Robust Control of Doubly Fed Induction Generator for Wind Turbine Under Sub-Synchronous Operation Mode

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Energy Procedia 74 ( 2015 ) 886 – 899

ScienceDirect

Peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD) doi: 10.1016/j.egypro.2015.07.824

Robust Control of Doubly Fed Induction Generator for Wind Turbine Under Sub-Synchronous Operation Mode

Khouloud Bedoud

^a,b

*, Mahieddine Ali-rachedi

^c

, Tahar Bahi

^d

, Rabah Lakel

^b

, Azzeddine Grid

^a

aWelding and NDT Research Centre (CSC). BP 64 Cheraga, Algeria.

bAutomatic Laboratory and Signals, Badji Mokhtar University, Annaba, Algeria.

cPreparatory School in Sciences and Technics, Annaba, Algeria.

dElectrical department, Badji Mokhtar University, Annaba,Box 12, 2300 Algeria.

Abstract

This paper presents a modeling and a robust control of doubly fed induction generator for wind generation system. The whole system is presented in d-q-synchronous reference frame. The regulation of the electromagnetic torque , stator reactive power control and neuronal controller are applied in order to control the rotor currents of the DFIG. For to improve the controller robustness, the study is validated through simulation using software Matlab/Simulink, studies on a 1.5 MW DFIG wind generation system compared with conventional proportional integral controller. Performance and robustness results obtained will be presented and analyzed.

Peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD).

Keywords:Wind power generation, Modeling, Control, Doubly fed induction generator, Neuronal controller, Performances;

* * Corresponding author. Tel.: +213-388-759-82; fax: +213-388-760-05 E-mail address:[email protected]

Peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD)

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1. Introduction

Faced to the worldwide demand for the conservation of nature and maintaining the biodiversity of natural environments, the world is heading towards renewable energy to produce electricity. Wind power is one of the cleanest sources of renewable energy that allow producing the green energy. However, wind energy is a natural resource that features many advantages since while producing electricity they do not propagate any gas greenhouse effect, do not degrade the quality of the air and do not pollute nor the soils or waters. Furthermore, it do not produce toxic or radioactive waste [1, 4]. Nowadays, wind generation system based on a doubly fed induction generator (DFIG) are employed widely in large wind farms fat has its many advantages: a very good energy efficiency, robust sensorless operation [5,6] as well as ease exploitation and control, fault-tolerant, auto-fault detection power converters [7]. In addition, the power converter is usually rated at 25-30% of the generator power rating [8-11] For such several advantages, this machine has generated a lot of curiosity on the part of researchers have tried to develop strategies to best exploit its strong points [12].

The conventional "PI" controller is extensively used in the control of doubly fed induction generator which his parameters are initially calculated according to the DFIG parameters. But in practice, the machine parameters change inevitably during the time. The problematic studied in this work is to find a compromise between the change of the parameters of the DFIG and the efficiency of the control. To solve this problem, we used the neuronal controller (NNT).

The paper is organized as follows. Section 2, describes the modeling studied system. The various control algorithms for optimal turbine operation and control of active and reactive power will be presented in section 3. The proposed NNT controller performance is compared with conventional proportional integral controller (PI), the results of simulations obtained are presented and discussed for validating the proposed controller in Section 4.

Finally, the conclusion is drawn in section 5.

Nomenclature

ܲ_௦,ܳ_௦ stator active and reactive power ߱s, ߱r synchronous and rotor angular frequency

ܲ_௥,ܳ_௥ rotor active and reactive power ߩ air density

ܶ௘௠ DFIG electromagnetic torque (N m) ܸ wind speed

݀,ݍ synchronous reference frame index R rotor radius

ܸ௦ௗ,௤ stator d–q frame voltage Ȝ tip-speed ratio

ܸ_௥ௗ,௤ rotor d–q frame voltage π_௧௨௥ aeroturbine rotor speed

݅௦ௗ,௤ stator d–q frame current π_௠ generator speed

݅_௥ௗ,௤ rotor d–q frame current G gearbox ratio

߮_ୱୢ,୯ stator d–q frame flux ܬ turbine total inertia

߮୰ୢ,୯ rotor d–q frame flux ܬ௧௨௥,ܬ௚௘௡ rotor and DFIG inertia

ܴ_௦,ܴ_௥ stator and rotor Resistances ݂ turbine total external damping ܮ௦,ܮ௥ stator and rotor self Inductances ı Coefficient of dispersion.

