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ON THE ELECTROMAGNETIC TORQUE PULSATION, TORSIONAL OSCILLATIONS, FAULT DETECTION AND DIAGNOSIS IN THE

SUBSYNCHRONOUS CASCADE DRIVE

IOANNIS P. TSOUMAS* and ATHANASIOS N. SAFACAS Electromechanical Energy Conversion Laboratory

Department of Electrical and Computer Engineering University of Patras

Greece

SUMMARY In the present paper a thorough study of the electromagnetic torque pulsation of the subsynchronous cascade drive (SCD) is carried out via simulation of a 4 MW drive installed in the cement industry. For the initial investigation, the shaft train and the mechanical coupling are considered rigid. The influence of the asynchronous machine’s speed, of the load torque-speed characteristics and of the asynchronous machine’s parameters on the electromagnetic torque pulsation is investigated and analyzed in detail. The conclusions drawn by the study via simulation are verified by experimental investigation using a 5.5 kW drive in the laboratory. Additionally, in the frame of this paper, a four-mass model of the mechanical subsystem is taken into account in order to study the torsional oscillations of the shaft train, caused by the pulsation of the electromagnetic torque. Some guidelines are proposed regarding the design of the mechanical subsystem in order to avoid excessive torsional oscillations which may lead to severe mechanical damage in the shaft train. Finally, the case of faults in the power electronic converter of the drive is examined; more specifically open circuits in the diode rectifier which is connected to the rotor terminals. The afore-mentioned fault modes of operation of the drive are investigated via simulation and experiment. It is shown that this kind of fault causes electromagnetic torque pulsation with amplitude much higher than usual and with frequencies near the natural frequencies of the mechanical subsystem. Consequently, faults in the power electronic converter should be immediately detected in order to avoid damages in the mechanical subsystem, something which has been proven by the experience in service too. To this direction, a novel approach for real-time fault detection and accurate diagnosis is proposed, based on the analysis of the rotor current space vector’s characteristic quantities (instantaneous angle and instantaneous frequency). The proposed technique does not need averaging over one period, does not need any normalization and detects the fault efficiently, even during the transients caused by the fault. The merits of this approach are demonstrated by simulation and experimental investigation. KEYWORDS Subsynchronous cascade drive, electromagnetic torque pulsation, torsional vibration, fault diagnosis.

*ytsoumas@ece.upatras.gr

I. INTRODUCTION The subsynchronous cascade drive (SCD) is usually employed in high voltage applications in the MW range for torque and speed control of asynchronous machines, especially when the control is needed in limited speed range below the synchronous speed, so that the converter power is rated at only a part of the motor nominal power. One of its most widespread applications is to drive high power fans in the cement industry. The structure of the SCD is depicted in figure 1. The power electronic converter consists of a diode rectifier and a thyristor inverter. Occasionally the diode rectifier is replaced by a thyristor rectifier in order to reduce the size of the inductor in the DC link and to have a fault tolerant operation in case of interruptions in the mains supply [1]. A serious drawback of the SCD is the pulsation of the asynchronous motor electromagnetic torque due to the operation of the rectifier in the rotor circuit. Several investigations of the drive behaviour have been carried out in the past [2] - [5], which have proven the existence of significant electromagnetic torque pulsation. However, an extensive and in depth investigation regarding the influence of the load torque-speed characteristics and of the asynchronous machine parameters on the electromagnetic torque pulsations has not been carried out. Furthermore, no information has been published regarding the influence of these pulsations on the torsional oscillations of the mechanical subsystem (shaft, coupling) and how the parameters of the mechanical subsystem should be selected in order to avoid excessive torsional oscillations, especially for high power drives. The experience in service has shown that the torque pulsation may cause severe torsional oscillations and consequently catastrophic failure of the mechanical system. In situ measurements in the cement industry have also proven that lateral vibrations can be generated, which often result in damage at the motor bearings. In the present paper an analysis regarding the influence of the speed of the asynchronous machine, of the load torque-speed characteristics and of the asynchronous machine parameters on the electromagnetic torque pulsation is carried out. The impact of the afore-mentioned pulsation on the torsional oscillations of the mechanical part of the drive is also investigated. Purpose of the study is to provide a detailed analysis of the problems which may arise during the operation of the SCD and deduce some guidelines regarding the optimum design of the electromechanical system. The electromagnetic torque pulsation in case of faults in the power electronic converter is also investigated and a novel approach for real-time fault detection and accurate diagnosis is proposed, based on the analysis of the rotor current space vector’s characteristic quantities. II. ELECTROMAGNETIC TORQUE PULSATION The system depicted in fig. 1 has been simulated in Matlab/Simulink. Characteristic simulation results of a 4 MW subsynchronous cascade drive are depicted in the figures of the following page. In figure 2

Fig. 1. Basic structure of the subsynchronous cascade drive.

1

Fig. 2. Rotor phase current waveform at slip

s=1/5 (simulation results of a 4 MW drive).

