Doublyfed induction generator wind turbine modelling for detailed electromagnetic system studies

Published in IET Renewable Power Generation Received on 10th August 2012 Revised on 21st November 2012 Accepted on 17th December 2012 doi: 10.1049/iet-rpg.2012.0222 ISSN 1752-1416 Doubly-fed induction generator wind turbine modelling for detailed electromagnetic system studies Ting Lei, Mike Barnes, Meliksah Ozakturk Power Conversion Group, University of Manchester, M1 0QD, UK E-mail: Ting.lei-2@postgrad.manchester.ac.uk Abstract: Wind turbine (WT) technology is currently driven by offshore development, which requires more reliable, multi- megawatt turbines. Models with different levels of detail have been continuously explored but tend to focus either on the electrical system or the mechanical system. This study presents a 4.5 MW doubly-fed induction generator (DFIG) WT model with pitch control. The model is developed in a simulation package, which has two control levels, the WT control and the DFIG control. Both a detailed and a simplified converter model are presented. Mathematical system block diagrams of the closed-loop control systems are derived and verified against the simulation model. This includes a detailed model of the DC- link voltage control – a component which is usually only presented in abstract form. Simulation results show that the output responses from the two models have good agreement. The grid-side converter control with several disturbance inputs has been evaluated for three cases and its dynamic stiffness affected by operating points are presented. In addition, the relation of pitch controller bandwidth and torsional oscillation mode has been investigated using a two-mass shaft model. This model can be employed to evaluate the control scheme, mechanical and electrical dynamics and the fault ride-through capability for the turbine. 1 Introduction The trend of future wind turbine (WT) installations moving offshore is stimulating the need for high reliability and ever larger WTs in order to minimise cost. Two WT concepts currently used are considered to be suitable for the multi-megawatt offshore installations – the doubly-fed induction generator (DFIG) WT and the permanent magnet synchronous generator WT [1]. Currently the former with a capacity up to 5 MW has the largest market share. Increasingly comprehensive studies need to be carried out to evaluate the control strategies and system dynamic behaviour. These studies require accurate models. DFIG WTs have been investigated for many years [2–10]. In most of these, the converters are simplified as controllable voltage or current sources with only fundamental frequency components, which makes it impossible to implement a detailed study of power converter dynamics. The drive-train is often treated as a lumped-mass system, which means the induced torsional oscillations are neglected. In this paper, a PSCAD/EMTDC-based DFIG WT model with two control levels is provided. The DFIG control level involves the rotor-side converter (RSC) control and the grid-side converter (GSC) control. The WT control level involves the pitch control and the optimum torque tracking [4]. Mathematical analysis of each individual control system is carried out and the mathematical blocks (MB) have been verified against PSCAD/EMTDC simulation results. Two converter representations, with and without IGBT switches are used here, which are referred to as the full switched model (FSM) and the switch-averaged model (SAM). They both have been implemented for observing GSC control performances where the DC-link dynamic is involved. The latter is used to demonstrate the WT mechanical responses such as rotor speed and pitch angle to wind speed changes. Finally, a multi-mass shaft model is added to investigate the correlation of the pitch mechanism and shaft torsional modes. This PSCAD/EMTDC m odel can be used to evaluate the DFIG WT performances under different operating modes, control schemes and the grid integration capabilities. The paper is structured as follows. Section 2 presents the component modelling and equations. Sections 3 and 4 then elaborate the DFIG-level and WT-level control systems, respectively, as well as the mathematical analysis and simulation results. Section 5 concludes the main results. 