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Direct torque control-based power factor control of a DFIG
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Special Issue on Emerging and Renewable Energy: Generation and Automation Special Issue on Emerging and Renewable Energy: Generation and Automation
Direct torque control-based power factor control of a DFIG Direct torque control-based power factor control of a DFIG The 15th International on District AyrirSymposium Wiama*, Haddi Alia Heating and Cooling
Ayrir Wiama*, Haddi Alia
Assessing the feasibility of using the heat demand-outdoor temperature function for a long-term district heat demand forecast Advanced Sciences and Technologies Team, University of ABDELMALEK ESSAÄDI, (ENSATe) Tetouan 93030, Morocco a Advanced Sciences and Technologies Team, University of ABDELMALEK ESSAÄDI, (ENSATe) Tetouan 93030, Morocco a
Abstract a,b,c Abstract I. Andrić *, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc This paper proposes the Direct Torque Control (DTC) of a Wind Energy Conversion System (WECS) based on a Doubly Fed a IN+ Center for Innovation, Technology andfactor Policy Research Superior Técnico,technique Av.System Roviscoaims Pais at 1, 1049-001 Lisbon, Portugal This paper proposes the Direct Torque Control (DTC) of strategy. a- Instituto Wind Energy Conversion (WECS) based on athe Doubly Fed Induction Generator (DFIG) with power control The proposed controlling generator b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Induction Generator (DFIG) with power factor control strategy. The proposed technique aims at controlling the generator electromagnetic torque and rotor flux while controlling the power factor at the stator terminals. The proposed control is achieved c Département Énergétiques et Environnement -the IMT Atlantique, 4 rue Alfred 44300 Nantes,control Franceissoachieved electromagnetic torque andSystèmes rotor flux while controlling thefrom power factor at the Power stator terminals. The proposed through generating the referential electromagnetic torque Maximum PointKastler, Tracking (MPPT) control that the through generating the referential electromagnetic Maximum rotor Power Point Tracking (MPPT) control so that the maximum power is extracted for each different windtorque speed,from and the referential flux from the reactive power reference. maximum power is extracted for each different wind speed, and the referential rotor flux from the reactive power reference. Copyright © 2019 Elsevier Ltd. All rights reserved. ©Abstract 2019 The Authors. Published by Elsevier Ltd Copyright © 2019 Elsevierunder Ltd. All rights reserved. Selection and peer-review responsibility of the scientific committee of the Special Issue on Emerging and Renewable Selection and peer-review under responsibility of the scientific committee of the 6th International Conference on Emerging and Selection and peer-review under responsibility ofICEREGA the scientific committee of the Special Issue on Emerging and Renewable Energy: Generation and Automation. Renewable Energy: Generation Automation, District heating networks are and commonly addressed in the2018. literature as one of the most effective solutions for decreasing the Energy: Generation and Automation. greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat Keywords: Wind energy; DFIG; MPPT; DTC; power factor control. sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, Keywords: Wind energy; DFIG; MPPT; DTC; power factor control. prolonging the investment return period. The main scope of this paper is to assess the feasibility of using the heat demand – outdoor temperature function for heat demand 1.forecast. Introduction The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 1.buildings Introduction that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district Over the scenarios past decade, energy(shallow, industryintermediate, has been interested variablethe speed WECS based Currently the renovation werewind developed deep). Toin estimate error, obtained heatDFIG. demand values were Over the past decade, wind energy industry has been interested in variable speed WECS based DFIG. Currently the DFIG occupies an essential part in variable speed generator technologies market [1]–[3]. Consequently, several control compared with results from a dynamic heat demand model, previously developed and validated by the authors. DFIG occupies an essential part in variable speed generator technologies market [1]–[3]. Consequently, several control methods have been emerging. In general, the control allows the system to track a desired response for a given input The results showed that when only weather change is considered, the margin of error could be acceptable for some applications methods have been emerging. Inlower general, allows the tooperation track a However, desired response for a given input (the error in annual demand than the 20%control all weather scenarios considered). after introducing renovation while rejecting the effects ofwas any disturbances infororder to obtain asystem correct of it. Different control techniques scenarios, the error value increased up to 59.5% (depending the andoperation renovation combination considered). while rejecting theineffects of any disturbances intechniques, order to on obtain a correct of scenarios it. Different control techniques have been treated the literature. Among these the weather direct torque control. The been value treated of slopeincoefficient increased on these average within the the range of 3.8% upcontrol. to 8% per decade, that corresponds to the have the literature. Among techniques, direct torque decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and * improve the accuracy heat demand estimations. Corresponding author. of Tel.: +212 699 903 163. *
E-mail address:author. [email protected] Corresponding Tel.: +212 699 903 163.
© E-mail 2017 The Authors. Published by Elsevier Ltd. address: [email protected] Peer-review under ©responsibility theAllScientific Committee of The 15th International Symposium on District Heating and 1876-6102 Copyright 2019 Elsevier of Ltd. rights reserved. Cooling.and Selection peer-review under responsibility the scientific 1876-6102 Copyright © 2019 Elsevier Ltd. All of rights reserved. committee of the Special Issue on Emerging and Renewable Energy: Generation and Automation. Selection and peer-review under responsibility of the scientific committee of the Special Issue on Emerging and Renewable Energy: Generation and Automation. Keywords: Heat demand; Forecast; Climate change
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of the scientific committee of the 6th International Conference on Emerging and Renewable Energy: Generation and Automation, ICEREGA 2018. 10.1016/j.egypro.2019.04.031
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The DTC is widely applied to the DFIG in the literature [4]–[9]. It was first proposed and applied in the mid-80s by Takahachi and Noguchi to control an induction machine [10]. Because of its simplicity and robustness, DTC has been extended from squirrel cage induction machines to other types of machines, such as the permanent magnet synchronous machines in the late 90s [11], and the doubly fed induction machines in the early 2000s [12]. In fact, the first industrial applications of the DTC were developed by ABB (a global leader group in industrial technology) in the 80s. ABB has initiated a research program on the DTC technique since 1988, following the publication of the theoretical work by Blaschke and Depenbrock in 1971 and 1985. The DTC is based directly on the control of the generator electromagnetic torque and rotor flux by selecting an optimal voltage vector to apply to the rotor side converter (RSC) of the DFIG without using speed or position sensors, neither pulse width modulation nor current regulators. Unlike the Direct Power Control (DPC) (a control that is based on the same principle of the DTC and aims at controlling the stator active and reactive powers in a way that ensures the control of the stator power factor) [13], the DTC -since its first applications- has only been used to control the electromagnetic torque and the rotor flux. The control of the electromagnetic torque ensures the extraction of the maximum power and therefore secures the control of the active power since it is a direct function of it. On the other hand, the direct control of the rotor flux does not necessarily ensure the control of the reactive power because the relation between them is not obvious. Therefore, choosing a flux reference randomly will not guarantee a good power factor control. Hence, a modified DTC strategy is proposed in this paper in order to achieve stator power factor control simultaneously while controlling the electromagnetic torque and the rotor flux of the generator. Accordingly, this paper has developed as follows: the modeling of the global WECS based DFIG is presented in section 2. The proposed DTC technique is detailed in section 3. The simulation results are discussed in section 4. Eventually, the conclusions of this work are provided in section 5. Nomenclature Cp fv G Irα , Irβ Isα , Isβ Jm Jt Ls , Lr M p R Rs , Rr Tem Tm VDC Vrα , Vrβ Vs Vsα , Vsβ β ρ σ φsα , φsβ φrα , φrβ Ωm Ωt
The turbine power coefficient. The friction coefficient. The gearbox coefficient. Rotor currents in the αβ frame. Stator currents in the αβ frame. The generator inertia. The turbine inertia. Stator and rotor phase inductances. Mutual inductance. Number of poles pair of the machine. The blade radius. Stator and rotor phase resistances. The electromagnetic torque. The mechanical torque. The DC bus voltage. Rotor voltages in the αβ frame. Stator voltage. Stator voltages in the αβ frame. Pitch angle. The air density. Leakage coefficient. Stator fluxes in the αβ frame. Rotor fluxes in the αβ frame. The generator speed. The mechanical speed of the turbine.
