Fault Simulation and Pattern Recognition in a Modular Generator under two different Power Converter Configurations Marios C. Sousounis and Markus A. Mueller, Member, IEEE
Abstract—Key focus of this paper is the investigation of condition monitoring and fault-tolerant control in the modular multi-stage air-cored permanent magnet synchronous generator called ‘C’ core generator under different electrical connections. Condition monitoring and fault-tolerant control have been identified as a means of improving the reliability and availability of offshore or inaccessible renewable energy devices. As a result, two different ways of connecting modular generator stages are presented. Based on the above topologies two wind turbine models are designed in MATLAB®/Simulink® and fault-tolerance is investigated by implementing single electrical faults in one of the stages, such as single phase open circuit, diode short circuit, two phase short circuit and diode open circuit. It was found that the first topology offers fault-tolerance against the single phase open circuit fault while the second offers isolation between generator stages in all types of faults. Finally, the signal processing techniques of alpha – beta current locus, Power Spectral Density analysis and Continuous Wavelet Transformation have been implemented in order to extract detectable patterns of the electrical faults. Index Terms—Fault tolerance, condition monitoring, fault detection, Permanent magnet machines.
I. INTRODUCTION
A
s more offshore renewable energy devices -offshore wind turbines and marine energy converters- are being deployed at inaccessible sites under harsh conditions, the need for increased reliability and operability of these devices has risen. Even more so, in order to reduce operation and maintenance costs (O&M) and maximise renewable energy availability. Studies [1], [2] carried out for wind turbines showed that the O&M costs in offshore projects is about the 25% - 30% of the energy generation costs which is substantially higher than that in onshore projects. The increased O&M costs are the result of high unpredicted failure rate of the wind turbine and its subcomponents. In addition, offshore devices have high rated power, and therefore energy The completion of this paper was made with the help of the postgraduate programme co-funded through the Act “Bursary Programme Greek State Scholarship Foundation with the process of individualized assessment of academic year 2011-2012” by the resources of O.P. “Education and Lifelong Learning” of the European Social Fund (ESF) and the NSRF, of 2007-2013. M. C. Sousounis and M. A. Mueller are with the Institute for Energy Systems, University of Edinburgh, Edinburgh, EH3 9JL, UK (phone: +44(0)131 650 5629 email:
[email protected]).
lost due to failures has a significant impact on revenue as well, increasing the risk of investments. What is more, a failure can result in large downtimes as a result of the inaccessible and the harsh offshore environment. According to [1] and [3] unscheduled maintenance of the generator and the gearbox accounts for 42% of the total downtime of a wind turbine. The reliability can be increased by using Condition Monitoring (CM) techniques at the generator and adopting Direct Drive technology [4]. CM [5] is the continuous evaluation of the health of a system throughout its serviceable life. Data is collected during the operation of the device and is analysed using appropriate techniques in order to predict and identify component failures. In addition, maintenance can be planned at the right time minimising repair costs and downtime. However, the availability of renewable energy at inaccessible sites will still be reduced due to downtime. Therefore, fault-tolerant control (FTC) of the renewable energy generators is highly desirable for multi-MW devices. Fault-tolerance is defined by [6] as the ability of a system to continue operating after a fault has been identified in one of its components. Therefore, in a fault-tolerant system a failure does not immediately shutdown the system but rather, it continues to operate at reduced output until maintenance takes place. Studies [4], [7] bear out that Direct Drive generators and their power electronics still have high failure rates but direct drive technology offers a great opportunity to improve the reliability and availability of generators by utilising a number of concepts. Different designs have been suggested [8] – [10] in order to mitigate problems appearing in high rated direct drive generators such as unstable air-gap, heavy and expensive supporting structure with high volume and expensive fully rated power electronics. In this paper an air-cored multi-stage permanent magnet generator [10], known as C-core generator, will be examined due to its modularity and the advantages this demonstrates for FTC. The aim of this study is to: • Explore different ways of achieving fault tolerance in the C-core generator. • Simulate possible and most frequent electrical faults in the generator and the power electronics of a wind turbine using SimPowerSystemsTM toolbox of Simulink®.
