UNCERTAINTY ANALYSIS OF MEASURING SYSTEM FOR INSTANTANEOUS POWER RESEARCH

Transcription

1 Metrol. Meas. Syst., Vol. XIX (0), No. 3, pp METROLOGY AND MEASUREMENT SYSTEMS Index , ISSN UNCERTAINTY ANALYSIS OF MEASURING SYSTEM FOR INSTANTANEOUS POWER RESEARCH Ariel Dzwonkowski, Leon Swędrowski Gdansk University of Technology, Faclty of Electrical and Control Engineering, l. Nartowicza /, Gdansk, Poland , l.swedrowski@ely.pg.gda.pl, ) Abstract The electrical power drawn by an indction motor is distorted in case of appearance of a certain type of failres. Under spectral analysis of the instantaneos power one obtains the components which are connected with definite types of damage. An analysis of the amplitdes and freqencies of the components allows to recognize the type of falt. The paper presents a metrological analysis of the measrement system sed for diagnosis of indction motor bearings, based on the analysis of the instantaneos power. This system was implemented as a set of devices with dedicated software installed on a PC. A nmber of measrements for ncertainty estimation was carried ot. The reslts of the measrements are presented in the paper. The reslts of the aforementioned analysis helped to determine the measrement ncertainty which can be expected dring bearing diagnostic measrements, by the method relying on measrement and analysis of the instantaneos power of an indction machine. Keywords: measring system, metrological analysis, power measrements, measrement ncertainty, indction motor diagnostics. 0 Polish Academy of Sciences. All rights reserved. Introdction Diagnostics of electric machines allows to assess the technical condition of a machine withot the necessity for its disassembly, throgh analysis of diagnostic signals generated by the machine and their comparison with reference signals. De to the fact that the majority of failres in electric motors is cased by bearing damage, one can observe a particlarly dynamic development in this area of diagnostics [-4]. There are varios methods for bearing diagnosis. The most commonly sed ones are based on vibration measrement. However, those methods cannot be sed in the absence of direct access to the engine. In sch cases, the diagnosis is possible based on the measrement and analysis of the vales of the engine power spply. In this manner, converters can be monted on the electric cable spplying the engine which is sitated away from the machine. The diagnostics is possible as the bearing damages generate an additional component in the spectrm of motor crrent [5-8]. Frthermore, the waveform of the instantaneos vales of the power is deformed. In this way, one of the possible diagnostic symptoms is the instantaneos power consmed by the motor. The measring system designed for investigation of instantaneos power is presented in this article. Fig. illstrates the block diagram of the system. De to the fact that the expected diagnostic components in the power signal have low vales [5] in comparison with other components of this signal, their own noise shold be small and the measring system has to be highly accrate. While designing the system, Article history: received on Jan. 0, 0; received in revised form on May 5, 0; accepted on Jly 0, 0; available online on Sept. 8, 0.

2 A. Dzwonkowski, L Swędrowski: UNCERTAINTY ANALYSIS OF MEASURING SYSTEM FOR INSTANTANEOUS POWER RESEARCH particlar attention was paid to these characteristics and the finished system was sbjected to thorogh examination. Fig.. Block diagram of the system for measring instantaneos power in diagnostics of indction motor bearings, where: M tested machine, PU voltage converter, PIU crrent-voltage converter, KP measrement cage, DAQ data acqisition card NI PXI 446, FA anti-aliasing filter, A/C analogdigital converter, K PC compter with software, UM programme modle mltiplying crrent and voltage, FFT programme modle calclating the Forier transform, ZA programme modle for instantaneos power analysis. The sbject of this article is a metrological analysis of the system designed for measring instantaneos vales of active power in diagnostics of indction motor bearings.. Metrological analysis of the measring system This chapter presents the metrological analysis of the measring system sed in the research. The prpose of the metrological analysis of the system for measring instantaneos power was to assess the ncertainty of measrements performed with the se of this system. The measring system consisting of a FLUKE 5500A calibrator and a Keithley 00 mltimeter was sed to assess the ncertainty of the measring system consisting of a CV voltage converter and a CT-5T crrent-voltage converter. The reslts of these analyses will allow to define the measrement ncertainty which can be expected while performing diagnostic research of indction motor bearings, sing the method of instantaneos power measrement and analysis in certain conditions at a test stand. In the measring system sed for instantaneos power measrements, the measrement fnction is presented by the following formla: p( t) = ( t) i( t). () As the measrement of instantaneos power is an indirect one [9-], the ncertainty (p), assming no correlation between the ncertainties of measred vales, is defined by the following dependence: p p ( p) = ( ) + ( i), () i where: (p) ncertainty of instantaneos power measrement, () voltage measrement variance, (i) crrent measrement variance. In accordance with formla (), it is necessary to determine voltage measrement variance () and crrent measrement variance (i) in order to determine the ncertainty of instantaneos power measrement (p). The procedre which has to be followed while determining these variances is presented in Fig.. 574

