- Email: [email protected]
Synthesis and organic photovoltaic (OPV) properties of triphenylamine derivatives based on a hexafluorocyclopentene “core”
Doubly Fed Induction Generator Wind Turbine Control for a maximum Power Extraction Mohamed HILAL
Mohamed MAAROUFI
Mohamed OUASSAID
Dept. of Electrical Engineering University Mohamed V Ecole Mohammadia des Ingénieurs Rabat, Morocco [email protected]
Dept. of Electrical Engineering University Mohamed V Ecole Mohammadia des Ingénieurs Rabat, Morocco [email protected]
Dept. of Industrial Engineering Ecole Nationale de Science Appliquées Safi, Morocco [email protected]
Abstract— Wind turbine WT occupies gradually a large part in world energy market, Doubly fed induction generator DFIG is mostly used in WT, it allow highly flexible active and reactive power generation control. These machines are driven by power collaborating converters: voltage source converter VSC and rotor-side converter RSC protected using crowbar protection against transient over current. This paper develops a DFIG dynamic model, driven by wind turbine model using PSCAD/EMTDC a powerful tool allowing power system analysis to investigate simulations. A control strategy is also established using PI regulator to control stator-grid power flow according to maximum power point tracking MPPT strategy. Index Terms—Renewable energy, Wind turbine, DFIG, MPPT, PSCAD/EMTDC, PWM , CRPWM, Tracking curve
I. ρ,λ , ,β , , , Ω , Ω , , , ,
Air Density , Tip Speed Ratio Rotor Radius , Equivalent wind speed Aerodynamic Efficiency , Pitch angle Aerodynamic Power , Aerodynamic Torque Total Wind Turbine Inertia , Viscous friction ,
Rotor Inertia , Generator Inertia , Gear Ratio Turbine Speed, Mechanical speed Direct and Quadratic Stator Voltages Direct and Quadratic Rotor Voltages Rotor Reference Voltages in abc Frame Direct and Quadratic VSC output Voltages
,
Dq VSC output Reference Voltages
, , , , , , , M , ,
NOMEMCLATURE
,
, , L,R
,
Direct and Quadratic Stator Currents Direct and Quadratic Rotor Currents Direct and Quadratic VSC output Currents Direct and Quadratic Stator Flux Direct and Quadratic Rotor Flux Per phase stator and rotor resistance Total cyclic stator and rotor inductances Magnetizing inductance Stator , Rotor , Slip angle Stator , Rotor Pulsation Active , Reactive Stator and Rotor Power Transformer Per phase Inductance and Resistance
II.
INTRODUCTION
Wind energy is the fastest growing source of new electrical generation capacity in the world, and it is expected to remain so in the future in spite of wind forecasting small period with important probability error and wind speed fluctuations which makes wind conversion systems vulnerable to power network stability. Variable speed technology is more attractive because of new power electronic component capabilities and shipper prices. Allowing a flexible and decoupled active and reactive power control, a Doubly Fed Induction Generator Wind Turbine DFIGWT is the most grid connected wind conversion system [1],[2]. PSCAD/EMTDC is a powerful tool for studying transient electrical network behavior. Its graphic user interface allows users to construct electric schemes, run simulations, analyze results, and manage data in a graphical environment. Its library of models supports most of power plant AC, DC components and controls. It provides the flexibility of building user-defined models either by assembling them visually using existing models or by utilizing an intuitively graphical design editor and writing codes in Fortran, PSCAD script, C and MATLAB. It provides a powerful resource for assessing the impact of new power technologies in the power network [3][4]. Different control strategies have been proposed in the literature for voltage, frequency, active and reactive power control [5]. In this paper, we present a dynamic DFIGWT model based on vector control strategy carried through a synchronous rotating dq referential, with the q-axis aligned with the stator flux position. The frequency converter is built by two self-commutated back-to-back PWM converters controlled independently allowing flexible active and reactive power control. Converters and associated control strategies are simulated using PSCAD/EMTDC. Results are presented to show behavior and performances and validate theoretical analysis of the proposed structure. This document is organized as follows : A wind turbine WT components description will be given in section IV, each WT component is modeled according to its relating equations and our vector control strategy in sections V,VI. Simulation results and interpretation are given in section VII. All used symbol in this paper are listed in section I.
