Đang tải... (xem toàn văn)
JOURNAL OF SCIENCE & TECHNOLOGY • No 95 2013 OPTIMAL DESIGN OF A PERMANENT MAGNET SYNCHRONOUS GENERATOR FOR WIND TURBINE SYSTEM THIET KE TOI UU MAY P H A T DIEN D 6 N G B O NAM CHAM VfNH CUXJ CHO H S[.]
JOURNAL OF SCIENCE & TECHNOLOGY • No 95 - 2013 OPTIMAL DESIGN OF A PERMANENT MAGNET SYNCHRONOUS GENERATOR FOR WIND TURBINE SYSTEM THIET KE TOI UU MAY P H A T DIEN D N G B O NAM CHAM VfNH CUXJ CHO H S T H N G PHONG DIEN Nguyen The Cong, Nguyen Thanh Khang Tran Due Hoan Hanoi University of Science and Technology Institut National Polytechnique de Toulouse Received February 25, 2013; accepted April 22, 2013 ABSTRACT The exploitation of wind energy is developed in recent year because it has a source of clean, non-polluting and renewable energy Nevertheless, in the development of wind energy, the demand in research and development is always focus on the efficiency energy and minimized cost of wind turbine system This paper descnbes the methodology to design, optimization and simulation of a 15kW at low wind speed (6m/s) the design will be focused to Permanent Magnet Synchronous Generator (PMSG) dedicated to wind turbine systems Firstly, the model of wind turbine system direct-dnve with wind speed, wind turbine will be presented Secondly, a coupled electromagnetic, thermal model used in design ofa PMSG will be demonstrated The developed genetic algorithm (GA) approach is presented in three parts: the basic principles of the GAs the constrained optimization conversion and the multiobjective (power maximization and mass minimization) optimization method Finally, an analysis of the multiobjective optimization method robustness is performed and applied in the case of 15 k]M PMSG According to the obtained results, the optimal design of a PMSG by genetic algorithms to solve the efficiency wind energy is simulated and analysis Keywords: Wind Energy, PMSG, Genetic Algorithm T M TAT Khai thdc ndng luting gid dang diroc quan tdm vd phdt triin m^nh mS giai doan hi$n vi dd Id m^t ngudn ndng luvng tdi tao sach, khdng gdy nhiim Tuy nhidn, qud trinh phdt triin vd Cmg dung phong didn, cd hai khd khdn lim nhit Id qud trinh ndng cao hi$u suit vd gidm thiiu tdi da chl phi cOa hd thdng Bdi bdo ndy s§ trinh bdy phirong phdp thiit ki tdi uv vd md phdng cho hd thing didn gid 15kW d vdn tic gid trung binh thip Id 6m/s, qud trinh thiit ki s§ t$p tnjng vdo tii iru hda mdy phdt ding 6$ nam chdm Vinh cu-u Phin ddO cda bdi bdo s6 trinh bdy md hinh hda v$n tic gid vd tudiine phin tiip theo tdc gid s6 di vdo md td md hinh thiit ki mdy phdt v&i cdc nghiin cuv vi didn tir tnfdng tin thit vd md hlnh nhi$t Phux>ng phdp tdi uv hda mdy phdt phong di$n bdng thudt todn gen vdi cdc hdm myc tidu (ci,rc d^i hda cdng suit vd ci/c tiiu hda khdi luong mdy phdt) v&i cdc rdng budc thiit ki s§ dugc trinh bdy phin ba cua bdi bdo Trong phin cudi cOa bdi viit, nhdm tdc gid sg c/jpn mOt mdy phdt cu thi tir kit qud tdi uv di md phdng vd phdn tich kit qud INTRODUCTION confrol Optimum wind energy exfraction is achieved by running the Wind Turbine '^^"'^^^ ^^^ ^°'*^g^ °^ *h^ P'^SG in many different ways strategies have made it possible to Generator (WTG) in variable speed because of Opportune wind turbine architecture is the higher energy gain and the reduced stresses Using the Permanent Magnet Synchronous Generator (PMSG) the design can be even more simplified by its high efficiency and advantages in start-up condition [1],[2] However, die recent advancements in power electronics and designed using mathematical model of the system Once the model is made and tested sufficiently, the controller for an optimal command sfrategy is developed so the wind turbine can perform always in die maximum power point JOURNAL OF SCIENCE & TECHNOLOGY • No 95 - 2013 MODELING WIND TURBINE SYSTEM The design composes the wind speed, turbine and PMSG as Fig.l and its losses model also estimate for the calculation of output power Fig Power coefficient of wind turbine Fig I System design: Wind speed, wind turbine and PMSG 2.1 Wind speed model In order to robust modeling, the wind speed have to variation in interval sufficient large Thus, the stochastic model of wind speed by decomposing a discrete Fourier transformation with the mean value 6m/s is used in this works [3] The wind speed so that expressed as: V^ (0 = + 0,2 sin(0,1047/) + sin(0,26650 (1) +sin(l, 2930r) + 0.2 sin(3,6645/) 2.2 Wind turbine model The conversion efficiency of the system from wind power to electrical power is given by the product of the power coefficient Cp [3], alternator efficiency and power-electronic converter efficiency Overall efficiency is defined as the average conversion from energy available in the wind to electrical energy produced - Static model: The mechanical power developed by a wind turbine rotor varies according to the equation: P,=-pC^iA)7rR^V: n„ where (2) (3) ,/?