3 Metrol. Meas. Syst., Vol. XIX (0), No. 3, pp The variance of measrement card indication correction ( ) and the variance of voltage converter ratio estimation (k ), have to be assessed in order to determine the voltage measrement variance (). To define the (k ) variance, it is necessary to assess the following: variance of standard otpt voltage vale -, voltage measrement variance reslting from scatter of reslts measred with a mltimeter - 3, variance reslting from the limiting error of the mltimeter - 4. To define the crrent measrement variance (i), it is necessary to take into consideration the variance of measrement card indication correction ( ) and to determine the variance of crrent-voltage converter ratio estimation (k ). In order to assess the (k ) variance, it is necessary to define the following: variance of standard otpt crrent vale - 5, voltage measrement variance reslting from scatter of reslts measred with the mltimeter - 6, variance reslting from the limiting error of the mltimeter - 7. ( k ) = c + ( ) c ( ) ( ) = c ( k ) + c ( ) 5 6 ( ) = ( p) = i ( ) + ( i) ( i) = c ( k ) + c ( ) 7 8 ( k ) = c + 3 ( ) c4 ( i) Fig.. Procedre to be followed while determining ncertainty of instantaneos power measrement (p) in a measring system with voltage-voltage and crrent-voltage converters; c, c, c 3, c 4, c 5, c 6, c 7, c 8 - sensitivity coefficients. The next sbsection of this chapter presents the methodology for assessing vales of the variances listed above in a measring system with a voltage converter and a crrent-voltage converter... Uncertainty of voltage measrement The otpt voltage of a voltage converter is defined by the following dependence: = k, (3) where: otpt voltage of voltage converter, k ratio of voltage converter, inpt voltage of voltage converter. 575

4 A. Dzwonkowski, L Swędrowski: UNCERTAINTY ANALYSIS OF MEASURING SYSTEM FOR INSTANTANEOUS POWER RESEARCH The converter was tested for a nmber of freqencies and a few inpt voltage vales in order to assess the ncertainty of voltage measrement. In the measring system, a voltage vale is defined by the measrement fnction which constittes the basis for assessment of voltage measrement ncertainty. The voltage measrement variance () is defined by the following dependence [9 - ]: ( ) k ( k ) = + ( ), (4) where: (k ) variance of voltage converter ratio estimation, ( ) variance of measring voltage with a data acqisition card.... Variance of voltage converter ratio estimation The variance of voltage converter ratio estimation can be written as follows: k ( ) + ( ) k ( k) =, (5) where: (k ) variance of voltage converter ratio estimation, ( ) variance of average voltage vale, measred with the Keithley 00 mltimeter, ( ) variance of the average vale of the voltage connected to the converter inpt. The variance of average otpt voltage vale of the converter - ( ) is closely related to measrement ncertainty of the Keithley mltimeter and defined by the following dependence [9-]: ( ) 3 + =, (6) where: 3 measrement ncertainty reslting from scatter of reslts measred with the Keithley 00 mltimeter, 4 ncertainty reslting from the limitation error of the Keithley 00 mltimeter, presented in the specification by the prodcer. In the condcted research, the Flke 5500A calibrator generated the inpt signal for the converter. The variance of the average vale of voltage connected to the converter inpt - ( ) is presented by the following formla: ( ) 4 =, (7) where: - variance of the otpt voltage vale in the Flke 5500A calibrator, presented in the specification by the prodcer. The abovementioned tested converter was the type CV LEM converter. The tests were done for 6 freqency vales: 50 Hz, 75 Hz, 90 Hz, 0 Hz, 500 Hz, 000 Hz; for each of them at 6 different voltage vales: 0 V, 50 V, 00 V, 50 V, 00 V, 30 V. The measrements were repeated 50 times. The components were calclated for each variant, in accordance with formla (5), (6) and (7). Table presents the maximal obtained vales of variance components. Based on the assessed variances, we can observe that the ratio of voltage converter for freqencies of 0 Hz, 500 Hz and 000 Hz is characterized by the lowest ncertainty vale. In contrast, this ncertainty reaches its highest vale for the freqency of the power network, 576

