In this paper, an identification method of motor parameters for the diagnosis of rotor bar defects in the squirrel cage induction motor is proposed. It is difficult to distinguish the degree of deterioration by a conventional diagnostic method such as Fourier analysis. To overcome the difficulty, a motor simulator is used to identify the degree of deterioration of rotors in the squirrel cage induction motor. Using this method, the deterioration of rotor bars in the motor can be estimated quantitatively

Asada, Hideki

Doumae, Yukihiro

Imai, Jun

Kitamura, Akira

Konishi, Masami

Okayama University Scientific Achievement Repository

Memoirs of the Faculty of Engineering, Okayama University, Vo1.35, Nos.1&2, pp.47-51, March 2001Diagnostic method for induction motorusing simplified motor simulatorYukihiro DOUMAE", Masami KONISHI"", lun IMAI"",Hideki ASADA""" and Akira KITAMURA*""(Received December 19, 2000)In this paper, an identification method of motor parameters for the diagnosis of rotor bar defects in thesquirrel cage induction motor is proposed. It is difficult to distinguish the degree of deterioration by aconventional diagnostic method such as Fourier analysis. To overcome the difficulty, a motor simulatoris used to identify the degree of deterioration of rotors in the squirrel cage induction motor. Using thismethod, the deterioration of rotor bars in the motor can be estimated quantitatively.1 INTRODUCTIONSquirrel cage induction motors are widely used for driving facilities of various plants because of their high reliability and ease ofmaintenance. As the diagnostic method of rotor bar defects of induction motor, measurement of leakage flux and frequency analysisof stators current are studied(l). However, these methods can not clearly and quantitatively recognize the extent of deterioration ofthe rotors. To solve the problem, we have developed a simplified mathematical model of voltage and driving torque equations forthe induction motor which consists of one pair of poles and six rotor bars. In the following, mathematical models for the inductionmotor and its application to diagnosis are described together with an identification method of rotor bar resistance using the models.2 MATHEMATICAL MODEL FOR INDUCTION MOTORHere, a simplified induction motor with a single pair of poles and six rotating slots is analyzed. The equilibrium equations forvoltages and torques of induction motor are given as follows(2,3):2.1 Equilibrium Equation For VoltagesZ••Zr. ~:: ).( ~: ) (1)As for the variables in equation (1), Z•• is a matrix whose diagonal elements-are R. +pl. and the others are pM., Z.r is a matrixwhose (i,j) element is pMcos{9 - (i - I)a + (j - I),B} and Zr. is a matrix which is the transpose of matrix Z.r. Zrr is a matrixwhose (i,i) element is Rbi +R.i +Rb(i+l) +R. +p2(h +1.) + (n'-I)M., (i,i+ 1) and (i+ I,i) elements are -Rb(i+l) -p(lb +Mr ),and the other elements are -pMr • V. is the voltage vector of the stator, I. is the current vector of the stator, I r is the current vectorof the rotor, p is the differentiation operator, R. is the resistance of each stator, Rb is the resistance of each rotor, R. is the endresistance of the rotor, L. is the inductance of each stator, L b is the leakage inductance of the rotor, L. is the leakage inductance ofthe rotor end, M is the mutual inductance between each stator and the rotor, M. is the mutual inductance between the stators, M ris the mutual inductance between the rotors, a is the phase angle of the stator and ,B is the electric phase angle of the rotor.2.2 Equilibrium Equation For Torque(2)Where, If. and lb. are the current components of stator current in the direction of phase angle a and its orthogonal directionrespectively, IT! and IT2 are the current components of rotor current in the direction of phase angle a and its orthogonal directionrespectively, W m is the rotating speed, J is the rotating inertia, TL is the loading torque, P is the number of the pair of poles, thevalue of Mm is the square root of the value 3mM/2, Tn is n/P and n is the number of rotor slots. Modifying equation (1) such thatthe left side of the equation is the differential term and the right side is the remaining term, we obtain equation (3):• Graduate school of natural science and technology•• Department of Electrical and Electronic Engineering••• Kobe Steel, ltd.ApX=BX+U47(3)48 Yukihiro DOUMAE, Masami KONISHI, lun IMAI, Hideki ASADA and Akira KITAMURAMultiply the inverse of matrix A to both sides of equation (3), we obtain:(4)Equations (2) and (4) are the fundamental equations used in the motor simulator describing the c,haracteristics of the inductionmotor.3 GENERATION OF FAILURE DATA USING MOTOR SIMULATORNumerical solution of the simultaneous equations (2) and (4) can be calculated by the Runge-Kutta & Gill method(4). Moreover,using the calculated time series data of the solution, we can analyze it by Fourier transformation.Here, we simulated