Revue des Energies Renouvelables ICESD’11 Adrar (2011) 261 – 270
261
A PMSG wind turbine control based on passivity
F. Achouri * , A.Y. Achour and B. Mendil †
Department of Electrical Engineering, University of Bejaia, Targa Ouzemour, Bejaia, Algeria
Abstract – In this paper, a standard passivity based control is applied to permanent magnet synchronous generator (PMSG) in wind turbine connected to the grid via a PWM back to back three phase converter. The controller is designed using the non linear, model of PMSG generator and it is guaranteed to have tracking properties for the electric and mechanical references as (currents and speed respectively); it also guarantees the internal stability of the system exploiting energy dissipation (passivity) concepts. The performance of the proposed approach is evaluated based on the various simulations results carried out under Matlab/Simulink software.
Keywords: Wind energy conversion, Variable speed, Permanent Magnet Synchronous Generator PMSG, Nonlinear systems, Nonlinear control, Passivity-Based Control (PBC).
1. INTRODUCTION
These last years, many sources of renewable energy are developed, mainly on wind and solar power. Their advantages appear in the absence of harmful emissions and they present inexhaustible resources. The wind energy is the most promising renewable source [1-3].
This is due, particularly, to the evolution of power semiconductors, decreasing equipment costs, and the development of the wind turbines industry which tends to have capacity of 2 MW or more. The modern wind turbines always use variable speed operation, this allows: variable speed operating, high efficiency and the extracted power is optimized for the weak and middle winds [4, 5]. With the advance of power electronics technology and permanent magnets materials in generator rotor, direct- driven permanent magnet synchronous generators have increasingly drawn more interests to wind turbine systems, this allows: better efficiency, easier controllability, decrease mechanical stress , acoustic noise and no need for reactive magnetizing current [6-8].
The topology used is subjected to a number of control techniques. They include pitch angle control for limiting the output power, generator PMSG control for maintaining the desired rotor speed and grid side inverter control for active, reactive power flow control, and constant DC link control.
The PMSG control type based on PBC nonlinear control, its goal is obtained through an energy shaping of the process using lyapunov functions. Damping terms are injected to ensure lyapunov stability conditions [9-11] (improve the convergence to a desired minimum and keep Lyapunov energy function positive). The whole system is decomposed as the feedback interconnection of passive mechanical and electrical subsystems.
In this paper, we are interested with the modeling of the whole system consisting of the wind turbine based on PMSG connected to a back-to-back PWM power converter
* achouri.fouzia@yahoo.fr ; achouryazid@yahoo.fr
† bmendil@yahoo.fr
and a DC bus link. The generator side converter controls the electromagnetic torque, and therefore the extracted power.
This control is based on PBC nonlinear controller. While the grid side converter plays an important role on the control transfer and power quality it is controlled by pulse width modulation (PWM) obtained from proportional integral regulator of currents sent to electrical grid. And power limitation for high wind speed is obtained by pitch control.
The studied system is given in figure 1.
Fig. 1: Process structure
For the best presentation of our work, this article is organized as follows. Section 2 is dedicated to the wind turbine model with a PI speed control. The PBC control design of the PMSG is outlined in section 3. The active and reactive powers PI control side network is established in section 4. The performance of the control system is evaluated in section 5. Section; 6 concludes this paper.
2. WIND TURBINE MODELING
The amount of power capacity of being produced by wind turbine, Pt, is dependent on the power coefficient Cp which, in turn, is dependent on the ratio , between the turbine angular velocity t, and the wind speed V [5, 12, 13]. It is given by
v3 R2 )
, p( 2 C 1
Pt (1)
where is the air density, R is the blade length and v is the wind velocity.
The turbine torque is the ratio of the output power to the shaft speed t t
Pt
t
(2)
The ratio , called the tip speed ratio, is give:
v tR
(3)
The power coefficient is given by:
1 i
e 21 ) 5 4 . 1 0 115 ( 5 . 0 ) , p(
C
(4)
With,
1 2 035 . 0 08 . 0 1 i
1
ICESD’2011: A PMSG wind turbine control based on passivity 263 The power coefficient Cp is given in (, ) function for different values of , and curves are shown in figure 2.
