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Measurement of induction motor speed from induced slip frequency signal 1985

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MEASUREMENT OF INDUCTION MOTOR SPEED FROM INDUCED SLIP FREQUENCY SIGNAL by CAI JI-YUAN > A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of E l e c t r i c a l Engineering We accept-this thesis as conforming to the required standard Research Supervisor Members of the Committee, P air Head of the Department Members of the Department of E l e c t r i c a l Engineering THE UNIVERSITY OF BRITISH COLUMBIA December, 1985 © C a i Ji-Yuan, 1985 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. 1 further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date DE-6(3/81) ABSTRACT A method to detect the s l i p of a three-phase or single-phase induction motor and hence determine the motor speed i s proposed. A pick-up c o i l i s placed i n close proximity to the motor and by sui t a b l e a m p l i f i c a t i o n and f i l t e r i n g of the weak s l i p frequency s i g n a l , the s l i p frequency s i g n a l component i s i s o l a t e d f o r the speed measurement. No device needs to be attached to the motor shaft. Experimental r e s u l t s from four t e s t induction motors show that the proposed method of speed measurement i s f u l l y f e a s i b l e and applies to normal loads, i . e . , f o r s l i p l e s s than 13% with considerable accuracy. Therefore, even the speed of sealed induction motor such as those used i n r e f r i g e r a t o r s can be e a s i l y measured. i i TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i i i LIST OF ILLUSTRATIONS i v LIST OF TABLES v ACKNOWLEDGEMENT • v i 1. INTRODUCTION 1 1.1 General 1 1.2 P r i n c i p l e of Operation and Performance Equation of Induction Motors 1 1.3 Previous Method of S l i p Frequency Measurement 4 1.4 Proposed Method of S l i p Frequency Measurement 4 2. FEASIBILITY TEST OF SPEED MEASUREMENT TECHNIQUE 6 2.1 Description of Measurement and C i r c u i t 6 2.2 C a l c u l a t i o n of S l i p Frequency f 7 2.3 Measurement of Supply Frequency 8 2.4 Experimental Results 8 3. CONSTRUCTION OF SPEED MEASUREMENT CIRCUIT 14 3.1 The O v e r a l l S l i p Frequency Measurement C i r c u i t 14 3.2 Inductive Device Choke 18 3.3 Second Order Butterworth Low-Pass F i l t e r 18 3.4 Input Buffer and Attenuator 22 3.5 Phase S h i f t e r 23 4. EXPERIMENTAL RESULTS 25 4.1 Discussion of Experimental Results 36 4.2 Supply Frequency Signal Component 39 4.3 Measurement of Pole Pairs 39 5. CONCLUSION 43 REFEFENCES 44 APPENDICES 46 A l . Derivation of the frequency Response Equation fo r Second Order Butterworth Low-Pass F i l t e r 46 A2. Ca l c u l a t i o n of S l i p Frequency Signal Component 49 i i i LIST OF ILLUSTRATIONS Figure Page 2.1 Signal Pickup and Detection with Choke and Galvanometer ».... 6 2.2 Equivalent C i r c u i t of Figure 2.1 7 2.3 S l i p Frequency Waveform of Motor ml 10 2.3 S l i p Frequency Waveform of Motor m2 10 2.5 Supply Frequency Waveform of Motor ml 10 2.6 Supply Frequency Waveform of Motor m2 10 2.7 Speed Comparison 12 3.1 O v e r a l l Block Diagram of S l i p Frequency Measurement 15 3.2 C i r c u i t Components 16 (a) Phase S h i f t e r 16 (b) Choke 16 (c) Phasor Diagram of Phase S h i f t e r 16 (d) Input Buffer G 16 (e) Attenuator G 16 ( f ) Second Order Butterworth Low-Pass F i l t e r Stage (each of them from F i l t e r 1 to F i l t e r 6) 16 4.1 Experimental Setup 26 4.2 Comparison of Expected and Detected S l i p Frequency f o r Induction Motor (a) Ml (b) M2 (c) M3 (d) M4 • 38 4.3 Amplitude Ratio of 60 Hz Supply Frequency Signal to S l i p Frequency Signal 40 4.4 Location Diagram of Pole Pairs Measurement 41 4.5 Choke Voltage Waveform at Several Locations 41 (a) Supply Frequency Reference Waveform 41 (b) at L± (c) at L ? (d) at L 3 41 A l . l Second Order Butterworth Low-Pass F i l t e r 46 A2.1 Gain Curve of Three I d e n t i c a l Second Order Butterworth F i l t e r Stages i n Cascade 50 i v LIST OF TABLES Table Page 2.1 S p e c i f i c a t i o n of Motors and Instruments 9 2.2 Measured Values at No Load 10 2.3 Measurement Results 11 3.1 S p e c i f i c a t i o n of C i r c u i t s i n Figure 3.2 17 4.1 Motor S p e c i f i c a t i o n s 25 4.2 Experimental Results of Motor Ml 27 4.3 Experimental Results of Motor M2 29 4.4 Experimental Results of Motor M3 31 4.5 Experimental Results of Motor M4 33 4.6 Waveform Evaluation of Detected S l i p Frequency 37 A2.1 Calculated G., (N<3) 52 Nodb A2.2 Calculated G M (N>3) 54 v ACKNOWLEDGEMENT I wish to express my deepest gratitude to my supervisor, Dr. Malcome Wvong for h i s valuable assistance, constant encouragement and correct guidance i n my graduate program and the preparation of t h i s t h e s i s . I s i n c e r e l y wish to thank my wife, Hui Chun, for the cooperation, understanding and encouragement during the ent i r e period of the study. v i 1 1. INTRODUCTION 1.1 General One of the most important trends i n va r i a b l e speed drives i s the use of induction motors. This technique has been studied i n recent years [1-6], because the induction motor can be used i n a v a r i e t y of poor working con- d i t i o n s and at l e s s expense than dc machines. It i s widely used i n ac drives with constant speed requirements. Great progress i n t h y r i s t o r and power-transistor i n v e r t e r design has made i t possible to use induction motors i n variable-speed drive systems. High performance of induction motor drives can be obtained by complex loop c o n t r o l systems, such as s l i p frequency co n t r o l [2-4], f l u x c o n t r o l [2-4], and vector c o n t r o l or phase-locked loop [pLL] co n t r o l [5,6]. But the parameter of r o t a t i n g speed must be a v a i l a b l e as a measure- ment f o r these co n t r o l systems. Conventional speed measurement requires a tachometer, transducer or device to be attached to the motor shaft . There would be l e s s i n s t a l l a t i o n and maintenance costs i f speed could be measured without shaft attachment of any such gadget. 