1 INTRODUCTION 2 MODELLING AND EXPERIMENTAL TOOLS

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1 Investigation of Harmonic Emissions in Wound Rotor Induction Machines K. Tshiloz, D.S. Vilchis-Rodriguez, S. Djurović The University of Manchester, School of Electrical and Electronic Engineering, Power Conversion Group, Sackville Street Building, Manchester, UK, M3 9PL Abstract - This paper investigates current harmonic emissions and the nature and the manifestation of the electromagnetically induced vibration signature in wound rotor induction machines. The strength and consistency of harmonic signatures between three industrial WRIMs with different design parameters is examined. A numerical harmonic model is used to predict and investigate WRIMs stator and rotor currents and electromagnetic torque signals spectra. The model results are verified by comparison with experimental measurements made on two laboratory test rigs. The presented model and experimental results demonstrate significant and highly consistent current and vibration signals spectral contents patterns between the considered industrial WRIM designs. Keywords: Induction machine, current spectrum, electromagnetic torque spectrum, vibration spectrum. INTRODUCTION Induction machines play a key role in the field of electromechanical energy conversion. A considerable proportion of installed and currently manufactured MW scale variable speed wind turbines use wound rotor induction machine (WRIM) drives. Electrical signal harmonics and electromagnetically induced vibrations in WRIM applications have recently started attracting increased attention [-9]. Detailed understanding of the origins and reliable prediction of the patterns of these emissions is important and affects a number of aspects of generator operation. This primarily concerns the generated power quality [-4], but also the electrical or mechanical signal spectral analysis based condition monitoring techniques [6,8,-] and the development of potential sensor-less speed estimation schemes for robust velocity measurement [9,3-6]. Strong harmonic signatures in WRIM electrical signals have recently been reported in [5,7-8,,-3]. WRIM electromagnetically induced vibrations have been less researched in literature, but are of considerable interest in condition monitoring applications [6,]. In addition, [9] showed that frame vibrations can be used to determine rotor speed of a squirrel-cage induction machine (SCIM) with a relatively low cost piezoelectric material vibration sensor. Understanding the nature of these vibrations in WRIMs could therefore lead to development of similar applications. While harmonic emissions in WRIMs remain largely unexplored, the literature on stator line current harmonics in SCIMs [4-6] suggests a strong link between the manifestation of spectral components and machine design parameters; only for certain favourable combinations of machine design factors are specific components to be expected in the stator line current spectrum. This work aims to investigate harmonic emissions in WRIMs by undertaking modelling and experimental analysis of three different industrial machine designs rated at 3 kw and 7.5 kw. The presented work utilises a numerical harmonic model [5] to predict and investigate the stator and rotor currents and electromagnetic torque signals spectra. The model predictions are used to research the manifestation of spectral components in current and torque signals and their consistency between the considered machine designs. This work also employs two separate laboratory test rigs for experimental research of the current and vibration signals spectral contents in the considered WRIM designs. The presented analysis shows a good agreement between predicted and experimental results and demonstrates the presence of clearly defined harmonic signatures in electrical and mechanical signals. Furthermore, the results indicate a high level of consistency between the observed spectral patterns of different WRIMs. The influence of supply unbalance on the observed spectral signatures is evaluated by relating the harmonic model predictions to corresponding laboratory signals measured for on-line operating conditions. The load dependency of the reported spectral effects is investigated in tests for the rated operating range of the studied machine designs. MODELLING AND EXPERIMENTAL TOOLS The machine modelling technique used in this work employs the established concepts of generalized harmonic analysis [7]. The model is presented in [5] and is based on conductor distribution functions, which cater for higher order harmonic effects when calculating machine parameters. The appropriate