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A novel power splitting drive train for variable speed wind power generators
Renewable Energy 28 (2003) 2001–2011 www.elsevier.com/locate/renene
A novel power splitting drive train for variable speed wind power generators Xueyong Zhao ∗, Peter Maißer Institute of Mechatronics at the Chemnitz University of Technology, Reichenhainer Strasse 88, 09126 Chemnitz, Germany Received 14 March 2003; accepted 25 March 2003
Abstract In this paper a novel electrically controlled power splitting drive train for variable speed wind turbines is presented. A variable speed wind turbine has many advantages, mainly it can increase the power yield from the wind, alleviate the load peak in the electrical-mechanical drive train, and posses a long life time, also, it can offer the possibility to store the briefly timely wind-conditioned power fluctuations in the wind rotor, in which the rotary masses are used as storages of kinetic energy, consequently, the variable speed wind turbines are utilized in the wind power industry widely. In this work, on the basis of a planetary transmission a new kind of drive train for the variable speed wind turbines is proposed. The new drive train consists of wind rotor, three-shafted planetary gear set, generator and servo motor. The wind rotor is coupled with the planet carrier of the planetary transmission, the generator is connected with the ring gear through an adjustment gear pair, and the servo motor is fixed to the sun gear. By controlling the electromagnetic torque or speed of the servo motor, the variable speed operation of the wind rotor and the constant speed operation of the generator are realized, therefore, the generator can be coupled with the grid directly. At the nominal operation point, about 80% of the rotor power flow through the generator directly and 20% through the servo motor and a small power electronics system into the grid. As a result, the disadvantages in the traditional wind turbines, e.g. high price of power electronics system, much power loss, strong reaction from the grid and large crash load in the drive train will be avoided. 2003 Elsevier Science Ltd. All rights reserved. Keywords: Wind turbine; Novel drive train; Power splitting transmission
∗
Corresponding author. Tel.: +49-371-531-4683; fax: +49-371-531-4669. E-mail address: [email protected] (X. Zhao).
0960-1481/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0960-1481(03)00127-7
2002
X. Zhao, P. Maißer / Renewable Energy 28 (2003) 2001–2011
1. Introduction Variable wind turbines are widely used in the renewable energy technology in the world. This is because, that from economical and technical points of view they have many advantages [1], e.g. they can increase the power yield from the wind, offer the possibility to store the briefly timely wind-conditioned power fluctuations in the wind rotor, smooth the electric power output, alleviate the load peak in the mechanical–electrical drive train, and as a result, achieve a long life time. To realize the variable speed operation, conventionally, a rectifier-dc-link-converter is employed to decouple the variable generator speed and the constant grid frequency [2]. However, this approach has some disadvantages, e.g. the rectifier-dc-link-converter hardware is very expensive on commercial market, especially for large wind turbines, it causes ca 10–15% power losses due to the rectification and inversion, also, there are strong reactions from the grid. To overcome the disadvantages of this conventional approach, some new alternative concepts for the variable speed drive trains were proposed, in which a power converter system is not used any longer and the generator is connected with the grid directly [3,5,6,8]. In [6], a hydrostatic drive train consists of hydraulic pumps, hydraulic storages and hydraulic motors. The variable speed of the wind rotor is realized by controlling the hydraulic pumps and the hydraulic motors connected with the generator. For small wind turbines, a V-belt continuously variable transmission (c.v.t.) with two spring-loaded pulleys is proposed [5], with this solution, the c.v.t. can regulate automatically and adjust its transmission ratio corresponding to the torque applied on the driving pulley. With an adequate design of the springs, a characteristic relationship between the torque and the transmission ratio, which closely approximate the conditions required for optimal system operation, are obtained. In [3], a hybrid variable speed transmission with two stages of planetary transmissions is also given, in which the ring gear speed of the second stage is controlled by three synchronous electrical machines to keep the rotor speed variable, while the speed of the synchronous generator coupled with the sun gear of the second stage is held constant. In this paper, for the variable speed drive trains, a power splitting transmission is proposed, in which an electrically controlled planetary transmission and two adjustment gear pairs are adopted. The transmission posses three input und output shafts, one of the two output shafts is coupled with the generator, another is fixed to the servo motor. By controlling the speed of the servo motor, the generator speed is kept constant and its frequency converter system is deserted, at the same time, the wind rotor runs with the variable speed in correspondence with the timely changeable wind speed to reach the optimal operation.
2. Configuration of the novel variable speed drive train Fig. 1 shows the variable speed drive train, which is composed of the wind rotor, planetary transmission, generator , servo motor and two adjustment gear pairs. The
X. Zhao, P. Maißer / Renewable Energy 28 (2003) 2001–2011
Fig. 1.