•
Extract recognizable faulted patterns from currents using different Condition Monitoring techniques.
II. THE MODULAR GENERATOR – C CORE GENERATOR The evolution and development of the ‘C’ core generator is described analytically by M.A. Mueller & A.S. McDonald in [10]. The ‘C’ core generator is an air-cored permanent magnet synchronous machine named after the modules that compose the rotor. Each rotor module is C-shaped with one permanent magnet in either C-arm as shown in Fig. 1. In addition, the ‘C’ core module offers a longitudinal and a transversal flux path resulting in less active steel needed [10].
Fig. 1. 'C' core rotor module (a) Longitudinal flux path (b) Transversal flux path [10].
Another feature of the ‘C’ core machine is that it does not have iron in the stator and so it is called air-cored. Therefore no attraction forces are induced between the rotor and the stator. The air-gap flux density in air-cored machines is usually lower than iron-cored machines because the stator and air-gap have a higher magnetic reluctance than iron [10]. Apart from the rotor modularisation using the ‘C’ core modules, the unique topology of the machine offers the ability for further modularity by stacking smaller machines axially (stages) at the same radius [11] (Fig. 2). Consequently, by stacking a number of smaller machines, multi-MW generators can be built with the same rotor radius as the smaller machines.
above offers many structural and maintenance advantages in renewable energy applications, especially offshore. According to [10] the structural mass of a c-core generator could be less than half compared to a standard generator. In addition, the modularity of the rotor and stator c-core model is advantageous regarding reliable operation and reduced maintenance requirements. As stated before, offshore wind O&M costs are expected to be high reaching 20 - 30% of levelised production costs [11]. Consequently, ‘C’ core generator technology described above, with less weight than conventional generators and modularity enables the removal of parts of the machine rather than the whole generator when a fault occurs. This feature perfectly fits for the purposes of large multi-MW generators in offshore and onshore renewable energy applications. In the c-core generator, the lack of magnetic attraction forces between stator and rotor simplifies the removal of faulted modules without the need for specialist barges [11]. On top of that, condition monitoring techniques could be established to detect the exact location and the severity of the fault. The properly informed maintenance staff will be able to replace faulted modules faster, reducing the total downtime of the renewable energy device during maintenance. In [12] the necessary considerations to develop a faulttolerant control system are discussed. Evaluating ‘C’ core concept, the requirements of fault-tolerance between the stages are met through redundancy, partitioning and modularity of the machine. III. CASE STUDY: WIND TURBINE SYSTEM The ‘C’ core generator analysed in the current study is a hypothetical 60kW generator consisted of four 15kW stages. Two different ways of connecting the stages are examined. A single 15kW ‘C’ core generator has been designed, built and tested [13], the details of which are given in Table I. TABLE I PARAMETERS OF THE 15KW 'C' CORE GENERATOR
Fig. 2. Schematic diagram of the axial flux 'C' core generator with four stages [11].
The modular assembly of the ‘C’ core generator described
Parameter
Value
Units (SI)
Stator phase resistance Pole Pairs (p) Inertia (J) q-axis inductance d-axis inductance Flux linkage (λ) Nominal wind speed Nominal speed
1.04 16 62.3 0.01 0.01 2.87 12 150
Ohm kg.m2 H H mWb m/s rpm
Rated phase current
16.6
A
Each phase has 8 coils, the two coils connected in series and four parallel paths. Since ‘C’ core generator is a three phase machine the total number of coils is 24. The wind turbine model accepts as inputs the wind speed and the rotational speed of the rotor in order to calculate optimum top speed ratio (λopt), power coefficient through a look-up table and finally the mechanical torque (Tm), which
will be used as an input to the generator model. The rotational speed of the rotor is acquired from the generator while the wind speed input is a real-time wind speed waveform (Fig. 3). 14
Wind Speed (m/s)
13.5 13 12.5 12 11.5 11 10.5 0
2
4
6
8
10 Time (s)
12
14
16
18
20
since in the ‘C’ core generator phases are not physically isolated and fault tolerance is achieved between generator stages, short circuit faults between phases must also be considered. The list of faults modelled is given below and schematic diagrams of the faults on the topology models are shown in Fig. 5a and Fig. 5b. • Open circuit fault of one phase • Diode short circuit • Short circuit fault between two phases • Diode open circuit Faults that demonstrate similar results will not be presented for the sake of simplicity.
