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Operation Analysis and Control of DFIG-Based Wind Turbine under Harmonically Distorted Unbalanced Grid Voltage Conditions HAMID ARAB ISLAMIC AZAD UNIVERSITY TEHRAN SOUTH BRANCH TEHRAN, IRAN [email protected] Abstract—Doubly Fed Induction Generators (DFIGs) for their flexible control system and low price converters are taken into consideration as a first choice for wind turbine’s generator, these days. In this paper, it’s proposed a control system which keeps wind turbine connected to grid in Non-ideal condition like harmonically distorted and unbalanced grid voltage condition. Vector control method is used for designing the proposed control system. The proposed voltage sequence decomposer makes it possible to control both of unbalanced and harmonically distorted grid voltage conditions at the same time. Here, the aim of control system is to reduce pulsations of electromagnetic torque and total active output power of DFIG. For proving the accurate operation of proposed control system in such a kind of condition, Simulations of the proposed control strategy for a DFIG-based wind power generation system are carried out using MATLAB/Simulink software. Keywords- Wind Turbine – DFIG – Harmonically Distorted Unbalanced conditions – PI-R controller – Vectorcontrol I. INTRODUCTION A ccording to the fact that doubly fed induction generators (DFIGs) are widely used these days, the main drawback of them, sensitivity to grid voltage properties, has got more importance. Effects of balanced and unbalanced voltage sags were studied in [1]. Depend on the amplitude of voltage sag, system could be controllable or not. This problem for DFIGs' operation under unbalanced grid voltage conditions was well investigated in [2]. Also, operation and control of grid connected DFIG-based wind turbines under harmonically grid voltage conditions have been interested for many researchers during the last few years [3-4]. Harmonically distortion of stator voltage could bring some problems such as resonant pulsations in electromagnetic torque and active/reactive output power. Plenty of control methods are proposed for solving these problems. PI controllers are one of them [1]. This controller is not suitable for encountering Non-Ideal voltage conditions. Recently, control methods based on PI-R controller were widely used in DFIG system for operating in harmonically distorted or unbalanced stator voltage conditions. In this paper, a new control system is proposed for keeping DFIG-based wind turbine connected to the grid in worst NonIdeal grid voltage conditions that is existence of harmonically distortion and unbalanced grid voltage conditions at the same time. This paper is organized as follows. Section II studies behaviors of DFIG and describes operation of Grid-Side and Rotor-Side converters under harmonically distorted unbalanced grid voltage conditions. Section III discusses the proposed PI-R current controllers in detail whereas simulations results are presented in section IV. Finally, section V draws the conclusion. II. ACTIVE AND REACTIVE OUTPUT POWER OF DFIG UNDER HARMONICALLY DISTORTED UNBALANCED GRID VOLTAGE CONDITIONS Under distorted unbalanced grid voltage conditions, there are eight stator voltage components, viz., V sdq , V sdq , V sdq 5 and V sdq 7 . Stator active and reactive power can be calculated as follows [10] 3 ˆ Ps JQs V sdq I sdq 2 Fig. 2 shows the spatial relationships between the stator stationary s s reference frame, rotor r r frame rotating at the angular speed of r , dq and dq reference frames rotating at the respective angular speed of s and s , finally dq 5 and dq 7 reference frames rotating at the angular speed of 5s and 7s , respectively. Electromagnetic power ( Pe ) could be written in matrix form as follows I rd I rq I rd 3L I Pe m r C 5rq I 2Ls s rd55 I rq 5 I 7 rd 7 I rq7 7 Figure 1. Spatial relationships between the stationary αβ reference frame, the rotor r r reference frame, dq , dq , dq 5 and dq 7 Under harmonically distorted unbalanced conditions, if vector F