978-1-61284-732-0/11/$26.00 ©2010 IEEE
Figure 3. General DFIGWT modeled In PSCAD/EMTDC.
IV.
Figure 1. Doubly-Fed Induction Generator Wind Turbine.
III.
STUDY SYSTEM DESCRIPTION
The proposed wind energy conversion system DFIGWT depicted in Fig.1, have the most commercial wind turbine used structure [1][2]. A DFIG is a standard machine controlled with a frequency converter built by two PWM converters linked using DC link capacitor. The all DFIGWT parts are modeled in PSCAD/EMTDC, the control scheme is depicted in Fig.2. The two PI regulators determines the rotor reference currents , that the measured currents , should follow to permit active and reactive is power decoupled control. The slip angle used in transformation to get rotor reference currents. The measured machine speed Ω and reactive power Q are compared to their references. The aggregated study system model is given at Fig.3; each unit contains a parts sub-model. The turbine unit includes WT aerodynamic model, its output torque drives DFIG used from PSCAD/EMTDC Library PL. The RSC & VSC unit includes rotor-side, grid-side converters and DC link with their controls. Wind is generated with four components to be realistic using wind source component from PL.
WIND TURBINE COMPONENTS
A. Aerodynamic Model The aerodynamic model is governed by a nonlinear formula giving the mechanical power extracted from the wind, aerodynamic coefficient , Tip speed ratio TSR λ and aerodynamic torque , they are expressed by the well-known equations (1,2,3,4) [7]: .Ω
λ
(1)
. . π.
.
. . π.
.
λ, β
. Ω λ
λ, β
.
(3)
evolution depending on λ and β , it depend Fig.4 shows on turbine geometry, for most commercialized three pale wind turbine power efficiency it is about 0.45 when β is null. [7].
λ, β
0.5176
0.4β
λ
1
λ
λ
1 0.08β
0.0068λ
λ
5
(4)
0.035
β
Figure 4. Aerodynamic Efficiency
Figure 2. DFIG Vector Control Strategy control scheme
(2)
1
λ , β).
B. Drive Train Model A drive-train model represents wind turbine mechanical behavior. The turbine blades and associated low speed rotates more slowly, and are connected to the high speed generator shaft through a gearbox, while generator rotating at synchronous speed. All rotating components of the drive train
are characterized by an aggregated inertia moment (5), which depends on the component mass and geometry. Most components also have a rotational damping, due to wind resistance and bearing friction. To simplify the electrical model of the wind turbine, the drive train is modeled entirely on the high-speed side [7]. (5) V.
DFIG WIND TURBINE
A. DFIG Description DFIGWT depicted at Fig.1 are used in most commercial wind turbines [2]. The DFIG stator windings are directly connected to the grid and his rotor windings are connected to the grid through a frequency converter. In modern DFIG designs, the frequency converter is built by two selfcommutated PWM converters, rotor- and grid-side converters, with an intermediate DC voltage link created by the capacitor in the middle, it decouples the operation of the two converters, thus allowing their design and operation to be optimized. The two back-to-back PWM converters are controlled independently through decoupled dq vector control approaches decoupling which controls reactive power, and which controls the machine torque and therefore the active power. B. DFIG Modeling In αβ reference frame stator and rotor voltage are expressed respectively (6,7) [8]. α β α β
.
α
α
β
β
.
α
α
β
β
.
0 0 0 0
0
,
0
.
(11)
0
Ω
.
.Ω
(12)
. .
(8)
0
(9)
0
(10)
0
0
Electromagnetic and mechanic torque are expressed in (12) where is the equivalent inertia from (5). The stator and rotor active and reactive power are given by (13) [8].
(7)
0,
0 0
.
Applying dq transformation to (6,7) with taking account of the simplification above, stator and rotor voltage becomes respectively (9,10). .
0
(6)
In dq reference frame according to the vector control approaches, and assuming that stator’s resistance can be neglected, stator flux and voltage components are simplified and expressed in (8). ,
Figure 5. DFIG Maximum Power Point Tracking Strategy..
Stator and rotor flux fields are developed by the current circulation in the rotor and stator windings according to the control strategy that consists to align stator flux to axis and stator voltage to axis. This approach permits an independent control between active and reactive power which are respectively proportional to the current component and the current component. The expressions of stator and rotor flux fields are given in (11) [8].
