Eropean Association for the Development of Renewable Energies, Environment and Power Qality (EA4EPQ) International Conference on Renewable Energies and Power Qality (ICREPQ ) Santiago de Compostela (Spain), 8th to 0th March, 0 wo Control Strategies for Aggregated ind rbine Model with Permanent Magnet Synchronos Generator M. J. Mercado-Vargas a, Fjin Deng b, O. Rabaza a, E. Alameda-Hernandez a, Zhe Chen b a Section of Electrical Engineering. Department of Civil Engineering Granada University Camps of Fente Neva, 807, Granada, Spain Phone: +4 958 400 (ext. 448), e-mail: mjmercado@gr.es, ealameda@gr.es, ovio@gr.es b Department of Energy echnology Aalborg University Pontoppidanstræde 0, 90, Aalborg, Denmark Phone: +45 5 8 84, email: fde@et.aa.dk, zch@et.aa.dk Abstract. he behavior of an aggregated wind trbine model with permanent magnet synchronos generator is sted when a wind flctation or a grid strbance happens. wo control strategies are sed for the generator-side converter and they are also sed to evalate the low-voltage ride-throgh capability of the aggregated model. MALAB/Simlink has been sed for the simlations and the reslts show that the proposed aggregated model behavior follows closely the detailed one and, therefore, it is a good way to represent the wind trbine reaction. Key words Aggregated model, permanent magnet synchronos generator, rotor speed control, active power control, lowvoltage ride-throgh capability.. Introdction ind energy penetration in power systems is growing day by day. In former times, when the amont of wind generation was very small compared to other energy otpt technologies, network operator contions sally reqired wind farms to sconnect nder any strbances to avoid damages to the grid. Nowadays, as wind energy penetration in power systems has increased, it is really important that wind generation contines to operate dring grid strbances, and sally the network operator wants to prect the behavior of power grids with a large presence of wind farms. Complete wind farm models represent the reaction of wind trbines to grid strbances and wind flctations. However, as the size of wind farms keep increasing, it is not practical to simlate the entire wind farm by representing each invidal trbine. o simplify and redce calclation time, it is common to represent the whole wind farm by grops of trbines or by one single eqivalent trbine. he aggregated wind farm models with variable speed wind trbines have not been sted for a long time, and most of the investigations are focsed on dobled fed indction generators (DFIG) [], []. However, de to the attractive characteristics of the variable speed wind trbine with permanent magnet synchronos generator (PMSG) verss other configrations [], the need to stdy the aggregated models with PMSG based wind trbines has arisen [4]. In this paper, the variable-speed wind trbines with the detailed model and the aggregated model are introdced. wo control strategies inclng speed control and power control are respectively sed for the aggregated wind trbine model so as to evalate its performance nder the wind flctation and grid strbance, as well as its lowvoltage ride-throgh (LVR) capacity [5], [6].. Detailed model of a wind farm o represent the wind farm behavior, first, its detailed model has been developed accorng to widely sed PMSG wind trbine models in literatre sch as [7], [8]. Fig. shows a typical configration of a PMSG wind trbine. A. Rotor model he mechanical power extracted from the wind can be expressed as follows [7], = π R CP θ P ρ ( λ, ) V () where P is the mechanical power extracted by the wind trbine rotor, ρ is the air density, R is the trbine rotor https://doi.org/0.4084/repqj0.698 8 RE&PQJ, Vol., No.0, April 0
ras, C P is the power coefficient and V is the wind speed. Fig.. Block agram of the wind trbine based on PMSG C P is a measrement of how efficiently the wind trbine converts the wind energy into the trbine mechanical energy, and it is a fnction of the tip speed ratio, λ, and the blade pitch angle, θ. he tip speed ratio is defined as follows, R = V where r is the rotor anglar speed. r λ () It can be conclded that when the pitch angle is eqal to zero, the power coefficient attains its maximm vale for an optimal tip speed ratio and so, the power extracted from the wind is maximized [8]. From () it can be derived that the mechanical torqe is, B. Drive train model λ 5 m = ρ π R C. () P r ( λ, θ ) he mechanical power is transfered to the generator throgh the drive train. In a rect-drive PMSG wind trbine, a gearbox is not needed, becase a mltipole generator allows it to operate at low speeds, therefore