three cases of motor characteristics; First is the case where the motor load is zero, second is the case with aconstant load value and third is the case of a changing load. In each case, rotor resistance is changed in three ways, first is with newrotors, second is with a single deteriorated rotor and the third is with a pair of deteriorated rotors. That is, simulation studies weremade for these nine cases. In the following, the calculated result for rotating speed is described.3.1 Simulation For Non-load OperationFigure 1 shows the rotating speed of motor for each condi-tion. As shown in the figure, no distinction exists between thethree kinds of resistance in the rotor bar. The reason for this phe-nomenon is apparent because no slips occur in the case of non-loadoperation.!300-c~200~'3 1008°0~~~~-'5~~~"-'--;'10;';---'---'Time(s)Figure 1 Rotating speed without load3.2 Simulation For Operation With LoadFigure 2 shows the rotating speed with three different rotor resistances in the case of constant load. As shown in the figure,rotating speed fluctuates according to rotor deterioration.Time(s)2.(c)11 370 ' ':::- 'f \ -, " - Il5. ,'/-/.... ;v'-"'. '- /r-·k ., >r"'~'" .~\. 1\. '}'. " \, \ /\' ; \....i \ 1.\.J ..~\! I ., \ \. 1 ....( ~! \': \. j \-5 ..( : '. Ii '. 1.J " I }'... \,' \1 \' 'R RRb~b2 \0 bl,1>436R5 7.5Time(s)2.(b)Figure 2 Effects of rotor resistance on rotating speed(constant load)°0!-~~~~5:-----~1O;c-'-'Time(s)2.(a)i 300~-c~200bO.~ 10083.3 Simulation Of .Load Change CasesAs is shown in figure 3, rotating speed fluctuates with change of load similar to the deterioration of rotor.new rotor!-c~ 370'f36g.75~~'-;!;-7~~......",7.,..5 ~~-!,Time(s)3.(c)36g..,..5~~.........,7!;--~~-;;7..,..5~~---!Time(s)3.(b)oo!-------;5,.......~~~..,1;';;0,....----'Time(s)3.(a)! 3001200bO.~ 100gFigure 3 Effects of rotor resistance on rotating speed(changing load)Diagnostic method for induction motor using simplified motor simulator 494 DATA ANALYSIS BY FOURIER TRANSFORMSimulated data can be analyzed by Fourier transformation. Figure 4 shows the analyzed result for non defect rotors.As shown in the figure 4, a single clear peak exists at source frequency. For the comparison, deteriorated data are analyzed byFourier transformation and the results are shown in figure 5. As is apparent from these figures, there exist sub peaks related to thepower source frequency. So, the occurrence of the deterioration can be detected from the existence of such sub peaks by the Fouriertransformation.Next, the progress of deterioration is analyzed by the same method. Figure 6 shows the results of Fourier analysis for changing rotorresistance. As is apparent from this figure, it is difficult to distinguish the change in rotor resistance. The difficulty in recognizingthe degree of deterioration is revealed from the results. For more precise analysis, it is necessary to develop a new analyzing methodof deterioration.10'16'F- --'"--------=t10' r--~---r--~------,10°10"Figure 6 Fourier analysis of stator current(changing rotor resistance)Figure 5 Fourier transform of statorcurrent(deterioration case)10' r--~---,---~------,10°10"~10'2~ 10.310-410-'IO';\;-O--~-'-------'~--~--'-~'64S6~£! 10S8 60 62frequency(Hz)Figure 4 Fourier transform of statorcurrent(non defect case)5 IDENTIFICATION METHOD OF MOTOR PARAMETERSUSING MOTOR SIMULATORTo overcome the problem stated above, we studied a new diagnostic method usingthe motor simulation model described in the previous sections. In our method, the valueof rotor resistance is identified using data of the stator current and those of the inputvoltage which are measurable.The identification is carried out by the procedure as shown in figure 7.As shown in figure 7, input voltage Vs is used to calculate stator current I; by amathematical model of the induction motor, assuming the value of rotor resistance R b•Then, calculated stator current I; is compared with measured stator current Is. If adifference exists between I; and I., rotor resistance is modified reflecting the differencein the estimation of stator current. After iteration of these procedures, the value of Rbconverges to its real value.5.1 Identification Of One Unknown RbInitial arrangement of three phase current type stators and six rotors are given as shown in figure 8. As shown in the figure,variables of stator currents and rotor resistances are named. These are from a to c for Is and from 1 to 6 for R b respectively.Taking Rbi as the initial value, stator current I;a is calculated using the mathematical model of the induction motor. These I;avalues over time are compared with measured I sa time series data. Figure 9 shows the variation of E which is the ratio of Isa andI;a over time. Here, the ratio is defined as follows.