is assumed to be a parameter like voltage, current or flux, it contains both positive and negative sequence components plus 5th and 7th harmonic components. So, F could be expressed as Fdq Fdq Fdq 5 Fdq 7 Fdq Fdq e j 2s t Fdq55e j 6s t Fdq7 7 e j 6s t By substituting (2) in (1), the stator active and reactive power are given, respectively, by Ps Ps 0 Ps sin 2 sin(2s t ) Ps cos 2 cos(2s t ) Ps sin 6 sin(6s t ) Ps cos 6 cos(6s t ) Q s Q s 0 Q s sin 2 sin(2s t ) Q s cos 2 cos(2s t ) Q s sin 6 sin(6s t ) Q s cos 6 cos(6s t ) According to simplification process used in [7-8], stator active and reactive power could be expressed in matrix form as follows Ps 0 Qs 0 Ps sin 2 Qs sin 2 Ps cos 2 Qs cos 2 Ps sin 6 Qs sin 6 Ps cos6 Qs cos6 I rd V sq I rq V sd I rd V sq I V sd 3L m 3 A 5 B I 5rq 2s Ls 2L s V rd55 sq55 I rq 5 V sd 5 I 7 V 7 rd 7 sq 7 I rq7 7 V sd7 7 Where [C] is given in the appendix, too. Also, active and reactive power transferred to grid through GSC contains dc component, sin 2s , cos 2s , sin 6s and cos 6s . Here, the first three above components are just taken into account, for simplification. V sd Pg 0 Q V sq g0 Pg cos 2 3 V sd Pg sin 2 2 V sq V Q g cos 2 sq V sd Q g sin 2 III. V sq V sd V sd V sq V sq V sd V sd V sq V sd V sq V sq V sd V sq V sd I gd V sq I gq V sd I gd V sd I gq V sq PROPOSED CONTROLLER DESIGN A. Phase angle of fundamental voltage and sequential decomposition of stator voltage When the network voltage is unbalanced or harmonically distorted, the traditional PLL approach is not capable of tracking the input voltage accurately because the PI controller used in PLL is only effective to regulate dc components [10]. In [5] a sequence decomposer has been proposed that was suitable just for harmonically distorted conditions, but this section is going to design a new software decomposition method and an improved PLL scheme, suitable for harmonically distorted unbalanced grid voltage conditions. As Fig. 3 shows, firstly, fundamental stator voltage component is extracted in reference frame and then its phase angle will be computed. Where [A] and [B] are given in the appendix. The electromagnetic torque of DFIG is calculated as P Te e where p is the number of pole pairs. r p Figure 2. Block diagrom of the improved PLL, suitable for harmonically distorted unbalanced conditions In reference frame and with taking into account 5th and 7th harmnic components, stator voltage is as follows V V cos(s ) V cos(s ) V 5 cos(5s 5 ) V 7 cos(7s 7 ) V V V 5 V 7 V V sin( ) V sin( ) V sin(5 ) s s 5 s 5 V 7 sin(7s 7 ) V V V 5 V 7 Where s s t and , , 5 and 7 are referred to the initial angle shifts of the corresponding voltage components. After computing the first- and second- and third-order differentials of V and V in (8) with respect to s and gathering V , V ' , V '' and V ''' together into matrix form, it could be written as follows V V V V ' V 5 V '' V ''' K V 7 V V V V ' V V '' 5 V 7 V ''' V V V V ' V 5 V '' V 7 K 1 V ''' V V V V ' V V '' 5 V 7 V ''' Where T s is sample time. Differential components could be calculated for V from the similar way. Thus, the positive and negative sequence and also harmonic components of stator voltage can be calculated by instituting results of (12) for corresponding component in (11). Ⅰ Electromagnetic torque resonant pulse mitigation. 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 5 7 1 25 49 1 125 343 Consequently, inversing the coefficient matrix can make it simplified and result will be as follows 1 1 1 1 5 7 1 25 49 1 125 343 0 0 0 0 0 0 0 0 0 0 0 0 dV V (t ) V (t T s ) V ' d s sT s dV ' V (t ) 2V (t T s ) V (t 2T s ) V '' d s (sT s )2 dV '' V (t ) 3V (t T s ) 3V (t 2T s ) V (t 3T s ) V ''' d s (sT s )2 B. control targets determination and current references The control targets in designed control system are as follows Where [K] is the coefficient matrix 1 1 1 1 K 0 0 0 0 Meanwhile, the first- and second- and third- order differentials of V whit respect to s could also be calculated in the discrete forms as 0 0 0 0 1 1 1 1 Ⅱ Reducing resonant pulses of wind turbines total