ܮ_୫ mutual inductance CNV1/CNV2 First converter/Second converter

2. Wind Turbine Conversion System Modeling

A wind turbine conversion system is a system that converts the wind turbines mechanical energy obtained from wind into electrical energy through a generator calibrated according to nominal turbine speed, number of generator pole-pairs and network frequency [11, 13, 14]. Fig. 1 shows the synoptic scheme of the studied system.

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Fig. 1. Schematic diagram of DFIG wind turbine

The main parts of this scheme are the wind turbine, the gearbox and generator. The rotor-side converter (RSC) and the grid-side converter (GSC) connected back-to-back by a dc-link capacitor. The two converters, network side CNV2 and rotor side CNV1 are ordered in Pulse Width Modulation [15-16]. In typical mode of operation, the rotor delivers active power to the grid when the DFIG operates in super-synchronous speed and absorbs active power from the grid (or from the generator stator) when the DFIG operates in sub-synchronous speed. The DFIG stator usually delivers active power to the grid in both sub-synchronous and super-synchronous speeds [10]. The models of the different components of the wind-turbine generation system are described below.

2.1. Turbine Modeling

The theoretical power produced by the wind is given by [17- 19]:

ܲ_௧௨௥ =ܥ௣.^ఘ.ௌ.௏^య

ଶ (1) Where C_୮ denotes power coefficient of wind turbine, its evolution depends on the blade pitch angle ( ) and the tip-VSHHGUDWLRȜZKLFKLVGHILQHGas [17- 19]:

ɉ=^ୖ^.^౪౫౨

୚ (2) From summaries achieved on a wind of 1.5 MW, the expression of the power coefficient for this type of turbine can be approximated by the following equation [20]-[21]:

C_୮=ቀ0.35െ ൫0.0167(Ⱦ െ2)൯ቁ ൭sin ቆ ^{஠(஛ା଴.ଵ)}

ቀଵହ.ହି൫଴.ଷ(ஒିଶ)൯ቁቇ൱ െ ൫0.00184(ɉ െ3)(Ⱦ െ2)൯ (3) The aerodynamic torque expression is given by [22]:

ܶ_௧௨௥ =^௉^೟ೠೝ

_೟ೠೝ=ܥ_௣.^ఘ.ௌ.௏^య

ଶ . ^ଵ

_೟ೠೝ (4) The gearbox is installed between the turbine and generator to adapt the speed of the turbine to that of the generator [22]:

_௠௘௖=ܩ._௧௨௥ (5) The friction, elasticity and energy losses in the gearbox are neglected.

ܩ= ^்^೟ೠೝ

்_೘೐೎ (6)

mec

࢏࢘ ࢊ,ࢗ_࢓ࢋ࢙

Pr

Aeroturbine rotor

3ph, 50

Filter

ࢂ_ࢊࢉ

CNV1 CNV2

Rotor side converter

Grid side converter Ps

DFIG Gearbox

tur

Wind

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The mechanical equations of the system can be characterized by [22]:

ܬ^ௗπ^೘೐೎

ௗ௧ +݂π_௠௘௖=ܶ_௠௘௖െ ܶ_௘௠ (7) With: ܬ=^௃^೟ೠೝ

ீ^మ +ܬ_௚௘௡

2.2. Modeling the DFIG with stator field orientation

The Park model of DFIG is given by the equations below [21, 23-24]:

ቐܸ௦ௗ =ܴ௦݅௦ௗ+^ௗఝ^ೞ೏

ௗ௧ െ ߱௦߮௦௤

ܸ_௦௤=ܴ_௦݅_௦௤+^ௗఝ^ೞ೜

ௗ௧ +߱_௦߮_௦ௗ (8) ቐܸ௥ௗ=ܴ௥݅௥ௗ+^ௗఝ^ೝ೏

ௗ௧ െ ߱௥߮௥௤

ܸ_௥௤ =ܴ_௥݅_௥௤+^ௗఝ^ೝ೜

ௗ௧ +߱_௥߮_௥ௗ (9) As the d and q axis are magnetically decoupled, the stator and rotor flux are given as:

൜߮௦ௗ=ܮ௦݅௦ௗ+ܮ௠݅௥ௗ

߮_௦௤=ܮ_௦݅_௦௤+ܮ_௠݅_௥௤ (10)

൜߮௥ௗ=ܮ௥݅௥ௗ+ܮ௠݅௦ௗ

߮௥௤=ܮ௥݅௥௤+ܮ௠݅௦௤ (11) With: ܮ_௦=ܮ_௙௦+ܮ_௠

ܮ_௥=ܮ_௙௥+ܯ^ଶܮ_௠ The active and reactive powers are defined as:

൜ܲ_௦=ܸ_௦ௗ݅_௦ௗ+ܸ_௦௤݅_௦௤

ܳ_௦=ܸ_௦௤݅_௦ௗെ ܸ_௦ௗ݅_௦௤ (12)

൜ܲ௥=ܸ௥ௗ݅௥ௗ+ܸ௥௤݅௥௤

ܳ௥=ܸ௥௤݅௥ௗെ ܸ௥ௗ݅௥௤ (13) Consequently, the d-q orientation has to be synchronized with the stator flux (see Fig.2).

Fig. 2. Orientation of the d-q frame

The DFIG model is presented in synchronous dq reference frame where the d-axis is aligned with the stator flux linkage vector ߮௦, and then, (߮_௦௤= 0, ߮௦ௗ=߮௦)[19, 24]. In addition, considering that the resistance of the stator

ࡾࢉ

ࡿࢉ

0 Stator axis șU

ࡿࢇ

ࡾ_ࢇ

ࡿ࢈

ࡾ_࢈

ࢂ࢙ࢗ

࣐ࢊ࢙

d q

șH șV

d-q frame

Rotor axis

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winding (ܴ_௦) is neglected and the grid is supposed stable with voltage ݒ_௦and synchronous angular frequency ( ߱_௦) constant what implies ߮_௦ௗ=ܿݏݐ, the voltage and the flux equations of the stator windings can be simplified in steady state as [23-26]:

ቊ ܸ௦ௗ=^ௗఝ^ೞ೏

ௗ௧ = 0

ܸ_௦௤=߱_௦.߮_௦ௗ =ܸ_௦ (14) The stator and rotor voltages are given by [21]:

ቐ ܸ௦ௗ=^ோ^ೞ

௅_ೞ߮௦ௗെ^ோ_௅^ೞ

ೞܮ௠݅௥ௗ

ܸ_௦௤=െ^ோ^ೞ

௅_ೞܮ_௠݅_௥௤+߱_௦߮_௦ௗ (15) ቐ ܸ_௥ௗ=ܴ_௥݅_௥ௗ+ߪ.ܮ_௥^ௗ௜^ೝ೏

ௗ௧ +݁_௥ௗ

ܸ_௥௤=ܴ_௥݅_௥௤+ߪ.ܮ_௥^ௗ௜^ೝ೜

ௗ௧ +݁_௥௤+݁_ఝ (16) Where:

ە

ۖ

۔

ۖۓ݁௥ௗ=െߪ.ܮ௥.߱௥.݅௥௤

݁௥௤=ߪ.ܮ௥.߱௥.݅௥ௗ

݁ఝ=߱௥.^ெ

௅_ೞ.߮௦ௗ

ߪ= 1െ ൬ ^ெ

ඥ௅ೞ௅_ೝ൰

ଶ

(17)

The stator and the rotor active and reactive power can be rewritten as follows [21]:

ە

ۖۖ

۔

ۖۖ

ۓ P_ୱ=െ^୚^౩^.୑

୐_౩ . i_୰୯ Q_ୱ= ^୚^౩^మ

୐_౩ன_౩െ^୑.୚^౩

୐_౩ . i_୰ୢ

P_୰= g.^୚^౩^.୑

୐_౩ . i_୰୯ Q_୰= g.^୚^౩^.୑

୐_౩ . i_୰ୢ

(18)

The electromagnetic torque is as follows [21]:

ܶ௘௠=െܲ.^ெ

௅_ೞ߮௦ௗ.݅௥௤ (19)

3. Wind Turbine Control System 3.1. Control structure

The block diagram of the whole system control in Park reference frame is illustrated in Fig.3. In this work, the two controls studied are:

- extraction of the maximum wind power control “MPP” (Maximum Power Point) from the wind for a wide range of wind speeds,

- control of CNV1.