. . .
(13)
. .
C. Maximum Power Point Tracking The wind turbine aerodynamic model provides the extracted power from wind which depends on , blade pitch is provided by angle β and proportional to wind velocity. optimal TSR λ , below the rated wind speed, the turbine extract maximum power according to maximum power point tracking MPPT characteristic Fig.5, illustrated by a curve joining maximums given for different wind speed curves, the speed setpoint is set to give maximum power there is generally no need to vary the pitch angle. Above the rated wind speed, to keep the machine at the rated output power pitch control is applied. VI.
FREQUENCY CONVERTER
The frequency converter is built by two self-commutated back-to-back PWM converters controlled independently allowing flexible active and reactive power control, rotor-side converter RSC and grid-side voltage source converter VSC, with an intermediate DC voltage link which decouples converter operations [8][9].
Figure 6. Rotor Reference Currents generation. Figure 7. RSC IGBT Firing Pulses using CRPWM Controler.
A. Rotor-side converter 1) Stator Flux Location : The instantaneous stator rotating flux vector location is delivered through (6) by integrating stator voltages α and β (after removal of resistive voltage drop). Filtering is required in order to eliminate any residual DC component from quantities α and β introduced by the integration process. The resulting equations given in (14) shows instantaneous stator flux location. ψα ψ
vα ψα θ
R . iα dt
ψβ
vβ
ψβ
θ
tg
θ
ω .ω
dt
.
.
(15)
, = 0) stator voltage In dq reference frame ( = is aligned to d-axis, equation (15) becomes (16) in this reference frame after dq transformation
R . iβ dt
.
(16)
α β
(14)
2) Rotor Current Generation : Using two PI regulators, having and as inputs, rotor reference currents and which should be injected by the RSC in the rotor widdings are computed according to desired machine speed , the rotor will be located at . Thus, with a reference frame attached to the rotor, the stator’s magnetic field vector will be located at slip angle = − used in dq to abc transformation to obtain instantaneous values for the desired rotor currents. The relating model is depicted at Fig.6. 3) Rotor-Side Converter Conrol : Using current reference pulse width modulation CRPWM, the reference currents are generated with RSC by adjusting IGBTs firing pulses according to a reglable tolerance , to limit reference current up and down value , relating scheme is given at Fig.7. Pulses are applied to IGBTs of the RSC depicted at Fig.8. 4) Grid-side converter: The voltage source converter VSC regulates DC bus capacitor voltage in order to guarantee an unity power factor to exchange reactive power through the stator. It use a regulation loop of a DC voltage regulator according to and drives . VSC is linked to grid trough a transformer having inductance L and resistance R per phase. VSC output voltages , , and currents , , and grid voltages , are expressed in abc reference frame in (15)[10].
changes it causes not Equation (16) shows that when , but only a change in , which should be controlled by , decoupling control between also a transient change in and is done using (17). 0 0 . .
.
(17) . .
. . . .
Figure 8. Rotor-Side Converter (RSC).
Figure 11. Voltage Source Converter VSC.
Figure 9. DC voltage regulator Control with Id and Iq decoupled
Equation (17) let the error in the i loop affect L. x and in the i loop, L. x . The resulting equations are decoupled. VSC relating control diagram using feedback PI control is shown above in Fig.9. , from (16) are d and q VSC output currents components of primary windings transformer currents after , are outputs of the removal of DC component. generated VSC voltage after limitation and transformation according to stator’s voltage field vector location . Fig.10 shows VSC firing pulse scheme. The VSC is linked to grid through a transformer the relating scheme is located at Fig.11. VII. SIMULATION RESULTS In this section we present the simulation results DFIGWT modeled in PSCAD/EMTDC according to vector control strategy seen above. RSC, VSC and DC link capacitor are controlled to have voltage references. A (DFIG) is used from PSCAD/EMTDC library. To attest that WT can absorb or generate reactive power to power network, the setpoint is switched, during simulation, from a negative to a positive value, different other values are also successfully tested.