active power. So, according to control targets listed above, current references are supposed to be calculated. For first target satisfaction (13) must be satisfied, which is possible via RSC as follows: Pe cos 2 0 Pe sin 2 0 Pe cos 6 0 Pe sin 6 0 As a result, according to (6), current references could be obtained. For next control target, based on (3) and (7), the total active power generated by the system can be represented as Ptotal Ps Pg (Ps 0 Pg 0 ) (Ps sin 2 Pg sin 2 )sin 2s t (Ps cos 2 Pg cos 2 ) cos 2s t Ps cos 6 cos 6s t Ps sin 6s t In (21) stator voltage components are obtained in terms of stator voltage differentials. So, if stator voltage differentials could be computed, stator voltage component will be obtained. Thus, to mitigate the oscillation of the total active power output, it is necessary to control the GSC such that with making change in Pg sin 2 and Pg cos 2 oscillating terms with twice the grid frequency should be equal to zero, i.e. Ps sin 2 Pg sin 2 0 Ps cos 2 Pg cos 2 0 Thus, for the GSC, the required reference values for the positive sequence currents can be obtained according to Pg*0 Figure 3. Schematic diagram of the proposed control syestem under harmonically distorted unbalanced grid voltage conditions (or V dc* ) and Q g* 0 . The important matters for different control targets under unbalanced conditions are negative sequence current references [7] that could be obtained by substituting (15) to (7). C. Proposed control system Fig.3 shows the proposed control system. As it is shown, the measured stator voltage is decomposed sequences are used for current references calculation. Also, fundamental component is used for stator voltage phase-angle calculation. Finally, after current references are calculated, all of them will be transferred to the dq reference frame, to avoid the current from decomposing that makes a slow and inaccurate control system. PI-R controller is a reciprocal regulator. It means, if it is regulated for 6ωs, it will work properly for -6ωs. It is composed by two parts. PI part is responsible for dc component of power and the resonant part is in charge of control the resonant power oscillations.[8] In this paper, PI-R controller is used for both of RSC and GSC. Control blocks are shown in Fig. 4 and Fig. 5, respectively. As it’s shown in Fig. 4, PI-R controller in RSC is regulated at ±6ωs for encountering harmonic distortion in grid voltage and at ±2ωs for facing unbalanced stator voltage conditions. According to the fact that GSC plays just a control role for supplying active and reactive power, it is regulated just for mitigating resonant oscillations caused by unbalanced conditions in total output active power. Figure 4. PI-R controller for RSC suitabla for harmonically distorted unbalanced conditions Figure 5. PI-R controller for GSC suitable for unbalanced conditions In this paper, by calculating the unbalance factor [2] and harmonic distortion, in unbalanced or harnomically distorted grid conditions, just needed parts of control system are getting to work. IV. SIMULATION RESULTS Simulations of the proposed control strategies for a DFIGbased wind-power-generation system are conducted by using Matlab/Simulink. The DFIG is rated at 1.5 MW. This rated power is considered as 1 P.u and reference reactive power is assumed to be 0 P.u. Fig. 6 shows the schematic diagram of the tested system. Discrete models are used with a simulation time step of 5 μs. The nominal converter dc link voltage is set at 1100 V. An AC programmable source is used for generating 4 and 3 percent 5th and 7th harmonic components, respectively, in stator voltage during 3-3.2 sec. also, 10% single phase voltage sag occurs to the grid at the same time period. Simulation results for rotor currents that are the main control parameters in proposed control system are shown in Fig. 7. Figure 6. Scheme of the simulated system system to dynamic variations in electrical domain is too much lower than the mechanical one. As a result of this fact, fluctuations in output power and electromagnetic torque caused by