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Robust Control of Doubly Fed Induction Generator for Wind Turbine Under Sub-synchronous Operation Mode
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 74 (2015) 886 – 899
International Conference on Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES15
Robust Control of Doubly Fed Induction Generator for Wind Turbine Under Sub-Synchronous Operation Mode Khouloud Bedouda,b*, Mahieddine Ali-rachedic, Tahar Bahid, Rrabah Lakelb, Azzeddine Grida a Welding and NDT Research Centre (CSC). BP 64 Cheraga, Algeria. Automatic Laboratory and Signals, Badji Mokhtar University, Annaba, Algeria. c Preparatory School in Sciences and Technics, Annaba, Algeria. d Electrical department, Badji Mokhtar University, Annaba,Box 12, 2300 Algeria. b
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. © by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2015 2015Published The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD). 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.: +213-663-350-589; fax: +213-388-759-82 E-mail address:[email protected]
1876-6102 © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4 .0/). Peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD) doi:10.1016/j.egypro.2015.07.824
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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 ǡ ܳ௦ ܲ ǡ ܳ ܶ ݀ǡ ݍ ܸ௦ௗǡ ܸௗǡ ݅௦ௗǡ ݅ௗǡ ߮ୱୢǡ୯ ߮୰ୢǡ୯ ܴ௦ ǡ ܴ ܮ௦ ǡ ܮ ܮ୫
stator active and reactive power rotor active and reactive power DFIG electromagnetic torque (N m) synchronous reference frame index stator d–q frame voltage rotor d–q frame voltage stator d–q frame current rotor d–q frame current stator d–q frame flux rotor d–q frame flux stator and rotor Resistances stator and rotor self Inductances mutual inductance
߱s, ߱r ߩ ܸ R λ π௧௨ π G ܬ ܬ௧௨ ǡ ܬ ݂ σ CNV1/CNV2
synchronous and rotor angular frequency air density wind speed rotor radius tip-speed ratio aeroturbine rotor speed generator speed gearbox ratio turbine total inertia rotor and DFIG inertia turbine total external damping Coefficient of dispersion. 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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3ph, 50
Ps
Gearbox
Wind
Ωtur
Pr
Ωmec DFIG
࢘ࢊǡ̴ࢋ࢙ ࢂࢊࢉ CNV1
CNV2
Rotor side converter
Grid side converter
Filter
Aeroturbine rotor
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 Ǥ
ఘǤௌǤ య
(1)
ଶ
Where ୮ denotes power coefficient of wind turbine, its evolution depends on the blade pitch angle (Ⱦ) and the tip-speed ratio (λ) which is defined as [17- 19]:
ɉൌ
ୖǤΩ౪౫౨
(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]: ୮ ൌ ቀͲǤ͵ͷ െ ൫ͲǤͲͳሺȾ െ ʹሻ൯ቁ ൭ቆ
ሺାǤଵሻ
ቇ൱ െ ൫ͲǤͲͲͳͺͶሺɉ െ ͵ሻሺȾ െ ʹሻ൯
ቀଵହǤହି൫Ǥଷሺஒିଶሻ൯ቁ
(3)
The aerodynamic torque expression is given by [22]:
ܶ௧௨ ൌ Ωೠೝ ൌ ܥ Ǥ ೠೝ
ఘǤௌǤ య ଵ ǤΩ ଶ ೠೝ
(4)
The gearbox is installed between the turbine and generator to adapt the speed of the turbine to that of the generator [22]: Ω ൌ ܩǤ Ω௧௨
(5)
The friction, elasticity and energy losses in the gearbox are neglected.
ܩൌ
்ೠೝ ்
(6)
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The mechanical equations of the system can be characterized by [22]:
ܬ
ௗΩ ௗ௧
With: ܬൌ
݂Ω ൌ ܶ െ ܶ ೠೝ ீమ
(7)
ܬ
2.2. Modeling the DFIG with stator field orientation The Park model of DFIG is given by the equations below [21, 23-24]: ௗఝ
ܸ௦ௗ ൌ ܴ௦ ݅௦ௗ ೞ െ ߱௦ ߮௦ ௗ௧ ቐ ௗఝ ܸ௦ ൌ ܴ௦ ݅௦ ೞ ߱௦ ߮௦ௗ
(8)
ܸௗ ൌ ܴ ݅ௗ ೝ െ ߱ ߮ ௗ௧ ቐ ௗఝೝ ܸ ൌ ܴ ݅ ߱ ߮ௗ
(9)
ௗ௧ ௗఝ
ௗ௧
As the d and q axis are magnetically decoupled, the stator and rotor flux are given as: ߮௦ௗ ൌ ܮ௦ ݅௦ௗ ܮ ݅ௗ ൜߮ ൌ ݅ ܮ ݅ ܮ ௦ ௦ ௦ ߮ௗ ൌ ܮ ݅ௗ ܮ ݅௦ௗ ൜߮ ൌ ݅ ܮ ݅ ܮ ௦
(10) (11)
With: ܮ௦ =ܮ௦ +ܮ ܮ =ܮ ܯଶ ܮ The active and reactive powers are defined as: ܲ௦ ൌ ܸ௦ௗ ݅௦ௗ ܸ௦ ݅௦ ൜ ܳ௦ ൌ ܸ௦ ݅௦ௗ െ ܸ௦ௗ ݅௦ ܲ ൌ ܸௗ ݅ௗ ܸ ݅ ൜ ܳ ൌ ܸ ݅ௗ െ ܸௗ ݅
