Wind generation systems can be divided into variablespeed generation systems and fixed-speed generation systems. Variable-speed systems are more attractive than fixed-speed systems due to the improved wind energy production and its reduction of flicker problems. Nowadays, the most-used topologies for variable-speed wind turbines are doubly-fed induction generators with wound rotors, induction generators with squirrel cage rotors and synchronous generators with permanent magnets (Spera, 2009). In these three cases, one of the most popular grid connection topologies is to adopt back-to-back voltage source inverters to interface with the grid (Baroudi et al., 2005) to provide unity power factor and low harmonic distortion of current, as shown in Figure 1. The synchronous generator is connected to the grid through a full-scale back-to-back PWM converter and the conversion stage consists of a rotor-side converter and a grid-side converter. This work was supported by the Engineering and Physical Sciences Research Council, U.K., and Nheolis, France under the Dorothy Hodgkin Postgraduate Awards (DHPA) scheme and under Grant EP/J001333/1.
Many different control strategies have been developed for back-to-back PWM converters in wind power applications. Normally, the maximum power point tracking is achieved by controlling the rotor-side converter and the DC link voltage is controlled by the grid-side converter (Pena et al., 1996a,b; Cardenas and Pena, 2004; Teodorescu and Blaabjerg, 2004; Portillo et al., 2006; Bueno et al., 2008; Singh et al., 2011). In this case, the DC link voltage is increased due to the continuous operation of wind turbine and generator when grid faults happen. The gridside converter may be out of control when grid voltage sags happen because voltage sags reduce generator torque (Gomis-Bellmunt et al., 2008), which accelerates the rotor and causes mechanical instability unless normal voltage levels are quickly restored. As a fail-safe mechanism against equipment damage, wind turbines are designed to automatically disconnect themselves from the utility grid under these extreme conditions (McGranaghan et al., 1993; Bollen, 2000). Therefore, in some other strategies, the rotor-side converter controls the DC link voltage and the grid-side converter controls the power of the wind turbine fed to the grid (Yuan et al., 2009; Hansen and Michalke, 2009; Kim et al., 2010). In both cases, the control strategies are mainly based on the vector control approach in the d-q reference frame to control the direct component and the quadrature component, respectively. In this paper, an original control strategy based on the synchronverter technology, which is to operate a converter to mimic a synchronous machine (Zhong and Weiss, 2011), is proposed for back-to-back converters in wind power applications. The rotor-side converter is run as a synchronous motor and the grid-side converter is run as a synchronous generator. As a result, the whole system behaves as a generator–motor–generator system.
LCL filter
~
Grid
PMSG
Three-phase rectifier
Three-phase inverter
Figure 1. Connection of wind power generation system to grid through back-to-back converters. 2. OVERVIEW OF THE SYNCHRONVERTER TECHNOLOGY A synchronverter is an inverter (converter) that mimics a synchronous generator (machine) (Zhong and Weiss, 2009, 2011). The core of the controller is the mathematical model of a synchronous generator, which is then wrapped with some functions to regulate the real power and reactive power, voltage and frequency. In this paper, the controllers wrapped around the model will be developed according to the applications in wind power. Hence, only the mathematical model of synchronous machines is outlined, as this is the core for the controllers of the two converters. Assume that the three identical stator windings of a synchronous generator are distributed in slots around the periphery of the uniform air gap. The stator windings can be regarded as concentrated coils having self-inductance L, mutual inductance −M ( with M > 0, the negative sign is due to the 2π 3 phase angle) and resistance Rs .
θ
Rs , Ls
ia
⎤
⎢ cos(θ − 2π ) ⎥ ⎥ cosθ =⎢ 3 ⎦, ⎣ 4π ) cos(θ − 3
⎡
sinθ
⎤
2π ⎥ ⎢ )⎥ = ⎢ sin(θ − sinθ 3 ⎦, ⎣ 4π ) sin(θ − 3
where θ is the rotor angle with respect to the Phase A winding. Then the phase terminal voltages v = [ va vb vc ]T of a generator can be written as di (1) v = e − Rs i − Ls , dt where Ls = L + M and e = [ ea eb ec ]T is the back emf due to the rotor movement given by − Mf dif cosθ. (2) e = Mf if θ˙ sinθ dt
The mechanical part of the generator is governed by 1 θ¨ = (Tm − Te − Dp θ˙g ), (3) J
where ·, · denotes the conventional inner product in R3 .
va
Rf , Lf
Field voltage v f
cosθ
where J is the moment of inertia of all the parts rotating with the rotor; Dp is a damping factor; Tm is the mechanical torque and Te is the electromagnetic torque
, (4) Te = Mf if i, sinθ
a-axis Rotor field axis
⎡
Dp
M
Tm
if
1 Js
Te vb ib
P Q
vc ic
b-axis
c-axis
Figure 2. Structure of an idealised three-phase round-rotor synchronous machine. Denote the flux vector and the current vector as Φa ia Φ = Φb , i = ib , Φc ic respectively, and introduce vectors
θ
1 s
θ
Eqn.(2) Eqn.(4) Eqn.(5)
M f if
e
i
Figure 3. The model of a synchronous machine. The real power and reactive power are, respectively, ˙ f if < i, sinθ >, P = θM ˙ Q = −θM f if < i, cosθ >.
