14th International Power Electronics and Motion Control Conference, EPE-PEMC 2010
New Control Strategy for Variable Speed Wind Turbine with DC-DC converters Vladimir Lazarov*, Daniel Roye†, Dimitar Spirov*† and Zahari Zarkov* *
Technical University-Sofia, Bulgaria, e-mail:
[email protected],
[email protected],
[email protected] † G2ELab, INP Grenoble, Saint-Martin-d'Hères, France, e-mail:
[email protected]
Abstract— The paper studies the performance of variable speed wind turbine (VSWT) configuration with noninverting buck-boost converter. The wind turbine systems consist of permanent magnet synchronous generator (PMSG) connected to diode rectifier, DC chopper and load. New control strategy, based on the maximum power point tracking (MPPT) and limited power point tracking (LPPT) algorithms is used to improve the system operation. When necessary to limit the power injected to the grid, due to system operator demands, a control unit is implementing to switch between two regimes of wind turbine operation: at maximum power and at limited power. The MPP tracker is simple perturb and observation (P&O) controller in combination with two optimum wind turbines power/torque versus speed characteristics. Two control loops: inner feed forward current control loop and outer voltage control closed loop are applied for the non-inverting buck-boost converter. The performance of the dynamic models and the control loops is tested under various wind conditions. The simulation results are shown. The results prove the strategy and models reliability. Keywords—wind energy, converter control, modeling, simulation.
I. INTRODUCTION The permanent magnet synchronous generator (PMSG) based variable speed wind turbines (VSWTs) is widely used in the wind industry because of his advantages such as compact size and weight, dense flux, etc. To operate in
VSWT system, this generator should be connected either with controlled rectifier or diode rectifier. Thus, two configurations are possible: full size back-to-back configuration with two voltage source converters as rectifier and inverter and DC capacitor and configuration with DC-DC converter. The Boost converter is most used DC chopper for such configuration, possessing important advantages in islanding systems (micro hydro turbines) or in hybrid operation systems [1]. However, the boost converter has a major drawback limiting the range of the voltages and respectively the generator speed. For the present study, novel configuration with diode rectifier and non-inverting buck-boost DC chopper is investigated. The non-inverting buck-boost converter is interesting for his ability to produce higher or lower DC voltage than the source voltage [2]. This specific feature of the converter may be very useful in the cases of high wind speeds and when the network system operator demands less power to be transferred into the grid [3]. Combined with appropriate control strategy, the advantages of this particular DC-DC converter can ensure the VSWT with more flexibility and operation time. The proposed new control strategy is combination of hybrid MPPT algorithm [4] for the normal operation of the VSWT and Limited Power Point Tracking (LPPT) logic algorithm for the limit power operation and represent an electrical mode to limit the aero dynamical power instead of using mechanical pitch system. The advantages of the faster electrical system response and his relatively simple control can make the VSWT very attractive for standard networks application, as well for smart grid systems. VSWT Electrical unit
VSWT Aero dynamical / Mechanical unit
DC
Wind profile
Wind turbine
Drive train
Speed PMSG
Diode rectifier
DC
Boost converter
Duty ratio
P elect
LOAD
VSWT Control unit
MPPT Controller
speed
LPPT Operator Fig. 1. Control concept of VSWT with non-inverting buck-boost DC-DC converter.
978-1-4244-7855-2/10/$26.00 ©2010 IEEE
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Control strategy
d
II. SYSTEM MODELING The considered configuration is presented in Fig. 1. In order to investigate the different modes of operations, every element of the conversion system is modelled and simulations are performed. The models are developed in the MATLAB/Simulink® software environment. A. Wind turbine model The wind turbine extracts the wind aero dynamical power. The model of the wind turbine uses several inputs to estimate precisely the mechanical torque and power, such as: the wind speed, the blade pitch angle and the rotor speed. The wind speed is provided by a wind model. Detailed wind models for complex aero dynamical calculation can be found in [5]and [6]. For the electrical simulations in this study, simplifying model is used. Typical wind profile is shown on Fig. 2.
15 Wind speed [m/s]
The turbine rotor swing is described by a standard onemass model. B. PMSG and diode rectifier models The models of the generator and the diode rectifier (DR) are developed using the SimPowerSystem® library in the Matlab/Simulink®. The DR is universal bridge 3 arms diode rectifier.
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C. Non-inverting buck-boost converter model The non-inverting buck-boost converter has two switches, driven synchronously by PWM modulator as it is shown in Fig. 4.