the generator is rectly copled to the wind trbine rotor. he drive train is represented by the one-mass model, where all rotating masses (hb, blades and rotor of generator) are represented by one element. his model is defined by the following eqation, m dr e = J eq (4) where m is the mechanical torqe, e is the electrical torqe and J eq is the eqivalent inertia of the rotating system. C. Permanent magnet synchronos generator model he dynamic model of the PMSG has been bilt in the d-q reference frame rotating at electrical speed with the position of the rect axis aligned along the permanent magnet flx position. he stator voltage eqations in d-q reference frame have the following form [7], sd sd = Rs sd Lsd + e Lsq (5) sq ( L ) sq sq = Rs sq Lsq + e ψ (6) m sd sd where sd, sq are the generator voltages, i sd, i sq, are the generator crrents, R s is the stator winng resistance, L sd, L sq are the stator indctances, Ψ m is the magnet flx and e is the generator anglar speed. As the PMSG ses a srface magnet generator, the indctances in d-q reference frame are identical and the electromagnetic torqe can be expressed as [7], e = p p ψ m where p p is the nmber of pole pairs. D. Power converter model he PMSG is rectly connected to the grid throgh a back-to-back (BB) converter. It consists of two identical voltage sorce converters and a capacitor which is connected between them. As the power losses are ignored, the dynamic behavior of the DC-link can be expressed by the following eqation, d dc q (7) = ( I dc R I dc I ) (8) C where dc is the DC-link voltage, C is the vale of the DClink capacitor, I dc-r is the rectifier crrent and I dc-i is the inverter crrent. he generator-side converter, which acts as a rectifier, converts the generator s low AC freqency to DC. he DC voltage is stabilized by the DC-link capacitor and converted frther by the grid-side converter into 50 Hz AC, which is spplied to the grid. A fll scale power converter decoples the generator from the grid and allows fll controllability of the system. E. Protection system model hen a voltage p occrs at the AC otpt terminals of the wind trbine, the maximm active power that the wind trbine can export to the grid is redced in proportion to the terminal voltage redction. An energy imbalance appears in the wind trbine compared to its operation at nstrbed terminal voltage becase the otpt power is qickly redced by the inverter controller while the inpt power extracted from the wind cannot be redced as qickly. hen the LVR capability of the wind trbine is analyzed, it is clearly seen that the impact of the energy imbalance is significant. As proposed in [6], instead of storing the excess energy in the DC-link, a resistor is inserted in the DC circit to ssipate the excess energy and restore the balance. his braking resistor balances otpt torqe variations and https://doi.org/0.4084/repqj0.698 9 RE&PQJ, Vol., No.0, April 0
prevents the DC-link voltage from rising excessively. he resistor is controlled sing a power electronic switch, as Fig. shows. Fig.. Braking resistor scheme [6] controllers; after the PI, compensation terms are added to improve the dynamic response. he d-axis crrent reference is kept at zero becase, as eqation (7) shows, the generator torqe may be controlled rectly by the q-axis crrent component [7]. In that way, the torqe will be obtained by sing the minimm vale of the stator crrent amplitde. In control strategy I, the q-axis crrent reference is obtained from the rotor speed controller as shown in Fig., and the rotor speed reference is obtained from eqation (). F. Grid model he dynamic model of the grid connection when selecting a reference frame rotating synchronosly with the grid voltage space vector is the following [7], = cd Rg L + g L (9) = cq Rg i L g L i (0) where, are the grid voltages, cd, cq are the voltage components of grid side converter, i, i, are the grid crrents, R g is the grid resistence, L, L are the grid indctances and g is the grid freqency. As the d-axis of the reference frame is oriented along the grid voltage ( r = + j 0.), the active and reactive g powers can be expressed as, Q P = g g = ( ) (). () From () and (), it can be dedced that the active and reactive power control can be achieved by controlling the rect and qadratre crrent components, respectively [8].. Control system A. Control strategies Fig.. Generator side converter control scheme Control strategy I In control strategy II, the q-axis crrent reference is obtained from the active power controller as shown in Fig. 4, and the active power reference is obtained from the following eqation [8], where, K P e _ ref = K () opt