Modeling and Control of the Offshore wind energy system based on 5MW DFIG connected to grid M.S.Camara; M.B. Camara, Member, IEEE; B.Dakyo, Member, IEEE Laboratoire GREAH –UFRST - Université Le Havre 25 Rue Philippe Lebon, 76058 Le Havre, FRANCE
[email protected],
[email protected],
[email protected]
H.Gualous, Member, IEEE Laboratoire LUSAC – IUT de Cherbourg Octeville Université de Caen Rue Louis Aragon, 50100 Cherbourg -Octeville, FRANCE
[email protected]
Abstract—This paper presents the control strategies of an offshore wind energy system based on 5MW Doubly Fed Induction Generator (DFIG). The DFIG seems to be interesting for such high power wind generator systems. The proposed control strategies include the Maximum Power Tracking (MPPT) for the DFIG speed control, the active/reactive power control, and the DC-bus voltage control method. To show the performances of the control strategies, some simulation results are presented and analyzed using Matlab/Simulink software. Keywords - Active power; Control Strategy; Converter; DC-bus Control; Doubly Fed Induction Generator (DFIG); Offshore energy; Stand alone; Variable Speed, Maximum Power Tracking (MPPT), Reactive power; Wind energy.
I. Pn Rt G ρ Rs ; Rr M J P Usef Vdcref Rf ; Lf C
NOMENCLATURE
DFIG rated power Radius of the wind turbine Gear box Density of air Stator and the rotor resistances Mutual inductance Total moment of inertia Number of pair of poles RMS tension in the stator DC-bus voltage reference Parameters of the filter DC-bus capacitor II.
5 MW 61.5m 90 1.22kg/m3 12 mΩ ; 21 mΩ 13.5mH 1000kg.m2 2 950V 500V to 660V 50mΩ; 0.22mH 44mF
INTRODUCTION
The industry of the wind generators knew has spectacular growth during the last years. Before the wind generators power does not reach the order of the megawatts. For this reason, the major part of the first models is based on the permanent magnet synchronous generator (PMSG) or the conventional asynchronous generator (CAG). The conventional asynchronous generator is generally connected to the turbine through a gear box. The permanent magnet synchronous generators can be coupled to the turbine via a gear box or directly without a gearbox if the generator has a high number of poles [1], [2]. Due to increase of the power in the order of megawatts, today until 10 MW, this solution presents several disadvantages for example: - The converters and the filters are designed according to the rated power of the generator.
978-1-4673-5943-6/13/$31.00 ©2013 IEEE
Fig.1: Wind energy system using a DFIG.
In this case, the size and the weight increases which correspond to increasing of the system cost, [2]; - The losses of the converter increases if the wind generator power is important, which affects the global efficiency of the system. To solve these problems, the DFIG seems to be an interesting solution. Using the DFIG in the offshore wind energy system presents the following advantages: - A speed’s variation of ± 30% which correspond to the value of the slip g of the speed around the speed of synchronism. This variation limits the power in the rotor to
g.Ps , where Ps presents the power in the stator. This last
one enables to reduce the size, the weight and cooling system for the converter in the rotor [3]; -The wind energy disturbances are less important compared to that of the PMSG and the conventional asynchronous generator, [4]; - The losses of the converter are less important and the system efficiency can be improved; - The power factor can be controlled through the converter like to the synchronous generator, [5]. Indeed, the active and reactive powers can be controlled through the converters in the DFIG side, [2], [6]. The studied system presented in Fig.1 includes, a wind turbine for mechanical power capturing, a gear box, a back to back converter for energy management, the grid and the load for energetic consumption simulation. III.
