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A novel hybrid transmission for variable speed wind turbines
Renewable Energy 83 (2015) 78e84
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
A novel hybrid transmission for variable speed wind turbines Damir Jelaska*, Srdjan Podrug, Milan Perkusi c University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Split, Croatia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 March 2014 Accepted 8 April 2015 Available online
We herein advance a novel, power summation hybrid transmission, which has the ability to convert the variable speed of a wind turbine rotor shaft into the constant speed required at a generator shaft for a whole range of wind speeds, thereby eliminating the need for a frequency converter. The transmission consists of a single one-stage planetary gear train (PGT) with three rotating shafts and a simple control system consisting of a few sensors and a control motor controlled by a microprocessor. One of the PGT shafts is the input, another is the output, and the third is coupled to the control motor as second input. The optimal tip-speed ratio is kept constant at low wind speeds by controlling the speed of the control motor, maximising the capture of energy from the wind. The wind-rotor speed continues to vary above the rated wind speed zone, but the rotor shaft power is kept constant by using the same control system. In this way, a constant electrical power output is achieved without altering the blade pitch, i.e., with the rotor in a fixed geometry. A frame design procedure for the transmission is proposed, efficiency expressions are derived, an example transmission operation is presented and efficiency comparisons to a mainstream variable speed wind turbine are carried out. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Planetary gear train Power circulation Control system Efficiency
1. Introduction Concerns over global environmental threats and energy crises have contributed to the increasing use of renewable energy technologies. The production of electrical power from wind is the fastest growing and most cost effective sustainable energy technology. The objective of any system for utilising wind energy is to capture as much wind energy as possible at the lowest possible cost. There have been many attempts to achieve this using horizontal-axis wind turbines, which should deliver power at a constant frequency, whether they are connected to the grid or not. Many common appliances will not function properly if a constant frequency is not maintained [1]. Wind turbine rotors achieve their maximum efficiency at a particular tip-speed ratio. Therefore, stiffgrid-connected, constant-speed turbines, in which the wind rotor is connected to a generator at a fixed speed ratio, operate suboptimally. Whilst such turbines require no frequency converter, any rapid changes in electrical output will either cause the generator to be damaged or cause the generator circuit breaker to open.
* Corresponding author. University of Split, FESB, R. Boskovi ca 32, 21000 Split, Croatia. E-mail address: [email protected] (D. Jelaska). http://dx.doi.org/10.1016/j.renene.2015.04.021 0960-1481/© 2015 Elsevier Ltd. All rights reserved.
The fatigue loads are also increased, resulting in a reduced lifetime of the system or in an increased size and cost of the gearbox. It is therefore necessary either to control the power output from the wind rotor or to find a way of transforming the varying voltage and frequency to make the generated power compatible with the electrical grid [2]. Variable speed wind turbines have recently been used, which have a constant optimal tip-speed ratio below the rated wind speed and a constant speed and power output above it [3]. This type of turbine has a number of advantages: i) below the rated wind speed, the speed of the wind rotor varies with the wind speed to maintain the maximum power efficiency (commonly by controlling the torque of the generator shaft); ii) control of the rotor torque significantly reduces variations in gearbox torque above the rated level; iii) low rotor speeds in slow winds result in significantly lower aerodynamically generated acoustic emission than that obtained from other turbines; iv) the rotor can operate as a flywheel, smoothing the torque variations caused by short-lived power fluctuations in the rotor that may be caused by varying wind conditions. The shortcomings of variable speed turbines are that they require frequency converters and complex control systems. Electrical harmonics are also a critical issue for these turbines because they distort the normally smooth sinusoidal voltage [2]. The solution to the problem of capturing the maximum amount of wind energy at the minimum production cost has become a key challenge for designers and scientists, and considerable efforts have
D. Jelaska et al. / Renewable Energy 83 (2015) 78e84
been made to develop various transmissions [4e13]. In all of them, a variable speed wind turbine is used with a transmission that gives a constant output speed over the entire range of possible wind speeds and a constant power output in the most effective range of wind speeds. Here, we comment on some of the most successful, in our opinion, all hybrid types of continuously variable transmission (CVT) and all comprising at least one PGT. Other transmissions [10e13] are not considered here because of their relatively low efficiencies due to friction member (belting or traction drives). Idan and Lior [4] proposed a hybrid variable speed transmission with two planetary transmission stages in which the annulus gear speed of the second stage (three rotating shafts) was controlled by three servo-motor generators (SMGs) to maintain the optimal rotor speed for a given wind speed, while the speed of the conventional asynchronous generator coupled with the sun gear was held constant. This design fulfils most of our requirements, but has some shortcomings, including a high cost for the electronics because of the three SMGs used to balance the radial forces, the fact that one fixed ratio PGT stage seems to be surplus, and that, when operated as a generator, the SMGs need a frequency converter to deliver power to the grid. Hicks and Cunliffe [5] presented a transmission consisting of a single PGT with its output shaft connected to the induction generator through a bevel gear drive, and the third shaft connected to a single SMG, which, assisted by the control system, made it possible to maintain the output shaft at a constant (±15%) speed. The shortcomings of this transmission are that the output speed is not quite constant, the bevel gear pair increases the transmission cost and power losses, and there are problems associated with the delivery of the SMG power to the grid. Zhao and Maiber [6] designed a power-split transmission with an electronically controlled PGT and two adjustment gear pairs, with one of the PGT shafts connected to the rotor shaft over the gear pair, another coupled to the generator, and the third shaft connected to the SMG. The output generator speed was kept constant by controlling the speed of the servo motor. Apart from the questionable use of two additional gear drives, which increase the machine costs and power losses, the same problems arise when delivering the SMG power as previously described. In another scheme [7], a transmission has a single PGT, achieving a constant output speed by controlling the variable third shaft speed using a torque converter driven by the output shaft. Although this is an interesting, innovative solution, beside the transmission, there was a conventional gear drive which additionally increases the power losses and production costs. Each of the transmissions considered above has problems associated with connecting the SMGs to the grid. Namely, an important question has not been addressed in those papers: are the SMGs connected to the same high voltage grid as main generator or to some other, low voltage grid? If the former is true, then the additional transformer is needed between SMGs and the grid. When the power of SMGs is delivered to the grid, the frequency converter is needed to be built in. The recently developed independently controllable transmission is also capable of running the output shaft at controllable speed independent of the input speed, even without control system [8,9]. This promises to solve most of the problems associated with variable-speed transmissions including in wind turbines. The transmission consists of two PGTs with three rotating shafts connected by two gear drives. However, there is one surplus output shaft with a variable, uncontrollable speed. The problem remains of how to manage the power of this shaft. We herein advance a simple, hybrid CVT that can convert the variable speed of a wind turbine rotor into a constant generator shaft speed over an entire range of wind speeds [14]. It has all of the advantages of a variable speed turbine, capturing the maximum wind energy in the low-wind-speed zone, and allowing a constant
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electrical frequency to be produced without using a frequency converter. The transmission consists of a single PGT controlled by a control system, which is also used to maintain a constant power from the wind rotor shaft at wind speeds greater than the rated. 2. General description of novel transmission system The transmission system consists of a simple, power summation PGT, with a positive basic gear ratio and a control system. The transmission input shaft is connected to the wind turbine rotor; the second, hollow shaft is connected to the control motor; and the third, output shaft (passing through control motor shaft) is connected to the generator (Fig. 1). The transmission input shaft (wind rotor shaft) is connected to the central gear 1 shaft of the PGT, the output shaft is connected to the central gear 3 shaft, and the planet carrier (later simply called the carrier) shaft is connected to the control motor shaft. Planets 2 and 20 are in one piece with a shaft that is supported by the carrier C. The rotational speeds of the shafts of the three main PGT members, central gear 1, central gear 3 and the carrier (i.e., the speeds of the rotor, generator and control motor shafts nR, nG, and nM, respectively) are related to the basic gear ratio i0 of the PGT by the Willis equation [15,16]:
nR i0 nG þ ði0 1ÞnM ¼ 0;
(1)
where the basic gear ratio is defined as
i0 ¼
z2 z3 n1 nc nR nM ¼ ¼ ; z1 z02 n3 nc nG nM
(2)
where z1, z2, z3 and z20 are the numbers of teeth on gears 1, 2, 3 and 20 , respectively, and n1, n3, and nc are the rotational speeds of gears 1 and 3 and the carrier C, respectively. The basic PGT gear ratio should not be chosen arbitrarily, and its constraints, as well as those on the speed ratio, must be determined for this type of transmission. First, the signs (þ/) of the speed and torque must be determined for each shaft. As usual, the input speed and torque are taken to be positive. Then, for a chosen positive basic gear ratio 0 < i0 < 1, from Eq. (4), the generator shaft torque becomes negative, as does the control motor shaft torque (from the torque equilibrium equation). Therefore, the rotor shaft is the (torque) summation shaft, and the generator shaft is the power summation shaft. Because the control motor shaft power is positive
Planetary gear train 2
2´
C 1
3 Control motor
Generator
Rotor Fig. 1. Schematic of the proposed wind turbine drive-train.
