Torque and power limitations of a shunt connected inverter based WECS

Transcription

1 Proceedings of the 5th WSEAS Int. Conf. on Power Systes and Electroagnetic Copatibility, Corfu, Greece, August 3-5, 5 (pp ) orque and power liitations of a shunt connected inverter based WECS AON KUPERMAN*, RAU RABINOVICI*, GEORGE WEISS** *Electrical and Coputer Engineering Departent Ben-Gurion University of the Negev Beer-Sheva ISRAE **Electrical Engineering Departent Iperial College ondon UK Abstract: - A variable speed wind energy conversion syste based on a squirrel cage autonoous induction generated is covered in this paper for operation in high wind speeds. In this case, the turbine ust liit the fraction of the wind power captured so that safe electrical and echanical loads are not exceeded. Different control strategies based on induction achine characteristics for fixed-pitch turbines are discussed. Extended siulation results are presented for ain control approaches. Key-Words: Renewable energy, variable speed, power and torque control, wind turbine, induction generator. Introduction Over the past two decades, a great deal of effort was ade to develop different types of wind energy conversion systes (WECS). Wind is one of the fastest growing sources of alternative power in the world today. WECS present two operating odes, according to the way the wind turbine is connected to the grid. In the first, fixed-speed ode, the turbine-generator unit is directly connected to the grid, fixing the generator rotational speed to be around the grid frequency. In the second, variable speed ode, power converters are inserted between the generator and the greed, allowing the rotational speed and electrical frequency to vary independently. Usually the regulation objectives rely on the wind speed. Variable speed wind turbines have three ain operation regions. First region includes the turbine starting-up. In low and ediu speeds, the objection is to capture as uch energy as possible (region two) [, ]. Since the power electronics circuitry is able to control the generator output, variable speed ode is useful in this operating region. When the power or speed liit of a wind turbine is reached, they should be liited in order to prevent the generator and turbine overloading. his happens at high wind speeds [3]. his is the region three. his paper focuses on this region. iitation of the power output in high winds in necessary on all wind turbines, otherwise the turbine will be overloaded. he usual ethods for power liitation are stall regulation or pitch regulation. On turbines with noral stall regulation, the blades are rigidly fixed to the turbine hub and cannot be turned around their longitudinal axis during operation. he pitch setting angle between blades and hub is adjusted during coissioning of the turbine. It ay require fine-tuning for site-specific conditions. Stall regulated blades are designed so the airflow over the blades theselves causes higher drag in high winds and thereby autoatically restricts the power output. By this passive use of the aerodynaic characteristics of the blades, the power regulation is siple and rugged under all conditions. he peak loads in high wind are oderate. On the other hand, noral stall regulation has the disadvantage that the axiu power output ay depend on the air density and on the surface roughness of the blades. herefore, changes in the axiu power output ay occur fro suer to winter and dirty blades ay cause the peak power to drop. On pitch regulated turbines, the blades are ounted on the rotor hub with turntable bearings. hey can be turned around their longitudinal axis during operation. In high winds the pitch setting of the blades is continuously adjusted away fro stall point, reducing the blade lift to yield precisely the axiu power specified. his requires a rather coplicated active regulation syste, which can be sensitive towards turbulence in high winds. herefore, pitch regulation in practice requires a special generator with fully or partially variable speed, allowing for a slight acceleration in rotor speed at wind gusts. Otherwise, the active regulation is unable to follow the variations of the wind and excessive peak loads will occur [4]. he cobination of stall

