on wound rotor induction machine rotor electrical

Accepted for presentation at IET PEMD 2016, Glasgow, UK

ON WOUND ROTOR INDUCTION MACHINE ROTOR ELECTRICAL UNBALANCE RECOGNITION USING STATOR FRAME VIBRATION SPECTRAL ANALYSIS D.S. Vilchis-Rodriguez†, S. Djurović†, N. Sarma†, K. Tshiloz†, A.C. Smith† and Y. Wei* †

School of Electrical and Electronic Engineering, University of Manchester, United Kingdom *Zhengzhou University of Light Industry, People’s Republic of China Email: [email protected], [email protected]

Keywords: Condition monitoring, induction machine, pulsating torque, vibration spectrum, rotor electrical unbalance

Abstract This paper investigates the torque and vibration signal spectra of wound rotor induction machines when subjected to different levels of rotor electrical unbalance. A harmonic machine model numerical study is first performed to identify the electromagnetic torque signal spectral components related to operation without or with electrical unbalance. Once the understanding of the correlation between the operating conditions and the torque spectral content is established, a series of laboratory tests are conducted to evaluate the manifestation and detectability of electromagnetically induced vibration matching the identified disturbance frequencies in the torque model study. The magnitude of rotor electrical unbalance spectral signature in the vibration signal is assessed for a range of unbalance levels in measurements taken on two different wound rotor machine designs.

1 Introduction With the increasing use of wind turbines (WTs) for electric power generation the utilisation of wound rotor induction machines (WRIM) as power conversion devices has escalated significantly. DFIG Type-III wind turbines [1], which rely on WRIMs for their operation, have been recently estimated to account for as much as 65% of the wind market share [2]. WTs are commonly installed in remote locations, making their maintenance challenging and costly; the operation and maintenance (O&M) cost can account for up to approximately 25% of the income generated during WT lifetime [3]. Condition based maintenance policies are seen as a promising way to drive down the O&M cost in wind farm installations. Consequently, the development and utilisation of condition monitoring systems (CMS) aimed at enabling effective realtime diagnosis in WTs have gained prominence in both the industrial and the academic arena. The available WT failure mode studies indicate a considerable contribution of generator related failures to WT down time [4]. Amongst these, bearing faults constitute the most prominent failure mode, accounting for anywhere between 50% and 70% of the reported generator fault incidents. The reported combined contribution of WT generator stator and rotor electrical failures comes in at a

relatively close second place, contributing approximately 30% of the total reported failures [5]. Given the prominence and the mechanical nature of bearing failures, vibration based CMS, which are the conventional choice for rotating machinery mechanical integrity diagnosis, are now fitted as standard in WT drive trains to monitor the condition of the generator and other drive train components [6, 7]. While these vibration based diagnostic systems have been shown to be reliable in drive train mechanical fault detection, they are significantly less effective and do not cater for high fidelity generator electrical fault diagnostics [6]. It has however recently been shown that more detailed electrical unbalance related information can be available in the generator frame vibration signal spectrum [8-12]. Enhancing the existing WT CMS by integration of improved, vibration based, electrical fault recognition capability would therefore present an opportunity for maximising their competency. An electrical fault or unbalance in an induction generator can give rise to the appearance of specific electromagnetic torque frequency components and the associated disturbance of the magnetic attractive force between the rotor and the stator at identical frequencies [13]. These effects will aggregate with the potential to give rise to frame vibration spectral components at matching frequencies, the magnitudes of which will largely be dependent on the investigated machine design’s mechanical system response [9, 13]. The recognition of electrical fault or unbalance conditions was shown to be possible by monitoring the changes in the identified electromagnetically induced vibration components [8-13]. A WRIM rotor electrical unbalance will inevitably result from presence of brush gear failure/wear or winding electrical fault. Improving the reliability of rotor electrical unbalance recognition is therefore potentially very useful as it can provide information of an impending electrical problem on the rotor [14, 15]. In this work, the vibration signature of two different WRIMs is analysed for spectral indicators of rotor electrical unbalance under different levels of unbalance severity. First, a numerical model is used to identify unbalance related components in the machine torque signal. Experimental work is then undertaken to evaluate the extent to which the predicted pulsating torque frequencies and the associated matching frequency air-gap magnetic force disturbance are manifested in the frame vibration signal of two different laboratory WRIMs.