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and its torque is negative, its speed is negative (i.e., the opposite direction to the generator shaft). Because the power and torque of the generator shaft are both negative, its speed is positive. The following constraints for the basic gear ratio and speed ratio for the central gears were obtained for the distributions of the speed, torque and power signs for the three rotating shafts, in accordance with previously published work [15,16]:
TR þ TM þ TG ¼ 0;
(5)
where TG is the generator shaft torque, using
TM ¼ h0 i0 1; TR
(6)
the input power ratio is derived as follows:
i0 < 1
0 < nR =nG < i0 :
(3)
This transmission is based on the ability of a PGT to rotate two shafts at variable speeds, while keeping the speed of the third shaft constant. For the proposed transmission, the generator shaft speed is kept constant over the entire range of wind speeds, and the control motor shaft runs at a speed that allows the rotor shaft to run at a speed that maintains a constant optimum tip-speed ratio in the low-wind-speed zone. Thus, the maximum amount of energy is captured from the wind. Above the rated wind speed, the rotor shaft is forced to run at a speed that results in a constant power output without a pitch control system and using only a low-cost wind rotor with a fixed geometry. The rated speed is defined as the lowest steady-state wind speed at which the turbine can produce the rated power. Large drops in voltage are not expected with this turbine because of the constant electrical frequency produced. Because of this and its high efficiency, a synchronous generator seems to be the most appropriate choice, although the simple asynchronous generator can be used. Because the control motor runs at low speeds and in a narrow speed range, an AC asynchronous motor with a speed control member can be used with this turbine configuration. The control system consists of a microprocessor, a control motor and at least three sensors (for the wind speed, wind rotor speed and wind rotor torque). The microprocessor receives signals from the sensors, converts them into the commanding signal for the motor speed, and then sends this signal to the control member of the control motor. This controller is, of course, just part of the turbine supervisory control system.
PM n ¼ ðh0 i0 1Þ M : PR nR
The transmission efficiency htr for the positive rolling power transferred from the rotor to the generator shaft is simply derived from the torque ratio of the central gear shafts, using Eqs. (1) and (5),
PG h ð1 i Þ htr ¼ ¼ 0 0 : PR þ PM h nR i þ 1 nR 0 0 nG nG
Because the speeds of the three rotating shafts are known for any wind speed, the steady-state torque and power ratios can be calculated, as can the transmission efficiency. The power and torque of each shaft can therefore be determined if the power or torque of the rotor shaft is known. The most important transmission parameter is the ratio between the control motor power PM and the rotor shaft power PR, hereafter termed the input power ratio. There are two reasons for this: i) the control motor is an auxiliary device and should have as low power as possible to reduce the turbine production cost, and ii) the control motor delivers less power to the transmission than it takes from the generator output power (see below), which causes a decrease in the total efficiency as the control motor power increases. The input power ratio is obtained from the torque ratio of the PGT central gear shafts TG/TR for the rolling power that flows from the shaft of central gear 1 (the rotor) to the shaft of central gear 3 (the generator) [15,16]:
TG ¼ h0 i0 ; TR
(4)
where h0 is the basic PGT efficiency. Accounting for the torque equilibrium equation
(8)
The power losses in the PGT bearings and seals and from idle motion are not included in Eq. (8) and the efficiency vary slightly from constant value of 0.988 obtained for assumed value of h0 ¼ 0.988 for all external gears, which means that the change of transmission ratio nR/nG slightly affects the efficiency and power losses. That is not in accordance with expression for the power losses of wind turbine planetary gear box, obtained by testings [3]. It is established there that, mostly as result of the relative increase in the ventilation and splash losses of the carrier with planets at power lower than rated, the planetary transmission efficiency significantly decreases with a decrease in the power, i.e. the wind speed. Therefore, the theoretical expression (8) is not quite reliable for wind speeds lower than the rated. Because the causes of the increased power loss are the same, the equation for calculating their values in kilowatts, in typical wind turbine gearboxes [3], can be used for the transmission:
PL;GB ¼ 3. Power and efficiency
(7)
½ð10=3 þ 2NÞPr þ 5NPi 1000
(9)
where Pi is the operating power level in kW, Pr is the rated power in kW, and N is the number of stages. By substituting N ¼ 1 in Eq. (9), the transmission power loss variation within the entire wind speed range can be approximated as follows:
PL;tr ¼
ð16=3ÞPr þ 5Pi 1000
(10)
It is interesting, and one more proof of validity of the expression (9), that, for the rated power, the efficiency calculated on the basis of Eq. (10) is obtained to be 0.988, same as pursuant to Eq. (8). The efficiencies calculated for a part load, i.e. for wind speed lower than rated are significantly reduced e up to 0.85 at cut-in speed. The rest mechanical losses, including the losses in main bearing and the power needed for the yaw system to operate, are included in the efficiency correction factor hrest, which also acts to decrease the generator input power. Our power and efficiency analyses are carried out assuming that the control motor is fed directly from the generator stator, i.e., it is driven by a portion (PM/hM) of the generator output power hGhrestPG (Fig. 2). The control motor power therefore flows from the control motor, through the transmission and generator, and back to the control motor, with power losses from the transmission, generator and control motor. Therefore, the generator output power is split into two parts, the power PM/hM required to drive the control motor and the remainder, which is the transformer input power,
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Fig. 2. Schematic of the turbine power flows.