r C 5 p _ max opt = ρ π R. (4) λopt On the other hand, the objectives of the grid-side converter controller are to keep the DC-link voltage constant and to control the reactive power delivered to the grid. o achieve these objectives, the control system is also strctred in a nested-loop, as shown in Fig. 5. he inner loop controls the grid crrents and the oter one controls the DC-link voltage. he q-axis grid crrent is kept at zero in order to maintain the reactive power eqal to zero. he aim of the generator-side converter controller is to work at the rotor speed that extracts the maximm power from the wind withot exceeng the wind trbine working limits. o achieve this objective, the control system is strctred in a nested-loop consisting of an inner loop to control the stator crrents, and an oter loop to control the rotor speed or the active power depenng on the control strategy selected. In both control strategies, the reqired d-q components of the voltage vector are derived from two PI crrent Fig. 4. Generator-side converter control scheme Control strategy II https://doi.org/0.4084/repqj0.698 40 RE&PQJ, Vol., No.0, April 0
C eq = n C. (7) -he aggregated grid connection dynamic model is also represented by the invidal model, given by eqations (9)-(0), with the grid impedance n times smaller. 5. Simlation reslts Fig. 5. Grid-side converter control scheme B. Pitch angle control system he pitch angle controller is only active in high wind speeds. It prevents the rotor speed or the generator active power, depenng on the control strategy sed, from becoming too high, changing the blade pitch in order to redce Cp and therefore the power extracted from the wind. he wind farm modeled in this paper contains x5 M srface-monted PMSG wind trbines connected to the grid, as shown in Fig. 6. he simlation stdy compares the detailed and eqivalent models of the wind farm taking into accont the fferent generator-side converter control strategies sed in this paper, when a wind step from.70m/s to 5m/s at s is applied to the system. In control strategy I, the pitch angle controller maintains the optimal pitch angle when the generator active power is less than the rated power. hen the power is above the rated vale, this controller limits the generator active power to the rated vale. In control strategy II, the pitch angle controller maintains the optimal pitch angle when the rotor speed is less than the rated speed. hen the rotor speed is above the rated vale, this controller limits the rotational speed to the rated vale. 4. Aggregate model of wind farms An eqivalent model of a wind farm with PMSG wind trbines is proposed in this paper. he model is based on aggregating wind trbines into an eqivalent wind trbine considering the following aspects: -Re-scaled power capacity, which means that its rated power is eqal to n times the rated power of the invidal one, where n is the nmber of aggregated wind trbines. -he aggregated wind trbine is represented by an eqivalent mechanical torqe which is n times the rated mechanical torqe of the invidal wind trbines. n eq = mi i= m (5) -he inertia of the aggregated wind trbine is also n times the inertia of the invidal wind trbines. ' J = n. (6) eq J eq -he aggregated wind trbine is connected to an eqivalent PMSG, which its dynamic model is the same as the invidal generator model, given by the eqations (5)-(6), with the stator impedance n times smaller. -he BB converter is considered ideal and the DC-link voltage between the two voltage sorce converters is constant. he dynamic behavior of the DC-link can be expressed by (8), with a redefined capacitor, A. Control strategy I Fig. 6. Simlation system In control strategy I, when wind speed changes the mechanical torqe increases rapidly, as shown in Fig. 7. he electrical torqe also increases bt p to a certain limit de to generator crrents design restrictions, then there is a torqe imbalance and the rotor accelerates. hen the active power is overrated, the pitch controller changes the blade pitch in order to redce Cp and therefore the mechanical torqe, to restore the energy balance. In adtion, inpt and otpt power of the BB converter mst be eqal, so the changes in the generator power are also transmitted into the grid, as shown in Fig. 8. Fig. 9 shows how the DC-link voltage increases in order to keep the energy balance in the power converter. B. Control strategy II In control strategy II, when wind speed changes the mechanical torqe increases rapidly, as shown in Fig. 0. As the power extracted by the generator from the air kinetic energy is limited to the rated vale, de to the design restrictions, the wind trbine rotor accelerates mch more than in control strategy I. hen rotor speed is https://doi.org/0.4084/repqj0.698 4 RE&PQJ, Vol., No.0, April 0