2 Proceedings of the 5th WSEAS Int. Conf. on Power Systes and Electroagnetic Copatibility, Corfu, Greece, August 3-5, 5 (pp ) and pitch control have been recently used by soe anufacturers. However, it is a very coplex and expensive ethod. Fixed-pitch control strategies are considered in this paper. Siilar work was presented for a back-to-back converter based WECS in []. his paper presents a different converter configuration. Induction achines operating as autonoous generators fro renewable energy sources have received uch attention recently. Autonoous induction generators (AIG) are cheap, siple and robust. However, while they are capable to generate active power, they are unable to produce the reactive power needed for their own excitation. he classical solution of this proble is to connect capacitors in parallel with the AIG. he ain drawback is then the lack of ability to control the terinal voltage and frequency under non-constant load and speed conditions. herefore, capacitor-excited AIGs have poor voltage and frequency stability [5, 6]. Shuntconnected voltage source converters (VSCs) iprove the AIG output voltage and frequency. In addition, their rating is around % of the AIG rating, reducing the size and cost of the overall syste [7-9]. herefore instead of using a full rating controlled rectifier in variable speed WECS, it is possible to use an uncontrolled diode rectifier together with AIG-shunt connected VSC cobination. Such a syste, shown in Fig., is presented in this paper. It consists of a horizontal axis wind turbine, connected through a gear box to a squirrel-cage AIG. A shunt connected voltage sourced inverter is connected to generator terinals to regulate the output voltage and frequency. he output voltage is then rectified by a diode bridge and injected to the grid by a grid connected inverter. he disadvantage of this schee is the non-constant DC voltage at the uncontrolled rectifier output. the syste was presented, there are two ain control actions: MPP and power control. MPP is achieved by controlling the electrical frequency to follow a known trajectory. he generator output power is easured and copared to the axiu available power at given frequency. he difference is processed and the result is a new frequency coand to the constant V/Hz controller. On the grid side, the grid connected inverter is controlled to supply defined aounts of active and reactive power to the grid. he shunt connected inverter should supply/absorb no active power in steady state. herefore the reference active power for the gridconnected inverter should be equal to the generator output power. he reactive power reference can be chosen arbitrarily. his paper is organized as follows: Sections II and III describe the wind turbine and drive train, induction generator is addressed in section IV, control strategies are explained in section V, siulation results are given in section VI and the paper is concluded in section VII. Wind urbine Characteristics he power captured by a fixed-pitch wind turbine ay be presented as [] =, () 3 t( w) rpr CpVw P V ρ air density (kg/ 3 ) C p power coefficient of wind turbine V ω wind velocity (/s) R blade radius (). A wind turbine is characterized by its power coefficient (C p ) to tip-speed ratio (λ) curve, power coefficient is the ration between the energy captured by a turbine and the energy available in the wind; the tip-speed ratio (SR) is the ratio between the linear speed of the blade tip and the wind speed. he SR is given by l wt ΧR =, () Vw Fig. : Shunt connected inverter based WECS and ain control loops According to [], the region operation of ω t turbine rotational speed (rad/s) R blade radius () V ω wind velocity (/s). It is obvious fro () that for a fixed-speed turbine

3 Proceedings of the 5th WSEAS Int. Conf. on Power Systes and Electroagnetic Copatibility, Corfu, Greece, August 3-5, 5 (pp ) SR is inversely proportionally to the wind speed and varies across a wide range, because the rotor speed of induction generator connected to a fixedspeed turbine is alost constant (depending on slip) while the wind speed varies significantly. A typical C p (λ) curve is shown in Fig.. It is apparent fro () that the power production fro the wind turbine is axiized by operating at axiu power coefficient. herefore, the ain idea behind the variable-speed turbine applications is to keep the C p at its axiu value C p by controlling the rotor speed to follow the wind speed so that SR reains constant at its target value λ. his control action is also called axiu power point tracking (MPP). he turbine data is given in appendix. It is obvious that the rotor speed should be changed instantaneously, so that the extracted power would follow the ax(p in ) curve in order to extract axiu power fro the wind if there were no losses in the gear and the generator. Fro (), the wind speed is given by V w wt ΧR =. (3) l Hence, equation () can be rewritten as P 3 ιr ω 3 t( wt) = rpr Cp κ ϊ wt λl ϋ. (4) When operating at λ = λ, Eq.