Adaptive control for grid connected DFIG wind power generation system

ĐIều khiển thích nghi tuabin gió nguồn kép nối lưới điện truyền tải. A novel control strategy is presented for the backtoback PWM converters of the gridconnected DFIG wind power system to enhance the transient performance and reliability of the overall system during physical parameter uncertainty and certain grid disturbance. The system description is modeled by using the fieldoriented vector of the stator and voltageoriented vector of grid control. The rotorside and gridside converter controllers are designed in integration by utilizing nonlinear adaptive control technology. The theoretical analysis shows that the proposed controller can guarantee the system to achieve the maximal absorption of wind power, constant dcbus voltage, and constant voltage constant frequency output with respect to variable windspeed, parameter uncertainties and disturbance. The effectiveness of the proposed strategy is validated by the simulation comparison with the conventional PID controller.

Adaptive Control for Grid-Connected DFIG Wind Power Generation System Zhiguo Gao Xiaohong Jiao Chaobo Ge Institute of Electrical Engineering Yanshan University Qinhuangdao 066004, China Email: gaozhiguo1100@126.com Institute of Electrical Engineering Yanshan University Qinhuangdao 066004, China Email: jiaoxh@ysu.edu.cn Institute of Electrical Engineering Yanshan University Qinhuangdao 066004, China Email: 568276120@qq.com the probability of requirements is that wind turbines should remain connected and actively support to the grid during disturbances Accordingly, there has recently been a growing interest in the context of the grid connected wind turbine with DFIG, such as the dynamic responses[5], maximum power control strategy[6], performance evaluation and control scheme [7,8] for the operation during abnormal conditions Motivated by the reason above, this paper provides a control scheme for the grid connected wind turbine with DFIG through back-to-back PWM First, the overall model of a wind power system is described, including the DFIG and a vectorcontrolled converter connected between the rotor and the grid Adaptive voltage controllers of the rotor-side and grid-side converters are coordinately designed by utilizing nonlinear adaptive control technology under consideration of the system parameter uncertainty and grid disturbance, with the aim to control the generation of wind power in order to maximize the generated power with the lowest possible impact in the grid voltage and frequency during normal operation and under the occurrence of faults Meanwhile, the comparative simulation are presented between the proposed adaptive coordinated controllers and PID controllers, showing that better dynamic characteristics can be obtained using coordinated controllers Abstract—A novel control strategy is presented for the back-toback PWM converters of the grid-connected DFIG wind power system to enhance the transient performance and reliability of the overall system during physical parameter uncertainty and certain grid disturbance The system description is modeled by using the field-oriented vector of the stator and voltage-oriented vector of grid control The rotor-side and grid-side converter controllers are designed in integration by utilizing nonlinear adaptive control technology The theoretical analysis shows that the proposed controller can guarantee the system to achieve the maximal absorption of wind power, constant dc-bus voltage, and constant voltage constant frequency output with respect to variable wind-speed, parameter uncertainties and disturbance The effectiveness of the proposed strategy is validated by the simulation comparison with the conventional PID controller Keywords-doubly fed induction generator; back-to-back PWM; grid connection; wind power generation; adaptive control; disturbance attenuation I INTRODUCTION As well known, DFIG is mainly used in variable speed wind power systems due to its many advantages such as the improved power quality, high-energy efficiency and reduced power converter rating, etc Consequently, in the