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2. Modeling of a WECS based DFIG The basic structure of a WECS based DFIG is shown in Fig.1. The DFIG is powered by variable frequency power converters, typically two AC/DC and DC/AC converters connected by a DC bus. The DFIG provides power to the grid through its stator, while the rotor can inject, or absorb the power depending on the rotational speed of the generator [14]. Grid Stator Connection Power Electronic Converters Gearbox
DFIG Rotor Connection
+ + AC AC DC _- _- DC Control System
Fig. 1. the scheme of a WECS based DFIG.
2.1. Wind turbine modeling The power extracted from the wind is expressed as follows [15]: v is the wind speed. λ is the tip speed ratio, which is defined by:
𝑃𝑃𝑚𝑚 = 0.5ρ πR2 v 3 𝐶𝐶𝑝𝑝 (λ, β)
(1)
Ω𝑡𝑡 𝑅𝑅 𝑣𝑣
(2)
𝜆𝜆 =
The aerodynamic torque is expressed as follows: 𝑇𝑇𝑎𝑎𝑎𝑎𝑎𝑎 =
1 𝜌𝜌πR2 v 3 𝐶𝐶𝑝𝑝 (λ, β) 2Ω𝑡𝑡
(3)
The Gearbox model: The role of the gearbox is to adapt the slow speed of the turbine to the fast speed of the generator and the aerodynamic torque to the mechanical torque according to the following equations: 𝑇𝑇𝑎𝑎𝑎𝑎𝑎𝑎 𝐺𝐺 Ω𝑚𝑚 = Ω𝑡𝑡 . 𝐺𝐺
𝑇𝑇𝑚𝑚 = The wind turbine dynamic equation is given by:
2.2. MPPT control
𝐽𝐽𝑡𝑡 𝑑𝑑Ω𝑚𝑚 ( 2 + 𝐽𝐽𝑚𝑚 ) + 𝑓𝑓𝑣𝑣 . Ω𝑚𝑚 = 𝑇𝑇𝑚𝑚 − 𝑇𝑇𝑒𝑒𝑒𝑒 𝐺𝐺 𝑑𝑑𝑑𝑑
(4)
(5) (6)
The wind turbine must extract the maximum power for each different wind speed. This is achieved through the Maximum Power Point Tracking control (MPPT). The MPPT technique defines a referential torque for each different wind speed to adapt the mechanical speed of the generator to the wind speed, while maintaining a constant (often zero) pitch angle. The MPPT command can be obtained by several methods. The Tip Speed Ratio (TSR) based MPPT is widely used. Its objective is to keep λ at its optimum value λopt [16]–[19]. The referential torque is then obtained by maintaining the measured speed at its referential value given by:
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λopt v (7) R For a given wind turbine, the optimal value of the TSR must not change regardless the wind speed to ensure that the power extracted is the maximum [20]. Ωt_ref =
2.3. Modeling of the DFIG The DFIG general model is given in the αβ frame by applying the Clarke transformation to the three phases (abc) DFIG equations to obtain a simple model allowing an easy modeling and analysis of the DFIG. The stator and rotor voltages are respectively expressed as follows: Vsα = R s Isα +
:
Vsβ = R s Isβ +
Vrα = R r Irα + Vrβ = R r Irβ +
The stator and rotor flux equations are respectively given by: φsα φsβ φrα φrβ
The generator electromagnetic torque is described by:
2.4. Modeling of the rotor side converter
𝑇𝑇𝑒𝑒𝑒𝑒 =
d
dt d dt d
dt d dt
φsα
φsβ
(8)
φrα
φrβ
= Ls Isα + MIrα = Ls Isβ + MIrβ = Lr Irα + MIsα = Lr Irβ + MIsβ
(9)
3 𝑝𝑝𝑝𝑝 (φsα 𝐼𝐼𝑟𝑟𝑟𝑟 − φ𝑠𝑠𝑠𝑠 𝐼𝐼𝑟𝑟𝑟𝑟 ) 2 𝐿𝐿𝑠𝑠
(10)
The RSC shown in Fig.2, is a two-level voltage fed inverter modeled with ideal bidirectional switches. It is controlled by controlling the switches states 𝑆𝑆𝑎𝑎 , 𝑆𝑆𝑏𝑏 and 𝑆𝑆𝐶𝐶 . The output rotor voltage vector to apply to the RSC is given by:
𝑎𝑎 𝑏𝑏 𝑐𝑐
𝑆𝑆𝑎𝑎
̅𝑎𝑎 𝑆𝑆
⃗𝑟𝑟 = 𝑉𝑉 ⃗𝑟𝑟𝑟𝑟 + j𝑉𝑉 ⃗ 𝑟𝑟𝑟𝑟 𝑉𝑉
𝑆𝑆𝑏𝑏
̅𝑏𝑏 𝑆𝑆
(11)
𝑆𝑆𝑐𝑐
̅𝑐𝑐 𝑆𝑆
𝑉𝑉𝐷𝐷𝐷𝐷
Fig. 2. the rotor side converter.