2 System modelling A schematic diagram of the DFIG WT and its overall control systems are illustrated in Fig. 1. The turbine rotor is connected to the DFIG through a shaft system. The generator rotor is fed from the grid through a back-to-back converter which handles only the slip power (up to 30% of the rated power). www.ietdl.org 180 IET Renew. Power Gener., 2013, Vol. 7, Iss. 2, pp. 180–189 & The Institution of Engineering and Technology 2013 doi: 10.1049/iet-rpg.2012.0222 2.1 Aerodynamic modelling The aerodynamic model can be described by the equation of aerodynamic power or torque generated as the wind passes the turbine blades [11] P a = r 2 p R 2 a C p ( l , b )v 3 w (1) T a = r 2 p R 3 a C p ( l , b ) l v 2 w (2) with ρ is the air density (kg/m 3 ), R a is the radius of the rotor (m), v w is the wind speed upstream the rotor (m/s) and ω r is the rotor speed (rad/s). The power coefficient C p is a function of the tip speed ratio λ and the pitch angle β (deg.), for which the numerical approximation in [9] is used l = v r R a v w (3) 1 l i = 1 l + 0. 08 b − 0.035 b 3 + 1 (4) C p ( l , b ) = 0.22 116 l i − 0.4 b − 5  e − 12.5/ l i ()() (5) 2.2 Induction generator modelling The DFIG machine equations have been described in [5, 9]. Note that in Fig. 1, the currents are set as outputs from the stator and rotor. If generation convention is considered, the set of machine equations can be derived as v s =−R s i s + d c s dt + j v s c s (6) v r =−R r i r + d c r dt + j v s − v r  c r (7) c s =−L s i s − L m i r (8) c r =−L r i r − L m i s (9) with v is the voltage (kV), R is the resistance (Ω), i is the current (kA), ω s is the synchronous electric speed (rad/s), ψ is the flux linkage (Wb), L m is the mutual inductance between stator and rotor windings (H ). The subscripts s and r denote the stator and rotor quantities. 2.3 Back-to-back converter modelling Two voltage source inverters (VSI) are connected back-to-back via a DC-link to comprise the converter. This enables bidirectional power flow. In Fig. 2, the FSM is presented with all the IGBT switches and a PWM frequency of 4.5 kHz. This model provides a deeper insight of the converter dynamics over a short time scale. In the SAM, the converter is presented as two current-controlled voltage sources coupled through a DC-link. The DC-dynamics are based on the power balanc e between the RSC and GSC, which generates two current disturbances from the VSIs feeding into the DC-link. The SAM is suitable for inspecting the mechanical dynamics over a longer time scale without the disturbance from the switching noise 2.4 Shaft system modelling The shaft system has been presented as six, three, two and lumped-mass models in other research [12], among which the lumped and two-mass shaft models are often used to study the electric behaviours of the DFIG. It is suggested in [11] that for a generator with shaft stiffness lower than 3 pu/el. rad, a two- mass shaft model should be considered. PSCAD/EMTDC provides the standard models of the wound rotor induction machine and the multi-mass shaft. They can be interfaced with WT aerodynamic model and pitch controller as shown in Fig. 3. The performances of th e two-mass shaft model are investigated in Section 4. If not specified, the analysis refers to the lumped shaft model with a SAM converter in the paper. The model performances during single or three-phase fault conditions are presented in Fig. 4, where the stator and rotor voltages subject to significant changes when the grid voltages drop to 0 for 100 ms. Fig. 1 DFIG WT model and its overall control systems www.ietdl.org IET Renew. Power Gener., 2013, Vol. 7, Iss. 2, pp. 180–189 181 doi: 10.1049/iet-rpg.2012.0222 & The Institution of Engineering and Technology 2013 3 DFIG control The control system has been shown in Fig. 1, in which two control levels are identi fied based on different bandwidth s. The DFIG control consists of the RSC control and the GSC control. The former is used to provide decoupled control of the active and reactive power while the latter is mainly used to ensure a constant voltage on the DC-link [5, 7]. 