Fig. 3. Locus of the rotor current space vector

referred to the rotor reference frame at slip s=1/5 (simulation results of a 4 MW drive).

Fig. 4. Harmonic components of the rotor

current space vector referred to the rotor reference frame at slip s=1/5 (simulation results of a 4 MW drive).

Fig. 5. Locus of the stator current space vector

referred to the rotor reference frame at slip s=1/5 (simulation results of a 4 MW drive).

Fig. 6. Electromagnetic torque waveform at slip

s=1/5 (simulation results of a 4 MW drive).

Fig. 7. Electromagnetic torque harmonic compo-

nents at slip s=1/5 (simulation results of a 4 MW drive).

2

the waveform of the rotor current is depicted at slip value s=1/5 (n=1200 min-1). This slip value has been selected in order to facilitate the comparison between the frequencies of the harmonics of the electromagnetic quantities obtained by simulation and those expected by theoretical analysis, since all the harmonic components have frequencies at multiples of 10 Hz, which is the frequency of the fundamental harmonic for the specific slip value ( fR=sfS ). In figure 3 the locus of the rotor current space vector Ri

r is depicted, in a reference coordinate system rotating with the rotor (the capital

subscripts “D”, “Q” are used for the rotor quantities in the d – q axes). One can observe the characteristic hexagonal form of the locus and the periodicity of the space vector rotation at each 1/6 part of the locus. For a long time interval the space vector stands still on the vertices of the hexagon. During the current commutation in the rectifier’s diodes the vector moves from one vertex to the next. The average angular velocity of the vector rotation is equal to sωs , where ωs is the angular frequency of the stator supply voltage. Due to the periodicity of the vector rotation equal to 1/6 of the rotor period, the harmonic components of the rotor space vector are expected at frequencies equal to

(1 6 )Rn sf k f= + ⋅ ⋅s , (1) where sf is the frequency of the stator supply voltage and k = ±1, ±2, ±3, … . The simulation results come in agreement with equation (1), as it can be seen in figure 4 where the results of the Discrete Fourier Transform (DFT) of the rotor current space vector at slip value s=1/5 are depicted. The modulus of the harmonic components of the space vector

rRni is depicted in dB, normalized to the

amplitude of the fundamental 1rRi which has frequency equal to sfs=10 Hz. Figure 5 depicts the locus

of the stator current space vector in a reference frame rotating with the rotor (the lower-case subscripts “d”, “q” are used for the stator quantities in the d – q axes). Due to the presence of the diode rectifier in the rotor circuit the locus has not a circular form and the vector rotation has a periodicity equal to 1/6 of the rotor period. The segment AB is repeated 6 times during one rotor period, but at each repeat the vector has also turn at an angle equal to integer multiples of 600 . The stator space vector harmonic components (in a reference frame connected to the rotor) have frequencies equal to those of the rotor current vector, given by equation (1), but their amplitude is smaller, depending on the stator resistance and the leakage inductance of the asynchronous machine

Sir

[2]. The electromagnetic torque of the asynchronous machine can be calculated by the formula

* '( )e h s RM pL Im i i=r r

, (2)

where p is number of the asynchronous machine’s pole pairs, Lh is the magnetizing inductance, the asterisk indicates the complex conjugate and the accent-mark is used for the rotor quantities which are referred to the stator side, taking into account the voltage ratio between the stator and the rotor. The result of the interaction of the rotor and the stator current space vectors according to equation (2) is shown in figure 6, where the electromagnetic torque waveform is depicted. There is to see a significant torque oscillation with peak-to-peak amplitude, calculated equal to approximately 22% of the average value. From the harmonics point of view this pulsation can be analyzed as following: The harmonics of the rotor and stator space vectors which rotate with the same angular velocity produce constant electromagnetic torques; those which rotate with different angular velocities produce oscillating electromagnetic torques. The frequencies of these pulsating torques are equal to the difference of the frequencies between the harmonic components of the stator and rotor space vectors, that is

6Mn sf k f= ⋅ ⋅s , (3) where k = 1, 2, 3, … . For slip value s=1/5 the above formula results to fΜn = 60 Hz, 120 Hz, 180 Hz, …, as it can be also seen in figure 7 where the results of the DFT of the electromagnetic torque waveform are depicted. In the figures of the following page the results of an investigation of the SCD behaviour at different speeds are depicted; more specifically at the speed range 450 min-1- 1450 min-1. Characteristic quantities have been calculated at all integer multiples of 50 min-1, including also the speeds 1375 min-1 (s=1/12) and 1416,67 min-1 (s=1/18). The load torque ML has been considered constant, equal to 25000 Nm which is near the nominal torque of the asynchronous motor. The calculated average value of the electromagnetic torque is shown in figure 8. In figure 9 the calculated commutation angle � of the

3

4

Fig. 8. Calculated average value of the electro-

magnetic torque as a function of speed (simulation results of a 4 MW drive).

Fig. 9. Calculated commutation angle of the

rotor current as a function of speed (simulation results of a 4 MW drive).

Fig. 10. Rotor resistance referred to the stator side

as a function of speed.