changing in wind speed or wind turbulence are negligible. Figure 7. Rotor currents in abs reference frame a. Fig. 10 shows total output active power, stator output active and active power transferred through GSC between DFIG and grid. Since, the size of converters are partial scaled ( about 30% of DFIG rating ), GSC is just responsible for supplying a small portion of needed power and it is obvious in fig10 that the main part of output active power is generated by stator. d -axis component of RSC's current reference and response a. b. stator output active power q -axis component of RSC's current reference and response b. c. active power transferred through GSC d -axis component of GSC's current reference and response c. d. total output active power q -axis component of GSC's current reference and response Figure 8. simulation results for RSC and GSC currents in dq reference frame in addition to their current references d. Fig. 9 shows how rotor current components track rotor current references. Also it’s observable that GSC’s components have the same behaviour. In carried out simulation in this paper, it is assumed that the rotor speed is fixed at 1.2 P.u. it should be paid attention to this point that because of large inertia of wind turbine and generator, mechanical time constant is very larger than electrical time constant.in other words, the response time of electromagnetic torque Figure 9. Simulation results of output active powers and electrmagnetic torque of DFIG As Fig. 9 shows, the active power transferred through GSC is regulated to produce resonant pulsations in opposite of stator active power resonances to mitigate total output active power resonant pulsations. TABLE I. COMPARISON OF VARIOUS DFIG'S CONTROL SYSTEMS OPERATION UNDER DIFFEREN GRID CONDITIONS Control parameter P-R controller [7] PI-R controller [8] PI controller [8] Proposed controller Grid condition unbalanced Harmonically distorted Harmonically distorted Harmonically distorted unbalanced % I s5th - 2.48 4.87 1.53 % I s7th - 1.96 3.85 1.19 % I r29th - 2.08 4.18 3.02 % I r31th - 1.93 3.06 2.81 % I r31th 4.3 - - 1.92 P total Pulsation% 0.5 - - 4.31 T e Pulsation% - 0.35 5.69 3.24 Fig. 9.d shows the electromagnetic torque. As control system in this paper was designed to eliminate resonant components whit 2ws and 6ws angular frequencies in electromagnetic torque, it is observable from Fig. 9.d that electromagnetic torque has a few pulsations under harmonically distorted unbalanced conditions. Table. I is prepared for a better comparison between proposed control system and other related control systems under non-ideal grid conditions. There are some differences between obtained results of this paper and other researches results. These discrepancies derived from different decomposition methods and inequality of grid conditions. According to the table. I the current components in this paper have less harmonic pollutions than the corresponded components in other listed researches. This feature comes from mathematical inheritance of this paper’s decomposition method, whereas other decomposition methods are mostly based on filtering methods. Also, the amplitudes of resonant pulsations of active power and electromagnetic torque resulted from proposed control system are larger than control systems designed in [7] and [8] because the grid condition in this paper assumed to be harmonically distorted and unbalanced at the same time whereas those articles studied just one of these conditions. V. CONCLUSION The fact that DFIG’s rotor windings are connected directly to the grid has been made them very sensitive to disturbances. This paper, made it possible to control operation of DFIG under such a non-ideal conditions by proposing a novel method for stator voltage sequence decomposition and phase angle computation, under harmonically distorted unbalanced grid voltage conditions. At first control targets that are base of current references definition, were determined and then by using PI-R controllers in both of RSC and GSC resonant pulsations of total output