Simulation model of a Permanent Magnet Synchronous Generator for grid studies.

Transcription

1 International Conference on Renewable Energie and Power Quality (ICREPQ 14) Cordoba (Spain), 8 th to 1 th April, 214 exçxãtuäx XÇxÜzç tçw céãxü dâtä àç ]ÉâÜÇtÄ (RE&PQJ) ISSN X, No.12, April 214 Simulation model of a Permanent Magnet Synchronou Generator for grid tudie F. Belloni, R. Chiumeo, C. Gandolfi, A. Villa 1 1 Ricerca ul Sitema Energetico RSE.p.a. Via Rubattino 54, 2134, Milano, Italy Phone number: , belloni@re-web.it, Riccardo.Chiumeo@re-web.it, Chiara.Gandolfi@re-web.it, Alberto.Villa@re-web.it Abtract. Permanent Magnet Synchronou Generator are an emerging technology in wind power application. A implified Thevenin equivalent imulation model of a wind generator ha been developed in the ATPDraw environment and validated by comparing it dynamic with that of a Matlab/Simulink detailed model. The implified model include alo power electronic circuit, for interfacing the generator to a MV primary ditribution grid, and their control. A 2,5 MVA wind generator wa imulated in ATPDraw in order to ae flicker everity dependence upon different grid and circuit parameter. Simulation reult how a trong flicker everity dependence on grid hort circuit power and X/R line characteritic, in particular when generator upplie reactive power to the grid, a required by ome National tandard. Key word Permanent Magnet Synchronou Generator, imulation model, power electronic, flicker everity aement. 1. Introduction Onhore and offhore wind power i continuouly growing in Europe and worldwide. For intance, wind power hare of total intalled power capacity in EU ha increaed fivefold ince 2; from 2,2% in 2 to 11,4% in 212 [1]. Thi trend i confirmed alo in the firt half of 213 [2], with a 22 target of 23 GW of intalled wind power in EU [1]. The average power ize of new wind turbine i alo increaing, reaching the value of 3,8 MW in 213 [2]. In the recent year, a regard the on-hore plant, which repreent the majority of plant currently intalled, it i becoming a trend to intall average power plant, up to 2 MW, baed on Permanent Magnet Synchronou Generator (PMSG) intead of doubly-fed induction generator, more diffued in the pat. The firt, in fact, allow to decouple frequency and voltage level generated by the wind turbine from the network uing full power converter. Only in recent year, the power electronic ha reached a maturity that allow to make PMSG competitive compared to the traditional olution, in term of cot and payback time. In addition, the poibility to eaily vary the control trategie of power electronic converter allow to manage the generator in a much more veratile way than the traditional one and, if neceary, to provide auxiliary ervice to the network [3], [4]. Fig. 1. Block cheme of a Permanent Magnet Synchronou wind Generator and power electronic tage for grid connection. Grid connected PMSG are interfaced to electric grid through power electronic circuit. A typical cheme of a PMSG baed wind ytem i hown in Fig. 1. The ue of two controlled power electronic tage (rectifier and inverter) connected through a DC-link allow: a complete decoupling between grid and generator; the control of the active power generated by the PMSG, performed through the rectifier; the control of active and reactive power upplied to the grid, performed through the inverter. Sometime a diode bridge i ued a rectifier connected at the output of the PMSG. Even though more expenive, the active rectification i today preferred for larger intallation due to the higher efficiency and for the better controllability of the upplied power. The increaing importance PMSG are gaining puhe for tudie devoted to analye of interaction between the generation ytem and the grid. Such activitie require the development of imulation model of PMSG, power electronic converter and their control RE&PQJ, Vol.1, No.12, April 214

