2014 Ninth International Conference on Ecological Vehicles and Renewable Energies (EVER)
Flatness-based Control of a Variable-Speed WindEnergy System Connected to the Grid Merzak Aimene, Alireza Payman and Brayima Dakyo. GREAH Laboratory, University of Le Havre, Le Havre, France, 75, rue Bellot - 76058 Le Havre cedex FRANCE
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[email protected] Abstract— In this paper, a new nonlinear control method based on differential flatness is applied to a high-power wind energy conversion system connected to the grid. The control system is done by planning the appropriate trajectories on components of the output variable vector of the system. The main advantage of the proposed method is control of the system even during the transient state as well as the high performance. The studied system includes a three-bladed horizontal wind turbine and a permanent magnet synchronous generator (PMSG) which is connected to the grid through a back to back converter and a filter. In order to study performance of the control strategy, a random profile of the wind speed has been used. The simulation results obtained in Matlab/Simulink environment are presented to validate efficiency of the control strategy. Keywords— Flatness based control, Variable-speed, wind turbine, PMSG, Grid Control.
I.
INTRODUCTION
The problem of climate change, high price of oil, increasing resistance on the use of coal, oil and uranium are the main reasons of the rapid development of the production of wind energy [1]. At the end of 2010, wind power capacity installed worldwide has reached 193 GW, at the end of 2013 it reached 273 GW and it is expected that it should increase by more than 400% to reach 1,107 GW in 2030 [1]. The wind turbines can operate at fixed or variable speed. In the first case, the rotor speed is fixed at the speed which is determined by the frequency of the grid. In the second case, a direct drive permanent-magnet synchronous generator operating at variable speeds is connected to the grid through a full-scale frequency converter. That leads to economies and removing the difficult and expensive implementation of equipment [2].
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Various topologies and different methods have been proposed to product the electrical energy and to control the power delivered to the grid. In this paper, a new control strategy based on the flatness properties is proposed to control of a variable-speed wind energy system connected to the grid, shown on Fig.1. This method has been used to manage the energy in an electrical hybrid system [3,4], to control a permanent magnet synchronous motors in [5, 6] and to control induction machines in [7, 8], In [7], it has been shown that this type of control can improve performance of the system in transient state in comparison with the traditional vector control method. The main advantage of this control method is the ability of predicting behavior of the system state variables in the transient state as well as the steady state. The control system is done by planning the appropriate trajectories on components of the output variable vector of the system. For this purpose, reference trajectories are such planned that the maximum power can be extracted from the wind. To prove the efficiency of the proposed control method, several simulation results in Matlab \ Simulink for a 5 MW wind turbine are presented.
Fig.1: General Structure of studied system.
C. The Eltric Grid
II. MODEL OF THE SYSTEM
The configuration of the production system studied in this paper is sown in Fig.1. The system consists of a wind turbine based on PMSG connected to the grid through an electronic power interface. In the following, the model of each subsystem will be presented. A. Wind Turbine
The wind power is defined by equation (1) [8] : . . . . . (1) where is the air density (1.225kg/m3), stands for the radius of the rotor blade in (m) and represent the wind speed in (m/s). However, not all the wind power can be extracted by the turbine and so, a power coefficient ( ) is defined as: , . , . . . . . (2) depends on speed ratio λ (rad) and the blade pitch angle β (deg). It is also conventional to define a tip speed ratio (λ) as the ratio between the linear velocity of the blades and the wind speed, as presented in (3), where is the angular speed of the wind turbine (rad/s). Ω .
(3)
B. Permanent Magnet Synchronous Generator
The general model of the PMSG is obtained by considering only the fundamental harmonic of the flux distribution in the air-gap of the machine and by assuming the homopolar component is neglected [9, 10] To define easily the control strategy of the system, the analytical model of the PMSG related to the rotor reference is given in (4). 0
(4)
where , are the d-q axis voltages, , stand for the , represent the d-q axis d-q axis currents, is stator phase winding resistance and inductances, is the magnet flux. The active and reactive power at the stator are given by equations (5), [9-13]: (5) In generator operation, mechanical equation is expressed as: .Ω (6) where is the shaft mechanical torque, is the inertia of the rotor, represents the damping constant and Ω is the rotor speed. The electromagnetic torque can be expressed in the d-q reference as follows: (7)
The dynamic model of the electric grid is expressed in (8) [10]: . .
.
.
.
.
(8)
where and are the filter inductance and resistance and present the dq components of the grid (Fig.1), and stand for the dq components of the voltage, and are the dq-axis inverter output voltage, components of the current measured on the grid and is the fundamental frequency. III.