3.1 RSC control Stator-flux orientation is used for the RSC control in which the stator flux is collinear with the d-axis and the other rotor quantities are converted to this frame. The equations of the electric torque and the stator reactive power can be found in [5], which are modified here using generator convention, T e = 3 2 L m L ss c s i r q (10) Q s =− 3 2  2 √ V s L ss c s − 3 2  2 √ V s L m L ss i r d (11) where V s is the stator phase voltage in rms. Resolving (6)–(9), splitting the rotor voltage in d– q-components and neglecting the stator flux transients (dψ s / dt = 0) gives v r d ∗=−R r i r d − L c di r d dt + v slip L c i r q (12) v ∗ r q =−R r i r q − L c di r q dt − v slip L c i r d + v slip L m L ss c s (13) where v slip = v s − v r , L c = L rr − L 2 m L ss The MB diagram of RSC control is depicted in Fig. 5 , where the decoupling of d–q control-loops is achieved by adding the feed-forward compensation after the inner-loop PI controller. Reactive power control is cascaded with d-current control loop and electric torque control is cascaded with q-current control loop. The estimated quantities are marked by ‘^’ to distinguish them from the real quantities. In PSCAD/EMTDC, the DFIG WT is connected to the grid through a step-up transformer. Parameters used in the model are tabulated in appendix. The DFIG is set to the speed control mode with a nominal rotor speed. Responses from the MB are compared with PSCAD/ EMTDC simulations (‘PCD’), applying the same reference signals (Ref). In Fig. 6, the plots are resulted from a step input of Q ∗ s , T ∗ e , i ∗ r d , i ∗ r q at the four control loops separately. Note that in the lower plots, the time scale is smaller since the bandwidth of the current-loop is much higher than the power loops. It can be observed that the curves ‘MB’ and ‘PCD’ have a good agreement, indicating that the mathematical model can describe the software model accurately for this case. 3.2 GSC control of the DC-link In GSC control, the q-component controls the DC-link voltage and the d-component controls the reactive power. Positive current is considered from the grid to the converter. Fig. 3 Turbine rotor, two-mass shaft and DFIG model arrangements in PSCAD/EMTDC Fig. 2 Two converter models Upper: FSM, lower: SAM www.ietdl.org 182 IET Renew. Power Gener., 2013, Vol. 7, Iss. 2, pp. 180–189 & The Institution of Engineering and Technology 2013 doi: 10.1049/iet-rpg.2012.0222 Thus the voltage equations in the d–q frame are expressed as v g d = R gsc i g d + L gsc di g d dt − v s L gsc i g q + e g d (14) v g q = R gsc i g q + L gsc di g q dt + v s L gsc i g d + e g q (15) As shown in Fig. 7, the inner-loop control of the GSC consists of d–q loops with similar structure. The DC control loop Fig. 4 Model performances under fault conditions Left: single-phase fault, right: three-phase fault Fig. 5 Decoupled control block diagrams of the RSC a Inner-loop control system b Outer-loop control system www.ietdl.org IET Renew. Power Gener., 2013, Vol. 7, Iss. 2, pp. 180–189 183 doi: 10.1049/iet-rpg.2012.0222 & The Institution of Engineering and Technology 2013 should be cascaded with q-current control loop, the small signal model of which will be illustrated in the following paragraphs. Aligning the grid voltage to the q-axis (v g_d = 0) and applying power invariant principle to the DC and ac points. P c = 3 2 v g q i g q = V dc i dc g = V dc i dc r (16) The dynamics equation of capacitor (Fig. 2) can be described as C dV dc dt = i dc g + i dc r (17) Combining (16) into (17) and eliminating term i dc_g dV dc dt = i dc r C + 3v g q i g q 2CV dc (18) Taking partial derivatives of all variables D ˙ V dc = 1 C Di dc r + 3 2C K V Di g q + 3 2C K G Dv g q − 3 2C K V K G DV dc (19) K V = V g q0 V dc0 and K G = i g q0 V dc0 For steady state V dc0 i dc r0 =−1.5v g q0 i g q0 (20) The power change of the converter is then DP c = V dc0 Di dc r + DV dc i dc r0 = V dc0 Di dc r − 1.5K V K G DV dc  (21) Fig. 6 Mathematical verification of the RSC control Upper: outer-loop step response, lower: inner-loop step response Fig. 7 GSC control block diagrams Upper: current control loops, lower: small signal model of DC-link control loop www.ietdl.org 184 IET Renew. Power Gener., 2013, Vol. 7, Iss. 2, pp. 180–189 & The Institution of Engineering and Technology 2013 doi: 10.1049/iet-rpg.2012.0222 Equation (19) is the small signal model of DC-link. The subscript ‘0’ denotes a particular operating point. From the equation, DC-voltage