„,- blade radius [m] p = air density [kg/m^], r„, mechanical torque from wind blades p^^.m] Cl^ angular velocity (rotation speed) The type of wind turbine in this work is the three-bladed with the radius R,y=\Om (Fig.l) and the power coefficient Cp may be expressed as a function of the tip speed ratio A = R^Q.^/V^^ given by equation (e.g Fig.2): Cp [A.) = -0.003002992/1' -0.001168U^ +0.154 - Dynamic model: The dynamic equation for interaction between turbine-PMSG is written by equation of torque: '^ - T,„ = ^ ^ ^ + / « " * (4) dt where /"„,, T^m are respectively the wind turbine and electromagnetic of PMSG torques, J„, and f„ being the totai wind turbine inertia and viscous friction coefficient (Typically in this study, J„= 5.5N.m^ and/.=0.5) 2.3 Analytical sizing of permanent magnet motors The most important in the design PMSG model is the variables chosen have to be independent Thus, the sizing model of PMSM in this work has been developed in [4] This model depends on geometrical characteristics (number of pole pairp, number of slots per pole and phase Nspp, radius/length ratioJ^ =rj//^ and slot depth/ bore radius ratio Rdr=d Ir)^ well as electromechanical features (current density J^, yoke induction By, base speed Q^, corresponding power P^ at the base point and nominal voltage F,) The geometrical characteristics of PMSG are illustrated on Fig With this topology, we have to define the fundamentals dimensions that are calculated detail in reference [5], JOURNAL OF SCIENCE & TECHNOLOGY «No 95-2UI3 L^=^L„+L, (8) A typical value of the stator per phase resistance at rate load and average ambient temperature is: whereCT^,,is the conductivity of copper and /, = 7r(r, +0.5d,)/p is the end winding r Bore radius H Air gap I, Length active d Slot depth w, Slot width wr Tooth width d Rotor yolce thickness Stator yoke thickness dy The magnetic flux is approximated by ,=2K,N^^B„rJ,N^ 2.4 Losses model ofthe wind turbine system Fig PMSG topologies and nomenclature of geometrical dimensions In order to calculate the output power of the generator, the inductance and resistance of the armature winding must be known In the calculation of the tooth tip leakage inductance and magnetizing inductance, the permanent magnets are assumed to have the same permeability as air The main inductance Lm can be calculated as: (5) where V„ is the number of conductors per slot The slot leakage inductance can be computed as L,=2fi,lrPN,ppA^,Nl (6) where A^, is the specific permeance of the slot leakage For the proposed generator, with equal current in the upper and lower conductor in the slots, the average specific permeance of die slot leakage for the one coil side in the slot can be expressed as Ih, Xb,+b,) (10) Ih, b^+bj 62 (7) The corresponding stator inductance Z,,is given by the following relation: In the losses model of wind turbine and PMSG, we have examined the mechanic losses in turbine, copper loss and Iron loss in the PMSM Mechanic losses in the turbine: The copper losses of PMSG at a winding can be calculated from the resistance R, and the phase current /,: P, =3R.I^ (12) The core losses have to be calculated for each part ofthe iron core They are divided into hysteresis losses and eddy current losses As the different values of induction for the yoke and the teeth of stator, so the core losses in yoke are calculated as follows [5] Therefore, the core losses total in the PMSM is Pf.r=pc-^p^^pi^''+p:i (13) Finally, the output power of system is calculated by: P^.Jul=P.,na-P.ec-PM-Pj (14) 2.S Thermal model The proposed thermal model of PMSG in this paper is based on a lumped-parameter network of thermal resistances [5] The heat transfer modes considered are the conduction JOURNAL OF SCIENCE & TECHNOLOGY * No 95 - 2013 and convection modes The thermal horizontal mode is neglected because of the relatively low temperature difference between the generators parts Finally, the temperatures in the all regions of PMSG are found from differential equations: T = A7'+Bu OPTIMIZATION OF GENETIC ALGORITHM parameters are mentioned in Tab.l, its output power and weight are 15kW and 250kg, respectively (15) PMSG BY The optimization ofthe PMSG is carried out using a multiobjective genetic algorithm [6], Genetic algorithm base on the mechanics of natural selection and natural genetics, and implement in the most simplistic way, the concept of survival of the fittest The detail methodology is presented in [5] Fig Multiobjective optimization process In this optimization, two objectives are the maximized output power calculated by (14) and minimized the weight of PMSG (reduced material and maintenance cost) The optimization also has to respect five constraints to ensure the PMSG feasibility in relation to the parametric variation of design variables in the optimization process (Fig 4), these constraints concerned the number of conductors in one