WIND TURBINE SYSTEM MODELLING
A. Wind Turbine modeling In this section, the high power wind turbine modelling is considered. Moreover, considering the high power and low
velocity of the wind, the speed of the turbine will be rather slow, but this problem can be solved by using the gearbox. The theoretical power generated by the turbine is given in (1), where ρ is the density of the air; S is the circular area swept by the turbine; β is the angle of wedging of the blades, v is the wind speed in [m/s], [7]. 1 (1) P = ⋅ C (λ , β ) ⋅ ρ ⋅ S ⋅ v 3 t
p
2
The ratio between the tip speed of the turbine and wind speed is expressed in (2), where Ωt is the rotational speed of the turbine; Rt is the radius of the wind turbine. Ω ⋅ Rt (2) λ = t v
The coefficient of the power Cp represents the aerodynamic output of the turbine with theoretically limited value of 0.593 [7]. This coefficient can be estimated using (3), [8]. ⎧ ⎪ C p (λ , β ) = (0 . 35 − 0 . 00167 ⎪⎪ ⎨ − 0 . 00184 ⋅ (λ − 3 ) ⋅ (β − 2 ) ⎪ π ⋅ (λ + 0 . 1 ) ⎪A = 14 . 34 − 0 . 3 (β − 2 ) ⎩⎪
) ⋅ (β
− 2 ) ⋅ sin A
(3)
(4)
The gear box adapts the rotational speed and torque of the turbine to that of the generator as presented in (5) and (6), where G is the ratio of the gear box. (5) Ω = G ⋅Ωt C
m
=
(6)
C t G
According to the Fig.1, the mechanical equation of the system can be expressed as presented in (7), where Jt and Jm present respectively the inertia moments of the turbine and the generator ; fv is the coefficient due to the viscous rubbings of the generator; Ω is the rotational speed of the generator. ⎛ Jt ⎞ dΩ + f v ⋅ Ω = C m − C em ⎜ 2 + Jm ⎟ ⋅ G ⎝ ⎠ dt
Fig.2: Mechanical model of the turbine.
C em = p ⋅ M ⋅ (I sq ⋅ I rd − I sd ⋅ I rq )
(8)
B. Doubly Fed Induction Generator modelling The dynamic model of the DFIG in the dq axis can be writing as presented in (9); where Rs is the resistance in the stator winding; and Rr is the resistance in the rotor winding; ωs and ωr present respectively the pulsation in [rad/s], in the stator and in the rotor, [10]. ⎧ ⎪U sd ⎪ ⎪U ⎪ sq ⎨ ⎪U rd ⎪ ⎪ ⎪U rq ⎩
d φ sd − ω s ⋅ φ sq dt d φ sq = R S ⋅ I sq + + ω s ⋅ φ sd , ωr = ωs − p ⋅ Ω dt d φ rd = R r ⋅ I rd + − ω r ⋅ φ rq dt d φ rq = R r ⋅ I rq + + ω r ⋅ φ rd dt = R S ⋅ I sd +
(9)
The equations of the flux in the dq axis are presented in (10), where M is the mutual inductance between a phase in the stator and that of the rotor.
The simplified mechanical model of the turbine is presented in the Fig.2. In this model, the rotational speed of the turbine is slower, and the power losses of the turbine can be negligible compared to generator ones. Considering these assumptions, two masses mechanical model has been adopted as illustrated in Fig.2. The validity of this model compared to dynamic behaviour of the turbine has been verified by [9].The mechanical torque Ct of the wind turbine obtained from the mechanical power is expressed in (4). P Ct = t Ωt
The electromagnetic torque is expressed in following equation, where p is the number of poles pair.
(7)
⎧φsd ⎪φ ⎪ sq ⎨ ⎪φ rd ⎪φ rq ⎩
= Ls ⋅ I sd + M ⋅ I rd = Ls ⋅ I sq + M ⋅ I rq
(10)
= Lr ⋅ I rd + M ⋅ I sd = Lr ⋅ I rq + M ⋅ I sq
The active and reactive powers in the stator and the rotor of the DFIG can be estimated as following, [10-14].
⎧ Ps = U sd ⋅ I sd + U sq ⋅ I sq ⎪ ⎪Qs = U sq ⋅ I sd − U sd ⋅ I sq ⎨ ⎪ Pr = U rd ⋅ I rd + U rq ⋅ I rq ⎪Q = U ⋅ I − U ⋅ I rq rd rd rq ⎩ r
(11)
C. AC/DC Converter modelling This section presents the analytical model of the controlled rectifier used in back to back converter topology. Considering Fig.1, the measured currents in the DC-bus enable to write equation (12), where C is the DC-bus capacitor; Iond is the inverter input current; If1, If2 and If3 present the AC/DC converter (rectifier) input currents.