Fig. 3. Waveform of the real-time wind speed used as input to the model.
The schematic diagrams of the models used in the simulations are shown in Fig. 4a (topology 1) in which all stages are connected in parallel feeding into one rectifier and Fig. 4b (topology 2) in which each stage is connected to a separate rectifier.
Fig. 5. Schematic diagrams of the possible faults in a) topology 1 b) topology 2.
V. CONDITION MONITORING
Fig. 4. Schematic diagrams of the complete models of a) topology 1 b) topology 2.
IV. FAULT MODELING According to [11] the possible winding faults that may occur in an electrical machine and their power electronics must be restricted to the main electromagnetic faults. However,
Three different CM techniques for current monitoring are examined in this paper. Firstly, the transformation of threephase currents to alpha-beta currents (α – β) using the Clarke transformation (1) as proposed by [14] for PMSM.
Iα 1 − 12 2 3 I β = 3 ⋅ 0 2 Iγ 12 12
− 12 I a − 23 I b 1 2 Ic
(1)
− j 2πft ∫−T x(t )e dt T
2
(2)
Where Sx is the PSD, T is the chosen time interval, E is the expectation and x(t) is the signal in the time domain which is the three phase current output of the generator for the system in this paper. Defining the units of the PSD analysis, the Fourier transform of the current signal has units A/Hz and the magnitude squared of the Fourier transform has units (A/Hz)2. However, the inverse of time interval has units Hz therefore the overall units are A2/Hz. Because the system is electrical we can convert the units to W/Hz and apply logarithmic scale which leads to dBW/Hz. Finally, Continuous Wavelet Transform (CWT) is examined since it has been identified as a powerful tool to identify faults during variable speed operation and stochastic aerodynamic load [15], [16]. The CWT compares the selected signal to shifted and scaled versions of a wavelet function ψ. The CWT of a signal x(t) is implemented by the following equation. +∞
C (a, b; x(t ),ψ (t ) ) = ∫ x(t ) −∞
1 * t − b ψ dt a a
(3)
Where C(a,b;x(t),ψ(t)) is the computed wavelet coefficient, x(t) is the signal in the time domain, generator current in this paper, a is the scaling factor, b is the position parameter and ψ* is the complex conjugate of the wavelet function. The energy of each coefficient can be calculated using (4).
S = C2
(4)
The alpha – beta currents’ locus and PSD analysis were performed online in order to demonstrate their ability to create detectable faulted patterns during the operation of the system. For simulation purposes, CWT results were not performed online due to the involved computational needs which are also one of the disadvantages of this method. VI. SIMULATIONS AND DISCUSSION In this section only some of the significant results will be presented due to space constraints. All faults modelled are demonstrated in phase A of the first generator stage and CM
A. Open circuit fault of one phase 30 20
Topology 1 − Stage one three phase currents 30
Phase A Phase B Phase C
20
0
0
−10
−10
−20
−20
−30 11.98
Topology 1 − Stage two three phase currents Phase A Phase B Phase C
10
Iabc (A)
Iabc (A)
10
12
12.02
12.04 Time (s)
12.06
12.08
12.1 −30 11.98
12
12.02
12.04 Time (s)
12.06
12.08
12.1
Fig. 6. Comparing results of 3-phase currents between stage one (left) and stage two (right) during an open circuit fault at t = 12s in topology 1. 30 20
Topology 2 − Stage one three phase current Phase A Phase B Phase C
30 20
0
Phase A Phase B Phace C
0
−10
−10
−20
−20
−30 11.98
Topology 2 − Stage Two three phase currents
10
10
Iabc (A)
1 S x ( f ) = lim E T →∞ 2T
uses 3-phase currents of the first stage except otherwise stated. Rectifier faults are imposed to the upper phase A diode except otherwise stated.