(5)
The model can be described with the block diagram shown in Figure 3.
3. CONTROL OF THE ROTOR-SIDE CONVERTER As mentioned before, the rotor-side converter is to maintain a constant DC-link voltage. Hence, it is run as a PWM rectifier. Here, this is done via operating the PWM rectifier to mimic a synchronous motor. Denote the output voltage and current of the wind-turbine generator as vr = [ vra vrb vrc ]T and ir = [ ira irb irc ]T , respectively. The proposed control strategy is shown in Figure 4, which includes the model of a synchronous motor as the core of the control strategy. The model of a synchronous motor is more or less the same as the model of a generator discussed above, apart from that the direction of the stator current is defined opposite. Therefore, Equations (1) and (3) should be modified accordingly as vr = em + Rs ir + Ls
dir , dt
and 1 θ¨m = (Tme − Tmm − Dmp θ˙m ), Jm where the mechanical torque Tmm is the load to the motor. Here, this is generated by the PI controller that regulates the DC-link voltage. In order for the rotor-side converter, i.e., the virtual synchronous motor, to work properly, the frequency θ˙m inside the rectifier should be the same as or very close to the frequency θ˙r of vr and the terminal voltage should be synchronised with the voltage vr . Before the rectifier is connected to vr , its phase θm should be kept the same as that of vr in order to minimise the settling time following the connection. The traditional phase-locked loop (PLL) in the dq frame is not fast enough for this purpose (Ziarani et al., 2003). In this paper, the sinusoid-tracking algorithm (STA) (Ziarani and Konrad, 2004) is adopted to quickly provide the frequency signal and the phase information.
Figure 4. Control structure for the rotor-side converter The reactive power Qm of the rotor-side converter can be controlled to track the reference Qref . The tracking error between the reference value Qref and reactive power Qm 1 is fed into an integrator with a gain − K to regulate the field excitation Mf if so that the voltage em is changed. In order to obtain the unity power factor, Qref can be set as 0. 4. CONTROL OF THE GRID-SIDE CONVERTER
The control strategy involves in two channels: one to regulate the real power and the other to regulate the reactive power. The real power channel shown in Figure 4 has three cascaded control loops. The inner loop is the frequency regulation loop (with the feedback gain Dmp ), the middle loop is a torque loop (with the feedback coming from the current ir via the electromagnetic torque Tme ) and the outer loop is the DC-link voltage loop (with the feedback coming from the DC voltage Vdc ). The first two loops are part of the model of a virtual synchronous motor. When the rotor-side converter is connected to vr , its virtual frequency should track the frequency of vr . This can be done via feeding the difference between the frequency θ˙r obtained from the STA and the rectifier frequency θ˙m to the Dmp block, as done in the synchronverter (Zhong and Weiss, 2011). In this case, the constant Dmp represents the (imaginary) mechanical friction coefficient of the virtual motor. It is effectively the frequency droop coefficient defined as Dmp = − ∆∆T , which corresponds to that a θ˙m certain amount of change ∆T in the torque leads to the change ∆θ˙m in the frequency.
Figure 5. Control structure for the grid-side converter
The control objective for the grid-side converter is to send the maximum power generated from wind to the grid. Normally, variable-speed wind generation systems are more attractive than fixed-speed systems due to the high efficiency. However, it does not mean that the actual efficiency is always high in variable-speed generator systems. It depends on the control algorithm used to extract the output power from the wind turbine. An advanced technique will be designed to extract the maximum power from the wind turbine under all working conditions. In variable-speed generation systems, the wind turbine can be operated at its maximum power operating point for various wind speeds by maintaining the tip speed ratio to the value that maximises its aerodynamic efficiency. In order to achieve this ratio, the permanent magnet synchronous generator load line should be matched very closely to the maximum power line of the wind turbine. In a variable-speed wind turbine, the power Pw that can be obtained from wind is a cubic function of the wind speed vw , i.e, 1 3 Pw = ρπR2 vw Cp , (6) 2 where ρ is the air density, R is the turbine radius and . Cp = f (λ, β) is the power coefficient that depends on the tip speed ratio λ of the wind turbine and the angle of blades β. The tip speed ratio is defined as ωn R , λ= vw where ωn is the rotor speed of the turbine. Consequently, for different wind speeds, the optimal values of the tip speed and the pitch angle need to be followed in order to achieve the maximum Cp and therefore the maximum power output. The maximum power of the wind turbine can be calculated as 1 Rωn 3 Pm = ρπR2 Cpm ( ) = Kopt ωn3 , 2 λopt 5
where Kopt = 12 ρπCpm ( λR3 ). Taking the losses into opt account, the grid power reference can be chosen slightly smaller than Pm . In this paper, this is chosen as Pref = 0.95Koptωn3 . (7) This reference can be passed to the synchronverter so that the right amount of power is fed into the grid. The proposed control strategy for the grid-side converter is shown in Figure 5, where the inductor current, the capacitor voltage and the grid voltage are denoted as i = [ ia ib ic ]T , v = [ va vb vc ]T and vg = [ vga vgb vgc ]T , respectively. This is very similar to the controller for the synchronverter (Zhong and Weiss, 2011), with the real power reference set as (7). Because of the inherent capability of the synchronverter, this strategy is able to feed the real power to the grid while regulating the reactive power.