decade, the research of control problem for the grid-connected DFIG through back-to-back PWM has received much attention as one of preferred technology for wind power generation (see [1-8] and the references therein) Early research results mainly concentrated on the control strategy for the rotor-connected converter of DFIG, which applies the stator-flux-oriented vector technique to describe model of DFIG, and then design PI controller[1,3] or robust controller[2] to guarantee the wind power system to achieve the maximal absorption of wind power and the decoupling control for the active and reactive power of the generator Before connecting the stator of DFIG to the grid terminals, the stator voltage has to be adjusted to be synchronized with the line voltage Thus, some references handle DFIG control for the synchronization process, for example, [4] describes a smooth and fast synchronization scheme of DFIG to the grid as well as decoupling control of generator active and reactive power by using the stator flux-oriented control at normal operation With increased penetration of wind power into electrical grids, II SYSTEM DESCRIPTION AND CONTROL PROBLEM The basic configuration of a grid-connected DFIM wind power system is sketched in Fig Rg Lg u1a Lg u1b Rg Lg u1c Rg udc u2aL1 R1 u2bL1 R1 u2cL1 R1 Figure Diagram of grid-connected DFIG wind power system A Overall model of the controlled system For an induction generator, the stator field orientation control is based on the stator d-q model, where the reference frame rotates synchronously with respect to the stator flux, with the d-axis of the reference frame instantaneously overlaps the axis of the stator winding flux The stator flux linkage keeps constant when the system is in the steady-state operation Project Supported by Natural Science Foundation of Hebei Province (F2010001322) _ 978-1-4244-9690-7/11/$26.00 ©2011 IEEE  Te = n p Lm (isq ird − isd irq ) = Lm n pψ s irq / Ls and the stator resistance is ignored For such a reference frame selection, the rotor voltage equations can be written as dird ­ °u rd = Rr ird + σ dt − ω s 1σ irq ® dirq Lψ + ω s1 m s + ω s1σ ird °u rq = Rr irq + σ dt Ls ¯ PM = 0.5 ρπ R 2C p (λ , β )v3 = kω (λ )ω (1) (2) The active and reactive power can be respectively controlled by controlling the q and d-axis rotor current In addition, in the case of ignoring the copper and iron loss of the stator, the power relations for DFIG can be expressed as P = Pe , P1 = sPe ± P1' , Pe = Pm − Pm' 1− s (3) where Pe , Pm and Pm' represents electromagnetic power, input mechanical power and the mechanical losses of the generator, respectively P1 and P1' denote the rotor power and rotor losses, respectively Furthermore, the power transfer relationship of wind power generation systems is governed by P= ωs ( PM − PM' Pm' ) n pr (4) Jâ Ls ° ° L2ird = − R2ird + L2ω1irq + u1d + w2 ° L2irq = − L2ω1ird − R2irq − ω1c1 + u1q + w3 ® °Cudc = ( ed id − urd ird − urq irq + w4 ) 2udc ° ° L1id = − R1id + ωs L1iq + ed − u2 d ° L1iq = − R1iq − ωs L1id + eq − u2 q ¯ where PM ; PM0 are the mechanical power captured by wind turbine and mechanical wear of wind turbine, respectively Under the d-q reference frame, the equivalent circuit equations of rotor side converter can be described as ­ dird ° Lg dt = − Rg ird + Lgωs1irq + u1d − urd (5) ® dirq ° Lg = − Lgωs1ird − Rg irq + u1q − urq dt ¯ where denote equivalent resistance and inductance, are the output voltage of machine side converter in the d-q axes By combining (1) and (5), the integration model of generator and rotor side converter can be obtained as ­ ° L2 ® ° L2 ¯ dird = − R2 ird + L2ω s1irq + u1d dt dirq = − L2ω1ird − R2 irq − ω s1c1 + u1 q dt (9) where v is wind speed, ρ is air density, λ =ω R / v is tip-speed denotes power ratio, R is the radius of wind turbine, coefficient of wind turbine, is pitch angle In d-q coordinate, the circuit equation of grid side converter can be described as ­ did ° L1 dt = − R1id + ω s L1iq + ed − u d (10) ® diq ° L1 = − R1iq − ω s L1id + eq − u q ¯ dt are the grid EMF components in d,q-axis, where are AC voltage and current in drespectively and q-axis components