Fig. 11. Modulus of the 5th and 7th harmonic of

the rotor current space vector in relation to the modulus of the fundamental as a function of speed (simulation results of a 4 MW drive).

Fig. 12. Calculated peak-to-peak amplitude of the

electromagnetic torque pulsation in relation to its average value (simulation results of a 4 MW drive).

Fig. 13. Calculated amplitude of the 6th, 12th and

18th harmonic of the electromagnetic torque in relation to its average value as a function of speed (simulation results of a 4 MW drive).

rotor currents is depicted. Without taking into account the cases that the slip has value at integer multiples of 1/6 (these are special cases) one can see that the commutation angle tends to increase as the speed increases. This trend gets more distinct when the speed takes values greater than 1300 min-1. An explanation of the afore-mentioned fact can be given if one considers the well-known equivalent circuit of the asynchronous machine, where the rotor parameters are referred to the stator. In such a consideration the rotor resistance is a hyperbolic function of the slip ( R'

R / s ). For the specific 4 MW drive the values of the afore-mentioned quantity are depicted in figure 10. The hyperbolic increase of the resistance in the commutation circuit results in an increase of the commutation angle. The cases that the slip has values at multiples of 1/6 are special cases which will be discussed in this paper. In the graph of figure 11 the moduli of the 5th and the 7th harmonic of the rotor current space vector are depicted in relation to the modulus of the fundamental harmonic. Without taking again into account the cases that s=1/6, one can observe that the amplitude of the harmonics tends to decrease as the the speed inreases, due to the increase of the commutation angle. The torque pulsation decreases as the speed increases (figures 12 and 13), due to the fact that the commutation angle increases and therefore the rotor ant stator currents waveforms get closer to the sinusoidal form. An exception to the last remark is the case that the slip is equal to 1/6 (n=1200 min-1 for an asynchronous machine with two pole pairs). Despite the fact that the commutation angle increases and the amplitude of the rotor harmonics decreases, the torque pulsation increases (figure 12). The same stands for the dominant torque harmonic, i.e. the 6th harmonic (figure 13). In the specific slip value exceptional phenomena take place, which have been studied in [2] and [4]. The rotor current space vector harmonics rotate in relation to the stator with frequencies given by the following formula

' (1 6 )Rn sf k f= + ⋅s , (4)

where k = ±1, ±2, ±3, … . The rotating wave created by the 5th harmonic of the rotor current (k = -1), stands still in space at s=1/6 and therefore does not induce a corresponding harmonic in the stator windings. This would result in an impressive increase of the electromagnetic torque pulsation if the 5th harmonic of the rotor current remained unaffected [2]. But the effective reactance increases strongly for the 5th rotor harmonic [4], so its amplitude is greatly reduced at this slip value as it can be seen in figure 11. One can also observe in figure 9 an impressive increase of the commutation angle which can be easily explained by looking the graphs of figures 14 and 15 where the space vectors of the induced rotor voltage are depicted for a time interval equal to 1/6 of the rotor period at different values of the slip. During the specific time interval there is a commutation of the current in the diode rectifier from phase A to phase C, more specifically from the diode D6 to the diode D2 (see the numbers of the diodes in figure 1). During that commutation the rotor current space vector moves from the vertex of the hexagon located at -300 to the vertex located at +300. At slip s=1/5 the trajectory of the space vector of the induced rotor voltage has almost the form of a segment of a circle (figure 14). On the contrary, at slip s=1/5 the space vector’s trajectory has a complete different form. There is to see that

Fig. 14. Space vector of the induced rotor voltage

at slip s=1/5 during 1/6 of the rotor period (simulation results of a 4 MW drive).

Fig. 15. Space vector of the induced rotor

voltage at slip s=1/6 during 1/6 of the rotor period (simulation results of a 4 MW drive).