The αβ components of the rotor voltage are expressed as a function of 𝑆𝑆𝑎𝑎 , 𝑆𝑆𝑏𝑏 and 𝑆𝑆𝐶𝐶 as follows:
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2𝑉𝑉𝐷𝐷𝐷𝐷 𝑉𝑉𝑟𝑟𝑟𝑟 [𝑉𝑉 ] = 𝑟𝑟𝑟𝑟 3
1
[0
1 2 √3 2
−
1 2 √3 − 2 −
]
5
𝑆𝑆𝑎𝑎 [𝑆𝑆𝑏𝑏 ] 𝑆𝑆𝑐𝑐
(12)
The rotor voltage vector ⃗⃗⃗ 𝑉𝑉𝑟𝑟 can be in one of the eight positions resulted from the various combinations of the three switches states. Two of these positions are zero vectors: V0 and V7 (see Table 1) [21], [22]. Table 1. Rotor voltage vector generation according to the switches states. 𝑆𝑆𝑎𝑎
𝑆𝑆𝑏𝑏
𝑆𝑆𝑐𝑐
Vector
1
0
0
𝑉𝑉1
0
1
0
1 0 0 1 1
0
0
0 0
𝑉𝑉2
1
1
𝑉𝑉4
0
1
0
𝑉𝑉3
1
1
0 −2VDC 3 VDC 3 −VDC 3 −2VDC 3 −VDC 3 VDC 3 0
𝑉𝑉0
1
𝑉𝑉5 𝑉𝑉6
1
𝑉𝑉𝑟𝑟𝑟𝑟
𝑉𝑉𝑟𝑟𝑟𝑟
𝑉𝑉7
0
0 VDC √3 VDC √3
0
−VDC √3 −VDC 0
√3
3. Direct torque control strategy with power factor control The DTC technique is based on the selection of an optimal rotor voltage vector directly from the rotor flux and electromagnetic torque errors resulting from the comparison between the estimated and referential values, using hysteresis controllers [23], [24]. The DTC scheme is illustrated in Fig.3. RSC
𝑉𝑉𝐷𝐷𝐷𝐷
𝜑𝜑𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 MPPT control
Tem 𝑟𝑟𝑟𝑟𝑟𝑟
+
Tem
-
+𝜑𝜑𝑟𝑟
e𝜑𝜑
Flux Controller
𝐸𝐸𝜑𝜑
e 𝑇𝑇
Torque Controller
𝐸𝐸𝑇𝑇
Torque and flux estimation 𝑉𝑉𝑟𝑟 𝛼𝛼,𝛽𝛽 𝐼𝐼𝑟𝑟 𝛼𝛼,𝛽𝛽
𝜑𝜑𝑟𝑟𝛼𝛼 𝜑𝜑𝑟𝑟𝛽𝛽
Sa
Sb
Look-up Table
Sector Arctan n
Fig.3. the DTC strategy of the DFIG.
Sc
𝜃𝜃
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The electromagnetic torque and the rotor flux being the variables controlled in the DTC. They are estimated in the 𝛼𝛼𝛼𝛼 frame. The rotor flux is estimated as follows [25]: 2 + 𝜑𝜑 2 𝜑𝜑𝑟𝑟 = √𝜑𝜑𝑟𝑟𝑟𝑟 𝑟𝑟𝑟𝑟
(13)
𝑡𝑡
𝜑𝜑𝑟𝑟 𝛼𝛼,𝛽𝛽 = ∫ (𝑉𝑉𝑟𝑟 𝛼𝛼,𝛽𝛽 − 𝑅𝑅𝑟𝑟 𝐼𝐼𝑟𝑟 𝛼𝛼,𝛽𝛽 ) 𝑑𝑑𝑑𝑑
(14)
0
In order to control the stator power factor, the wind turbine must operate with a reactive power reference. For that, the referential rotor flux should be a function of the referential reactive power 𝑄𝑄𝑠𝑠∗ . It is obtained by considering the DFIG model developed in [26]–[28], where the stator flux is aligned with the d axis. Therefore, the referential rotor flux is given by: 2 L𝑟𝑟 2 𝜎𝜎L𝑟𝑟 L𝑠𝑠 ∗ 2 2 L𝑟𝑟 L𝑠𝑠 𝜎𝜎𝑇𝑇𝑒𝑒𝑒𝑒 𝑟𝑟𝑟𝑟𝑟𝑟 𝑄𝑄𝑠𝑠 ) + (− ) 𝜑𝜑𝑟𝑟 𝑟𝑟𝑟𝑟𝑟𝑟 = √( |φ𝑠𝑠 | − 𝑀𝑀 𝑀𝑀|𝜑𝜑𝑠𝑠 | 3 𝑀𝑀𝑉𝑉𝑠𝑠 3
The electromagnetic torque could be estimated using equation (10) which could be written as follows [27]:
𝜃𝜃
3 𝑀𝑀 |φ ||φ |𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑇𝑇𝑒𝑒𝑒𝑒 = 𝑝𝑝 2 𝐿𝐿𝑟𝑟 𝐿𝐿𝑠𝑠 − 𝑀𝑀² s r
(15)
(16)
: The phase angle difference between the rotor flux and the stator flux.
The stator flux |φs | is constant since the grid is assumed stable [29]–[31]. Therefore, the torque is controlled by the rotor flux |φr | and the angle θ. It is also necessary to locate the rotor flux vector to determine the sector where it is located based on the rotor flux angle θ. According to this angle, the sector is determined using Table 2. Table 2. Sector identification according to the angle θ. Rotor flux angle
Sector
(330°, 30°)
1
(30°, 90°)
2
(90°, 150°)
3
(150°, 210°)
4
(210°, 270°)
5
(270°, 330°)
6
Once the signals Eφ and ET that determine whether the torque /flux should increase, decrease or maintain constant, are defined by the hysteresis controllers, together with the information concerning the sector location of the rotor flux vector, it is possible to select the optimal rotor voltage vector based on Fig.4 and according to Table 3. Table 3. Rotor voltage vector selection. Sector EF=1
EF=-1
1
2
3
4
5
6
ET=1
V2
V3
V4
V5
V6
V1
ET =0
V7
V0
V7
V0
V7
V0
ET=-1
V6
V1
V2
V3
V4
V5
ET =1
V3
V4
V5
V6
V1
V2
ET =0
V0
V7
V0
V7
V0
V7
ET=-1
V5
V6
V1
V2
V3
V4
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𝛽𝛽𝑟𝑟 V4 V5
S3 V3
V6 V5
V5
S4
V3
V2
V6
V3 V1
V1
S1
S6 V2
V2
𝛼𝛼𝑟𝑟
V3
V6
S5
V1
V4
S2
V4 V5
V6
V4
V2 V1
Fig.4. representation of the rotor flux vector vertex for the different voltage vectors.