5 Metrol. Meas. Syst., Vol. XIX (0), No. 3, pp i.e. 50 Hz. The main component of the ncertainty vale for the freqency of 50 Hz is the measrement ncertainty reslting from the scatter of reslts measred with a mltimeter. Qantity symbol Table. Maximal vales of variance components for each of the freqencies. Distribtion of Maximal variance components for individal freqencies 50 Hz 75 Hz 90 Hz 0 Hz 500 Hz 000 Hz 3 [V ] normal.e-8.93e E-0 4.8E-0.57E E-8 4 [V ] rectanglar 9.67E E E E E E-6 [V ] rectanglar 3.70E E E E E E-3 (k) [V /V ] normal.79e-8.79e-8.79e-8.58e-8.57e-8.59e-8.. Variance of voltage measrement performed with a data acqisition card It was assmed that the variance of voltage measrement performed with a data acqisition card - ( ) is eqal to the variance of voltage measrement correction - ( 8 ). The estimation of variance of voltage measrement correction with the data acqisition card was defined from the following dependence: ( ) = , (8) where: ( 8 ) variance of determining the correction of measrement card indication, 9 variance reslting from scatter of measrement reslts obtained with a data acqisition card, 0 variance reslting from resoltion of measrement card indication, variance of the otpt voltage vale in the Flke 5500A calibrator. In the condcted research, we sed the NI PXI 03 measrement cage, in which the NI PXI 446 measrement card had been installed. The measrements were repeated 50 times for each of the voltage vales set in the standard: 0.3 V, 0.5 V, V, V, 3 V, 5 V, and at 6 freqency vales (identical to those sed for the voltage converter) for each of the voltage vales. For each of the combinations of voltage and freqency, the variance components were calclated in accordance with formla (8). Table presents maximal obtained vales of variance components (the variance of measring voltage with the data acqisition card) for each of the freqencies. For measrements of voltage sing the data acqisition card, it was assmed that the variance of the voltage is eqal to the variance of the designation of the amendment to indicate the measrement card: ( ) ( ) 8 =, (9) where: ( ) variance of voltage measrement performed with the data acqisition card. Qantity symbol Table. Maximal vales of variance components for individal freqencies. Distribtion Maximal variance components for individal freqencies 50 Hz 75 Hz 90 Hz 0 Hz 500 Hz 000 Hz 0 [V ] rectanglar 3.55E E E E E E-3 9 [V ] normal 3.4E-7.47E-9.83E-9.9E-9.3E-9.30E-9 [V ] rectanglar.69e-6.69e-6.69e-6.69e-6.69e-6.69e-6 ( 8) [V ] normal.69e-6.69e-6.69e-6.69e-6.69e-6.69e-6 577