Iabc (A)
Secondly, the calculation of the Power Spectral Density (PSD) of the three phase currents in order to locate harmonic components in the frequency domain after a fault has happened. PSD computes the distribution of average power of a random or periodic signal as a function of frequency. There are two different ways to calculate PSD, either by calculating the average of the Fourier transform magnitude squared, over a large time interval or by computing the Fourier transform of the auto-correlation function. In this paper the first approach of calculating PSD is employed and is shown in (2).
12
12.02
12.04 Time (s)
12.06
12.08
−30 12.1 11.98
12
12.02
12.04 Time (s)
12.06
12.08
12.1
Fig. 7. Comparing results of 3-phase currents between stage one (left) and stage two (right) during an open circuit fault at t = 12s in topology 2.
During an open circuit fault in phase A the faulted phase current goes to zero while the amplitude and frequency of phase B and C currents change so that the sum of the three phase currents is always zero. In topology 1 (Fig. 6) phase B and C currents are continuous with increasing amplitude. The peak value of the current after the fault is up to two times higher than the peak value of the healthy current. This is not the case in topology 2 (Fig. 7) where phase B and C currents appear with discontinuities and peak values lower than the ones during healthy operation. The reason of this is because there are time periods when all the rectifier diodes are reverse biased due to the level of the DC link voltage. Observing the way an open circuit fault in stage one affects currents in stage two we can see that in topology 2, despite the fault, stage two three-phase currents are unaffected whereas in topology 1 a small increase in the peak value of phase A and a small decrease in the peak values of phases B and C are demonstrated. In all cases stages three and four produce similar output as stage two does. B. Diode short circuit fault Currents generated by a diode short circuit fault are extremely high if high per unit inductance is not used. High currents can cause fault propagation or even lead to destructive damage. During a diode short circuit fault all stages in topology 1 have similar output as the one shown in Fig. 8 since they are connected to a single rectifier. The current waveform of the faulted phase takes a high positive mean value while the currents of the un-faulted phases take a negative mean value. This way the sum of the 3-phase currents is zero. In topology 2, the faulted stage has the output of Fig. 8 while the healthy
stages two, three and four generate the output of Fig. 9. We can easily observe that in topology 2 the faulted stage can be identified and isolated by analysing the currents whereas in topology 1 a generator shut down is required for maintenance. 200 150
Phase A Phase B Phase C
100
Iabc (A)
50 0
Currents generated by a short circuit fault between phases A and B are high if high per unit inductance is not used. During a short circuit fault between two phases all stages in topology 1 have similar output as shown in Fig. 10 since stages are connected in parallel. In topology 2, the faulted stage has the output of Fig. 10 while stages two, three and four generate the output of Fig. 11. So, fault tolerant control can be triggered in topology 2 by extracting the faulted patterns and isolating the faulted stage whereas in topology 1 shut down is required for maintenance. D. Diode open circuit fault
−50 −100
30
−150 11.98
20
12
12.02
12.04 Time (s)
12.06
12.08
Phase A Phase B Phase C
12.1 10
Fig. 8. Three-phase currents during a diode short circuit fault at t = 12s.
0 30 20
Topology 2 − Stage two 3−phase currents
−10
Phase A Phase B Phase C
−20
10
Iabc (A)
−30 11.98
12
12.02
0 −10 −20
30
12
12.02
12.04 Time (s)
12.06
12.08
12.1
Fig. 9. Stage two three-phase currents in topology 2 during a diode short circuit fault at t = 12s in stage one. Current waveforms are unaffected by the fault.