The simulation starts with speed control mode, is to 1.1 , it switches to torque mode after 0.5 second (sec) and remains during 10 sec. Wind Turbine is subjected to a fluctuating wind having four components: base wind 8 m/s, gust wind (velocity 0.5 m/s), ramp wind (maximum velocity 0.5 m/s) and wind noise, we also change the reactive power from 30 fixed initially to 25 at setpoint t=2 sec, we also caused a short three phase fault at t = 3 sec, during 0.15 sec, at stator busbar to test the model robustness. A
B
C
D
Figure 12. Aerodynamic model relating curves.
Figure 10. VSC IGBT Firing Pulses.
The results curves of wind speed v Fig.12-A, TSR λ Fig.12-B, aerodynamic coefficient C Fig.12-C and aerodynamic torque TRQ pu Fig.12-D corresponds to MPPT strategy, λ remains (around optimal value 8.088 , and C (around 0.48 so we have maximum power extraction from wind. Small C variations are due to the fact that the strategy while avoiding computes and provides a speed reference Ω the abrupt speed changes.
A
A
0.02
0.018 B
B
C
C
D
D
Figure 13. Mechanic & Electric model relatting curves.
Fig.13-A shows that machine speed ω follows as soon as torque mode is set, the gap doesn’tt exceed 0.1% this justifies rotor currents PI regulators parrameters justness. Machine speed deviates slightly from because inertia and torque prevents speed decreasing, the gap g is even bigger than torque exceeds its rated value, pitch control should be used to reduce torque, because of this gap λ is shifted from its optimal value and decreases slightly Fig.12-B,C. This testifies of a realistic correspondence of our aerodynamic model.
Figure 14. VSC moodel relating curves. A
B
Rms and three phase stator voltage at Figg.13-C,D are 10% around their rated value. The tree phase fauult at stator busbar has a lesser effects, a deepest voltage droop iss about 50% of the rated voltage during fault. The setpoints are a followed after short circuit duration this proves good model robustness.
C
DC link voltage capacitor VDC at Fig.14-A is stabilized at its setpoint VDC , the maximum error didn’t inncrease 4% during all simulation time, a slight overshoot (<1%) above VDC during fault is notified. , which coontrols VSC firing pulses are perfectly decoupled, is less afffected by fault.
D
Figure 15.
&
loopp model relating curves.
In Fig.15, we clearly notice that active and reactive power and , and are perfectly are respectively controlled by decoupled, reactive power setpoints (-30, 25MVAr) are followed without affecting active power. The positive and negative reactive power setpoints values are chosen to attest that WT can absorb or produce reactive power according to its necessity in connected power network. VIII. CONCLUSION DFIG has good power factor even when a slight difference between the machine speed and synchronous speed is made, and allow a highly flexible active and reactive power control. DFIG is also a standard machine, the falling of power electronics converter, gives the DFIGWT a great place in world turbine markets. The mathematical model of the system (WT, DFIG-Converters- Grid) has been implemented in PSCAD/EMTDC. Simulation demonstrates through this work, a correspondence between theatrical and practical analysis. Our future work will be on optimizing wind farm power generation and its contribution to frequency control. ACKNOWLEDGMENT The authors would like to thank the PSCAD support team members at Manitoba HVDC Centre, They also show their best regards for Professors of Department of Electrical and Computer Engineering, University of Manitoba.