rotor skew and spatial distributions of the stator and rotor conductors are taken into account for each of the investigated machine designs. The model assumes a smooth air gap and neglects any air gap permeance variation; winding coils are represented as point conductors lying on the stator or rotor surface. In order to represent the behaviour of the laboratory machines used for experimental research, their physical parameters were characterised in tests and along with the operational data recorded during experiments, used as numerical model inputs. Three separate numerical models were developed as part of this work, each representing one of the investigated machine designs. Fig.: Machine A (4 pole, 3 kw) Fig.: Machine B (4 pole, 7.5 kw) Fig.3: Machine C (6 pole, 7.5 kw)

2 Two laboratory test rigs were used for the experimental research. The first test rig uses a 3 kw, 4 pole, 5 Hz 48/36 stator/rotor slot star connected Marelli E4F5M4 WRIM (shown in Fig.) coupled by a common shaft to a DC motor prime mover. The second test rig can accommodate two different WRIM 7.5 kw 5 Hz star connected designs: a 4 pole, 48/36 stator/rotor slot VEM 6M4 WRIM [8] and a 6 pole, 54/48 stator/rotor slot VEM 6L6 WRIM [8], shown in Figs.-3, respectively. The three WRIMs are driven by either a 4 kw or a 5.5 kw DC motor, respectively. Both rigs utilise commercial DC speed drives to run the DC motors and drive the WRIMs in either the generating or the motoring regime. The considered machines are in a 4 pole or a 6 pole design to reflect the two topologies commonly used in the wind industry. Three-phase power analysers were used in WRIM stator and rotor circuits to monitor and record current and voltage rms values. The rotational speed was measured by means of 4ppr incremental encoders on both test rigs. The stator and rotor currents were measured using a LeCroy CP5 precision current sensor and recorded with a LeCroy WaveSurfer digital oscilloscope. The recorded current data was processed in MATLAB using a proprietary FFT routine in the - khz bandwidth with the resolution of. Hz. The vibration signal was recorded by installing a Bruel&Kjær [9] piezoelectric accelerometer in the radial direction on the top of the drive end bearing. The accelerometer output signal was conditioned using a high fidelity Bruel&Kjær Pulse vibration measuring platform [9]. The vibration signal FFT analysis was performed with.5 Hz resolution for the investigated - khz bandwidth. This bandwidth was found to be of most interest, due to the relatively high magnitude of spectral components. 3 MODELLING STUDY OF HARMONIC EMISSIONS A model study was carried out to investigate the spectral content of the stator and rotor currents and electromagnetic torque in the considered WRIM designs. The results obtained for operating speeds of 455 rpm and 965 rpm are presented in this section for illustration purposes. For all three machines, operation with balanced windings and balanced supply was initially simulated in the model. The results for steady-state stator line current, rotor current and electromagnetic torque spectra are shown in Figs.4-, respectively. The spectral magnitudes in the presented data are normalized with respect to the fundamental component for the current signals and the DC component for the electromagnetic torque signals. The spectral frequencies contained in the WRIM stator current signal were shown to be determined by stator-to-rotor field interactions and described by the following expression [5]: k ind s f s f 6k, k =,,, 3 () where f s is the supply frequency, s is the fractional slip and k corresponds to the air-gap fields pole-pair numbers. The stator line current spectra shown in Figs.4-6 are seen to contain a clearly defined set of components in the investigated bandwidth. For machines A and B these can be observed at 4, 34, 53, 63, 8.9 and 9.9 Hz, while for machine C these are present at 39.4, 339.4, 59., 69., 88.5 and 98.5 Hz. While the individual component magnitudes vary between machine designs, the presented spectral contents patterns are seen to be consistent between all three machines and contain a clearly defined set of six components. The frequencies of these are seen to be largely related to the machine pole-pair number and the operating speed in the presented results. Similarly, examination of the model results for the rotor current spectra shown in Figs.9- reveals a number of distinct frequency components in the investigated bandwidth. For machines A and B these can be seen at 89.4, 9.7, 58.6, 583.5, 87.4 and Hz, while for machine C these can be identified at 87.9, 9., 577.3, 58.6, 867 and 87.3 Hz. As observed in the predicted stator current