relative tolerance of 10−3 and a maximum step size of 2µs. The parameters of the system used in the simulations are given in Table 1. The wind turbine extracts power from wind and then converts it into mechanical power. The power coefficient Cp is calculated by using the following formula (Sun et al., 2003): 12.5 116 − 0.4 − 5)e− β Cp (λ, β) = 0.22( β with β=
1 −
1 λ+0.08λ
0.035 λ3 +1
.
For the simulated wind turbine, the optimal tip speed ratio λopt is 6.8 and the maximum power coefficient Cpm is 0.419. Table 1. Parameters of the system. Parameters Air density Rotor radius Inertia of the PMSG Mf if of the PMSG Friction factor of the PMSG Pole pairs of the PMSG Winding inductance of the PMSG Winding resistance of the PMSG DC-link voltage DC-link capacitance Inductance on the inverter side Inductance on the grid side Capacitance of the LCL filter Grid phase voltage (rms) Switching frequency
Value 1.2 [kg/m3 ] 1.2 [m] 0.0065 [kg·m2 ] 0.5 [V·s] 0 [N·m·s] 4 4 [mH] 0.135 [Ω] 400 [V] 5000 [µF] 2.2 [mH] 1.1 [mH] 22 [µF] 110 [V] 5 [kHz]
The simulation was carried out according to the following sequence of actions: 1) start the system, but keeping all the IGBTs off with the initial wind speed of 12m/s to establish the DC link voltage first (with Rdc = 150Ω); 2) start operating the IGBTs for both converters at t = 0.5s with Vref = 400V and Qref = 0 for the rotor-side converter to regulate the DC link voltage (with Rdc = 150Ω) and with Pref = 0 and Qref = 0 for the grid-side converter to synchronise with the grid; 3) turn the circuit breaker on to connect the grid-side converter to the grid at t = 0.8s . 4) set Pref = 0.95Koptωn3 at t = 1.5s and disconnect the DC load Rdc = 150Ω to send the maximum power to the grid; 5) change the wind speed to 15m/s at t = 3s. It is worth noting that, in the real system, the DC load Rdc is often referred to as a crowbar system, which can be activated when the DC-bus voltage exceeds a certain level.
5. SIMULATION RESULTS 5.1 Performance of the rotor-side converter Simulations were carried out to verify the control strategy described above in Matlab 7.6/Simulink/SimpowerSystems. The parameters for the rotor-side converter are given in The solver used in the simulations was obe23tb with a Table 2.
Table 2. Control parameters for the rotor-side converter Values
Parameters
Values
Jm Dmp Km
0.0122 6.0793 2430.1
Kp Ki
0.8 2
Cp
Parameters
with the voltage and, hence, the reactive power Qm was zero and the unity power factor was obtained.
Table 3. Control parameters for the grid-side converter Parameters
Values
0.0122 6.0793
K Dq
2430.1 386.7615
400 300 200 100 0 −100 −200 −300 2.8
vra
700 600 500 400 300 200
3.1
3.2
Tm [Nm]
Q [Var]
3 Time [s]
2 3 Time [s]
4
5
Pref
0
1
P
2 3 Time [s]
4
5
1000 500 0 −500 −1000
0
1
2 3 Time [s]
4
5
0
1
2 3 Time [s]
4
5
(b) Rotor speed
speed [rad/s]
(c) Reactive power Q sent to the grid 330 325 320 315 310 305 300
θ˙g
0
1
θ˙
2 3 Time [s]
4
5
(d) Grid frequency θ˙g and the frequency θ˙ of the grid-side converter 0
1
2 3 Time [s]
4
5
(c) DC-link voltage θ˙r
0
1
2 3 Time [s]
θ˙m
4
5
0
1
2 3 Time [s]
300 200 100 0 −100 −200 2.8
vga
2.9
3 Time [s]
ia
3.1
3.2
(e) Phase a voltage and current on the grid side Figure 7. Performance of the grid-side converter.