() can be rewritten as l w t ΧR w =. (5) V Cobining () and (4), the equation of the ax(p in ) curve is given by 3 ι R ω 3 in = t wt = rp p κ w ϊ t ax( P ) P ( ) R C λl ϋ. (6) It is well known, that the wind speed cannot be precisely and reliably easured. he MPP can be achieved by changing the rotor speed according to (6) without easuring the wind speed, if there were no losses in the gear and the generator. 3 Drive rain Modeling he acceleration and deceleration of the generator rotor speed is described by the following equation []: ( J J ) g D G G g g + t w + wg = t - g J g generator inertia J t turbine inertia G gear ratio t turbine torque g generator torque D daping constant. he turbine torque is given by t t (7) Pt =. (8) w It is clear fro Fig. (6), that when the power extracted fro the wind is higher than the power deanded by the load, the rotor accelerates and vice-versa. In MPP operation, all the power extracted fro the wind is transferred to the load; generator rotor accelerates and decelerates in order to track the axiu power curve. Power Coefficient, Cp ip-speed Ratio Fig. : Power coefficient versus SR 4 Induction Generator An induction achine is odeled using the following equations [3]: disd wrk r ks wr u =- i sd sd + i sq + i rd + irq + dt s s r s s disq wrk r wr ks usq =- i rq sd - i sq - i rd + i + dt s s s r s ( 9) dird kr wrkrs wrr ksu = i sd rq sd - i sq - i rd + i + dt s s r r r dirq wrk r s kr wr i r ku s sq = sd + i dt sq + i rq rd - i - s = 3 ( i i - i i ) g rq sd rd sq s ( l, C ) p r r r

4 Proceedings of the 5th WSEAS Int. Conf. on Power Systes and Electroagnetic Copatibility, Corfu, Greece, August 3-5, 5 (pp ) s = s + r = r + s r - s = r = r s r - s ks = s kr = r s = s Rs r = r Rr isd, isd- instantaneous values of direct- and quadrature- axis stator current coponents respectively and expressed in the stationary reference frae ird, i - instantaneous values of direct- and rd quadrature- axis rotor current coponents respectively and expressed in the stationary reference frae s, - self- and leakage inductances of the stator s respectively r, - self- and leakage inductances of the rotor r respectively - agnetizing inductance s, r - stator and rotor transient tie constants respectively u sd, u sd - instantaneous values of direct- and quadrature- axis stator voltage coponents respectively and expressed in the stationary reference frae w - angular rotor speed r Magnetizing reactance is shown in Fig. 3. electrical frequency F in that should be aintained in order to keep the power flow unidirectional (generator operation only). Generator output power versus electrical frequency curves for different wind speeds are shown in Fig. 4. Maxiu power curve can also be coputed for optial power capture in region. herefore easuring the wind speed, rotor speed or the electrical frequency are equivalent actions. Induction achine external speed-power characteristics and possible output power curves at different wind speeds are shown in Fig.5. Any point under the achine characteristic curve is possible; any point above the curve can daage the achine and should be avoided and in presence of high wind speeds power liitation should be perfored ax ( Pout ) Vw = 8 /s Vw = 9 /s Vw = /s Vw = /s Vw = /s Fin Per unit frequency, F Fig. 4: Generator per phase output power versus electrical frequency Fig. 3: Measured agnetizing reactance 5 Control Strategies It was shown in [], that instead of onitoring the rotational speed, it is possible to onitor the electrical frequency (which is known fro constant V/Hz controller) in order to perfor MPP. It should be noted, that there is a iniu value of Fig. 5: Generator output power characteristics In addition, speed liitation should be also considered ainly because of two reasons. First, a certain level of acoustic noise should not be reached. Second, physical liitations of turbine and generator rotational speed exist and ust be taken into