10
5
Fig. 3. Power coefficient curves for 2kW wind turbine model.
0
10
20
30
40
50 Time [s]
60
70
80
90
100
Fig. 2. Typical wind profile.
The aero dynamical power is described by (1)
Pwind
1 = ρAν 3C p (λ, θ) 2
Fig. 4. Non-inverting buck-boost converter.
(1)
Where ρ is the air density equal to 1.225 kg/m3, A is the turbine blade surface, v is the wind speed and Cp is turbine power coefficient which depends on the tip speed ratio (2) and θ is the pitch angle. The power coefficient is different for every particular turbine and a convenient way to reproduce the power curve is found in [7], using (2) and (3). ⎛a ⎞ C p = a1 ⎜⎜ 2 − a3θ − a4 ⎟⎟e ⎝ λi ⎠
− a5 λi
⎛ 1 b ⎞ λ = ⎜⎜ − 3 2 ⎟⎟ i ⎝ λ + b1θ θ + 1 ⎠
This model is similar to the model of the buck-boost converter, but the output voltage polarity is not inverted. The voltage ratio is defined as:
VDCout = −u (1 − u ) VDCin
Where VDCin is the supply voltage, VDCout is the output voltage and u is the duty cycle ratio. The state-space equation of the converter (5) can be used in average Simulink models.
(2)
⎡ ⎡ x1 ⎤ ⎢ 0 ⎢ x ⎥ = ⎢1 − u ⎣ 2⎦ ⎢ ⎣ C
(3)
The coefficients ai and bi are chosen to fit very small power wind turbine (approximately 2 kW). The pitch angle is θ and λ is the tip speed ratio (TSR). The power coefficient of the turbine is shown in Fig. 3.
(4)
1− u ⎤ ⎡u ⎤ L ⎥ ⎡ x1 ⎤ + ⎢ ⎥V 1 ⎥ ⎢⎣ x2 ⎥⎦ ⎢ L ⎥ DCin ⎥ − ⎣0⎦ C ⎦
−
(5)
Depending on the control strategy, the converter is driven in buck or in boost mode. The non-inverting buckboost converter model is implemented in the study simulations using the electrical ports of Matlab SimPowerSystems® library, reproducing the electrical circuit in Fig. 4.
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D. Converter control The model of the converter control is based on linear PI current regulator and pulse width modulator, generating the drive signal. The regulator compares the current trough the boost inductance signal with current reference set point from the power point tracker and the error is process to the PWM generator. The converter drive diagram can be seen in Fig. 5. Power point tracker
i*
e
Current sense
PI
d
PWM
u
i
Fig. 5. DC-DC converter controller.
III. NEW POWER CONTROL STRATEGY In order to extract the maximum power available at various wind speeds, two different control algorithms are normally applied to the VSWT: pitch angle control and speed (torque) control. The pitch control algorithm is used to change the pitch angle and the blades turn out slightly of the wind stream as so limiting the aero dynamical power in above rated wind speeds. This control acts directly upon an additional hydraulic system and is very important to protect the blades from breaking. The speed control algorithm serves to keep the generator rotor speed in certain boundaries. As the wind
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x 10
14
12
Power [W ] Power [W]
5
6m/s 8m/s 10m/s 11m/s 12m/s 13m/s 14m/s MPP curve LPP curve at 90% LPP curve at 80% LPP curve at 70% LPP curve at 50%
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fluctuates, the rotor will accelerate or decelerate in order to maintain that TSR, which give the maximum power coefficient. The control governs the generator by power converters electrical means. The grid synchronization is also accomplished by the converters (not considered in this work). As the foreseen power converter configuration consists of passive diode rectifier and of DC-DC converter, the speed control is achieved by the noninverting buck-boost converter. The reference signal for the converter drive is derived from the power point tracker. The tracker is ruled by new control strategy. The strategy is focused on the possibility to control the VSWT in the right-side of power coefficient curve, only using the wind turbine generator and the power converters, instead of the pitch mechanism. This strategy is based on hybrid MPP tracker [8] with simple perturb and observation (P&O) algorithm [9], limited power point tracker, switch logic algorithm and predefined power/torque versus speed wind turbine characteristics. Two specific regime of operation are distinguished: normal turbine operation and restricted turbine operation. When the conditions are normal, i.e. all produced electric power is authorised to be grid injected, the control strategy rely on the MPPT algorithm to keep the turbine converting the maximum available aero dynamical power. When conditions change, i.e. the network system operator enforces the turbine to limit the power transferred to the grid below of the maximum available, the switch logic algorithm enables the LPPT algorithm. The algorithm keeps the turbine at one of the limited power point curves, as it can be seen on Fig. 6, depending on the restricted conditions.