active power and electromagnetic torque were mitigated. Superiority of this paper to the other similar researches could be a comprehensive considered condition that is harmonically distortion and unbalance conditions simultaneously. Finally, the obtained results according to the non-ideal conditions of tested system were satisfaction. APPENDIX V sd V sq 0 0 V sd V sq V sd V sq V sd V sq V sd V sq V V sq V sd V sq sd 0 0 0 0 A 0 0 0 0 V 5 V 7 V 5 V 7 0 0 sd 5 sd 7 sq 5 sq 7 V sq5 5 V sq7 7 V sd7 7 V sd5 5 0 0 5 7 5 7 V V V V 0 0 sq 5 sq 7 sd 5 sd 7 7 5 7 5 0 0 V sd 7 V sd 5 V sq 7 V sq 5 V sd5 5 V sq5 5 V sd7 7 V sq7 7 V sq55 V sd55 V sq7 7 V sd7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 V sd V sq V sd V sq V sq V sd V sq V sd V sq V sd V sq V sd V sd V sq V sd V sq V sd V sq V sq V sd V sd B V sq V 5 V 7 sd 7 sd 5 V sq55 V sq7 7 5 7 V sq 5 V sq 7 V 7 V 5 sd 7 sd 5 V sq V sd sd sd sq sq sd sq sq sd sd sq V sq sd sd sq sq sd V V V V V V V V V V V V V V sq55 V sq7 7 V sd7 7 V sd55 V sd5 5 V sd7 7 V sq7 7 V sq5 5 V V sd55 V 5 sq 5 V sq55 V 5 sd 5 V sd7 7 V 7 sq 7 0 0 0 0 0 0 0 0 0 0 V 0 0 V sd 0 V sq 0 V sd 0 0 0 0 0 0 V sq V sq V sd V sd V sd V sq V sq V sq V sd V sq7 7 V sd7 7 0 0 0 0 V sq V sd V sd V sq V sd V sq V sd V sq V sq55 V sd55 V sq7 7 V sd7 7 V sd V sq V sd 0 0 0 0 V sq C V V sq V sd V sq 0 0 0 0 5 sd 7 5 7 V V V V 0 0 V V V V sq 5 sq 7 sd 5 sd 7 sq sd sq sd 5 7 5 7 V 0 0 V sd V sq V sd V sq sd 5 V sd 7 V sq 5 V sq 7 REFERENCES [1] [2] [3] Mansour Mohseni, Student Member, IEEE,SyedM.Islam, Senior Member, IEEE, " Impacts of Symmetrical and Asymmetrical Voltage Sags on DFIG-Based Wind Turbines Considering Phase-Angle Jump, Voltage Recovery, and Sag Parameters " IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 26, NO. 5, MA 2011. M. Itsaso Martinez, Gerardo Tapia, Ana Susperregui, Member, IEEE, " DFIG Power Generation Capability and Feasibility Regions Under Unbalanced Grid Voltage Conditions" IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 4, DECEMBER 2011.I. S. Jacobs and C. P. Bean, “Fine particles, thin films and exchange anisotropy,” in Magnetism, vol. III, G. T. Rado and H. Suhl, Eds. New York: Academic, 1963, pp. 271–350. Changjin Liu, Frede Blaabjerg, Fellow, IEEE, " Stator Current Harmonic Control With Resonant Controller for Doubly Fed Induction Generator " IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 27, NO. 7, JULY 2012. [4] [5] [6] Van-Tung Phan, Member, IEEE, and Hong-Hee Lee, Member, IEEE. " Control Strategy for Harmonic Elimination in Stand-Alone DFIG Applications With Nonlinear Loads " IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 26, NO. 9, SEPTEMBER 2011. Hailiang Xu, Student Member, IEEE, et al." Operation of WindTurbine-Driven DFIG Systems Under Distorted Grid Voltage Conditions: Analysis and Experimental Validations" IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 27, NO. 5, MAY 2012. Lingling Fan, Senior Member, IEEE and et al. "Harmonic Analysis of a DFIG for a Wind Energy Conversion System "IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 25, NO. 1, MARCH 2010. [7] Jiabing Hu, Student Member, IEEE, and Yikang He, Senior Member, IEEE. " Reinforced Control and Operation of DFIG-Based Wind-PowerGeneration System Under Unbalanced Grid Voltage Conditions " IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 24, NO. 4, DECEMBER 2009. [8] Jiabing Hu, Member, IEEE, and et al. " Dynamic Modeling and Improved Control of DFIG Under Distorted Grid Voltage Conditions" IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 1, MARCH 2011. [9] Tao Sun, Zhe Chen, Senior Member, IEEE, and Frede Blaabjerg, Fellow, IEEE. "Flicker Study on Variable Speed Wind Turbines With Doubly Fed Induction Generators "IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 20, NO. 4, DECEMBER 2005. [10] G. Abad, J. Lo ´pez, M. A. Rodr ıguez, L. Marroyo, and G. Iwanski. " Doubly Fed Induction Machine " Modeling and Control for Wind Energy Generation, First Edition. 2011 the Institute of Electrical and Electronic Engineers, Inc. Published 2011 by JohnWiley&Sons, Inc.