2 The aim of thi work i to decribe the implementation, in the ATPDraw environment, of a implified model of a PMSG interconnected to a ditribution grid with power electronic circuit. The validation of the PMSG model i performed comparing it behaviour with a complete model developed in the Matlab/Simulink environment. The implified model i then employed to ae the flicker emiion of a 2,5 MVA wind generator for different grid condition. Even though the tudy cae reported in thi work are quite imple, the decribed modelling approach can be profitably employed for more complex tudie [5]. 2. PMSG theoretical model Even though the theoretical model of a PMSG wind generator i reported in literature, it' worth recalling here ome baic theoretical concept. A hown in Fig. 1, the ytem i compoed by a wind turbine, a PMSG, a controlled rectifier and a controlled Voltage Source Inverter with an output filter and a MV/LV tranformer for grid coupling. It i poible replacing the controlled rectifier with a diode bridge rectifier and a DC/DC converter, but thi implementation uually ha lower efficiency and le control flexibility. A. Wind turbine The power extracted from the wind by the turbine blade i given by: P 1 ρπ C p λ β ) v w = r (, (1) where ρ i the air denity, r i the blade radiu, v w i the wind peed and C p i the power coefficient, depending on the tip peed ratio λ and on the pitch angle β of the blade. λ i equal to the ratio of the blade peed and the wind peed. The dependence of C p on λ and β i hown in Fig. 2 [6]. di di e [ v r i + nx i ] d N = ω d d q q (2) xd q ωn x q [ v ri ( x i + ψ ) n] = (3) T =ψ i + dn M q q q d d ( xd xq ) idiq [ T + T Bn] e m M (4) = (5) where: i d, i q : generator current over d and q axe; v d, v q : generator voltage over d and q axe; ω N : electrical angular peed; n: turbine rotational peed; x d, x q : tator reactance over d and q axe; r : tator reitance; ψ M : rotor permanent magnet flux; T e, T m : electromagentic torque and mechanical torque; B: friction coefficient. All quantitie of (2) (5) are expreed in a d-q rotating frame ynchronou to the PMSG rotor flux. In a round rotor machine (x d = x q ), from (4) it emerge that the generator active power i proportional to the quadratureaxi current i q which i the main electrical control parameter. C. Controlled rectifier The controlled rectifier circuit allow the generation of three voltage at the output of the PMSG with wanted amplitude and angle by acting on the open/cloe tatu of the ix controlled witche. The current upplied by the PMSG depend on thee voltage and on the leakage inductance of the generator. Starting from (2) (5), it i convenient to expre voltage over d-q axe, o that the circuit can control the direct and quadrature current upplied by the generator. Even though different control cheme are applicable, here the o called field oriented control i ued [3]. Control block cheme i repreented in Fig. 3. In the adopted control cheme, the rotating peed of the PMSG rotor i compared to a reference value, calculated by a Maximum Power Point Tracking (MPPT) loop, and the peed error i proceed by a Proportional-Integral-Derivative (PID) regulator, in the form: H ki ( ) = k p + kd (7) PID + where k p i the proportional gain, k i the integral gain and k d the differential gain. The rotating peed reference i choen by a MPPT in order to maximize (1). Fig. 2. Power curve dependencie from tip peed ratio at different pitch angle. B. Permanent Magnet Synchronou Generator The dynamic equation governing the operation of a PMSG are: Fig. 3. Rectifier control block cheme RE&PQJ, Vol.1, No.12, April 214

3 The output of the PID regulator repreent the q-axi current reference for the rectifier, while the d-axi reference i kept to zero in order to minimize loe. Both current reference are compared with the relevant current value and error are proceed by two Proportional- Integral (PI) regulator, in the form: H ki ( ) = k p (8) PI + where again k p repreent the proportional gain and k i the integral gain. Output of the regulator are further proceed for obtaining three modulating ignal which are ent to a Pule Wih Modulation (PWM) tage for the generation of 6 command ignal for the controlled witche of the rectifier. D. Voltage Source Inverter The Voltage Source Inverter (VSI) topology employed in thi work i a three-leg bridge, with IGBT witche. The control cheme for the VSI i repreented in Fig. 4. Fig. 4. Voltage ource inverter control. Adopting uch a reference frame allow controlling eparately the inverter active power, proportional to the i d current, and the inverter reactive power, proportional to the i q current. The i d reference value i calculated by an outer voltage loop by proceing through a PI regulator the difference