1.2 The P r i n c i p l e of Operation and Performance Equation of Induction Motors Some important aspects of induction motors w i l l be b r i e f l y reviewed here. As we know, there are two kinds of ac motors,namely,synchronous and asynchronous motors, the l a t t e r being more commonly known as induction motors. Induction motors are widely used i n ac drive systems because of low c a p i t a l and maintenance costs. The p r i n c i p l e of operation of an induction motor i s d i f f e r e n t from that of a synchronous motor which has a speed always equal to the synchronous speed produced by a r o t a t i n g magnetic f i e l d . When three phase voltage 2 i s applied to the s t a t o r of a three phase induction motor, a r o t a t i n g magnetic f i e l d e x i s t s i n the space, at a angular speed corresponding to the supply frequency and cuts the rotor windings. Current flows i n the s h o r t - c i r c u i t e d r o t or windings, and sets up a ro t a t i n g magnetic f i e l d which i n t e r a c t s with the sta t o r f i e l d . The torque produced r e s u l t s i n r o t a t i o n of the motor ro t o r . With motion the current i n the rotor i s at a frequency which r e f l e c t s the r e l a t i v e movement of the ro t o r with respect to the r o t a t i n g magnetic f i e l d set up by the s t a t o r windings. I f a s i g n a l corresponding to the frequency of the ro t o r current can be picked up i n the v i c i n i t y of the motor then the speed of the motor can be r e a d i l y determined. Indeed, the speed of the motor w i l l never reach the speed of the r o t a t i n g magnetic f i e l d set up by the s t a t o r , the s o - c a l l e d synchronous speed. The speed of the induction motor depends upon the motor s i z e , mechanical load, e t c . Usually, f o r rated load f o r most induction motors, the speed range i s from 99% to 92% of synchronous speed ( i . e . rotor current frequency i s 0.6 Hz to 5 Hz f o r 60 Hz motors). In order to c a l c u l a t e the motor speed by measuring r o t o r current frequency, the r e l a t i o n s among induction motor parameters need to be reviewed. s l i p s i s defined as follows: n-n^ s = ~n~~ ( 1 . 1 ) where n i s synchronous speed. n^ i s ro t o r speed, i . e . asynchronous speed. The r o t o r rotates at asynchronous speed such that the s l i p frequency i s given by 3 f g = s f (1.2) where f i s s l i p frequency f i s supply frequency. The frequency of r o t o r current i s at s l i p frequency. It i s obvious that i f s = 1 the motor stays at rest because the r o t a t i n g magnetic f i e l d cuts the rotor at synchronous speed corresponding to the supply frequency. The s l i p can never be zero because the r o t o r would need to run at synchronous speed and t h i s would not be possible because no voltage would be i n - duced i n the r o t o r . Substituting (1.1) into (1.2) we get: n-n, f = ^ f s n since 60f n = — (1.*) where p i s the number of pole p a i r s . Eliminating f i n (1.3) and (1.4) f = (n-n. ) -2— , „ c x s 1 60 (1.5) and eliminating n i n (1.3) and (1.4) f - f rij = 60 (1.6) I f supply frequency f = 60 Hz then eqn. (1.6) becomes n. = - (3600 - 60 f ) (1.7) 1 p s Let N = 60 f (1.8) s or f = - ^ r C 1 - 9 ) s bO then n = - (3600 - N) (1.10) ' 1 P Here N i s the frequency of the s i g n a l which w i l l be found i n the simple experiment discussed i n chapter 2. 4 From (1.6) derived above, actual motor speed can be determined through measurement of s l i p frequency, f , the given supply frequency, f and the number of pole p a i r s , p. 1.3 Previous Method of S l i p Frequency Measurement Ishida, M. and Iwata, K. (7) and (8) have proposed the use of rotor s l o t harmonics to determine the s l i p frequency of induction motors. The air-gap f l u x of an induction motor when fed by a balanced sinusoidal power supply contains the space harmonics, due to v a r i a t i o n of reluctance of the rotor and stator s l o t s and to s p a t i a l d i s t r i b u t i o n of stator windings. The influence of s t a t o r s l o t s to harmonics i n s t a t o r voltage can be neglected i n comparison with that of r o t o r s l o t s . Thus, when the motor i s operating each s t a t o r winding contains both components of the fundamental and s l o t harmonic voltages. The detection of the s l o t har- monics can be obtained by the use of three single-phase transformers. The primary of each single-phase transformer i s connected i n p a r a l l e l to each st a t o r winding and a l l the secondary windings of the transformer i n seri e s f o r output. The s l i p frequency f can be detected only f o r motors with the number of r o t o r s l o t s equal to 3n + 1 f o r n = 1, 2, 3, reported by the authors. Experimental r e s u l t s show good l i n e a r i t y of s l i p frequency measured by the proposed method with respect to that measured by conven- t i o n a l means i n the range of s l i p frequency up to +30% of the s t a t o r frequency. However, t h i s method can only be used where the number of the r o t o r s l o t s per pole p a i r i s known and i s equal to 3n ± 1. l.H Proposed Method of f l i p Frequency Measurement In t h i s thesis a d i f f e r e n t method of s l i p frequency measurement of an induction motor and hence i t s speed w i l l be reported. By the use of 5 an inductive pick-up c o i l i n the v i c i n i t y of the induction motor i t i s found that only two major s i g n a l components, namely, the supply frequency (60 Hz) and the s l i p frequency (f"g)» ex i s t i n the inductive choke voltage. Even though there i s very poor s i g n a l to noise r a t i o , f o r the s l i p f r e - quency s i g n a l with respect to the supply frequency, the supply frequency ("noise") s i g n a l can be f i l t e r e d out. The unique s l i p frequency, f , / s can then be detected to determine the motor speed. The method does not require the attachment of any device to the motor shaft and the number of rotor s l o t s to be known, etc. Therefore, i t o f f e r s the measurement of the induction motor f o r more convenience. The t he s i s p ro j ec t i s aimed at i n v e s t i g a t i n g t h i s concept o f us ing the s l i p frequency component of leakage f l u x a v a i l a b l e in the f i e l d around an i nduc t i on motor to determine the motor speed. However,the o p t i - m i z a t i o n o f the i n d u c t i v e p i c k - u p t r a n s d u c e r , f i 1 t e r stages and the d i s p l a y o f the speed s i g n a l i s not attempted in t h i s t h e s i s . A simple experiment to check the f e a s i b i l i t y of the proposed method i s discussed i n chapter 2. The r e s u l t of that experiment guided the design of the f i n a l speed measurement c i r c u i t , d e t a i l s of which are given i n chapter 3. F i n a l l y , t e s t r e s u l t s f o r four induction motors are given and discussed i n chapter 4. 6 2. FEASIBILITY TEST OF SPEED MEASUREMENT TECHNIQUE To te s t the f e a s i b i l i t y of the speed measuring technique, a simple experiment was done using an inductive pick-up c o i l and a galvanometer. The experiment w i l l indicate two important points, namely; (1) The s l i p frequency s i g n a l f exi s t s i n the space around the motor when i t i s running. (2) The s l i p frequency s i g n a l together with a strong s i g n a l at the supply frequency, 60 Hz, would be picked up by an inductive device, such as a choke and could be detected a f t e r s u i t a b l e f i l t e r i n g . 