REFERENCES [1]
The European Wind Energy Association (EWEA). (1999). Green peace and wind industry unveil global energy blue print [Online]. Available: http://www.ewea.org/src/press.htm [2] F. V. Hulle, “Large scale integration of wind energy in the European power supply: analysis, issues and recommendations,” EWEA, Tech. Rep., Dec. 2005. [3] Manitoba HVDC Research Center, PSCAD/EMTDC Power System Simulation Software User’s Manual, Version 4, 2008 release. [4] O.Anaya-Lara and E. Acha, “Modeling and analysis of custom power systems by PSCAD/EMTDC,” IEEE Trans. Power Delivery, vol. 17, no. 1, pp. 266-272, Jan. 2002. [5] L. Mihet-popa, I. BOLDEA, “Control Strategies for Large Wind TurbineApplication,” Journal of Electrical Engineering, Vol. 7, Edition 3rd, ISSN 1582-4594. 2006. [6] S. Muller, M. Deicke and R. W. De Doncker, “Doubly Fed Induction Generator Systems for Wind Turbines,” IEEE Industry Applications Magazine, Vol. 8, No. 3, 26-33, May/June 2002. [7] J. G. Slootweg, S. W. H. de Haan, H. Polinder, and W. L. Kling, “Modeling wind turbine in power system dynamics simulations,” in Proc. IEEE Power Engineering Society Summer Meeting, Vancouver, BC, Canada, Jul. 2001, pp. 15U˝ 19. [8] R. Pena, J.C. Clare and G.M. Asher, “Doubly fed induction generator using back to back PWM converters and its application to variable speed wind energy generation,” IEE Proc. Electrical Power Applications, Vol. 143., No.3., May 1996. [9] T. Sun, Z. Chen, and F. Blaabjerg, “Transient analysis of grid-connected wind turbines with DFIG after an external short-circuit fault,” presented at the Nordic Wind Power Conf., Chalmers Univ. Technol., Gothenburg, Sweden, Mar. 2004. [10] J. B. Ekanayake, L. Holdsworth, X. G. Wu, and N. Jenkins, “Dynamic modeling of doubly fed induction generator wind turbines,” IEEE Trans. Power Electron., vol. 18, no. 2, pp. 803–809, May 2003.
Mohamed MAAROUFI
Mohamed OUASSAID
Dept. of Electrical Engineering University Mohamed V Ecole Mohammadia des Ingénieurs Rabat, Morocco [email protected]
Dept. of Electrical Engineering University Mohamed V Ecole Mohammadia des Ingénieurs Rabat, Morocco [email protected]
Dept. of Industrial Engineering Ecole Nationale de Science Appliquées Safi, Morocco [email protected]
Abstract— Wind turbine WT occupies gradually a large part in world energy market, Doubly fed induction generator DFIG is mostly used in WT, it allow highly flexible active and reactive power generation control. These machines are driven by power collaborating converters: voltage source converter VSC and rotor-side converter RSC protected using crowbar protection against transient over current. This paper develops a DFIG dynamic model, driven by wind turbine model using PSCAD/EMTDC a powerful tool allowing power system analysis to investigate simulations. A control strategy is also established using PI regulator to control stator-grid power flow according to maximum power point tracking MPPT strategy. Index Terms—Renewable energy, Wind turbine, DFIG, MPPT, PSCAD/EMTDC, PWM , CRPWM, Tracking curve
I. ρ,λ , ,β , , , Ω , Ω , , , ,
Air Density , Tip Speed Ratio Rotor Radius , Equivalent wind speed Aerodynamic Efficiency , Pitch angle Aerodynamic Power , Aerodynamic Torque Total Wind Turbine Inertia , Viscous friction ,
Rotor Inertia , Generator Inertia , Gear Ratio Turbine Speed, Mechanical speed Direct and Quadratic Stator Voltages Direct and Quadratic Rotor Voltages Rotor Reference Voltages in abc Frame Direct and Quadratic VSC output Voltages
,
Dq VSC output Reference Voltages
, , , , , , , M , ,
NOMEMCLATURE
,
, , L,R
,
Direct and Quadratic Stator Currents Direct and Quadratic Rotor Currents Direct and Quadratic VSC output Currents Direct and Quadratic Stator Flux Direct and Quadratic Rotor Flux Per phase stator and rotor resistance Total cyclic stator and rotor inductances Magnetizing inductance Stator , Rotor , Slip angle Stator , Rotor Pulsation Active , Reactive Stator and Rotor Power Transformer Per phase Inductance and Resistance
II.