Fig. 2: Power coefficient of wind turbine model
The power coefficient maximal value corresponds to the optimal value of the tip speed ratio opt, it is given for itch value of pitch angle , and the power takes its maximal value at this point.
3 3 ref
opt R5 max _ Cp 2 1 opt _
Pt
(5)
R v opt ref
(6)
When the wind speed reached the nominal value, the pitch angle regulation enters in operation in order to decrease the power coefficient, and the simplified representation of wind turbine control diagram is shown in figure 3a. and the control of the pitch angle is showed in figure 3b.
Like the PMSG do not needs the gearbox, we take m
t
, ref *m (7)
Fig. 3a: Control diagram of wind turbine
Fig. 3b: Pitch angle regulator 3. PMSG MODELING
To obtain the mathematical model of the PMSG, we have taken these assumptions [5, 13]: Permeability of the fully laminated cores is assumed to be infinite. Saturation, iron losses end winding, and slot effects are neglected. Only linear magnetic materials are considered. Under these assumptions [5, 12, 13], the electrical model for the machine can be expressed by:
Vdq f p m
idq Ldq m idq
Rs t d idq d
Ldq (8)
t d d m J em f
m
(9)
Where J is the mechanical inertia, f is the damping coefficient, and r is the external torque. The generated torque is calculated using
q) f i iq id q) d L L ((
2p 3
em
(10)
To complete the model of the electrical subsystem, we first recall that fluxes and currents are related through the inductance
f idq Ldq
dq
(11)
From (9) and (11), we obtain the alternative expression:
idq Rs Vdq dq p m
dq
(12)
The desired electrical dynamic of the PMSG is given by:
*dq s i dq R p m
dq
(13)
*dq T i p dq 2 3
Cem (14)
4. PASSIVITY BASED CONTROL OF PMSG 4.1 Passivity
The basic idea of the passivity consists in shaping the total energy of the system then in adding a damping term. EL equation allows to obtain easily the formulation after having formulated the total energy of the system [10], it is modified to desired (minimum) value. The system converge towards this minimum also if the control able to inject an additive dissipative term to the system, then the convergence to the derived state can be improved with respect to that obtained by natural dissipation given by the system.
The PBC control considers the plant as the interconnection between electrical and mechanical subsystems. The controller calculation depends only on the electrical part.
ICESD’2011: A PMSG wind turbine control based on passivity 265 The mechanical subsystem is considered as a passive disturbance. This leads to the block diagram of figure 4.
Fig. 4: Control device interconnection The input / output relation of electric system modeled is given by:
Ceme dq e Y
m
*dq e i
E
: (15)
s f J
r) ( em m Ym
e:Em em r
(16)4.2 Design of the PBC
During the synthesis the stability procedure in the sense of Lyapunov which is developed in [15], we lead to use the equation (12) and (13), and the state fluxes error equation is given by:
dq* dq
ef (17)
The dynamic equation of the error of the flux is obtained from equations (12), (14) and give:
* ) dq p m
dq*
* ( idq Rs ef p m
ef (18)
In order to give a proof for the convergence of the error of the flux ef , the Lyapunov theory of stability is used.
Given the following quadratic function [14, 15]
ef T ef 2 ) 1 ef f(
V (19)
For which the time derivative, around a trajectory, is given by:
)
* ) dq p m
dq*
* ( idq Rs T ( ef f) e f(
V (20)
The lyapunov derivative function (20) is negative defined only if the following condition is satisfied [19]
f) f e K
* ) dq p m
dq* ( 1 ( Rs
*dq
i (21)
Where Kf is a damping injection which ensures the process stability and improves the convergence to the desired minimum.