2003
Layout of the power splitting drive train.
core of the drive train is the planetary gear set consisting of a central arranged sun gear, a ring gear and several on the planet carrier held planetary gears. The planet carrier is the input of planetary gear set, it is connected with the wind rotor through an adjustment gear pair with speed ratio ir, while the ring gear is the output, which is coupled with the generator also through an adjustment gear pair with speed ratio ig, the sun gear is the adjustment driven by the servo motor, then, the generator is coupled directly and the servo motor is coupled with the electrical grid through a small power electronics system. The speeds of the three shafts of the planetary gear set are arbitrarily adjustable, therefore, the speeds of the wind rotor, generator and servo motor can be arbitrarily selected in accordance with eq. (2). Each speed can be specified by the other two speeds clearly. In this way, the wind rotor speed can be varied, the generator speed holds constant and is directly connected with the grid. This design concept has a lot of advantages, e.g. smaller dynamic tooth contact forces and high efficiency. Both synchronous generator and asynchronous generator with squirrel-cage rotor can be used in the construction draft, in this work, a asynchronous squirrel cage generator is the privileged choice due to its robust construction, relatively low construction cost and operational flexibility as well as good operational reliability. In principle, almost all rotating electrical machines can be selected for the servo motor, however, because of some special characteristics of the wind turbines, some technical and economic requirements have to be considered. The servo motor should be able to run in a wide speed range with reversible rotation direction and have high torque even at low speeds, also, it must be able to bear the short time overloading for the case of very strong gust, certainly, it should be controlled easily and quickly to its expected goals, accordingly, the d.c. machine is a suitable selection.
3. Variable speed operation The main parameter that defines the planetary gear set behavior is its speed ratio i0. To get the angular speed relationship of the planetary gear set, the operation of
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X. Zhao, P. Maißer / Renewable Energy 28 (2003) 2001–2011
the planetary gear set is treated in two special cases. In the first case, the planet carrier is kept standing, the ring gear and the sun gear run in opposite rotation directions. In the second case, with the standing ring gear, the planet carrier and the sun gear run in the same direction. Then, the general operation can be regarded as the overlay of the two special cases, and the speed ratio i0 is calculated according to Willis formula [4] as follows: i0 ⫽
wsun⫺wcarrier wring⫺wcarrier
(1)
whereby wsun, wring and ωcarrier are the angular speeds of the sun gear, ring gear and planet carrier, respectively. If the speed ratio of two adjustment gear pairs are defined by ir = wrot / wcarrier and ig = wgen / wring, then, the kinematic relationship of the drive train in accordance with eq. (1) reads (1⫺i0) ig wrot ⫹ i0 ir wgen⫺ir ig wser ⫽ 0,
(2)
in which wrot, wgen and wser are the angular speeds of the wind rotor, the generator and the servo motor, respectively. From above, by controlling the servo motor speed wser, the rotor speed wrot can be kept variable for the constant optimal tip speed ratio with respect to the changing wind speed in part load operation, while the generator speed wgen holds constant or approximately constant, simultaneously, the rotor power is optimized and split into the generator power and servomotor power [9].
4. Power splitting performance For the recognition of the fundamental characteristics of the power splitting, the drive train is considered in the quasi steady state, that means, that the kinetic energy of the rotary masses are neglected. In reality, there are mechanical tooth and bearing frictions in the drive train, these frictions will cause torque and power losses, which can be characterized by the efficiencies hr, hg for the two adjustment gear pairs and h0 for the planetary gear set. In the case of the standing planet carrier, the efficiency h0 is defined by h0 ⫽ ⫺
冉
冊
Tring Tring wring ⫽⫺ . Tsun wsun i0Tsun
(3)
Tring and Tsun are the torques acting on the shafts of ring gear and sun gear, respectively. Since the flow direction of the rolling power in the sun gear shaft is variable, the efficiency h0 is changing in accordance with the operation states [7]. From eq. (3), the efficiency h0 is rewritten as Tring h0 ⫽ ⫺ i0Tsun with
(4)
X. Zhao, P. Maißer / Renewable Energy 28 (2003) 2001–2011
⫽
Tsun(wsun⫺wcarrier) . |Tsun(wsun⫺wcarrier)|
2005
(5)
Then, the torque relationships in the planetary transmission read Tsun ⫽
1 ·T i0h0 ⫺1 carrier
(6)
Tring ⫽
i0h0 ·T . 1⫺i0h0 carrier
(7)
and