INTRODUCTION
Wind energy is the fastest growing source of new electrical generation capacity in the world, and it is expected to remain so in the future in spite of wind forecasting small period with important probability error and wind speed fluctuations which makes wind conversion systems vulnerable to power network stability. Variable speed technology is more attractive because of new power electronic component capabilities and shipper prices. Allowing a flexible and decoupled active and reactive power control, a Doubly Fed Induction Generator Wind Turbine DFIGWT is the most grid connected wind conversion system [1],[2]. PSCAD/EMTDC is a powerful tool for studying transient electrical network behavior. Its graphic user interface allows users to construct electric schemes, run simulations, analyze results, and manage data in a graphical environment. Its library of models supports most of power plant AC, DC components and controls. It provides the flexibility of building user-defined models either by assembling them visually using existing models or by utilizing an intuitively graphical design editor and writing codes in Fortran, PSCAD script, C and MATLAB. It provides a powerful resource for assessing the impact of new power technologies in the power network [3][4]. Different control strategies have been proposed in the literature for voltage, frequency, active and reactive power control [5]. In this paper, we present a dynamic DFIGWT model based on vector control strategy carried through a synchronous rotating dq referential, with the q-axis aligned with the stator flux position. The frequency converter is built by two self-commutated back-to-back PWM converters controlled independently allowing flexible active and reactive power control. Converters and associated control strategies are simulated using PSCAD/EMTDC. Results are presented to show behavior and performances and validate theoretical analysis of the proposed structure. This document is organized as follows : A wind turbine WT components description will be given in section IV, each WT component is modeled according to its relating equations and our vector control strategy in sections V,VI. Simulation results and interpretation are given in section VII. All used symbol in this paper are listed in section I.
978-1-61284-732-0/11/$26.00 ©2010 IEEE
Figure 3. General DFIGWT modeled In PSCAD/EMTDC.
IV.
Figure 1. Doubly-Fed Induction Generator Wind Turbine.
III.
STUDY SYSTEM DESCRIPTION
The proposed wind energy conversion system DFIGWT depicted in Fig.1, have the most commercial wind turbine used structure [1][2]. A DFIG is a standard machine controlled with a frequency converter built by two PWM converters linked using DC link capacitor. The all DFIGWT parts are modeled in PSCAD/EMTDC, the control scheme is depicted in Fig.2. The two PI regulators determines the rotor reference currents , that the measured currents , should follow to permit active and reactive is power decoupled control. The slip angle used in transformation to get rotor reference currents. The measured machine speed Ω and reactive power Q are compared to their references. The aggregated study system model is given at Fig.3; each unit contains a parts sub-model. The turbine unit includes WT aerodynamic model, its output torque drives DFIG used from PSCAD/EMTDC Library PL. The RSC & VSC unit includes rotor-side, grid-side converters and DC link with their controls. Wind is generated with four components to be realistic using wind source component from PL.
WIND TURBINE COMPONENTS
A. Aerodynamic Model The aerodynamic model is governed by a nonlinear formula giving the mechanical power extracted from the wind, aerodynamic coefficient , Tip speed ratio TSR λ and aerodynamic torque , they are expressed by the well-known equations (1,2,3,4) [7]: .Ω
λ
(1)
. . π.
.
. . π.
.
λ, β
. Ω λ
λ, β
.
(3)
evolution depending on λ and β , it depend Fig.4 shows on turbine geometry, for most commercialized three pale wind turbine power efficiency it is about 0.45 when β is null. [7].
λ, β
0.5176
0.4β
λ
1
λ
λ
1 0.08β
0.0068λ
λ
5
(4)
0.035
β
Figure 4. Aerodynamic Efficiency
Figure 2. DFIG Vector Control Strategy control scheme
(2)
1
λ , β).
B. Drive Train Model A drive-train model represents wind turbine mechanical behavior. The turbine blades and associated low speed rotates more slowly, and are connected to the high speed generator shaft through a gearbox, while generator rotating at synchronous speed. All rotating components of the drive train
are characterized by an aggregated inertia moment (5), which depends on the component mass and geometry. Most components also have a rotational damping, due to wind resistance and bearing friction. To simplify the electrical model of the wind turbine, the drive train is modeled entirely on the high-speed side [7]. (5) V.
DFIG WIND TURBINE
A. DFIG Description DFIGWT depicted at Fig.1 are used in most commercial wind turbines [2]. The DFIG stator windings are directly connected to the grid and his rotor windings are connected to the grid through a frequency converter. In modern DFIG designs, the frequency converter is built by two selfcommutated PWM converters, rotor- and grid-side converters, with an intermediate DC voltage link created by the capacitor in the middle, it decouples the operation of the two converters, thus allowing their design and operation to be optimized. The two back-to-back PWM converters are controlled independently through decoupled dq vector control approaches decoupling which controls reactive power, and which controls the machine torque and therefore the active power. B. DFIG Modeling In αβ reference frame stator and rotor voltage are expressed respectively (6,7) [8]. α β α β
.
