BASIC SPECIFICATION REGARDING THE WIND POWER SYSTEMS CONTROL

The paper proposes an original metod to control the wind power system at variable wind speed. In the case of those high power wind systems that presents large inertia moments due to the variable wind speed, the rotation speed of both wind turbine and permanent magnet synchronous generator can not be modified in a timely manner so as to ensure the turbine operating in maximum power points. Therefore, the paper presents two control structures. First structure is based on the load calculation of permanent magnet synchronous generator and the second is based on the load modifying by using controllers. The rotation speed of turbine estimation has been used as reference in the both structures.


INTRODUCTION
The wind speed ranges as in (1), and the best results are achieved, into the technical-economical working domain, for the interval 12 ÷ 15 m/s.
In the case of wind power systems operation due to time variation of wind speed, a lot of important issues occure, they are the following: 1. load generator determination is perform in order to accomplish the maximum of captured energy for a long time period (days); 2. most efficient control methods determination from the both technical and economical points of view; 3. some real mathematical models determination for wind turbine and electrical generator (generator that usually has permanent magnets); 4. boundaries establishing between to fit the initial conditions, (regarding speed and load of the generator) in the case of electrical network plugging, is achieved by simulation; 5. establishing the quality of base duty cycles for different control structures shall be determined by simulation.
In the most works [1,21] the control methods at full power are proposed, which may result in a shutdown of the turbine because the artificially increased power is not obtained from the wind, but from the kinetic energies variation of rotating masses. Considering this reason, it is more fair to operate at maximum energy obtained in a large time interval, by the order of days. Thus, it is necessary to determine the speed of generator (RPM or reference angular speed), so that the energy captured by the wind turbine reach the maximum value, taking in to account that the wind speed varies significantly in time.
The RPM reference value can be achieved by various methods:  requiring the generator load resistance that is calculated by using the mathematical models of both wind turbine, permanent magnet sincronus generator and by measuring the wind speed, as well;  using controllers that modify the generator load in order to obtain the reference speed.
At certain values of the controller constants, override and instability occur in the case of controller adjusting. If the dependence of reference angular speed by the wind speed is given by the manufacturing company of turbine, these situations can be avoided.
The load resistance of generator can be calculated and the wind system, which consists of wind turbine coupled to permanent magnet synchronous generator, works in optimum energy parameters, if the reference angular speed is known.
RPM modification of the generator is slowly due to the very high inertia momentums of wind turbine and it can not follow a fast variation of the wind speed, as required to operate in the maximum power points [1], [3], [15].

Specifications
1. Due to the high mechanical inertia, the simulations and all the other theoretical and practical results must have intervals of at least several days (typically more than 10[h]).
2. The best control systems should provide the maximum wind energy captured in a long time interval.
3. The wind system control at maximum power obtained from the electrical generator leads to turbine braking and, also, to the artificially power increasing for the moment. This artificially power increasing is not obtained from wind, but from the kinetic energies variation of rotating masses. But in the end, after a long time period, the obtained energy is less than the previous case.
4. On the other hand, the control of wind system at the maximum energy, which is achieved from the electric generator, is the right solution from technical and economical point of view and it requires estimating the fundamental quantities-dependent by the wind speed, such as: wind turbine RPM, current intensity or generator load resistance.
Optimum control of wind system involves capturing the maximum energy at variable wind speed. This requires both RPM and torque control of the turbine, and also adapting the generator load to the wind speed.
Within the sampling interval Δt, the electrical generator has to take both the maximum available wind energy and the kinetic energies difference of rotating masses, and the real RPM of the generator goes to the reference RPM (optimal RPM). M a r c h 1 4 , 2 0 1 4 On the interval Δt and at V(t) wind speed, the maximum available wind energy is achieved by taking the RPM (the reference speed) and the variations of kinetic energies and increasing (or decreasing) the additional load of the electrical generator.
The wind system works optimally (at the maximum energy) when the wind turbine (TV) has the maximum possible energy in a given time interval, by the order of days.

Mathematical model of wind turbine
The experimental mechanical characteristic of wind turbine is given by an analytical function whose characteristics passes through the experimental points, as shown in figure 1, [3].
An original model of wind turbine is considered, the model allows estimating the optimum reference angular speed ωref.
Equation (2) represents the proposed analytical expression of the wind turbine torque that is reduced to the generator shaft.
where A and B are achieved by the experimental mechanical characteristics, V is the wind speed, and ω is the mechanical angular speed. .

Fig 1: The experimental mechanical characteristics
The value of mechanical characteristic (MTV(ω)) is obtained by using (3).  .  The average speed, which is VMEDIE=6.3[m/s], can be expressed in another form by using (4), it is shown in figure 5.

Fig 5: The modeled wind speed
If the generator speed is assumed as being constant (having a certain value), and the wind speed has a sinusoidal variation, the issue is to determine the RPM of generator so that the captured energy, by the wind turbine (TV) in the time T, to be maximal.