C⋅
dV dc = (S a ⋅ I f 1 + S b ⋅ I f 2 + S c ⋅ I f 3 ) − I ond dt
2 ⋅ Sa ⎧ ⎪U Sa = ⎪ 2 ⋅ Sb ⎪ ⎨U Sb = ⎪ 2 ⋅ Sc ⎪ ⎪U Sc = ⎩
− Sb − Sc ⋅ V dc 3 − Sa − Sc ⋅ V dc 3 − Sa − Sb ⋅ V dc 3
(12)
(13)
The analytical model of the converter is given in (13), where, Vdc is the DC-bus voltage, Sa, Sb and Sc present the three phase
Fig.3: Model of the grid.
Fig.5: Principle of the control.
Fig.4: Model of the load.
Pulse With Modulation (PWM) signals applied to rectifier. D. Grid and Load Modeling The main goal of this section consists to establish the models of the grid and the load. To establish these models, the balanced three phase system is considered. The model of the grid is presented in Fig.3. In this figure, the stator is connected to the grid through a transformer which is materialized by the transformation ratio m. Based on the Fig.3; the resulting equation is presented in (14), where e1, e2 and e3 present the conventional three phase emf of the network. dI res 1 ⎧ ⎪V st 1 − e1 = R res ⋅ I res 1 + L res ⋅ dt ⎪ dI res 2 ⎪ ⎨V st 2 − e 2 = R res ⋅ I res 2 + L res ⋅ dt ⎪ dI res 3 ⎪ ⎪⎩V st 3 − e 3 = R res ⋅ I res 3 + L res ⋅ dt
(14)
- The DC-bus voltage control through the AC/DC converter (rectifier) connected to grid. A. DFIG Speed Control Strategy To control the DFIG speed, the optimal reference of the speed expressed in (16) is used. This reference is obtained from the MPPT technique. The control strategy of the DFIG speed is illustrated in Fig.6. Ω
ref
=
λ opt ⋅ v
(16)
Rt
The coefficients of the IP controller obtained from the closed loop analysis are expressed in (17), where ωnd and tsd are
The load modelling is same to that of the grid without the emf component. The equivalent circuit of the load is illustrated in Fig.4. The analytical model of the load is presented in (15), where Rch and Lch are respectively the resistance and the inductance of the load. dI ch 1 ⎧ ⎪V ch 1 = R ch ⋅ I ch 1 + L ch ⋅ dt ⎪ dI ch 2 ⎪ ⎨V ch 2 = R ch ⋅ I ch 2 + L ch ⋅ dt ⎪ dI ch 3 ⎪ ⎪⎩V ch 3 = R ch ⋅ I ch 3 + L ch ⋅ dt
Fig.6: DFIG Speed Control loop.
(15)
IV. SYSTEM CONTROL STRATEGY The principle of the proposed control strategy is presented in Fig.5. This strategy includes: - The DFIG speed control based using the optimal reference obtained from the Maximum Power Tracking (MPPT) technique; - The active and reactive powers control using the inverter connected to rotor;
respectively the dynamics of the system, and the response time of the system.
⎧⎪ K p = 2 ⋅ ξ ⋅ ω nd ⋅ J , ω nd = 5 . 8 ⎨ 2 t sd ⎪⎩ K i = ω nd ⋅ J
(17)
B. Active and Reactive Power Control Strategy
To simplifying the DFIG control strategy, the majority of authors choose a reference frame related to the stator. However, this choice is not best in this application, i.e. the parameters to be controlled are in to stator (Ps, Qs), the choice of an axes system shifted 90° behind on the vector of stator voltage (Vsd = 0 and Vsq = Vs) is much more advantageous [11]. In more to this assumption, the flux in the stator is oriented in the direction of d axis, i.e. (φsd = φs and φsq = 0). In the offshore wind energy applications, the high power generators are generally used, which enables to neglecting the resistance in the stator. Based on these assumptions, the approximate electrical power (active and reactive) in the stator and the rotor can be expressed as presented in (18).
Like to DFIG speed control, the IP controller is used for DCbus voltage management. The coefficients of this controller are given in (21), where ωn and tsdc are respectively the dynamics of the system, and the response time of the system.
⎧⎪ K pdc = 2 ⋅ ξ ⋅ ω n ⋅ C , ⎨ ⎪⎩ K idc = ω n2 ⋅ C V.