2 Model Study In order to identify the rotor electrical unbalance related electromagnetic torque components a mathematical model of a WRIM based on the principles of generalised harmonic analysis is used in this section [16, 17]. The model caters for higher order harmonic effects and enables numerical analysis of an arbitrary winding configuration. The model has been applied on a known 4-pole 30kW laboratory WRIM. The design data and measured operational parameters were used as model inputs to enable investigation of the electrical and mechanical effects of interest in the torque signal of the examined machine topology. Operation at a typical operating speed of 1560rpm was simulated for illustration purposes. The influence of speed ripple effects was eliminated from or introduced into the numerical analysis in separate simulation runs. This was achieved either by maintaining the speed solution at a constant pre-set numerical value in the model iterations or by resolving the WRIM mechanical characteristic for speed at each iteration step in the numerical algorithm, i.e. allowing the speed ripple to influence the machine behaviour [18]. The torque signal spectrum is investigated in the bandwidth of 0-1kHz in this work. Fig. 1 and Fig. 2 show the simulation results for the electromagnetic torque signal spectrum during machine operation without or with the speed ripple effects, respectively. s is assumed to represent the absolute value of rotor slip in all figure text in this paper. The torque signal spectrum was assessed for four scenarios of interest for operation with or without the speed ripple effects: a) balanced supply and windings; b) unbalanced supply and balanced windings; c) balanced supply and stator windings, unbalanced rotor windings; d) unbalanced supply, balanced stator windings and unbalanced rotor windings. A 3% unbalance is assumed when modelling the stator supply unbalance, reflecting the unbalance levels measured during laboratory experiments. The rotor windings unbalance was modelled by increasing the value of resistance for one of the rotor phase windings by 20% of its rated value in the simulations. This procedure allows for a general illustration of the spectral effects of rotor electrical unbalance however further unbalance levels were investigated in the experimental work presented in Section 3. The p-pole pair WRIM torque signal spectral frequencies for operation with or without supply unbalance can be predicted based on the derivations put forward in [9, 19]: |6kpfr|

(1)

|2f±6kpfr|

(2)

where: fr is the rotor rotational frequency, f is the supply fundamental frequency and k=0,1,2,3... It can be shown that the expression in (1) predicts the torque components present in the torque spectrum for machine operation with electrical

balance, while that in (2) yields the frequencies of additional spectral components resulting from the presence of stator supply unbalance. The results for balanced machine operation shown in Fig. 1a and Fig. 2a suggest that the only components present in the torque spectrum are those of electromagnetic origin existing at 6kpfr frequencies, i.e. the 12th, 24th and 36th rotational frequency harmonics, as per (1). Speed ripple is seen not to have an impact on the torque spectrum of a balanced machine. With the presence of stator supply unbalance additional components arise in the torque spectrum; these are found at 2f sidebands around the 6kpfr frequency components and at twice supply frequency, as defined by expression in (2). As expected, no speed ripple effects can be observed in the torque spectrum for this operating scenario and the results obtained with and without speed fluctuation in Fig. 1b and Fig. 2b, respectively, are seen to be identical. The presence of rotor electrical unbalance during machine operation with balanced supply and stator windings is seen to result in additional ±2sf sidebands on the existing components in the torque spectrum and a pulsating torque component at double slip frequency, in accordance with the general principles reported in [18, 21, 21]. With the presence of a rotor electrical unbalance the predicted influence of the speed ripple is seen to become more significant, giving rise to additional sidebands at integer multiples of ±2sf, as illustrated by comparison of spectra presented in Fig. 1c and Fig. 2c. Finally, the spectral content predictions shown in Fig. 1d and Fig. 2d, obtained for machine operation with both stator supply unbalance and rotor electrical unbalance, indicate that the trends observed for case c) (Figs. 1c and 2c) remain valid. The rotor electrical unbalance induced ±2sf sidebands are formed on all spectral components present in the torque spectrum (i.e. those given by (2)). The sideband component content is seen to be further amplified by the presence of speed ripple, clearly illustrated by comparison of model results in Fig. 1d and Fig. 2d. A detailed view of the narrowband spectrum containing the sideband effects around the 36fr component is shown in Fig. 3 for illustration purposes. Closely similar spectral trends have been observed in model predictions for all the other components in the spectrum. The scale of the observed spectral effects will largely be determined by the investigated machine design’s rotor inertia and the magnitude of the existing electrical unbalance [18].