PT ¼ hG hrest PG þ PM =hM ;
(11)
where hG and hM are the efficiencies of the generator and control motor, respectively. The transformer input power can be derived from Eqs. (7), (8) and (11):
1 htr hG hrest hM nM PT ¼ ðh0 i0 1Þ htr hG hrest PR : hM nR
(12)
Therefore, the real output power of the wind turbine delivered to the grid is
1 htr hG hrest hM nM Pout ¼ hT ðh0 i0 1Þ htr hG hrest PR ; hM nR
(13)
where hT is the transformer efficiency. It slightly varies with the wind speed, i. e. with the part load fraction over 0.23 [3], from 0.99 at 0.23 part load fraction, over 0.993 at 0.5 part load fraction to 0.992 at full load (cut-off speed). In calculations, this value is deemed constant and equal to 0.992. The power-train efficiency, hPT, which includes the power losses from the rotor shaft to the transformer output, equals
Pout P 1 htr hG hM hrest : hPT ¼ ¼ hT htr hG hrest M PR PR hM
(14)
The overall turbine efficiency, accounting also for the wind energy losses in the blades, is equal to the product of the power-train efficiency and the constant, maximum value of the power coefficient, CP,max. Same as power-train efficiency, as expected, it decreases with increasing the input power ratio PM/PR and decreasing all the efficiencies. When efficiency is found to be unfavourable, a different basic gear ratio and/or a different PGT shaft distribution, or some type of composed PGT, should be chosen. 4. Turbine operation A wind turbine with the proposed transmission can keep the generator shaft speed constant over the entire range of wind speeds, keep the tip-speed ratio constant in the low-wind-speed zone, and keep the electrical power output constant in the zone above the rated wind speed. This is achieved using the control system, which enables the rotor shaft to run at the speed necessary to obtain the required turbine system state for the current wind speed. In the low-wind-speed zone, the microprocessor receives the measured wind speed signal and calculates the optimal tip-speed ratio l from the maximum power coefficient expression, CP,max ¼ CP,max(l), as demonstrated by Carlin et al. [2]. For a constant l value, the necessary rotor speed for the current measured wind speed and the required control motor speed to match the given generator speed are calculated using Eq. (1). The control motor
81
speed signal is sent to the control unit of the control motor, making it run at a speed that, in turn, makes the rotor run at the necessary speed to achieve a constant and optimal tip-speed ratio, resulting in maximum energy capture. When the wind speed signal is estimated not enough reliable, the optimal tip speed ratio can be achieved simply by maximising the rotor power: the control system would be set to change the rotor speed until the maximum rotor power is achieved for a certain state of wind. In the medium-speed zone, between the constant lopt zone and the zone above the rated wind speed, the rotor is allowed to run freely. The control motor shaft speed is controlled, enabling a constant generator speed for the measured rotor speed and given generator shaft speed. When the level of permitted acoustic emission is reached in this zone, the control system can keep the rotor, control motor and generator shaft speed constant, avoiding the undesirable noise. Although the blades are designed to stall in the zone above the rated wind speed, the same control system can be used to make the rotor shaft power curve as flat as possible. To achieve constant power from the rotor shaft for the current measured rotor shaft torque, the wind rotor speed should be
nR ¼
30 Pr ; p TR
(15)
where Pr is the rotor rated power that is known. When the output power is rated, PR is then calculated by the microprocessor using Eq. (13). The commanding signal nM for the required motor shaft speed, according to Eq. (1), is sent to the control motor from the microprocessor,
nM ¼
nR i0 nG : 1 i0
(16)
This speed allows a constant wind-rotor-shaft power to be maintained, along with a constant generator shaft speed. Clearly, a surplus or lack of aerodynamic power above the rated speed is compensated by the control motor. The generator is fed with a constant rotor power and the variable control motor power,
PG ¼ hPGT ðPR þ PM Þ:
(17)
Therefore, in the zone above the rated wind speed, the wind rotor and control motor shaft speeds are variable, and the generator speed is constant. The control motor and generator shaft power values are variable, and the wind rotor power is constant; the torques of all three main shafts are variable. Because the control motor power flow circulates from the control motor through the transmission and generator and back to the control motor, it does not significantly affect the power output delivered to the grid. This means that a constant rotor power reaches the grid, after being reduced by the transmission, generator, transformer and other mechanical power losses. Because the power losses vary with the wind speed (i.e., with the speeds of the shafts), the turbine output power deviates slightly from a constant value. Our simple control system, consisting of a control motor, a microprocessor and a few sensors, is therefore able to i) keep the generator shaft speed constant from the cut-in to the cut-off speeds, ii) keep the tip-speed ratio constant to achieve maximum energy capture in the low-wind-speed zone, and iii) keep the rotor power constant above the rated speed. By different algorithm given to microprocessor, this control system is able to keep constant the torque, instead the power. In such a way, the load increase of the power-train can be prevented, which could cause the cost increase. However, it would also result in variable output power which is not desirable.
It must be stressed that this transmission is considered for quasi-steady-state operation, which means that the kinetic energy of the rotary masses is neglected. This also means that, because of the acceleration of the rotating masses when the rotor and control motor speeds and torques change, it is hard to attain the most appropriate shaft speeds or to achieve a truly constant nominal rotor power in the zone above the rated speed. 5. Example transmission operation
350
80
300
70
250
60
200
50
150
40
100
30 power speed
50
As an example of the proposed transmission, a positive ratio PGT was chosen with a basic gear ratio:
i0 ¼
z2 $z3 22$19 ¼ 0:079558: ¼ z1 $z02 71$74
This PGT is feasible even for typical performance levels, having (three pairs of) planets in two planes. A 3-D transmission scheme is shown in Fig. 3. In the animation, the transmission shows the anticipated shaft speeds. Supplementary video related to this article can be found at http://dx.doi.org/10.1016/j.renene.2015.04.021. A steady-state operating scheme for a 310 kW wind turbine rotor of a fixed geometry, with the transmission and control systems described here, with an optimal tip-speed ratio lopt of 8.5 resulting in CP,max ¼ 0.5045, a rated wind speed vw, rated of 12.52 m/ s, a rotor diameter D of 24.2 m, and a constant generator speed nG of 1000 min1, is illustrated in Fig. 4. This scheme is an example rather than a suggestion, because the exact rotor speed variation, and especially the wind speed at which rotor begins to stall, depends on the shape of blades, which are not designed herein. Thus, the rotor speed operating scheme is inscribed in accordance with literature [1,4] and other. The power operating scheme at wind speeds below the rated is obtained by known rotor power formula depending on the cube of wind speed. The rated rotor power of 310 kW is defined with rated wind speed. Although the efficiencies of all the components decrease with a decrease in the wind speed (i.e., with a partial load), the generator, control motor, transmission basic efficiency, efficiency correction factor and transformer efficiency were approximated constant and were estimated to be hG ¼ 0.98, hM ¼ 0.98, h0 ¼ 0.988, hrest ¼ 0.996, and hT ¼ 0.992, respectively. Although the rating of the example turbine is 300 kW, in order to illustrate the efficiency competitiveness of the proposed turbine to recent mainstream turbines of megawatt ratings, the ultimate reach of the efficiencies hG, hM, hrest
0 0
5
10
15
20
speed, min-1
D. Jelaska et al. / Renewable Energy 83 (2015) 78e84
power, kW
82
20 10 25
wind speed, m/s Fig. 4. Operating scheme for the example turbine rotor.