These controls will be considered separately in the following sections.

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Fig. 3. Block diagram of the wind control system [27]

3.2. Control objectives

The operation of a wind turbine at variable speed is generally more beneficial over constant speed operation.

Fig.4 shows the crucial advantage of variable speed wind turbines compared to fixed speed. If the wind speed varies

ܸଵand ܸ_ଶ to the speed ɘଵof the DFIG is unchanged, the power varies from ܲଵto ܲ_ଶ. In addition, the maximum power is equal to ܲ_ଷ.In case we want to extract the maximum power should be changed by ɘ_ଵand ɘ_ଶthus make the variable speed depending on the wind speed. The extraction of maximum power control is to adjust the torque of the DFIG to extract maximum power. The red dotted line indicates the optimal power points for respectively ܸ= 10m/s and 12m/s, where the ܥ_௣coefficient is kept at its maximum value.

Fig. 4. Turbine power versus rotor speeds of generator 6

ࢀ_ࢋ࢓^כ

Filter

ࢂࢊࢉ

CNV1 CNV₂

࢏ࢊ,ࢗ ࢌ_࢓ࢋ࢙

2

Grid

abc dq

࢓ࢋࢉ

MPP

mec

tur

࢏_{࢘ ࢊ,ࢗ_࢓ࢋ࢙}

Pr

P_s

DFIG

࢏_{ࢊ,ࢗ ࢘_࢓ࢋ࢙}

࢏_{ࢊ࢘_࢘ࢋࢌ}

࢏ࢗ࢘_࢘ࢋࢌ

ࣂ࢘ ࢂ_ࢊࢉ

ࢂ_{ࢊ࢘_࢘ࢋࢌ}

ࢂ_{ࢗ࢘_࢘ࢋࢌ}

Decoupling/compensation

dq

abc

PWM

ࣂ_࢙

Rotor currents control

Rotor currents calculation

ࡼࡿ_࢘ࢋࢌ

ࡽ_{ࡿ_࢘ࢋࢌ} ^ࢂ^{ࢊࢌ_࢘ࢋࢌ}

Decoupling/compensation

ࢂࢗࢌ_࢘ࢋࢌ ࢏_{ࢗࢌ_࢘ࢋࢌ}

࢏_{ࢊࢌ_࢘ࢋࢌ}

Filter currents control

ࡽ_{ࢌ_࢘ࢋࢌ}

ࢂ_{ࢊࢉ_࢘ࢋࢌ}

÷

ࢂ࢙ࢗ

DC bus control dq

abc 6

PWM

0 100 200 300 400

0 2 4 6 8 10 12x 10⁴

Rotor Speed (rad/sec)

Turbine Power (W)

w2 P2

P3

MPP w1

V2=12

V1=10 P1

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The power extracted from the wind is maximized when the rotor speed is such that the power coefficient is optimal ܥ_௣௢௣௧. Therefore, we must set the tip speed ratioon its optimal value ɉ_୭୮୲.Fig. 5 illustrates the principle of MPP control without speed control of the rotation speed [28-29]:

Fig. 5. Block diagram without speed control

Fig. 6 show the variation of the power coefficient (ܥ_௣)versus the tip-speed ratio ( ) for the values of the pitch angleߚ=2°, 3° and 4°. This figure indicates that there is one specific point (ߣ_௢௣௧,ܥ௣௢௣௧)at which the turbine is most efficient for ߚ=2°.