(12) (13)
Consequently, the d-q orientation has to be synchronized with the stator flux (see Fig.2). ࡿ࢈
࣐ࢊ࢙
ࡾ࢈ ࢂ࢙
d-q frame
d q θr
θs
ࡾࢇ Rotor axis
θe 0
Stator axis
ࡿࢇ
ࡿࢉ ࡾࢉ 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 ൌ Ͳǡ ߮௦ௗ ൌ ߮௦ ሻ [19, 24]. In addition, considering that the resistance of the stator
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winding (ܴ௦ ሻis neglected and the grid is supposed stable with voltage ݒ௦ and synchronous angular frequency ( ߱௦ ሻ constant what implies ߮௦ௗ ൌ ܿݐݏ, the voltage and the flux equations of the stator windings can be simplified in steady state as [23-26]: ௗఝ
ܸ ൌ ೞ ൌ Ͳ ௗ௧ (14) ቊ ௦ௗ ܸ௦ ൌ ߱௦ Ǥ ߮௦ௗ ൌ ܸ௦ The stator and rotor voltages are given by [21]: ோ ߮ െ ೞ ܮ ݅ௗ ೞ ௦ௗ ೞ ோ െ ೞ ܮ ݅ ߱௦ ߮௦ௗ
ܸ௦ௗ ൌ
ቐ ܸ௦ ൌ
ோೞ
(15)
ೞ
ௗ
ೝ ݁ௗ ௗ௧ ቐ ௗೝ ܸ ൌ ܴ ݅ ߪǤ ܮ ݁ ݁ఝ
ܸௗ ൌ ܴ ݅ௗ ߪǤ ܮ
(16)
ௗ௧
Where: ݁ௗ ൌ െߪǤ ܮ Ǥ ߱ Ǥ ݅ ۓ ۖ ݁ ൌ ߪǤ ܮ Ǥ ߱ Ǥ ݅ௗ ݁ఝ ൌ ߱ Ǥ
ெ
Ǥ ߮௦ௗ ۔ ଶ ெ ۖ ߪ ൌ ͳെ൬ ൰ ە ඥೞ ೝ
(17)
ೞ
The stator and the rotor active and reactive power can be rewritten as follows [21]: ౩ Ǥ Ǥ ୰୯ ۓୱ ൌ െ ۖ ۖ ൌ ୱ ۔ ۖ ۖ ە
౩
మ ౩ ౩ ன౩
୰ ൌ Ǥ ୰ ൌ Ǥ
െ
Ǥ౩
౩ ౩ Ǥ ౩ ౩ Ǥ ౩
Ǥ ୰ୢ
Ǥ ୰୯
ሺͳͺሻ
Ǥ ୰ୢ
The electromagnetic torque is as follows [21]: ܶ ൌ െܲǤ
ெ ೞ
߮௦ௗ Ǥ ݅
(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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Grid
Ps Ωtur Pr
Ωmec DFIG
CNV1 ࢘ࢊǡ̴ࢋ࢙
ࢀࢋכ
dq
dq PWM
ࢂࢊ̴࢘࢘ࢋࢌ abc
ࢊǡ̴࢘ࢋ࢙
ࣂ࢘
ࢂࢊࢌ̴࢘ࢋࢌ
abc
ࢂࢌ̴࢘ࢋࢌ
Filter currents control
6 ࢂ̴࢘࢘ࢋࢌ dq
Decoupling/compensation
6
PWM
ࢊ̴࢘࢘ࢋࢌ
Decoupling/compensation
̴࢘࢘ࢋࢌ
Rotor currents control
Rotor currents calculation
ࡼࡿ̴࢘ࢋࢌ
CNV2
Filter
MPP
ࡽࡿ̴࢘ࢋࢌ
abc ࢊǡࢌ̴ࢋ࢙
ࢂࢊࢉ
Ωࢋࢉ
2
ࢊࢌ̴࢘ࢋࢌ ൊ
DC bus ࢂ ࢊࢉ̴࢘ࢋࢌ control
ࢌ̴࢘ࢋࢌ
ࢂ࢙
ࣂ࢙
ࢂࢊࢉ
ࡽࢌ̴࢘ࢋࢌ
Fig. 3. Block diagram of the control system of the wind [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 ܸଵ and ܸଶ to the speed ɘଵ of the DFIG is unchanged, the power varies from ܲଵ toܲଶ . In addition, the maximum power is equal toܲଷ . In case we want to extract the maximum power should be changed by ɘଵ and ɘଶ thus 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. 4
12
x 10
Turbine Power (W)
P3 P2 10
w1
w2
MPP
8 V2=12 P1 6
4 V1=10
2 0 0
100 200 300 Rotor Speed (rad/sec) Fig. 4. Turbine power versus rotor speeds of generator
400
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The power extracted from the wind is maximized when the rotor speed is such that the power coefficient is optimalܥ௧ . Therefore, we must set the tip speed ratio on its optimal valueɉ୭୮୲ . Fig. 5 illustrates the principle of MPP control without speed control of the rotation speed [28-29]: Aeroturbine rotor ࣅ
ࢼ
(3)
Gearbox π࢚࢛࢘
(2)
πࢋࢉ
(5)
ࢂ
(4)
ࢀ࢚࢛࢘
(6)
ࢀࢋࢉ ࢀࢋכ
Model
πࢋࢉ
(7)
+
-
Control ࢚ Ǥ ࣋Ǥ ࣊Ǥ ࡾ Ǥ ࡳ Ǥ ࣅ࢚
Ǥ π
MPP control without speed control Fig. 5. Block diagram without speed control
Fig. 6 show the variation of the power coefficient (ܥ ሻ versus the tip-speed ratio (ɉ) for the values of the pitch angle ߚ=2°, 3° and 4°. This figure indicates that there is one specific point ሺߣ௧ ǡ ܥ௧ ሻ at which the turbine is most efficient for ߚ=2°. 0.4
Power coefficient Cp
0.35
X: 7.98 Y: 0.35
0.3 0.25
ࢼ ൌ ι ࢼ ൌ ι ࢼ ൌ ι
0.2 0.15 0.1 0.05 0 0
2
4
6
8
10
12
Tip-speed ratio lumbda 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 ୰୯ and ୰ୢ 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 ݅ௗ̴ ǡ ̴݅ are given by:
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Khouloud Bedoud et al. / Energy Procedia 74 (2015) 886 – 899 ఝ
݅ௗ̴ ൌ ೞ െ ೞ Ǥ ܳ௦̴ ெ ெǤೞ ቐ ೞ כ ̴݅ ൌ െ Ǥ ܶ
(20)
ெǤǤఝೞ
ࢋ࢘ࢊ
࢘ࢊ̴ࢋ࢙ ࢘ࢊ̴࢘ࢋࢌ
െ
PI
ࢂ࢘ࢊ̴࢘ࢋࢌ
+
ࢋ࢘ ̴࢘࢘ࢋࢌ
PI
െ
̴࢘ࢋ࢙
ࢂ̴࢘࢘ࢋࢌ
ࢋ࣐ 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 matrixܹ, a bias vectorܾ, and an output vectorܽ. 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 LevenbergMarquardt (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].