4. Simulations and results The proposed control strategy was simulated in MATLAB & Simulink for a variable wind speed profile as shown in Fig.5 (a). The simulation parameters are given in the appendix. The reactive power reference was set to 0 Vars to ensure a unit power factor.
(a)
(b)
Fig.5. (a) the wind speed profile; (b) the mechanical speed of the turbine (rad.s-1).
Fig.5 (b) shows the turbine speed response that tracks perfectly its reference. What demonstrates the effectiveness of the adopted MPPT control.
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Fig.6 (a) and Fig.6 (b) expose the electromagnetic torque response and rotor flux response respectively. Both controlled magnitudes track their set values in a very quick response time (equal to 7 ms). Moreover, the electromagnetic torque presents some undulations which are known as a common inconvenient of the DTC control due to the use of hysteresis controllers.
(a)
(b)
Fig.6. (a) the electromagnetic torque (N.m); (b) the rotor flux (Wb).
Furthermore, the sector location of the rotor flux vector shown in Fig. 7 (a) shows that the rotor flux vector passes periodically through the six sectors. Which explains its circular trajectory shown in Fig.7 (b). Several circular trajectories are superposed because the generated referential rotor flux has different values for different wind speeds.
(a)
(b) Fig.7. (a) the rotor flux sector location; (b) the rotor flux 𝛼𝛼𝛼𝛼 plots.
The stator power factor illustrated in Fig.8 shows that the control of the power factor is ensured for each different wind speed. Which proves the effectiveness of the proposed control strategy.
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Fig.8. the power factor at stator terminals.
5. Conclusions This paper has presented the direct torque control of a wind energy conversion system based on a doubly fed induction generator with a new strategy of generating the referential rotor flux as a function of the referential reactive power. The proposed control technique is based on selecting a suitable rotor voltage vector to apply to the rotor side converter, in order to control the rotor flux and the electromagnetic torque while controlling the power factor at the stator terminals. The simulation results have demonstrated that the proposed strategy provides better performance in terms of tracking references, responding quickly and ensuring a good power factor control. Yet, there is one inconvenient which is the occurrence of some undulations that are common in the classical DTC strategy as well. According to the literature review, those undulations are basically related to the use of hysteresis controllers. Thus, a future study can be extended to ameliorate the proposed control using controllers other than hysteresis ones, such as artificial intelligence-based controllers. Appendix. Simulation parameters Table 4. The parameters used in simulation. Parameters
Values
R
3.1 m
G
5.4
Jt
0.042 Kg.m²
fv
6.73e-3 N.m.s.rad-1
Rs
0.455 Ω
Rr
0.62 Ω
Ls
0.084 H
Lr
0.081 H
M
0.078 H
Jm
0.3125 Kg.m²
References [1] R. Tiwari, K. Kumar, N. R. Babu, and K. R. Prabhu, “Coordinated MPPT and DPC Strategies for PMSG based Grid Connected Wind Energy Conversion System,” Energy Procedia, vol. 145, pp. 339–344, 2018.
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[2] S. Abdelmalek, S. Rezazi, and A. T. Azar, “Sensor Faults Detection and Estimation for a Dfig Equipped Wind Turbine,” Energy Procedia, vol. 139, pp. 3–9, 2017. [3] A. Rini Ann Jerin, N. Prabaharan, K. Palanisamy, and S. Umashankar, “FRT Capability in DFIG based Wind Turbines using DVR with Combined Feed-Forward and Feed-Back Control,” Energy Procedia, vol. 138, pp. 1184–1189, 2017. [4] A. Ben Amar, S. Belkacem, and T. Mahni, “Direct torque control of doubly fed induction machine,” Int. J. Energ., vol. 2, no. 1, pp. 11–14, 2017. [5] S. Arnalte, J. C. Burgos, and J. L. Rodriguze-Amenedo, “Direct Torque Control of a Doubly-Fed Induction Generator for Variable Speed Wind Turbines,” Electr. Power Components Syst., 2010. [6] A. A. Hassan, A. M. El-Sawy, and O. M. Kamel, “Direct Torque Control of a Doubly fed Induction Generator Driven By a Variable Speed Wind Turbine,” J. Eng. Sci., vol. 41, no. January, pp. 199–216, 2013. [7] A. Abbou, H. Mahmoudi, and K. Elyaalaoui, “Direct Torque Control of a Doubly Fed Induction Generator of Wind Turbine for Maximum Power Extraction Anass,” in 2014 International Renewable and Sustainable Energy Conference (IRSEC), 2014, no. 2, pp. 2–7. [8] S. Tamalouzt and T. Rekioua, “Direct Torque and Reactive Power Control of Grid Connected Doubly Fed Induction Generator for the Wind Energy Conversion,” in 2014 International Conference on Electrical Sciences and Technologies in Maghreb (CISTEM), 2014. [9] S. A. Hussain, M. Soni, and N. Goel, “CONTROLLING OF DOUBLY FED INDUCTION GENERATOR USING DIRECT TORQUE CONTROL,” Int. J. Sci. \& Eng. Res., vol. 7, no. 5, pp. 1839–1846, 2016. [10] I. Takahashi and T. Noguchi, “A New Quick-Response and High-Efficiency Control Strategy of an Induction Motor,” IEEE Trans. Ind. Appl., vol. IA-22, no. 5, pp. 820–827, 1986. [11] C. French and P. Acarnley, “Direct torque control of permanent magnet drives,” IEEE Trans. Ind. Appl., vol. 32, no. 5, pp. 1080–1088, 1996. [12] K. P.Gokhale, D. W.Karraker, and S. J.Heikkila, “CONTROLLER FOR A WOUND ROTOR SLIP RING INDUCTION MACHINE,” US6448735, 2002. [13] Z. Boudries, D. Rekioua Ziani, and M. Sellami, “Direct power control of a PWM rectifier fed autonomous induction generator for wind energy applications,” Energy Procedia, vol. 36, pp. 391–400, 2013. [14] J. S. Solís-Chaves, M. S. Barreto, M. B. C. Salles, V. M. Lira, R. V. Jacomini, and A. J. Sguarezi Filho, “A direct power control for DFIG under a three phase symmetrical voltage sag condition,” Control Eng. Pract., vol. 65, no. March, pp. 48–58, 2017. [15] H. Belmili, S. Boulouma, B. Boualem, and A. M. Fayçal, “Optimized Control and Sizing of Standalone PV-wind Energy Conversion System,” Energy Procedia, vol. 107, no. September 2016, pp. 76–84, 2017. [16] Y. Errami, A. Obbadi, S. Sahnoun, M. Barara, M. Ouassaid, and M. Maaroufi, “Control of High-Power Wind Energy Conversion System Fed by Multi-level Converters,” Energy Procedia, vol. 119, pp. 214–227, 2017. [17] A. Dida and D. Benattous, “Fuzzy logic based sensorless MPPT algorithm for wind turbine system driven DFIG,” in 3rd International Conference on Control, Engineering and Information Technology, CEIT 2015, 2015. [18] S. Cai and H. Wen, “Modeling and MPPT Control of DFIG Wind Energy System,” in International Conference on Renewable Power Generation (RPG 2015), 2015. [19] C. Balasundar, S. Sudharshanan, and R. Elakkiyavendan, “Design of an Optimal Tip Speed Ratio Control MPPT Algorithm for Standalone WECS,” Int. J. Res. Appl. Sci. Eng. Technol., vol. 3, no. V, 2015. [20] M. A. Abdullah, A. H. M. Yatim, C. W. Tan, and R. Saidur, “A review of maximum power point tracking algorithms for wind energy systems,” Renew. Sustain. Energy Rev., vol. 16, no. 5, pp. 3220–3227, 2012. [21] M. R. Agha Kashkooli, S. M. Madani, and R. Sadeghi, “Improved Direct Torque Control of DFIG with reduced torque and flux ripples at constant switching frequency,” in 7th Power Electronics, Drive Systems and Technologies Conference, PEDSTC 2016, 2016, no. Pedstc, pp. 58–63. [22] A. Zemmit, S. Messalti, and A. Harrag, “A new improved DTC of doubly fed induction machine using GA-based PI controller,” Ain Shams Eng. J., pp. 0–8, 2016. [23] O. Ouledali, A. Meroufel, P. Wira, and S. Bentouba, “Direct Torque Fuzzy