5 Proceedings of the 5th WSEAS Int. Conf. on Power Systes and Electroagnetic Copatibility, Corfu, Greece, August 3-5, 5 (pp ) account. However, power liitation is ainly considered, because the syste usually reaches power liit when the speed is still in the perissible range [4,5]. Consider a generator with output power curves at different speeds as shown in Fig. 6. At noral wind speeds, generator output power should track the ax(p out ) curve to extract axiu power fro the wind. At high wind speeds, different scenarios can occur. If the upper speed liit (v ax ) is reached before the power liit, fro point A the syste no longer follows the axiu power curve. he electrical frequency is kept constant by the constant V/f controller; therefore the rotation speed can only grow slightly with the slip. If the wind speed increases, we ove up fro point A to point B, the power liit is et. If the wind speed further increases, the output power should be kept constant. Because the speed liit is also reached, the only way to keep the power at its rated value is to ove left fro the point B along the P ax curve, by decreasing the rotation speed and electrical frequency. he ain drawback of this strategy is the torque behavior. twice the rated speed, therefore oveent to the right is preferable to evade the excess torque possibility. Soeties, if the axiu rotational speed liit is soewhat flexible, instead of following the AB part of the target power curve (Fig.6), the syste follows the AB curve of Fig. 8, which is not strictly vertical, i.e. the angle θ is less then 9 o. Using this strategy, disadvantages of near-rated fixed speed, like severe torque and output surge with wind turbulence, are avoided [6]. herefore setting the angle θ to o we gain constant electrical output; setting the angle θ to 45 o we gain a constant torque operation (constant power to speed ratio), which is a very desirable feature Increasing orque Constant Power C Decreasing orque Pax v ax v ax C B D A Per unit speed, v Fig. 7: orque behavior for different power liitation strategies ax ( Pout ) Per unit speed, v Fig. 6: Different scenarios for speed and power he torque, which is given by the ration between power and speed, increases if the power is kept constant and the speed decreases and there is a danger of excessive torque. If the power liit is reached before the upper speed liit (v ax ), the ax(p out ) curve is followed by the syste up to point C, the rated power is reached. If the wind speed is further increasing, the syste can ove on the ax(p out ) line either left or right to point D. he oveent to the left is characterized by increased torque, while oveent to the right causes the torque to decrease, as shown in Fig. 7. Usually, if the acoustic noise is out of concern, the axiu allowable speed is around B A Per unit speed, v Fig. 8: Constant torque liitation strategy 6 Siulation Results and Discussion he presented syste was odeled and siulated using MAAB and SIMUINK packages [7]. DC link and grid-connected inverter represented by a variable resistance. he resistance value is changed by the power controller according B*

6 Proceedings of the 5th WSEAS Int. Conf. on Power Systes and Electroagnetic Copatibility, Corfu, Greece, August 3-5, 5 (pp ) to the power deand. he reactive power reference is set to be zero. Only the first haronic of the shunt-connected inverter was taken into consideration. First, the syste was siulated under constant-power liitation. he wind speed is shown in Fig. 9(a). he generator output power and torque are shown in Fig. 9(b) and 9(c), respectively. It is clear that the power is liited to 8W at the highspeed wind region. he torque is decreasing when the speed, which is shown in Fig. 9(d), together with electrical frequency, is increasing for constant power. he turbine power coefficient is presented in Fig. 9(e). It is clear that it oves away fro its optiu value during the power liiting operation. Fig. presents the generator output power locus as function of tie. It is clear that the trajectory of the power is siilar for both region and region 3. For the increasing wind speed the power follows the axiu power curve, and then enters the power liiting region. For decreasing wind speed, the power is liited by the rated value, and then enters the axiu power tracking region. he second siulation was perfored under constant-torque liitation. he angle θ was set to 45 o to keep a constant torque in speed liiting operation. he siulation results are shown in Fig.. he wind speed is shown in Fig. (a). he generator output power and torque are shown in Fig. (b) and (c), respectively. It is clear that the power increases proportionally to speed at the highspeed wind region, assuring the torque reains constant. Generator speed and electrical frequency are shown in Fig. 9(d). he turbine power coefficient is presented in Fig. 9(e). It is clear that it oves away fro its optiu value during the speed liiting operation. Fig. presents the generator output power locus as function of tie. It is clear that the trajectory of the power is siilar for both region and region 3. For the increasing wind speed the power follows the axiu power curve, and then enters the speed liiting region and vice versa. 