dynamics are affected by several components: the first two terms are the injected currents at the DC-link, which will charge or discharge the capacitor; the last two terms reflect the impact of grid voltage and DC-voltage changes. In the closed-loop control system, [Fig. 7 and (19)], the first and third terms can be treated as external disturbances that cause the change of DC-voltage, while the second term is the controlled current obtained from the negative feed-back loop, trying to return DC-voltage to its operating point. On the other hand, the first and last terms constitute the converter power change, as shown in (21). With K G being negative, the last term is actually a positive feedback term that counteracts with the controlling term, introducing an energy buffer effect. The DC-control loop has been analysed for three different cases A. DC voltage step change. B. Electric torque (power) step change. C. Grid voltage drop with 80% remaining voltage. Case A: Step responses of DC-loop and q-current loop are shown in Fig. 8. In the plots of DC voltage output responses, there are two from software simulations, that is, SAM and FSM and the others are from MB diagrams of varying complexity. In an order of complexity, these include a simplified MB that ignores the disturbance feedback term 1.5K V K G ΔV dc , full MBs that consider this feedback term and then additionally disturbance-terms Δi dc_r , Δv g_q , respectively. The plots of SAM and FSM show that the mean value of the FSM matches with the SAM. PWM switching is presented in the current waveform but not apparent in the DC-voltage waveform because of the smoothing effect. All the plots from MBs of DC-voltage control can match with the software simulations except the MB_full. Since there is no change in the converter (ΔP c = 0), the terms ΔV dc and Δi dc_r will counteract each other and must be considered together in this case, as shown in (21). The effect of Δv g_q can be ignored if the grid is assumed to be stiff. Case B and C: The DC-voltage responses to a Te-step and grid voltage sag are shown in the lower two plots of Fig. 9.In both cases, the DC reference value is set to be constant. The disturbance signal i dc_r is the main factor that causes the output DC-voltage change, which is illustrated in the upper plots. It can be observed that the mean value of FSM is lower than the SAM because of the switching losses in the IGBTs. The contributions of two other disturbance inputs are evaluated as shown in the lower plots. Three curves from MBs are shown, which are the MB with all the three disturbance terms, the one neglecting the term ΔV dc and the one neglecting the term Δv g_q . In case B, the MB response will slightly deviate from the software simulation if ΔV dc is not considered, which plays a more important role than Δv g_q in the DC-dynamics. However, the term Δv g_q shows more Fig. 8 Mathematical verification of the GSC control Upper: case A – DC-loop step response, lower: current-loop step response Fig. 9 DC-control disturbance factor analyses for different cases Left: case B – Te steps from 1.2 to 1.3 pu, right: case C – Grid voltage drops to 80% of nominal value www.ietdl.org IET Renew. Power Gener., 2013, Vol. 7, Iss. 2, pp. 180–189 185 doi: 10.1049/iet-rpg.2012.0222 & The Institution of Engineering and Technology 2013 impact in case C, because of significant grid voltage oscillations. In normal WT operating condition, case B is the most common situation, where the reference electric torque or power changes because of a wind speed chang e. The grid disturbance-term Δv g_q can be ignored. Now the dynamic stiffness (DS) [13] of DC-link system can be evaluated for varying operating points. This describes the resistance of the system to a certain disturbance. Considering only the key disturbance input Δi dc_r , resulting from the change of input power ΔP DS = DP DV dc = V dc0 Di dc r DV dc = V dc0 Cs + 1.5v g q0 K G + K P  + 1.5v g q0 K i s (22) Fig. 10 illustrates the DS when varying two parameters’ operating points, V dc0 and v g_q0 , respectively, both of which are changed from 0.7 to 1.3 times of their nominal values. The DS is only sensitive to V dc0 for higher frequencies because of the first term in (22) and it is sensitive to v g_q0 for middle and low frequencies because of the other two terms. As is shown in the figure, the higher the DC-voltage or the grid voltage is, the higher the system DS will be. Software simulations have been presented in Fig. 11, where the DS of the system has been evaluated for three different V dc0 and the electric torque is oscillating at 150 Hz with 0.2 pu amplitude. 