Control of PMSM based on SVM,” Energy Procedia, vol. 74, pp. 1314–1322, 2015. [24] H. Bouzeria, C. Fetha, T. Bahi, I. Abadlia, Z. Layate, and S. Lekhchine, “Fuzzy Logic Space Vector Direct Torque Control of PMSM for Photovoltaic Water Pumping System,” Energy Procedia, vol. 74, pp. 760–771, 2015. [25] I. Hamzaoui, F. Bouchafaa, A. Talha, and S. G. Malla, “Advanced control for wind energy conversion systems with flywheel storage dedicated to improving the quality of energy,” Int. J. Hydrogen Energy, vol. 41, no. 45, pp. 20832–20846, 2016. [26] W. Ayrir, M. Ourahou, and A. Haddi, “Fuzzy power control of a variable speed DFIG-based wind turbine,” in Proceeding of The third International Conference on Optimization and Applications (ICOA’2017), 2017, pp. 135–139. [27] G. Abad, J. Lopez, M. A. Rodriguez, L. Marroyo, and G. Iwanski, DOUBLY FED INDUCTION MACHINE. Hoboken, New Jersey: John Wiley and Sons, Inc., 2011. [28] C. M. Rocha-Osorio, J. S. Solís-Chaves, I. R. S. Casella, C. E. Capovilla, J. L. Azcue Puma, and A. J. Sguarezi Filho, “GPRS/EGPRS standards applied to DTC of a DFIG using fuzzy – PI controllers,” Int. J. Electr. Power Energy Syst., vol. 93, pp. 365–373, 2017. [29] Y. Li et al., “An Improved DTC Controller for DFIG-Based Wind Generation System,” in 2016 IEEE 8th International Power Electronics and Motion Control Conference, 2016, pp. 6–9. [30] Z. Liu, O. A. Mohammed, and S. Liu, “A Novel Direct Torque Control of Doubly-Fed Induction Generator Used for Variable Speed Wind Power Generation,” in 2007 IEEE Power Engineering Society General Meeting, 2007, no. 1, pp. 1–6. [31] M. Machmoum, A. Hatoum, and T. Bouaouiche, “Flicker mitigation in a doubly fed induction generator wind turbine system,” Math. Comput. Simul., vol. 81, no. 2, pp. 433–445, 2010.
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Special Issue on Emerging and Renewable Energy: Generation and Automation Special Issue on Emerging and Renewable Energy: Generation and Automation
Direct torque control-based power factor control of a DFIG Direct torque control-based power factor control of a DFIG The 15th International on District AyrirSymposium Wiama*, Haddi Alia Heating and Cooling
Ayrir Wiama*, Haddi Alia
Assessing the feasibility of using the heat demand-outdoor temperature function for a long-term district heat demand forecast Advanced Sciences and Technologies Team, University of ABDELMALEK ESSAÄDI, (ENSATe) Tetouan 93030, Morocco a Advanced Sciences and Technologies Team, University of ABDELMALEK ESSAÄDI, (ENSATe) Tetouan 93030, Morocco a
Abstract a,b,c Abstract I. Andrić *, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc This paper proposes the Direct Torque Control (DTC) of a Wind Energy Conversion System (WECS) based on a Doubly Fed a IN+ Center for Innovation, Technology andfactor Policy Research Superior Técnico,technique Av.System Roviscoaims Pais at 1, 1049-001 Lisbon, Portugal This paper proposes the Direct Torque Control (DTC) of strategy. a- Instituto Wind Energy Conversion (WECS) based on athe Doubly Fed Induction Generator (DFIG) with power control The proposed controlling generator b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Induction Generator (DFIG) with power factor control strategy. The proposed technique aims at controlling the generator electromagnetic torque and rotor flux while controlling the power factor at the stator terminals. The proposed control is achieved c Département Énergétiques et Environnement -the IMT Atlantique, 4 rue Alfred 44300 Nantes,control Franceissoachieved electromagnetic torque andSystèmes rotor flux while controlling thefrom power factor at the Power stator terminals. The proposed through generating the referential electromagnetic torque Maximum PointKastler, Tracking (MPPT) control that the through generating the referential electromagnetic Maximum rotor Power Point Tracking (MPPT) control so that the maximum power is extracted for each different windtorque speed,from and the referential flux from the reactive power reference. maximum power is extracted for each different wind speed, and the referential rotor flux from the reactive power reference. Copyright © 2019 Elsevier Ltd. All rights reserved. ©Abstract 2019 The Authors. Published by Elsevier Ltd Copyright © 2019 Elsevierunder Ltd. All rights reserved. Selection and peer-review responsibility of the scientific committee of the Special Issue on Emerging and Renewable Selection and peer-review under responsibility of the scientific committee of the 6th International Conference on Emerging and Selection and peer-review under responsibility ofICEREGA the scientific committee of the Special Issue on Emerging and Renewable Energy: Generation and Automation. Renewable Energy: Generation Automation, District heating networks are and commonly addressed in the2018. literature as one of the most effective solutions for decreasing the Energy: Generation and Automation. greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat Keywords: Wind energy; DFIG; MPPT; DTC; power factor control. sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, Keywords: Wind energy; DFIG; MPPT; DTC; power factor control. prolonging the investment return period. The main scope of this paper is to assess the feasibility of using the heat demand – outdoor temperature function for heat demand 1.forecast. Introduction The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 1.buildings Introduction that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district Over the scenarios past decade, energy(shallow, industryintermediate, has been interested variablethe speed WECS based Currently the renovation werewind developed deep). Toin estimate error, obtained heatDFIG. demand values were Over the past decade, wind energy industry has been interested in variable speed WECS based DFIG. Currently the DFIG occupies an essential part in variable speed generator technologies market [1]–[3]. Consequently, several control compared with results from a dynamic heat demand model, previously developed and validated by the authors. DFIG occupies an essential part in variable speed generator technologies market [1]–[3]. Consequently, several control methods have been emerging. In general, the control allows the system to track a desired response for a given input The results showed that when only weather change is considered, the margin of error could be acceptable for some applications methods have been emerging. Inlower general, allows the tooperation track a However, desired response for a given input (the error in annual demand than the 20%control all weather scenarios considered). after introducing renovation while rejecting the effects ofwas any disturbances infororder to obtain asystem correct of it. Different control techniques scenarios, the error value increased up to 59.5% (depending the andoperation renovation combination considered). while rejecting theineffects of any disturbances intechniques, order to on obtain a correct of scenarios it. Different control techniques have been treated the literature. Among these the weather direct torque control. The been value treated of slopeincoefficient increased on these average within the the range of 3.8% upcontrol. to 8% per decade, that corresponds to the have the literature. Among techniques, direct torque decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and * improve the accuracy heat demand estimations. Corresponding author. of Tel.: +212 699 903 163. *
E-mail address:author. [email protected] Corresponding Tel.: +212 699 903 163.