4.3 Flux and torque reference
After transformations, the desired fluxes are:
- according d-axis, the flux is reduced to rotorique flux
* f d
(22)
- according q-axis, the flux is reduced to:
em* p f
Lq 3
* 2
q
(23)
The proposed strategy to evaluate the desired torque is given in [15]
z r
*m
* J
em
(24)
0 b , a
;
* ) m ( m
b z a
z (25)
The obtained controller based on these equations is illustrated by figure 5. The global control structure with PBC and PMSG is given by figure 6.
Fig. 5: The PBC controller structure
Fig. 6: The PBC control of the PMSG
5. NETWORK ACTIVE AND REACTIVE POWER CONTROL It is clear that active and reactive powers are proportional to d-axis current component id and q-axis current component iq respectively [16].Therefore, we can achieve the decoupled control of the active and reactive powers through id and iq.
Fig. 7: Control grid side inverter
ICESD’2011: A PMSG wind turbine control based on passivity 267 The DC-link voltage controller, of PI type, has been used to guarantee constant DC- link voltage and to generate the reference d-axis current component, i*d, to the inner control loop. Since we want grid-side reactive power to be zero, we set i*q = 0. The whole vector control scheme for the grid-side converter is shown in figure 7.
6. SIMULATION RESULTS FOR WHOLE SYSTEM
We present the simulation results for the PMSG connected to the network through an ideal ac/ac direct converter. To control the power exchanged between the stator and the network, we used the PBC control. The signal in figure 8 represents a proposed wind profile covering a speed range between 7 m/s and 14 m/s, where the nominal wind turbine speed is in average at 12 m/s.
Fig. 8: Wind speed Fig. 9: Pitch angle
Fig. 10: Power factor Fig. 11: Rotor speed
Fig. 12: Electromagnetic torque Fig. 13: Electromagnetic torque with R=1.5 Rs and J=2 Js
Figure 9 and 10 show the pitch angle and Cp response which varied with the wind in order to adapt the extracted turbine torque to the PMSG torque. In first simulation test, the PMSG was driven by a reference speed of 45rd/s in average shown in figure 11. The electromechanical torque tracks perfectly the motor torque given by the wind turbine as shown in figure 12.
The robustness of the PBC against the PMSG parameter changes is verified by increasing the resistor value to 30 % and the inductances (Ld and Lq) values to 10 %.
From the results of figure 13 and 14, we can see the good behavior of our controller.
The speed, the currents, and the electromagnetic torque also follow perfectly the reference inputs.
Fig.14: Rotor speed Fig. 15: Stator active and reactive powers
Fig. 16: Power factor Fig. 17: Network active power
Fig. 18: Network reactive power Fig. 19: Filtered current
Figure 15 shows the stator powers. The reactive power is maintained around zero to keep the power factor at unity figure 16.
ICESD’2011: A PMSG wind turbine control based on passivity 269 The PMSG supplies the network with active power Pg= - 3000 W in average Figure 17. The reactive power is function of the quadratic current which is maintained around zero (Fig. 18) and the AC current is shown in Figure 19.
7. CONCLUSION
This paper is devoted to the analysis, modeling and simulation of a variable speed wind turbine using a PMSG generator. Passivity based controller designed for whole model of the PMSG, which exploits system properties (energy) and structure and use them to achieve the output tricking error. It considers the PMSG as a non linear system that captures the behavior of the generator system in a more accurate fashion.
The Controller allows an elaborated control of the torque, current and speed and it allows a good robustness to the global control system structure. The presence of external or internal disturbances does not affect significantly the behavior of the PMSG.
Compared with feedback linearization control, the proposed PBC controller has shown improved control performances in simulations (settling time and references values) and it is able to maximize the electric power by keeping the power factor at unity at all time.
The control of the grid side converter is obtained by vector control (PI) which ensures the active power transfer to the grid, regulates the level of the reactive power, and maintains the DC-link voltage constant.
REFERENCES
[1] S. Muller, M. Deicke and R.W.D. Doncker, ‘Doubly-Fed Induction Generator Systems for Wind Turbine’, IEEE Industry Applications Magzine, pp. 26 – 33, May/June, 2002.