5

for a specific time interval the q-component of the space vector remains almost zero. The q-component of the space vector is proportional to the voltage difference between phases B and C, the one which is responsible for the commutation between the diodes D6 and D2. The result is that the commutation tends to stop for a while, something which leads to an impressive increase of the commutation angle. For this reason the rotor currents waveforms become more sinusoidal and instead of having a tremendous increase of the torque pulsation, there is an increase of approximately 2,5% (figure 12). A more realistic case study is that of the load torque being proportional to the square of the angular speed of rotation, since the SCD is usually used to drive high power fans and pumps. Characteristic results of such an investigation are depicted in the figures of the next page. In figure 16 the calculated average value of the asynchronous machine’s electromagnetic torque is shown. The graph of figure 17 depicts the commutation angle of the diode rectifier as a function of speed. There is to see a significant decrease of the commutation angle as the speed (and the consequently the load torque) decreases. This is to be expected since the average value of the DC link current is approximately proportional to the average value of the electromagnetic torque. The decrease of the DC link current leads to a decrease of the commutation angle which in turn results in an increase of the amplitude of the rotor current harmonics in relation to the amplitude of the fundamental (figure 18). An unexpected result is the following: as it can be seen in figure 19, despite the fact that the harmonic content of the rotor currents increases, the electromagnetic torque pulsation gets smaller as the speed (and consequently the load) decreases! The same stands for the amplitude of the electromagnetic torque harmonic components (figure 20). At the same time the average value of the electromagnetic torque is reduced, something which leads to a significant decrease of the torque pulsation in absolute values as the speed decreases (figure 21). The above discussed drive behaviour is confirmed by experimental results taken at a 5.5 kW drive in the laboratory. Characteristic experimental results are depicted in figures 22-29. In figures 22 and 23 the loci of the rotor and stator space vector respectively are shown at slip s=1/5. The graph of figure 24 depicts the measured waveform of the torque on the motor shaft at slip s=1/5. This waveform has been measured using a torque sensor (straingauge). There is to see a dominant torque pulsation with frequency 6sfs (there are six oscillations during one rotor period which is 0.1 sec for the specific slip value) due to the operation of diode rectifier connected to the rotor terminals. When the motor operated without the power electronic converter (with the rotor terminals short-circuited) the dominant pulsation had frequency equal to that of the shaft rotation; an oscillation caused by misalignments and imbalances that always exist. The DFT of the waveform of figure 24 is depicted on the graph of figure 25. One can observe the dominant harmonic component with frequency 6sfs=60 Hz, which has amplitude equal to -17 dB in relation to the average value, that is 14% of the average torque value. An experimental investigation of the drive operational behaviour has been carried out, considering the load torque proportional to the square of the angular speed of rotation, which is the usual load characteristic of the SCD. The calculate average torque value on the rotor shaft as a function of speed is shown in figure 26. In figure 27 the calculated commutaion angle as a function of speed is depicted. A significant decrease of the commutation angle takes place as the speed (and the consequently the load torque) decreases, something which leads to an increase of the amplitude of the rotor space vector’s harmonics (figure 28). Despite this fact, the amplitude of the 6th harmonic of the shaft torque in relation to its average value decreases, something which comes in agreement with the simulation results. This unexpected simulation and experimental result has been investigated in [6] and it has been found out that, besides the commutation angle of the rotor currents, there is an additional factor which affects the amplitude of the electromagnetic torque pulsation. According to equation (2) the instantaneous electromagnetic torque is proportional to the modulus of the outer product of the stator and rotor current space vectors. The stator current space vector can be expressed as

'S h R

SS

L ii

LΨ + ⋅

=

r rr

, (5)

which is the sum of two terms: one term proportional to the rotor current vector Rir

st slip values approac

and one term

proportional to the stator flux vector . The stator flux vector locus in mo hes SΨr

6

Fig. 16. Calculated average value of the electro-

magnetic torque as a function of speed (simulation results of a 4 MW drive).

Fig. 17. Calculated commutation angle of the

rotor current as a function of speed (simulation results of a 4 MW drive).

Fig. 18. Modulus of the 5th and 7th harmonic of

the rotor current space vector in relation to the modulus of the fundamental as a function of speed (simulation results of a 4 MW drive).

Fig. 19. Calculated peak-to-peak amplitude of the

electromagnetic torque pulsation in relation to its average value (simulation results of a 4 MW drive).

7

Fig. 20. Calculated amplitude of the 6th, 12th and

18th harmonic of the electromagnetic torque in relation to its average value as a function of speed (simulation results of a 4 MW drive).

Fig. 21. Calculated amplitude of the 6th, 12th and

18th harmonic of the electromagnetic torque as a function of speed (simulation results of a 4 MW drive).

Fig. 22. Locus of the rotor current space vector

referred to the rotor reference frame at slip s=1/5 (experimental results of a 5.5 kW drive).

F

rs=1/5 (experimental results of a 5.5 kW drive).

ig. 23. Locus of the stator current space vector eferred to the rotor reference frame at slip

Fig. 24. Motor shaft torque waveform at slip

s=1/5 (experimental results of a 5.5 kW drive).

cr

Fig. 25. Electromagnetic torque harmonic omponents at slip s=1/5 (experimental esults of a 5.5 kW drive).

Fig. 26. Calculated average value of the shaft

torque as a function of speed (experimental results of a 5.5 kW dr ive).

Fig. 27. Calculated commutation angle of the rotor

current as a function of speed (experimental results of a 5.5 kW drive).

8

Fig. 28. Modulus of the 5th and 7th harmonic of

the rotor current space vector in relation to the modulus of the fundamental as a function of speed (experimental results of of a 5.5 kW drive).

Fig. 29. Calculated amplitude of the 6th harmonic

of the shaft torque in relation to its average value as a function of speed (experimental results of a 5.5 kW drive).

the form of a circle (with exception the cases that the slip takes values at integer multiples of 1/6). The instantaneous angle of the stator flux space vector lags almost 900 to the stator voltage space vector angle (something which stands especially for high power asynchronous machines, which have a small stator resistance). As the load decreases the average value of the angle difference between the rotor current space vector and the stator voltage space vector decreases too, something expected from theoretical analysis [6] and also confirmed by the simulation results (figure 30). A theoretical investigation carried out in [6], using equations (2) and (5) has also shown that the decrease of the afore-mentioned angle leads to a decrease of the electromagnetic torque pulsation. This is the reason why the electromagnetic torque pulsation decreases as the load decreases, despite the fact that the rotor currents get less sinusoidal (because the commutation angle decreases).