α
α
β
β
.
α
α
β
β
.
0 0 0 0
0
,
0
.
(11)
0
Ω
.
.Ω
(12)
. .
(8)
0
(9)
0
(10)
0
0
Electromagnetic and mechanic torque are expressed in (12) where is the equivalent inertia from (5). The stator and rotor active and reactive power are given by (13) [8].
(7)
0,
0 0
.
Applying dq transformation to (6,7) with taking account of the simplification above, stator and rotor voltage becomes respectively (9,10). .
0
(6)
In dq reference frame according to the vector control approaches, and assuming that stator’s resistance can be neglected, stator flux and voltage components are simplified and expressed in (8). ,
Figure 5. DFIG Maximum Power Point Tracking Strategy..
Stator and rotor flux fields are developed by the current circulation in the rotor and stator windings according to the control strategy that consists to align stator flux to axis and stator voltage to axis. This approach permits an independent control between active and reactive power which are respectively proportional to the current component and the current component. The expressions of stator and rotor flux fields are given in (11) [8].
. . .
(13)
. .
C. Maximum Power Point Tracking The wind turbine aerodynamic model provides the extracted power from wind which depends on , blade pitch is provided by angle β and proportional to wind velocity. optimal TSR λ , below the rated wind speed, the turbine extract maximum power according to maximum power point tracking MPPT characteristic Fig.5, illustrated by a curve joining maximums given for different wind speed curves, the speed setpoint is set to give maximum power there is generally no need to vary the pitch angle. Above the rated wind speed, to keep the machine at the rated output power pitch control is applied. VI.
FREQUENCY CONVERTER
The frequency converter is built by two self-commutated back-to-back PWM converters controlled independently allowing flexible active and reactive power control, rotor-side converter RSC and grid-side voltage source converter VSC, with an intermediate DC voltage link which decouples converter operations [8][9].
Figure 6. Rotor Reference Currents generation. Figure 7. RSC IGBT Firing Pulses using CRPWM Controler.
A. Rotor-side converter 1) Stator Flux Location : The instantaneous stator rotating flux vector location is delivered through (6) by integrating stator voltages α and β (after removal of resistive voltage drop). Filtering is required in order to eliminate any residual DC component from quantities α and β introduced by the integration process. The resulting equations given in (14) shows instantaneous stator flux location. ψα ψ
vα ψα θ
R . iα dt
ψβ
vβ
ψβ
θ
tg
θ
ω .ω
dt
.
.
(15)
, = 0) stator voltage In dq reference frame ( = is aligned to d-axis, equation (15) becomes (16) in this reference frame after dq transformation
R . iβ dt
.
(16)
α β
(14)
2) Rotor Current Generation : Using two PI regulators, having and as inputs, rotor reference currents and which should be injected by the RSC in the rotor widdings are computed according to desired machine speed , the rotor will be located at . Thus, with a reference frame attached to the rotor, the stator’s magnetic field vector will be located at slip angle = − used in dq to abc transformation to obtain instantaneous values for the desired rotor currents. The relating model is depicted at Fig.6. 3) Rotor-Side Converter Conrol : Using current reference pulse width modulation CRPWM, the reference currents are generated with RSC by adjusting IGBTs firing pulses according to a reglable tolerance , to limit reference current up and down value , relating scheme is given at Fig.7. Pulses are applied to IGBTs of the RSC depicted at Fig.8. 4) Grid-side converter: The voltage source converter VSC regulates DC bus capacitor voltage in order to guarantee an unity power factor to exchange reactive power through the stator. It use a regulation loop of a DC voltage regulator according to and drives . VSC is linked to grid trough a transformer having inductance L and resistance R per phase. VSC output voltages , , and currents , , and grid voltages , are expressed in abc reference frame in (15)[10].
changes it causes not Equation (16) shows that when , but only a change in , which should be controlled by , decoupling control between also a transient change in and is done using (17). 0 0 . .
.
(17) . .
. . . .
Figure 8. Rotor-Side Converter (RSC).
Figure 11. Voltage Source Converter VSC.