Fig.7: Active and Reactive Power Control Strategy.
⎧ ⎪ Ps ⎪ ⎪ ⎪Q s ⎪ ⎨ ⎪P ⎪ r ⎪ ⎪Q ⎪⎩ r
≈ U ≈ U
sq
⋅I
sq
≈ g ⋅U = g ⋅U
⋅I
sq
sd
= −U U
=
s
⋅
⋅φ
Ls
M ⋅ ⋅I Ls
s
s
M ⋅ I rq Ls
⋅
s
s
−
U
(18)
⋅M ⋅ I rd Ls
s
rq
M ⋅ I rd Ls
The proposed control strategy of the power (active and reactive) in the stator is presented in Fig.7, where PID is the conventional PI controller; Z presents a parameter which is expressed in the following equation.
(L
Ζ =
s
⋅ Lr − M Ls ⋅ Lr
2
)
(19)
The coefficients of the PI Controllers used in the inner and outer loops are respectively presented in (20). ⎧ ⎪K ⎪ ⎨ ⎪K ⎪⎩
pir
iir
= =
2 . 197 ⋅ Ζ ⋅ L r t ir 2 . 197 ⋅ R r t ir
, ⎧⎪ K ⎨ ⎪K ⎩
pp
ip
=
t ir tp
= 2 . 197 ⋅ t
ωn =
5 .8 t sdc
SIMULATION RESULTS
The system simulation is carried out in following conditions: - the wind speed average value is fixed at 12m/s, the wind turbine speed reference Ωref is estimated as expressed in (16), -the reference of the reactive power Qref is respectively fixed at (500, 0 and -500) kVAr, - the active power reference is fixed to 60% of the wind turbine maximum power, -the DCbus voltage reference is respectively fixed at 500V and 660V. By convention, the sign of power (active and reactive) is assumed negative for the supplied power and positive in contrary conditions (for consumed power). Fig.9 shows the wind speed variation, where the minimum and maximum values are respectively 9m/s and 15m/s. The wind turbine mechanical speed control result is presented in Fig.10. These curves show the proposed control strategy is satisfactory, i.e. measured speed is identical to reference speed from the MPPT control. The active and reactive powers measured at the stator of the DFIG are respectively presented in Fig.11 and Fig.12. These results allow to concluding the control strategy presented in Fig.7 is sufficient. The measured power compared to the reference ones shows that this control strategy takes into account the wind speed variation.
(20) p
C. DC-bus Voltage Control Strategy The control strategy of the DC-bus voltage is illustrated in Fig.8, where the reference current Idref is obtained from the DC-bus voltage control loop. Iqref is fixed to zero to obtain a power factor equal to 1.
Fig.8: DC-bus Voltage Control Strategy.
(21)
Fig.9: Wind speed profile.
Fig.10: DFIG speed control result
the grid Ires1. VI. CONCLUSION
Fig.11: Active power control result.
Due to the wind speed variations, the Doubly Fed Induction Generator (DFIG), presents an interesting solution for compensation of the variability of the primary source in acceptable proportions and guarantees a good quality of the produced energy. The simulation results show that the proposed control strategies are performing for offshore wind energy management. Based on the simulations results, the DFIG seems to be well fitted for offshore wind energy applications. VII. APPENDIS TABLE1 : USED PARAMETERS FOR SIMULATIONS
CONTROL LOOP DFIG speed control loop Rotor currents control loop Active and Reactive power control loops DC-bus voltage control loop;
Fig.12: Reactive power control result.
Fig.13: DC-bus voltage control result.
Fig.14: Measured currents in the load connection point.
Fig.13 presents the DC-bus voltage control result. This curve shows that the measured voltage follows the reference ones, which enables to conclude that the proposed control is performing. The measured currents on the load connection point are presented in Fig.14. This curve shows that the measured current from the stator Is1 is equal to the sum of the current consumed by the load Ich1 and the injected current in
PARAMETERS λopt=9; Cmax = 0.525;Kp = 509; Ki = 12960 ; tsd = 0.5s ; tir = 0.14s ; Kpir = 0.0047 ; Kiir = 0.3296 tp = 0.15s ; Kpp = 0.9333 ; Kip = 0.3296 tsdc = 0.5s ; Kpdc = 8.932 Kidc = 925.1
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