and hT are estimated for megawatt ratings. The transmission efficiency is calculated pursuant to Eq. (10). The powers and torques of all of the shafts, including the output electrical power, together with the transmission and power-train efficiency, were determined for this operating scheme by means of MATLAB on the basis of presented or derived herein. They are shown in Fig. 5 for the entire range of wind speeds. It is notable that a maximum control motor power of 101 kW and a maximum generator power of 405 kW are needed for this machine. Thus, the generator and control motor should be designed for approximately those power values. Because the generator power delivered to the control motor was variable, the electrical power output in the zone above the rated wind speed was not quite constant, but varied within the range 293.15 ± 1.45 kW. The speed histories of the three main transmission shafts, measured in situ, at slowly varying wind speeds (i.e., excluding gusts) over 200 s (following previously published work [4]), are shown in Fig. 6 on the basis of Eq. (1). The optimised and free-run power histories of the rotor shaft are compared in Fig. 7. The green (in web version) shaded area between the power histories represents the energy gained by optimising the power coefficient. It is important to compare the efficiency of this novel turbine system with that of a mainstream variable speed wind turbine system. The overall efficiency of the proposed turbine, htot, which is the ratio of the output power delivered to the grid and the input wind power (energy per time), is equal to the product of the power coefficient CP,max and power train-efficiency hPT, while the overall efficiency of a typical variable speed wind turbine equals
htot;t ¼ CP;max $hGB $hG $hrest $hFC $hT
(18)
where hGB is the gearbox efficiency calculated by Eq. (9), and hFC is the frequency converter efficiency, which is taken constant and equal to 0.992. A comparison of the efficiencies shows that the transmission efficiency is always higher than the gearbox efficiency because it varies from 0.88 at the cut-in speed to 0.988 at the rated speed, while the gearbox efficiency varies from 0.845 at the cut-in speed to 0.976 at the rated speed. However, the ratio of htot to htot,t is the real measure for comparison the efficiencies of the presented and mainstream turbine system. It is obtained as follows: PM 1htr hG hM hrest
htr hG hrest PR htot hM ¼ htot;t hGB hG hrest hFC Fig. 3. 3-D animated model of the transmission.
:
(19)
The diagram of its variation is presented in Fig. 8. It can be observed that its gradients coincide with the gradients of the
D. Jelaska et al. / Renewable Energy 83 (2015) 78e84
200
a)
14
100
12
wind speed, m/s
power, kW
0 -100 -200 -300
-500
8
4 1200
generator speed, min-1
60 40 20
1000 800 600
0
100
-20
80 60
rotor generator motor
-40 -60
speed, min-1
torque, kNm
10
6
output motor generator
-400
b)
83
1 c) 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5
40 20 0 -20 motor rotor
-40
efficiency
-60 0
20
40
60
80
100
120
140
160
180
200
time, s Fig. 6. Speed diagrams for the turbine components at slowly varying wind speeds.
transmission power - train 0
5
10
15
20
25
wind speed, m/s Fig. 5. Power, torque and efficiency variations for the example turbine.
transmission power-train efficiency (Fig. 5c). At wind speeds greater than 8.9 m/s, the overall efficiency of turbine having the proposed transmission is higher, by up to 2.1%, than that of the turbine having typical gearbox, whereas below 8.9 m/s, it is always less, as much as the wind speed is closer to the cut-in speed. The reason is the increase in the input power ratio at low wind speeds. Compared to the overall efficiencies of other hybrid transmissions [4e9], because of their additional gear drive(s) or torque converter that cause additional power losses, the efficiency of turbine having the proposed transmission is significantly higher.
constant electrical power to be maintained without blade pitch control, i.e., with fixed rotor geometry. Because there is no need neither for a blade pitch system, nor for a frequency converter, the production cost of a wind turbine using this system is significantly lower than the cost of other variable speed wind turbines. This transmission is more efficient than typical gearboxes and other hybrid and ordinary CVTs, and the overall efficiency of a turbine using it is assessed to be slightly higher than that of a typical
6. Concluding remarks A novel hybrid transmission is proposed for use in variable speed wind turbines. This transmission can convert a variable wind rotor speed into a constant generator shaft speed over the entire wind speed range. Controlling the wind rotor speed allows the optimal constant tip-speed ratio to be maintained in the low-windspeed zone, enabling maximum energy capture. A constant wind rotor power in the zone above the rated wind speed allows a
Fig. 7. Comparison of the optimised and free-run rotor shaft powers at slowly varying wind speeds, as in Fig. 6.
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1.1
Further investigation is required to determine the dynamic behaviour of the proposed system in relation to the overall control system design and the behaviour of the electrical components. Test benches and simulation programs for the turbine system are planned, in the Power Transmission Laboratory in the Mechanical Engineering Department of the University of Split, Croatia.
1.05 1
ηtot/ηtot,t
0.95 0.9 0.85 0.8
Acknowledgements
0.75 0.7 0.65 0.6 0
5
10
15
20
25
This study was supported by the Ministry of Education, Science and Sport of the Republic of Croatia [grant number 023-06921951749].
wind speed, m/s References Fig. 8. Ratio of total efficiencies of the proposed and mainstream wind turbine.
variable-speed wind turbine for mid- and high-wind speeds, whereas for wind speeds of less than 8.9 m/s, it is found to be slightly lower. Thus, it is indeed competitive to the mainstream variable speed wind turbines, and for sure, prevail to wind farms wind turbines situated at the sites with higher annual mean wind speed, such as off-shore wind farms. The proposed transmission offers other advantages, including i) a lower probability of current harmonics because a constant frequency and constant electrical power are delivered to the grid in the zone above the rated wind speed; ii) high operational reliability thanks to a low number of gears and other components, iii) lower cost, higher efficiency and a simpler control system with fewer problems connecting the SMG to the grid compared to existing hybrid wind turbine transmissions; iv) it is applicable whether the turbine is grid connected or standalone and whether the grid is stiff or not, and v) low inertia compared to variable pitch systems which respond slowly to wind speed variations [2,4,17]. However, the wind turbines that will use this transmission would have some shortcomings, including increased power of built-in electric machines, reduced overall efficiency close to cut-in speed and increase in rotor torque attitude above the rated speed that could increase the size of the components. Although the elimination of frequency converter and pitch control system seems to be sufficient to conclude that capital costs of the proposed turbine system are significantly lower than that of the mainstream variable speed wind turbine system, the cost comparison would be welcome.