Since the planetary gear set has a negative ratio, the torques Tsun and Tring have the same signs, while they have the opposite sign with torque Tcarrier. From the previous kinematic and kinetic relationships, the power splitting performance is described by Pgen ⫽
i0 ir hg hr h0 wgen ·P ig (i0h0 ⫺1) wrot rot
Pser ⫽
冉
and
(8)
冊
i0 ir hr wgen hr(1⫺i0) ·P , ⫺ 1⫺i0h0 ig (i0h0 ⫺1) wrot rot
(9)
in which Prot, Pgen and Pser denote the powers of the wind rotor, generator and servo motor, respectively. If the power loss due to the mechanical friction is not taken into account, the input and output powers hold in balance in the stationary operating state. With h0 = 1, hr = 1 and hg = 1, eqs. (9) and (10) reduce to Pgen ⫽ and
i0ir wgen ·P ig(i0⫺1) wrot rot
冉
(10)
冊
i0 ir wgen ·P . Pser ⫽ 1⫺ ig (i0⫺1) wrot rot
(11)
Obviously, the power splitting behavior is dependent on both the gear speed ratios and angular speeds. The generator speed wgen is constant, it depends on the frequency f of the grid and the number p of pole pair w0gen ⫽
2pf . p
(12)
From eq. (2) , the rotor speed wrot in the special case wser = 0 is ¯ rot ⫽ w
i0ir ·w0 , ig(i0⫺1) gen
(13)
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X. Zhao, P. Maißer / Renewable Energy 28 (2003) 2001–2011
¯ rot is the so-called basic rotor speed. Then, the generator und servo motor in which w power can be written in accordance with eqs. (10) and (11) Pgen ⫽ and
¯ rot w ·P , wrot rot
(14)
冉 冊
(15)
¯ rot w ·P . Pser ⫽ 1⫺ wrot rot
Thus the power splitting performance can be represented as functions of the relative ¯ rot. Ideally, if the wind rotor operates with the basic rotor speed rotor speed wrot / w ¯ rot, the servo motor remains standing and the rotor power is transferred completely w into the generator, the servo motor must support a reaction torque. When the rotor ¯ rot, the servo motor acts as a generator, speed is larger than the basic rotor speed w which turning the mechanical power into electrical power, otherwise, the servo motor plays the roll of a motor, which draws the power from the grid and transfers it back into the planetary transmission, as a result, the generator transfers more power than the rotor power. In practice, the transmission should be designed in such a way, that within the main operation range the servo motor works as a generator, in order to avoid unnecessary power losses. As an example, Figs. 2 and 3 show respectively the operation principle and power performance of a model wind turbine in the wind speed range from 0 to 20 m/s. Generally, within the wind speed range up to 11.5 m/s, the wind rotor runs with the variable speed for the constant tip speed ratio and consequently the optimal power factor cp. In this range, the servo motor draws power from the grid in order to hold the rotor speed to be variable according to the wind speed variations, and the power capture of the wind rotor to be maximal. Within the wind speed range from 11.5 to 14.5 m/s, both the generator and the servo motor act as the generator, the rotor power flows partially through the generator and through the servo motor into the grid. Above the rated operation point with strong wind vw ⬎ 14.5 m / s the rotor power
Fig. 2.
Operation principle of the wind rotor.
X. Zhao, P. Maißer / Renewable Energy 28 (2003) 2001–2011
Fig. 3.
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Power splitting performance of the drive train.
and the rotor speed are limited to their rated values. The rotor power flows predominantly through the generator (ca 80%) directly and smaller partially (ca 20%) through the servo motor and its power electronics system into the grid. From this example, it is clear, that for the same variable speed operation and maximal power captures of the wind rotor only a small power electronics system is needed to match the servo motor, its power is only ca 20% of the conventional one, as a result, the construction price, the negative effects of the power electronics system are greatly reduced.
5. Transmission efficiency To calculate the overall efficiency h of the transmission, the whole operation range are divided into two operation ranges: ¯ rot, the rotor power Prot is the positive input power, while the generator 앫 wrot ⬎ w power Pgen and the servo motor power Pser are the negative output powers. ¯ rot, the rotor power Prot and servo motor power Pser are the positive input 앫 wrot ⬍ w powers, and only the generator power Pgen is the negative output power. In the first case, the overall efficiency h is calculated by h⫽
hr(1⫺i0) hriri0(1⫺hgh0 ) wgen ⫹ . 1⫺h0 i0 ig(1⫺h0 i0) wrot
(16)
The overall efficiency h depends not only on the friction losses hr, hg and h0, but also on the rolling power flow direction. If wsun ⬎ wcarrier, the rolling power flows from the ring gear to the sun gear, therefore, = ⫺1. In accordance with eq. (16), the efficiency becomes h⫽
hrh0(1⫺i0) hriri0(h0⫺hg) wgen ⫹ . h0⫺i0 ig(h0⫺i0) wrot
(17)
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X. Zhao, P. Maißer / Renewable Energy 28 (2003) 2001–2011