(d) Electric speed θ˙r of the PMSG and the speed θ˙m of the virtual synchronous machine 50 40 30 20 10 0
1
(b) Real power P sent to the grid and its reference Pref 2.9
[V/A]
ωn [rad/s] speed [rad/s]
Voltage [V]
500 400 300 200 100 0
5000 4000 3000 2000 1000 0
ira
(a) Voltage and current of Phase a before and after the change of the wind speed 150 120 90 60 30 0
0
(a) Power coefficient of the wind turbine P [W]
Values
J Dp
[V/A]
Parameters
0.5 0.4 0.3 0.2 0.1 0
4
5
(e) Torque of the wind turbine Figure 6. Performance of the rotor-side converter. The responses of the rotor-side converter are shown in Figure 6. The DC-link voltage was maintained very well at 400V after the system is connected to the grid. Obviously, the rotor-side converter worked under the variablefrequency-variable-amplitude mode and it well tracked the frequency of vr , which is in proportion to the rotor speed. The current drawn by the rotor-side converter was in phase
5.2 Performance of the grid-side converter The parameters for the grid-side converter are shown in Table 3, which were chosen largely the same as the ones for the rotor-side converter. The simulation results are shown in Figure 7. The connection of the system to the grid was very smooth without noticeable dynamics. The power coefficient Cp was kept almost maximum all the time after the system was requested to send the maximum power to the grid at t = 1.5sec and the real power P tracked the reference power Pref very well. Therefore, the maximum power point tracking was achieved by the gridside converter. When the wind speed changed, the power sent to the grid was changed very quickly. 6. CONCLUSIONS In this paper, a synchronverter-based control strategy is proposed for back-to-back converters applied in variable
speed wind turbines equipped with PMSG. The DC link voltage is controlled by the rotor-side converter and the MPPT is achieved by the grid-side converter. Both converters are controlled according to the recently-developed synchronverter technology. Hence, the whole system is equivalent to a generator–motor–generator system. The proposed control strategy is able to maintain normal operation for the wind turbine. REFERENCES Baroudi, J., Dinavahi, V., and Knight, A. (2005). A review of power converter topologies for wind generators. In Proc. of IEEE International Conference on Electric Machines and Drives, 458–465. Bollen, M.H. (2000). Understanding Power Quality Problems: Voltage Sags and Interruptions. Wiley-IEEE Press. Bueno, E., Cobreces, S., Rodriguez, F., Hernandez, A., and Espinosa, F. (2008). Design of a back-to-back NPC converter interface for wind turbines with squirrel-cage induction generator. IEEE Trans. Energy Convers., 23(3), 932–945. Cardenas, R. and Pena, R. (2004). Sensorless vector control of induction machines for variable-speed wind energy applications. IEEE Trans. Energy Convers., 19(1), 196–205. Gomis-Bellmunt, O., Junyent-Ferre, A., Sumper, A., and Bergas-Jan, J. (2008). Ride-through control of a doubly fed induction generator under unbalanced voltage sags. IEEE Trans. Energy Convers., 23(4), 1036–1045. Hansen, A. and Michalke, G. (2009). Multi-pole permanent magnet synchronous generator wind turbines’ grid support capability in uninterrupted operation during grid faults. IET Proc. Renewable Power Generation, 3(3), 333–348. Kim, K.H., Jeung, Y.C., Lee, D.C., and Kim, H.G. (2010). Robust control of PMSG wind turbine systems with back-to-back PWM converters. In Proc. of the 2nd Power Electronics for Distributed Generation Systems (PEDG), 433–437. McGranaghan, M., Mueller, D., and Samotyj, M. (1993). Voltage sags in industrial systems. IEEE Trans. Ind. Appl., 29(2), 397–403. Pena, R., Clare, J., and Asher, G. (1996a). Doubly fed induction generator using back-to-back PWM converters and its application to variable-speed wind-energy
generation. IEE Proc. Electric Power Appli., 143(3), 231–241. Pena, R., Clare, J., and Asher, G. (1996b). A doubly fed induction generator using back-to-back PWM converters supplying an isolated load from a variable speed wind turbine. IEE Proc. Electric Power Appli., 143(5), 380–387. Portillo, R., Prats, M., Leon, J., Sanchez, J., Carrasco, J., Galvan, E., and Franquelo, L. (2006). Modeling strategy for back-to-back three-level converters applied to highpower wind turbines. IEEE Trans. Ind. Electron., 53(5), 1483–1491. Singh, M., Khadkikar, V., and Chandra, A. (2011). Grid synchronisation with harmonics and reactive power compensation capability of a permanent magnet synchronous generator-based variable speed wind energy conversion system. IET Proc. Power Electron., 4(1), 122–130. Spera, D. (2009). Wind turbine technology: fundamental concepts of wind turbine engineering. ASME Press. Sun, T., Chen, Z., and Blaabjerg, F. (2003). Voltage recovery of grid-connected wind turbines after a shortcircuit fault. In Proc. of Industrial Electronics Society (IECON), 2723–2728. Teodorescu, R. and Blaabjerg, F. (2004). Flexible control of small wind turbines with grid failure detection operating in stand-alone and grid-connected mode. IEEE Trans. Power Electron., 19(5), 1323–1332. Yuan, X., Wang, F., Boroyevich, D., Li, Y., and Burgos, R. (2009). DC-link voltage control of a full power converter for wind generator operating in weak-grid systems. IEEE Trans. Power Del., 24(9), 2178–2192. Zhong, Q.C. and Weiss, G. (2009). Static synchronous generators for distributed generation and renewable energy. In Proc. of IEEE PES Power Systems Conference & Exhibition (PSCE). Zhong, Q.C. and Weiss, G. (2011). Synchronverters: Inverters that mimic synchronous generators. IEEE Trans. Ind. Electron., 58(4), 1259–1267. Ziarani, A.K. and Konrad, A. (2004). A method of extraction of nonstationary sinusoids. Signal Processing, 84(8), 1323–1346. Ziarani, A.K., Konrad, A., and Sinclair, A.N. (2003). A novel time-domain method of analysis of pulsed sine wave signals. IEEE Trans. Instrum. Meas., 52(3), 809– 814.