of the grid converter, respectively are the equivalent resistance and induction Ignoring the line loss and switching device switch loss, according to energy conservation, grid side input power equals to stored power of the DC side capacitance and excitation power of the rotor side, therefore: du Cudc dc = ( ed id + eqiq − urd ird − urqirq ) (11) dt Conservation of energy for converter side: 95 du ed id = cudc dc + P2 (12) dt 100 Considering external disturbance and (6), (7), (10) and (11), we can get the overall model of DFIG wind power system: ­ · 1§ nLmψ sωs irq − B + w1 = ă k where represent rotor voltage and currents in is rotor resistance d-q axis reference frame, respectively is leakage factor, , , represent rotor, stator inductance and mutual inductance, respectively is slip frequency, , represent synchronous angular speed is the number of pole pairs and rotor speed, respectively The stator active and reactive power can be described as Lmψ s ω s ­ irq °° P = u sd isd + u sq isq = − L ® ψs s − Lm ird °Q = u sq isd − u sd isq = ω sψ s Ls °¯ (8) The power PM produced by the wind is given by (13) where n = n p ng , wi (i = 1," , 4) denote external disturbances B Control problem formulation Generally, for the wind power system (13), the main goals of the control strategies are: (1) Maximize the produced energy in the assurance of a secure functioning of the turbine; (2) Control the active power supplied by the turbine in order to optimize the operating point and limit the active power in case of high wind speed; (3) Control the reactive power flow between the generator and the grid, especially in the case of weak grids, where voltage fluctuations can occur, to guarantee the quality of the grid voltage Moreover, it should be noted that during system operation there exist uncertainties, including parameters uncertainty and external disturbance, such as, physical variables B and are of susceptible Thus, let , , be unknown parameters Therefore, the task in this paper is to (6) where c1 = Lmψ s / Ls , R2 = Rr + Rg , L2 =σ + Lg The motion equation of wind turbine with DFIG is described as P dω (7) J + Bω = M − n g Te dt ω where , denote the moment of inertia, viscous friction coefficient of wind turbine and generator, respectively Te denotes electromagnetic torque generated, which can be calculated by  design the global controllers for the rotor-side and grid-side converters to ensure the wind power system (13) to achieve the above control objective regardless of uncertain parameters and external disturbance during normal operation and under the occurrence of faults To this end, define: ν isd isq ω ird irq udc u1q u1d id u2d θˆ u2q iq θˆ x1 = ω − ω , x2 = ird − i , x3 = irq − i , x4 = udc − u , x5 = id − i , x6 = iq − i ∗ ∗ rd ∗ rq ∗ dc ∗ d ∗ q then (16) can be rewritten as Figure Block diagram of the grid connected wind power control system ­ ∗ °x1 = J ( f1 ( x1 , kω ,ω ) −θ1 x3 −θ2 x1 + w1 ) ° f2 ( x2 , x3 , irq∗ ,ω∗ ) + u1 + w2 °x2 = L ° °x3 = f3 ( x2 , x3 , ird∗ ,ω∗ ) + nx1θ3 + u2 + w3 L2 ê đ Lr Lr ∗ ∗ °x4 = d « Ex5 + f4 ( x2 , x3 ,ird ,ω ) + ( x2 + ird ) w2 + ng x1irqθ3 L L 2 ¬ ° º L L ° − r (ωs − ng x1 − ngω∗ ) x3θ3 + r ( x3 + irq∗ ) w3 + w4 » ° L2 L2 ¼ ° R R °x5 = − x5 + ωs x6 − u3 , x6 = − x6 − ωs x5 − u4 L1 L1 °¯ ( ( ) ) III ADAPTIVE COORDINATED CONTROLLER DESIGN In this section, an adaptive controller based on coordination will be designed for system (14) by utilizing the nonlinear recursive technique First, to design controller, the following coordinate transformation is utilized for the system (14) ∗ ξ = ( x4 + udc ) + d1 ( x2 + ird∗ ) + d1 ( x3 + irq∗ ) − d1udc∗ − d1ird∗ − d1irq∗ ( + R − u1 = u1 d − L r u = u1 q − L r ∗ d ird dt ∗ dirq dt ∗ rd 2 ∗ rq Lr L2 ∗ rd Lr L2 ∗ 1d Lr L2 ∗ rq Lr L2 2 (15) where Thus, we get the following conclusion Proposition1: For system (14), if a coordinated controller for the rotor-side converter and grid-side converter is designed as: )( x + 2i x ) + ( x + i ) v + x u )( x + 2i x ) + ( x + i ) v + x u R2 Lr L2 R2 σ r L2 ξ = d ( Ex5 + f + I1 x2 w2 + c2θ + I1 x3 w3 + w4 ) fi = − R2 xi ± L2ω s x j B L2 n ( x1 + ω ∗ ) x j B L2 nirq∗ x1 , i , j = 2,3(i ≠ j ) ( Then, it follows˖ with d1 = 3/(2C ) , f1 = kω x12 + 2kωω ∗ x1 , f ( x2 , x3 , ird∗ ,ω ∗ ) = Rr − 2x2 R1 ­ °u1 =− f2 − L γ − L2k2 x2 , u4 =− L x6 −ωs x5 + k6 x6 ê u = L ôk z + x − f3 − 2z3 − (∂α1 )2 z − nx1θ3 ° 2 ¬ 3 L2 L2γ J 2γ ∂x1 L2 ° ∂α ∂α º ∂α1 ˆ θ x +θˆ x + ω∗ + 1τˆ» + ° ∂τˆ ¼ J ∂x1 ∂ω∗ ° 1 Đ ã R1 (16) đu3 = L x5 +ωs x6 + E {ξ4 + J ∂x f1 1x3 x1 + 2 ă x z4 J â 1ạ 1 ∂α2 ° + f + nx1θˆ3 + u2 + (Ex5 + f4 + c2θˆ3 ) ( f +u ) + L2 ∂x2 L2 ∂x3 ∂ξ4 ° 2 § ∂α2 ∂α2 · ∂α2 ˆ ∂α2 ∗ ∂α2 ∗ § ∂α2 · ° + ă L x + I1x2 ¸ z4 + ˆ θ3 + ∂i∗ irq + ∂i∗ irq + ă x z4 â 2 â 4ạ 4ạ rq rq + ∂α2 u∗ + ∂α2 u∗ + § ∂α2 + I x ∂α2 · z + k z } 1q 1d ăâ L2 x3 áạ u1q u1d ∗ 1q ª di ∗ u d − ( L1 dtd − R1id∗ + ω s L1iq∗ ) , ẳ L1 ê diq ∗ ∗ ∗ ∗ º u q − ( L1 dt − R1iq + ω s L1id ) + R r irq − L r ω 1ird + u rq , u = ẳằ L ơô ∗ , u3 = + R r ird − L r ω 1irq + u rd ( ∗ , id∗ , iq∗ are the reference values of the wind where ω ∗ , ird∗ , irq∗ , udc turbine speed, current d-q components of generator rotor, DC voltage and current d-q components of grid-side, respectively, which can be obtained by the following relationship To electively extract wind power while at the same time maintaining safe operation, the wind turbine should be driven according to the three fundamental modes associated with wind speed, maximum allowable rotor speed and rated power[9] Consequently, the desired wind turbine speed ω ∗ and the expected captured wind power PM∗ are given According to the requirement for reactive power, the expected reactive power Q∗ can be known Further, by (2), (4) and (12), , and can be obtained To achieve the control of unity power factor of converter, the value of is Therefore, the control problem of this paper is to design an adaptive controller for the system (14) where, is an estimate for the unknown parameter , which makes the resulting closed-loop system operate safely and stably and achieve the control goal in the presence of the parameter perturbation and external disturbance, i.e the speed of wind turbine achieves asymptotically tracking the desired speed trajectory based on the maximum capture of wind energy Simultaneously, the voltage of DC side is constant and the grid-side converter exports electrical energy of constant voltage and constant frequency in the required power factor The diagram of integrated control system of wind power generation system is shown in Fig ) ( ( ) ) and the adaptive update law is chosen as follows˖ z ∂α z ∂α2 z ∂α1 ­ ˆ z4 ∂α2 x3 − x3 ,θˆ2 = x1 − x1 °θ1 = r1J ∂x1 r1J ∂x1 r2 J ∂x1 r2 J ∂x1 đ Đ ã Đ ã c 2 = ă + z4 nx1 ă z3 + z4 , = 111T ( x1 ) r3 â r3L2 â x3 (17) where 1(x1) = êơ f1x1 − x12 2x12 γ º¼ , k2,k3,k6 >0 are tuning parametersˈ α1 , α are the virtual control inputs determined in the proofˈ Γ1 = diag{r4 , r5 , r6} ˈ ri > 0, (i = 1," 6) ˈThen the resulting closedloop system has the following operation performance: (1) when w = ˈ the system is Lyapunov stable at the equilibrium and states x can converge to the origin, namely, ω → ω ∗ , ird → ird∗ , irq → irq∗ , udc → udc∗ , id → id∗ , iq → iq∗ as t → +∞ (2) when w ≠ , the system from the disturbance input w to the penalty output signal y = [ ρ1x1 ρ x2 ρ3 z3 ρ 4ξ ρ5 z5 ρ6 x6 ]Τ ) has -gain not large than γ , ρi are weighted coefficients Outline of Proof: The controller (16) and the adaptive update law (17) are derived by nonlinear adaptive backstepping design technique, where Lyapunov function of the closed-loop  system is recursively constructed The proposition is obtained according to Lyapunov stability theorem and LaSalle invariant principle as well as L2-gain disturbance attenuation technique impact in the grid voltage and frequency during normal operation and under the occurrence of faults with parameter uncertainties and external disturbance, such as in case and case IV SIMULATION VALIDATION The effectiveness of the designed controller is validated by simulation in MATLAB/SIMULINK and the comparison with that of PID controller is given A simulated wind speed and the corresponding desired speed of wind turbine are shown in Fig w* 1.96 * 1.94 14 1.92 80 100 120 The following two operation cases are discussed The fault considered in