Region of MPPT control
Region of LPPT control
10
8
6
4
2
0
0
1
2
3
4 Mechanical speed [rad/s]
5
Fig. 6. Regions of MPP and LPP control.
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6
7
8
Over again, the switch logic algorithm recalls the hybrid MPPT algorithm, when restricted conditions are cancelled. Normally, the MPP tracker count on the P&O algorithm to find the maximum point. The algorithm is implemented and is shown in Fig. 7 and Fig. 8.
P(k); ω(k)
250
Torque (Nm)
200
150
100
Inputs 50
0 0
ΔP = P(k) - P(k-1); Δω = ω(k) - ω(k-1);
10
20
30
40
50
60
70
Speed (rad/s)
Discretization MPP curve
LPP curve at 70%
LPP curve at 40%
Fig. 9. Predefined torque curves.
Kt = Δω/ΔP; |Δω*(k)| = |ΔP(k).Kt|
IV. SIMULATION RESULTS The simulations with models of the above mentioned configuration in MATLAB/Simulink® were performed. The non-inverting buck-boost converter is controlled in boost mode, which is suitable for variable speed wind turbine operation. The input and output converter voltages are shown in Fig. 11, following lightly the changes of the wind profile at Fig. 10. The inductor current and the reference current show adequate convergence and fast controller response in Fig. 12.
Initialization
If (Δω*(k-1) = = 0) S = Sign [ΔP]; else S = Sign [ΔP].Sign[Δω*(k-1)]; Δω*(k) = S.|ΔP(k).Kt| Computation
7
Wind speed [m/s]
If (|ΔP(k)| < = P band) ω*(k) = ω*(k-1); else ω*(k) = ω*(k-1) + Δω*(k); Update; End;
Output
ω*(k)
6.5
6
5.5 0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
1.6
1.8
2
Time [s]
Fig. 10. Wind speed.
Fig. 7. Perturb and observe (P&O) algorithm. 660 640
w
1/Z
620
P
1/Z
DC voltage [V]
600
W*
Non-inverting buck-boost DC voltage Diode rectifier DC voltage
580 560 540
Kt
520 500
Fig. 8. Simplified Simulink model of the P&O controller.
480 0.4
0.6
0.8
1
1.2
1.4
Time [s]
Nevertheless, when sudden large change in the wind speed occurs, the MPP tracker use predefined turbine characteristics of the MPPT curve as it shown in Fig. 9.
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Fig. 11. DC voltages at real wind conditions.
3
controller seems to be promising. Nevertheless, investigation in more complex voltage control strategy for the non-inverting buck-boost chopper is foreseen to improve the advantages of this type of converter in high wind speed region and increased rotor speed. The advantages of the LPP control strategy can be also applied in hybrid systems and autonomous grids, along with noninverting buck-boost converter or other power converter configuration as boost DC-DC converter.
Converter current Reference current
2.8 2.6 2.4 Current [A]
2.2 2 1.8 1.6 1.4 1.2 1 0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Time [s]
Fig. 12. Reference and converter currents with MPPT control.
2200 2000
ACKNOWLEDGMENT The authors would like to thank the Bulgarian National Research Fund for the financial support (contract EE 106/07) and the Technical University-Sofia for the financial aid (contract 102ни225-1/2010) REFERENCES
P curve MAX P curve DC converter with LPPT at 100% P curve DC converter with LPPT at 70%
[1]
1800
Power [W]
1600 Restricted condition of 70%
[2]
1400 1200 1000
[3]
800 600 0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Time [s]
[4]
Fig. 13. Maximum and converter power curve with MPP and LPP tracking.
The converter power curve is close to the turbine maximum power curve for about 10 m/s wind speed of the modeled turbine, as it shown on Fig. 13(upper curves) and the turbine convert almost all available power. The converter power curve is below the imposed restricted limit, in Fig. 13 (bottom curve), even thought the turbine continues to operate and to transfer electric power to the network. V. CONCLUSION The simulation results display satisfying convergence of the converter power curve with the turbine maximum power curve and good performance of the LPP tracker. The non-inverting buck-boost converter operates satisfactorily with the new control strategy and the combination of the non-inverting chopper and this new
[5]
[6] [7] [8]
[9]
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