3 Experimental Results In order to evaluate the degree to which the spectral disturbances reported in the numerical study can be observed in the frame vibration signal a series of experiments were carried out on two laboratory test rigs. The first rig is comprised of a 240V, 50Hz, 30kW 4-pole WRIM driven by a speed controlled DC machine to enable operation at sub or super-synchronous speeds. The second rig contains a 240V, 50Hz, 7.5kW 4-pole WRIM also driven by a speed controlled prime mover dc motor. Operation in the generating regime was investigated in the experiments on both test rigs, with the

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d) Unbalanced supply rotor resistive unbalance. Fig. 1 Predicted electromagnetic torque spectrum, constant 1560rpm

machines’ stator terminals connected directly to the grid and their rotor terminals short-circuited. The stator frame vibration was measured with a a Bruel & Kjaer (B&K) Deltatron type 4394 accelerometer mounted at the top of the endplate on the load side of the machine. The recorded vibration signal was processed and recorded using the B&K proprietary Pulse vibration monitoring platform with a resolution of 6400 lines in a 1kHz bandwidth [22]. Given the inherently asymmetrical nature of any practical machine it is reasonable to expect that all the components identified in section 2 can, to a degree, be present in the machine vibration spectrum. This is valid even under what would normally be considered ‘quasi-balanced’ operating conditions (i.e. grid supplied healthy machine operation).

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d) Unbalanced supply, rotor resistive unbalance Fig. 2 Predicted electromagnetic torque spectrum, 1560rpm, speed allowed to fluctuate

However, with the presence of a more severe electrical unbalance a more considerable increase in the magnitude of the unbalance related components would be expected. In order to characterise the nature of the investigated vibration signal of the 30kW machine, the frame vibration measurements were first taken for the WRIM rotor driven at a constant speed of ≈1560rpm by the prime mover and with no winding excitation. The machine was then energised from the grid and frame vibration recorded for the same operating speed. Fig. 5 shows the measured vibration signal spectra obtained for balanced machine operation with and without stator excitation. The rotational speed harmonics are seen to exist in the vibration spectrum even when no stator excitation is present. These components are generally known to be

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Fig. 3 Electromagnetic torque narrowband spectrum, case d)

primarily of mechanical origin and related to inherent mechanical unbalances in the machine [13]. The application of excitation results in an increase in the magnitude of the already existing fr harmonics, but also in the appearance of additional spectral components due to electromagneticmechanical interactions. The components at 6kpfr frequencies, matching those predicted by the model to exist in the torque signal, are seen to exhibit a general rise in the measured vibration signal of an excited 30kW machine. The pulsating torque components along with the accompanying air-gap force disturbance at matching frequencies can give rise to matching frequency components in the vibration signal and further excite/damp any existing vibration components of mechanical origin. The resulting magnitude of the electromagnetically induced vibration components will however not depend solely on the degree of existing electromagnetic excitation, but also on the mechanical properties of the system [9, 23]. A detailed view of the narrowband spectra containing the 6kpfr frequencies is shown in Fig. 6a; for the investigated four-pole 30kW machine design the 36fr frequency component in the vibration signal was observed to exhibit a particularly clear increase with excitation, as can be observed in the measured data. The simulation results in section 2 showed that the primary effect of the rotor resistive unbalance in a balanced machine is expected to be manifested as magnitude increase of the ±2sf sidebands around the 6kpfr frequencies (for the laboratory machine designs and the investigated bandwidth these are located at the 12th, 24th and 36th fr harmonics). A zoom-in of the measured narrowband spectra around the 6kpfr components for 30kW machine operation without and with a rotor resistive unbalance are shown in Fig. 7a. An additional resistance of approximately twice the rated rotor phase resistance was connected to one of the WRIM rotor phase windings to experimentally emulate a rotor electrical unbalance on both the 30kW machine (nominal rotor resistance ≈0.092Ω)