2.1 Description of Measurement and C i r c u i t The c i r c u i t diagram of s i g n a l pick-up and detection i s shown i n Fi g . 2.1. The choke i s placed beside the motor i n order to pick up the si g n a l from the rotor c i r c u i t of the motor. High inductance and appro- p r i a t e volume i n the choke would be best. The inductive voltage i n the choke ( c a l l e d choke voltage i n t h i s t h e s i s ) i s indicated i n the c i r c u i t by the galvanometer, which i s highly s e n s i t i v e to dc or low frequency OSCILLOSCOPE F i g 2.1 Signal Pickup and Detection with Choke and Galvanometer 7 current. The current value i s determined by the deviation of the l i g h t spot on the scaled glass. The galvanometer also plays the r o l e of a mechanical low-pass f i l t e r because i t s mechanical i n e r t i a w i l l only allow i t to follow the dc or low frequency s i g n a l and cuts o f f higher frequency s i g n a l s , such as that of the supply frequency 60 Hz. The s i g n a l com- ponent of supply frequency may be measured and displayed on the o s c i l l o - scope by connecting the leads of the choke d i r e c t l y to the input of the o s c i l l o s c o p e . 2.2 C a l c u l a t i o n of S l i p Frequency f r i O S C I L L O S C O P E Fig 2.2 Equivalent C i r c u i t of Fig 2.1 The equivalent c i r c u i t to measure the s l i p frequency f and i t s amplitude produced by rotor current i s shown i n F i g . 2.2 where r . : choke resistance x r : galvanometer resistance g r : external v a r i a b l e resistance e V g : s l i p frequency voltage component i n choke Its amplitude V g can be derived as follows 8 We have f = — (1.9) s 60 Also V = Ig( r , + r + r ) (2.1) s 6 i e g The current Ig i n eqn. (2.1) i s given by Ig = Ag- sg (2.2) where A g i s the amplitude of the l i g h t spot defection of the galvanometer and sg i s the galvanometer s e n s i t i v i t y . -6 sg = 0.0035 x 10 a. Su s t i t u t i n g (2.2) into (2.1) V = A • sg ( r , + r +r ) (2.3) s s to i e g In the experiment the s l i p frequency f i s obtained by counting the number of o s c i l l a t i o n s N of the galvanometer l i g h t spot f o r one minute. 2.3 Measurement of supply frequency The strong r o t a t i n g magnetic f i e l d e x i s t s i n the space around the motor when i t i s running so that the supply frequency 60 Hz i s also induced i n the choke. I f the switch K i s opened so that the choke voltage i s applied d i r e c t l y to the input of the o s c i l l o s c o p e , as indicated i n F i g . 2.2, the wave form on the os c i l l o s c o p e indicates 60 Hz frequency and i t s ampli- tude which can be read from the s c a l e . Even though the choke voltage contains both signal components of s l i p frequency and supply frequancy 60 Hz, they are f a r enough apart and the supply frequency s i g n a l i s much stronger than the s l i p frequency s i g n a l , that the wave form of supply frequency i s hardly d i s t o r t e d at a l l . 2.4 Experimental Results Measurements were c a r r i e d out on two single-phase induction motors at no load. The s p e c i f i c a t i o n of motors and instruments employed i s shown i n Table 2.1. The measurement, wave form and r e s u l t s are given i n the 9 Tables and Figures as follows: (1) Table 2.2 shows the measured s i g n a l components of s l i p and supply frequencies. (2) Figure 2.3 and Figure 2.4 show the s l i p frequency wave forms f o r the two motors. (3) Figure 2.5 and Figure 2.6 show the supply frequency wave form seen.on the os c i l l o s c o p e . (4) Table 2.3 shows the f i n a l r e s u l t s f o r f , n , V , V and Table 2.1 S p e c i f i c a t i o n of Motors and Instruments Motor choke galvanometer Pole P a i r s P Phase Power (Hp) r i L (H) Sens. Sg r (a/mm) " (0) ml (Motorl) c 2 1 1/3 92 18.9 3 . 5 * l ( f 9 25 m2 (Motor2) 1 1 1/40 92 18.9 3.5X10 - 9 25 10 Table 2.2 Measured Values at no Load Motor Actual Speed Stroboscope (rpm) S l i p Frequency Component C i r c u i t Supply Frequency Component r i r e r g Frequency Amplitude (n) Frequency Amplitude (N/min) A (mm) s f60 ( H z ) V60 (v. pk-pk) Galvanometer Oscilloscope ml 1792 16 48 92 330 25 60.5 1.2 m2 3495 105 10 92 3300 25 59.7 1.83 3490 110 10 92 3300 25 59.7 1.83 3486 114 10 92 3300 25 59.7 1.83 Fi g 2.4 S l i p frequency Waveform of Motor m2 Fi g 2.6 Supply Frequency Waveform of Motor m2 11 Table 2.3 Measurement Results Actual S l i p Measured Components Ratio Motor Speed Stroboscope n' (rpm) S S l i p Frequency f s (Hz) Motor Speed (rpm) S l i p Frequency Voltage V s (v) Supply Frequency Voltage V60 ( V ) v, /v 60 s Galvanometer Oscilloscope ml 1792 0.44% 0.26 1792 75*10~ 6 1.2 16 X10 3 m2 3495 2.91% 1.75 3495 119 x10" 6 1.83 15.3 X10 3 3490 3.05% 1.83 3490.2 119 x10~ 6 1.83 15.3*103 3486 3.16% 1.90 3486 1 1 9 X 1 0 - 6 1.83 15.3 X10 3 The following indicates sample c a l c u l a t i o n f o r motor m̂  using the measurements and values of Tables 2.1 and 2.2. From eqn. (1.9), (1.10) and Table 2.2 with p = 2 f = N s .16 0 > 2 6 H z s 60 60 n, = - (3600 - 60 f ) = - i (3600 - 60 x 0.26) = 1792 rpm. 1 p s 2 From eqn. (2.3) and Tables 2.1 and 2.2, the amplitude of s l i p frequency voltage i s V s = V S S < r i + r e + rg> _9 Sg = 3.5 x 10 a/mm r . = 92 fi r = 330 Q r = 25 n i e g and A = 48 mm p = 2 s r So V = 48 x 3.5 x 10" 9 (92 + 330 + 25) = 75 x 1 0 - 6 v. s From Table 2.3 the act u a l speed n ^ measured by a stroboscope as compared with the speed n^ measured by the arrangement of choke and galvanometer are drawn i n F i g . 2.7. any point on the str a i g h t 12 Fi g 2.7 Speed Comparison l i n e means that the measured speed i s equal to actual speed. The measured values of Table 2.3 agree exactly. From the above r e s u l t s some important points can be made: (1) The speed as calculated using the o s c i l l a t i o n per minute of the galvanometer l i g h t spot are i d e n t i c a l with those measured with a stroboscope, which i s generally acceptable as accurate speed measurement. So the proposed method w i l l c o r r e c t l y determine the induction motor speed at no load. (2) There e x i s t s multiple frequency s i g n a l components i n the f i e l d around the motor when i t i s operating. Obviously, the choke voltage w i l l contain at le a s t the s i g n a l components of supply frequency 60 Hz and s l i p frequency f that are r e l a t e d to the motor speed. From Table 2.3 i t can be estimated that the range of f f o r the induction motors v a r i e s from 0.2 5 Hz at no load up to 5 Hz, i . e . that the speed range from 1792 rpm down to 1650 rpm f o r a four-pole motor. 