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The present paper deals with the modeling and control of Wind Energy Conversion System WECS based Doubly Fed Induction Generator DFIG using the slip energy recovery principle. The proposed drive system uses a Matrix Converter (MC) to transfer the slip energy of the rotor into the mains instead of using cascaded ac-dc-ac converter whilst the stator side is fixed to the grid. Operation at both sub-synchronous and super-synchronous regions is possible with the proposed drive system. The different level control strategies for maximum power point tracking and active-reactive power are discussed. Simulation results of the proposed doubly fed induction generator drive system show the good performance of the control system strategy for both transient and steadystate conditions.

Wind energy conversion systems (WECS) are generally equipped with Doubly Fed Induction Generator (DFIG) functioning at variable speed. For fixed-pitch turbines operating in partial load, maximum energy capture avail- able in the wind generator can be achieved if the turbine rotor operates on the Optimal Regime Characteristic (ORC). This regime can be obtained by tracking some target variables: the optimal rotational speed, depending proportionally on the wind speed, or the optimal rotor power [

Several configurations for variable speed wind energy conversion system based on Doubly Fed Induction Generator are available in the literature. We cite some examples; the first one is the slip energy dissipation: here the stator side is directly fixed to the grid whereas the rotor side is connected to a rectifier converter. In the out- put of this converter, a resistive load is connected via a DC-DC converter. Its main role is keeping the DFIG in the stable part of torque-speed characteristic, and this is achieved by varying the slip energy to feed the resistive load, where the rotor energy changes according to speed variation. The main disadvantage of this configuration is its bad efficiency especially when the slip energy increases to an important value [

The second topology is Kramer structure: in order to minimize the losses caused by the previous configura- tion, a DC-DC converter and resistive load are replaced by DC-AC inverter to inject the slip energy into the gid. So this structure allow the generation only in hyper synchronous regime [

The third topology known as Scherbius structure, employs a DFIG using a back-to-back PWM converters or line commutated cycloconverter connected between rotor side and mains [

In this paper, by numerical simulation we investigate the role of Maximum Power Point Tracking (MPPT) controller in a variable speed WECS to control the power conversion. In this way, the classical PI control is widely used, owing its popularity to some key features. Its design procedure is quite simple. It requires little feed- back information and gives rise to solutions easy to implement, with intrinsic robustness properties which can be employed over most plants having smooth models [

The configuration of WECS is based on a DFIG well adapted for large speed variation range fed by a Matrix Converter (MC) used as the interface between the electrical generator and the grid side. Its main purpose is to control the speed and the rotor side currents of wound-rotor induction motor. Such a configuration can offer the advantages given by back-to-back converters while converting ac power in a single stage and eliminating the large dc link capacitor. In addition, the control scheme required by ac-ac conversion scheme is simpler than that of a two-stage power conversion [

• To avoid the generation of overvoltages, produced by the short-circuit impedance of the power supply, due to the fast commutation of currents;

• To eliminate high-frequency harmonics in the input currents.

Several variable-speed WECS configurations are being widely used in literature. The studied configuration in the present paper is a fixed pitch Horizontal Axis Wind Turbines HAWT. The power characteristics of the wind turbine of the studied system have a maximum for each wind speed. All these maxima form the so-called Op- timal Regime Characteristics ORC given by

The studied configuration has a power coefficient (aerodynamic efficiency)

The power coefficient

Power captured by a wind turbine vs. high speed shaft

Aerodynamic efficiency versus tip speed ratio

The equations that describe a doubly fed induction generator are identical to those of the squirrel cage induction generator; the only exception is that the rotor winding is not short-circuited. We assume balanced voltages and non-ground connection points regime. Two orthogonal axes are defined, the

In order to obtain a decoupled control of active-reactive powers, the DFIG model requires all quantities to be expressed in the stator flux reference frame where [

The rotor voltage expressions are simplified as:

The stator current expressions are:

The expression for the electrical torque:

The stator active-reactive powers expressions are:

Note that:

where

Despite some drawbacks such as high number of power semiconductor devices, the limitation of maximum load voltage to 86% of the supply voltage, no need for energy storage element, the matrix converters have received recently a wide attention especially in motion control. The three-phase to three-phase direct matrix converter has been extensively researched due to its potential as a replacement for the traditional AC-DC-AC converter in AC motor drives for the following benefits [

• Adjustable input displacement factor, irrespective of the load;

• The capability of regeneration (four-quadrant operation);

• High quality input and output waveforms;

• The lack of bulky and limited lifetime energy storage components, such as electrolytic capacitors.