simulations is a symmetrical three phase short circuit fault which occurs on one of the transmission lines (1) Uncertain parameters and external disturbance: In the operation the physical variables B and contain uncertainties and there exists external disturbance (2) The occurrence of faults: The system is in a pre-fault operation state, a symmetrical three phase fault of grid voltage occurs at t=80s The simulation results in case1 are shown in Fig.4 and Fig.5 To compare the control performance, the curve is also given for the system under the action of PID controller The simulation results in case2 are shown in Fig 60 t/s 90 rq i •A • rd i •A • i 50 t/s w (m /s) i •A • i • A• [1] * iq iq q i • A• [3] PID * id id -5 PID 100 50 t/s [4] 100 t/s Figure The response curves of the closed-loop system in case v1 v2 v3 v4 [5] -200 v3,v4• V• v1,v2• V• 1000 -1000 -2000 -400 -600 [6] 20 40 60 80 100 -800 120 20 40 t/s 60 80 100 120 t/s 50 70 60 , , 30 20 3 40 , , 50 [7] -50 -100 10 0 20 40 60 t/s 80 100 120 80 100 120 i* i* q PID d PID 50 100 -5 50 100 t/s Figure The response curves of the closed-loop system in case 100 2000 60 t/s t/s rq 10 d i • A• -4 [2] 0 50 40 -2 -3 PID -1 -4 20 i -1 i* rq t/s -3 0 10 q 0.1 100 -2 100 0.05 50 PID 0.06 0.04 50 t/s 100 0.2 0 PID REFERENCES 50 t/s 0.15 PID Irq 0.08 0.02 0 dc 349.4 rd 10 i*rq 0.1 i rd 10 100 0.12 * i rd u rd i PID 50 t/s 349.8 i* 15 dc u 347 100 15 350 120 20 u* 348 50 20 349.6 30 349 t/s PID 1.9 1.85 350 dc 1.85 u* 350.2 1.95 1.95 1.9 dc u•V • w• m /s• 2.05 351 w* w PID id 350.4 w* w PID d c 2.1 2.1 2.05 u•V • 60 t/s rq 40 i • A• 20 Figure Wind speed and the desired speed ω ∗ of the wind turbine q 1.9 100 t/s i• A • 50 rd 12 d 16 w(m /s) v(ra d /s) 1.98 d c v 18 V CONCLUSION In this paper, the adaptive coordinated control of rotor-side converter and grid-side converter is investigated via the vector control strategy The theoretical analysis shows the designed controller can guarantee the system on grid operation has good dynamic performance irrespective of uncertain parameters and external disturbance The simulation results also illustrate that the proposed control scheme can achieve the maximal absorption of the wind power according to three wind turbine operation modes, control the active power supplied by the turbine to optimize the operating point, control the reactive power flow between the generator and the grid to guarantee the quality of the grid voltage -150 20 40 60 t/s 80 100 [8] 120 Figure Control inputs and estimates of adaptive parameters From the simulation results, it can be concluded that: The nonlinear adaptive coordinated controller proposed in this paper can effectively improve transient stability of the system and achieve the control aim maximizing the generated power with the lowest possible [9]  R Pena, J.C Clare, G.M Asher, "Doubly fed Induction generator using back-to-back PWM converters and its application to variable-speed wind-energy generation" IEE Proc.-Electric Power Application,vol 143, no 3, pp 231-241, May 1996 S Peresada, A Tilli, A.Tonielli "Robust active-reactive power control of a doubly-fed induction generator" Proceedings of the 24th Annual Conference of the IEEE, 1998 A Tapia, G Tapia, J X Ostolaza, and J R Saenz, “Modeling and control of a wind turbine driven doubly-fed induction generator,” IEEE Trans Energy Conv., vol 18, 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speed control of wind turbines using nonlinear and adaptive algorithms" Journal of Wind Engineering and Industrial Aerodynamics, vol.85, pp.293-308, 2000  ... the control of unity power factor of converter, the value of is Therefore, the control problem of this paper is to design an adaptive controller for the system (14) where, is an estimate for. .. rated power[ 9] Consequently, the desired wind turbine speed ω ∗ and the expected captured wind power PM∗ are given According to the requirement for reactive power, the expected reactive power. .. , wi (i = 1," , 4) denote external disturbances B Control problem formulation Generally, for the wind power system (13), the main goals of the control strategies are: (1) Maximize the produced