Loughborough University, Leicestershire, LE11 3TU, United Kingdom Email: [email protected]. ∗∗ The University of Sheffield, Sheffield, S1 3JD, United Kingdom Tel: +44-114 22 25630, fax: +44-114 22 25683, Email: Q.Zhong@Sheffield.ac.uk.
Abstract Back-to-back PWM converters are becoming a realistic alternative to the conventional converters in high-power wind-energy applications. In this paper, a control strategy based on the synchronverter technology is proposed for back-to-back PWM converters. Both converters are run as synchronverters, which are mathematically equivalent to the conventional synchronous generators. The rotor-side converter is responsible for maintaining the DC link voltage and the grid-side converter is responsible for the maximum power point tracking (MPPT). Simulation results show that the proposed method operates properly. Keywords: Synchronverter, virtual synchronous generators, back-to-back converter, wind turbine, maximum power point tracking (MPPT), voltage sags 1. INTRODUCTION During the last decade, more and more attention has been paid to utilising renewable energy sources to tackle the energy crisis we are facing. Wind power has been regarded as one of the main renewable power sources to replace/complement fossil fuels. Wind energy has many advantages such as no pollution, relatively low capital cost involved and the short gestation period. Many countries have set strategic plans to develop technologies for utilising wind power and a lot of researchers have shifted into this area. Wind generation systems can be divided into variablespeed generation systems and fixed-speed generation systems. Variable-speed systems are more attractive than fixed-speed systems due to the improved wind energy production and its reduction of flicker problems. Nowadays, the most-used topologies for variable-speed wind turbines are doubly-fed induction generators with wound rotors, induction generators with squirrel cage rotors and synchronous generators with permanent magnets (Spera, 2009). In these three cases, one of the most popular grid connection topologies is to adopt back-to-back voltage source inverters to interface with the grid (Baroudi et al., 2005) to provide unity power factor and low harmonic distortion of current, as shown in Figure 1. The synchronous generator is connected to the grid through a full-scale back-to-back PWM converter and the conversion stage consists of a rotor-side converter and a grid-side converter. This work was supported by the Engineering and Physical Sciences Research Council, U.K., and Nheolis, France under the Dorothy Hodgkin Postgraduate Awards (DHPA) scheme and under Grant EP/J001333/1.
Many different control strategies have been developed for back-to-back PWM converters in wind power applications. Normally, the maximum power point tracking is achieved by controlling the rotor-side converter and the DC link voltage is controlled by the grid-side converter (Pena et al., 1996a,b; Cardenas and Pena, 2004; Teodorescu and Blaabjerg, 2004; Portillo et al., 2006; Bueno et al., 2008; Singh et al., 2011). In this case, the DC link voltage is increased due to the continuous operation of wind turbine and generator when grid faults happen. The gridside converter may be out of control when grid voltage sags happen because voltage sags reduce generator torque (Gomis-Bellmunt et al., 2008), which accelerates the rotor and causes mechanical instability unless normal voltage levels are quickly restored. As a fail-safe mechanism against equipment damage, wind turbines are designed to automatically disconnect themselves from the utility grid under these extreme conditions (McGranaghan et al., 1993; Bollen, 2000). Therefore, in some other strategies, the rotor-side converter controls the DC link voltage and the grid-side converter controls the power of the wind turbine fed to the grid (Yuan et al., 2009; Hansen and Michalke, 2009; Kim et al., 2010). In both cases, the control strategies are mainly based on the vector control approach in the d-q reference frame to control the direct component and the quadrature component, respectively. In this paper, an original control strategy based on the synchronverter technology, which is to operate a converter to mimic a synchronous machine (Zhong and Weiss, 2011), is proposed for back-to-back converters in wind power applications. The rotor-side converter is run as a synchronous motor and the grid-side converter is run as a synchronous generator. As a result, the whole system behaves as a generator–motor–generator system.