6 A. Dzwonkowski, L Swędrowski: UNCERTAINTY ANALYSIS OF MEASURING SYSTEM FOR INSTANTANEOUS POWER RESEARCH Based on the obtained reslts, it can be observed that the ncertainty of standard correction is the main component of ncertainty vale related to measring voltage with the data acqisition card. The vale is greater by a few ranges of vale than the remaining components of ncertainty of voltage measrements performed with the data acqisition card..3. Complex variance of voltage estimation The complex variance of voltage estimation - () was calclated in accordance with dependence (4). Table 3 presents sample calclation reslts regarding the complex ncertainty of voltage measrements, for the power network freqency of 50 Hz. Qantity Xi Table 3. Bdget of voltage estimate ncertainty for the freqency of 50 Hz. Qantity estimate xi Standard variance (xi) Distribtion of Sensitivity coefficient ci Share in complex variance i(y) 4.60 V.69E-6 V normal 50 V/V.3E+4 V k 0.0 V/V.75E-4 V /V normal 500 V /V 6.76E-0 V V normal 6.3E- V Standard ncertainty () 0.5 V With the confidence level assmed at 95% and the extension coefficient k =, the extended ncertainty U of voltage measrement can be determined from the following formla [9-]: = k (), (0) U where: U extended ncertainty of voltage measrement, k extension coefficient, () complex variance of voltage estimation. The extended ncertainty of voltage measrement for the freqency of 50 Hz is: U = 0.50 V. The bdget of voltage estimate ncertainty for the freqency of 0 Hz is presented in Table 4. U Qantity Xi Qantity estimate xi Table 4. Bdget of voltage estimate for freqency of 0 Hz. Standard variance (xi) Distribtion of Sensitivity coefficient ci Share in complex variance i(y) 4.60 V.69E-6 V normal 50 V/V 4.E-3 V k 0.0 V/V 3.56E-0 V /V normal 500 V /V.57E- V V normal.00e- V Standard ncertainty ().4 E- V The extended ncertainty of voltage measrement at the freqency of 0 Hz is: - =.40 = V. Based on the performed calclations, the reslt of voltage measrement for the freqency of 50 Hz, at the assmed confidence level and extension coefficient can be written down as: U = (30.00 ± 0.50) V. The reslt of voltage measrement for the freqency of 0 Hz, at the assmed confidence level and extension coefficient can be written down as: U = (30.00 ± 0.8) V. 578

7 Metrol. Meas. Syst., Vol. XIX (0), No. 3, pp Comparing the vales of extended ncertainty for the freqencies of 50 Hz and 0 Hz, it can be stated that for the freqency of 50 Hz this level of ncertainty is higher than in the measrements performed for the freqency of 0 Hz. These ncertainties do not exceed % of the vale of the measred voltage..4. Uncertainty of crrent measrement In the measring system, the crrent vale is defined by the measrement fnction, which is the basis for assessment of crrent measrement ncertainty: k i =, () where: otpt voltage of crrent-voltage converter, k ratio of crrent-voltage converter, i inpt crrent of crrent-voltage converter. The variance of crrent measrement is defined by the following dependence [9-]: ( i) k i i = ( k ) + ( ), () where: (i) crrent measrement variance, i crrent measred at the inpt of the crrentvoltage converter, ( ) variance of voltage measrement performed with the data acqisition card, (k ) variance of crrent-voltage converter ratio estimation. The vales of the assessed variances of ncertainty related to voltage measrement performed with the data acqisition card defined in p.., were sbstitted in the above dependence of variance vales concerning voltage measrements performed with the data acqisition card - ( )..4.. Variance of crrent-voltage converter ratio estimation The variance of crrent-voltage converter ratio estimation is given as: k ( ) ( i) + k ( k) =, (3) i where: (k ) variance of crrent-voltage converter ratio estimation, ( ) - variance of average otpt voltage vale of the crrent-voltage converter, ( i) - ncertainty of the average vale of crrent connected to converter inpt. The variance of average otpt voltage vale of the crrent-voltage converter - ( ) is closely related to the measrement ncertainty of the Keithley 00 mltimeter and amonts to: ( ) 6 + =, (4) where: average voltage vale, measred with the Keithley 00 mltimeter, 6 measrement ncertainty reslting from scatter of reslts measred with the Keithley 00 mltimeter, 7 ncertainty reslting from limitation error of the Keithley 00 mltimeter, presented in the specification by the prodcer