spectra, the presented rotor currents spectral content patterns, while manifested at varying magnitudes, can be seen to be consistent between the investigated machines. Model predictions for the machines steady-state electromagnetic torque spectra are shown in blue in Figs.7-8 and Fig.. The WRIM electromagnetic torque spectral components are reported to manifest at frequencies given by [6]: k find 6 k s f s, k =,,, 3 () where k relates to air-gap fields pole-pair numbers. The harmonic rich nature of WRIM currents is seen to result in a range of pulsating torque frequencies in the three separate industrial machine designs. These can be identified at 9, 58 and 873 Hz for machines A and B, and at 89.4, 579. and Hz for machine C. While there are relative differences between the observed magnitudes of these components, the presented data demonstrate a consistent spectral content pattern in the electromagnetic torque signal of the investigated machines. These torque pulsations will be transferred to the machine shaft and will also be reflected in the machine frame vibration signals [6]. The reported frequencies for the three machine designs can be calculated from equations () and () using appropriate values of fractional slip and constant k, as shown in Table. In order to investigate the influence of supply unbalance a 3% stator voltage imbalance was applied in the numerical models. The investigated voltage imbalance is assumed to exist in magnitude only for the purpose of this research. The considered imbalance value is typical of that measured in the laboratory supply during experiments. No changes originating from the existence of supply unbalance could be noticed in the predicted spectral content of stator and rotor currents, and these remain as shown in Figs.4-6 and Figs.9-. Table : Calculated current and torque frequencies [Hz]

3 Torque [db] Torque [db] Hz 34.8 Hz 63 Hz 53 Hz 9.9 Hz 8.9 Hz Fig.4: Predicted stator current spectrum, Machine A Hz 8.9 Hz 53 Hz 9.9 Hz Hz 63 Hz Fig.5: Predicted stator current spectrum, Machine B Hz 69. Hz 98.5 Hz 39.4 Hz 59. Hz 88.5 Hz Fig.6: Predicted stator current spectrum, Machine C Hz 9.8 Hz Hz Unbalanced supply Balanced supply 39.8 Hz 87.8 Hz 97.9 Hz 58 Hz 77.9 Hz 48 Hz 68 Hz Fig.7: Predicted torque spectrum, Machine A Hz Unbalanced supply Balanced supply 9.8 Hz 87.9 Hz Hz 58 Hz 48 Hz 77.9 Hz 9.8 Hz 39.8 Hz 68 Hz Fig.8: Predicted torque spectrum, Machine B Torque [db] Hz 89.4 Hz 9.7 Hz 58.6 Hz Hz 87.4 Hz Hz Fig.9: Predicted rotor current spectrum, Machine A Hz 9.7 Hz 87.4 Hz Hz Hz 89.4 Hz 58. Hz Fig.: Predicted rotor current spectrum, Machine B Hz 58.6 Hz 9. Hz 87.3 Hz Hz 867 Hz Hz Fig.: Predicted rotor current spectrum, Machine C Unbalanced supply Hz Balanced supply 89.4 Hz 579. Hz Hz Hz 479. Hz 679. Hz 89.4 Hz Hz Hz Fig.: Predicted torque spectrum, Machine C The results for electromagnetic torque signal in unbalanced supply operating conditions are superimposed in red on the predicted electromagnetic torque spectra obtained for a simulated balanced operation in Figs.7-8 and Fig.. These reveal that a number of additional spectral components arise in the electromagnetic torque spectrum due to the presence of voltage imbalance. These can be observed for the considered operating conditions at, 9.8, 39.8, 48, 68, 77.9 and 97.9 Hz for machines A and B, and at, 89.4, 389.7, 479., 679., and Hz for machine C. 3

4 4 EXPERIMENTAL RESULTS To experimentally verify the model results and facilitate a direct comparison with the data presented in section 3, a number of experiments were performed on the two laboratory test rigs. In these the four pole machines were operating at 455 rpm and the six pole machine operated at 965 rpm. The experiments were performed for machines operating on line, under the existing inherent laboratory grid supply. The measured voltage asymmetry present in the supply was typically at a level of 3% phase voltage magnitude unbalance. The vibration, stator current and rotor current signals were recorded in the experiments. The measured data for the 4 pole 3 kw WRIM, the 4 pole 7.5 kw WRIM and the 6 pole 7.5 kw WRIM are shown in Figs.3-. The corresponding model predictions in section 3 and the presented measured data are seen to be in good agreement. The measured data are seen to be noisier than the model predictions and contain the supply harmonic induced spectral effects that are not considered in the model analysis in this research. Small differences between the measured and calculated frequency values in Figs.4- are due to the inherent speed measurement error and the model assumption of an ideal 5 Hz supply Hz 34.6 Hz 5 Hz 9.5 Hz 35 Hz 63 Hz 53. Hz 8.6 Hz 45 Hz -8 5 Hz 3 