4 WT control 4.1 Controller development For the WT control, the system measures the rotor speed and uses it to generate references both to the pitch system of the WT and to the DFIG control level (Fig. 1). There are two different control algorithms for this control level. At lower wind speeds, the pitch angle remains at the optimum value (0 degrees) and the optimum torque will be tracked according to a pre-defined curve [11] T opt g = K opt v 2 r (23) At higher wind speeds, the pitch control is activated to remove excessive power extracted from wind. The two control modes sometimes work together to regulate the WT in the high wind region [4, 12, 14]. The model presented here considers the case where the two controllers operate independently for their respective regions. A non-linear transfer function is employed to generate the torque-speed look-up table. The pitch controller with full-non-linear plant model is illustrated as in Fig. 12a. The actuator introduces a lag between the actual pitch angle and the commanded pitch from the PI controller. This controller is designed with a bandwidth of one-magnitude-order smaller than the electric torque control loop. The actuator time constant is τ = 0.2 s. J t is the total rotational inertia. The wind speed v w acts as the external disturbance experienced by turbine rotor and the generator torque T g is treated as an internal disturbance signal on the shaft system and it is fixed at the rated value for the higher wind speed region. The system model should be linearised in order to evaluate its control performance. The linearisation process of different mass systems has been performed in [15] and this methodology is applied in [16] to design the PI controller. Here the method is extended to lower wind speed region and will be justified by software simu lations. At a particular operating point ω r0 , β 0 , v w0 , the aerodynamic torque can be expressed as T a = T a v r0 , u 0 , v w0  + g D v r + z D b + h Dv w (24) Fig. 10 DS at different operating points Fig. 11 Software simulation of DC-link DS in response to Te oscillations www.ietdl.org 186 IET Renew. Power Gener., 2013, Vol. 7, Iss. 2, pp. 180–189 & The Institution of Engineering and Technology 2013 doi: 10.1049/iet-rpg.2012.0222 where g = ∂T a ∂ v r , z = ∂T a ∂ b , h = ∂T a ∂v w The rotor dynamics can be described as J t d v r dt = T a − T g (25) For the higher wind speed region T g = T a0 , therefore D ˙ v r = A D v r + BD b + B d Dv w (26) where A = γ/J t , B = ζ/J t ,C=η/J t , For the lower wind speed region T g = T g0 + 2K opt v r0 △ v r (27) where T g0 = T a0 , eliminating the pitch controller D ˙ v r = (A − C)D v r + B d Dv w (28) with C = 2K opt ω r_0 /J These two linear models are depicted in Figs. 12b and c. For the WT-level control simulation, the induction machine should be held in torque control mode after the initial transient to interface with the aerodynamic model. The system responses at two operating points (op) are shown in Fig. 13, where Op1: v w0 = 15 m/s, ω r0 = 1.2 pu, β = 10° Op2: v w0 = 9 m/s, ω r0 = 0.78 pu, β =0° On the left plots, as wind rises, the pitch angle increases in order to maintain the rotor speed within the threshold (denoted as ‘Thr’). On the right plots, the pitch angle is maintained at 0 degrees despite of the wind speed change. The rotor speed increases proportionally with the wind speed, to maintain the optimum tip-speed ratio. The very low response is because of the large system inertia. In both cases, the results from ‘PCD’ and ‘MB’ match very well. With the lumped-mass shaft model, no torsional oscillations are presented even though the pitch controller is relatively fast. Fig. 12 WT pitch control mechanism a Pitch control with full-non-linear plant model b Linearised control model for higher wind speed region c Linearised control model for lower wind speed region Fig. 13 Mathematical verification of the WT-level control left: 0.5 m/s v w step at op 1, right: 0.5 m/s v w