[1] Burton T, Sharpe D, Jenkins N, Bossanyi E. Wind energy handbook. Chichester, UK: John Wiley and Sons; 2011. [2] Carlin PW, Laxson AS, Muljadi EB. The history and state of the art of variablespeed wind turbine technology. Wind Energy 2003;6:129e69. [3] Jamieson P. Innovation in wind turbine design. Chichester, UK: John Wiley and Sons; 2011. [4] Idan M, Lior D. Continuously variable speed wind turbine: transmission concept and robust control. Wind Eng 2000;24:151e67. [5] Hicks RJ, Cunliffe F. Optimised gearbox for modern wind turbines. In: Proc. EWEC 2004; 24e27 November 2004. London. [6] Zhao X, Maißer P. A novel power splitting drive train for variable speed wind power generators. Renew Energy 2003;28:2001e11. €ller M, Basteck A, Pfister J. Grid compatibility of variable speed [7] Müller H, Po wind turbines with directly coupled synchronous generator and hydrodynamically controlled gearbox. In: Proc. 6th Int. workshop on large-scale integration of w. power and transm. Networks for offshore W. Farms, Delft; 26e28 October 2006. p. 307e15. [8] Hwang GS, Lin CC, Tsay DM, Liao WH, Kuang JH, Chern TL. Kinematic analyses of a parallel-type independently controllable transmission. Int J Autom Smart Technol 2011;1:87e92. [9] Hwang GS, Lin CC, Tsay DM, Kuang JH, Chern TL. Power flows and torque analyses of an independently controllable transmission with a parallel type. In: Proc. World Congress on Engineering, vol. III; 6e8 July 2011. London. [10] Mangialardi L, Mantriota G. Dynamic behaviour of wind power systems equipped with automatically regulated continuously variable transmission system. Renew Energy 1996;7:185e203. [11] Boukhezzar L, Lupu L, Signerdidjane H, Hand M. Multivariable control strategy for variable speed, variable pitch wind turbines. Renew Energy 2007;32: 1273e87. [12] Parrish BE. Continuously variable transmission. US Patent 6387004, 2002. [13] Lahr DF, Hong DW. The operation and kinematic analysis of a novel cambased infinitely variable transmission. ASME DETC. 2006. Paper 99634. [14] Jelaska D. Transmissions with independently controllable output speed. Croatian Patent P20120521A, 2012. [15] Jelaska D. Gears and gear drives. Chichester, UK: John Wiley & Sons; 2012. [16] Müller HW. Epicyclic drive trains. USA: Wayne State University Press; 1982. [17] Dijkstra S, Bongers P, Van Baars GE. Control of wind turbine systems to reduce vibration and fatigue loading. In: Proc. of European wind energy conference, Thessaloniki; 10e14 October 1994.
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
A novel hybrid transmission for variable speed wind turbines Damir Jelaska*, Srdjan Podrug, Milan Perkusi c University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Split, Croatia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 March 2014 Accepted 8 April 2015 Available online
We herein advance a novel, power summation hybrid transmission, which has the ability to convert the variable speed of a wind turbine rotor shaft into the constant speed required at a generator shaft for a whole range of wind speeds, thereby eliminating the need for a frequency converter. The transmission consists of a single one-stage planetary gear train (PGT) with three rotating shafts and a simple control system consisting of a few sensors and a control motor controlled by a microprocessor. One of the PGT shafts is the input, another is the output, and the third is coupled to the control motor as second input. The optimal tip-speed ratio is kept constant at low wind speeds by controlling the speed of the control motor, maximising the capture of energy from the wind. The wind-rotor speed continues to vary above the rated wind speed zone, but the rotor shaft power is kept constant by using the same control system. In this way, a constant electrical power output is achieved without altering the blade pitch, i.e., with the rotor in a fixed geometry. A frame design procedure for the transmission is proposed, efficiency expressions are derived, an example transmission operation is presented and efficiency comparisons to a mainstream variable speed wind turbine are carried out. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Planetary gear train Power circulation Control system Efficiency
1. Introduction Concerns over global environmental threats and energy crises have contributed to the increasing use of renewable energy technologies. The production of electrical power from wind is the fastest growing and most cost effective sustainable energy technology. The objective of any system for utilising wind energy is to capture as much wind energy as possible at the lowest possible cost. There have been many attempts to achieve this using horizontal-axis wind turbines, which should deliver power at a constant frequency, whether they are connected to the grid or not. Many common appliances will not function properly if a constant frequency is not maintained [1]. Wind turbine rotors achieve their maximum efficiency at a particular tip-speed ratio. Therefore, stiffgrid-connected, constant-speed turbines, in which the wind rotor is connected to a generator at a fixed speed ratio, operate suboptimally. Whilst such turbines require no frequency converter, any rapid changes in electrical output will either cause the generator to be damaged or cause the generator circuit breaker to open.
* Corresponding author. University of Split, FESB, R. Boskovi ca 32, 21000 Split, Croatia. E-mail address: [email protected] (D. Jelaska). http://dx.doi.org/10.1016/j.renene.2015.04.021 0960-1481/© 2015 Elsevier Ltd. All rights reserved.
The fatigue loads are also increased, resulting in a reduced lifetime of the system or in an increased size and cost of the gearbox. It is therefore necessary either to control the power output from the wind rotor or to find a way of transforming the varying voltage and frequency to make the generated power compatible with the electrical grid [2]. Variable speed wind turbines have recently been used, which have a constant optimal tip-speed ratio below the rated wind speed and a constant speed and power output above it [3]. This type of turbine has a number of advantages: i) below the rated wind speed, the speed of the wind rotor varies with the wind speed to maintain the maximum power efficiency (commonly by controlling the torque of the generator shaft); ii) control of the rotor torque significantly reduces variations in gearbox torque above the rated level; iii) low rotor speeds in slow winds result in significantly lower aerodynamically generated acoustic emission than that obtained from other turbines; iv) the rotor can operate as a flywheel, smoothing the torque variations caused by short-lived power fluctuations in the rotor that may be caused by varying wind conditions. The shortcomings of variable speed turbines are that they require frequency converters and complex control systems. Electrical harmonics are also a critical issue for these turbines because they distort the normally smooth sinusoidal voltage [2]. The solution to the problem of capturing the maximum amount of wind energy at the minimum production cost has become a key challenge for designers and scientists, and considerable efforts have
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been made to develop various transmissions [4e13]. In all of them, a variable speed wind turbine is used with a transmission that gives a constant output speed over the entire range of possible wind speeds and a constant power output in the most effective range of wind speeds. Here, we comment on some of the most successful, in our opinion, all hybrid types of continuously variable transmission (CVT) and all comprising at least one PGT. Other transmissions [10e13] are not considered here because of their relatively low efficiencies due to friction member (belting or traction drives). Idan and Lior [4] proposed a hybrid variable speed transmission with two planetary transmission stages in which the annulus gear speed of the second stage (three rotating shafts) was controlled by three servo-motor generators (SMGs) to maintain the optimal rotor speed for a given wind speed, while the speed of the conventional asynchronous generator coupled with the sun gear was held constant. This design fulfils most of our requirements, but has some shortcomings, including a high cost for the electronics because of the three SMGs used to balance the radial forces, the fact that one fixed ratio PGT stage seems to be surplus, and that, when operated as a generator, the SMGs need a frequency converter to deliver power to the grid. Hicks and Cunliffe [5] presented a transmission consisting of a single PGT with its output shaft connected to the induction generator through a bevel gear drive, and the third shaft connected to a single SMG, which, assisted by the control system, made it possible to maintain the output shaft at a constant (±15%) speed. The shortcomings of this transmission are that the output speed is not quite constant, the bevel gear pair increases the transmission cost and power losses, and there are problems associated with the delivery of the SMG power to the grid. Zhao and Maiber [6] designed a power-split transmission with an electronically controlled PGT and two adjustment gear pairs, with one of the PGT shafts connected to the rotor shaft over the gear pair, another coupled to the generator, and the third shaft connected to the SMG. The output generator speed was kept constant by controlling the speed of the servo motor. Apart from the questionable use of two additional gear drives, which increase the machine costs and power losses, the same problems arise when delivering the SMG power as previously described. In another scheme [7], a transmission has a single PGT, achieving a constant output speed by controlling the variable third shaft speed using a torque converter driven by the output shaft. Although this is an interesting, innovative solution, beside the transmission, there was a conventional gear drive which additionally increases the power losses and production costs. Each of the transmissions considered above has problems associated with connecting the SMGs to the grid. Namely, an important question has not been addressed in those papers: are the SMGs connected to the same high voltage grid as main generator or to some other, low voltage grid? If the former is true, then the additional transformer is needed between SMGs and the grid. When the power of SMGs is delivered to the grid, the frequency converter is needed to be built in. The recently developed independently controllable transmission is also capable of running the output shaft at controllable speed independent of the input speed, even without control system [8,9]. This promises to solve most of the problems associated with variable-speed transmissions including in wind turbines. The transmission consists of two PGTs with three rotating shafts connected by two gear drives. However, there is one surplus output shaft with a variable, uncontrollable speed. The problem remains of how to manage the power of this shaft. We herein advance a simple, hybrid CVT that can convert the variable speed of a wind turbine rotor into a constant generator shaft speed over an entire range of wind speeds [14]. It has all of the advantages of a variable speed turbine, capturing the maximum wind energy in the low-wind-speed zone, and allowing a constant