20
12.06
12.08
12.1
Topology 2 − Stage two 3−phase currents Phase A Phase B Phase C
10
Iabc (A)
−30 11.98
12.04 Time (s)
Fig. 12. Three-phase currents during a diode open circuit fault in upper leg of phase A at t = 12s.
0
−10
C. Short circuit fault between two phases
−20
150 100
Phase A Phase B Phase C
−30 11.98
Iabc (A)
50
12.02
12.04 Time (s)
12.06
12.08
12.1
0
−50 −100 −150 11.98
12
12.02
12.04 Time (s)
12.06
12.08
12.1
Fig. 10. Three-phase currents during short circuit fault between phases A and B at t = 12s. Topology 2 − Stage two 3−phase currents
30 20
Phase A Phase B Phase C
10
Iabc (A)
12
Fig. 13. Stage two three-phase currents in topology 2 during a diode open circuit fault at t = 12s in stage one. Current waveforms are unaffected by the fault.
0
−10 −20 −30 11.98
12
12.02
12.04 Time (s)
12.06
12.08
12.1
Fig. 11. Stage two three-phase currents in topology 2 during a short circuit fault between phases A and B at t = 12s in stage one. Current waveforms are unaffected by the fault.
During a diode open circuit fault all stages in topology 1 have similar output, Fig. 12, since they are connected to a single rectifier. The mean value of the faulted phase current is positive and a discontinuity appears since diodes are reversed biased during a period of time due to the voltage level of the DC link. In topology 2, the faulted stage output is as shown in Fig. 12 while stages two, three and four generate the output of Fig. 13. E. Locus of alpha – beta currents Results acquired using locus of α – β currents do not have significant differences between the two topologies and thereby a mix of results is presented in Figs. 14 – 17. We can observe that α – β currents’ locus always produces different patterns, when different faults occur. These faulted patterns are quite different from the normal operation ones and thus they are easily identifiable. What is more, α – β currents’ locus can produce an identifiable pattern of the exact faulted phase. This can be seen in Fig. 14 where the open phase can be determined by
observing the direction of the pattern created. The same is demonstrated in Fig. 15 for a diode short circuit fault of the upper leg of the rectifier.
currents within the designed limits of the system.
Topology 2 − Alpha Beta Currents 30
Topology 1 − Alpha Beta Currents
0 −10
−10
0 10 Alpha Current (A)
Phase A Open Circuit Fault
20 0 −20 −40 −20
20
−10
Topology 1 − Alpha Beta currents 20
0 10 Alpha Current (A)
20
Topology 2 − Alpha Beta Currents
20 10 0 −10 −20
20
Phase B Open Circuit Fault
Beta Current (A)
10
−20 −20
Normal Operation Phase A diode Open Circuit Fault
Topology 1 − Alpha Beta Currents 40
Normal Operation
Beta Current (A)
Beta Current (A)
20
Beta Current (A)
Beta Current (A)
Phase C Open Circuit Fault
10 0 −10 −20 −40
−20
0 20 Alpha Current (A)
10
−30 −30
0
−20
−10 0 10 Alpha Current (A)
20
Topology 2 − Alpha Beta Currents 100
50
Beta Current (A)
Beta Current (A)
Normal Operation Phase A diode Short Circuit Fault
0
−50
50
Normal Operation Phase C diode Open Circuit Fault
0
−200
−150
−100 −50 Alpha Current (A)
0
50
−20
0
20 40 60 80 Alpha Current (A)
100
120
Fig 15. Comparing results of α – β currents’ locus during normal operation and diode short circuit fault of different phases.
Topology 1 − Alpha Beta Currents
Beta Current (A)
60
Normal Operation Short Circuit Fault between phases A and B
40 20 0 −20 −40 −60 −100
−50
20
30
30
Fig. 14. Comparing results of α – β currents’ locus during normal operation and open circuit fault of different phases. Topology 1 − Alpha Beta currents
−10 0 10 Alpha Current (A)
Fig. 17. Comparing results of α – β currents’ locus during normal operation and phase A diode open circuit fault.