13 (3) The amplitude r a t i o of Vgg to V g reaches up to 16 x 10 approximately f o r motor m̂ . The amplitude of supply frequency component Vg Q i s much greater than the amplitude of the s l i p frequency component. Therefore, a multi-stage f i l t e r with a m p l i f i c a t i o n has to be designed to i s o l a t e the weaker s l i p frequency component V g from the much stronger supply frequency s i g n a l component Vg Q. (4) The determination of the motor speed not only depends upon the measured f but the synchronous speed has to be known i . e . the number of pole p a i r s f o r the motor has to be known. The equa- t i o n (1.6) e x h i b i t s t h i s r e l a t i o n 1 p s The number of pole pa i r s may be determined experimentally or from nameplate s p e c i f i c a t i o n . This parameter p w i l l be assumed to be given f o r the speed determination. It i s to be noted that the e r r o r of the s l i p frequency amplitude w i l l increase with frequency because of the mechanical i n e r t i a of galvanometer. So the galvanometer can be considered as a mechanical low-pass f i l t e r with low corner frequency. 14 3. CONSTRUCTION OF SPEED MEASUREMENT CIRCUIT The simple experiment described i n chapter 2 demonstrated the f e a s i b i l i t y of the technique to measure the speed of an induct ion motor by use of the s l i p frequency s i g n a l present the magnetic f i e l d around the motor. But the simple measurement set up using a galvanometer i s l i m i t e d i n i t s a b i l i t y to measure the whole range of speeds with varying load f o r d i f f e r e n t kinds of induction motors. Therefore, a more sophisticated f i l t e r c i r c u i t needs to be designed to replace the mechanical f i l t e r represented by the galvanometer. Major f a c t o r s to be considered i n the c i r c u i t design are: (1) The measurement c i r c u i t i s to use an active f i l t e r , with operational amplifiers as the act i v e elements, and with multi-stage f i l t e r i n g . Each f i l t e r stage should attenuate the supply frequency s i g n a l and amplify the weak s l i p frequency component. (2) Each f i l t e r stage should work within the l i n e a r range of the operational a m p l i f i e r i ^ . within ± 13 vo l t s (3) For the detection of the s l i p frequency f o r various motors, the multi-stage f i l t e r c i r c u i t should provide output at each stage because the number of f i l t e r stages needed varies with the type of induction motors and t h e i r speed. (4) The amplitude of the detected s l i p frequency can a l so be calculated through the multi-stage f i l t e r . 3.1 The Ov e r a l l S l i p Frequency Measurement C i r c u i t The o v e r a l l c i r c u i t i s shown i n Figure 3.1 and comprises the following: 15 (1) Signal pickup i . e . inductive device, choke (2) Second order Butterworth low pass f i l t e r (3) Input buffer and attenuato_r (4) A l t e r n a t i v e supply frequency phase s h i f t e r The d e t a i l e d c i r c u i t s f o r each of the above are shown i n Figure 3.2. PHASE S H I F T E R C H O K E INPUT BUFFER G- Fl LTER 1 out Put 1 F l LTER 2 Fl L T E R 3 ATTENUATOR G a output 2 O output 3 F I L T E R 4 °f Fl LT ER 5 G f F ILT ER 6 G f ou t pu 16 output 4 output 5 F i g 3.1 Overall Block Diagram of S l i p Frequency Measurement 16 Input Buffer (b) (d) (e) (f) (a) Phase S h i f t e r F i g 3.2 C i r c u i t Components (b) Choke (c) Phasor Diagram of Phase S h i f t e r (e) Attenuator G (d) Input Buffer G i ( f ) Second Order Butterworth Low Pass F i l t e r Stage (each of them from F i l t e r 1 to F i l t e r 6) 17 T a b l e 3 .1 S p e c i f i c a t i o n o f C i r c u i t s i n F i g 3 . 2 Choke 150 H e n r y P h a s e S h i f t e r T 1 2 0 / 6 . 3 R 0-500kQ p v2 R . 0 -20 kfi y i C 3 5 y F I n p u t B u f f e r R_ . 100 kn FX R f l 155 k?2 R 22 kfi. P A t t e n u a t o r R . 1. Mfi G =1 a l a l R 9 + R , R 150 kfi G . — — = 1 / 7 . 4 a a R . + R _+R , a l a2 a i R a 3 5 ' 6 ^ G a3= R 1 + R a ' + R = 1 / 2 ° 6 a l a2 a i R 22 kfi P F i l t e r l t o F i l t e r 6 R_ 50 kn F R 10 kS2 Rĵ  6 .8 kn R2 56 kn C 0 . 3 2 , 0 . 4 7 , 1 . 0 , 2 . 4 7 , 4 . 4 y F N o t e : S e l e c t i o n o f Rp, R f , R 1 , R 2 > C f o r F i l t e r l t o F i l t e r 6 i s d e s c r i b e d i n s e c t i o n 3 . 3 18 3.2 Inductive Device Choke This device picks up, by magnetic induction, the s i g n a l frequency components of i n t e r e s t . The strength of the s i g n a l pickup depends upon the core s i z e , inductance and the l o c a t i o n of the choke r e l a t i v e to the motor. A choke with an inductance of 150 Henry i s a r b i t r a r i l y selected. The design of better transducer was not attempted. 3.3 Second Order Butterworth Low-Pass F i l t e r This i s the most impotant part i n the o v e r a l l c i r c u i t and consists of s i x second order Butterworth f i l t e r stages. The second order low-pass Butterworth f i l t e r has f l a t c h a r a c t e r i s t i c s i n the pass band and rather sharp cut o f f i n the stop band. No r i p p l e i n the frequency response curve makes the c a l c u l a t i o n of f i l t e r gain ea s i e r . The proper s i z e of amplified s l i p frequency s i g n a l component a f t e r each stage of f i l t e r i n g should be obtained. The design of a second order Butterworth low-pass f i l t e r w i l l be discussed i n the following. (1) Frequency Response Equation The frequency response equation of each f i l t e r stage can be expressed as follows G(OJ) = G 1 _ (JL_)2 + 2 5 (j ±- ) c c where G 1 + —— i s the dc gain of the f i l t e r (3.3) c 1 i s the cut o f f frequency (3.4) + (3.5) i s the damping c o e f f i c i e n t See the d e r i v a t i o n i n d e t a i l i n Appendix A l . 19 When _ _1_ the f i l t e r equation i s then J2 |G(co)| - • , * (3.6) 1 + ( — V and the E; = s u b s t i t u t i n g i n t o eqn. (3.5) /2 (3.7) R2 C2 The f i l t e r stage has an attenuation of -40 dB/decade and the t o t a l attenuation c h a r a c t e r i s t i c i s proportional to the number of f i l t e r stages. The values of the c i r c u i t elements can be determined from the above three equations (3.3), (3.4), (3.7). (2) Parameter Value Determination For s i m p l i c i t y of c i r c u i t c a l c u l a t i o n i n d e n t i c a l values were chosen for capacitors and i n Figure 3.2 ( f ) . Now eqn. (3.4), (3.7) become f " - i - / - i - c 2 T T C A J R^R (3.8) where f i s the corner frequency (3.9) From eqn. (3.8) the corner frequency f only depends upon the capacitor C i f R^ and are kept constant. Furthermore, R^ and R̂  can be calculated from eqn. (3.3), (3.8), (3.9) once the parameters G, f and C are given. The values of f , G and C are selected as follows: c' a. f = 1 8 Hz c The corner frequency f i s selected to be 18 Hz because i t i s b a s i c a l l y s u f f i c i e n t f o r measurement of the whole range