79
electrical frequency to be produced without using a frequency converter. The transmission consists of a single PGT controlled by a control system, which is also used to maintain a constant power from the wind rotor shaft at wind speeds greater than the rated. 2. General description of novel transmission system The transmission system consists of a simple, power summation PGT, with a positive basic gear ratio and a control system. The transmission input shaft is connected to the wind turbine rotor; the second, hollow shaft is connected to the control motor; and the third, output shaft (passing through control motor shaft) is connected to the generator (Fig. 1). The transmission input shaft (wind rotor shaft) is connected to the central gear 1 shaft of the PGT, the output shaft is connected to the central gear 3 shaft, and the planet carrier (later simply called the carrier) shaft is connected to the control motor shaft. Planets 2 and 20 are in one piece with a shaft that is supported by the carrier C. The rotational speeds of the shafts of the three main PGT members, central gear 1, central gear 3 and the carrier (i.e., the speeds of the rotor, generator and control motor shafts nR, nG, and nM, respectively) are related to the basic gear ratio i0 of the PGT by the Willis equation [15,16]:
nR i0 nG þ ði0 1ÞnM ¼ 0;
(1)
where the basic gear ratio is defined as
i0 ¼
z2 z3 n1 nc nR nM ¼ ¼ ; z1 z02 n3 nc nG nM
(2)
where z1, z2, z3 and z20 are the numbers of teeth on gears 1, 2, 3 and 20 , respectively, and n1, n3, and nc are the rotational speeds of gears 1 and 3 and the carrier C, respectively. The basic PGT gear ratio should not be chosen arbitrarily, and its constraints, as well as those on the speed ratio, must be determined for this type of transmission. First, the signs (þ/) of the speed and torque must be determined for each shaft. As usual, the input speed and torque are taken to be positive. Then, for a chosen positive basic gear ratio 0 < i0 < 1, from Eq. (4), the generator shaft torque becomes negative, as does the control motor shaft torque (from the torque equilibrium equation). Therefore, the rotor shaft is the (torque) summation shaft, and the generator shaft is the power summation shaft. Because the control motor shaft power is positive
Planetary gear train 2
2´
C 1
3 Control motor
Generator
Rotor Fig. 1. Schematic of the proposed wind turbine drive-train.
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and its torque is negative, its speed is negative (i.e., the opposite direction to the generator shaft). Because the power and torque of the generator shaft are both negative, its speed is positive. The following constraints for the basic gear ratio and speed ratio for the central gears were obtained for the distributions of the speed, torque and power signs for the three rotating shafts, in accordance with previously published work [15,16]:
TR þ TM þ TG ¼ 0;
(5)
where TG is the generator shaft torque, using
TM ¼ h0 i0 1; TR
(6)
the input power ratio is derived as follows:
i0 < 1
0 < nR =nG < i0 :
(3)
This transmission is based on the ability of a PGT to rotate two shafts at variable speeds, while keeping the speed of the third shaft constant. For the proposed transmission, the generator shaft speed is kept constant over the entire range of wind speeds, and the control motor shaft runs at a speed that allows the rotor shaft to run at a speed that maintains a constant optimum tip-speed ratio in the low-wind-speed zone. Thus, the maximum amount of energy is captured from the wind. Above the rated wind speed, the rotor shaft is forced to run at a speed that results in a constant power output without a pitch control system and using only a low-cost wind rotor with a fixed geometry. The rated speed is defined as the lowest steady-state wind speed at which the turbine can produce the rated power. Large drops in voltage are not expected with this turbine because of the constant electrical frequency produced. Because of this and its high efficiency, a synchronous generator seems to be the most appropriate choice, although the simple asynchronous generator can be used. Because the control motor runs at low speeds and in a narrow speed range, an AC asynchronous motor with a speed control member can be used with this turbine configuration. The control system consists of a microprocessor, a control motor and at least three sensors (for the wind speed, wind rotor speed and wind rotor torque). The microprocessor receives signals from the sensors, converts them into the commanding signal for the motor speed, and then sends this signal to the control member of the control motor. This controller is, of course, just part of the turbine supervisory control system.
PM n ¼ ðh0 i0 1Þ M : PR nR
The transmission efficiency htr for the positive rolling power transferred from the rotor to the generator shaft is simply derived from the torque ratio of the central gear shafts, using Eqs. (1) and (5),
PG h ð1 i Þ htr ¼ ¼ 0 0 : PR þ PM h nR i þ 1 nR 0 0 nG nG
Because the speeds of the three rotating shafts are known for any wind speed, the steady-state torque and power ratios can be calculated, as can the transmission efficiency. The power and torque of each shaft can therefore be determined if the power or torque of the rotor shaft is known. The most important transmission parameter is the ratio between the control motor power PM and the rotor shaft power PR, hereafter termed the input power ratio. There are two reasons for this: i) the control motor is an auxiliary device and should have as low power as possible to reduce the turbine production cost, and ii) the control motor delivers less power to the transmission than it takes from the generator output power (see below), which causes a decrease in the total efficiency as the control motor power increases. The input power ratio is obtained from the torque ratio of the PGT central gear shafts TG/TR for the rolling power that flows from the shaft of central gear 1 (the rotor) to the shaft of central gear 3 (the generator) [15,16]:
TG ¼ h0 i0 ; TR
(4)
where h0 is the basic PGT efficiency. Accounting for the torque equilibrium equation
(8)
The power losses in the PGT bearings and seals and from idle motion are not included in Eq. (8) and the efficiency vary slightly from constant value of 0.988 obtained for assumed value of h0 ¼ 0.988 for all external gears, which means that the change of transmission ratio nR/nG slightly affects the efficiency and power losses. That is not in accordance with expression for the power losses of wind turbine planetary gear box, obtained by testings [3]. It is established there that, mostly as result of the relative increase in the ventilation and splash losses of the carrier with planets at power lower than rated, the planetary transmission efficiency significantly decreases with a decrease in the power, i.e. the wind speed. Therefore, the theoretical expression (8) is not quite reliable for wind speeds lower than the rated. Because the causes of the increased power loss are the same, the equation for calculating their values in kilowatts, in typical wind turbine gearboxes [3], can be used for the transmission:
PL;GB ¼ 3. Power and efficiency
(7)
½ð10=3 þ 2NÞPr þ 5NPi 1000
(9)
where Pi is the operating power level in kW, Pr is the rated power in kW, and N is the number of stages. By substituting N ¼ 1 in Eq. (9), the transmission power loss variation within the entire wind speed range can be approximated as follows:
PL;tr ¼
ð16=3ÞPr þ 5Pi 1000
(10)
It is interesting, and one more proof of validity of the expression (9), that, for the rated power, the efficiency calculated on the basis of Eq. (10) is obtained to be 0.988, same as pursuant to Eq. (8). The efficiencies calculated for a part load, i.e. for wind speed lower than rated are significantly reduced e up to 0.85 at cut-in speed. The rest mechanical losses, including the losses in main bearing and the power needed for the yaw system to operate, are included in the efficiency correction factor hrest, which also acts to decrease the generator input power. Our power and efficiency analyses are carried out assuming that the control motor is fed directly from the generator stator, i.e., it is driven by a portion (PM/hM) of the generator output power hGhrestPG (Fig. 2). The control motor power therefore flows from the control motor, through the transmission and generator, and back to the control motor, with power losses from the transmission, generator and control motor. Therefore, the generator output power is split into two parts, the power PM/hM required to drive the control motor and the remainder, which is the transformer input power,
D. Jelaska et al. / Renewable Energy 83 (2015) 78e84
Fig. 2. Schematic of the turbine power flows.