8 A. Dzwonkowski, L Swędrowski: UNCERTAINTY ANALYSIS OF MEASURING SYSTEM FOR INSTANTANEOUS POWER RESEARCH In the research discssed here, the Flke 5500A calibrator generated the inpt signal for the converter. The variance of the average vale of crrent connected to the converter inpt - is presented by the following formla: ( i) ( i) = 5, (5) where: 5 ncertainty of otpt crrent vale of Flke 5500A calibrator, presented in the specification by the prodcer. The tests on the crrent-voltage converter type CT-5T were performed for 6 freqency vales: 50 Hz, 75 Hz, 0 Hz, 50 Hz, 500 Hz, 000 Hz, at 6 different vales of crrent intensity: 50 ma, 500 ma, A,.9 A,.5 A,.9 A, for each of these freqencies. The measrements were repeated 50 times. The components were calclated for each of the variants in accordance with formlae (3), (4) and (5). Table 5 presents the maximal vales obtained of these components. Qantity symbol Table 5. Maximal vales of variance components for individal freqencies. Distribtion of Maximal variance components for individal freqencies 50 Hz 75 Hz 90 Hz 0 Hz 500 Hz 000 Hz 6 [V ] normal 5.4E E-5.06E E E E-5 7 [V ] rectanglar 6.33E E E E E E-6 5 [A ] rectanglar 3.48E E E E E E-6 (k) [V /A ] normal 7.E E-6.34E E E E-6 The above consideration shows that the main component of ncertainty related to crrentvoltage converter ratio is the measrement ncertainty reslting from scatter of reslts measred with the Keithley 00 mltimeter..4.. Complex variance of crrent estimate The complex variance of crrent estimate was calclated based on dependence (). Sample calclation reslts for crrent measrement complex variance were obtained for two freqency vales: 50 Hz and 0 Hz. The ncertainty bdget of crrent estimate for the freqency of 50 Hz is presented in Table 6. Qantity Xi Table 6. Uncertainty bdget of crrent estimate for the freqency of 50 Hz. Qantity estimate xi Standard variance (xi) Distribtion of Sensitivity coefficient ci Share in complex variance i(y).90 V.69E-6 V normal A/V.69E-6 A k V/A 7.E-6 V /A normal.9 A /V 6.07E-5 A i.90 A normal 6.4E-5 A Standard ncertainty (i) 7.90E-3 A At the assmed confidence level eqal to 95% and the extension coefficient k =, the extended ncertainty U i of crrent measrement can be determined from the following dependence [9-]: U i = k (i), (6) where: U i extended ncertainty of crrent measrement, k extension coefficient, (i) complex variance of crrent estimation. 580

9 Metrol. Meas. Syst., Vol. XIX (0), No. 3, pp Using formla (6), we calclated the extended ncertainty of crrent measrement at the freqency of 50 Hz. This ncertainty amonts to: U = = A. The ncertainty bdget of crrent estimate for the freqency of 0 Hz is presented in Table 7. Qantity Xi Table 7. Uncertainty bdget of crrent estimate for the freqency of 0 Hz. Qantity estimate xi Standard variance (xi) Distribtion of Sensitivity coefficient ci Share in complex variance i(y).90 V.69E-6 V normal A/V.69E-6 A k V/A 8.38E-6 V /A normal.9 A /V 7.05E-5 A i.90 A normal 7.E-5 A Standard ncertainty (i) 8.50E-3 A The dependence (6) was sed to assess the extended ncertainty. For the freqency of 0 Hz, this ncertainty amonts to: U = = A. Based on the performed calclations, the reslt of crrent measrement for the freqency of 50 Hz, at the assmed confidence level and sensitivity coefficient can be written down as: I = (.90 ± 0.0) A. Based on the performed calclations, the reslt of crrent measrement for the freqency of 0 Hz, at the assmed confidence level and sensitivity coefficient can be written down as: I = (.90 ± 0.0) A. Comparing the vales of extended ncertainty of crrent measrement for the freqencies of 50 Hz and 0 Hz, it can be stated that these ncertainties do not exceed 5% of the vale of the measred crrent..5. Uncertainty of instantaneos power measrement The ncertainty of instantaneos power measrement was calclated based on formla (), i.e. the sqare root of the sm of voltage measrement variance () and crrent measrement variance (i) [9-]. The standard ncertainty vales of instantaneos power measrement for the same freqency vales, at which the voltage-voltage and crrent-voltage converters were tested, are presented in the graph Fig. 3. Fig. 3. Graph presenting the dependence of instantaneos power measrement ncertainty (p) on the freqency in the measring system with voltage-voltage and crrent-voltage converters. 3. Conclsions It can be inferred from the above reslts that the highest level of ncertainty in instantaneos power measrements is characteristic for the measrements performed at the 58