of motor since the o v e r a l l 20 cut o f f frequency w i l l decrease with an increasing number of f i l t e r stages. Most induction motors operate at speeds corresponding t o ^ s l i p s of l e s s than 8% i . e . f les s than 5 Hz. s R F b. G = 6 i . e . G = 1 t — — = 6 R f and R p = 50 K ft, R f = 10 K ft are selected. Considering the minimum s l i p frequency component V g i n choke voltage, which —6 happens to be at the lowest s l i p frequency, a value of 75 x 10 was obtained (see Table 2.3) i n the simple experiment of chapter 2. So t h i s value of V . should be amplified to the proper value V"*" . a f t e r t o t a l smin . smm si x f i l t e r stages. For the s e l e c t i o n G = 6, the amplified output V" . should be c smin V . = G 5 ' V . = 6 5 x 75 x 10~ 6 = 3.5 v o l t s smin smin Therefore, the output of 3.5 v at the s i x t h f i l t e r stage i s a reasonable value to be measured and the s e l e c t i o n G = 6 i s reasonable. c. C = 0.47 uF By use of the above s e l e c t i n g parameter values, (G=6, f c=18 Hz — 6 C=0.47 x 10 F ) , R^ and R 2 can be worked out by so l v i n g the eqn. (3.3), (3.8), (3.9) as follows: R F G = 1 +_£. = 6 R. since _p c 2nC ^ R 1R 2 R, R, 1 1 2 (27if C ) 2 (2TT x 18 x 0.47 x 10 6 ) 2 c N so R 1R 2 = 0.0354 x 1 0 1 0 (3.10) 21 (6-1) = 1.414 (3.11) Let R„ s u b s t i t u t i n g x into eqn. (3.11). X + X _5 X 1.414 x - 4 = 0 X = 2.83 or -1.39 The correct s o l u t i o n i s x = 2.83 R2 Then / = 2.83 R 2 = Q.O^ C R_ = 8 R, V R 1 R 2 = 0.0354 x 10 10 6.65 x 10 ft = 53.5 x 10 ft Therefore, R^ = 6.8 K ft and = 56 K using a v a i l a b l e r e s i s t o r values. Now v e r i f y the E, and f by s u b s t i t u t i n g the selected a c t u a l values R± = 6.8 K ft, R 2 = 56 K ft, C = 0.47 uF into eqn. (3.5), (3.8). so { hr-R i + J R 2 - (G-l) R2 } = 0.5 { 56 I 6.8 t_ . x 6-8 \hr + (6-1} 6.8 56 = 0.74 2irc ./R^ 6.28 x 0.47 x 10 6.8 x 56 x 10 = 17.3 Hz 22 The actual £ =0.74 and f = 17.3 Hz are close to the selected c values of f = 18 Hz and £ = 0.707. The corner frequency f i s varied by using d i f f e r e n t values of capacitors while keeping a l l other element values f i x e d . C = 0.32, 0.47, 1.0, 2.47, 4.4 yF The attenuation f o r each f i l t e r stage i s -40 dB/decade and the t o t a l attenuation from input to output i s proportional to the number of stages employed. Successful detection of s l i p frequency f o r measuring each speed heavily r e l y upon the reasonable s e l e c t i o n of both corner frequency and t o t a l attenuation. 3.4 Input Buffer and Attenuator The input stage of the measuring c i r c u i t consists of a noninverting operational a m p l i f i e r with high input impedance, as indicated i n Figure 3.1, Figure 3.2(d). I f the s i g n a l from the choke, which has high induc- tance, i s d i r e c t l y connected to the f i r s t f i l t e r i n g stage that includes the capacitance feedback c i r c u i t the c i r c u i t w i l l become unstable and o s c i l l a t i o n s w i l l take place. Therefore, the input operational a m p l i f i e r acts as a b u f f e r stage between the choke s i g n a l source and the input of the f i r s t f i l t e r stage. As mentioned previously, the design of each f i l t e r stage must be such that the weak s l i p frequency s i g n a l component V*s w i l l be amplified and the supply frequency s i g n a l component w i l l be attenuated. The r a t i o of these two s i g n a l s Vg^ to V at any f i l t e r stage indicates the degree of f i l t e r - ing. Where more than four stages of f i l t e r i n g i s required, the attenuator c i r c u i t i s required to maintain o p e r a t i o n i n the l i n e a r region of the operational a m p l i f i e r . A l t e r n a t i v e l y , attenuation could have been provided i n each f i l t e r stage. 23 3.5 Phase S h i f t e r One of the objectives to use a f i l t e r i s to attenuate the supply- frequency s i g n a l component 60 Hz i n the mixed source s i g n a l so that the s l i p frequency component can be i d e n t i f i e d , thus the r a t i o of Vg Q to V g can be minimized a f t e r each f i l t e r stage. The phase s h i f t e r having supply frequency can also be used i n the same r o l e as the f i l t e r by providing a phase-shaf ted supply frequency s i g n a l . How i t works i s shown i n Figures 3.1, 3.2. The phase s h i f t e r (Figure 3.1) can vary i t s output phase r e l a t i v e to the phase of the supply frequency component of the choke voltage. Let the phase s h i f t e r output superpose on the choke voltage and adjust the phase and magnetude o f phase s h i f t e r ou tpu t . Then the i n - put of buffer w i l l have a greatly attenuated supply frequency component. Hence the number of f i l t e r stages required would be l e s s . The major components i n the phase s h i f t e r shown i n Figure 3.2(a) include the centre- tapped transformer T , variable r e s i s t o r and capacitor C^. The function of T^ i s to reduce the supply vo l t age to a s u i t a b l e s i z e . The p r i n c i p l e of phase s h i f t e r can be r e a d i l y found i n the c i r c u i t diagram Figure 3.2(a),(c). The f i x e d supply voltage V with centre tap supplies the s e r i e s RC c i r c u i t i n the closed-loop c i r c u i t ACBD. The voltage V^g across always lags by 90° across the variable r e s i s t o r R 2_» The p o t e n t i a l D r e l a t i v e to ground C w i l l move on the c i r c l e shown i n Figure 3.2(c) i f the r e s i s t o r R ^ v a r i e s . In order to obtain a v a r i a b l e voltage output R v 2 i s used. The switch i s a reversing switch which allows the phase s h i f t e r to work i n another h a l f c i r c l e . For example, once the reverses, the p o t e n t i a l D w i l l f a l l i n t o symmetric D' i n the next h a l f c i r c l e (Figure 3.2(c)). So the range of phase angle f o r t h i s c i r c u i t can change t h e o r e t i c a l l y from 0° to 360°. However, i t 24 i s impossible to use an i n f i n i t e value of capacitor, and the actual range of phase s h i f t e r mainly depends upon the siz e of capacitor used. 25 4. EXPERIMENTAL RESULTS The proposed method of speed measurement was tested on four d i f f e r e n t induction motors. The s p e c i f i c a t i o n s f o r these motors are given in Table 4.1. Table 4.1 Motor S p e c i f i c a t i o n s F u l l Load Horse Rated Rated Motor Speed (rpm) Type of Motor Power P (Hp) Current I (a) Voltage V (v) . Ml 1725 3-phase wound rotor 1/3 1.7 220 M2 1725 3-phase s q u i r r e l cage 1/4 1.5 220 M3 1725 1-phase s q u i r r e l cage 1/4 5.5 120 M4 1690 3-phase wound rotor 2.5 8 208 The experimental setup i s shown i n Figure 4.1. A choke i s placed i n the v i c i n i t y of the t e s t motor and i s l e f t i n p o s i t i o n throughout the t e s t . Its output i s taken to a f i l t e r , as discussed i n chapter 3. The f i l t e r output i s then fed to a Universal Waveform Analyzer which i s a 68000 micro- processor-based instrument. The dc generator i s mechanically-coupled to the induction motor, and with i t s resistance load provides a v a r i a b l e motor load. The ac t u a l motor speed i s measured by a stroboscope f o r comparison with that determined from the s l i p frequency. The number of f i l t e r stages, value of f i l t e r capacitor and attenuator gain were adjusted f o r best s l i p frequency determination. The amplitude of the s l i p frequen- cy signal component can be determined by the use of the f i l t e r gain fomulae and c h a r a c t e r i s t i c curves as described in appendix A2. 