Fig. 6. Power coefficient versus tip speed ratio

3.3. Rotor side Converter Control CNV1

As seen in equation (19) and (20) that the electromagnetic torque and the stator reactive power can be controlled by means of the DFIG current i୰୯and i୰ୢrespectively. The model of DFIG in d-q reference frame with stator field orientation shows that the rotor currents can be controlled independently. Fig. 7 shows the bloc rotor currents control diagram with ݅௥ௗ_௥௘௙,݅௥௤_௥௘௙are given by:

Model Control

Gearbox Aeroturbine

rotor

MPP control without speed control π࢚࢛࢘

ࢀ_࢓ࢋࢉ

ࢀ_࢚࢛࢘

࡯_࢖

ࣅ π_࢓ࢋࢉ

π࢓ࢋࢉ

ࢼ

ࢂ

ࢀࢋ࢓כ

࡯࢖࢕࢖࢚.࣋.࣊.ࡾ^૞

૛.ࡳ^૜.ࣅ_࢕࢖࢚^૜ .π࢓૛

(6) ⁺ (7)

-

(3) (2) (5)

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0 2 4 6 8 10 12

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

X: 7.98 Y: 0.35

Tip-speed ratio lumbda

Power coefficient Cp

ࢼ=૛^° ࢼ=૜^° ࢼ=૝^°

(8)

ቐ

݅_{௥ௗ_௥௘௙}=^ఝ^ೞ೏

ெ െ_ெ.௏^௅^ೞ

ೞ೜.ܳ_{௦_௥௘௙}

݅_{௥௤_௥௘௙}=െ_ெ.௉.ఝ^௅^ೞ

ೞ೏

.ܶ_௘௠^כ (20)

Fig. 7.Bloc diagram of rotor currents control

3.4. Design of the Neuronal Network Controller

The objective of this work is to design a new controller in order to assure a robust control of the DFIG facing the parametric changes. In this section, we presented the design of the proposed neuronal network controller. A network can have several layers. Each layer has a weight matrix ܹ, a bias vector ܾ, and an output vector ܽ. The number of hidden layers and the number of neurons in each layer are not definitive. The determination of the combinations of hidden layers and the number of neurons in each layer which can give the best performance for a given problem has no general guidelines. In our case, the number of hidden layers and the number of neurons in each hidden layer were chosen heuristically on a trial and error basis [30]. After several attempts, we opted for two hidden layers containing 06 neurons where the first hidden layer has 04 neurons and the second has 02 neurons, Fig.8 show the structure of the neuronal controller. The type of numerical optimization techniques for neural network training is Levenberg- Marquardt (LM) which is a combination of gradient descent and Newton’s Method with the mean square error performance function. It was designed to approach second-order training speed without having to compute the Hessian matrix [31-33]. This algorithm appears to be the fastest method for training moderate-sized feedforward neural networks (up to several hundred weights). It also has an efficient implementation in MATLAB software, because the solution of the matrix equation is a built-in function, so its attributes become even more pronounced in a MATLAB environment [34]. The linear transfer function “purelin” are used in the final layer of multilayer networks that are used as function approximators. The sigmoid activation function “tansig“ is commonly used in the hidden layers of multilayer Networks [35].

Fig. 8. Structure of the neuronal controller

ࢋ_࢘ࢊ

࢏࢘ࢊ_࢓ࢋ࢙

࢏_{࢘ࢗ_࢓ࢋ࢙}

ࢂ_{࢘ࢗ_࢘ࢋࢌ}

ࢋ࣐

࢏࢘ࢗ_࢘ࢋࢌ

࢏࢘ࢊ_࢘ࢋࢌ

ࢋ_࢘ࢗ

PI

ࢂ_{࢘ࢊ_࢘ࢋࢌ}

+ +

++ + +

+െ

െ

ࢀࢋ࢓_࢓ࢋ࢙

ࢀࢋ࢓כ

࢝_૝૞

࢝૝૟

࢝૜૟

࢝_૜૞

࢝_૛૟

࢝_૛૞

࢝૚૞

࢝૚૟

࢝_૚૚

࢝_૚૜

࢝_૚૛

࢝૚૝

f

f f f

f f

+

f

-

Input Output

࢏࢘ࢗ_࢘ࢋࢌ

࢈૛

࢈૚

࢈૜

࢈૝

࢈૞

࢈_૟

࢈ૠ

Hidden layers

࢝_૞ૠ

࢝૟ૠ

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4. Simulation and interpretation