9

Fig. 30. Maximum, minimum and average value

of the angle difference between the rotor current space vector and the stator voltage space vector as a function of speed (simulation results of a 4 MW drive).

Fig. 31. Calculated peak-to-peak amplitude of the

electromagnetic torque pulsation in relation to its average value as a function of speed when the rotor leakage inductance is doubled (simulation results of a 4 MW drive).

Fig. 32. Calculated commutation angle of the

rotor current as a function of speed when the rotor leakage inductance is doubled (simulation results of a 4 MW drive).

Fig. 33. Calculated average value of the angle

difference between the rotor current space vector and the stator voltage space vector as a function of speed (simulation results of a 4 MW drive).

order to make an init l investigation of the drive torsional behaviour one can initially consider a simple two-mass model, as depicted in figure 34, where the symbols k and c and for the stiffness and the damping coefficient respectively, JM is the motor moment of inertia and JL is the load moment of inertia. By examining the torsional mode shape of such a system one can make a very important remark; due to the fact that in fan driving systems the load moment of inertia is many times greater than the motor moment of inertia, the ratio JL/JM has a large value, something which results to a significant strain on the shaft. However, this simple two-mass system is not a very realistic approach. A more realistic approach is to use a four-mass model (figure 36) in order to express mathematically the mechanical system. This model is described by the following equations:

The above remark explains the simulation results presented in figures 31 and 33. In figure 31 the calculated peak-to-peak amplitude of the electromagnetic torque pulsation in relation to its average value as a function of speed when the rotor leakage inductance is doubled. There is to see that by doubling the rotor leakage inductance the torque pulsation increases, although the commutation angle increases (figure 31) and the rotor currents become more sinusoidal. This happens because by doubling the rotor leakage inductance, the rotor currents lag in relation to the stator voltage increases (figure 33). Similar results are obtained if the stator leakage inductances gets doubled [6]. III. TORSIONAL OSCILLATIONS In ia

st

Fig. 34. Two-mass torsional system.

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Fig. 35. Torsional mode shape of a two-mass torsional system.

1( )θ θ θΜ Μ − Μ⋅ + ⋅ − =&&M C P C P eJ k M

1 1 1 1 2

1 2

( ) ( )

) ( )

θ θ θ θ θ

θ θ

θ θ θ

−

−

⋅ + ⋅ − + ⋅ − =

+ ⋅ − =

⋅ + ⋅ − = −

&&

&&

C P C P M C P C P M C P C P C P

C P L C P L

J k k

k

J k M

0

02 2 2(θ θ θ⋅ + ⋅ −&&C P C P C P C P C PJ k

2( )−L L C P L L C P L

The system described by equations (6) has three eigenfrequencies of oscillation. In order to investigate the possibility of resonance one has to construct the so-called “Cambell diagram” or “interference diagram” depicted in figure 37. On that diagram the frequencies of the three first harmonics of the SCD’s torque pulsation are depicted as a function of speed, as well as the eigenfrequencies of the shaft train. The three eigenfrequencies are depicted with thick lines in order to emphasize the fact that there

. (6)

ccording to the investigation of the previous section, the electromagnetic torque pulsation when the ad torque is proportional to the square of the angular rotation speed, increases significantly in

is an uncertainty in the eigenfrequencies calculation, due to the uncertainty in the estimation of the exact value of the stiffness coefficients and the moments of inertia of the mechanical system. The small circles on the diagram depict the resonance points. Alo

Fig. 36. Four-mass torsional system.

11

12

absolute values in the speed range 1000 min-1-1500 min-1 (see figure 21). Thence it arises that it is preferable for the eigenfrequencies to have a large value, so that resonance takes place at the speed range below 1000 min-1, where the torque pulsation is small. Additionally, if all the eigenfrequencies had value above 210 Hz there wouldn’t be possibility of resonance with the strongest and most dangerous harmonic component of the torque pulsation (the one that has frequency equal to six times the slip frequency). The afore-mentioned remarks should be taken into account when designing the shaft trains of this kind of drives in order to increase the stiffness coefficients of the shaft train. However, the possibility of resonance can’t always be eliminated, so prudent design practice considers elastomer-type couplings necessary in this type of drives [7]. Among others, this type of couplings cause a considerable torsional damping (hysteresis damping). The stiffness coefficient of the afore mentioned couplings is not constant, but it depends on the angle of twist [8], as depicted on figure 38. Characteristic simulation results of the electromechanical system of the 4 MW drive are depicted in figures 39-41 and 43-45. Initially the case of resonance of the harmonic of the electromagnetic torque with frequency 12sfs with a torsional eigenfrequency of the mechanical system in the region 1240 min-1- 1260 min-1 (see figure 37) has been investigated via simulation. In figure 39 the speed of the asynchronous machine in this region of resonance is depicted. In most speed regions the speed oscillates with frequency 6sfs , which is the dominant harmonic of the torque pulsation. On the contrary, at this speed region the dominant speed oscillation has frequency equal to 12sfs , due to resonance with the specific harmonic component of the torque pulsation. However, the specific resonance does not cause excessive torsional stresses on the shafts and the coupling (as it can be seen in figures 40 and 41), due to the damping caused mainly by the elastomer-type coupling. The afore-mentioned resonance has been observed in the installed MW drive