Since the sun gear speed wsun is larger than the planet carrier speed wcarrier, there is the angular speed relationship wsun ⬎ wcarrier ⬎ wring,
(18)
from which results the following formula (1⫺i0)ig wrot wsun ⫽ i0 ⫹ ⬎ 1. wring ir wgen
(19)
In the case of i0 = ⫺4, there is ¯ rot. wrot ⬎ 1.25 w
(20)
This means, the overall efficiency h represented by eq. (19) applies only under the ¯ rot. If the sun gear speed wsun is smaller than the planet carrier condition wrot ⬎ 1.25 w speed wcarrier, i.e. wsun ⬍ wcarrier, the rolling power flows from the sun gear to the ring gear, under this condition, there is ¯ rot, ¯ rot ⬍ wrot ⬍ 1.25 w w
(21)
the overall efficiency h becomes h⫽
hr(1⫺i0) hriri0(1⫺hgh0) wgen ⫹ . 1⫺i0h0 ig(1⫺i0h0) wrot
(22)
¯ rot. The wind In the second case, the wind rotor runs with the angular speed wrot⬍ w rotor and servo motor powers are the positive input powers, only the generator power is the negative output power, then, the overall efficiency is calculated by h⫽
hrhgh0 iri0(1⫺hgh0) . wrot (h0 ig i0⫺ ig i0 hr⫺ig ⫹ ig hr) ⫹ ir i0 hr wgen
(23)
Since the sun gear speed wser and the torque Tser of the servo motor are negative, the rolling power is positive by the sun gear and negative by the ring gear, consequently, = 1 and h0 = 1. Fig. 4 shows the overall efficiency h with the relative wind rotor speed ¯ rot with h0 = 0.985, hr = 1and hg = 1, that means, that the friction losses of wrot / w both adjustment gear pairs are neglected. Fig. 5 illustrates the overall efficiency h with the individual efficiencies h0 = 0.985, hr = 0.99and hg = 0.99. Both figures show, that the variable speed transmission has a operation speed range, in which it ¯ rot, the overall achieves the higher efficiency. At the rotor speed wrot = 1.25 w efficiency reaches its maximal value, h = 0.9821. Certainly, the overall efficiency of the complete drive train is determined not only by the efficiency of the transmission, but also by the efficiency of the electrical machines and power converter system.
X. Zhao, P. Maißer / Renewable Energy 28 (2003) 2001–2011
2009
¯ rot (h0 = 0.985, hr = 1 Fig. 4. Efficiency of the transmission with the relative wind rotor speed wrot / w and hg = 1).
¯ rot (h0 = 0.985, hr = Fig. 5. Efficiency of the transmission with the relative wind rotor speed wrot / w 0.99 and hg = 0.99).
6. Operation range The effective power supply of the wind turbine depends not only on the power factor of the wind rotor, but also on the efficiency of the transmission, generator, etc. From the economical point of view, the high power factor cp of the wind rotor and the high overall efficiency h of the transmission are necessary. Consequently, a suitable basic wind rotor speed should be selected, within a certain range of it, only small control power of the servo motor is needed and the high transmission efficiency is possible.
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X. Zhao, P. Maißer / Renewable Energy 28 (2003) 2001–2011
Fig. 6 shows the speed diagram of the wind rotor, generator and servo motor, it demonstrates the performances of the angular speeds in the drive train, the distances between the speeds result from the speed ratios. In this figure, the ‘a’ line represents the operation with not moving servo motor, the rotor speed is equal to the basic ¯ rot, and the overall efficiency h reaches its maximum. wind rotor speed wrot = 1.25 w Since in the part load operation the wind speed is smaller than its nominal value, in order to achieve the constant tip speed ratio, so that the optimal power output is realized, the wind rotor speed adapts the wind speed, but the efficiency decreases with the relative wind rotor speed. In the full load operation, the wind speed exceeds its nominal value, the rotor speed must be limited by pitch adjustment to its rated value, the power factor of the wind rotor is small, but the efficiency achieves thereby its large value. Therefore, a compromise between optimal power output of wind rotor and maximum efficiency of the transmission can not be avoided. If the rotor speed can oscillate from the basic rotor speed ca 15%, then the operation range is determined as ¯ r, ¯ r ⬍ wr ⬍ 1.43 w 1.06w
(24)
in which the overall efficiency changes from 0.98 to 0.982.
7. Conclusion A novel continuously variable speed drive train for the modern wind turbines is proposed by utilizing a planetary gear set with two degrees of freedom. By varying the speed of the servo motor fixed with the sun gear, the variable speed operation of the wind rotor coupled with the planet carrier and the constant speed operation of the generator are realized. At nominal operation point, ca 80% of the rotor power
Fig. 6.
Speed diagram of the drive train.
X. Zhao, P. Maißer / Renewable Energy 28 (2003) 2001–2011
2011
flow through the generator directly and 20% through the servo motor into the grid. As a result, a new kind of drive train with a relative low construction price of the power electronics system, less power loss, weak reaction from the grid and small crash load could be established.