In this section, the behavior of the doubly fed induction generator was carried out using the MATLAB/Simulink environment under the variation of machine parameters, notably: rotor self inductances, stator self inductances and rotor resistance are studied. Indeed, the problem with the PI controller is that its parameters (K and I) are initially adjusted according to the nominal parameters of the machine, knowing that the machine parameters change inevitably during the time. Therefore, our interest consists to the use of the neuronal controller in order to have a robustness control vis-à-vis parametric changes. The system performance with the proposed controller is compared with a conventional PI controller. The system parameters, MPP control and controller gains are given in Appendix A and B respectively. In the case where the machine parameters are nominal, Fig.9 shows that the d and q components of rotor currents, electromagnetic torque and reactive power follow their references according to table 2 (see appendix A). All these grandeurs evolve without notable overshoot (D) and static error, and that their response time is acceptable. In the aim to test the robustness of the proposed controller, the parameters value has been changed as follows: variation of the stator and the rotor self inductances (+20%). However, the effects of the considered variations have been studied separately (Fig.10 and Fig.11). The variations of ܮ_௠,ܮ_௦,ܮ_௥and ܴ_௥have been tested and simultaneously represented (Fig.12).

Concerning the variation of ܮ_௦(+20%), the simulation results are shown in Fig.10, where it is found that the system response with neuronal controller remains remarkably insensible to the variation of the stator inductance.

Contrary to the system response with PI controller, it witness an impotently overshoot and response time (tr) of the electromagnetic torque equal to 0.775 × 10^ସand 0.162srespectively. Similarly, for the change of ܮ_௥(+20%), the overshoot (0.85 × 10^ସ) and response time (tr=0.171s) are very important as in the previous case. Finally, Fig.12 shows the case where all the parameters ܮ௠ (+20%), ܮ௦(+25%), ܮ௥ (+25%) and ܴ௥ (+50%) are changed simultaneously. In this case, the system performances with PI controller are highly degraded and the system becomes even unstable. Sum up, the simulation results of NNT controller show good performances in term of:

response time and overshoot (see Appendix A table 3).

1 1.05 1.1

-1000 0

1000 I_{rq NNT}

I_{rq PI}

1 1.05 1.1

-500 0 500 1000

I_{rd PI} I_{rd NNT}

0 0.5 1 1.5 2

-2000 -1500 -1000 -500 0 500 1000 1500 2000 2500

Time (sec) I_{rq Ref} I_{rq NNT} I_{rq PI}

0 0.5 1 1.5 2

-1500 -1000 -500 0 500 1000 1500 2000

Time (sec)

I_{rd Ref} I_{rd NNT} I_{rd PI}

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0 0.5 1 1.5 2 -2000

-1000 0 1000 2000

Time(sec)

I_{rd NNT}

I_{rd PI}

0 0.5 1 1.5 2

-2000 0 2000 4000

Time (sec)

I_{rq Ref} I_{rq NNT} I_{rq PI} I_{rq PI}

I_{rq NNT}

0 0.5 1 1.5 2

-1 0 1 2

x 10⁴

Time(sec)

T_{em Ref} T_{em NNT} T_{em PI}

T_{em PI}

0.775*10⁴

Tem NNT

tr =0.162

0 0.5 1 1.5 2

-2 -1 0 1 2

x 10⁶

Time(sec)

Qs Ref Q

s NNT Q

s PI

Qs NNT

Q_{s PI}

Fig. 9. System response without machine parameters changes

Fig. 10. System response with stator self inductance change Ls (+20%)

0 0.5 1 1.5 2

-2 -1.5 -1 -0.5 0 0.5 1 1.5

2x 10⁶

Time(sec)

Q_{s Ref} Q_{s NNT} Q_{s PI}

0 0.5 1 1.5 2

-1.5 -1 -0.5 0 0.5 1 1.5

2x 10⁴

Time(sec)

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Fig. 11. System response with rotor self inductance change Lr (+20%)

0 0.5 1 1.5 2

-3000 -2000 -1000 0 1000 2000 3000

Time(sec)