© E-mail 2017 The Authors. Published by Elsevier Ltd. address: [email protected] Peer-review under ©responsibility theAllScientific Committee of The 15th International Symposium on District Heating and 1876-6102 Copyright 2019 Elsevier of Ltd. rights reserved. Cooling.and Selection peer-review under responsibility the scientific 1876-6102 Copyright © 2019 Elsevier Ltd. All of rights reserved. committee of the Special Issue on Emerging and Renewable Energy: Generation and Automation. Selection and peer-review under responsibility of the scientific committee of the Special Issue on Emerging and Renewable Energy: Generation and Automation. Keywords: Heat demand; Forecast; Climate change
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of the scientific committee of the 6th International Conference on Emerging and Renewable Energy: Generation and Automation, ICEREGA 2018. 10.1016/j.egypro.2019.04.031
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The DTC is widely applied to the DFIG in the literature [4]–[9]. It was first proposed and applied in the mid-80s by Takahachi and Noguchi to control an induction machine [10]. Because of its simplicity and robustness, DTC has been extended from squirrel cage induction machines to other types of machines, such as the permanent magnet synchronous machines in the late 90s [11], and the doubly fed induction machines in the early 2000s [12]. In fact, the first industrial applications of the DTC were developed by ABB (a global leader group in industrial technology) in the 80s. ABB has initiated a research program on the DTC technique since 1988, following the publication of the theoretical work by Blaschke and Depenbrock in 1971 and 1985. The DTC is based directly on the control of the generator electromagnetic torque and rotor flux by selecting an optimal voltage vector to apply to the rotor side converter (RSC) of the DFIG without using speed or position sensors, neither pulse width modulation nor current regulators. Unlike the Direct Power Control (DPC) (a control that is based on the same principle of the DTC and aims at controlling the stator active and reactive powers in a way that ensures the control of the stator power factor) [13], the DTC -since its first applications- has only been used to control the electromagnetic torque and the rotor flux. The control of the electromagnetic torque ensures the extraction of the maximum power and therefore secures the control of the active power since it is a direct function of it. On the other hand, the direct control of the rotor flux does not necessarily ensure the control of the reactive power because the relation between them is not obvious. Therefore, choosing a flux reference randomly will not guarantee a good power factor control. Hence, a modified DTC strategy is proposed in this paper in order to achieve stator power factor control simultaneously while controlling the electromagnetic torque and the rotor flux of the generator. Accordingly, this paper has developed as follows: the modeling of the global WECS based DFIG is presented in section 2. The proposed DTC technique is detailed in section 3. The simulation results are discussed in section 4. Eventually, the conclusions of this work are provided in section 5. Nomenclature Cp fv G Irα , Irβ Isα , Isβ Jm Jt Ls , Lr M p R Rs , Rr Tem Tm VDC Vrα , Vrβ Vs Vsα , Vsβ β ρ σ φsα , φsβ φrα , φrβ Ωm Ωt
The turbine power coefficient. The friction coefficient. The gearbox coefficient. Rotor currents in the αβ frame. Stator currents in the αβ frame. The generator inertia. The turbine inertia. Stator and rotor phase inductances. Mutual inductance. Number of poles pair of the machine. The blade radius. Stator and rotor phase resistances. The electromagnetic torque. The mechanical torque. The DC bus voltage. Rotor voltages in the αβ frame. Stator voltage. Stator voltages in the αβ frame. Pitch angle. The air density. Leakage coefficient. Stator fluxes in the αβ frame. Rotor fluxes in the αβ frame. The generator speed. The mechanical speed of the turbine.
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2. Modeling of a WECS based DFIG The basic structure of a WECS based DFIG is shown in Fig.1. The DFIG is powered by variable frequency power converters, typically two AC/DC and DC/AC converters connected by a DC bus. The DFIG provides power to the grid through its stator, while the rotor can inject, or absorb the power depending on the rotational speed of the generator [14]. Grid Stator Connection Power Electronic Converters Gearbox
DFIG Rotor Connection
+ + AC AC DC _- _- DC Control System
Fig. 1. the scheme of a WECS based DFIG.