between the DC-link voltage and a reference value. In thi way, the DC-link voltage i maintained contant and all the active power coming from the rectifier i upplied to the grid. In fact: dv P DC = ic = irect, DC = iinv, DC rect = P inv where V DC i the DC-link voltage, i C i the DC-link capacitor current, i rect,dc i the DC current of the rectifier, i inv,dc i the DC current of the inverter, P rect i the active power of the rectifier and P inv the active power of the inverter. The q-axi current reference i uually et to zero in order to minimize conduction loe, but different value can be poible in ome cae, according to different National tandard. For intance the Italian tandard [7] require that the inverter hould exchange reactive power in cae of grid under-voltage or over-voltage. For thi reaon, a uitable outer loop for the calculation of the i q reference i added to the control. The coupling of the inverter to the MV ditribution grid i made with a LV/MV tranformer which winding ratio and their relative phae diplacement mut be taken into account within the control of the inverter. (9) Again, the control aim at the regulation of the inverter current repreented on the rotating d-q axe. In thi cae, rotating frame i ynchronou to the grid voltage. Fig. 5. ATPDraw implementation of the wind generator ytem. 2. Wind generator implified model in ATPDraw A implified model of a wind PMSG ytem ha been developed into the Alternative Tranient Program Draw (ATPDraw) environment 1. The ATPDraw implementation of the generator ytem i repreented in Fig. 5, where main part are put into evidence. 1 ATPDraw, verion 5.7p RE&PQJ, Vol.1, No.12, April 214

4 A. Permanent Magnet Synchronou Generator model The PMSG i here repreented through an ideal voltage three phae generator with leakage inductance and reitance connected in erie to the output (Thevenin equivalent) [8]. Such a implification in the generator repreentation, that hould be validated, allow reducing the computational complexity of evaluating the olution of the equation (2) (5). In thi way, it i poible to inert the implified PMSG model within larger ytem in order to perform tudy of Ditributed Generator (DG) integration within complex ditribution grid [5]. The model validation i dicued in the next ection. B. Power electronic circuit model Both controlled rectifier and VSI are repreented with their witching behaviour. For implicity, witche are repreented only with their conduction tatu, being ON or OFF, dependent on a logical gate ignal. At the ACoutput of the inverter three inductor are connected and a hunt filter i added for high frequency harmonic attenuation. Detailed control of both the circuit, according to the cheme of Fig. 3 and Fig. 4, have been implemented uing ATPDraw model. Since a Thevenin equivalent i ued a PMSG model, no rotating peed regulation i needed. For thi reaon, the rotating peed control loop of Fig. 3 i not implemented in the implified model. LV/MV tranformer with nonlinear magnetizing curve i employed for grid coupling. C. MV ditribution grid model For thi work, a implified Thevenin equivalent model of a MV ditribution grid i employed. The hort circuit power and the X/R characteritic of the grid at the point of connection of the wind generator can be varied by changing the equivalent line impedance. 3. Wind generator detailed model in Matlab/Simulink A detailed model of a Permanent Magnet Synchronou Generator wa developed in the Matlab/Simulink environment by implementing (2) (5) through Simulink block, a repreented in Fig. 6. The input of the ytem are the voltage generated by the controlled rectifier, which wa alo repreented in Simulink a an averaged model [9]. The input of the PMSG are the voltage generated by the rectifier, expreed in the rotating d-q frame, and it output are the d-axi current, the q-axi current and the angular peed of the generator, which are ued a input for the rectifier control. The inverter i not repreented here, but a reitor i connected in parallel to the DC-link capacitor in order to drain the exact power produced by the PMSG. A 2,5 MVA wind generator wa ued in thi work. Main deign parameter of the machine are given in TABLE I. TABLE I. 2,5 MVA wind generator main deign parameter. Rectifier Nominal power A Nr 2,5 MVA Nominal AC voltage V CA,N 4 V Switching frequency f