26 Resistanse Load Choke I I- Induction Motor z F i l t e r i n g C i r c u i t Universal Waveform Analyzer Fi g 4.1 Experimental Setup Experimental r e s u l t s f o r the four induction motors are given i n Table 4.2 to 4.5. The following symbols are used i n the Tables. I Motor current n Actual speed measured by the stroboscope, 3. (* means speed at or closest to rated speed ) N Number of the f i l t e r stages at which the output i s measured C Value of capacitor used i n the f i l t e r stages G Gain of the attenuator a f S l i p frequency v Amplitude of f at the f i l t e r output n n v sin Frequency of "noise" s i g n a l Amplitude of f at f i l t e r c i r c u i t output Motor speed c a l c u l a t e d from the measured f through (1.7) Calculated input amplitude of the f component by eqn. (A2.14) v n ^ n Calculated input amplitude of the f component by eqn. (A2.14) v gQ Induced supply frequency (60 Hz) amplitude i n the choke Table 4.2 Experimental Results of Motor Ml M oto r F i l t e r i n g C i r c u i t O u t p u t of F i l t e r i n g C i r c u i t Input ' V60Ain ( * 1 0 3 ) 1 fa) n a (rpm) N C (MF) G. W a v e f o r m (H«) (v) «n V„ (H») (v) Ca lcu l a t ed (V) n, (rpm) ( » v ) v » i n v n i n 1.14 1770 3 1.0 0.98 0.24 2.93 .032 1770 0.73 0.1 1.02 1.4 6 0.32 1/206 0.18 30 0.14 0.52 8.3 1.2 1755 3 1.0 1.56 0.44 4.3 .034 1753 1.41 0.12 1.07 0.7C 6 0.32 1/206 30 0.16 9.5 1.3 1740 3 1.0 1.94 0.74 1742 2.25 1.1 0.49 6 0.32 1/206 /\/\s 0.65 30 0.18 1.87 10.7 1.45 1710* 3 1.0 A A A A 2.96 0.12 1711 3.8 1.18 0.3 6 0.32 1/206 A A A A 1.13 30 0.23 3.3 13.6 1.65 1680 3 1.0 A A A A 3.9 1.86 1683 6.5 1.29 0.20 6 0.32 1/206 A A A A 1.67 30 0.3 4.96 17.8 Table 4.2 (continued) Motor Filtering Circuit Output of Fi l ter ing Circuit Input' ( X 1 0 J ) 1 "a (rpm) N • C (MF) G. Waveform (Hi) (v) (Hi) (v) Calculated V60 (v) n, (rpm) (mv) v t i n v nin 1.86 1650 3 1.0 AAAAA 5.08 2.16 1647 8.49 1.33 0.16 6 0.32 1/206 AAAAA 2.23 30 0.31 6.7 18.4 2.06 1620 . 3. 1.0 AAAAAA 5.86 2.03 1624 9.89 1.37 0.14 6 0.32 1/206 AAAAAA 2.75 30 0.33 8.4 19.6 t : In these two cases each one has a low rate of o s c i l l a t i o n 2.93 Hz & 4.3 Hz about i t s centre speed 1770 & 1755 as observed by a stroboscope Table 4.3 Experimental Results of Motor M2 M oto r F i l ter ing Ci rcui t Output of F i l t e r i n g C i r c u i t Input' V 6 o A i n (*10 3) 1 fa) "a (rpm) N c (MF) 6 a W a v e f o r m ( H i ) ( v ) 'n V„ ( H i ) (v) Calculated (V) n, (rpm) (mv) V » i n ^n i n 1.1 1778 3 4.4 0.73 .052 1778 0.186 0.38 2.04 6 0.32 1/7.4 30 19.1 40.8 1.1 1767 3 . 4.4 1.1 .067 1767 0.27 0.362 1.15 6 0.32 1/7.4 30 17.5 37.4 1.15 1755 3 4.4 1.52 .055 1754 0.34 0.345 1.01 6 0.32 1/7.4 30 15.2 32.5 1.15 1740 3 4.4 hAA\A 1.96 .034 1741 0.46 0.346 0.75 6 0.32 1/7.4 30 13.5 <• 28.9 1.15 * 1725 5 1.0 AAA 2.5 .74 1725 0.50 0.362 0.72 6 0.32 1/7.4 30 9.51 20.4 i Table 4.3 (continued) M oto r F i l te r ing Circuit O u t p u t of F i l t e r i n g C i rcu i t 1 nput' V6o/Kin (*103) 1 (a) n a (rpm) N C (MF) W a v e f o r m (Hi) (v) 'n V„ (Hi) (v) Calculated V60 (V) n, (rpm) (mv) v s i n v n i n 1.2 1710 5 1.0 1/7.4 A A A / 2.92 .792 1712 0.552 0.346 0.63 6 0.32 1/7.4 30 8.14 17.4 1.27 1695 5. 1.0 1/7.4 A A A A 3.46 .865 1696 0.646 0.337 0.52 6 0.32 1/7.4 30 7.14 15.2 1.37 1680 5 1.0 1/7.4 A A A A A 4.1 .933 1677 0.728 0.334 0.46 6 0.32 1/7.4 30 6.28 13.4 Table 4.4 Experimental Results of Motor M3 M o t o r F i l te r ing C i rcu i t O u t p u t of F i l t e r i n g C i rcu i t Input' V60Ain ( xio 3) 1 (a) "a (rPm) N C ( M F ) W a v e f o r m (Hz) (v) (Hi) (v) Calculated. (V) n 1 (rpm) (mv) i n v n i n 5.1 1882 5 1.0 1/7.4 0.61 0.31 1782 0.21 3.88 18.5 6 0.32 1/7.4 30 4.5 9.6 5.1 1770 5. 1.0 1/7.4 1.03 .547 1769 0.37 3.44 9.3 6 0.32 1/7.4 30 3.7 7.9 5.16 1755 5 1.0 1/7.4 1.48 .801 1756 0.56 3.11 5.5 6 0.32 1/7.4 /\y\ 30 3.2 6.8 5.4 1740 5 1.0 1/7.4 / w 2.07 .946 1738 0.68 2.96 4.4 6 0.32 1/7.4 AAA 30 2.5 5.3 5.7 1725* 5 1.0 1/7.4 AAA 2.53 1.0 1724 0.73 2.7 3.7 6 0.32 1/7.4 AAA 30 2.1 4.5 Table 4.4 (continued) M o t o r F i l ter ing Circuit O u t p u t of F i l t e r i n g C i rcu i t Input' ( * 1 0 3 ) 1 <a) "a (rpm) N C ( J* F ) c. W a v e f o r m ( H i ) (v) ( H i ) (v) Calculated (v) n t (rpm) (mv) v » i n v n i n 5.95 1710 5 1.0 1/7.4 AAA/ 2.94 1.09 1712 0.814 2.48 3.0 6 0.32 1/7.4 AAA/ 30 1.8 3.9 Table 4.5 Experimental Results of Motor M4 M o t o r F i l ter ing Circuit Ou tput of F i l t e r i n g C i rcu i t Input' ^W în ( X103) 1 fa) "a (rpm) N C (MF) 6 a W a v e f o r m ( H i ) (v ) ( H i ) (v) Calculated (V) n t (rpm) (mv) v » i n v n i i » 1.3 1770 3 4.4 1.05 .029 1769 0.11 0.45 3.5 3 1.0 1.04 .034 1769 0.128 6 0.32 1/7.4 30 5.55 15.9 1.72 1740 3 4.4 / \ / \ 2.03 .017 1739 0.23 0.48 2.0 3 1.0 / X X X 2.05 .079 1739 0.24 6 0.32 1/7.4 30 13.8 29.5 2.2 1710 3 1.0 AAA 3.08 0.11 1708 0.35 0.50 1.45 6 0.32 1/7.4 30 15.7 33.6 2.7 1680* 3 1.0 A A A A 3.9 0.17 1683 0.58 0.50 0.87 6 0.32 1/7.4 15.6 1.74 24.4 6.9 0.28 4.9 Table 4.5 (continued 1) M o t o r F i l te r ing C ircui t Output of F i l t e r i n g C i rcu i t Input' V6oAin (X10 3) 1 (*) "a (rpm) N C (<"F) G a W a v e f o r m (Hi) (v) 'n V „ (Hz) (v) Ca lcu lated (V) n 1 (rpm) (mv) v s i n v n i n 3 . 2 3 1650 3 1 . 0 A A A A A 5 . 1 0 . 2 1647 0 . 7 9 0 . 5 0 0 . 6 3 6 0 . 3 2 1/7.4 12.7 2 . 0 2 2 . 5 1 0 . 8 0 . 2 7 4 . 6 3 . 7 1620 3. 1 . 0 A A A A A A / 6 . 0 4 0 . 2 3 1617 1.1 0 . 5 0 0 . 4 5 6 0 . 3 2 1/7.4 V U A V W U A i 21 1 2 . 5 3 3 . 2 4 . 4 4 . 0 4 1 4 . 2 4 . 2 2 1590 3 1 . 0 AAAAAAA 7 . 0 1 0 . 2 4 1586 1 . 5 5 0 . 5 1 0 . 3 3 6 0 . 3 2 1/206 1 9 . 5 0 . 6 6 4 . 8 4 . 5 7 1560 3 1 . 0 AAAAM 8 . 0 0 . 2 3 1560 2 . 0 2 0 . 5 1 0 . 2 5 6 0 . 3 2 1/206 12.7 0 . 3 7 1 7 . 6 0 . 6 5 1 . 3 5 3 . 5 4 . 9 1530 3 1 . 0 ^ V V V A A / V \ A A 9 . 1 0 . 1 6 6 . 8 4 0 . 1 2 1 6 . 6 . 0 1 5 1527 2 ' 0 3 0 . 7 4 . 0 7 5 0 . 5 1 0 . 2 5 6 0 . 