Input
Hidden layers
f ࢈
࢝
ࢀࢋכ
ࢀࢋ̴ࢋ࢙
࢝ ࢝
f
࢝
f
࢝
࢈
࢝
࢈
࢝
f
࢝ ࢝ ࢝
f
+ -
Output
࢝
࢈
f
࢈
࢝
࢈ Fig. 8. Structure of the neuronal controller
࢝ૠ
f ࢝ૠ
࢈ૠ
̴࢘࢘ࢋࢌ
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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 ofܮ , ܮ௦ , ܮ and ܴ have been tested and simultaneously represented (Fig.12). Concerning the variation of ܮ௦ (+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 toͲǤͷ ൈ ͳͲସ and ͲǤͳʹ respectively. Similarly, for the change of ܮ (+20%), the overshoot (ͲǤͺͷ ൈ ͳͲସ ) and response time (tr=ͲǤͳͳ) 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). 2000
2500 I
1500
rd Ref
I
rd NNT
I
rd PI
I
2000
rq Ref
I
I
rq NNT
rq PI
1500 1000
1000
500
500
0
0 -500
-500
-1000 -1000
-1500
-1500 0
0.5
1 Time (sec)
1.5
2
1000
0.5
1 Time (sec)
1000
500
1.5
Irq
NNT
Irq
PI
0
0
I I
-500
-2000 0
1
rd PI
-1000
rd NNT
1.05
1.1
1
1.05
1.1
2
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4
2
6
x 10
2 T
1.5
T
em Ref
T
em NNT
em PI
x 10
Q
1.5
Q
s Ref
Q
s NNT
s PI
1
1
0.5
0.5
0 0
-0.5
-0.5
-1
-1
-1.5
-1.5 0
0.5
1 Time(sec)
1.5
2
-2 0
0.5
1 Time(sec)
1.5
I
I
2
Fig. 9. Response of system without machine parameters changes
I 2000
rd Ref
I
I
rd NNT
4000
rd PI
I
rq Ref
I
rq NNT
rq PI
rq PI
2000
1000
I I
0 -1000
I
-2000 0
0.5 4
1 Time(sec)
-2000
rd PI
1.5
0
2
0.5
1 Time (sec)
Q
Q
6
x 10 2
rq NNT
0
rd NNT
1.5
2
x 10 T
em Ref
T
T
em NNT
2
em PI
s Ref
Q
s NNT
s PI
Q
s PI
0.775*104
1
1 T
em NNT
Q
s NNT
0
0
T
em PI
-1 -1 0
tr =0.162
0.5
1 Time(sec)
1.5
2
-2 0
0.5
1 Time(sec)
Fig. 10. Response of system with stator self inductance change Ls (+20%)
1.5
2
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I
2000
I
rd Ref
I
rd NNT
I
3000
rd PI
I
rq Ref
I
rq NNT
rq PI
2000 1000
1000 I
0
I
0
rd NNT
I I
-1000 0
0.5
-1000 rd PI
1.5
2
-3000 0
0.5
1 Time(sec)
Q
Q
6
x 10
T
em Ref
T
em NNT
em PI
s Ref
2
2
4
T
em NNT
T
s PI
Q
s PI
1
0
Q
s NNT
0.85*10
1
1.5
x 10 T
2
rq NNT
-2000
1 Time(sec)
4
rq PI
em PI
0
Q
s NNT
-1 0
-1
tr =0.171
0.5
1 Time(sec)
1.5
2
-2 0
0.5
1 Time(sec)
1.5
2
Fig. 11. Response of system with rotor self inductance change Lr (+20%)
I
3000
I
rd Ref
rd NNT
I
6000
rd PI
2000
I
rq Ref
I
rq NNT
rq PI
4000
1000
2000
0
I
-1000
I 0
rd NNT
I
-2000 -3000 0
I
0.5
I
rq PI
-2000
rd PI
1 Time(sec)
rq NNT
1.5
2
-4000 0
0.5
1 Time(sec)
1.5
2
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4
x 10 3
T
T
em Ref
T
2
em NNT
T
3
x 10
em PI
Q
Q
s Ref
2
s NNT
Q
s PI
Q
s PI
em PI
1
1
Q
T 0
s NNT
0
em NNT
-1
-1
-2
-2 0
0.5
1 Time(sec)
1.5
2
0
0.5
1 Time(sec)
1.5
2
Fig. 12. Response of system 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 Rotor diameter Gearbox ratio Friction coefficient ǣ ݂ Moment of inertiaܬ Stator voltage/Frequency ܴݏȀܴ( ݎΩ) ݉ܮȀݏ݂ܮȀ( ݎ݂ܮH) Number of pole pairs:
1.5MW 45m 100 0.0024 1000 690V/50Hz 0.00297/0.00382 0.01212/0.000121/0.0000573 2
M
1
Table 2. Operation Statues of the Simulated DFIG Status
Time (sec)
1 2 3 4
0 < t0.5 0.5 < t1 1 < t1.7 1.7 < t2
Reactive power (MVar) 0 -1 0.8 -0.7
Time (sec) 0 < t0.3 0.3 < t1 1 < t2
Electromagnetic torque (N.m) 0 -1 1
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Table 3. Response time and overshoot of NNT and PI controllers for ܮ௦ (+20%) and ܮ (+20%)
NNT controller ࡸ࢙ (+20%) ࡸ࢘ (+20%) PI controller
ࡸ࢙ (+20%) ࡸ࢘ (+20%)
ࢀࢋ (tr/Dmax) ͲǤͲͻͻȀͲ ͲǤͳͳʹȀͲ ͲǤͳʹȀͲǤͷ ൈ ͳͲସ ͲǤͳͳȀͲǤͺͷ ൈ ͳͲସ
ࡽ࢙ (tr/Dmax) ͲǤͲͻʹȀͲ ͲǤͳͲͷȀͲ ͲǤͳͶȀͲǤͺͺͷ ൈ ͳͲ ͲǤͳ͵ȀͲǤͻͷ ൈ ͳͲ
Appendix B. MPP control and controller gains ൜
ߣ௧ ൌ Ǥͻͺ ܥ௧ ൌ ͲǤ͵ͷ
For the synthesis of the regulators we opted for the method of poles compensation. ࢚࢘= 0.05s ݎܮ ࡷ ൌ ߪ כൌ ͲǤͲͳͲ ݐ ܴݎ ࡵൌ ൌ ͲǤʹʹͻʹ ݐ
References [1] The renewable energies website. Available: http://www.les-energies-renouvelables.eu/avantages-et-inconvenients-de-lenergie eolienne.html [2] Lu MS, Chang CL, Lee WJ, and Wang L. Combining the wind power generation system with energy storage equipment. IEEE Trans. Ind. Applicat 2009; 45: 2109–2115. [3] Wenyi Liu, Baoping Tang, Yonghua Jiang. Status and problems of wind turbine structural health monitoring techniques in China: Review. Renewable Energy 2010; 35: 1414–1418. [4] World Wind Energy Report 2008, WWEA (World Wind Energy Association). [5] Cardenas R, Pena R, Proboste J, Asher G and Clare J. MRAS observer for sensorless control of standalone doubly fed induction generators. IEEE Transaction on Energy Convertion 2005; 20: 710–718. [6] Shen B, Mwinyiwiwa B, ZhangY, Oo BT. Sensorless Maximum Power Point Tracking of Wind by DFIG Using Rotor Position Phase Lock Loop (PLL). IEEE Transactions on Power Electronics 2009; v. 24, no. 4. [7] Karimi S, Gaillard A, Poure P, Saadate S. FPGA-Based Real-Time Power Converter Failure Diagnosis for Wind Energy Conversion Systems”, IEEE Transactions on Industrial Electronics 2008; v. 55, no. 12. [8] Tazil M, Kumar V, Bansal RC, Kong S, Dong ZY, Freitas W, MathurHD. Three-phase doubly fed induction generators: an overview. IET Electric Power Applications 2010; 4: 