The MC converter is based on bi-directional switches and replaces the rectifier, inverter and energy storage element of the AC-DC-AC converter in only one stage thereby reducing the size of the conversion chain but in- creasing the control complexity.

It must be mentioned that the load current must not be interrupted abruptly, because the inductive nature of the load will generate an important overvoltage that can destroy the components. In addition, operation of the switches cannot short-circuit two input lines, because this switching state will originate short circuit currents [

Referenced to the neutral point N, the relation between the load and input voltages of the DMC is expressed as:

where

the relation of the voltages is given by

Applying Kirchhoff’s current law to the switches, the following equation can be obtained:

Considering the current vectors

the equation for the current is

where

MC current and voltage input

MC current and voltage output

The input filter model is shown in

where

with

The filter parameters are chosen in order of high rank harmonics eliminating with into account the next con- siderations [

• The cut-off frequency of the filter should be lower than the switching frequency and higher than the funda- mental frequency of the input AC source.

• The input power factor should be kept maximum for a given minimum output power.

MC current and voltage output

Single stage input filter

• The lowest volume and/or weight of capacitor and chokes is used in the design procedure.

• The voltage drop in the inductor should be at its minimum value.

To ensure an optimal regime it must manipulate the aerodynamic efficiency coefficient by regulating the speed generator in order to keep

The DFIG torque is controlled to maintain the tip speed ratio at its optimal value. The speed setpoint is derived from the optimal tip speed ratio as:

where

Current and voltage source after filtering

Current and voltage source after filtering

The closed loop transfer function is:

In order to obtain a first order system behavior:

the controller parameters’ are expressed as:

Complete model scheme of the studied drive system is illustrated by

The numerical simulations are evaluated on Matlab-Simulink hardware for 5 seconds in several conditions for the wind speed variations as it is given by the profile of

Figures 12-18 illustrate respectively the high speed shaft tracking of the DFIG, the electromagnetic torque; the aerodynamic torque, the aerodynamic power, the optimal regime characteristic; the tip speed ratio TSR and the aerodynamic efficiency

Figures 19-22 depict the stator active and reactive powers injected in the grid via the RLC filter, the MC output voltage which is the rotor voltage

PI control scheme

Grneral control schem

Wind speed profile

Also, Figures 24-26 depict the MC input current, with input voltage in both sub-synchronous regime and hy- per-synchronous regime, in the sub-synchronous mode. They are in phase, but when HSS exceeds the syn- chronous speed they become shifted with π. The next

Speed shaft tracking

Electromagnetic torque tracking

Aerodynamic torque

Aerodynamic power

Tip speed ratio compared with the optimal value

Tip speed ratio compared with the optimal value

Aerodynamic efficiency

Active and reactive generated power

(a) Rotor terminal voltage and its reference; (b) Zoom in Rotor terminal voltage—MC voltage output

(a) Stator current ias; (b) Zoom on stator current ias

Rotor current iar (MC output current)

Rotor line voltage vabr

(a) MC input current iari; (b) Zoom on MC input current iari

_{}

Rotor input current and input voltage of the MC

Rotor input current and input voltage of the MC

Unfiltered stator current and voltage isra

Filtered stator current and voltage i’sra

Fourier transform for the unfiltered current source isra

Fourier transform for the filtered current source i’sra

RLC filter proofed by the THD for both unfiltered and filtered current signals where it is observed (_{i}_{’sra} = 0.4808 (48%) for the unfiltered current to THD_{i’sra} = 0.0482 (4.82%) (

In this paper, we investigate by simulation results the effectiveness of a proposed control method for maximizing the power harvested from the wind. A general model and control laws are analyzed and simulated for optimal power production of a variable speed wind turbine equipped with a doubly fed induction generator. The control system is based on traditional PI controllers. The supply side converter is a matrix converter with SVM modula- tion technique.

Over the different simulation results, it is observed that the performance of the WECS system is enhanced in terms of tracking speed and torque, oscillations around optimal power points and especially low current distortion in the grid side obtained by inserting a RLC filter before connecting with the grid.