Improvement of sliding mode power control applied to wind system based on doubly-fed induction generator

ABSTRACT


INTRODUCTION
Lately, the use of renewable energies (i.e., wind and solar photovoltaic) to increase in an incredible way thanks to the scarcity of combustibles.Wind energy is supposed to be the best in terms of quality and price [1].There are several research studies about the wind turbine.In particular, the ones with asynchronous generators.Although, they have a low cost and simple maintenance as advantage but, they require more expensive equipment and complex control.Therefore, in the recent years, the wind turbine system moved towards the doubly-fed induction generator (DFIG) machine which has higher quality and larger power density [2].Furthermore, the DFIG reduces the mechanical stress by removing the necessity of the multiplicator which improves the system's reliability [3] and decreases the maintenance costs by directly coupling the turbine and the shafts of the generator [4].
Due to the high variability of the wind speed, it's difficult to obtain a satisfactory performance of the Wind turbine System.Recently, this latter is designed to extract the maximum power point (MPP) power from the wind speed, which is commonly known as the maximum power point tracking (MPPT) strategy.Different methods have been developed in order to maintain the operating point of maximum efficiency.The most widespread control strategy is the optimum power/torque tracking, where the use of the proportional and integral (PI) controller.However, this strategy alone doesn't realize a better performance.Hence, there are other control methods such as the backstepping, fuzzy logic, and sliding mode control (SMC) [5], [6].This paper is repatriated as follows: Section 2 presents the description of the wind system (turbine, DFIG, inverter, DC-bus, and filter).Section 3 discusses the principle of operation of the sliding mode command as well as its application on our system.Section 4 shows and interprets the results of the simulation.Finally, a conclusion in Section 5.

MODELING OF WIND SYSTEM BASED ON DFIG
The conversion chain includes in series a speed multiplier to increase the speed of rotation to about 1500 rpm, a doubly fed induction generator (DFIG) operating at variable speed, Three-phase converters adjust the frequency of the wind turbine to that of the electricity grid to which it is connected (50 Hz in Morocco) [7].The transformation of the power of the aerogenerator into kinetic energy then into mechanical energy of rotation is done in two parts: at the turbine rotor (primary shaft), which captures part of the kinetic energy of the wind present to convert it into mechanical energy at the generator rotor (secondary shaft), which obtains mechanical energy and converts it into electrical energy as shown in Figure 1 [8].
Figure 1.Architecture of the control

Wind-turbine model
The model of the turbine is modeled from the following system of equations (1)-( 9) [9], [10]: The Figure 2 shows the evolution of the power coefficient as a function of λ for different values of β [11], [12].

Maximization of power control without speed control
While the variation of the wind speed in steady state is low compared to the electrical time constants of the system, we assume that the speed of rotation of the DFIG is fixed and neglecting the effect of the viscous torque f, the dynamic equation of the turbine becomes (12).From (12) we obtain the static equation describing the stationary state of the turbine (13).The reference electromagnetic torque is determined from an estimate of the aerodynamic torque given by ( 14) and we obtain equation (15).The orientation angle of the blades β is assumed to be constant and the estimated speed of the turbine is calculated from the mechanical speed (16).The estimated wind speed is given by equation (17).On the base of the previous equations, we can then write the equation of the reference electromagnetic couple (18) [13], [14].

DFIG model
The equations of the DFIM in the reference of Park are written as [15], [16]:

With: M=M sr =M rs
The electromagnetic torque is expressed as a function of the currents and the flows by [18]: The fundamental equation of dynamics is: V s(d,q) ,V r(d,q) : Stator and rotor voltages in the reference of Park.

Model of the two-level voltage inverter
To connect the generator which undergoes a variable speed with the network, it is necessary to go through a stage of power electronics in order to control the power injected.we use 2 RSC and GSC conversion stages, converters which consists of IGBTs as shown in Figure 4.
. The expression of the simple voltages is presented by the following system [19]:

−
The matrix form of simple tensions becomes [20]: we associated with Each arm of the inverter a binary command value Si, where i = a, b, c: we replace (24) in (23), we get: The single voltages of the inverter become proportional to the states of the control quantities of the switches (Sa, Sb, Sc).

DC-bus model
The DC bus as shown in Figure 5 interconnects the two converters of the wind system (RSC and GSC).The latter allows the transfer of power between two sources at different frequencies.It is modeled by (26) [21].

SLIDING MODE CONTROLLER
The basic idea of sliding mode control design is first to attract the states of the system to a suitably selected region, and then to design a control law that will always keep the system in that region.Where the design of the sliding mode control algorithm is defined by three complementary steps [22]:

Choice of sliding surface
For a non-linear system presented in the following form (28), where A (x,t) and B (x,t) are two continuous and uncertain non linear functions assumed to be bounded [23].