References [1] Hau E. Windkraftanlagen, Technik, Einsatz, Wirtschaftlichkeit. Berlin: Springer, 1996. [2] Heier S. Windkraftanlagen im Netzbetrieb, 2. Auflage. Stuttgart: B. G. Teubner, 1996. [3] Idan M, Lior D. Continuously variable speed wind turbine: transmission concept and robust control. Wind Engineering 2000;24(3):151–67. [4] Loomann J. Zahnradgetriebe, 3rd ed. Berlin: Springer, 1996. [5] Mangialardi L, Mantriota L. Dynamic behavior of wind power systems equipped with automatically regulated continuously variable transmission. Renewable Energy 1996;7(2):185–203. [6] Rehfeldt K. Untersuchungen zur Modellbildung von Windkraftanlagen mit hydrostatischem Treibstrang und deren Regelung auf der Basis der Fuzzy-Logik. VDI Verlag, Reihe 8, Nr.538. [7] Volmer J et al. Getriebetechnik — Umlaufra¨ dergetriebe. Berlin: VEB Verlag Technik, 1972. [8] Zhao X, Maißer P, Tenberge P. Leistungsverzweigter Antriebsstrang fu¨ r drehzahlvariable Windkraftanlagen. Magazin fu¨ r Erneuerbare Energien 2001;11(9):44–9. [9] Zhao X, Maißer P, Tenberge P. Variable speed wind turbine with novel power splitting transmission — modeling by electromechanical system methodology. Proceedings of 2001 European Wind Energy Conference and Exhibition, Denmark; 2001. p. 593–598.
A novel power splitting drive train for variable speed wind power generators Xueyong Zhao ∗, Peter Maißer Institute of Mechatronics at the Chemnitz University of Technology, Reichenhainer Strasse 88, 09126 Chemnitz, Germany Received 14 March 2003; accepted 25 March 2003
Abstract In this paper a novel electrically controlled power splitting drive train for variable speed wind turbines is presented. A variable speed wind turbine has many advantages, mainly it can increase the power yield from the wind, alleviate the load peak in the electrical-mechanical drive train, and posses a long life time, also, it can offer the possibility to store the briefly timely wind-conditioned power fluctuations in the wind rotor, in which the rotary masses are used as storages of kinetic energy, consequently, the variable speed wind turbines are utilized in the wind power industry widely. In this work, on the basis of a planetary transmission a new kind of drive train for the variable speed wind turbines is proposed. The new drive train consists of wind rotor, three-shafted planetary gear set, generator and servo motor. The wind rotor is coupled with the planet carrier of the planetary transmission, the generator is connected with the ring gear through an adjustment gear pair, and the servo motor is fixed to the sun gear. By controlling the electromagnetic torque or speed of the servo motor, the variable speed operation of the wind rotor and the constant speed operation of the generator are realized, therefore, the generator can be coupled with the grid directly. At the nominal operation point, about 80% of the rotor power flow through the generator directly and 20% through the servo motor and a small power electronics system into the grid. As a result, the disadvantages in the traditional wind turbines, e.g. high price of power electronics system, much power loss, strong reaction from the grid and large crash load in the drive train will be avoided. 2003 Elsevier Science Ltd. All rights reserved. Keywords: Wind turbine; Novel drive train; Power splitting transmission
∗
Corresponding author. Tel.: +49-371-531-4683; fax: +49-371-531-4669. E-mail address: [email protected] (X. Zhao).
0960-1481/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0960-1481(03)00127-7
2002
X. Zhao, P. Maißer / Renewable Energy 28 (2003) 2001–2011
1. Introduction Variable wind turbines are widely used in the renewable energy technology in the world. This is because, that from economical and technical points of view they have many advantages [1], e.g. they can increase the power yield from the wind, offer the possibility to store the briefly timely wind-conditioned power fluctuations in the wind rotor, smooth the electric power output, alleviate the load peak in the mechanical–electrical drive train, and as a result, achieve a long life time. To realize the variable speed operation, conventionally, a rectifier-dc-link-converter is employed to decouple the variable generator speed and the constant grid frequency [2]. However, this approach has some disadvantages, e.g. the rectifier-dc-link-converter hardware is very expensive on commercial market, especially for large wind turbines, it causes ca 10–15% power losses due to the rectification and inversion, also, there are strong reactions from the grid. To overcome the disadvantages of this conventional approach, some new alternative concepts for the variable speed drive trains were proposed, in which a power converter system is not used any longer and the generator is connected with the grid directly [3,5,6,8]. In [6], a hydrostatic drive train consists of hydraulic pumps, hydraulic storages and hydraulic motors. The variable speed of the wind rotor is realized by controlling the hydraulic pumps and the hydraulic motors connected with the generator. For small wind turbines, a V-belt continuously variable transmission (c.v.t.) with two spring-loaded pulleys is proposed [5], with this solution, the c.v.t. can regulate automatically and adjust its transmission ratio corresponding to the torque applied on the driving pulley. With an adequate design of the springs, a characteristic relationship between the torque and the transmission ratio, which closely approximate the conditions required for optimal system operation, are obtained. In [3], a hybrid variable speed transmission with two stages of planetary transmissions is also given, in which the ring gear speed of the second stage is controlled by three synchronous electrical machines to keep the rotor speed variable, while the speed of the synchronous generator coupled with the sun gear of the second stage is held constant. In this paper, for the variable speed drive trains, a power splitting transmission is proposed, in which an electrically controlled planetary transmission and two adjustment gear pairs are adopted. The transmission posses three input und output shafts, one of the two output shafts is coupled with the generator, another is fixed to the servo motor. By controlling the speed of the servo motor, the generator speed is kept constant and its frequency converter system is deserted, at the same time, the wind rotor runs with the variable speed in correspondence with the timely changeable wind speed to reach the optimal operation.