PT ¼ hG hrest PG þ PM =hM ;
(11)
where hG and hM are the efficiencies of the generator and control motor, respectively. The transformer input power can be derived from Eqs. (7), (8) and (11):
1 htr hG hrest hM nM PT ¼ ðh0 i0 1Þ htr hG hrest PR : hM nR
(12)
Therefore, the real output power of the wind turbine delivered to the grid is
1 htr hG hrest hM nM Pout ¼ hT ðh0 i0 1Þ htr hG hrest PR ; hM nR
(13)
where hT is the transformer efficiency. It slightly varies with the wind speed, i. e. with the part load fraction over 0.23 [3], from 0.99 at 0.23 part load fraction, over 0.993 at 0.5 part load fraction to 0.992 at full load (cut-off speed). In calculations, this value is deemed constant and equal to 0.992. The power-train efficiency, hPT, which includes the power losses from the rotor shaft to the transformer output, equals
Pout P 1 htr hG hM hrest : hPT ¼ ¼ hT htr hG hrest M PR PR hM
(14)
The overall turbine efficiency, accounting also for the wind energy losses in the blades, is equal to the product of the power-train efficiency and the constant, maximum value of the power coefficient, CP,max. Same as power-train efficiency, as expected, it decreases with increasing the input power ratio PM/PR and decreasing all the efficiencies. When efficiency is found to be unfavourable, a different basic gear ratio and/or a different PGT shaft distribution, or some type of composed PGT, should be chosen. 4. Turbine operation A wind turbine with the proposed transmission can keep the generator shaft speed constant over the entire range of wind speeds, keep the tip-speed ratio constant in the low-wind-speed zone, and keep the electrical power output constant in the zone above the rated wind speed. This is achieved using the control system, which enables the rotor shaft to run at the speed necessary to obtain the required turbine system state for the current wind speed. In the low-wind-speed zone, the microprocessor receives the measured wind speed signal and calculates the optimal tip-speed ratio l from the maximum power coefficient expression, CP,max ¼ CP,max(l), as demonstrated by Carlin et al. [2]. For a constant l value, the necessary rotor speed for the current measured wind speed and the required control motor speed to match the given generator speed are calculated using Eq. (1). The control motor
81
speed signal is sent to the control unit of the control motor, making it run at a speed that, in turn, makes the rotor run at the necessary speed to achieve a constant and optimal tip-speed ratio, resulting in maximum energy capture. When the wind speed signal is estimated not enough reliable, the optimal tip speed ratio can be achieved simply by maximising the rotor power: the control system would be set to change the rotor speed until the maximum rotor power is achieved for a certain state of wind. In the medium-speed zone, between the constant lopt zone and the zone above the rated wind speed, the rotor is allowed to run freely. The control motor shaft speed is controlled, enabling a constant generator speed for the measured rotor speed and given generator shaft speed. When the level of permitted acoustic emission is reached in this zone, the control system can keep the rotor, control motor and generator shaft speed constant, avoiding the undesirable noise. Although the blades are designed to stall in the zone above the rated wind speed, the same control system can be used to make the rotor shaft power curve as flat as possible. To achieve constant power from the rotor shaft for the current measured rotor shaft torque, the wind rotor speed should be
nR ¼
30 Pr ; p TR
(15)
where Pr is the rotor rated power that is known. When the output power is rated, PR is then calculated by the microprocessor using Eq. (13). The commanding signal nM for the required motor shaft speed, according to Eq. (1), is sent to the control motor from the microprocessor,
nM ¼
nR i0 nG : 1 i0
(16)
This speed allows a constant wind-rotor-shaft power to be maintained, along with a constant generator shaft speed. Clearly, a surplus or lack of aerodynamic power above the rated speed is compensated by the control motor. The generator is fed with a constant rotor power and the variable control motor power,
PG ¼ hPGT ðPR þ PM Þ:
(17)
Therefore, in the zone above the rated wind speed, the wind rotor and control motor shaft speeds are variable, and the generator speed is constant. The control motor and generator shaft power values are variable, and the wind rotor power is constant; the torques of all three main shafts are variable. Because the control motor power flow circulates from the control motor through the transmission and generator and back to the control motor, it does not significantly affect the power output delivered to the grid. This means that a constant rotor power reaches the grid, after being reduced by the transmission, generator, transformer and other mechanical power losses. Because the power losses vary with the wind speed (i.e., with the speeds of the shafts), the turbine output power deviates slightly from a constant value. Our simple control system, consisting of a control motor, a microprocessor and a few sensors, is therefore able to i) keep the generator shaft speed constant from the cut-in to the cut-off speeds, ii) keep the tip-speed ratio constant to achieve maximum energy capture in the low-wind-speed zone, and iii) keep the rotor power constant above the rated speed. By different algorithm given to microprocessor, this control system is able to keep constant the torque, instead the power. In such a way, the load increase of the power-train can be prevented, which could cause the cost increase. However, it would also result in variable output power which is not desirable.
It must be stressed that this transmission is considered for quasi-steady-state operation, which means that the kinetic energy of the rotary masses is neglected. This also means that, because of the acceleration of the rotating masses when the rotor and control motor speeds and torques change, it is hard to attain the most appropriate shaft speeds or to achieve a truly constant nominal rotor power in the zone above the rated speed. 5. Example transmission operation
350
80
300
70
250
60
200
50
150
40
100
30 power speed
50
As an example of the proposed transmission, a positive ratio PGT was chosen with a basic gear ratio:
i0 ¼
z2 $z3 22$19 ¼ 0:079558: ¼ z1 $z02 71$74
This PGT is feasible even for typical performance levels, having (three pairs of) planets in two planes. A 3-D transmission scheme is shown in Fig. 3. In the animation, the transmission shows the anticipated shaft speeds. Supplementary video related to this article can be found at http://dx.doi.org/10.1016/j.renene.2015.04.021. A steady-state operating scheme for a 310 kW wind turbine rotor of a fixed geometry, with the transmission and control systems described here, with an optimal tip-speed ratio lopt of 8.5 resulting in CP,max ¼ 0.5045, a rated wind speed vw, rated of 12.52 m/ s, a rotor diameter D of 24.2 m, and a constant generator speed nG of 1000 min1, is illustrated in Fig. 4. This scheme is an example rather than a suggestion, because the exact rotor speed variation, and especially the wind speed at which rotor begins to stall, depends on the shape of blades, which are not designed herein. Thus, the rotor speed operating scheme is inscribed in accordance with literature [1,4] and other. The power operating scheme at wind speeds below the rated is obtained by known rotor power formula depending on the cube of wind speed. The rated rotor power of 310 kW is defined with rated wind speed. Although the efficiencies of all the components decrease with a decrease in the wind speed (i.e., with a partial load), the generator, control motor, transmission basic efficiency, efficiency correction factor and transformer efficiency were approximated constant and were estimated to be hG ¼ 0.98, hM ¼ 0.98, h0 ¼ 0.988, hrest ¼ 0.996, and hT ¼ 0.992, respectively. Although the rating of the example turbine is 300 kW, in order to illustrate the efficiency competitiveness of the proposed turbine to recent mainstream turbines of megawatt ratings, the ultimate reach of the efficiencies hG, hM, hrest
0 0
5
10
15
20
speed, min-1
D. Jelaska et al. / Renewable Energy 83 (2015) 78e84
power, kW
82
20 10 25
wind speed, m/s Fig. 4. Operating scheme for the example turbine rotor.