]. Figure 42 depicts measurements of the speed of the asynchronous machine in the installed cement which in all likelihood is caused by the ar 1260 min-1 and not near 1245 min-1 as

ed by theoretical investigation, but this speed difference lies within the error margins regarding the estimation of the stiffness coefficients and the moments of inertia of the mechanical system. As expected by theoretical and simulation investigation, the specific resonance does not cause problems to the installed system. In figures 43 and 44 characteristic simulation results are depicted for the cas of reso nce o electromagnetic torque harmonic with frequency 6sfs with a torsional eigenfrequency of the mechanical system at the speed region near 1440 min-1. This is the worst case of resonance for the

4[9industry drive. There is to see speed oscillations near 1260 min-1

fore-mentioned resonance. The speed oscillation takes place neaexpect

e na f the

Fig. 37.Cambell diagram for the investigated 4 MW SCD.

Fig. 38. Stiffness coefficient of the elastomer-

type coupling in the installed 4 MW drive as a function of the angle of twist.

Fig. 39. Speed of the asynchronous machine in the

region of resonance of the 12th harmonic of the electromagnetic torque with a torsional eigenfrequency of the mechanical system (simulation results of a 4 MW drive).

Fig. 40. Torsional torque on the shaft of the

asynchronous machine in the region of resonance of the 12th harmonic of the electromagnetic torque with a torsional eigenfrequency of the mechanical system (simulation results of a 4 MW drive).

Fig. 41. Torsional torque on the elastomer-type

coupling in the region of resonance of the 12th harmonic of the electromagnetic torque with a torsional eigenfrequency of the mechanical system (simulation results of a 4 MW drive).

system under study. There is to see that the maximum torque value reaches 200000 Nm, a value high enough to cause a plastic deformation of the shaft. The maximum torque on the coupling reaches 210000 Nm, a value high enough to destroy the coupling. The damping coefficient of the selected coupling is not capable of an adequate suppression of the torsional oscillations in this case. IV. FAULTS IN THE POWER ELECTRONIC CONVERTER The electromagnetic torque pulsation of the SCD is much stronger in case of faults in the power electronic converter connected to the rotor terminals according to simulation results. This kind of faults can lead to unexpected excessive torsional stresses and consequently to damages in the mechanical system, something which has been proven by an incident during commissioning of a 5500 HP SCD [10]. A backfiring in the power electronic converter had initiated an excitation of the shaft tring. The coupling hub was broken resulting into flying coupling fragments and the fan shaft and the s

motor were seriously damaged.

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Fig. 42. Measured speed and vibration in an installed 4 MW drive [9].

Fig. 43.

agnetic torque with a torsional

4. Torsional torque on the elastomer-type coupling in the region of resonance of the 6th harmonic o

Fig. 4

f the electromagnetic torque with a torsional eigenfrequency of

Torsional torque on the shaft of the asynchronous machine in the region of resonance of the 6th harmonic of theelectrom

Another example of fault in the power electronic converter is the case of an open diode. The waveform of the electromagnetic torque in this case is depicted in figure 45. There is to see an

the mechanical system (simulation results of a 4 MW drive).

eigenfrequency of the mechanical system (simulation results of a 4 MW drive).

increased scillation of the electromagnetic torque, compared to the normal operation. The DFT of this

onic components at all the torque pulsation is now

owaveform is depicted in figure 46, where one can see that there are harmmultiples of the slip frequency. The strongest harmonic component of located at the slip frequency and its amplitude is -8.16 dB in relation to the average value (approximately 39% of the average value). The second stronger harmonic at two times the slip frequency has amplitude equal to -9.85 dB, which is approximately 32% of the average value. The harmonic component with frequency 6sfs has amplitude 19.5% of the average value. Consequently, as it deduced by the observation of the graph in figure 46, the oscillating components not only have greater amplitude compared to normal operation, but they are also located at an increased number of slip-dependent frequencies, increasing the possibility of mechanical resonance.

14

Fig. 45. Electromagnetic torque waveform at slip

s=1/5 when one diode of the rectifier is open-circuited (simulation results of a 4 MW drive).

Fig. 46. Electromagnetic torque harmonic compo-

nents at slip s=1/5 when one diode of the rectifier is open-circuited (simulation results of a 4 MW drive).