2.1. Wind turbine modeling The power extracted from the wind is expressed as follows [15]: v is the wind speed. λ is the tip speed ratio, which is defined by:
𝑃𝑃𝑚𝑚 = 0.5ρ πR2 v 3 𝐶𝐶𝑝𝑝 (λ, β)
(1)
Ω𝑡𝑡 𝑅𝑅 𝑣𝑣
(2)
𝜆𝜆 =
The aerodynamic torque is expressed as follows: 𝑇𝑇𝑎𝑎𝑎𝑎𝑎𝑎 =
1 𝜌𝜌πR2 v 3 𝐶𝐶𝑝𝑝 (λ, β) 2Ω𝑡𝑡
(3)
The Gearbox model: The role of the gearbox is to adapt the slow speed of the turbine to the fast speed of the generator and the aerodynamic torque to the mechanical torque according to the following equations: 𝑇𝑇𝑎𝑎𝑎𝑎𝑎𝑎 𝐺𝐺 Ω𝑚𝑚 = Ω𝑡𝑡 . 𝐺𝐺
𝑇𝑇𝑚𝑚 = The wind turbine dynamic equation is given by:
2.2. MPPT control
𝐽𝐽𝑡𝑡 𝑑𝑑Ω𝑚𝑚 ( 2 + 𝐽𝐽𝑚𝑚 ) + 𝑓𝑓𝑣𝑣 . Ω𝑚𝑚 = 𝑇𝑇𝑚𝑚 − 𝑇𝑇𝑒𝑒𝑒𝑒 𝐺𝐺 𝑑𝑑𝑑𝑑
(4)
(5) (6)
The wind turbine must extract the maximum power for each different wind speed. This is achieved through the Maximum Power Point Tracking control (MPPT). The MPPT technique defines a referential torque for each different wind speed to adapt the mechanical speed of the generator to the wind speed, while maintaining a constant (often zero) pitch angle. The MPPT command can be obtained by several methods. The Tip Speed Ratio (TSR) based MPPT is widely used. Its objective is to keep λ at its optimum value λopt [16]–[19]. The referential torque is then obtained by maintaining the measured speed at its referential value given by:
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λopt v (7) R For a given wind turbine, the optimal value of the TSR must not change regardless the wind speed to ensure that the power extracted is the maximum [20]. Ωt_ref =
2.3. Modeling of the DFIG The DFIG general model is given in the αβ frame by applying the Clarke transformation to the three phases (abc) DFIG equations to obtain a simple model allowing an easy modeling and analysis of the DFIG. The stator and rotor voltages are respectively expressed as follows: Vsα = R s Isα +
:
Vsβ = R s Isβ +
Vrα = R r Irα + Vrβ = R r Irβ +
The stator and rotor flux equations are respectively given by: φsα φsβ φrα φrβ
The generator electromagnetic torque is described by:
2.4. Modeling of the rotor side converter
𝑇𝑇𝑒𝑒𝑒𝑒 =
d
dt d dt d
dt d dt
φsα
φsβ
(8)
φrα
φrβ
= Ls Isα + MIrα = Ls Isβ + MIrβ = Lr Irα + MIsα = Lr Irβ + MIsβ
(9)
3 𝑝𝑝𝑝𝑝 (φsα 𝐼𝐼𝑟𝑟𝑟𝑟 − φ𝑠𝑠𝑠𝑠 𝐼𝐼𝑟𝑟𝑟𝑟 ) 2 𝐿𝐿𝑠𝑠
(10)
The RSC shown in Fig.2, is a two-level voltage fed inverter modeled with ideal bidirectional switches. It is controlled by controlling the switches states 𝑆𝑆𝑎𝑎 , 𝑆𝑆𝑏𝑏 and 𝑆𝑆𝐶𝐶 . The output rotor voltage vector to apply to the RSC is given by:
𝑎𝑎 𝑏𝑏 𝑐𝑐
𝑆𝑆𝑎𝑎
̅𝑎𝑎 𝑆𝑆
⃗𝑟𝑟 = 𝑉𝑉 ⃗𝑟𝑟𝑟𝑟 + j𝑉𝑉 ⃗ 𝑟𝑟𝑟𝑟 𝑉𝑉
𝑆𝑆𝑏𝑏
̅𝑏𝑏 𝑆𝑆
(11)
𝑆𝑆𝑐𝑐
̅𝑐𝑐 𝑆𝑆
𝑉𝑉𝐷𝐷𝐷𝐷
Fig. 2. the rotor side converter.
The αβ components of the rotor voltage are expressed as a function of 𝑆𝑆𝑎𝑎 , 𝑆𝑆𝑏𝑏 and 𝑆𝑆𝐶𝐶 as follows:
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2𝑉𝑉𝐷𝐷𝐷𝐷 𝑉𝑉𝑟𝑟𝑟𝑟 [𝑉𝑉 ] = 𝑟𝑟𝑟𝑟 3
1
[0
1 2 √3 2
−
1 2 √3 − 2 −
]
5
𝑆𝑆𝑎𝑎 [𝑆𝑆𝑏𝑏 ] 𝑆𝑆𝑐𝑐
(12)
The rotor voltage vector ⃗⃗⃗ 𝑉𝑉𝑟𝑟 can be in one of the eight positions resulted from the various combinations of the three switches states. Two of these positions are zero vectors: V0 and V7 (see Table 1) [21], [22]. Table 1. Rotor voltage vector generation according to the switches states. 𝑆𝑆𝑎𝑎
𝑆𝑆𝑏𝑏
𝑆𝑆𝑐𝑐
Vector
1
0
0
𝑉𝑉1
0
1
0
1 0 0 1 1
0
0
0 0
𝑉𝑉2
1
1
𝑉𝑉4
0
1
0
𝑉𝑉3
1
1
0 −2VDC 3 VDC 3 −VDC 3 −2VDC 3 −VDC 3 VDC 3 0
𝑉𝑉0
1
𝑉𝑉5 𝑉𝑉6
1
𝑉𝑉𝑟𝑟𝑟𝑟
𝑉𝑉𝑟𝑟𝑟𝑟
𝑉𝑉7
0
0 VDC √3 VDC √3
0
−VDC √3 −VDC 0
√3
3. Direct torque control strategy with power factor control The DTC technique is based on the selection of an optimal rotor voltage vector directly from the rotor flux and electromagnetic torque errors resulting from the comparison between the estimated and referential values, using hysteresis controllers [23], [24]. The DTC scheme is illustrated in Fig.3. RSC
𝑉𝑉𝐷𝐷𝐷𝐷
𝜑𝜑𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 MPPT control
Tem 𝑟𝑟𝑟𝑟𝑟𝑟
+
Tem
-
+𝜑𝜑𝑟𝑟
e𝜑𝜑
Flux Controller
𝐸𝐸𝜑𝜑
e 𝑇𝑇
Torque Controller
𝐸𝐸𝑇𝑇
Torque and flux estimation 𝑉𝑉𝑟𝑟 𝛼𝛼,𝛽𝛽 𝐼𝐼𝑟𝑟 𝛼𝛼,𝛽𝛽
𝜑𝜑𝑟𝑟𝛼𝛼 𝜑𝜑𝑟𝑟𝛽𝛽
Sa
Sb
Look-up Table
Sector Arctan n
Fig.3. the DTC strategy of the DFIG.