LCL filter
~
Grid
PMSG
Three-phase rectifier
Three-phase inverter
Figure 1. Connection of wind power generation system to grid through back-to-back converters. 2. OVERVIEW OF THE SYNCHRONVERTER TECHNOLOGY A synchronverter is an inverter (converter) that mimics a synchronous generator (machine) (Zhong and Weiss, 2009, 2011). The core of the controller is the mathematical model of a synchronous generator, which is then wrapped with some functions to regulate the real power and reactive power, voltage and frequency. In this paper, the controllers wrapped around the model will be developed according to the applications in wind power. Hence, only the mathematical model of synchronous machines is outlined, as this is the core for the controllers of the two converters. Assume that the three identical stator windings of a synchronous generator are distributed in slots around the periphery of the uniform air gap. The stator windings can be regarded as concentrated coils having self-inductance L, mutual inductance −M ( with M > 0, the negative sign is due to the 2π 3 phase angle) and resistance Rs .
θ
Rs , Ls
ia
⎤
⎢ cos(θ − 2π ) ⎥ ⎥ cosθ =⎢ 3 ⎦, ⎣ 4π ) cos(θ − 3
⎡
sinθ
⎤
2π ⎥ ⎢ )⎥ = ⎢ sin(θ − sinθ 3 ⎦, ⎣ 4π ) sin(θ − 3
where θ is the rotor angle with respect to the Phase A winding. Then the phase terminal voltages v = [ va vb vc ]T of a generator can be written as di (1) v = e − Rs i − Ls , dt where Ls = L + M and e = [ ea eb ec ]T is the back emf due to the rotor movement given by − Mf dif cosθ. (2) e = Mf if θ˙ sinθ dt
The mechanical part of the generator is governed by 1 θ¨ = (Tm − Te − Dp θ˙g ), (3) J
where ·, · denotes the conventional inner product in R3 .
va
Rf , Lf
Field voltage v f
cosθ
where J is the moment of inertia of all the parts rotating with the rotor; Dp is a damping factor; Tm is the mechanical torque and Te is the electromagnetic torque
, (4) Te = Mf if i, sinθ
a-axis Rotor field axis
⎡
Dp
M
Tm
if
1 Js
Te vb ib
P Q
vc ic
b-axis
c-axis
Figure 2. Structure of an idealised three-phase round-rotor synchronous machine. Denote the flux vector and the current vector as Φa ia Φ = Φb , i = ib , Φc ic respectively, and introduce vectors
θ
1 s
θ
Eqn.(2) Eqn.(4) Eqn.(5)
M f if
e
i
Figure 3. The model of a synchronous machine. The real power and reactive power are, respectively, ˙ f if < i, sinθ >, P = θM ˙ Q = −θM f if < i, cosθ >.
(5)
The model can be described with the block diagram shown in Figure 3.
3. CONTROL OF THE ROTOR-SIDE CONVERTER As mentioned before, the rotor-side converter is to maintain a constant DC-link voltage. Hence, it is run as a PWM rectifier. Here, this is done via operating the PWM rectifier to mimic a synchronous motor. Denote the output voltage and current of the wind-turbine generator as vr = [ vra vrb vrc ]T and ir = [ ira irb irc ]T , respectively. The proposed control strategy is shown in Figure 4, which includes the model of a synchronous motor as the core of the control strategy. The model of a synchronous motor is more or less the same as the model of a generator discussed above, apart from that the direction of the stator current is defined opposite. Therefore, Equations (1) and (3) should be modified accordingly as vr = em + Rs ir + Ls
dir , dt
and 1 θ¨m = (Tme − Tmm − Dmp θ˙m ), Jm where the mechanical torque Tmm is the load to the motor. Here, this is generated by the PI controller that regulates the DC-link voltage. In order for the rotor-side converter, i.e., the virtual synchronous motor, to work properly, the frequency θ˙m inside the rectifier should be the same as or very close to the frequency θ˙r of vr and the terminal voltage should be synchronised with the voltage vr . Before the rectifier is connected to vr , its phase θm should be kept the same as that of vr in order to minimise the settling time following the connection. The traditional phase-locked loop (PLL) in the dq frame is not fast enough for this purpose (Ziarani et al., 2003). In this paper, the sinusoid-tracking algorithm (STA) (Ziarani and Konrad, 2004) is adopted to quickly provide the frequency signal and the phase information.