10 A. Dzwonkowski, L Swędrowski: UNCERTAINTY ANALYSIS OF MEASURING SYSTEM FOR INSTANTANEOUS POWER RESEARCH freqency of 90 Hz, while the lowest level for the measrements at the freqency of 500 Hz. In both measrement lines, i.e. of voltage and crrent, the largest contribtion to the ncertainty bdget is made by crrent and voltage converters respectively. Between these two, the ncertainty of the crrent converter has a decidedly higher vale even five times higher at certain points. The extended ncertainty U p of instantaneos power measrement was also assessed. This ncertainty was determined at the assmed confidence level of 95% and the extension coefficient k =. For example, at the freqency of 50 Hz, the ncertainty U p = 3.9 VA, and at the freqency of 0 Hz - U p = 4.00 VA. The ncertainty U p = 3.9 VA occrred for the freqency of 50 Hz, the voltage vale of 30 V and the crrent vale of.9 A. Therefore, a fll notation of the reslt of instantaneos power measrement can be presented as: p = (04 ± 4) VA. Ths, the ncertainty of an instantaneos power measrement system does not exceed % of the measred vale of instantaneos power. Acknowledgements This work was spported by the Polish Ministry of Science and Higher Edcation (grant No. 389/B/T0/00/38). References [] Bellini, A., Immovilli, F., Rbini, R., Tassoni, C. (008). Diagnosis of bearing falts of indction machines by vibration or crrent signals: A critical comparison. IEEE Indstry Applications Society Annal Meeting, 5-9, -8. [] Swędrowski, L. (00) Crrent measrements and analysis for indction motor diagnostics. Metrol. Meas. Syst., 7(), [3] Dzwonkowski, A., Swędrowski, L. (00). Motor Bearing Diagnostics Performed by Means of Laser Vibrometer. In Proc. Conference SDEMPED 0, 8th IEEE Symposim on Diagnostics for Electrical Machines, Power Electronics and Drives, Bologna, Italy, -5 [pdf]. [4] Swędrowski, L. (00). Diagnostics of indction motor bearings possibility of measrements. In Proc. Eighth International Conference on Condition Monitoring and Machinery Failre Prevention Technologies CM 00. BINDT. -0 [pdf]. [5] Swędrowski, L., Rsek, J. (009). Model and laboratory simlation of a indction motor for diagnostic prposes. Metrol. Meas. Syst., 6(4), [6] Bellini, A., Immovilli, F., Rbini, R., Tassoni, C. (008), Diagnosis of bearing falts in indction machines by vibration or crrent signals: A critical comparison. Conf. Rec. IEEE IAS Ann. Meeting, Edmonton, AB, Canada, -8. [7] Schoen, R.R., Habetler, T.G., Kamran, F., Bartheld, R.G. (995) Motor bearing damage detection sing stator crrent monitoring. IEEE Trans. Ind. Appl., 3(6), [8] Thomson, W.T., Fenger, M. (00). Crrent signatre analysis to detect indction motor falts. Indstry Applications Magazine, IEEE, 7(4), [9] Evalation of measrement data. (009). An introdction to the Gide to the expression of ncertainty in measrement and related docments, JCGM 04. [0] Evalation of measrement data. (008). Gide to the expression of ncertainty in measrement, JCGM 00, GUM 995 with minor corrections, First edition. [] Birch, K. (00) Measrement Good Practice Gide, Estimating Uncertainties in Testing, An Intermediate Gide to Estimating and Reporting, Uncertainty of Measrement in Testing. British Measrement and Testing Association, 36, ISSN