75-89. [9] Anaya-Lara O, Jenkins N, Ekanayake J, Cartwright P, Hughes M. Wind energy generation: Modelling and control. Chichester, UK: John Wiley & Sons, 2009. [10] Oliveira RV, Zamadei JA, Hossi CH. Robust Tuning of the Control Loops of DFIG Wind Turbine Systems. IEEE International Conference on Control Applications (CCA) Part of 2011 IEEE Multi-Conference on Systems and Control Denver, CO, USA. September 28-30, 2011. [11] Tremblay E, Atayde S, Chandra A. Direct Power Control of a DFIG-based WECS with Active Filter Capabilities. IEEE Electrical Power & Energy Conference, 2009. [12] Hofmann W, Okafor F. Doubly-Fed Full-Controlled Induction Wind Generator for Optimal Power Utilization. in Proceeding of 4th IEEE International Conference on Power Engineering and Drive Systems 2001; 1: 355 – 361. [13] Dalibor P, Zarko C, Vlastimir N, Shahaboddin S, Miss LMK, Nor AB, Ainuddin WAW. Adaptive neuro-fuzzy maximal power extraction of wind turbine with continuously variable transmission. Energy 2014; 64 : 868-874. [14] Bedoud K, Lakel R, Ali-Rachedi M, Lekhchine S, Bahi T. Modeling a chain of wind energy conversion based on a doubly fed induction. 21st Congress of Mechanics French Bordeaux 2013; 26 to 30 August. [15] Baroudi JA, Dinavahi V, Knight AM. A review of power converter topologies for wind generators. Renewable Energy 2007; 32: 23692385. [16] Qiao Wei, Zhou Wei, Aller Jos M and Ronald G. Harley. Wind Speed Estimation Based Sensorless Output Maximization Control for a Wind Turbine Driving a DFIG. IEEE Trans. on Power Electronics 2008; 23: 1156-1169. [17] Beltran B, Sliding al. Mode power control of variable speed wind energy conversion systems. IEEE Trans. Energy Conversion 2008; 23: 551-558. [18] Fernando D.B, Hrnan De Battista, Ricardo JM. Wind Turbine Control Systems Advances in Industrial Control Series. Springer. [19] Barambones O, Durana JMG, Kremers E. Adaptive robust control to maximizing the power generation of a variable speed wind turbine. International Conference on Renewable Energy Research and Applications IEEE, ICRERA 2013; Madrid, Spain, 20-23 October.
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[20] Abdin ES, Xu W. Control design and Dynamic Performance Analysis of a Wind Turbine Induction Generator Unit. IEEE Trans on Energy Conversion 2000; v. 15, no. 1. [21] Gaillard A. Wind system based on the DFIG: contribution to the study of the quality of the electric energy and the continuity of service. Doct. thesis, Henri Poincare University, Nancy-I, France, April 2010. [22] Abdeddaim S, Betka A. Optimal tracking and robust power control of the DFIG wind turbine. Electrical Power and Energy Systems 2013; 49: 234-242. [23] Boukhezzar B, Siguerdidjane H. Nonlinear control with wind estimation of a DFIG variable speed wind turbine for power capture optimization. Energy Conversion and Management 2009; 50: 885-892. [24] Kassem AM, Hasaneen KM, Yousef AM. Dynamic modeling and robust power control of DFIG driven by wind turbine at infinite grid. Electrical Power and Energy Systems 2013; 44: 375-382. [25] Zamanifar M, Fani B, Golshan MEH, Karshenas HR. Dynamic modeling and optimal control of DFIG wind energy systemsusing DFT and NSGA-II. Electric Power Systems Research 2014; 108: 50-58. [26] Ghennam T, Berkouk EM, François B. Modeling and Control of a Doubly Fed Induction Generator (DFIG) Based Wind Conversion System. IEEE International conference on power engineering, energy and electrical drives (POWERENG) 2009; March 18-20. [27] Bedoud K, Ali-rachedi M, Lakel R, Bahi T. Modeling and Control of the Wind Energy Conversion Systems Based on DFIG Under Sub- and Super-Synchronous Operation Modes. Conférence Internationale des Energies Renouvelables CIER’14, Monastir, Tunisie 2014; Dec19-21. [28] Fernandez LM, Garcia CA, Jurado F. Comparative study on the performance of control systems for doubly fed induction generator (DFIG) wind turbines operating with power regulation. Energy 2008; 33: 1438-1452. [29] M Boutoubat, Mokrani L, Machmoum M. Control of a wind energy conversion system equipped by a DFIG for active power generation and power quality improvement. Renewable Energy 2013; 50: 378-386. [30] Barambones O. A robust wind turbine control using a Neural Network based wind speed estimator. IEEE conference publications, International Joint Conference on Neural Networks (IJCNN) 2010, pp. 1-8. [31] Djeriri Y. Vectorial control of DFIG integrate to the wind system. Magister memory, Sidi Bel-Abbes university, December 2009. [32] Yathley D. Back Propagation Neural Networks for Non-Linear Self Tuning Adaptive Control. IEEE Control Systems Magazine 1990; 10:44 – 48. [33] Hagan MT, Menhaj M. Training feed-forward networks with the Marquardt algorithm. IEEE Transactions on Neural Networks 1999; 5:989993. [34] help matlab: neural networks toolbox 2010. [35] Martin MHB, Howar TH, Demuth B: Neural Network Toolbox User’s Guide, R2014a.