Figure 4. Control structure for the rotor-side converter The reactive power Qm of the rotor-side converter can be controlled to track the reference Qref . The tracking error between the reference value Qref and reactive power Qm 1 is fed into an integrator with a gain − K to regulate the field excitation Mf if so that the voltage em is changed. In order to obtain the unity power factor, Qref can be set as 0. 4. CONTROL OF THE GRID-SIDE CONVERTER
The control strategy involves in two channels: one to regulate the real power and the other to regulate the reactive power. The real power channel shown in Figure 4 has three cascaded control loops. The inner loop is the frequency regulation loop (with the feedback gain Dmp ), the middle loop is a torque loop (with the feedback coming from the current ir via the electromagnetic torque Tme ) and the outer loop is the DC-link voltage loop (with the feedback coming from the DC voltage Vdc ). The first two loops are part of the model of a virtual synchronous motor. When the rotor-side converter is connected to vr , its virtual frequency should track the frequency of vr . This can be done via feeding the difference between the frequency θ˙r obtained from the STA and the rectifier frequency θ˙m to the Dmp block, as done in the synchronverter (Zhong and Weiss, 2011). In this case, the constant Dmp represents the (imaginary) mechanical friction coefficient of the virtual motor. It is effectively the frequency droop coefficient defined as Dmp = − ∆∆T , which corresponds to that a θ˙m certain amount of change ∆T in the torque leads to the change ∆θ˙m in the frequency.
Figure 5. Control structure for the grid-side converter
The control objective for the grid-side converter is to send the maximum power generated from wind to the grid. Normally, variable-speed wind generation systems are more attractive than fixed-speed systems due to the high efficiency. However, it does not mean that the actual efficiency is always high in variable-speed generator systems. It depends on the control algorithm used to extract the output power from the wind turbine. An advanced technique will be designed to extract the maximum power from the wind turbine under all working conditions. In variable-speed generation systems, the wind turbine can be operated at its maximum power operating point for various wind speeds by maintaining the tip speed ratio to the value that maximises its aerodynamic efficiency. In order to achieve this ratio, the permanent magnet synchronous generator load line should be matched very closely to the maximum power line of the wind turbine. In a variable-speed wind turbine, the power Pw that can be obtained from wind is a cubic function of the wind speed vw , i.e, 1 3 Pw = ρπR2 vw Cp , (6) 2 where ρ is the air density, R is the turbine radius and . Cp = f (λ, β) is the power coefficient that depends on the tip speed ratio λ of the wind turbine and the angle of blades β. The tip speed ratio is defined as ωn R , λ= vw where ωn is the rotor speed of the turbine. Consequently, for different wind speeds, the optimal values of the tip speed and the pitch angle need to be followed in order to achieve the maximum Cp and therefore the maximum power output. The maximum power of the wind turbine can be calculated as 1 Rωn 3 Pm = ρπR2 Cpm ( ) = Kopt ωn3 , 2 λopt 5
where Kopt = 12 ρπCpm ( λR3 ). Taking the losses into opt account, the grid power reference can be chosen slightly smaller than Pm . In this paper, this is chosen as Pref = 0.95Koptωn3 . (7) This reference can be passed to the synchronverter so that the right amount of power is fed into the grid. The proposed control strategy for the grid-side converter is shown in Figure 5, where the inductor current, the capacitor voltage and the grid voltage are denoted as i = [ ia ib ic ]T , v = [ va vb vc ]T and vg = [ vga vgb vgc ]T , respectively. This is very similar to the controller for the synchronverter (Zhong and Weiss, 2011), with the real power reference set as (7). Because of the inherent capability of the synchronverter, this strategy is able to feed the real power to the grid while regulating the reactive power.
relative tolerance of 10−3 and a maximum step size of 2µs. The parameters of the system used in the simulations are given in Table 1. The wind turbine extracts power from wind and then converts it into mechanical power. The power coefficient Cp is calculated by using the following formula (Sun et al., 2003): 12.5 116 − 0.4 − 5)e− β Cp (λ, β) = 0.22( β with β=
1 −
1 λ+0.08λ
0.035 λ3 +1
.