step at op 2 www.ietdl.org IET Renew. Power Gener., 2013, Vol. 7, Iss. 2, pp. 180–189 187 doi: 10.1049/iet-rpg.2012.0222 & The Institution of Engineering and Technology 2013 4.2 Controller coordination To illustrate the relation of pitch controller bandwidth region and the turbine torsional mode, the responses of a two-mass WT model to a wind step is simulated for different pitch controller bandwidths. Results are obtained by stepping the wind speed from 13 to 14 m/s, as shown in Fig. 14. Significant mechanical oscillations are presented in the rotor speed and pitch angle, which are known as torsional oscillations. The torsional frequency of the WT can be calculated from [11] f T = 1 2 p  K s v 0 (H turbine + H generator ) 2H turbine H generator  = 2.55 Hz (29) where K s is the shaft stiffness (pu/el. rad), ω 0 is the synchronous electric speed (rad/s), H is the moment of inertia (s). In Fig. 14, lower pitch bandwidth can produce smoother but slower response and can result in longer over speed. Torsional oscillations occur as the pitch bandwidth approaches 0.2 Hz, where the controller bandwidth begins to interfer the shaft natural frequency. The responses will become unstable if a Fig. 14 Torsional oscillations observed for a two-mass drive-train system at different controller bandwidths Fig. 15 Electrical oscillations induced by torsional modes – a comparison of both shaft models Fig. 16 Controller adjustment and coordination www.ietdl.org 188 IET Renew. Power Gener., 2013, Vol. 7, Iss. 2, pp. 180–189 & The Institution of Engineering and Technology 2013 doi: 10.1049/iet-rpg.2012.0222 further increase in the controller bandwidth occurs. This phenomenon is also observed in the electric parameters such as stator and rotor power, converter DC-current and voltage, which are depicted in Fig. 15 for a 0.2 Hz pitch bandwidth. The torsional mode is not presented for the lumped-shaft model but is very apparent for the two-mass shaft model. This may accelerate converter thermal fatigue and cause grid disturbance and therefore should be minimised. A pitch bandwidth of 0.1 Hz should be chosen here since this gives similar response to a faster controller without oscillations. The overall system contains five closed-loop control systems whose bandwidths are restricted within limited regions. The speed of electric controllers, that is, RSC and GSC control, should be faster than the mechanical pitch control system; as well they should avoid the network frequency f SYN .The inner-loop controller in the cascaded control system should be four to ten times faster than the outer-loop so that they can be treated separately. The speed of GSC DC-link control f GSC_DC needs to be no smaller than the RSC current control loop f RSC_i in order achieve instant power transfer and minimise the voltage transients on the capacitor. Owing to very large inertia of the WT rotor, the electrical controller system will not excite the shaft torsional mode even when their bandwidths are very close. The controllers are adjusted as in Fig. 16, from which their constants can therefore be obtained based on the MB diagrams. 5 Conclusions With future WTs moving towards offshore, very large turbines will be installed making the reliability more critical. Comprehensive studies on the WT behaviours and control systems are needed in order to improve their design and operation. This paper presents a complete DFIG WT model and its overall control systems. The interaction of the WT control level with the DFIG control level has been presented in the paper. A FSM with IGBTs and a SAM are implemented. The former is suitable for detailed studies of short-time transient behaviours while the latter is more sensible for investigating mechanical responses over a longer time scale. Mathematical models of individual control-loops are developed and tested. The r esults are consistent with the PSCAD/EMTDC simulations. These are used to adjust the controller bandwidth and damping in the software model. DS of DC-link to power changes is analysed for different operating points. Analysis shows that higher stiffness can be achieved by increasing the grid voltage or the DC-link voltage. It can be observed that torsional oscillations may be excited by a fast pitch controller. This indicates the two-mass shaft model is necessary for studying the controller coordination especially when pitch control is involved. What is more, it can induce electrical oscillations and may further impose stresses on power electronics or grid stability. 