slot, the maximum temperature associated with the copper windings in the PMSG, the demagnetization limit of the magnets and the minimum of slot width RESULTS AND DISCUSSION Fig shows the global Pereto-optimal front of output power and weight of PMSG obtained by optimization process with 100 individuals and 200 generations In this figure, we present an optimal solution whose : lor;ri>ndiClon / X Fig.5 Optimization results Pareto-optimalfront In order to validate the design of optimal solution exfracted from the Pareto-optimal front and obtained with the less accurate sizing, we take the simulation of wind turbine system, this simulation is taken by Matlab/simulink as Fig with the wind speed is calculate by (1) during 30s (Fig 7) In this simulation, to respect the electrical circuit simulation, phases of PMSG are connected directly with a diode bridge and debited on DC bus 600V This simulation topology enforces the methodology of this concept because it is fully "passive" (without the power electronic and confrol) and can be demonstrated the natural adaptation between wind turbine and optimized PMSG Tab I Parameters of optimal PMSG Geometric parameters Bore radius r, [m] 0.382 Length active Ir [m] 0.77 Air gap stator-rotor g [m] 0.011 Magnet thickness /„ ]m\ 0.044 0.014 Slot width w, [m] Tooth width Wrfm] 0.014 Stator yoke thickness dy 0.012 rmi Rotor yoke thickness d \m 0.012 Electromasnetic parameters Resistance R, fl^l 12.3 0.52 Inductance L, [HI 12.0 Flux [Wbl Nominal voltage F,[V] 300 Nominal torque fNml 3300 Number of pole pairs p 20 J JOURNAL OF SCIENCE & TECHNOLOGY « No 95 - 2013 Rotation speed of PMSG is shown on Fig naturally depends on the variation of wind speed with the mean value 3.5 rad/s (33.4 rpm) and the maximal value of electromagnetic torque of PMSG and wind turbine is 4.5 kNm (Fig.9) we can confirm that the wind turbine system in this study is low speed and high torque Fig Rotation speed of PMSG ilOOO !>»^VW^ f\/*^ • 3000 2000 1000 PMSG [ Fig Torque of wind turbine and PMSG • •I r Fig6 Wind turbine system simulation in Matlab/simulink Power production of wind turbine and PMSG is shown on Fig 10 We note the output power of PMSG is nearly the captured power of wind turbine, particularly in the area of low wind speeds, this result proves efficacy of this concept in objective of exploiting wind system at low wind speed In the area of high wind speeds (>8m/s), the difference power of turbine and PMSG can be explained by the losses in system and the without of power electronic control Fig 10 Wind turbine and PMSG power Three phases current of PMSG on 300 ms is zoom out on Fig 11, we observe that phase current in PMSG is sinusoidal and symmefric Note that the current of PMSG is proportion ofthe wind speed, i.e when the wind speed increases the current increased Fig 11 PMSG current Fig Wind speed '^ V I 'A f^-J CONCLUSIONS This paper tries to optimize and to maximize the power production of wind turbine system at low mean wind speed by optimal design of PMSG All results prove that the model developed Is effectiveness to adaptation between wind turbine and PMSG in systems of 15kW at low base wind speed and also excite a motivation to realize a prototype in the future works JOURNAL OF SCIENCE & TECHNOLOGY * No 95 - 2013 REFERENCES H Slootweg, E De Vries, "Inside wind turbines Fixed vs Variable speed" Renewable Energy Worid magazine, 2003 A Grauers, "Efficiency of three wind energy generator systems", Department of Elecfric Power Engineering, Chalmers University of Technology, Sweden E Hau, "Wind turbines: Fundamentals, Technologies, Application, Economics, 2"'' edition Spring-Verlag, 2006 G Slemon, X Liu, "Modeling and desing optimization of permanent magnet synchronous motors", Elecfric Machines and Power systems, Vol 20, pp.71-92,1992 B Sareni, A Abdelli, X Roboam, D H Tran, "Model simpification and optimization of a passive wind turbine generator" Renewable Energy, Vol 34, N''12, pp 2640-2650, Dec 2009 K Deb, "Multiobjective optimization using evolutionary algorithms", John Wiley & Sons, Chichester, 2001 Author's address: Nguyen The Cong-Tel: 0903418713 -Email: cong nguyenthe@hust.edu Department: Elecfric-Etectronic Equipments School of Electrical Engineering Hanoi University of Science and Technology No 1, Dai Co Viet Str., Ha Noi, Viet Nam ... R^Q.^/V^^ given by equation (e.g Fig.2): Cp [A.) = -0.003002992/1'' -0.001168U^ +0.154 - Dynamic model: The dynamic equation for interaction between turbine-PMSG is written by equation of torque:... Department: Elecfric-Etectronic Equipments School of Electrical Engineering Hanoi University of Science and Technology No 1, Dai Co Viet Str., Ha Noi, Viet Nam ... sizing of permanent magnet motors The most important in the design PMSG model is the variables chosen have to be independent Thus, the sizing model of PMSM in this work has been developed in