2. Configuration of the novel variable speed drive train Fig. 1 shows the variable speed drive train, which is composed of the wind rotor, planetary transmission, generator , servo motor and two adjustment gear pairs. The
X. Zhao, P. Maißer / Renewable Energy 28 (2003) 2001–2011
Fig. 1.
2003
Layout of the power splitting drive train.
core of the drive train is the planetary gear set consisting of a central arranged sun gear, a ring gear and several on the planet carrier held planetary gears. The planet carrier is the input of planetary gear set, it is connected with the wind rotor through an adjustment gear pair with speed ratio ir, while the ring gear is the output, which is coupled with the generator also through an adjustment gear pair with speed ratio ig, the sun gear is the adjustment driven by the servo motor, then, the generator is coupled directly and the servo motor is coupled with the electrical grid through a small power electronics system. The speeds of the three shafts of the planetary gear set are arbitrarily adjustable, therefore, the speeds of the wind rotor, generator and servo motor can be arbitrarily selected in accordance with eq. (2). Each speed can be specified by the other two speeds clearly. In this way, the wind rotor speed can be varied, the generator speed holds constant and is directly connected with the grid. This design concept has a lot of advantages, e.g. smaller dynamic tooth contact forces and high efficiency. Both synchronous generator and asynchronous generator with squirrel-cage rotor can be used in the construction draft, in this work, a asynchronous squirrel cage generator is the privileged choice due to its robust construction, relatively low construction cost and operational flexibility as well as good operational reliability. In principle, almost all rotating electrical machines can be selected for the servo motor, however, because of some special characteristics of the wind turbines, some technical and economic requirements have to be considered. The servo motor should be able to run in a wide speed range with reversible rotation direction and have high torque even at low speeds, also, it must be able to bear the short time overloading for the case of very strong gust, certainly, it should be controlled easily and quickly to its expected goals, accordingly, the d.c. machine is a suitable selection.
3. Variable speed operation The main parameter that defines the planetary gear set behavior is its speed ratio i0. To get the angular speed relationship of the planetary gear set, the operation of
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X. Zhao, P. Maißer / Renewable Energy 28 (2003) 2001–2011
the planetary gear set is treated in two special cases. In the first case, the planet carrier is kept standing, the ring gear and the sun gear run in opposite rotation directions. In the second case, with the standing ring gear, the planet carrier and the sun gear run in the same direction. Then, the general operation can be regarded as the overlay of the two special cases, and the speed ratio i0 is calculated according to Willis formula [4] as follows: i0 ⫽
wsun⫺wcarrier wring⫺wcarrier
(1)
whereby wsun, wring and ωcarrier are the angular speeds of the sun gear, ring gear and planet carrier, respectively. If the speed ratio of two adjustment gear pairs are defined by ir = wrot / wcarrier and ig = wgen / wring, then, the kinematic relationship of the drive train in accordance with eq. (1) reads (1⫺i0) ig wrot ⫹ i0 ir wgen⫺ir ig wser ⫽ 0,
(2)
in which wrot, wgen and wser are the angular speeds of the wind rotor, the generator and the servo motor, respectively. From above, by controlling the servo motor speed wser, the rotor speed wrot can be kept variable for the constant optimal tip speed ratio with respect to the changing wind speed in part load operation, while the generator speed wgen holds constant or approximately constant, simultaneously, the rotor power is optimized and split into the generator power and servomotor power [9].