and the 7,5kW (nominal rotor resistance ≈0.066Ω) laboratory machine. The experimental data demonstrate that the rotor inherent electrical unbalance induced ±2sf sidebands and their integer multiples (i.e. ±2nsf, n=1, 2 , 3…) can exist for machine operation in ‘balanced’ conditions, resulting from inevitable electrical unbalance that is characteristic of any practical system. These magnitudes are however seen to exhibit a clear increase when significant rotor unbalance (i.e. one rotor phase resistance doubles) is applied. The model study results in section 2 suggest that identical trends may be observed on the supply unbalance induced components. Fig. 7b shows a measured narrowband vibration spectrum containing an arbitrary supply induced frequency at 2f+12fr (≈412Hz for the investigated operating speed). It can be seen that the presence of a more severe rotor unbalance than that inherent to the machine results in a magnitude increase of 2sf sidebands around this component, further confirming the previously observed spectral trends. Similar behaviour could be identified on all other supply unbalance induced frequencies in the measured vibration spectrum. In order to investigate the generality of the observed rotor unbalance induced spectral phenomena identical experiments were undertaken on a four-pole 7.5kW laboratory machine operating at a nominal super-synchronous speed of ≈1542rpm. The measured narrowband vibration spectra containing the 6kpfr frequency components for machine operation without and with a rotor electrical unbalance are shown in Fig. 8a (as this is also a four-pole machine these are found at 12th, 24th and 36th rotational speed harmonic). The spectral trends in the vibration signal of the 7.5kW machine are identical to those identified for the larger 30kW WRIM design; while low magnitude 2sf sidebands are present during ‘balanced’ operation due to an inherent rotor electrical asymmetry the existence of a more severe electrical unbalance results in a clear magnitude increase of these components. In addition, identical trends can be observed on the supply unbalance induced components. This is illustrated by the measured narrowband spectra around the 2f+12fr (≈408Hz for the investigated operating speed-component) shown in Fig. 8b and seen to exhibit a consistent behaviour with that found for the 6kpfr components. The presentation of this particular supply unbalance related component was chosen to facilitate direct comparison with the measurements of the same component on the bigger machine shown in Fig. 7b, however closely consistent behaviour was observed for other unbalance induced components in the investigated vibration signal bandwidth of the 7.5kW machine.

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Fig. 6. Vibration spectrum for 30kW machine operation at 1560rpm with and without excitation, narrowband spectra containing the 6kpfr components -3

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a) Narrowband spectra containing the 6kpfr components b) Supply unbalance induced component (2f+12fr) Fig. 7. Vibration spectrum for 30kW machine operation at 1560rpm without and with rotor resistive unbalance -3

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a) Narrowband spectra containing the 6kpfr components b) Supply unbalance induced component (2f+12fr) Fig. 8. Vibration spectrum for 7.5kW machine operation at 1542rpm without and with rotor resistive unbalance.

A minor rotational speed change arising from the introduction of rotor electrical unbalance was observed during experiments on the 7.5kW and was determined to arise due to limitations in the speed controller set-up on the test rig dc prime mover motor; the effects of this can be observed in the data shown in Fig. 8 as a small change in the ‘carrier’ and sideband frequencies with the change of rotor winding resistance. No speed variation resulting from the rotor resistance magnitude change took place during the 30kW machine experiments. The observed spectral effects in the vibration signal are however largely consistent in terms of general spectral content patterns between the two investigated machine designs. While the identified 2sf sideband magnitude increase is for the most part clearly manifested in both machines, there are differences in the observed magnitude levels on individual spectral components as would be expected from two considerably different machine geometries with different electromagnetic and mechanical characteristics. Finally, in order to examine the 2sf sideband magnitude change relationship with the rotor unbalance severity the magnitude variations of the sidebands around the 6kpfr frequencies for different levels of rotor resistive unbalance were measured and resulting data shown in Fig. 9. The 30kW machine was run at ≈1560rpm and the 7.5kW at ≈1542rpm during the experiments. As can be observed in the figure an

increase in the level of resistive unbalance is followed by an increase in the magnitude of the related 2sf sidebands. This data demonstrates a clear correlation between the unbalance severity and the magnitude of the spectral sidebands, suggesting that monitoring of the variation in the sidebands magnitude may potentially provide useful information on an existing unbalance severity.

4 Conclusions This paper assesses the effects of supply and rotor unbalance in the torque and vibration spectra of two industrial WRIMs. A harmonic model study is first undertaken to investigate the general spectral effects of the rotor electrical unbalance on the torque signal of the WRIM. It is shown that the primary effect of rotor unbalance is reflected as twice slip frequency sidebands around the existing spectral components in the torque signal. An experimental study is then performed to examine the frame vibration signals of two laboratory WRIM machines operating with varying degrees of rotor electrical unbalance. It is shown that identical spectral disturbances originating from rotor electrical unbalance that were identified in the numerical torque signal study can be recognised in the measured vibration signal spectra. The presented results enable a better understanding of the spectral nature of the WRIM’s vibration signal and the information it

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Fig. 9 Vibration spectra for 30kW (top) and 7.5kW (bottom) machines operating at 1560rpm and 1542rpm and with different levels of unbalance.

contains that may provide useful indication of the rotor windings electrical integrity and enable improved recognition of rotor electrical unbalance based on vibration signal analysis.

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