6 Acknowledgment The authors thank the Engineering and Physical Sciences Research Council for supporting this work through grant no. EP/H018662/1 – Supergen ‘Wind Energy Technologies’. 7 References 1 Li, H., Chen, Z.: ‘Overview of different wind generator systems and their comparisons’, IET Renew. Power Gener., 2008, 2, (2), pp. 123–138 2 Chondrogiannis, S.: ‘Technical aspects of offshore wind farms employing doubly-fed induction generators’. PhD thesis, University of Manchester, 2007 3 Ekanayake, J.B., Holdsworth, L., Wu, X., Jenkins, N.: ‘Dynamic modeling of doubly fed induction generator wind turbines’, IEEE trans. Power Syst., 2003, 18, (2), pp. 803–809 4 Hansen, A.D., Sorensen, P., Lov, F., Blaabjerg, F.: ‘Control of variable speed wind turbines with doubly-fed induction generators’, Wind Eng., 2004, 28, (4), pp. 411–434 5 Hopfensperger, B., Atkinson, D.J., Lakin, R.A.: ‘Stator-flux-oriented control of a doubly-fed induction machine with and without position encoder’, IEE Proc. Electr. Power Appl., 2000, 147, (4), pp. 241–250 6 Pannell, G.: ‘Grid fault ride through for wind turbine doubly-fed induction generators’. PhD Thesis, Newcastle University, 2008 7 Peña, R., Clare, J.C., Asher, G.M.: ‘Doubly fed induction generator using back-to-back PWM converters and its application to variable speed wind-energy generation’, IEEE Proc. Elecr. Power Appl., 1996, 143, (3), pp. 231–241 8 Slootweg, J.G., de Haan, S.W.H., Polinder, H., Kling, W.L.: ‘General model for representing variable speed wind turbines in power system dynamics simulation’, IEEE Trans. Power Syst., 2003, 18, (1), pp. 144–151 9 Slootweg, J.G., Polinder, H., Kling, W.L.: ‘Dynamic modelling of a wind turbine with doubly fed induction generator’. IEEE Proc. on Power Engineering Society, Vancouver, BC, Canada, 2001 10 Todd, R.: ‘High power wind energy conversion systems’. EngD thesis, University of Manchester, 2006 11 Akhmatov, V.: ‘Analysis of dynamic behaviour of electrical power systems with large amount of wind power’. PhD thesis, Ørsted DTU, Technical University of Denmark, 2003 12 Muyeen, S.M., Ali, M.H., Takahashi, R., et al.: ‘Comparative study on transient stability analysis of wind turbine generator system using different drive train models’, IET Renew. Power Gener., 2007, 1, (2), pp. 131–141 13 Lorenz, R.D., Schmidt, P.B.: ‘Synchoronized motion control for process automation’. Industry Applications Society Annual Meeting, October 1989, pp. 1693–1698 14 Bossany, E.A.: ‘The design of closed loop controllers for wind turbines’, Wind Energy, 2000, 3, (3), pp. 149–163 15 Wright, A.D.: ‘Modern control design for flexible wind wurbines’. Report no. TP-500-35816, NREL, 2004 16 Wright, A.D., Fingersh, L.J.: ‘Advanced control des1ign for wind turbines-part 1: Control design, implementation, and initial tests’. Report no. TP-500-42437, NREL, 2008 8 Appendix Parameters that are used in the DFIG WT model rating 4.5 MVA rated wind speed 12 m/s cut-in wind speed 3.5 m/s rotor diameter 112 m gear box ratio 1:120 H turbine 3s H generator 0.5 s spring constant (K s ) 0.7 pu/el.rad generator self-damping 0.032 pu turbine self-damping 0.022 pu mutual damping 1 pu stator voltage (L–L, RMS) 1 kV stator/rator turns ratio 1 L s 0.09241 pu R s 0.00488 pu L r 0.09955 pu C dc_link 3.5 pu L m 3.95279 pu V dc 1kV www.ietdl.org IET Renew. Power Gener., 2013, Vol. 7, Iss. 2, pp. 180–189 189 doi: 10.1049/iet-rpg.2012.0222 & The Institution of Engineering and Technology 2013 . 2012 doi: 10.1049/iet-rpg.2012.0222 ISSN 1752-1416 Doubly-fed induction generator wind turbine modelling for detailed electromagnetic system studies Ting Lei, Mike Barnes, Meliksah Ozakturk Power Conversion. ‘Grid fault ride through for wind turbine doubly-fed induction generators’. PhD Thesis, Newcastle University, 2008 7 Peña, R., Clare, J.C., Asher, G.M.: ‘Doubly fed induction generator using back-to-back. induction generator wind turbines’, IEEE trans. Power Syst., 2003, 18, (2), pp. 803–809 4 Hansen, A.D., Sorensen, P., Lov, F., Blaabjerg, F.: ‘Control of variable speed wind turbines with doubly-fed induction