Sensorless Control of Brushless Doubly-Fed Generator Using Luenberger Observer Based Wind Energy Conversion Systems

Received Mar 14, 2018 Revised May 31, 2018 Accepted Jun 6, 2018 This paper investigates the use of Luenberger observer for sensorless power control of brushless double fed induction machine (BDFM) in wind energy conversion systems, the control strategy for flexible power flow control is developed by applying flux-oriented vector control (technique), In order to estimate the rotor speed, an adaptive algorithm based on Lyapunov stability theory will be design. Finally, the analyzed and simulation results in MATLAB/ Simulink platform confirmed the good dynamic performance of this new sensorless control for BDFG based variable speed wind turbines.


INTRODUCTION
In recent years, the electrical machine has expanded considerably with the development of power electronics and data processing, in this way a many researchers developed the difference observation, for estimating the rotor speed and parameters identification of electrical machine. The Brushless double fed induction motor is one of the most important ac machines used because of its low cost and high reliability [1].
Sensorless control has been successfully applied to the BDFG based on an extended Kalman filter observer [2], The rotor speed estimator is designed by a phase locked loop ignoring the power winding resistance [3], and MRAS observer scheme based on the stator current of the control winding (CW) yessed the a phase locked loop (PLL) is proposed by [3].
The Luenberger observer is a well-known method for the sensorless control of cage induction machines, there are few reports related to the use of Luenberger observer for sensorless control of DFIG [4][5][6], when has been proved to be a good compromise between accuracy and complexity, and is able to work at wide speed range [7].
This paper discussed of a novel sensorless vector control of BDFG using Luenberger observer (LO), the error between the observed value and the true value considered the rotor speed , based on Lypunov's stability theory.
And the flux equations are given as: The electromagnetic torque of BDFG is expressed as [3]: The active and reactive powers of BDFM are as follows: ) i V i V ( 2 3 Q dp dp dp qp p   (10)

VECTOR CONTROL DESIGN FOR BDFG
In this section, the vector control of BDFM will be presented, to achieve regulation of the active and reactive power between the BDFG and the grid [9], [10]. The vector control of BDFM is similar of the principle of classical vector control of DFIM, which it based of annulled the quadrature component of the PW flux, and suppose the p R is neglected, the Equations (2) and (5) can be written as follow: The rotor currents can be described using the power stator current:

The PW Currents Regulation
The mathematical mode of BDFG in the steady state given by [11], s are the slips, which can be expressed as: Used (14), (15) (16), (11) (13), The control winding can be expressed as : The third term: Shows another cross and the general block control diagram is shown in Figure 2.

THE LUENBERGER OBSERVER
Using the six-order model of the Brushless doubly-fed induction machine in fixed stator d-q axis reference frame with PW current, CW current and rotor current components as state variables.
The dynamic model of the BDFM is given in (d-q) reference frame that is used in LO for state observation, the model is given below: The system matrix A, the input matrix B and the output matrix C are given as: Where: The Luenberger observer which estimates the all stator currents will be designed using the BDFM model.
The Luenberger matrix gain L is chosen so that the poles of the characteristic matrix AL= A + LC to be stable. So, all eigenvalues of AL should have negative real parts.
The poles can be placed by solving the differential equation, thus the matrix gain L can be calculated by the function (PLACE) Pole placement technique in MATLB.

Estimation of the Rotor Speed
The estimation error of the state variable giving by: A  is the error between the two matrices as being exclusively caused by the error between the real and the estimated speed Where k is a positive constant. Usually the following proportional and integral adaptation mechanism, in order to improve the response of the rotor speed estimation.

WIND TURBINE MODEL
In this work a horizontal axis wind turbine is used, which the mechanical power of the wind can be derived as: Where  =air density, R =radius of Blades,  =wind speed and Cp = power coefficient which can be derived as: The power conversion coefficient defined as: Where t  =the turbine rotor speed. The wind turbine is normally characterized between Cp and γ for the given values of pitch angle (   ) is as illustrated in Figure 3.

Pitch Angle Controller Design
The advantage of pitch angle control is mor efficiency in low wind, small variation in the pitch angle can give strongly influenced by of the blade respect to the direction of the wind or to the plane of rotation. Used the wind velocity υ, the reference rotor speed for extracting the MPPT is obtained by: The gearboxes in a typical wind turbine increase the speed of the generator by the relation t m G   The pitch controller is employed to regulation the rotor speed at the maximum used the rotor speed measure and the reference speed, which can find by the Equation (36).
A simple proportional-integral (PI) controller is used to regulation, this regulator followed by limitation to fixing the angle to between the maximum and the minimum angle as shown in Figure 4.

SIMULATION RESULTS
The senseless control developed has been implemented in a MATLB 7.0 /simulation, The BDFM used in this simulation model is 3Y-3Y connected and its stator winding is 2-6 poles. The machine parameters presented by J. Poza [3] are used in this simulation as showed in table 1.
To verify the state estimation performance extensive simulation tests were carried out to compare the sensouless control under different wind speed.
A step change in wind speed is simulated in Figure 6, the wind speed is start at 5m/S, at 7second, the wind speed suddenly become 7m/S

CONCLUSION
In this study we presented in detail sensorless control strategy for (BDFG) in variable speed wind turbine generators used Luenberger observer, a vector control strategy using power winding flux-oriented scheme is proposed to assess the decoupage of active and the reactive power, the observer gains are selected by the pole placement method and the stability of the observer is analyzed using the Lyapunov theory.
The simulation results show effectiveness of the optimal power sensorless operating methods in low and high wind speed, we can conclude the MPPT senseless operating methods proposed only by measuring phase voltages and currents therefore it can improve the control system dependability and energy conversion competence efficiency.