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ScienceDirect Energy Procedia 74 (2015) 886 – 899
International Conference on Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES15
Robust Control of Doubly Fed Induction Generator for Wind Turbine Under Sub-Synchronous Operation Mode Khouloud Bedouda,b*, Mahieddine Ali-rachedic, Tahar Bahid, Rrabah Lakelb, Azzeddine Grida a Welding and NDT Research Centre (CSC). BP 64 Cheraga, Algeria. Automatic Laboratory and Signals, Badji Mokhtar University, Annaba, Algeria. c Preparatory School in Sciences and Technics, Annaba, Algeria. d Electrical department, Badji Mokhtar University, Annaba,Box 12, 2300 Algeria. b
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. © by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2015 2015Published The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD). 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.: +213-663-350-589; fax: +213-388-759-82 E-mail address:[email protected]
1876-6102 © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4 .0/). Peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD) doi:10.1016/j.egypro.2015.07.824
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887
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 ǡ ܳ௦ ܲ ǡ ܳ ܶ ݀ǡ ݍ ܸ௦ௗǡ ܸௗǡ ݅௦ௗǡ ݅ௗǡ ߮ୱୢǡ୯ ߮୰ୢǡ୯ ܴ௦ ǡ ܴ ܮ௦ ǡ ܮ ܮ୫
stator active and reactive power rotor active and reactive power DFIG electromagnetic torque (N m) synchronous reference frame index stator d–q frame voltage rotor d–q frame voltage stator d–q frame current rotor d–q frame current stator d–q frame flux rotor d–q frame flux stator and rotor Resistances stator and rotor self Inductances mutual inductance
߱s, ߱r ߩ ܸ R λ π௧௨ π G ܬ ܬ௧௨ ǡ ܬ ݂ σ CNV1/CNV2
synchronous and rotor angular frequency air density wind speed rotor radius tip-speed ratio aeroturbine rotor speed generator speed gearbox ratio turbine total inertia rotor and DFIG inertia turbine total external damping Coefficient of dispersion. 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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3ph, 50
Ps
Gearbox
Wind
Ωtur
Pr
Ωmec DFIG
࢘ࢊǡ̴ࢋ࢙ ࢂࢊࢉ CNV1
CNV2
Rotor side converter
Grid side converter
Filter
Aeroturbine rotor
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 Ǥ
ఘǤௌǤ య
(1)
ଶ
Where ୮ denotes power coefficient of wind turbine, its evolution depends on the blade pitch angle (Ⱦ) and the tip-speed ratio (λ) which is defined as [17- 19]:
ɉൌ
ୖǤΩ౪౫౨
(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]: ୮ ൌ ቀͲǤ͵ͷ െ ൫ͲǤͲͳሺȾ െ ʹሻ൯ቁ ൭ቆ
ሺାǤଵሻ
ቇ൱ െ ൫ͲǤͲͲͳͺͶሺɉ െ ͵ሻሺȾ െ ʹሻ൯
ቀଵହǤହି൫Ǥଷሺஒିଶሻ൯ቁ
(3)
The aerodynamic torque expression is given by [22]:
ܶ௧௨ ൌ Ωೠೝ ൌ ܥ Ǥ ೠೝ
ఘǤௌǤ య ଵ ǤΩ ଶ ೠೝ
(4)
The gearbox is installed between the turbine and generator to adapt the speed of the turbine to that of the generator [22]: Ω ൌ ܩǤ Ω௧௨
(5)
The friction, elasticity and energy losses in the gearbox are neglected.
ܩൌ
்ೠೝ ்
(6)
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The mechanical equations of the system can be characterized by [22]:
ܬ
ௗΩ ௗ௧
With: ܬൌ
݂Ω ൌ ܶ െ ܶ ೠೝ ீమ
(7)
ܬ
2.2. Modeling the DFIG with stator field orientation The Park model of DFIG is given by the equations below [21, 23-24]: ௗఝ
ܸ௦ௗ ൌ ܴ௦ ݅௦ௗ ೞ െ ߱௦ ߮௦ ௗ௧ ቐ ௗఝ ܸ௦ ൌ ܴ௦ ݅௦ ೞ ߱௦ ߮௦ௗ
(8)
ܸௗ ൌ ܴ ݅ௗ ೝ െ ߱ ߮ ௗ௧ ቐ ௗఝೝ ܸ ൌ ܴ ݅ ߱ ߮ௗ
(9)
ௗ௧ ௗఝ
ௗ௧
As the d and q axis are magnetically decoupled, the stator and rotor flux are given as: ߮௦ௗ ൌ ܮ௦ ݅௦ௗ ܮ ݅ௗ ൜߮ ൌ ݅ ܮ ݅ ܮ ௦ ௦ ௦ ߮ௗ ൌ ܮ ݅ௗ ܮ ݅௦ௗ ൜߮ ൌ ݅ ܮ ݅ ܮ ௦
(10) (11)
With: ܮ௦ =ܮ௦ +ܮ ܮ =ܮ ܯଶ ܮ The active and reactive powers are defined as: ܲ௦ ൌ ܸ௦ௗ ݅௦ௗ ܸ௦ ݅௦ ൜ ܳ௦ ൌ ܸ௦ ݅௦ௗ െ ܸ௦ௗ ݅௦ ܲ ൌ ܸௗ ݅ௗ ܸ ݅ ൜ ܳ ൌ ܸ ݅ௗ െ ܸௗ ݅
(12) (13)
