Lyapunov based Control Strategy for DFIG based Wind Turbines to Enhance stability and Power

Control


░ 1. INTRODUCTION
The literature has offered a wide range of control strategies for wind turbines looking to produce the maximum electrical Energy.Most of them are based on various nonlinear control methods that fall under the umbrella of traditional techniques.
[1]- [2].In regular traditional methods Most of the times the controller gain is not tuned as per the turbulent wind, so unable to generate required electrical torque and optimum power tracking [22] and in all the traditional methods the electrical torque is proportional to square of rotor speed.The method described here is significant because it enables adaptive tracking of the rotor speed via power coefficient calculation even in the case of turbulent wind.The approach described in this article can trace the maximum power points without the need for a perturbation or dither signal.
The Lyapunov-based stability technique is one of the best used methods for calculating the stability parameters of nonlinear electrical systems.It mainly focuses on a transient stability and gives exact fault clearance time.Lyapunov-based methods are founded on the fundamental tenet that every physical system includes an energy with a positive value that may be represented by an energy function.(EF) [3].The system is stable if and only if the energy of the system is positive and its time derivative is negative or if it is equated it to zero then the system is stable and will get maximum value of real power [4] otherwise any system can deteriorate.In [4], When two unique WTs were connected to a single grid, and EF was used to ensure the system's stability.The proposed Lyapunov control strategy developed for wind turbine is used to ensure system stability and tracking path of maximum value of real powers with the help of power electronic based controllers [7]-[8].

Operating regions of wind turbine
Three separate locations have wind turbines.When the wind speed is lower than what is necessary, a turbine should be capable of generating the most electricity.In this case, the generating torque control keeps track of the rotor speed while the pitch angle is fixed.The turbine must operate in area III as shown in fig1 at its rated power continually.Here, there is more wind energy available than can be measured for collection.The turbine works with less efficiency, as a result.The generating torque is kept constant, and the rotor speed is constrained by pitch control, reducing changes in output power.The output power must be considered because it is affected by the rotor speed and torque product and must be kept constant at its rated value.Both constant torque and constant power techniques are pertinent to Region III in fig. 1 The blade pitch and generator torque work together to control the rotor speed in Region II in fig 1, which is sandwiched between Regions I and III.Due to its connection to the region of maximum power, this region might occasionally be disregarded.

░2.PROPOSED CONTROL STRATEGY of MPPT
Figure 1, By developing highly effective power electronic converters, wind systems can better integrate with the grid and provide higher-quality power.Before wind power can be developed and used to generate the maximum power, many issues must be resolved.Utilizing as much power as possible will boost productivity of wind energy conversion system.But existing P&O strategy can fail when the wind speed changes so quickly.The proposed technique in this paper will track the maximum power point effectively for wind changes.Unfortunately, the perturb-and-observe(P&O) technique necessitates the introduction of a dithering or perturbation signal that deviates from the track of maximum power points.

Fig. 2: Block diagram of DFIG Based Wind Energy Conversion System
The proposed method uses three control loops.The rotor speed squared determines the electrical torque, and three control rules allow for real-time adaptive adjustment of the proportional coefficient.Once the intended rotor speed and power capture coefficient are determined, the first control law uses feedback linearization to calculate the target electrical torque instantly.The real time power capture values determined by second control law; the required speed of rotor is generated by third control law.

Control law 1: Electrical/generator torque,
Due to nonlinear nature of wind the generated aerodynamic torque is also nonlinear in nature i.e.
* =  ̂(, WR) − ()(1) The system will become linear by using feedback linearization through variable input signal.Using this feedback linearization, the nonlinear terms in torque and power equations can be cancelled and we can estimate the exact value of power capture coefficient using the following formula The equation of motions From above three equations the Generated torque will be proportional to desired torque.
The strategy is to make  ̇ a non-positive quantity.So, the first term in equation ( 13) is chosen to be zero, that is,  ̂ ( ̃ +  ̂ ̇) = 0 Therefore, the equation ( 12) is simplified as Herein,  ̂ in equation ( 14) is not equal to zero and other term which is in parenthesis will become zero.Therefore The adaptive PT controller result including power capture co efficient estimation with feedback linearization can be written as: Where  1 () and  2 are time varying parameters.

Control Law 3
The maximum-Power Tracking seeking law can also be extracted by.Substitution of () =    ̃ and  ̂ ̇ from equations ( 17) & ( 15) From above equation the,   * ̇ is calculated to ensure that ( 20) is always a non-positive value.In order to maintain a nonpositive value  ̇≤ 0 in equation ( 16), one can select   * ̇∝ (− ̃) and proportional constant   adequately as much as high to maintain large non positive value with respect to third term in equation 16. therefore, the required speed of rotor can be formulated as At this point where (    ) ⁄ =0 gives optimum power and peak value of Cp with constant wind velocity.

WITH SIMULATION
The Wind turbine of 1.5MW capacity system includes transmission line integration model, power converters with back-to-back connections along with DFIG driven gear system of turbine is modeled in MATLAB/Simulink in order to verify proposed control strategy mentioned in this paper.The wind speed profile with two step changes is considered as input, The feasibility of the suggested technique was examined using abrupt step increases in wind speed and turbulent unsteady wind in region 2 of the wind turbine, and the findings are provided in this section.Control parameters, , kp, ke were taken to get result of control strategy10x106and10x105,0.002 respectively.According to fig9.At t=1.7 sec, a step shift from 7 m/sec to 20 m/sec occurs, and second shift happened at t=7 sec to 20m/sec.At times t=3 sec and t=7 sec, the recommended MPPT control is in its ON and OFF states.The results of the simulation and the control circuit are depicted in the diagram below, along with the wind speed, real and VAR powers, rotor speed, produced torque, and power capture coefficient.In order to test the viability of the suggested control strategy/ technique, wind speed profiles and abrupt step changes in wind speed with turbulent wind in second region of wind turbine with 1.5MW rating were used.The results are presented in this section.

Fig. 7 :
Fig. 7:Simulation Diagram of Proposed MPPT Wind Energy Conversion System

Fig. 8 :
Fig. 8: Simulation Block of Control CircuitAccording to results shown in fig 9,10,11, the determined rotor speed automatically in tune to maintain Cp (0.37 p.u.) at maximum value.For various wind speed conditions, the controller adjust the parameters to maintain desired speed and power capture coefficient.From the above three control loop operations irrespective of wind velocity profiles the coefficient of power is always trying to reach maximum value.