and hT are estimated for megawatt ratings. The transmission efficiency is calculated pursuant to Eq. (10). The powers and torques of all of the shafts, including the output electrical power, together with the transmission and power-train efficiency, were determined for this operating scheme by means of MATLAB on the basis of presented or derived herein. They are shown in Fig. 5 for the entire range of wind speeds. It is notable that a maximum control motor power of 101 kW and a maximum generator power of 405 kW are needed for this machine. Thus, the generator and control motor should be designed for approximately those power values. Because the generator power delivered to the control motor was variable, the electrical power output in the zone above the rated wind speed was not quite constant, but varied within the range 293.15 ± 1.45 kW. The speed histories of the three main transmission shafts, measured in situ, at slowly varying wind speeds (i.e., excluding gusts) over 200 s (following previously published work [4]), are shown in Fig. 6 on the basis of Eq. (1). The optimised and free-run power histories of the rotor shaft are compared in Fig. 7. The green (in web version) shaded area between the power histories represents the energy gained by optimising the power coefficient. It is important to compare the efficiency of this novel turbine system with that of a mainstream variable speed wind turbine system. The overall efficiency of the proposed turbine, htot, which is the ratio of the output power delivered to the grid and the input wind power (energy per time), is equal to the product of the power coefficient CP,max and power train-efficiency hPT, while the overall efficiency of a typical variable speed wind turbine equals
htot;t ¼ CP;max $hGB $hG $hrest $hFC $hT
(18)
where hGB is the gearbox efficiency calculated by Eq. (9), and hFC is the frequency converter efficiency, which is taken constant and equal to 0.992. A comparison of the efficiencies shows that the transmission efficiency is always higher than the gearbox efficiency because it varies from 0.88 at the cut-in speed to 0.988 at the rated speed, while the gearbox efficiency varies from 0.845 at the cut-in speed to 0.976 at the rated speed. However, the ratio of htot to htot,t is the real measure for comparison the efficiencies of the presented and mainstream turbine system. It is obtained as follows: PM 1htr hG hM hrest
htr hG hrest PR htot hM ¼ htot;t hGB hG hrest hFC Fig. 3. 3-D animated model of the transmission.
:
(19)
The diagram of its variation is presented in Fig. 8. It can be observed that its gradients coincide with the gradients of the
D. Jelaska et al. / Renewable Energy 83 (2015) 78e84
200
a)
14
100
12
wind speed, m/s
power, kW
0 -100 -200 -300
-500
8
4 1200
generator speed, min-1
60 40 20
1000 800 600
0
100
-20
80 60
rotor generator motor
-40 -60
speed, min-1
torque, kNm
10
6
output motor generator
-400
b)
83
1 c) 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5
40 20 0 -20 motor rotor
-40
efficiency
-60 0
20
40
60
80
100
120
140
160
180
200
time, s Fig. 6. Speed diagrams for the turbine components at slowly varying wind speeds.
transmission power - train 0
5
10
15
20
25
wind speed, m/s Fig. 5. Power, torque and efficiency variations for the example turbine.
transmission power-train efficiency (Fig. 5c). At wind speeds greater than 8.9 m/s, the overall efficiency of turbine having the proposed transmission is higher, by up to 2.1%, than that of the turbine having typical gearbox, whereas below 8.9 m/s, it is always less, as much as the wind speed is closer to the cut-in speed. The reason is the increase in the input power ratio at low wind speeds. Compared to the overall efficiencies of other hybrid transmissions [4e9], because of their additional gear drive(s) or torque converter that cause additional power losses, the efficiency of turbine having the proposed transmission is significantly higher.
constant electrical power to be maintained without blade pitch control, i.e., with fixed rotor geometry. Because there is no need neither for a blade pitch system, nor for a frequency converter, the production cost of a wind turbine using this system is significantly lower than the cost of other variable speed wind turbines. This transmission is more efficient than typical gearboxes and other hybrid and ordinary CVTs, and the overall efficiency of a turbine using it is assessed to be slightly higher than that of a typical
6. Concluding remarks A novel hybrid transmission is proposed for use in variable speed wind turbines. This transmission can convert a variable wind rotor speed into a constant generator shaft speed over the entire wind speed range. Controlling the wind rotor speed allows the optimal constant tip-speed ratio to be maintained in the low-windspeed zone, enabling maximum energy capture. A constant wind rotor power in the zone above the rated wind speed allows a
Fig. 7. Comparison of the optimised and free-run rotor shaft powers at slowly varying wind speeds, as in Fig. 6.
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Further investigation is required to determine the dynamic behaviour of the proposed system in relation to the overall control system design and the behaviour of the electrical components. Test benches and simulation programs for the turbine system are planned, in the Power Transmission Laboratory in the Mechanical Engineering Department of the University of Split, Croatia.
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ηtot/ηtot,t
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Acknowledgements
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This study was supported by the Ministry of Education, Science and Sport of the Republic of Croatia [grant number 023-06921951749].
wind speed, m/s References Fig. 8. Ratio of total efficiencies of the proposed and mainstream wind turbine.
variable-speed wind turbine for mid- and high-wind speeds, whereas for wind speeds of less than 8.9 m/s, it is found to be slightly lower. Thus, it is indeed competitive to the mainstream variable speed wind turbines, and for sure, prevail to wind farms wind turbines situated at the sites with higher annual mean wind speed, such as off-shore wind farms. The proposed transmission offers other advantages, including i) a lower probability of current harmonics because a constant frequency and constant electrical power are delivered to the grid in the zone above the rated wind speed; ii) high operational reliability thanks to a low number of gears and other components, iii) lower cost, higher efficiency and a simpler control system with fewer problems connecting the SMG to the grid compared to existing hybrid wind turbine transmissions; iv) it is applicable whether the turbine is grid connected or standalone and whether the grid is stiff or not, and v) low inertia compared to variable pitch systems which respond slowly to wind speed variations [2,4,17]. However, the wind turbines that will use this transmission would have some shortcomings, including increased power of built-in electric machines, reduced overall efficiency close to cut-in speed and increase in rotor torque attitude above the rated speed that could increase the size of the components. Although the elimination of frequency converter and pitch control system seems to be sufficient to conclude that capital costs of the proposed turbine system are significantly lower than that of the mainstream variable speed wind turbine system, the cost comparison would be welcome.
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