Sc
𝜃𝜃
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The electromagnetic torque and the rotor flux being the variables controlled in the DTC. They are estimated in the 𝛼𝛼𝛼𝛼 frame. The rotor flux is estimated as follows [25]: 2 + 𝜑𝜑 2 𝜑𝜑𝑟𝑟 = √𝜑𝜑𝑟𝑟𝑟𝑟 𝑟𝑟𝑟𝑟
(13)
𝑡𝑡
𝜑𝜑𝑟𝑟 𝛼𝛼,𝛽𝛽 = ∫ (𝑉𝑉𝑟𝑟 𝛼𝛼,𝛽𝛽 − 𝑅𝑅𝑟𝑟 𝐼𝐼𝑟𝑟 𝛼𝛼,𝛽𝛽 ) 𝑑𝑑𝑑𝑑
(14)
0
In order to control the stator power factor, the wind turbine must operate with a reactive power reference. For that, the referential rotor flux should be a function of the referential reactive power 𝑄𝑄𝑠𝑠∗ . It is obtained by considering the DFIG model developed in [26]–[28], where the stator flux is aligned with the d axis. Therefore, the referential rotor flux is given by: 2 L𝑟𝑟 2 𝜎𝜎L𝑟𝑟 L𝑠𝑠 ∗ 2 2 L𝑟𝑟 L𝑠𝑠 𝜎𝜎𝑇𝑇𝑒𝑒𝑒𝑒 𝑟𝑟𝑟𝑟𝑟𝑟 𝑄𝑄𝑠𝑠 ) + (− ) 𝜑𝜑𝑟𝑟 𝑟𝑟𝑟𝑟𝑟𝑟 = √( |φ𝑠𝑠 | − 𝑀𝑀 𝑀𝑀|𝜑𝜑𝑠𝑠 | 3 𝑀𝑀𝑉𝑉𝑠𝑠 3
The electromagnetic torque could be estimated using equation (10) which could be written as follows [27]:
𝜃𝜃
3 𝑀𝑀 |φ ||φ |𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑇𝑇𝑒𝑒𝑒𝑒 = 𝑝𝑝 2 𝐿𝐿𝑟𝑟 𝐿𝐿𝑠𝑠 − 𝑀𝑀² s r
(15)
(16)
: The phase angle difference between the rotor flux and the stator flux.
The stator flux |φs | is constant since the grid is assumed stable [29]–[31]. Therefore, the torque is controlled by the rotor flux |φr | and the angle θ. It is also necessary to locate the rotor flux vector to determine the sector where it is located based on the rotor flux angle θ. According to this angle, the sector is determined using Table 2. Table 2. Sector identification according to the angle θ. Rotor flux angle
Sector
(330°, 30°)
1
(30°, 90°)
2
(90°, 150°)
3
(150°, 210°)
4
(210°, 270°)
5
(270°, 330°)
6
Once the signals Eφ and ET that determine whether the torque /flux should increase, decrease or maintain constant, are defined by the hysteresis controllers, together with the information concerning the sector location of the rotor flux vector, it is possible to select the optimal rotor voltage vector based on Fig.4 and according to Table 3. Table 3. Rotor voltage vector selection. Sector EF=1
EF=-1
1
2
3
4
5
6
ET=1
V2
V3
V4
V5
V6
V1
ET =0
V7
V0
V7
V0
V7
V0
ET=-1
V6
V1
V2
V3
V4
V5
ET =1
V3
V4
V5
V6
V1
V2
ET =0
V0
V7
V0
V7
V0
V7
ET=-1
V5
V6
V1
V2
V3
V4
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𝛽𝛽𝑟𝑟 V4 V5
S3 V3
V6 V5
V5
S4
V3
V2
V6
V3 V1
V1
S1
S6 V2
V2
𝛼𝛼𝑟𝑟
V3
V6
S5
V1
V4
S2
V4 V5
V6
V4
V2 V1
Fig.4. representation of the rotor flux vector vertex for the different voltage vectors.
4. Simulations and results The proposed control strategy was simulated in MATLAB & Simulink for a variable wind speed profile as shown in Fig.5 (a). The simulation parameters are given in the appendix. The reactive power reference was set to 0 Vars to ensure a unit power factor.
(a)
(b)
Fig.5. (a) the wind speed profile; (b) the mechanical speed of the turbine (rad.s-1).
Fig.5 (b) shows the turbine speed response that tracks perfectly its reference. What demonstrates the effectiveness of the adopted MPPT control.
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Fig.6 (a) and Fig.6 (b) expose the electromagnetic torque response and rotor flux response respectively. Both controlled magnitudes track their set values in a very quick response time (equal to 7 ms). Moreover, the electromagnetic torque presents some undulations which are known as a common inconvenient of the DTC control due to the use of hysteresis controllers.
(a)
(b)
Fig.6. (a) the electromagnetic torque (N.m); (b) the rotor flux (Wb).
Furthermore, the sector location of the rotor flux vector shown in Fig. 7 (a) shows that the rotor flux vector passes periodically through the six sectors. Which explains its circular trajectory shown in Fig.7 (b). Several circular trajectories are superposed because the generated referential rotor flux has different values for different wind speeds.
(a)
(b) Fig.7. (a) the rotor flux sector location; (b) the rotor flux 𝛼𝛼𝛼𝛼 plots.
The stator power factor illustrated in Fig.8 shows that the control of the power factor is ensured for each different wind speed. Which proves the effectiveness of the proposed control strategy.
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Fig.8. the power factor at stator terminals.
5. Conclusions This paper has presented the direct torque control of a wind energy conversion system based on a doubly fed induction generator with a new strategy of generating the referential rotor flux as a function of the referential reactive power. The proposed control technique is based on selecting a suitable rotor voltage vector to apply to the rotor side converter, in order to control the rotor flux and the electromagnetic torque while controlling the power factor at the stator terminals. The simulation results have demonstrated that the proposed strategy provides better performance in terms of tracking references, responding quickly and ensuring a good power factor control. Yet, there is one inconvenient which is the occurrence of some undulations that are common in the classical DTC strategy as well. According to the literature review, those undulations are basically related to the use of hysteresis controllers. Thus, a future study can be extended to ameliorate the proposed control using controllers other than hysteresis ones, such as artificial intelligence-based controllers. Appendix. Simulation parameters Table 4. The parameters used in simulation. Parameters
Values
R
3.1 m
G
5.4
Jt
0.042 Kg.m²
fv
6.73e-3 N.m.s.rad-1
Rs
0.455 Ω
Rr
0.62 Ω
Ls
0.084 H
Lr
0.081 H
M
0.078 H
Jm
0.3125 Kg.m²
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