−10 −20 −30
40
−20
0 50 Alpha Current (A)
100
Fig. 16. Comparing results of α – β currents’ locus during normal operation and short circuit fault between phases A and B.
However, in order for these patterns to be fully identifiable usually some operating cycles are needed. The time delay needed for the patterns to evolve might lead to fault propagation because, in the case of a diode circuit fault or a two phase short circuit fault for example, currents take very high values which can affect other parts of the system. The α – β technique could be used with a higher degree of confidence if higher per unit inductance was used which could limit
F. Power Spectral Density analysis The results, acquired using PSD analysis, are similar between the two different topologies. A number of changes in the characteristic frequencies produced by faults are identifiable when using PSD analysis. For example, in Fig. 18b the frequency component of phases B and C at three times the operating fundamental frequency (frequency output at the operating point is approximately 57Hz) is increased by 20dBW/Hz during an open circuit fault of phase A compared with the healthy operation shown in Fig. 18a. The same trend also appears during diode short and open circuit fault, Figs 18c and 18e respectively. During a short circuit fault between phases A and B the fundamental frequency component of phase A and B currents increases about 20dBW/Hz. It is noteworthy to mention that faults at the power electronics side generate multiple spectral peaks due to current separation and major changes in current waveform. On the other hand, faults at the generator side produce results based on the zeroing of the current of one phase and the change of the other two phases’ electrical cycle. However, PSD results are highly affected by variable speed operation and it is probable that the increase or change in the spectral peaks created by faults might overlap with other conditions generated by events, such as wind gusts or voltage dips. These conditions have to be studied before the development of a fault-tolerant control strategy based on PSD since they can trigger it falsely.
G. Continuous Wavelet Transformation results Analyzed Signal Ib (A)
20 0 −20 11.9
11.95
12
12.05
12.1
12.15
Frequency(Hz)
Scalogram Percentage of energy for each wavelet coefficient 113.77778 95.255814 81.92 71.859649 64 57.690141 52.512821 48.188235 44.521739 41.373737 38.641509 36.247788 34.133333 32.251969 11.9
−4
x 10 3.5 3 2.5 2 1.5 1 0.5
11.95
12
12.05 Time (s)
12.1
12.15
0
Fig. 19. Continuous Wavelet Transformation of stage one phase B current. At t = 12s an open circuit fault occurs at phase A of stage one. The operating frequency of the generator at the moment of fault is also shown. Analyzed Signal Ia (A)
0 −50
−100
Frequency(Hz)
−150 11.9
113.77778 95.255814 81.92 71.859649 64 57.690141 52.512821 48.188235 44.521739 41.373737 38.641509 36.247788 34.133333 32.251969 11.9
11.95
12 12.05 12.1 Scalogram Percentage of energy for each wavelet coefficient
12.15 −4
x 10 2.5
2
1.5
1
0.5
11.95
12
12.05 Time (s)
12.1
12.15
0
Fig. 20. Continuous Wavelet Transformation of stage one phase A current. At t = 12s a diode short circuit fault occurs at the upper leg of phase A. The operating frequency of the generator at the moment of fault is also shown.
Ia (A)
Analyzed Signal 50 0 −50
Frequency(Hz)
11.9
Fig. 18. Power Spectral Density analysis during a) Normal Operation b) Open circuit fault of phase A c) Diode short circuit fault d) Short circuit fault between phases A and B e) Diode open circuit fault. CH1 (red) depicts phase A current PSD, CH2 (green) phase B current PSD and CH3 (blue) phase C current PSD.
113.77778 95.255814 81.92 71.859649 64 57.690141 52.512821 48.188235 44.521739 41.373737 38.641509 36.247788 34.133333 32.251969 11.9
11.95
12 12.05 12.1 Scalogram Percentage of energy for each wavelet coefficient
12.15 −4
x 10 2.5
2
1.5
1
0.5
11.95
12
12.05 Time (s)
12.1
12.15
0
Fig. 21. Continuous Wavelet Transformation of stage one phase A current. At t = 12s a short circuit fault between phases A and B occurs. The operating frequency of the generator at the moment of fault is also shown.