7 Conclusion A speed sensorless wind energy conversion syste based on induction generator that is solid-state excited by a shunt connected voltage source converter operation in high wind speeds, was presented. he turbine liits the fraction of the wind power captured so that safe electrical and echanical loads are not exceeded. Different control strategies based on induction achine characteristics for fixed-pitch turbines were discussed. Extended siulation results are presented for the constant power and constant torque control strategies. It was shown that the syste operates well in both region, the axiu available power is extracted fro the wind; and region 3, the power or the speed should be liited to avoid overloading of the turbine or excess acoustic noise. References: [] P.W. Carlin, A.S. axson, E.B. Muljadi, he History and State of the Art of Variable-Speed Wind urbine echnology, Wind Energy, vol. 6, pp. 9-59, 3 [] A. R. Henderson, C. Morgan, B. Sith, H. C. Sorensen, R. J. Barthelie, B. Boesans, "Offshore Wind Energy in Europe A Review of the State of the Art," Wind Energy, vol. 6, pp. 35-5, 3 [3] F. D. Bianchi, R. J. Mantz, C. F. Christiansen, "Power Regulation in Pitch-Controlled Variable Speed WECS Above Rated Wind Speed," Renewable Energy, vol. 9, pp. 9-9, 4 [4] [5] B. Singh,, Induction generators a prospective, Electric Machines and Power Systes, vol. 3, pp , 995 [6] M. Eris, H. Ertan, M. Deirekler, B. Saribatir, Y. Uctug, M. Sezer, I. Cadirci, Various induction generator schees for wind-electricity generation, Electric Power Systes Research, vol. 3, pp. 7-83, 99 [7] M. Brennen, A. Abbondanti, Static exciter for induction generators, IEEE rans. Ind. Appl., vol. 3(5), pp. 4-48, 977 [8] R. Rabinovici, A. Kuperan, Autonoous Induction Generator with Solid-State Reactive Power Excitation, in Proc. of nd IEEE Conf. In Israel, [9] A. Kuperan, R. Rabinovici, Overview of Solid-State Excitation Schees for Autonoous Induction Generators, in Proc. of 3 rd IASED Conf. On PES, Marbella, Spain, 3 [] A. Kuperan, R. Rabinovici, A shunt connected inverter based variable speed wind turbine generation, Subitted to Electrootion5, Switzerland, 5 [] E. Muljadi, C. P. Butterfield, "Pitch- Controlled Variable Speed urbine Generation," IEEE rans. Ind. Appl., vol 37(), pp. 4-46, [] N. Horiuchi,. Kawahito, "orque and power liitations of variable speed wind turbines using pitch control and generator power control," IEEE Power Engineering Society Suer Meeting, vol., pp [3] P. Vas, Electrical Machines and Drives, New York: Oxford University Press, 99

7 Proceedings of the 5th WSEAS Int. Conf. on Power Systes and Electroagnetic Copatibility, Corfu, Greece, August 3-5, 5 (pp ) [4] A. Miller, E. Muljadi, D.S. Zinger, "A variable speed wind turbine power control," IEEE rans. Energy Conv., vol. (), pp. 8-86, 997 [5]. hiringer, J. inders, "Control by variable rotor speed of a fixed-pitch wind turbine operationg in a wide speed range," IEEE rans. Energy Conv., vol. 8(3), pp. 5-56, 993 [6] R. Cardenas, G.M. Asher, W.F. Ray, R. Pena, "Power liitation in variable speed wind turbines with fixed pitch angle," in Proc. of Opportunities and Advances in International Power Generation, pp , 996 [7] MAAB Users Guide, Mathworks Inc., 5 Vw, [/s] Pg, [W] g, [N] F, v - -, p.u Pg, [W] Vw, [/s] g, [N] F, v - - p.u Cp. Cp.3 Generator Output Power, Pg [W] tie, [sec] Fig. 9: Siulation results - (a) wind speed, (b) generator output power, (c) generator torque, (d) generator speed (dashed) and electrical frequency (solid), (e) turbine power coefficient Electrical Frequency, F p.u. Fig. : Generator output power locus tie, [sec] Fig. : Siulation results - (a) wind speed, (b) generator output power, (c) generator torque, (d) generator speed (dashed) and electrical frequency (solid), (e) turbine power coefficient Generator Output Power, Pg [W] Electrical Frequencu, F p.u. Fig. : Generator output power locus