Consequently, the d-q orientation has to be synchronized with the stator flux (see Fig.2). ࡿ࢈
࣐ࢊ࢙
ࡾ࢈ ࢂ࢙
d-q frame
d q θr
θs
ࡾࢇ Rotor axis
θe 0
Stator axis
ࡿࢇ
ࡿࢉ ࡾࢉ 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 ൌ Ͳǡ ߮௦ௗ ൌ ߮௦ ሻ [19, 24]. In addition, considering that the resistance of the stator
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winding (ܴ௦ ሻis neglected and the grid is supposed stable with voltage ݒ௦ and synchronous angular frequency ( ߱௦ ሻ constant what implies ߮௦ௗ ൌ ܿݐݏ, the voltage and the flux equations of the stator windings can be simplified in steady state as [23-26]: ௗఝ
ܸ ൌ ೞ ൌ Ͳ ௗ௧ (14) ቊ ௦ௗ ܸ௦ ൌ ߱௦ Ǥ ߮௦ௗ ൌ ܸ௦ The stator and rotor voltages are given by [21]: ோ ߮ െ ೞ ܮ ݅ௗ ೞ ௦ௗ ೞ ோ െ ೞ ܮ ݅ ߱௦ ߮௦ௗ
ܸ௦ௗ ൌ
ቐ ܸ௦ ൌ
ோೞ
(15)
ೞ
ௗ
ೝ ݁ௗ ௗ௧ ቐ ௗೝ ܸ ൌ ܴ ݅ ߪǤ ܮ ݁ ݁ఝ
ܸௗ ൌ ܴ ݅ௗ ߪǤ ܮ
(16)
ௗ௧
Where: ݁ௗ ൌ െߪǤ ܮ Ǥ ߱ Ǥ ݅ ۓ ۖ ݁ ൌ ߪǤ ܮ Ǥ ߱ Ǥ ݅ௗ ݁ఝ ൌ ߱ Ǥ
ெ
Ǥ ߮௦ௗ ۔ ଶ ெ ۖ ߪ ൌ ͳെ൬ ൰ ە ඥೞ ೝ
(17)
ೞ
The stator and the rotor active and reactive power can be rewritten as follows [21]: ౩ Ǥ Ǥ ୰୯ ۓୱ ൌ െ ۖ ۖ ൌ ୱ ۔ ۖ ۖ ە
౩
మ ౩ ౩ ன౩
୰ ൌ Ǥ ୰ ൌ Ǥ
െ
Ǥ౩
౩ ౩ Ǥ ౩ ౩ Ǥ ౩
Ǥ ୰ୢ
Ǥ ୰୯
ሺͳͺሻ
Ǥ ୰ୢ
The electromagnetic torque is as follows [21]: ܶ ൌ െܲǤ
ெ ೞ
߮௦ௗ Ǥ ݅
(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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Grid
Ps Ωtur Pr
Ωmec DFIG
CNV1 ࢘ࢊǡ̴ࢋ࢙
ࢀࢋכ
dq
dq PWM
ࢂࢊ̴࢘࢘ࢋࢌ abc
ࢊǡ̴࢘ࢋ࢙
ࣂ࢘
ࢂࢊࢌ̴࢘ࢋࢌ
abc
ࢂࢌ̴࢘ࢋࢌ
Filter currents control
6 ࢂ̴࢘࢘ࢋࢌ dq
Decoupling/compensation
6
PWM
ࢊ̴࢘࢘ࢋࢌ
Decoupling/compensation
̴࢘࢘ࢋࢌ
Rotor currents control
Rotor currents calculation
ࡼࡿ̴࢘ࢋࢌ
CNV2
Filter
MPP
ࡽࡿ̴࢘ࢋࢌ
abc ࢊǡࢌ̴ࢋ࢙
ࢂࢊࢉ
Ωࢋࢉ
2
ࢊࢌ̴࢘ࢋࢌ ൊ
DC bus ࢂ ࢊࢉ̴࢘ࢋࢌ control
ࢌ̴࢘ࢋࢌ
ࢂ࢙
ࣂ࢙
ࢂࢊࢉ
ࡽࢌ̴࢘ࢋࢌ
Fig. 3. Block diagram of the control system of the wind [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 ܸଵ and ܸଶ to the speed ɘଵ of the DFIG is unchanged, the power varies from ܲଵ toܲଶ . In addition, the maximum power is equal toܲଷ . In case we want to extract the maximum power should be changed by ɘଵ and ɘଶ thus 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. 4
12
x 10
Turbine Power (W)
P3 P2 10
w1
w2
MPP
8 V2=12 P1 6
4 V1=10
2 0 0
100 200 300 Rotor Speed (rad/sec) Fig. 4. Turbine power versus rotor speeds of generator
400
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The power extracted from the wind is maximized when the rotor speed is such that the power coefficient is optimalܥ௧ . Therefore, we must set the tip speed ratio on its optimal valueɉ୭୮୲ . Fig. 5 illustrates the principle of MPP control without speed control of the rotation speed [28-29]: Aeroturbine rotor ࣅ
ࢼ
(3)
Gearbox π࢚࢛࢘
(2)
πࢋࢉ
(5)
ࢂ
(4)
ࢀ࢚࢛࢘
(6)
ࢀࢋࢉ ࢀࢋכ
Model
πࢋࢉ
(7)
+
-
Control ࢚ Ǥ ࣋Ǥ ࣊Ǥ ࡾ Ǥ ࡳ Ǥ ࣅ࢚
Ǥ π
MPP control without speed control Fig. 5. Block diagram without speed control
Fig. 6 show the variation of the power coefficient (ܥ ሻ versus the tip-speed ratio (ɉ) for the values of the pitch angle ߚ=2°, 3° and 4°. This figure indicates that there is one specific point ሺߣ௧ ǡ ܥ௧ ሻ at which the turbine is most efficient for ߚ=2°. 0.4
Power coefficient Cp
0.35
X: 7.98 Y: 0.35
0.3 0.25
ࢼ ൌ ι ࢼ ൌ ι ࢼ ൌ ι
0.2 0.15 0.1 0.05 0 0
2
4
6
8
10
12
Tip-speed ratio lumbda 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 ୰୯ and ୰ୢ 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 ݅ௗ̴ ǡ ̴݅ are given by:
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Khouloud Bedoud et al. / Energy Procedia 74 (2015) 886 – 899 ఝ
݅ௗ̴ ൌ ೞ െ ೞ Ǥ ܳ௦̴ ெ ெǤೞ ቐ ೞ כ ̴݅ ൌ െ Ǥ ܶ
(20)
ெǤǤఝೞ
ࢋ࢘ࢊ
࢘ࢊ̴ࢋ࢙ ࢘ࢊ̴࢘ࢋࢌ
െ
PI
ࢂ࢘ࢊ̴࢘ࢋࢌ
+
ࢋ࢘ ̴࢘࢘ࢋࢌ
PI
െ
̴࢘ࢋ࢙
ࢂ̴࢘࢘ࢋࢌ
ࢋ࣐ 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 matrixܹ, a bias vectorܾ, and an output vectorܽ. 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 LevenbergMarquardt (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].