Convergence and existence conditions
To make the surface attractive and invariant, we returned to the second theorem of LYAPUNOV where the scalar function is defined positive by (31).The derivative of this function gives (32), and to guarantee the existence of the sliding mode, where the sliding variable S (x, t) tends towards zero, it suffices to ensure that (32) is defined negative (33).

Determination of the law of control
The control law is defined by the relation (34), With: u + and u -are continuous functions (35) where u -≠ u + .The control by sliding modes is composed of two terms: u eq : the equivalent control vector, u n : The stabilizing command [24].(39)

Determination of the basic discontinuous command un:
The simplest discontinuous command u n is given by (40), where K is the command gain.This type of control has a drawback known by "CHATTERING".To solve this problem in this case we replaced the "SIGN" function by the "SAT" function [25]:

APPLICATION OF THE SLIDING MODE COMMAND TO THE DFIG 4.1. Control of the converter on the DFIG (RSC) side and on the network side (GSC)
Considering the sliding surface proposed by SLOTINE (42), For n=1; the sliding surface of the active and reactive power is given by (43), where P sref and Q sref are the references of stator powers (active and reactive) of DFIG and Q fref and P fref are the references of powers (reactive and active) of RL filter [26].
We replace each term by its expression given by ( 44), the derivative of the sliding surface becomes as ( 45) and ( 46) [27].

ISSN: 2088-8694 
Improvement of sliding mode power control applied to wind system based on … (Btissam Majout) 449 Figure 6.SMC control applied to DFIG wind turbine system

Tracking and regulation for SMC
In this test, we considered the aerodynamic power according to the MPPT as a reference of active power, and zero as reference for reactive power.

Test with constant speed (rung speed):
Figure 7 shows the results obtained for the application of the control by Sliding mode to a wind power system at the base of the DFIG.According to these results, the active powers Ps Figure 7(a) and reactive Qs Figure 7(b) follow the reference.The stator currents Ir Figure 7(c) and the rotor currents Figure 7(d) are of good quality and follow the given instruction.In Figures 7(e) and (f) the stator and rotor currents are sinusoidal with a frequency of 50 Hz, a THD less than 5%, which implies that the wind power system respects the conditions of connection with the electrical grid.

Test with variable speed:
During this test the wind profile illustrated in Figure 8 was applied to the DFIG.According to the curves illustrated in the Figure 8 we notice a good behavior of the machine in spite of the variation of the wind, where the generator follows the references of the powers without overshoot and with an almost zero error.And the electromagnetic torque of the DFIG varies according to the wind speed, and proportional to the active stator power generated.We can notice that in spite of the variations of the wind, the stator current Is-abc remains sinusoidal with a fixed frequency 50Hz equivalent to that of the network.The DC bus voltage shows that it follows its reference value quickly without overshooting with a small static error.The slip value g is negative this implies that the functioning of the DFIG is in hypo-synchronous.8(e) and (f) the stator and rotor currents are sinusoidal with a frequency of 50 Hz, a THD less than 5%, which implies that the wind power system respects the conditions of connection with the electrical grid.these tests show the validation of our model proposed for the sliding mode technique; in order to validate it complementarily there remains the robustness test (against the parametric variation)

Robustness tests
In this test, we varied the parametric variables of the DFIG (resistance RR and Rs) by + 50% of their nominal values.It is noted that the decoupling between these two powers remains achievable with the same response time despite the variation of the resistance's Rr and Rs as shown in Figure 9.This shows the robustness of the control by sliding mode facing this variation.

CONCLUSION
A first sliding order of the sliding mode control has been designed and implemented in order to control the output power of a DFIG generator based-WECS.The simulation results prove that the SMC approach is easy to implement and has a quick response with a robust performance against variations in the wind profile and the disturbances in all the system.

Figure 2 .
Figure 2. Evolution of the coefficient Cp as a function of the specific speed λ

Figure 4 .
Figure 4. Diagram of the two-level inverter

Figure 7 .
Figure 7. Results of the control by sliding mode of the DFIG for rung speed; (a) active power ps, (b) reactive power Qs, (c) d-q stator current, (d) dq rotor current, (e) abc stator current, (f) abc rotor current

Figure 8 .
Figure 8. Results of the control by sliding mode of the DFIG for variable speed; (a) active power Ps, (b) Reactive Power Qs, (c) d-q stator current, (d) dq rotor current, (e) abc stator current, (f) abc rotor current

Figure 9 .
Figure 9. Robustness test with variation of resistances Rr and Rs for a variable wind speed .