Regulation of the Excitation Reactive Power of the Asynchronous Wind Turbine at Variable Speed ()
1. Introduction
In remote areas, the asynchronous wind turbines are the most widely used ones for the electricity generation. They, generally, do not produce reactive power, for this reason, the use of the capacitor banks connected in parallel to the terminals of the stator coils of the asynchronous generator, for the generation of the needed reactive power, is necessary.
This article is divided into three parts:
Firstly, from the experimental tests, we have modeled and simulated, in transient state, under MAT-LAB/ SIMULINK environment, an isolated wind system composed by: Turbine, multiplier, Shaft, self-excited asynchronous machine of 1.5 kw, static inverters AC-DC, LC filter, and resistive load [1-4].
Secondly, we have determined the shaft angular speed of the induction generator according to wind speed, the turbine parameters and the multiplier, the resistive torque and frictions [5].
In the third part and in taking account that the output voltage of the asynchronous generator varies with the sudden change of wind speed and load [3-6], we have developed a law and adaptive control for regulating the output voltage of the system at a constant value [6-10]. The adaptive control is based on the use of reactive power necessary to excite the asynchronous generator.
Finally, the simulation results obtained are discussed to show that the output voltage is exactly controlled at the desired value.
2. Modeling of the Isolated Wind System
In this part of this work, we modelled and simulated a system consisting of a wind turbine with blades of length R, involving an asynchronous generator with gearbox of speed gain M.
2.1. The Turbine Model
The power of the wind is defined by:
(1)
where is the air density, R is the blade length, and V the wind speed.
The aerodynamic power appearing with the rotor of the turbine is given by:
(2)
Such as: represents the aerodynamic performance of the wind turbine. The ratio speed is the relationship between the linear velocity of the blades and the speed of the wind
(3)
Where is a mechanical rotation speed of the turbine, for the turbine used in this study, the reactive power coefficient is approached by the following formula [7]:
(4)
Figure 1 shows the variation of the coefficient (Equation (4)) as a function of lambda. By using the preceding equation we deduced the aerodynamic torque according to the Equation (5):
(5)
2.2. Model of the Gear
The torque of the generator is given by Equation (6) and the mechanical speed appeared on the shaft of the generator given by the Equation (7).
(6)
(7)
M is the gear ratio.
2.3. Dynamic Equation of the Generator Shaft
(8)
And
(9)
(10)
(11)
where is the mechanical torque, the electromagnetic torque produced by the generator and the viscous friction torque. The schematic model of the mechanical equation is given by Figure 2.
2.4. Model of the Self-Excited Induction Generator SEIG
The classical electrical equations of the SEIG in the Park frame are written as follows:
(12)
are respectively the voltage and current output of the generator in the model of Park.
and are respectively the resistance and inductances of the stator and rotor winding, is the main inductance and is the rotor speed, p is the number of pole pair.
(13)
The electromagnetic torque is given by the following formula:
(14)
2.4.1. Steady-State Model
The Self-excited Induction Generator SEIG is modelled in the steady-state by using the equivalent diagram shown in the Figure 3:
The linear model of SEIG considers that the magnetizing inductance is constant, which is not true, as it’s seen in the Figure 4, because the magnetic material used for manufacturing is not linear.
It is very essential to take into account the saturation effect of the magnetic circuit and of the variation of magnetizing inductance.
To approach the characteristics of the induction machine (All the experimental points Lm) by a mathematical function, we used an approximation method.
The experimental curve of the magnetic inductance is divided into three parts
For
For
Figure 3. The Phase equivalent circuit of the SEIG.
Figure 4. Magnetizing inductance of the induction machine.
For
2.4.2. Transient Model of SEIG
By taking into account the initial conditions for the process of self excitation, the transient state of (SEIG) is represented in the model of Park by the matrix according to:
Kq and Kd are constant, they represent respectively the initial induced voltages of the d-axis and q-axis axes (d,q).
Vcqo and Vcdo are initial voltages of the capacitor bank on the two axes d and q.
From this matrix we have developed a mathematical model of the asynchronous generator that we use in the simulation of the wind system.
2.5. Simulation Results of Wind Systems
To simulate the wind system (SEIG and turbine), we used a machine wound rotor and a turbine of characteristics mentioned in Tables 1 and 2 respectively.
2.5.1. Start-Up with No Load
In this part of our work, we discuss the simulation results.
Figure 5 illustrates the voltage of leadless starting of the SEIG versus time. The starting time is about 2.7 seconds for a wind speed and a capacity constants of .
Also, we propose to simulate and analyze the behaviour of the system when the electrical (capacity, load) and the mechanical parameters (speed) vary, and to study the influence of the variation of each parameters on the stability and the performance of the installation.
Figure 6 illustrates the variation of the angular velocity on the generator shaft for various values of the wind speed. We observe that the mechanical speed varies proportionally with the wind speed.
Figure 7 shows the curves of RMS voltage Vs of a phase stator during the start-up period for different values of capacity. We note that the voltage changes for each value of the capacity.
Figure 8 shows the evolution of the RMS voltage (Vs) when the generator is driven empty and loaded gradually.