I_{rq Ref} I_{rq NNT} I_{rq PI}

Irq NNT

Irq PI

0 0.5 1 1.5 2

-1000 0 1000 2000

Time(sec)

I_{rd NNT}

I_{rd PI}

0 0.5 1 1.5 2

-1 0 1 2

x 10⁴

Time(sec)

T_{em PI} T_{em NNT}

0.85*10⁴

tr =0.171

0 0.5 1 1.5 2

-2 -1 0 1 2

x 10⁶

Time(sec)

Q_{s Ref} Q_{s NNT} Q_{s PI} Q_{s PI}

Q_{s NNT}

0 0.5 1 1.5 2

-3000 -2000 -1000 0 1000 2000 3000

Time(sec)

I_{rd NNT} I_{rd PI}

0 0.5 1 1.5 2

-4000 -2000 0 2000 4000 6000

Time(sec)

I_{rq Ref} I_{rq NNT} I_{rq PI}

I_{rq NNT} I_{rq PI}

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Fig. 12. System response with machine parameters changes Lm (+20%), Ls (+25%), Lr (+25%) and Rr (+50%)

5. Conclusion

In this paper, a modeling of DFIG based wind turbine under sub-synchronous operation mode and NNT controller is proposed. To achieve, these works are validated through simulation studies on a 1.5 MW DFIG wind generation system compared with conventional proportional integral current control design. The simulation results using software Matlab/Simulink show that the NNT controller gives good performance, efficient and more robust under parameters variations of the DFIG. The calculation of weight matrix (W)and bias vector (b)of NNT controller in function of the input/output data without knowledge of the DFIG parameters, explain his robustness to the parameter variations compared with PI controller which is initially adjusted according to the nominal parameters of the DFIG.

Appendix A.

Table 1. Font Simulated DFIG Wind Turbine Parameters

Rated power 1.5MW

Rotor diameter 45m

Gearbox ratio 100

Friction coefficient :ࢌ 0.0024 Moment of inertia ׷ ࡶ 1000 Stator voltage/Frequency 690V/50Hz

ࡾ࢙ / ܴݎ( ) 0.00297/0.00382

ࡸ࢓/ࡸࢌ࢙/ࡸࢌ࢘(H) 0.01212/0.000121/0.0000573 Number of pole pairs:࢖ 2

M 1

Table 2. Operation Statues of the Simulated DFIG Status Time (sec)

Reactive power (MVar)

Time (sec)

Electromagnetic torque

(N.m)

1 0 < t ൑ 0.5 0 0 < t ൑ 0.3 0

2 0.5 < t ൑1 -1 0.3 < t ൑ 1 -1

3 1 < t ൑ 1.7 0.8 1 < t ൑ 2 1

4 1.7 < t ൑ 2 -0.7

0 0.5 1 1.5 2

-2 -1 0 1 2 3

x 10⁴

Time(sec)

T_{em NNT} T_{em PI}

0 0.5 1 1.5 2

-2 -1 0 1 2 3x 10⁶

Time(sec)

Qs Ref Q

s NNT Q

s PI

Q_{s NNT} Qs PI

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Table 3. Response time and overshoot of NNT and PI controllers for ܮ_௦(+20%) andܮ௥(+20%)

ࢀࢋ࢓

(tr/Dmax)

ࡽ࢙

(tr/Dmax) NNT controller ࡸ࢙(+20%)

ࡸ_࢘(+20%)

0.099/ 0

0.112 / 0 0.092 / 0

0.105 / 0 PI controller ࡸ࢙(+20%)

ࡸ࢘(+20%) 0.162 / 0.775 × 10^ସ

0.171 / 0.85 × 10^ସ 0.146 / 0.885 × 10^଺ 0.163 / 0.95 × 10^଺

Appendix B. MPP control and controller gains

൜ߣ௢௣௧= 7.98 ܥ௣௢௣௧= 0.35

For the synthesis of the regulators we opted for the method of poles compensation.

࢚࢘ = 0.05s

ࡷ=ߪ כܮݎ ݐ௥

= 0.0106

ࡵ=ܴݎ ݐ௥

= 0.2292

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