(5)0_90~""""'20;!;0"'0-'-4"'0"'00;-'-7.60"'0-;:-0-'--;,8-:!:00"'0'--'-=1"'"0000calculation numberFigure 8 Initial arrangement of stators and rotors Figure 9 Variation of E over time50 Yukihiro DOUMAE, Masami KONISHI, lun IMAI. Hideki ASADA and Akira KITAMURA(6)(7)i = 1,·· ·,6E(n) > 0As shown in figure 9, the ratio of I sa with I:a has a certain relation only at the startingstage of rotation. Combining data in these duration repeatedly, data for identification ismade. An example of such data for the stator current is shown in figure 10.Using these data, the value of E tends to lie at less than one. Therefore the algorithm 0.2for identification is set to the following: 3:-Sj-lSj-lifelseEo(n) < Eo(n - 1) < 1 ar 1 < Eo(n - 1) < Eo(n) (8)Figure 10 Data prepared for identificationwhere Sj is the control factor to stabilize the convergence of the identification algorithm, n is the repeating number of data. Eomeans the value of E at the starting points of repeat of data as shown in figure 10.The identification processes by this algorithm are shown in figures 11 and 12. Figure 11 shows the convergence processes fordifferent initial values. As shown in these figures, the values of RbI and Rb2 successfully converge to their real values after severalhundred iterations. Starting from sufficiently large rotor resistance, it approaches its real value smoothly.o4.----~----,---~--__.............- :;;~-----j..................:::..:::..-==..=...~---_1:1..1020~-~---;1-f.00~0"--~-"'20-!::.0""'0---'calculation number1000800200 400 600calculation numbero10·••••••••••••••:-:=•••",.------:1I020~-~--·Ic!;:OO.--~--;;;!200calculation number11.(a) 11.(b)Figure 11 Identified result of RbI Figure 12 Identified result of Rb25.2 Identification Of Two Unknown RbSIn the case of two unknown R b values, it is necessary to use current data from two stators. Similar to one unknown Rb case, wedefine two ratios E 1 and E2 as follows.(9)(10)In the case of two unknown R bs , both E1 and E 2 are used for the identifications of Rbi and Rb2 simultaneously.The algorithm of the' identification is as follows:(11)(12)-Slj-lSlj-lifelseElO(n) < ElO(n - 1) < 1 or 1 < ElO(n - 1) < ElO(n) (13)S2j = { -S2j-lS2j-lifelse (14)Diagnostic method for induction motor using simplified motor simulator 51where S'j and S2j are the control factors stabilizing the convergence of the identification algorithm, n is the repeating number of thedata and Z, and Z2 are reflecting factors of E, and E 2 for iterative modification. E ,O and E 20 mean the value of E, and E2 at thestarting points of repeat of data, the same as one unknown Rb case.The identification process by this algorithm is shown in figure 13. As shown in the figure, the RbI and Rb2 values successfullyconverge to their real values after several hundred iterations.105 ,Rb2iii 104//\...10' Rbi ",------~-------10'o!-"'-:z:±o"""o~""40:!-:0""""'-6:c!0:::-0~-;:8';'00""""'--:1c:!00·0calculation number10'0~~2"'0~0~-40-.!cn0~-;6'*0"0~-;:8cicOO;;-'-1,-;!00(calculation number(a)For the case of costantload TL = 0.5 (b)For the case of time decreasing load TL = 0.5/tFigure 13 Identified result of RbI and Rb26 EXPERIMENTAL RESULTSUsing the algorithm stated above, rotor resistance are identified. In the table 1tested results are summarized.In the table 1, a circle means a successful result and a cross means a failedidentification.In the latter half of the previous section, the case of two unknown RbS weredealt with. As is shown there, RbI and Rb2 are mainly dependent on the ratiosE, and E2 respectively. From the standpoint of actual application, 6 RbS areto be identified using this algorithm. So, we defined the following algorithm:(16)(15)Table 1 Identified results for 6 rotor barsRbx RbI 0 0 X 0 0Rb2 0 0 0 0 0Rb3 X 0 0 0 0R&. X 0 0 0 0R b5 0 0 0 0 0R&6 0 0 0 X 07 CONCLUSIONMathematical models for the induction motor have been developed. Using the model we can simulate the dynamic characteristicsof induction motor. We have also developed an identification algorithm for rotor bar resistance. By this method we can quantitativelymonitor the progress of rotor deterioration. The usability of the method was ascertained using the simulated data based on theactual motor specifications. Compared with conventional Fourier analysis, this method has the advantage of diagnosing plural rotorbars simultaneously. Using this method, we can obtain the following advantages.1) It is not necessary to install a new sensor to diagnose the rotor bars.2) The diagnosis can be carried out regardless of loading conditions.3) The progress of deterioration of rotor bars can be monitored calculating rotor bar resistances continuously.REFERENCES(1) I. Morita: Factory Automation, 10, (1969), 26.(2) I. Morita: Trans. lEE Japan, nO-D, (1990), 798.(3) T. Nakano: Vector control system for alternating current motor, (1996).(4) J. Yamauchi, et al: Numerical analysis by digital computer-I, (1965), 128.

Diagnostic method for induction motor using simplified motor simulator

Abstract

Similar works

Full text

Available Versions

Okayama University Scientific Achievement Repository

Okayama University Digital Information Repository