w 195 Hz DC-Link Nominal voltage V DCN 11 V Maximal voltage V DCmax 14 V Capacitance C DC 1 mf Inverter Nominal power A Ninv 2,5 MVA Inductance L inv 7,64 µh (4%) Filter reitance R filt,inv 1 mω Filter capacitance C filt,inv 5 mf (fr = 814 Hz) Switching frequency f w 195 Hz LV/MV Tranformer Nominal power A Ntr 3 MVA Leakage inductance L k 3,5 µh (7%) Winding ratio n 2/22 Winding coupling Dy11n PI regulator DC voltage PI regulator Current loop regulator Rectifier control H PI,r () Inverter control H PI,vinv () H PI,iinv (),1 + 2, ,9, ,28 Fig. 6. Simulink detailed implementation of a PMSG. 4. PMSG implified model validation The validation of the implified model i made by comparing it dynamic behaviour with that of the Matlab detailed model. Some difference hould be conidered though: in the Thevenin equivalent active power i proportional to the d-axi current, while in the detailed model it i proportional to the q-axi current; imilarly, the reactive power i proportional to the q- axi current for the implified and to the d-axi current for the detailed model; the implified model rotational peed i fixed, while in the detailed model it can vary around the reference value during tranient; the voltage output of the detailed model can vary, while for the Thevenin equivalent it i fixed at it nominal value. Dynamic comparion have been made for the 2,5 MVA PMSG. Simulation reult for both model are reported in Fig. 7, where the behaviour of i d and i q for both model are repreented in cae of a tep change of generated active power. A it can be een, the dynamic of the implified model i very cloe to that of the detailed model, a part from the unavoidable difference already pointed out. The detailed model eem to how le dumped dynamic, probably due to the abence of paraitic in the model of the rectifier and to the miing interaction with the inverter RE&PQJ, Vol.1, No.12, April 214

5 dynamic. For the purpoe of thi paper the two model are equivalent, alo conidering that both the DC-link capacitor and the inverter decouple the PMSG from the ditribution grid. For thi reaon, the flicker aement reported hereafter were performed with the ATPDraw implified model only Id ref Id 6 Id ref Id a) b) Iq ref Iq ref 6 Iq 25 Iq c) d) Fig 7. Dynamic behaviour of generator current calculated from the detailed model of a PMSG (a and b) and from the implified model (c and d) in cae of a tep change of the active power. It hould be noted that i d and i q exchange their role in the two model. 5. PMSG flicker aement For the calculation of the flicker emiion of the PSMG, a flickermeter digital model wa implemented into Matlab according to [1]. The flickermeter model wa fed by grid voltage calculated through the ATP implified model. Due to imulation time contrain, only the hort term flicker coefficient P t wa evaluated and it wa calculated for 1 ([1] require a calculation of P t over 1 minute). Even though the hort term flicker coefficient here calculated i not in accordance to the tandard [1], it i ueful to ae the influence of ome grid and generator parameter on flicker everity. In order to produce flicker in the grid, active power variation of the primary ource were imulated, a in cae of wind gut. In the implified model power variation were implemented by uperimpoing a awtooth waveform with a given frequency to the d-axi current reference in the control loop of the rectifier. Variation of ±,8 pu (±2 kw) of active power were conidered, correpondent to variation of ±,8 pu of the current reference. Three type of parameter variation were conidered [11]: grid hort circuit power at the point of connection of the inverter; line X/R characteritic; capacitance of the DC-link. P t value are repeatedly calculated varying each conidered parameter over a given range. Simulation are performed with generator upplying power at different power factor. The main reult are reported in the next figure. In particular it poible to ay that: during generation/conumption of reactive power the P t increae and thi index preent revere dependency from the grid Short Circuit (Fig. 8); P pu = 2.5 MVA co(φ) = 1 co(φ) =,9 ind. co(φ) =,9 cap Grid hort circuit power [p.u.] Fig. 8. Flicker everity dependence on hort circuit power of the MV grid at the point of connection of the generator RE&PQJ, Vol.1, No.12, April 214