Fig. 47. Simulation results of a 4 MW drive - Rotor

current space vector angle versus time during open diode faults: a) Diode 1 open. b) Diode 2 open. c) Diode 3 open. d) Diode 4 open. e) Diode 5 open. f) Diode 6 open.

Fig. 48. Experimental results of a 5.5 kW drive -

Rotor current space vector angle versus time during open diode faults: a) Diode 1 open. b) Diode 2 open. c) Diode 3 open. d) Diode

4 open. e) Diode 5 open. f) Diode 6 open.

TABLE I

GLE TRANSITIONS IN CASE OF OPEN DIODES FAULTAN S

OPEN DIODE ANGLE TRANSITIONS DURING THE PRESENCE OF THE FAULT

D1 900 1500 2100 2700 900

D2 1500 2100 2700 3300 1500

D3 300 2100 2700 3300 300

D4 300 900 2700 3300 300

D5 300 900 1500 3300 300

D6 300 900 1500 2100 300

TABLE II

ANGLE TRANSITIONS IN CASE OF OPEN PHASE FAULTS

OPEN PHASE ANGLE TRANSITIONS DURING THE PRESENCE OF THE FAULT

A 900 2700 900

B 1500 3300 1500

C 300 2100 300

15

Also, this kind of asymmetric operation is closely related to the “Goerges phenomenon” [11]. Due to the asymmetry in the rotor circuit the torque speed characteristic curve will change and more specifically torque dips will take place at slips where the negative sequence rotor current space vector components, seen from a reference frame connected to the stator, stand still. Furthermore, the strong negative sequence rotor current components will produce subfrequency harmonics in the stator current, which in turn can cause a noticeable voltage flicker in the power supply system [11].Such an operation must be detected immediately in order to stop operation or continue operation at constant speed using the starting resistors.

The last decade a lot of research has been oriented towards the development of electric machines fault diagnosis techniques via Motor Current Signature Analysis (MCSA). MCSA can also be employed for the detection and localization of faults in power electronic converters, leading this way to a complete diagnostic system for electric drives. Several approaches have been proposed in the past

r open semiconductor fault diagnosis. Some of t re based on monitoring the current space vector

order to anotherdetection and localization of an fault. Ex

has be at in case of open circuit fault the space vector trajectory have a circular rm any more, but there will be a linear part in the trajectory that has a characteristic slope, depending

that the faulty transistor belongs to. However, this method is not applicable in the case examined here, since the switching frequency is low and the space vector trajectory has also these characteristic slopes during normal operation. It has been also proposed in [15] the use of the instantaneous frequency of the space vector as a diagnostic feature. In [16] it has been shown that the computation of the space vector’s instantaneous frequency, normalized to its mean value gives as a clear indication of the presence of an open diode. However it can not be determined which diode is open. Moreover, it has been proven that similar peaks occur when one rotor phase is open. A new approach for the detection of open circuit faults has been proposed by the authors of the present paper in [16] which does not need averaging over one period, does not need any normalization and detects the fault efficiently, even during the transients caused by the fault. The method is based on the alculation of the rotor current space vector angle. e values of the space vector angles during one

i(experimfigures, 300 up differen e of a fwhich d h case are haracteristic 180 transition which has been highli hted wansitions in case of open phase fault are listed. A monitoring system can detect two not normal angle ansitions and then, with the help of a lookup table based on tables I and II, the open circuit fault can

identified and located. The combined information of the instantaneous angle and the instantaneous frequenc also used for the real-time detection and localization of short-circuited diode V. CON SION An investigation of the asynchronous machine’s electromagnetic torque pulsatio rried out. It has be hown th ation angle there is another im strongly t ulsation ge value of the angle fferencespace vector and the stator voltage space vector. Due to the afore entioned is a decrease of the relative torque pulsation as the load decreases. Consequently (as it had been proven by simulatio d exper driving systems where the load torque is approximately proportional to the square of the angular speed of rota on, the most dangerous speed range regarding the torque pulsation is the range 1100 – 1500 min-1. As speed increases from 1000 min-1 to 1250 min-1 the mplitude of the torque pulsation gets double in absolute values.

fo hem amean value [12], [13], and others are based on monitocurrents [14]. In both the previously mentioned met

calculate the diagnostic variable. In [15]open semiconductor

en shown th

ring the normalized DC component of the phase hods averaging over one period is necessary in

approach has been employed for the amining the operation of a PWM inverter

will not itfoon the phase

c Throtor period in case of open diode faults are dep

ental results). They have been calculated in th the space vector angle does not rotate fromt trajectories which characterize the presenciode is open. The angle transitions in eac

0

cted in figures 47 (simulation results) and 48 e interval [ 00 , 360 0]. As it can be seen in these

to 3300 with steps of 600, but it follows aulty diode and can be used to identify listed in table I. In each case there is a ith bold numbers In table II the angle c g

trtrbe easily

y can bes [17].