Input
Hidden layers
f ࢈
࢝
ࢀࢋכ
ࢀࢋ̴ࢋ࢙
࢝ ࢝
f
࢝
f
࢝
࢈
࢝
࢈
࢝
f
࢝ ࢝ ࢝
f
+ -
Output
࢝
࢈
f
࢈
࢝
࢈ Fig. 8. Structure of the neuronal controller
࢝ૠ
f ࢝ૠ
࢈ૠ
̴࢘࢘ࢋࢌ
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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 ofܮ , ܮ௦ , ܮ and ܴ have been tested and simultaneously represented (Fig.12). Concerning the variation of ܮ௦ (+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 toͲǤͷ ൈ ͳͲସ and ͲǤͳʹ respectively. Similarly, for the change of ܮ (+20%), the overshoot (ͲǤͺͷ ൈ ͳͲସ ) and response time (tr=ͲǤͳͳ) 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). 2000
2500 I
1500
rd Ref
I
rd NNT
I
rd PI
I
2000
rq Ref
I
I
rq NNT
rq PI
1500 1000
1000
500
500
0
0 -500
-500
-1000 -1000
-1500
-1500 0
0.5
1 Time (sec)
1.5
2
1000
0.5
1 Time (sec)
1000
500
1.5
Irq
NNT
Irq
PI
0
0
I I
-500
-2000 0
1
rd PI
-1000
rd NNT
1.05
1.1
1
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Khouloud Bedoud et al. / Energy Procedia 74 (2015) 886 – 899
4
2
6
x 10
2 T
1.5
T
em Ref
T
em NNT
em PI
x 10
Q
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Q
s Ref
Q
s NNT
s PI
1
1
0.5
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0 0
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-0.5
-1
-1
-1.5
-1.5 0
0.5
1 Time(sec)
1.5
2
-2 0
0.5
1 Time(sec)
1.5
I
I
2
Fig. 9. Response of system without machine parameters changes
I 2000
rd Ref
I
I
rd NNT
4000
rd PI
I
rq Ref
I
rq NNT
rq PI
rq PI
2000
1000
I I
0 -1000
I
-2000 0
0.5 4
1 Time(sec)
-2000
rd PI
1.5
0
2
0.5
1 Time (sec)
Q
Q
6
x 10 2
rq NNT
0
rd NNT
1.5
2
x 10 T
em Ref
T
T
em NNT
2
em PI
s Ref
Q
s NNT
s PI
Q
s PI
0.775*104
1
1 T
em NNT
Q
s NNT
0
0
T
em PI
-1 -1 0
tr =0.162
0.5
1 Time(sec)
1.5
2
-2 0
0.5
1 Time(sec)
Fig. 10. Response of system with stator self inductance change Ls (+20%)
1.5
2
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Khouloud Bedoud et al. / Energy Procedia 74 (2015) 886 – 899
I
2000
I
rd Ref
I
rd NNT
I
3000
rd PI
I
rq Ref
I
rq NNT
rq PI
2000 1000
1000 I
0
I
0
rd NNT
I I
-1000 0
0.5
-1000 rd PI
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2
-3000 0
0.5
1 Time(sec)
Q
Q
6
x 10
T
em Ref
T
em NNT
em PI
s Ref
2
2
4
T
em NNT
T
s PI
Q
s PI
1
0
Q
s NNT
0.85*10
1
1.5
x 10 T
2
rq NNT
-2000
1 Time(sec)
4
rq PI
em PI
0
Q
s NNT
-1 0
-1
tr =0.171
0.5
1 Time(sec)
1.5
2
-2 0
0.5
1 Time(sec)
1.5
2
Fig. 11. Response of system with rotor self inductance change Lr (+20%)
I
3000
I
rd Ref
rd NNT
I
6000
rd PI
2000
I
rq Ref
I
rq NNT
rq PI
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1000
2000
0
I
-1000
I 0
rd NNT
I
-2000 -3000 0
I
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I
rq PI
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rd PI
1 Time(sec)
rq NNT
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2
-4000 0
0.5
1 Time(sec)
1.5
2
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Khouloud Bedoud et al. / Energy Procedia 74 (2015) 886 – 899 6
4
x 10 3
T
T
em Ref
T
2
em NNT
T
3
x 10
em PI
Q
Q
s Ref
2
s NNT
Q
s PI
Q
s PI
em PI
1
1
Q
T 0
s NNT
0
em NNT
-1
-1
-2
-2 0
0.5
1 Time(sec)
1.5
2
0
0.5
1 Time(sec)
1.5
2
Fig. 12. Response of system 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 Rotor diameter Gearbox ratio Friction coefficient ǣ ݂ Moment of inertiaܬ Stator voltage/Frequency ܴݏȀܴ( ݎΩ) ݉ܮȀݏ݂ܮȀ( ݎ݂ܮH) Number of pole pairs:
1.5MW 45m 100 0.0024 1000 690V/50Hz 0.00297/0.00382 0.01212/0.000121/0.0000573 2
M
1
Table 2. Operation Statues of the Simulated DFIG Status
Time (sec)
1 2 3 4
0 < t0.5 0.5 < t1 1 < t1.7 1.7 < t2
Reactive power (MVar) 0 -1 0.8 -0.7
Time (sec) 0 < t0.3 0.3 < t1 1 < t2
Electromagnetic torque (N.m) 0 -1 1
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Table 3. Response time and overshoot of NNT and PI controllers for ܮ௦ (+20%) and ܮ (+20%)
NNT controller ࡸ࢙ (+20%) ࡸ࢘ (+20%) PI controller
ࡸ࢙ (+20%) ࡸ࢘ (+20%)
ࢀࢋ (tr/Dmax) ͲǤͲͻͻȀͲ ͲǤͳͳʹȀͲ ͲǤͳʹȀͲǤͷ ൈ ͳͲସ ͲǤͳͳȀͲǤͺͷ ൈ ͳͲସ
ࡽ࢙ (tr/Dmax) ͲǤͲͻʹȀͲ ͲǤͳͲͷȀͲ ͲǤͳͶȀͲǤͺͺͷ ൈ ͳͲ ͲǤͳ͵ȀͲǤͻͷ ൈ ͳͲ
Appendix B. MPP control and controller gains ൜
ߣ௧ ൌ Ǥͻͺ ܥ௧ ൌ ͲǤ͵ͷ
For the synthesis of the regulators we opted for the method of poles compensation. ࢚࢘= 0.05s ݎܮ ࡷ ൌ ߪ כൌ ͲǤͲͳͲ ݐ ܴݎ ࡵൌ ൌ ͲǤʹʹͻʹ ݐ
References [1] The renewable energies website. Available: http://www.les-energies-renouvelables.eu/avantages-et-inconvenients-de-lenergie eolienne.html [2] Lu MS, Chang CL, Lee WJ, and Wang L. Combining the wind power generation system with energy storage equipment. IEEE Trans. Ind. Applicat 2009; 45: 2109–2115. [3] Wenyi Liu, Baoping Tang, Yonghua Jiang. Status and problems of wind turbine structural health monitoring techniques in China: Review. Renewable Energy 2010; 35: 1414–1418. [4] World Wind Energy Report 2008, WWEA (World Wind Energy Association). [5] Cardenas R, Pena R, Proboste J, Asher G and Clare J. MRAS observer for sensorless control of standalone doubly fed induction generators. IEEE Transaction on Energy Convertion 2005; 20: 710–718. [6] Shen B, Mwinyiwiwa B, ZhangY, Oo BT. Sensorless Maximum Power Point Tracking of Wind by DFIG Using Rotor Position Phase Lock Loop (PLL). IEEE Transactions on Power Electronics 2009; v. 24, no. 4. [7] Karimi S, Gaillard A, Poure P, Saadate S. FPGA-Based Real-Time Power Converter Failure Diagnosis for Wind Energy Conversion