3 2 1/206 Table 4.5 (continued 2) Muto r F i l te r ing C i rcu i t Output of F i l t e r i n g Ci rcui t Input' ( X 1 0 3 ) 1 <a> n a (rpm) N C ( M F ) G a W a v e f o r m (Hi) (v) 'n V„ (Hi) (v) Ca lcu la ted V60 (V) n, (rpm) (mv) V* i n ^n i n 5.3 1500 3 1.0 V \ A M M A 10.0 0.13 4.9 .031 14.7 .024 1500 2.4 0.12 2.66 0.52 0.25 6 0.32 1/206 5.7 1440 3 1.0 12.1 .068 1440 3.3 0.52 0.16 6 0.32 1/206 0.91 1.06 3.02 5.9 1380 6 0.32 1/206 13.7 0.67 8.8 0.87 1369 4.5 2.8 0.53 0.12 6.4 1320 6 0.32 1/206 15.9 1.16 5.86 0.57 1323 5.3 1.76 0.55 0.10 6.8 1260 6 0.32 1/206 18.1 1.24 2.73 0.32 1257 7.16 0.92 0.56 .078 7.5 1200 6 0.32 1/206 u 20.0 1.0 1.95 0.17 1200 7.7 0.48 0.58 .076 36 4.1 Discussion of Experimental Results The basic idea of using the s l i p frequency to determine the speed of induction motors r e l i e s on counting the zero axis crossings of the out- put s i g n a l waveform from the f i l t e r . Therefore, the shape of the wave- form i s important. Any d i s t o r t i o n i n the s i g n a l waveform w i l l a f f e c t the speed measurement. The s i g n a l waveform can be c l a s s i f i e d as fo l lows; (1) There i s no d i s t o r t i o n and the s i g n a l frequency i s exactly equal to the s l i p frequency f . (2) The waveform contains some noise but the frequency of the waveform i s s t i l l equal to the s l i p frequency f . (3) There i s considerable d i s t o r t i o n i n the waveform so that the frequency of the waveform i s no longer equal to the s l i p frequency f . The r e s u l t s f o r a l l measured f i l t e r outputs according to the above waveform c l a s s i f i c a t i o n are l i s t e d i n Table 4.6. The expected and measured s l i p frequency f o r each motor speed are shown i n Figure 4.2. From Figure 4.2 and Table 4.6 some important points can be deduced as follows: (1) The speed of an induction motor within the rated load, i . e . f o r s<13%, or f K& Hz, can be accurately measured by the proposed method. (2) The measured s l i p frequency would be f u l l y equal to the expected value i f there are no unstable f a c t o r s , such as f l u c t u a t i o n s i n the motor speed. (3) Proper f i l t e r parameter values, such as the corner frequency f , must be chosen to eliminate any noise i n the output s i g n a l . The s e l e c t i o n of C=1.0 yF, i . e . , f =4.5 Hz f o r three stages appears to be su i t a b l e f o r the four t e s t motors used. Table 4.6 Waveform Evaluation of Detected S l i p Frequency Motor C n (rpm) 1770 1755 1740 1725 1710 1695 1680 1650 1620 (yF) f s (Hz) 1 1.5 2 2.5 3 3.5 4 5 6 Ml 1.0 o o o o o o o 0.32 A A A A A A A M2 4 .4 or 1.0 o o o o o o o 0.32 X X X X X X X M3 1.0 o o o o o 0.32 A A A A A M4 4.4 o o 1.0 A A o o o o 0.32 X X X X Motor C (yF) n (rpm) 1590 1560 1530 1500 1440 1380 1320 1260 1200 f g (Hz) 7 8 9 10 12 14 16 18 20 M4 1.0 o o X A A 0.32 X X X X A X A o A Case (1) : o Case (2) : A Case (3) : x 38 fs(Hz) 1800 0 M3 1700 0.05 5 (c) *s (Hz) 20 1 0 (rpm) 1800 s 0 1600 0.11 1400 0.2 2 (d) M4 JO F i g 4.2 Comparision of Expected and Detected S l i p Frequency for Induction Motor (a) Ml (b) M2 (c) M3 (d) M4 x expected value o detected value case (1) case (2) 1200 (rpm) 0.33 s 39 4.2 Supply Frequency Signal Component The amplitude of the supply frequency f (60 Hz) component that i s induced i n the choke, of course, dejpends upon the l o c a t i o n of the choke with respect to the motor. Usually the choke i s placed as close as possible to the motor so as to pick up a strong s i g n a l . The 60 Hz s i g n a l i s the most important s i g n a l to be f i l t e r e d out i n the process of detecting the s l i p frequency. The number of f i l t e r stages required not only depends upon the amplitude of the 60 Hz s i g n a l but more importantly upon the amplitude r a t i o of the 60 Hz s i g n a l to the f s i g n a l . The v.^/v,. r a t i o s s ° 60 f of four motors are measured and indicated i n Figure 4.3. It i s found that the amplitude of the s l i p frequency s i g n a l increases greatly with increasing s l i p whereas the amplitude of the supply frequency s i g n a l varies very s l i g h t l y . From experimental r e s u l t s the s l i p frequency amplitude v s ^ n can be considered to be approximately proportional to the product of the motor current and the s l i p frequency. v . = I«f (4.1) s i n s The r a t i o of the amplitude of the supply frequency s i g n a l to the amplitude of the s l i p frequency s i g n a l governs how many f i l t e r stages are required. However, the c l o s e r the s l i p frequency i s to the supply frequency, the more d i f f i c u l t i s the f i l t e r i n g . 4.3 Measurement of Pole Pairs The motor speed n^ not only depends upon the measured s l i p frequency f but i s also r e l a t e d to the pole p a i r s , p, as given i n equation (1.6) and rewritten below: f - f • n. = S- 60 (1.6) 1 P V60/Vsin ( x 1 0 3 ) 41 v a F i g 4.5 Choke Voltage Waveform at Several Locations (a) Supply Frequency Reference Waveform (b) at L 1 (c) at L 2 (d) L 3 The following experiment i l l u s t r a t e s one way to measure the pole-pair value. The experiment uses the induction motor M3, which i s single phase. With the motor running, the p o s i t i o n of the choke i s varied around the 42 motor surface, as indicated i n Figure 4.4. The choke voltage i s connected to one channel of a two-channel o s c i l l o s c o p e while the 60 Hz supply wave- form i s connected to the other channel and i s used as timing reference (shown i n Figure 4.5(a)). The waveform of the choke voltage f o r d i f f e r e n t l o c a t i o n L , L and L (here a=90°, B= 180°) are shown i n Figure 4.5(b), ( c ) , ( d ) , r e s p e c t i v e l y . With the choke at l o c a t i o n the leftmost peak value of the choke voltage i s noted to be on the assumed v e r t i c a l l i n e aa' indicates that the mechanical angle a i s e l e c t r i c a l l y equivalent to 180°. S i m i l a r l y , moving the choke to l o c a t i o n L w i l l place the peak value back at l i n e aa' so that the mechanical angle 3 i s e l e c t r i c a l l y 360°. Therefore, the pole-pair value of the motor can be obtained as follows: 360° P = — (4.2) ^ (4.3) In t h i s example a=90° g=180° so p=2. It i s not very hard to explain. The choke voltage waveform at each l o c a t i o n with respect to the motor usually are the same but i t s phase angle with respect to the supply voltage v a r i e s . Therefore, the r e l a t i o n between e l e c t r i c a l and mechanical angle w i l l y i e l d the pole-pair value as given by equations (4.2) and (4.3). 