Hz 55 Hz Fig.3: Measured stator current spectrum, Machine A Hz 35 Hz 63.3 Hz 34.3 Hz 94 Hz 45 Hz 65 Hz 53.7 Hz 83.9 Hz -8 5 Hz - 5 Hz 55 Hz Fig.4: Measured stator current spectrum, Machine B 5 Hz 53. Hz Hz 55 Hz 4 Hz 8. Hz Hz 63. Hz 9. Hz -8-5 Hz 35 Hz Fig.5: Measured stator current spectrum, Machine C Although the presented stator currents and rotor currents spectra shown in Figs.3-8 are obtained for three different industrial machine designs with different design parameters, the data are seen to exhibit a strong consistency in the spectral content patterns. It has been shown in [6] that electromagnetic torque pulsations can be transferred to the machine shaft and result in machine frame vibration at identical frequencies. Hence, the electromagnetically induced vibration components contain relevant information about the operating condition of the machine. Given the prominence of vibration based commercial monitoring systems [] the nature and the consistency of the vibration signal spectral content in different machine designs ought to be assessed. The stator frame vibration spectra of machines A, B and C are shown in Figs.9-, respectively. These were measured synchronously with the corresponding current spectra in Figs.3-8. All the electromagnetic torque frequency components predicted by the numerical harmonic models can be observed in the corresponding measured vibration spectra. For the investigated operating speeds the spectral components present for balanced operation exist in the measured data at 9, 58 and 873 Hz for machines A and B, and at 9, 58 and 87 Hz for machine C Hz 9. Hz 89 Hz Hz 58.6 Hz 87. Hz 873. Hz Fig.6: Measured rotor current spectrum, Machine A.56 Hz Hz 9.7 Hz 58. Hz 584. Hz 87.7 Hz Hz Fig.7: Measured rotor current spectrum, Machine B.83 Hz Hz 58.5 Hz 88. Hz Hz 87. Hz Hz Fig.8: Measured rotor current spectrum, Machine C 4

5 A c c. [ m /s ] Hz Hz 97.6 Hz 9.8 Hz 9.6 Hz 39.8 Hz48. Hz 77.6 Hz 58.9 Hz 87.6 Hz 68.9 Hz A c c. [ m / s ] Fig.9: Measured vibration spectrum, Machine A Hz Hz 9.6 Hz 9.6 Hz39.3 Hz 48.8 Hz Hz 58.8 Hz Hz Hz 68. Hz A c c. [ m / s ] Hz Hz 9.3 Hz Fig.: Measured vibration spectrum, Machine B 9 Hz 39 Hz 48.3 Hz 58 Hz 68 Hz Hz 77 Hz 87.3 Hz In addition, the experimental data strongly exhibit the influence of supply unbalance, as demonstrated by the existence of the spectral components at, 9, 39, 48, 68, 77 and 97 Hz for machines A and B, and at, 9, 39, 48, 68, 77 and 97 Hz for machine C. The load dependency of the investigated current and vibration spectral components was evaluated in an experimental study. Steady-state stator currents, rotor currents and vibration signals were measured for a number of operating points within the rated operating range of the investigated machines. For the current signals measurements, the spectral data have been normalized with respect to the fundamental component. The vibration signals are normalized with respect to the fundamental rotational speed component. The measured magnitudes of the spectral components are shown in Figs.-3. The components in the stator current and electromagnetic torque signals results are labelled corresponding to the harmonic number constant k, as shown in Table. The study results for stator and rotor currents presented in Figs. and 5 demonstrate a general increasing trend in the spectral component magnitudes with load increase for machine A. The data presented in Figs.3 and 6 Fig.: Measured vibration spectrum, Machine C for machine B show a much lower load dependency of the observed spectral components magnitudes. The data for machine C current signals shown in Figs.4 and 7 show relatively uniform component magnitudes with low load sensitivity. The strongest stator current spectral magnitudes for machine A are k= pair, while for machine B the dominant spectral component magnitudes belongs to the upper spectral component defined by k=3. There is no clearly defined dominant magnitude in current results for machine C; a more pronounced difference in magnitude levels can be observed between spectral components for high loads, indicating that for this operating range the upper spectral component related to k= and the lower spectral component associated with k=3 of the stator current data are most dominant in the spectrum. The strongest rotor current spectral component magnitudes for machine A are the st and nd components, while for machine B the 6 th component is dominant. A significant difference in spectral components magnitude levels can be observed for low load operations of machine C, showing that for this speed range the nd, 4 th and 5 th components of the rotor current data are dominant in the spectrum. The measured vibration data demonstrate a strong manifestation of the observed spectral components for the 5