4. Power splitting performance For the recognition of the fundamental characteristics of the power splitting, the drive train is considered in the quasi steady state, that means, that the kinetic energy of the rotary masses are neglected. In reality, there are mechanical tooth and bearing frictions in the drive train, these frictions will cause torque and power losses, which can be characterized by the efficiencies hr, hg for the two adjustment gear pairs and h0 for the planetary gear set. In the case of the standing planet carrier, the efficiency h0 is defined by h0 ⫽ ⫺
冉
冊
Tring Tring wring ⫽⫺ . Tsun wsun i0Tsun
(3)
Tring and Tsun are the torques acting on the shafts of ring gear and sun gear, respectively. Since the flow direction of the rolling power in the sun gear shaft is variable, the efficiency h0 is changing in accordance with the operation states [7]. From eq. (3), the efficiency h0 is rewritten as Tring h0 ⫽ ⫺ i0Tsun with
(4)
X. Zhao, P. Maißer / Renewable Energy 28 (2003) 2001–2011
⫽
Tsun(wsun⫺wcarrier) . |Tsun(wsun⫺wcarrier)|
2005
(5)
Then, the torque relationships in the planetary transmission read Tsun ⫽
1 ·T i0h0 ⫺1 carrier
(6)
Tring ⫽
i0h0 ·T . 1⫺i0h0 carrier
(7)
and
Since the planetary gear set has a negative ratio, the torques Tsun and Tring have the same signs, while they have the opposite sign with torque Tcarrier. From the previous kinematic and kinetic relationships, the power splitting performance is described by Pgen ⫽
i0 ir hg hr h0 wgen ·P ig (i0h0 ⫺1) wrot rot
Pser ⫽
冉
and
(8)
冊
i0 ir hr wgen hr(1⫺i0) ·P , ⫺ 1⫺i0h0 ig (i0h0 ⫺1) wrot rot
(9)
in which Prot, Pgen and Pser denote the powers of the wind rotor, generator and servo motor, respectively. If the power loss due to the mechanical friction is not taken into account, the input and output powers hold in balance in the stationary operating state. With h0 = 1, hr = 1 and hg = 1, eqs. (9) and (10) reduce to Pgen ⫽ and
i0ir wgen ·P ig(i0⫺1) wrot rot
冉
(10)
冊
i0 ir wgen ·P . Pser ⫽ 1⫺ ig (i0⫺1) wrot rot
(11)
Obviously, the power splitting behavior is dependent on both the gear speed ratios and angular speeds. The generator speed wgen is constant, it depends on the frequency f of the grid and the number p of pole pair w0gen ⫽
2pf . p
(12)
From eq. (2) , the rotor speed wrot in the special case wser = 0 is ¯ rot ⫽ w
i0ir ·w0 , ig(i0⫺1) gen
(13)
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X. Zhao, P. Maißer / Renewable Energy 28 (2003) 2001–2011
¯ rot is the so-called basic rotor speed. Then, the generator und servo motor in which w power can be written in accordance with eqs. (10) and (11) Pgen ⫽ and
¯ rot w ·P , wrot rot
(14)
冉 冊
(15)
¯ rot w ·P . Pser ⫽ 1⫺ wrot rot
Thus the power splitting performance can be represented as functions of the relative ¯ rot. Ideally, if the wind rotor operates with the basic rotor speed rotor speed wrot / w ¯ rot, the servo motor remains standing and the rotor power is transferred completely w into the generator, the servo motor must support a reaction torque. When the rotor ¯ rot, the servo motor acts as a generator, speed is larger than the basic rotor speed w which turning the mechanical power into electrical power, otherwise, the servo motor plays the roll of a motor, which draws the power from the grid and transfers it back into the planetary transmission, as a result, the generator transfers more power than the rotor power. In practice, the transmission should be designed in such a way, that within the main operation range the servo motor works as a generator, in order to avoid unnecessary power losses. As an example, Figs. 2 and 3 show respectively the operation principle and power performance of a model wind turbine in the wind speed range from 0 to 20 m/s. Generally, within the wind speed range up to 11.5 m/s, the wind rotor runs with the variable speed for the constant tip speed ratio and consequently the optimal power factor cp. In this range, the servo motor draws power from the grid in order to hold the rotor speed to be variable according to the wind speed variations, and the power capture of the wind rotor to be maximal. Within the wind speed range from 11.5 to 14.5 m/s, both the generator and the servo motor act as the generator, the rotor power flows partially through the generator and through the servo motor into the grid. Above the rated operation point with strong wind vw ⬎ 14.5 m / s the rotor power
Fig. 2.
Operation principle of the wind rotor.
X. Zhao, P. Maißer / Renewable Energy 28 (2003) 2001–2011
Fig. 3.
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Power splitting performance of the drive train.
and the rotor speed are limited to their rated values. The rotor power flows predominantly through the generator (ca 80%) directly and smaller partially (ca 20%) through the servo motor and its power electronics system into the grid. From this example, it is clear, that for the same variable speed operation and maximal power captures of the wind rotor only a small power electronics system is needed to match the servo motor, its power is only ca 20% of the conventional one, as a result, the construction price, the negative effects of the power electronics system are greatly reduced.
