Sliding Mode Control (SMC) Of Permanent Magnet

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Energy Procedia 18 (2012) 43 – 52

Sliding Mode Control (SMC) Of Permanent Magnet Synchronous Generators (PMSG) M.S. Merzouga, H. Benalla and L. Louze a* a

LEC- Research Laboratory Department of Electrical Engineering, University of Mentouri Constantine, B.P. 325 , avenue Ain El Bey, Constantine 25017, Algérie

Abstract

This paper presents Sliding Mode Control of Permanent magnet synchronous generators. A comprehensive dynamical model of the PMSG in d-q frame and its control scheme is presented. Wind energy is a promising technology and becomes more and more interesting player on the market of energy production. Since the converter/capacitor model is nonlinear, the sliding mode technique constitutes a powerful tool to ensure the dc-bus voltage regulation. The simulation results show the method is simple and has high precision of control, and the system has good characteristics in steady state and during transients with permanent magnet synchronous generator. ©2012 2010Published PublishedbybyElsevier Elsevier Ltd. Selection and/or responsibility [name organizer] © Ltd. Selection and/or peerpeer-review review underunder responsibility of Theof TerraGreen Society. Keywords : PMSG ; SMC ; PWM ; IGBT ; Lyapunov ;

1. Introduction Permanent Magnet Synchronous Generators (PMSG) are receiving significant attention from industries for the last two decades. They have numerous advantages over the machines which are conventionally used. Current research in the design of the PMSG indicates that it has high torque to current ratio, large power to weight ratio, high efficiency, high power factor and robustness. Currently, there is much interest in using brushless electronically commutated servo machines in high performance electromechanical systems and the application of neodymium-iron-boron (Nd2Fe14B) and samarium cobalt (Sm1Co5 and Sm2Co17) rare-earth magnets results in high torque and power density, efficiency and controllability, versatility and flexibility, simplicity and ruggedness, reliability and cost, weight-to-torque and weight-to-power ratios, better starting capabilities. [1] * Corresponding author. Tel.-fax:. 031.81.90.13 E-mail address: [email protected].

1876-6102 © 2012 Published by Elsevier Ltd. Selection and/or peer review under responsibility of The TerraGreen Society. doi:10.1016/j.egypro.2012.05.016

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M.S. Merzoug et al. / Energy Procedia 18 (2012) 43 – 52

Sliding mode control (SMC) theory was introduced for the first time the context of the variable structure system (VSS). It has become so popular that now it represents this class of control systems. Even through, in its early stage of development, the SMC theory was over-looked because of the development in the famous linear control theory, [2] during the last 20 years it has shown to be a very effective control method. Sliding mode variable structure control which sliding mode can be designed is insensitive to system parameters change and load disturbance, and has the advantages of good robustness, quick response, and easy realization and so on. Accordingly, hopeful to design a control strategy of high quality by applying sliding mode control (SMC) to the control of PMSM. [3] For sliding mode controller, Lyaponov stability method is applied to keep the nonlinear system under control SMC provides a fast and accurate dynamic response. Also makes the system response insensitive to changes in parameters and load disturbance. 2. Mathematical model of the PMSG The dynamic model of PMSG has been built in the d-q rotating reference frame, where the q-axis goes ahead 90 from the d-axis with respect to the direction of rotation. The electrical model of the PMSG in the d-q synchronous reference frame, with the voltage and torque equations are given by : [4] [9] d (1) Vd = − RS I d − ϕd + ωr ϕq dt d (2) Vq = − RS I q − ϕq − ωr ϕd dt ϕd = Ld I d + ϕ (3)

ϕq = Lq I q

(4)

And the electromagnetic torque Te is given by: [10] 3 Te = P[( Ld − Lq )I d I q + I q ϕ )] 2

(a)

(5)

(b)

Fig. 1. Equivalent Circuit of a PMSG in the synchronous reference frame (a) d-axis, (b) q-axis.

3. Description of sliding mode control The implementation of this control method requires mainly three stages: 3.1. Sliding Surfaces J. Slotine proposes a form of general equation to determine the sliding surface. [5]

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M.S. Merzoug et al. / Energy Procedia 18 (2012) 43 – 52

§d · s( x,t ) = ¨ + λ ¸ © dt ¹

n −1

e( t )

(6)

With: e(t) is the error in the output state

e( t ) = xref ( t ) − x( t )

(7)

Ȝ is a positive coefficient 3.2. Conditions of convergence The convergence condition is defined by the equation of Lyapunov : S.S E 0

(8)

3.3. Controller Design Consequently, the structure of a controller consists of two parts; a first concerning the exact linearization and a second stabilizing.

u( t ) = ueq ( t ) + un

(9)

u eq (t) Corresponds to the equivalent control suggested, It is calculated on basis of the system behaviour along the sliding mode described by:

 x,t ) = 0 s(

(10)

un = − K sgn ( s )

(11)

Wher : K > 0 K: is the control gain

­1 ° sgn(s) = ®0 ° −1 ¯

s>0 s=0 s