CONTROL STRATEGY OF THE SYSTEM
As it can be seen from Fig.1, the turbine and the PMSG are connected to the grid through a back to back converter. The machine side converter (MSC) controls the rotation speed of the machine and therefore its torque while the grid side converter (GSC) ensures the DC-bus control and the active and reactive power management between the generator and the grid. This interface provides a nearly complete decoupling between the grid and the generator. In this paper, a flatness based method is proposed to control the MSC, and a classical method is employed to control the GSC. A. Flatness Description
The concept of flatness was introduced by M. Fliess, J. Lévine, Ph. Martin and P. Rouchon [14, 15]. This concept is used to control the dynamic behavior of a system, using a formalism of differential algebra. A dynamic system with state and input defined by: , is a flat system if and only if there is a flat output as , , ,…, , Where and can be written as functions of this flat output and its derivatives such that [13]: , ,…, . (9) , ,…, . (10) where: , : × and :
, →
. ,
:
, :
are regular functions. The differential flatness control offers many advantages in comparison with conventionally used commands, such as linear controls provided with two loops or PI correction nonlinear sliding mode control. In a flat system, all state variables and control are expressed as functions of a chosen flat output and its successive derivatives without integrating differential equations. Therefore, to control a system, the reference trajectories should be planned at first on the output variable components and then, the control variable components
can be calculated. Differential flatness provides a good performance towards the robustness and parameter variations [14].
the optimal speed is taken into account to generate the reference trajectory of .
B. Differential Flatness of the System
The system state space can be written as equation (11) from the mechanical equation and the model of the PMSM. The three components of the state variable vector are considered as currents , (coming from Park model) and the machine speed, Ω. Ω
(11)
Ω Ω
Ω
The state vector x and the control vector u are defined by: , ,Ω (12) , (13) Therefore the flat output y must be of the same order as the control vector (13). The mechanical speed Ω and the d-axis flux are considered as components of the flat output vector , Ω
(14)
From (11), It can be shown that: Ω
,
Fig.2: Maximum power according to the wind speeds.
In the second operation mode, the wind speed is . In this situation, the pitch angle of the higher than wind turbine should be such controlled that the nominal power of the turbine does not exceed the rated power of the generator. On the other words, once the generator nominal power is reached (at optimal wind speed), the output power of the turbine must be limited to this value by the control of the pitch angle as shown in Fig.3 [8]. Therefore, the optimal speed is taken into account to generate the reference trajectory of .
(15)
Ω
and:
, ,
Hence:
, ,
, ,
,
, ,
Fig.3: Pitch angle control method.
(16)
(17)
As it can be seen, the components of the state variable vector (15) and the control variable vector (17) are expressed as a function of the output vector components and its derivatives. It proves that the system is flat. In the following, the reference trajectory generation will be explained. C. Trajectory Planning
Two operation modes can be defined for a wind turbine generator according to the wind speed. In the first mode, the wind speed is less than the nominal speed, which corresponds to the nominal power of the PMSG. As it shows the Fig.2, in this operation mode, an optimal speed for the turbine can be found for each wind speed. This optimal speed corresponds to the maximum power which can be extracted from the wind. Therefore,
About the second output variable, , the constant is flux linkage produced by the permanent magnets, considered as the reference value. The trajectory planning is so important in a differential flatness based control because it defines the evolution of all the state and control variables (equations (9)-(10)). It is therefore interesting to impose a known trajectory to predict analytically the evolution of variables. To plan the desired trajectories on the output variable components, a second-order filter is applied to the , , to protect the system reference values, against the rapid and instantaneous changes of the variables. Therefore, the reference trajectory can be written as: 1
1
(18) where is the angular frequency of the second order system which is defined according to the desired rise , time of the variables, .
D. Control Law and the Control Parameters
,
In order to control the output vector its reference trajectories feedback controller is used as: 0
. .
0
,
_
,
a state
.
(19)
_
.
_
.
_
to
synchronize the output voltage of the inverter with the grid’s one [17]. The block-diagram of the PLL system is illustrated on Fig.6.
_
_
(20)
Such that: (21) The integral terms ensure a zero static error in steady state and compensate the model errors. The coefficients of regulators are designed such that the operating points are stable. and , obtained Substituting the fictive variables by the regulators in the equation (15), leads to calculate the control vector components , . These control variables are used to generate the command signals of the related convertor. Fig.4 shows the block diagram of the control method.
Fig.5:Energy management method bettween the PMSG and the Grid.
Fig.6: PLL block diagram.
In the PLL control system, the component of the grid voltage is controlled to be zero, which allows the decoupling of active and reactive power as the equation (23), [18]. .
(23)
.
Fig.4: Block-diagram of the proposed control for MSC.