Systems”, IEEE Transactions on Industrial Electronics 2008; v. 55, no. 12. [8] Tazil M, Kumar V, Bansal RC, Kong S, Dong ZY, Freitas W, MathurHD. Three-phase doubly fed induction generators: an overview. IET Electric Power Applications 2010; 4: 75-89. [9] Anaya-Lara O, Jenkins N, Ekanayake J, Cartwright P, Hughes M. Wind energy generation: Modelling and control. Chichester, UK: John Wiley & Sons, 2009. [10] Oliveira RV, Zamadei JA, Hossi CH. Robust Tuning of the Control Loops of DFIG Wind Turbine Systems. IEEE International Conference on Control Applications (CCA) Part of 2011 IEEE Multi-Conference on Systems and Control Denver, CO, USA. September 28-30, 2011. [11] Tremblay E, Atayde S, Chandra A. Direct Power Control of a DFIG-based WECS with Active Filter Capabilities. IEEE Electrical Power & Energy Conference, 2009. [12] Hofmann W, Okafor F. Doubly-Fed Full-Controlled Induction Wind Generator for Optimal Power Utilization. in Proceeding of 4th IEEE International Conference on Power Engineering and Drive Systems 2001; 1: 355 – 361. [13] Dalibor P, Zarko C, Vlastimir N, Shahaboddin S, Miss LMK, Nor AB, Ainuddin WAW. Adaptive neuro-fuzzy maximal power extraction of wind turbine with continuously variable transmission. Energy 2014; 64 : 868-874. [14] Bedoud K, Lakel R, Ali-Rachedi M, Lekhchine S, Bahi T. Modeling a chain of wind energy conversion based on a doubly fed induction. 21st Congress of Mechanics French Bordeaux 2013; 26 to 30 August. [15] Baroudi JA, Dinavahi V, Knight AM. A review of power converter topologies for wind generators. Renewable Energy 2007; 32: 23692385. [16] Qiao Wei, Zhou Wei, Aller Jos M and Ronald G. Harley. Wind Speed Estimation Based Sensorless Output Maximization Control for a Wind Turbine Driving a DFIG. IEEE Trans. on Power Electronics 2008; 23: 1156-1169. [17] Beltran B, Sliding al. Mode power control of variable speed wind energy conversion systems. IEEE Trans. Energy Conversion 2008; 23: 551-558. [18] Fernando D.B, Hrnan De Battista, Ricardo JM. Wind Turbine Control Systems Advances in Industrial Control Series. Springer. [19] Barambones O, Durana JMG, Kremers E. Adaptive robust control to maximizing the power generation of a variable speed wind turbine. International Conference on Renewable Energy Research and Applications IEEE, ICRERA 2013; Madrid, Spain, 20-23 October.
Khouloud Bedoud et al. / Energy Procedia 74 (2015) 886 – 899
[20] Abdin ES, Xu W. Control design and Dynamic Performance Analysis of a Wind Turbine Induction Generator Unit. IEEE Trans on Energy Conversion 2000; v. 15, no. 1. [21] Gaillard A. Wind system based on the DFIG: contribution to the study of the quality of the electric energy and the continuity of service. Doct. thesis, Henri Poincare University, Nancy-I, France, April 2010. [22] Abdeddaim S, Betka A. Optimal tracking and robust power control of the DFIG wind turbine. Electrical Power and Energy Systems 2013; 49: 234-242. [23] Boukhezzar B, Siguerdidjane H. Nonlinear control with wind estimation of a DFIG variable speed wind turbine for power capture optimization. Energy Conversion and Management 2009; 50: 885-892. [24] Kassem AM, Hasaneen KM, Yousef AM. Dynamic modeling and robust power control of DFIG driven by wind turbine at infinite grid. Electrical Power and Energy Systems 2013; 44: 375-382. [25] Zamanifar M, Fani B, Golshan MEH, Karshenas HR. Dynamic modeling and optimal control of DFIG wind energy systemsusing DFT and NSGA-II. Electric Power Systems Research 2014; 108: 50-58. [26] Ghennam T, Berkouk EM, François B. Modeling and Control of a Doubly Fed Induction Generator (DFIG) Based Wind Conversion System. IEEE International conference on power engineering, energy and electrical drives (POWERENG) 2009; March 18-20. [27] Bedoud K, Ali-rachedi M, Lakel R, Bahi T. Modeling and Control of the Wind Energy Conversion Systems Based on DFIG Under Sub- and Super-Synchronous Operation Modes. Conférence Internationale des Energies Renouvelables CIER’14, Monastir, Tunisie 2014; Dec19-21. [28] Fernandez LM, Garcia CA, Jurado F. Comparative study on the performance of control systems for doubly fed induction generator (DFIG) wind turbines operating with power regulation. Energy 2008; 33: 1438-1452. [29] M Boutoubat, Mokrani L, Machmoum M. Control of a wind energy conversion system equipped by a DFIG for active power generation and power quality improvement. Renewable Energy 2013; 50: 378-386. [30] Barambones O. A robust wind turbine control using a Neural Network based wind speed estimator. IEEE conference publications, International Joint Conference on Neural Networks (IJCNN) 2010, pp. 1-8. [31] Djeriri Y. Vectorial control of DFIG integrate to the wind system. Magister memory, Sidi Bel-Abbes university, December 2009. [32] Yathley D. Back Propagation Neural Networks for Non-Linear Self Tuning Adaptive Control. IEEE Control Systems Magazine 1990; 10:44 – 48. [33] Hagan MT, Menhaj M. Training feed-forward networks with the Marquardt algorithm. IEEE Transactions on Neural Networks 1999; 5:989993. [34] help matlab: neural networks toolbox 2010. [35] Martin MHB, Howar TH, Demuth B: Neural Network Toolbox User’s Guide, R2014a.
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