Specifications
The maximum power point PMAX1 of wind turbine has the coordinates (ωM1,PM1) at VMIN wind speed, while PMAX2 has the coordinates (ωM2,PM2) at VMAX wind speed.
The maximum power of wind turbine depends on the wind speed caracteristic, as in (5). M a r c h 1 4 , 2 0 1 4 Therefore, in the analyzed case of minimum wind speed VMIN=4[m/s] and maximum VMAX=8.6[m/s], the maximum power given by wind turbine has the following values:  can not be achieved, it could be concluded that the wind power system can not operate in the maximum power points. They being unable to work in the maximum power points, the problem is to determine the turbine RPM, so that the wind system to reach the maximum energy in a time period, by the order of days.

Mathematical model of the permanent magnet synchronus generator
In the current applications of wind systems, because the processes are slowly and possess high mechanical inertia, the simplified orthogonal model is used for the electrical generator. This model is given in [3]. In case of stady-state, the algebraic system from (8) for the permanent magnet synchronous generator is used.
where MPMSG=MG is the generator torque, R1 is stator winding resistance, Ld is the inductance of the stator winding on the d axis, Lq is the inductance of the stator winding on the q axis, p1 is the number of pole pairs, and ψM is permanent magnet flux.

Determining the generator load
The issue consists in determining the generator load, so that the RPM to oscillate around the optimum value.
By using (6), and integrating over a time period T, it is obtained:

CONTROL OF THE WIND SYSTEM
If the reference mechanical angular speed (ωref) is known, the reference load rezistance of generator can be determined. If the reference rezistance (R=138.83[Ω]) is known, the wind system control can be achieved in two ways:  the load resistance has a prescribed value;  the load resistance is modified by controllers.

P controller
The equation of P controller is given in (9)  

PI controller (the mechanical angular speed ω has a prescribed value)
The PI controller equation is given in (10).
The proportionality constant has the value:  The controller constants determination (K1 and K2) is done by following analysis of the below simulations.
The movement equation and the PI controller equation form a system of differential equations. This system models the behavior of anssembly and consists of wind turbine and permanent magnet synchronous generator.

PD controller (the mechanical angular speed ω has a prescribed value)
The PD controller equation is given in (11).

CONTROL STRUCTURE OF WIND SYSTEM
The generator load modification is done by the power converters interposed between the turbine and the energy storage block that can be achieved in two basic variants:   figure 19. The controller (R) modifies the generator load at the output (α) via the thyristors ignition angle of three-phase rectifier [7].

Case of electrical accumulators
The available maximum wind energy at the wind speed V(t), in the Δt time interval, is captured by taking the reference speed (ωref).

Case of electrical accumulators, super-capacitors, and network
Operating at the optimum speed (RPM), ω, is perform by estimating the wind speed using the anemometer (AN) from figure 20 and calculating the ωref. In this way, the power variation, which is generated by the variable wind speed, can be diminished by storing the power peaks in AE/SC by the proper control of power converters (DC-DC1 and DC-DC2).

Specifications
1. The control of rectifier R1 is achieved by considering the generator RPM.
2. The control of inverter I1 is achieved by maintaining constantly the power P3.
3. The control of both DC-DC1 and DC-DC2 converters is done by considering the power P2=P1-P3 and must follows the time variation of wind speed.

CONCLUSIONS
Paper shows how many issues involve the time variations of wind speeds.
The mathematical models of both, wind turbine and permanent magnet synchronus generator, allow the optimum RPM determination, such that the maximum captured energy.
By using the original mathematical models of wind turbine and permanent magnet synchronus generator, various operating modes have been simulated, and they were determined the energies obtained in conditions in that the mechanical angular speed was calculated using either instantaneous speed or average speed.
From the above simulations, the following important aspects of the wind system control can be observed: 1. In all the analyzed cases, the prescribed mechanical angular speed (ωref) for the generator load is achieved in 12200[s], ie 3.38[h].
2. If the load adjustment is achieved by using a P controller, the mechanical angular speed is accomplished in 3.38[h] and do not occur overrides.
The initial conditions, which are the mechanical angular speed ω(0) and the load resistance R(0), by their value, are not significantly influencing the behavior of system, in the sens of occuring the overides or the instabilities of the system controlling, by calculating the generator load as a prescribed value or by using the P controller that has been provided with the reference size ωref.

The control time is by the order of hours and it is ranging between 3[h]-5[h].
The influence of initial conditions on the system dynamics were analyzed and the solutions for reducing the duration of the transient process were proposed.
In this paper two management structures have been presented based on the obtained results.
All contributions presented in this paper are of great importance for both the technical and economical environment, and thus they can be used with confidence in practice, because they are experimental results achieved considering the real problems existing in the technical-economical environment, so they are not theoretically.