E. Energy Management Between the PMSG and the Grid
As it is mentioned above, a classical method is employed to control the GSC which includes two control loops. The first one (the inner loop) is based on the grid currents control, and the second one (the outer loop) is to regulate the voltage of the DC-bus and to control the reactive power, as shown on Fig.5. The active and reactive power injected to the grid is written as: (22) To send the produced energy to the grid, a Phase Locked Loop (PLL) system should be used to
Furthermore, the active power exchanged between the grid and the DC-bus is expressed as: . . (24) It should be noted that well-known PI controllers are used to ensure that the currents ( , ), DC-bus voltage ( ) and the reactive power ( ) follow their own reference values. IV.
SIMULATION RESULTS
In this section, simulation results obtained in Matlab/Simulink environment are presented for a 5MW wind turbine where a random wind profile with variable speed is used (fig.7) to study behavior of the system. The flat output variable components, Ω and , are presented in the Figs. 8 and 9, respectively. Everyone can see that these output variables follow well their own reference trajectories during the two mentioned operating modes (the wind speed lower or higher than the nominal speed, where vnom =11.5m/s). The wind
turbine is controlled to extract the maximum energy, when the rotation speed of the generator is lower than its nominal value (vnom =11.5m/s) as illustrated in Fig.10. However, when the wind speed is higher than the nominal value, the pitch angle shown on Fig.11 increases to limit the power produced by the generator to its nominal value. Therefore, the produced power stays at 5MW. , Fig.12 shows waveforms of state variables which are functions of the output variables and their derivatives obtained from (15). 12
Fig.9: Flat output 5.5
Pm Pele
Active power (W)
5 4.5 4 3.5 3 2.5
W ind speed W ind-optimal
2 0
11.5
20
40
60 Time (min)
80
100
120
Fig.10: Electric and mechanic Power of PMSG.
11
2
10.5 1.5
10
Pitch angle (°)
Wind speed (m/s)
.
6
x 10
9.5 9 0
20
40
60 Time (min)
80
100
0.5
120 0
Fig.7: Wind speed profile. 1.5
-0.5 0
20
40
60 Time (min)
80
100
120
Fig.11: Pitch angle. 1
500
0.5
Yw-mes Yw-ref 0 0
20
40
60 Time (min)
Fig.8: Flat output
80
100
120
.
PMSG dq-axis mesured currents (A)
Flat output Yw (m/s)
1
0 -500 -1000
Iq Id
-1500 -2000 -2500
12
Flat output Yd (Wb)
Yd-ref Yd-mes
20
40
60 Time (min)
80
100
120
Fig.12: The d-q axis currents of the PMSG.
11.5
11
10.5
10 0
-3000 0
20
40
60 Time (min)
80
100
120
The DC-bus voltage waveform is presented on Fig.13 where its reference value is fixed at 4700V. It can be seen that the DC-bus voltage follows well its reference and it is not affected by the variations of the generator’s speed. Fig. 14 shows the reactive power evaluation waveform which is absorbed by the system or is delivered to the grid. It can be seen that reactive power follows favorably its references. Finally, the zoomed in
three phases current delivered to the grid is presented on Fig.15. We can see that the current have a 50 Hz sinusoidal form. These simulation results prove efficiency of the proposed control strategy to the variable-speed wind energy system connected to the grid. 6000 Vdc-mes Vdc-ref
DC-link Voltage (V)
5000 4000 3000 2000 1000 0 0
20
40
60 Time (min)
80
100
120
Fig.13: DC bus voltage control. x 10
Qg-ref Qg-mes
Reactive power (VAR)
1.5 1 0.5 0 -0.5 -1 -1.5 -2 0
20
40
60 Time (min)
80
100
120
Fig.16: Reactive Power of grid. 3000
Zoom of grid currents (A)
2000 1000
The main purpose of this paper is developing of a flatness-based control method for a PMSG used in a variable speed wind-energy system connected to the grid via a back-to-back converter. The model of each subsystem is presented at first and it is proved that PMSG is flat. Then, the reference trajectories are planned on the output variables to ensure extracting the maximum power of wind. A classical control method is used to regulate the DC-bus voltage, to control the reactive power and to synchronize the output voltage of the inverter with the grid’s one. The proposed control strategy is simulated in MATLAB/Simulink. The output system variables follow well their reference trajectories and the system is such controlled that the maximum power can be extracted from the wind. The flatness based control method has a high dynamic performance and good robustness against parameter variations.
Wind turbine Radius: 56 m Number of blades: 3 Total inertia of the mechanical transmission: PMSG 5 Nominal power: 6.25mHΩ Stator resistance: 4.229mH Self-inductance: Permanent magnetic flux: 11.1464 Number of pole pairs: 75
10 kg.m2
/
DC bus and filter 4700 DC bus voltage: 0.04 Equivalent capacitance: 0.01mΩ Filter resistance: Filter inductance: 0.5mH REFERENCES
0
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CONCLUSION
Appendix
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2
V.
10.01 10.02 10.03 10.04 10.05 10.06 10.07 10.08 Time (min)
Fig.14: Zoom of grid currents.
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