CLU

n has been caen s at besides the commut portant factor that affects

between the rotor current he p ’s amplitude: the avera di-m factor there

n an imental results), for fanti

a

16

17

Additionally, eigenfrequencies near two times the stator voltage fre

978, Vol. 2,

gy Conversion, Vol. 20, No. 3, September 2005, pages 512 – 519). 3] A. Mendes, A. Cardoso “Fault diagnosis in a rectifier-inverter system used in variable speed ac drives by

rk’s vector approach” (European Conference on Power Electronics (EPE), land, 1999, Conference CD-ROM).

4] S. Abramik, W. Sleszynski, J. Nieznanski, H. Piquet, “Performance of diagnosis methods for IGBT open

nd, 2007, Conference CD-ROM).

The torque pulsation due to the operation of the rectifier may lead to excessive torsional oscillations in the shaft train. The torsional stresses are aggrevated by the fact that in fan-driving systems the load moment of inertia is many times greater than the motor moment of inertia. As a general guideline it can be said that the stiffness coefficient must have a high value, in order to move the eigenfrequencies out of the range of the relatively low frequencies of the torque pulsation harmonic components. However, the exact selection of the stiffness coefficients must be made taking into account that eigenfrequencies near the stator voltage supply frequency must be avoided, because this is the frequency of the electromagnetic torque oscillation during start-up.

quency must also be avoided, because that is the frequency of the torque oscillation during stator three-phase or two-phase short-circuits. Some fault modes of the rectifier of the subsynchronous cascade drive have been also concisely investigated and a novel approach for fault detection has been presented, based on the rotor current space vector angle patterns. In case of open circuit faults the proposed approach can easily detect and locate the fault. Short circuit faults can be also detected using combined information of the angle and the instantaneous frequency of the space vector. Further research is carried out at the moment for the evaluation of the performance of the proposed technique and the results will be published in the near future. BIBLIOGRAPHY [1] R. Olofson,, K. Aberg, P. Wikström, “A reactorless slip energy recovery system” (4th IEE International

Conference on Power Electronics and Variable Speed Drives, London – UK, 1990, pages 306-311). [2] A. Safacas “Investigation of the static and the dynamic behaviour of an asynchronous machine controlled

by a power electronic converter in the rotor” (Dissertation, University of Karlsruhe, 1971, in German). [3] A. Safacas “Calculation of the electromagnetic quantities of a slip-ring asynchronous machine controlled

by a power electronic converter” (ETZ-A, Vol. 93 No. 1, 1972, pages 16-20, in German). [4] H. Kleinrath “Torque pulsation of an induction motor with speed control by a static frequency converter

in the slip ring circuit” (International Conference on Electrical Machines ( ICEM ), Brussels, 1pages E3/8-1 – E3/8-9).

[5] B. Zahawi, L. Refoufi “Detailed Analysis of Harmonic effects in the static Kramer drive” (International Conference on Electrical Machines ( ICEM ), Espoo-Finland, 2000, pages 41 – 45).

[6] I. Tsoumas “Dynamic analysis of the subsynchronous cascade drive and development of fault diagnosis methods” (Dissertation, University of Patras, 2007, in Greek).

[7] C. Mayer, “Torsional Vibration Problems and Analysis of Cement Industry Drives” (IEEE Transactions on Industry Applications, Vol.17, No. 1, 1981, pages 81-89).

[8] Flexible Compression Sleeve Coupling (available at www.azhollink.nl/images/Elco%20pennen koppeling2.pdf, 2007).

[9] AGET HERACLES Cement Industry Technical Reports, 2004. [10] C. Meckel “Mechanical damage of a subsynchronous cascade drive due to torsional resonance”, (IEEE

IAS Cement Industry Technical Conference, Vancouver-Canada, 2001, pages 133-150). [11] H. Garbarino, E. Gross, “The Goerges phenomenon – Induction motors with unbalanced rotor

impedances” (AIEE Transactions, Vol. 69, 1950, pages 1569-1575). [12] D. Diallo, H. Benbouzid, D. Hamad, X. Pierre, “Fault detection and diagnosis in an induction machine

drive: a pattern recognition approach based on Concordia stator mean current vector” (IEEE Transactions on Ener

[1the average current PaLausanne-Switzer

[1circuit faults in voltage source active rectifiers” (IEEE Power Electronics Specialists Conference, Aachen-Germany, 2004, Conference CD-ROM).

[15] R. Peuget, S. Courtine, J. Rognon, “Fault detection and isolation on a PWM inverter by knowledge base model” (IEEE Transactions on Industry Applications, Vol. 34, No. 6, 1998, pages 1318-1326).

[16] I. Tsoumas, A. Safacas, “Fault detection in the subsynchronous cascade drive via analysis of the rotor current space vector” (International Conference on Electrical Machines (ICEM), Chania-Crete Island-Greece, 2006, Conference CD-ROM).

[17] I. Tsoumas, A. Safacas, “Investigation of a Novel Approach for Fault Diagnosis in Power Electronic Converters: The Case of the Subsynchronous Cascade Drive” (IEEE International Symposium on Diagnostics for Electric Machines, Power Electronics and Drives (SDEMPED), Krakow-Pola