6 the P t index i more influenced by the reitive part of the line impedance independently from grid hort circuit power (Fig. 9); P = 4 MVA = 6 MVA co(φ) =,9 ind. - P co(φ) =,9 cap. -P X/R Fig. 9. Flicker hort term index dependence on X/R line characteritic. the P t index i le influenced by the DC-link capacitor, in Fig. 1 a 4% variation of the nominal value of the DC capacitor ha been conidered. P pu = 1 mf co(φ) =,9 ind. - P co(φ) =,9 cap. - P C [p.u.] Fig. 1. Flicker everity dependence on DC-link capacitance. 6. Concluion The paper preent the implementation of a implified Thevenin equivalent model of a Permanent Magnet Synchronou Generator (PMSG) for wind power application. Such a implification in the generator repreentation allow reducing the computational complexity of evaluating the olution of the dynamic equation. In thi way, it i poible to inert the implified PMSG model within larger ytem in order to perform tudy of Ditributed Generator integration within complex ditribution grid. The implified model of the PMSG i developed in the ATPDraw environment, together with model of power electronic circuit and their control. The dynamic behaviour of the implified model are compared with thoe of a detailed PMSG model developed in Matlab/Simulink and a good compliance i found. The implified model i employed for the aement of flicker everity from a 2,5 MVA wind power ytem connected to a MV ditribution grid for different grid and generator parameter value. Simulation reult how a trong dependence of the flicker everity on the hort circuit power of the grid and on the X/R line characteritic, in particular when the generator upplie reactive power to the grid. Simulation alo how a weak dependence of the flicker everity from the DC-link capacitance. Even though the reported cae tudie are quite imple, uch a implified modelling approach i uited to be employed in complex grid tudie, where a number of generator are connected imultaneouly at a complex grid. Acknowledgement Thi work ha been financed by the Reearch Fund for the Italian Electrical Sytem under the Contract Agreement between RSE S.p.A. and the Minitry of Economic Development - General Directorate for Nuclear Energy, Renewable Energy and Energy Efficiency in compliance with the Decree of March 8, 26. Reference [1] European Wind Energy Aociation, Wind in power European tatitic, web ite: /Wind_in_power_annual_tatitic_212.pdf. [2] European Wind Energy Aociation, The European offhore wind indutry - key trend and tatitic 1t half 213 : /EWEA_OffhoreStat_July213.pdf. [3] O.B.K. Hanaoui, J. Belhadj, M. Elleuch, Direct drive permanent magnet ynchronou generator wind turbine invetigation, in Journal of electrical ytem, Vol. 4, Iue 3, September 28, pp [4] E. Maheri, A. Khedher, M. Faouzi Mimouni, The wind energy converion ytem uing PMSG controlled by vector control and SMC trategie, International Journal of Renewable Energy Reearch, Vol. 3, N.1, 213. [5] F. Belloni, R. Chiumeo, C. Gandolfi,, Permanent magnet wind generator: control trategie to manage voltage unbalance, International Conference on Renewable Energie and Power Quality, ICREPQ212, Santiago de Compotela, Spain, 28-3 March 212. [6] K. Belmokhtar, M. Lamine Doumbia, K. Agboou, Modelling and Power Control of Wind Turbine Driving DFIG connected to the Utility Grid, in Proc. of the International Conference on Renewable energie and Power Quality, ICREPQ 211, La Palma de Gran Canaria (Spain), 13th to 15th April, 211, pp [7] CEI -16, Regola tecnica di riferimento per la conneione di Utenti attivi e paivi alle reti AT ed MT delle impree ditributrici di energia elettrica, Italian tandard. [8] J. Mur-Amada, A. A. Bayod-Rujula, Flicker emiion of wind farm during continuou operation, IEEE Tranaction on Energy converion, vol. 17, Iue 1, March 212, pp [9] N. Mohan, T.M. Undeland, W.P. Robbin, Power Electronic: Converter, Application, and Deign, John Wiley and Son inc., Third edition. [1] IEC , Electromagnetic compatibility (EMC) part 4: teting and meaurement technique ection 15: flickermeter functional and deign pecification, Ed. 2., 21. [11] L. Meegahapola, A. Perera, Impact of wind generator control trategie on flicker emiion in ditributed network, 15th IEEE International Conference on Harmonic and Quality of Power, ICHQP212, Hong Kong, 17-2 June 212, pp RE&PQJ, Vol.1, No.12, April 214