[2] B.H. Chowary and S. Chellapilla, ‘Doubly-Fed Induction Generator for Variable Speed Wind Power Generation’, Electric Power System Research, Vol. 76, N°9-10, pp. 786 - 800, 2006.
[3] B. Chitti Babu and K.B. Mohanty, ‘Doubly-Fed Induction Generator for Variable Speed Wind Energy Conversion Systems, Modeling & Simulation’, International Journal of Computer and Electrical Engineering, Vol. 2, N°1, pp. 141 – 148, 2010.
[4] M. Chinchilla, S. Arnaltes and J.C. Burgos, ‘Control of Permanent-Magnet Generators Applied To Variable Speed Wind-Energy Systems Connected to the Grid’, IEEE Transactions on Energy Conversion, Vol. 21, N°1, pp. 130 – 135, 2006.
[5] W. Qiao, W. Zhou, J.M Aller and R.G. Harley, ‘Wind Speed Estimation Based Sensorless Output Maximization Control for a Wind Turbine Driving a DFIG’, IEEE Transactions on Power Electronics, Vol. 23, N°3, pp.1156 – 1169, May 2008.
[6] W. Cai, D. Fulton and K. Reichert, ‘Design of Permanent Magnet Motors Low Torque Ripples’, International Conference on Electrical Machines, ICEM’2000, pp. 1384 – 1388, Espoo, Finland, 2000.
[7] A.S. Neris, N.A. Vovos and G.B. Giannakopoulos, ‘A Variable Speed Wind Energy Conversion Scheme for Connection to Weak AC Systems’, IEEE Transactions on Energy Conversion; Vol. 14, N°1, pp. 122 – 127, 1999.
[8] G. Michalke, A.D. Hansen and T. Hartkopf, ‘Control Strategy of a Variable Speed Wind Turbine with Multiple Multipole Permanent Magnet Synchronous Generator’, in: Proceedings European Wind Energy Conference and Exhibition, EWEC’2007, Milan, Italia, 7 – 10 May, 2007.
[9] M. Becherif, R. Ortega, E. Mendes and S. Lee, ‘Passivity Based Control of a Doubly-Fed Induction Generator Interconnected with an Induction Motor’, 42nd Conference on Decision and Control, pp. 5657 – 5662, 2003.
[10] R. Ortega, A. Loria, P.J. Nicklasson and H. Sira Ramirez, ‘Passivity Based Control of Euler Lagrange systems’, Springer, Verlag, 1998.
[11] W. Qiao, L. Qu and R.G. Harley, ‘Control of IPM Synchronous Generator for Maximum Wind Power Generation Considering Magnetic Saturation’, IEEE Transactions on Industry Applications, Vol. 45, N°3, pp. 1095 – 1105, 2009.
[12] J. Belhadj and X. Roboam, ‘Investigation of Different Methods to Control a Small Variable- Speed Wind Turbine with PMSM Drives’, ASME Transactions on Journal of Energy Resources Technology, Vol. 129, September 2007.
[13] M. Ying, G. Li, M. Zhou and C. Zhao, ‘Modeling of the Wind Turbine with a Permanent Magnet Synchronous Generator for Integration’, IEEE Power Engineering Society General Meeting, pp. 1 – 6, 24 - 28 June 2007.
[14] S. Aïssi and R. Abdessamed, ‘A Doubly Fed Induction Motor Control Using Passivity’, Asian Journal of Information Technology, pp. 489 - 494, 2007.
[15] K. Kim, A. Charara and R. Ortega, ‘Pratical Application of Passivity Based Control for Induction Motor’, CESA IMACS Multiconference, Computational Engineering in Systems Applications, Lille, pp. 876 – 881, 9-12 July, 1996.
[16] R. Pena, J.C. Clare and G.M. Asher, ‘Doubly-Fed Induction Generator Using Back-to-Back PWM Converters and Its Application to Variable-Speed Wind-Energy Generation’, IEE Proceedings, Electric Power Applications, Vol. 143, N°3, pp. 231 - 241, 1996.