Figure 9. DC voltage regulator Control with Id and Iq decoupled
Equation (17) let the error in the i loop affect L. x and in the i loop, L. x . The resulting equations are decoupled. VSC relating control diagram using feedback PI control is shown above in Fig.9. , from (16) are d and q VSC output currents components of primary windings transformer currents after , are outputs of the removal of DC component. generated VSC voltage after limitation and transformation according to stator’s voltage field vector location . Fig.10 shows VSC firing pulse scheme. The VSC is linked to grid through a transformer the relating scheme is located at Fig.11. VII. SIMULATION RESULTS In this section we present the simulation results DFIGWT modeled in PSCAD/EMTDC according to vector control strategy seen above. RSC, VSC and DC link capacitor are controlled to have voltage references. A (DFIG) is used from PSCAD/EMTDC library. To attest that WT can absorb or generate reactive power to power network, the setpoint is switched, during simulation, from a negative to a positive value, different other values are also successfully tested.
The simulation starts with speed control mode, is to 1.1 , it switches to torque mode after 0.5 second (sec) and remains during 10 sec. Wind Turbine is subjected to a fluctuating wind having four components: base wind 8 m/s, gust wind (velocity 0.5 m/s), ramp wind (maximum velocity 0.5 m/s) and wind noise, we also change the reactive power from 30 fixed initially to 25 at setpoint t=2 sec, we also caused a short three phase fault at t = 3 sec, during 0.15 sec, at stator busbar to test the model robustness. A
B
C
D
Figure 12. Aerodynamic model relating curves.
Figure 10. VSC IGBT Firing Pulses.
The results curves of wind speed v Fig.12-A, TSR λ Fig.12-B, aerodynamic coefficient C Fig.12-C and aerodynamic torque TRQ pu Fig.12-D corresponds to MPPT strategy, λ remains (around optimal value 8.088 , and C (around 0.48 so we have maximum power extraction from wind. Small C variations are due to the fact that the strategy while avoiding computes and provides a speed reference Ω the abrupt speed changes.
A
A
0.02
0.018 B
B
C
C
D
D
Figure 13. Mechanic & Electric model relatting curves.
Fig.13-A shows that machine speed ω follows as soon as torque mode is set, the gap doesn’tt exceed 0.1% this justifies rotor currents PI regulators parrameters justness. Machine speed deviates slightly from because inertia and torque prevents speed decreasing, the gap g is even bigger than torque exceeds its rated value, pitch control should be used to reduce torque, because of this gap λ is shifted from its optimal value and decreases slightly Fig.12-B,C. This testifies of a realistic correspondence of our aerodynamic model.
Figure 14. VSC moodel relating curves. A
B
Rms and three phase stator voltage at Figg.13-C,D are 10% around their rated value. The tree phase fauult at stator busbar has a lesser effects, a deepest voltage droop iss about 50% of the rated voltage during fault. The setpoints are a followed after short circuit duration this proves good model robustness.
C
DC link voltage capacitor VDC at Fig.14-A is stabilized at its setpoint VDC , the maximum error didn’t inncrease 4% during all simulation time, a slight overshoot (<1%) above VDC during fault is notified. , which coontrols VSC firing pulses are perfectly decoupled, is less afffected by fault.
D
Figure 15.
&
loopp model relating curves.
In Fig.15, we clearly notice that active and reactive power and , and are perfectly are respectively controlled by decoupled, reactive power setpoints (-30, 25MVAr) are followed without affecting active power. The positive and negative reactive power setpoints values are chosen to attest that WT can absorb or produce reactive power according to its necessity in connected power network. VIII. CONCLUSION DFIG has good power factor even when a slight difference between the machine speed and synchronous speed is made, and allow a highly flexible active and reactive power control. DFIG is also a standard machine, the falling of power electronics converter, gives the DFIGWT a great place in world turbine markets. The mathematical model of the system (WT, DFIG-Converters- Grid) has been implemented in PSCAD/EMTDC. Simulation demonstrates through this work, a correspondence between theatrical and practical analysis. Our future work will be on optimizing wind farm power generation and its contribution to frequency control. ACKNOWLEDGMENT The authors would like to thank the PSCAD support team members at Manitoba HVDC Centre, They also show their best regards for Professors of Department of Electrical and Computer Engineering, University of Manitoba.
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