Figs. 19 – 21 demonstrate the results of CWT on generator currents during an open circuit fault of one phase, a diode short circuit fault and a short circuit fault between two phases respectively. The significant change in wavelet coefficients after a fault has happened is evident in all the cases presented. We can observe that in Fig. 19 the wavelet coefficients do not
increase immediately after the fault but rather after the current has a peak value twice as big compared to normal operation. In Fig 20 and Fig. 21 high wavelet coefficients are produced after the fault. CWT implemented in this paper could not identify the diode open circuit fault by monitoring the currents. VII. CONCLUSIONS Four different faults were simulated in order to determine the appropriate architecture for fault-tolerance in a four stage ‘C’ core generator. The study showed that topology 2 offers electrical isolation against all types of faults whereas topology 1 electrically isolates generator stages to tolerable levels during the single phase open circuit fault only. As a result, in topology 2, when a fault is identified in a generator stage it can be isolated and the remaining three healthy stages can operate normally producing ¾ of the previous total power. In terms of fault identification, locus of α – β currents can be used to identify the type and location of the fault, PSD analysis produces characteristic patterns during the different types of faults and finally further research is needed in order to extract identifiable patterns from all types of electrical faults using wavelet transformations. Future research will focus in the development of a fault identification tool that could exploit faulted patterns and isolate faults effectively by triggering fault tolerant control. ACKNOWLEDGEMENTS The authors would like to thank NGenTec Ltd for allowing publication and Juan Pablo Echenique for providing source code for plotting CWT. REFERENCES [1]
D. McMillan and G.W. Ault, “Quantification of Condition Monitoring Benefit for Offshore Wind Turbines,” WIND ENGINEERING, vol. 31, no. 4, May 2007, pp. 267–285. [2] G.J.W. Van Bussel and C. Schöntag, “Operation and maintenance aspects of large offshore windfarms,” Proc. Eur. Wind Energy Conf., Dublin, Ireland, Oct. 6-9, 1997, pp. 272-275. [3] P.J. Tavner, J. Xiang, and F. Spinato, “Reliability Analysis for Wind Turbines,” Wind Energy, vol. 10, pp. 1–18, 2007. [4] F. Spinato, P. J. Tavner, G. J. W. van Bussel, and E. Koutoulakos, “Reliability of wind turbine subassemblies,” IET Renew. Power Gener., vol. 3, no. 4, pp. 387–401, Dec. 2009. [5] P. Tavner, L. Ran, J. Penman, and H. Sedding, Condition Monitoring of Rotating Electrical Machines, 2nd ed. Stevenage, U.K.: IET, 2008, pp. 1-9. [6] H. Polinder, H. Lendenmann, R. Chin, and W.M. Arshad, “Fault tolerant generator systems for wind turbines,” Proc. IEEE International Electric Machines and Drives Conference, Miami, 3-6 May 2009, pp. 675-681. [7] D. McMillan and G. W. Ault, “Techno-economic comparison of operational aspects for direct drive and gearbox-driven wind turbines,” IEEE Trans. Energy Convers., vol. 25, no. 1, pp. 191–198, Mar. 2010. [8] E. Spooner, P. Gordon, and C.D. French, “Lightweight, ironless-stator, PM generators for direct-drive wind turbines,” in Proc. Int. Power Electronics, Machines and Drives Conf., Mar. 2004, vol. 1, pp. 29–33. [9] Z. Chen and E. Spooner, “A modular, permanent-magnet generator for variable speed wind turbines,” in Proc. IEE EMD 1995, pp. 453–457. [10] M.A. Mueller, and A.S. McDonald, “A Lightweight Low-speed Permanent Magnet Electrical Generator for Direct-drive Wind Turbines,” Wind Energy, vol. 12, no. 8, pp.768 – 780, 2009.
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