6 4 3 k = lower k = upper k = lower k = upper k = 3 lower k = 3 upper Fig.: Load dependency of stator current, Machine A k = lower k = upper k = lower k = upper k = 3 lower k = 3 upper Fig.3: Load dependency of stator current, Machine B k = lower k = upper k = lower k = upper k = 3 lower k = 3 upper Fig.4: Load dependency of stator current, Machine C operating range of all three machines. A reasonable degree of load dependency can be seen to exist in the majority of reported spectral components, with spectral component defined by k= being the dominant for machine A, k=3 dominating the machine B results and k= defining the strongest component for machine C. While the experimental data in Figs.-3 do not allow for drawing a general conclusion on load dependency patterns in the investigated machine designs, they demonstrate a consistency in spectral content presence in the examined signals for the rated operating range, thus indicating high detectability levels for realistic, on-line operating conditions. 5 CONCLUSION This paper investigates current harmonic emissions and electromagnetically induced vibration spectral signature in WRIMs. The strength and consistency of harmonic signatures between industrial WRIMs with different design parameters is investigated by numerical simulation and experimental measurements on two separate laboratory test rigs. Highly consistent spectral patterns between machines with different designs parameters were observed in this work. The results indicate that the reported spectral content is predictable and largely dependent on the machine pole-pair number and the operating speed. 6 REFERENCES [] M. Lindholm, Tony W. Rasmussen., Harmonic analysis of doubly fed induction generators, IEEE PEDS, Vol., 3. [] Sokratis T. Tentzerakis, Staviros A. Papathanassiou., An investigation of the harmonic emissions of wind turbines, IEEE Trans. on En. Conv, Vol., No., March 7. [3] S. Liang et al., A survey of harmonic emissions of a commercial operated wind farm, Proc. of IEEE ICPSTC,. [4] C. Larose, et al., Type-III wind power plant harmonic emissions: Field measurments and aggregation guidelines for adequate representation of hramonics, IEEE Tr. on Sust.En, st nd 3 rd 4 th 5 th 6 th Fig.5: Load dependency of rotor current, Machine A.5.5 st nd 3 rd 4 th 5 th 6 th Fig.6: Load dependency of rotor current, Machine B st nd 3 rd 4 th 5 th 6 th Fig.7: Load dependency of rotor current, Machine C Acceleration [%] Acceleration [%] Acceleration [%] k = k = k = Fig.8: Load dependency of vibration, Machine A 4 3 k = k = k = Fig.9: Load dependency of vibration, Machine B k = k = k = Fig.3: Load dependency of vibration, Machine C [5] S. Williamson, S. Djurovic., Origins of stator current spectra in DFIGs with winding faults and excitation asymmetries, Proc. of IEEE IEMDC, pp , May 9. [6] S. Djurovic, et al., Vibration monitoring for wound rotor induction machine winding fault detection, IEEE ICEM,. [7] G. Joksimovic., Stator current harmonics in saturated cage and wound rotor induction motors, Proc. of IEEE ICEM,. [8] A. Yazidi, et al., Rotor inter-turn short circuit fault detection in wound rotor induction machines. Proc. of IEEE ICEM,. [9] D. Wu, S. Pekarek., Using mechanical vibration to estimate rotor speed in induction motor drives, Proc. of IEEE PESC, 7. [] S. Djurovic et al., Condition monitoring of wind turbine induction generators with rotor electrical asymmetry, IET Ren. Pow. Gen, Vol. 6 (4), pp.7-6, July [] C. Crabtree., Survey commercially available condition monitoring systems for wind turbines, SuperGen Wind Energy Technologies Consortium, November. [] C. Crabtree, et al., Fault frequency tracking during transient operation of wind turbine generators, Proc. of. IEEE ICEM. [3] S. Djurovic, S. Djukanovic., A sensorless speed estimation method for wound rotor induction machine, Proc. of. IEEE IEMDC, pp , May. [4] S. Nandi et al., Selection criteria of induction machines for speed-sensorless drive applications, IEEE Ind. App. Conf., 3. [5] A. Ferrah et al., The effect of rotor design on sensorless speed estimation using rotor slot harmonics identified by adaptive digital filtering using the maximum likelihood approach,proc. of. IEEE Ind. App. Conf., pp.8-35, 997. [6] K. Hurst, T. Habetler., A comparison of spectrum estimation techniques for sensorless speed detection in induction machines, Prof. of. IEEE Ind. App. Con, Vol. 33, No. 4, 997. [7] S. Williamson et al., Generalised harmonic analysis for the steady-state performance of sinusoidal-excited cage induction motors, IEE Tr. on Elec. Pow. App, Vol. 3, No.3, 985. [8] [9] 6