5. Transmission efficiency To calculate the overall efficiency h of the transmission, the whole operation range are divided into two operation ranges: ¯ rot, the rotor power Prot is the positive input power, while the generator 앫 wrot ⬎ w power Pgen and the servo motor power Pser are the negative output powers. ¯ rot, the rotor power Prot and servo motor power Pser are the positive input 앫 wrot ⬍ w powers, and only the generator power Pgen is the negative output power. In the first case, the overall efficiency h is calculated by h⫽
hr(1⫺i0) hriri0(1⫺hgh0 ) wgen ⫹ . 1⫺h0 i0 ig(1⫺h0 i0) wrot
(16)
The overall efficiency h depends not only on the friction losses hr, hg and h0, but also on the rolling power flow direction. If wsun ⬎ wcarrier, the rolling power flows from the ring gear to the sun gear, therefore, = ⫺1. In accordance with eq. (16), the efficiency becomes h⫽
hrh0(1⫺i0) hriri0(h0⫺hg) wgen ⫹ . h0⫺i0 ig(h0⫺i0) wrot
(17)
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Since the sun gear speed wsun is larger than the planet carrier speed wcarrier, there is the angular speed relationship wsun ⬎ wcarrier ⬎ wring,
(18)
from which results the following formula (1⫺i0)ig wrot wsun ⫽ i0 ⫹ ⬎ 1. wring ir wgen
(19)
In the case of i0 = ⫺4, there is ¯ rot. wrot ⬎ 1.25 w
(20)
This means, the overall efficiency h represented by eq. (19) applies only under the ¯ rot. If the sun gear speed wsun is smaller than the planet carrier condition wrot ⬎ 1.25 w speed wcarrier, i.e. wsun ⬍ wcarrier, the rolling power flows from the sun gear to the ring gear, under this condition, there is ¯ rot, ¯ rot ⬍ wrot ⬍ 1.25 w w
(21)
the overall efficiency h becomes h⫽
hr(1⫺i0) hriri0(1⫺hgh0) wgen ⫹ . 1⫺i0h0 ig(1⫺i0h0) wrot
(22)
¯ rot. The wind In the second case, the wind rotor runs with the angular speed wrot⬍ w rotor and servo motor powers are the positive input powers, only the generator power is the negative output power, then, the overall efficiency is calculated by h⫽
hrhgh0 iri0(1⫺hgh0) . wrot (h0 ig i0⫺ ig i0 hr⫺ig ⫹ ig hr) ⫹ ir i0 hr wgen
(23)
Since the sun gear speed wser and the torque Tser of the servo motor are negative, the rolling power is positive by the sun gear and negative by the ring gear, consequently, = 1 and h0 = 1. Fig. 4 shows the overall efficiency h with the relative wind rotor speed ¯ rot with h0 = 0.985, hr = 1and hg = 1, that means, that the friction losses of wrot / w both adjustment gear pairs are neglected. Fig. 5 illustrates the overall efficiency h with the individual efficiencies h0 = 0.985, hr = 0.99and hg = 0.99. Both figures show, that the variable speed transmission has a operation speed range, in which it ¯ rot, the overall achieves the higher efficiency. At the rotor speed wrot = 1.25 w efficiency reaches its maximal value, h = 0.9821. Certainly, the overall efficiency of the complete drive train is determined not only by the efficiency of the transmission, but also by the efficiency of the electrical machines and power converter system.
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¯ rot (h0 = 0.985, hr = 1 Fig. 4. Efficiency of the transmission with the relative wind rotor speed wrot / w and hg = 1).
¯ rot (h0 = 0.985, hr = Fig. 5. Efficiency of the transmission with the relative wind rotor speed wrot / w 0.99 and hg = 0.99).
6. Operation range The effective power supply of the wind turbine depends not only on the power factor of the wind rotor, but also on the efficiency of the transmission, generator, etc. From the economical point of view, the high power factor cp of the wind rotor and the high overall efficiency h of the transmission are necessary. Consequently, a suitable basic wind rotor speed should be selected, within a certain range of it, only small control power of the servo motor is needed and the high transmission efficiency is possible.
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Fig. 6 shows the speed diagram of the wind rotor, generator and servo motor, it demonstrates the performances of the angular speeds in the drive train, the distances between the speeds result from the speed ratios. In this figure, the ‘a’ line represents the operation with not moving servo motor, the rotor speed is equal to the basic ¯ rot, and the overall efficiency h reaches its maximum. wind rotor speed wrot = 1.25 w Since in the part load operation the wind speed is smaller than its nominal value, in order to achieve the constant tip speed ratio, so that the optimal power output is realized, the wind rotor speed adapts the wind speed, but the efficiency decreases with the relative wind rotor speed. In the full load operation, the wind speed exceeds its nominal value, the rotor speed must be limited by pitch adjustment to its rated value, the power factor of the wind rotor is small, but the efficiency achieves thereby its large value. Therefore, a compromise between optimal power output of wind rotor and maximum efficiency of the transmission can not be avoided. If the rotor speed can oscillate from the basic rotor speed ca 15%, then the operation range is determined as ¯ r, ¯ r ⬍ wr ⬍ 1.43 w 1.06w
(24)
in which the overall efficiency changes from 0.98 to 0.982.
7. Conclusion A novel continuously variable speed drive train for the modern wind turbines is proposed by utilizing a planetary gear set with two degrees of freedom. By varying the speed of the servo motor fixed with the sun gear, the variable speed operation of the wind rotor coupled with the planet carrier and the constant speed operation of the generator are realized. At nominal operation point, ca 80% of the rotor power
Fig. 6.
Speed diagram of the drive train.
X. Zhao, P. Maißer / Renewable Energy 28 (2003) 2001–2011
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flow through the generator directly and 20% through the servo motor into the grid. As a result, a new kind of drive train with a relative low construction price of the power electronics system, less power loss, weak reaction from the grid and small crash load could be established.
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