overrated, the pitch controller changes the blade pitch in order to redce Cp and therefore the mechanical torqe, to restore the energy balance. If Fig. 7 and 0 are compared, it is clearly seen that in control strategy II, the wind trbine system takes more time to restore the steady-state than in control strategy I. Althogh it seems a sadvantage, actally this behavior is smoother so better for the wind trbines components. wold be an energy imbalance between the generator power and the grid power that wold reslt in an ndesirable high vale of the DC-link voltage. However, the braking resistor controls the power ssipation and the energy balance in the system is restored, as Fig. 4 shows. As mentioned before, inpt and otpt powers of the BB converter mst be eqal, so generator power is transmitted into the grid, as shown in Fig.. In this case, there is not an energy imbalance in the power converter and so the DC-link voltage remains constant, as shown in Fig.. Fig. 9. DC-link voltage. Control strategy I Fig. 7. Mechanical and electrical torqes. Control strategy I Fig. 0. Mechanical and electrical torqes. Control strategy II Fig. 8. Active power delivered to the grid. Control strategy I C. LVR capability he LVR capability of the wind farm is considered. he wind speed is given as a constant of.70m/s. A voltage p at point of common copling (PCC) is simlated with a redction of an 80% of rated vale dring second. Note that the maximm power delivered to the grid is rectly related to the terminal voltage redction, as shown in Fig.. ithot protection, there Fig.. Active power delivered to the grid. Control strategy II https://doi.org/0.4084/repqj0.698 4 RE&PQJ, Vol., No.0, April 0
As dedced from all figres shown, the aggregated model follows closely the detailed one in all the cases sted, regardless of the control strategy sed. 6. Conclsions his paper illstrates the behavior of an aggregated model with PMSG wind trbines, nder two control strategies, when a wind flctation or a grid strbance happens. In control strategy I, the generator-side converter controls the rotor speed; while, in control strategy II, it controls the generator active power. hen the wind speed changes rapidly, the simlation reslts show that the power control is a better control strategy becase, althogh the wind trbine system takes longer to reach again the steady-state, its behavior is smoother and therefore, the wind trbines components are less stressed. Fig.. DC-link voltage. Control strategy II Fig.. Active power delivered to the grid hen a voltage p occrs at PCC, the simlation reslts show that the LVR capability of the wind farm is good enogh de to the braking resistor action. Finally, the proposed aggregated model behavior follows closely the detailed one in all the cases sted. herefore, the proposed eqivalent model is a good way to represent the wind farm behavior, redcing calclation time withot losing information. References [] Akhmatov, V.; Kndsen, H. An aggregated model of a gridconnected, large-scale, offshore wind farm for power stability investigations- importance of windmill mechanical system. Electrical power and energy systems, No. 4, pp. 709-77, 00. [] Fernández, L.M. et al. Aggregated dynamic model for wind farms with dobly fed indction generator wind trbines. Renewable Energy, No., pp. 9-40, 008. [] Li, H.; Chen, Z. Overview of fferent wind generator systems and their comparisons. IE Renewable Power Generation, Vol., No., pp. -8, 008. [4] Conroy, J; atson, R. Aggregate modelling of wind farms containing fll-converter wind trbine generators with permanent magnet synchronos machines: transient stability stes. IE Renewable Power Generation, Vol., No., pp. 9-5, 009. [5] Deng, F.; Chen, Z. Low-voltage ride-throgh of variable speed wind trbines with permanent magnet synchronos generator. IECON Proceengs. 009. [6] Conroy, J. F.; atson, R. Low-voltage ride-throgh of a fll converter wind trbine with permanent magnet generator. IE Renewable Power Generation, Vol., No., pp. 8-89, 007. [7] Chinchilla, M.; Arnaltes, S.; Brgos, J. C. Control of permanent-magnet generators applied to variable-speed windenergy systems connected to the grid. IEEE ransactions on energy conversion, Vol., No., pp. 0-5, 006. [8] Fernández, L.M. et al. Operating capability as PQ/PV node of a rect-drive wind trbine based on a permanent magnet synchronos generator. Renewable Energy, No. 5, pp. 08-8, 00. Fig. 4. DC-link voltage https://doi.org/0.4084/repqj0.698 4 RE&PQJ, Vol., No.0, April 0