For the simulated wind turbine, the optimal tip speed ratio λopt is 6.8 and the maximum power coefficient Cpm is 0.419. Table 1. Parameters of the system. Parameters Air density Rotor radius Inertia of the PMSG Mf if of the PMSG Friction factor of the PMSG Pole pairs of the PMSG Winding inductance of the PMSG Winding resistance of the PMSG DC-link voltage DC-link capacitance Inductance on the inverter side Inductance on the grid side Capacitance of the LCL filter Grid phase voltage (rms) Switching frequency
Value 1.2 [kg/m3 ] 1.2 [m] 0.0065 [kg·m2 ] 0.5 [V·s] 0 [N·m·s] 4 4 [mH] 0.135 [Ω] 400 [V] 5000 [µF] 2.2 [mH] 1.1 [mH] 22 [µF] 110 [V] 5 [kHz]
The simulation was carried out according to the following sequence of actions: 1) start the system, but keeping all the IGBTs off with the initial wind speed of 12m/s to establish the DC link voltage first (with Rdc = 150Ω); 2) start operating the IGBTs for both converters at t = 0.5s with Vref = 400V and Qref = 0 for the rotor-side converter to regulate the DC link voltage (with Rdc = 150Ω) and with Pref = 0 and Qref = 0 for the grid-side converter to synchronise with the grid; 3) turn the circuit breaker on to connect the grid-side converter to the grid at t = 0.8s . 4) set Pref = 0.95Koptωn3 at t = 1.5s and disconnect the DC load Rdc = 150Ω to send the maximum power to the grid; 5) change the wind speed to 15m/s at t = 3s. It is worth noting that, in the real system, the DC load Rdc is often referred to as a crowbar system, which can be activated when the DC-bus voltage exceeds a certain level.
5. SIMULATION RESULTS 5.1 Performance of the rotor-side converter Simulations were carried out to verify the control strategy described above in Matlab 7.6/Simulink/SimpowerSystems. The parameters for the rotor-side converter are given in The solver used in the simulations was obe23tb with a Table 2.
Table 2. Control parameters for the rotor-side converter Values
Parameters
Values
Jm Dmp Km
0.0122 6.0793 2430.1
Kp Ki
0.8 2
Cp
Parameters
with the voltage and, hence, the reactive power Qm was zero and the unity power factor was obtained.
Table 3. Control parameters for the grid-side converter Parameters
Values
0.0122 6.0793
K Dq
2430.1 386.7615
400 300 200 100 0 −100 −200 −300 2.8
vra
700 600 500 400 300 200
3.1
3.2
Tm [Nm]
Q [Var]
3 Time [s]
2 3 Time [s]
4
5
Pref
0
1
P
2 3 Time [s]
4
5
1000 500 0 −500 −1000
0
1
2 3 Time [s]
4
5
0
1
2 3 Time [s]
4
5
(b) Rotor speed
speed [rad/s]
(c) Reactive power Q sent to the grid 330 325 320 315 310 305 300
θ˙g
0
1
θ˙
2 3 Time [s]
4
5
(d) Grid frequency θ˙g and the frequency θ˙ of the grid-side converter 0
1
2 3 Time [s]
4
5
(c) DC-link voltage θ˙r
0
1
2 3 Time [s]
θ˙m
4
5
0
1
2 3 Time [s]
300 200 100 0 −100 −200 2.8
vga
2.9
3 Time [s]
ia
3.1
3.2
(e) Phase a voltage and current on the grid side Figure 7. Performance of the grid-side converter.
(d) Electric speed θ˙r of the PMSG and the speed θ˙m of the virtual synchronous machine 50 40 30 20 10 0
1
(b) Real power P sent to the grid and its reference Pref 2.9
[V/A]
ωn [rad/s] speed [rad/s]
Voltage [V]
500 400 300 200 100 0
5000 4000 3000 2000 1000 0
ira
(a) Voltage and current of Phase a before and after the change of the wind speed 150 120 90 60 30 0
0
(a) Power coefficient of the wind turbine P [W]
Values
J Dp
[V/A]
Parameters
0.5 0.4 0.3 0.2 0.1 0
4
5
(e) Torque of the wind turbine Figure 6. Performance of the rotor-side converter. The responses of the rotor-side converter are shown in Figure 6. The DC-link voltage was maintained very well at 400V after the system is connected to the grid. Obviously, the rotor-side converter worked under the variablefrequency-variable-amplitude mode and it well tracked the frequency of vr , which is in proportion to the rotor speed. The current drawn by the rotor-side converter was in phase
5.2 Performance of the grid-side converter The parameters for the grid-side converter are shown in Table 3, which were chosen largely the same as the ones for the rotor-side converter. The simulation results are shown in Figure 7. The connection of the system to the grid was very smooth without noticeable dynamics. The power coefficient Cp was kept almost maximum all the time after the system was requested to send the maximum power to the grid at t = 1.5sec and the real power P tracked the reference power Pref very well. Therefore, the maximum power point tracking was achieved by the gridside converter. When the wind speed changed, the power sent to the grid was changed very quickly. 6. CONCLUSIONS In this paper, a synchronverter-based control strategy is proposed for back-to-back converters applied in variable
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