43 5. CONCLUSION A method of measuring the motor speed of an induction motor by detection of the s l i p frequency s i g n a l has been proposed i n t h i s t h e s i s . The measurement can be made without attachment of any devices to the motor shaft. In f a c t , the motor may be completely enclosed so that conventional speed measurement by the use of tachometers or stroboscopes would not be possib l e . Experimental r e s u l t s i n d i c a t e good agreement between act u a l motor speed and that measured by the proposed s l i p frequency method i n the range below a s l i p frequency of about 8 Hz that i s within the range of most 60 Hz induction motors. The method i s sui t a b l e f o r both s i n g l e - and three-phase induction motors and w i l l be applicable to sealed motors, such as motors used i n r e f r i g e r a t o r s , since access to the motor shaft i s not needed. The proposed method does require knowledge of the number of poles i n the motor. A simple method to determine t h i s experimentally was d i s - cussed i n chapter 4. The speed measurement c i r c u i t de sc r ibed in chapter 3 needs to be improved in the f o l l o w i n g r e spec t s : 0 ) The i n d u c t i v e t ransducer should be op t imized f o r best s l i p - f r e - quency s i g n a l p i c k u p . C2) Instead o f d e t e c t i o n by the waveform ana lyze r the s l i p frequency s i g n a l or the corresponding motor speed s i g n a l should be made a v a i l a b l e fo r d i s p l a y o r for use i n any speed c o n t r o l l oop . (3) The f i l t e r i n g and a m p l i f y i n g stages cou ld be op t imized for shar - per cut - o f f and improved s i g n a l - t o - n o i s e r a t i o o f the des i r ed s l i p frequency s i g n a l . 44 REFERENCES 1. Sawaki, N. and Sato, N., "Steady-State and S t a b i l i t y Analysis of Induction Motor Driven by Current Source Inverter", IEEE Trans, on IA. Vol. IA-13, pp.244-253. May/Jun., 1977. 2. Plunkett, A.B., "Direct Flux and Torque Regulation i n a PWM Invertor- Induction Motor Drive", IEEE Trans, on IA, Vol. IA-13, pp.139-146, Mar./Apr., 1977. 3. Plunkett, A.B., D'Atre, J.D. and Lipo, T.A., "Synchronous Control of a S t a t i c AC Induction Motor Drive", IEEE Trans, on IA, Vol. IA-15, pp.430-437, Jul./Aug., 1979. 4. Nabace, A., Otsuka, K., Uchino, H. and Kurosawa, R., "An Approach to Flux Control of Induction Motors Operated with Variable-Frequency Power Supply", IEEE Trans, on IA, Vol. IA-16, pp.342-350, May/Jun., 1980. 5. Bouler, P. and McLarren, S.G., "Slip-Frequency Limited Phase-Locked Loop Induction-Motor Drive", IEE P r o c , Vol. 127, pt.d, pp.51-54, Mar. 1980. 6. Moore, A.W., "Phase-Locked Loop f o r Motor Speed Control", IEEE Spectrum, 1973, A p r i l (10), pp.61-67. 7. Ishida, M. and Iwata, K., "A New S l i p Frequency'Detector of an Induction Motor U t i l i z i n g Rotor Slot Harmonics", IEEE/IAS, 1982 ISPCC Conf. R e c , pp.408-415. 8. Ishida, M. and Iwata, K., "A S l i p Frequency Detection Method of Induction Motor U t i l i z i n g Rotor Slot Harmonics", Conf. Rec. of 1980 Tokai Region Annual Meeting of IEE of Japan, pp.153, Nov. 1980. 45 9. Maisel, J.E. and K l i n g s h i r n , E.A., "Low-Frequency Spectral Analysis Using a Dynamometer-Type Wattmeter", IEEE Trans, on Education, Vol. E-25, No. 2, May 1982. 10. Davold, W., C i r c u i t Design f o r E l e c t r o n i c Instrumentation. APPENDICES A l . Derivation of the Frequency Response Equation f o r Second Order Butterworth Low-Pass F i l t e r U i n F i g A l . l Second Order Butterworth Low-Pass F i l t e r The noninverting second order low pass f i l t e r shown i n Figure A l . l i s used f o r the d e r i v a t i o n . The derivation i s based upon the " V i r t u a l Ground An a l y s i s " and assumes that (1) The open-loop gain of the operational a m p l i f i e r i s i n f i n i t e , i . e . , G = 0 0 ' o (2) Input impedance i s i n f i n i t e = °°. Therefore, input current I = o . n (3) Input voltage u +-u = 0 Equations f o r Figure A l . l by normal c i r c u i t analysis are as follows: U - = R 7 T 1 C U O < A I . D + = 1 + j u R 2 C 2 a (A1.2) 47 T = ^ - ( u . - u ) (A1.3) '1 R m a I . = j u c . ( u - u ) (A1.4) c l J 1 a o I. = ^ ( u - u ) (A1.5) 2 R 2 a + Solving t h i s group of equations the gain of f i l t e r G(u) Is expressed as G(ju) U ° U i n ( j ^ ) 2 + 2 5 ( j ^ - ) + 1 c G(u)) = — 2 (A1.7) i - <A2 • f-> c c where 5 i s the damping c o e f f i c i e n t C J c i s the inherent angular corner frequency Therefore, the amplitude response G.(w) and phase response <f>(w) i s r e a d i l y obtained by equation (A1.7). G( w) = — (A1.8) 2 \2 1 - w c 2? -1 w c cf>(w) = -tan" . - (A1.9) i - <A2 c 48 W h e r e G = l + ^ (ALIO) u) C J R 1 R 2 C 1 C 2 1 ' ( A l . l l ) g 1 { pfg. ( , . , )•/¥! } (A1.12) 2 y R l C l A / R 2 C 1 V R 2 C2 when 5 /2~ equation (A1.8) becomes l+(^-) W c This i s the second order Butterworth f i l t e r response. Substituting £ = — — into eqn. (A1.12) ST we therefore require R9c /R.c /^c 49 A 2 . Ca l cu la t ion of S l i p Frequency Signal Component A2.1 Gain Formulae and Curves of Three F i l t e r Stages i n Cascade The gain of three i d e n t i c a l f i l t e r stages i n cascade, as indicated i n Figure 3.1 i s given by: ^12H1 = G.-G* (A2.1) i n where ^3out ^ e o u t P u t °^ t n e t h i r d f i l t e r stage i s the input to the input b u f f e r G^ i s the gain of input b u f f e r G^ i s the gain of a sin g l e f i l t e r stage Usually the gain i s expressed i n dec i b e l s , which i s defined as follows: m / om where ^3oout ^ S ^ e o u" tP u" t °^ t n e t h i r d f i l t e r stage at f = 0 V . i s the input V. at f = 0 om r m G^^ i s the t o t a l gain i n dB, the input b u f f e r and the three f i l t e r stages i n cascade The gain curves i n Figure A2.1 are p l o t t e d from measurements made f o r three f i l t e r stages i n cascade f o r various values of capacitors C. These curves w i l l be used as c a l c u l a t i o n of measured s l i p frequency amplitude f o r various induction motor speeds. A2.2 Calc u l a t i o n of Slip-Frequency Signal Amplitude Through Any Number of F i l t e r Stages The number of f i l t e r stages a c t u a l l y used i n s l i p frequency measure- ments d i f f e r f o r various induction motors. The c a l c u l a t i o n of slip-frequency s i g n a l amplitude w i l l be discussed here. In Figure 3.1 the attenuator, G , cL 50 51 i s inserted between the t h i r d and the fourth f i l t e r stage, so that the deri v a t i o n of the gain equation w i l l be divided into two cases as follows; (1) When N ^ 3 Where N i s the number of f i l t e r stages. The gain f o r N f i l t e r stages i s given by S = ^ (A2.3) i n Where ^Nout ^ s ^ e output of "the Nth f i l t e r stage. From Figure 3.1 GN = ( G f ) N G i (A2.4) Assume V.T _ • _ Noout , A O c . G N o - — ( A 2 ' 5 ) o m Where G.T i s the gain G„ at f = 0 No 6 N VNoout i s t h e O U t P U t VNout at f = 0 So G„ = (G_ ) N G. = (G ) N G. (A2.6) No fo 1 0 fo l Where G,. i s the gain G_. at f = 0 fo & f and G. = G. 1 1 0 Therefore, the gain i n dB i s GNdb = 2 0 l o8lor- (A2.7) No GNdb = 2 0 l o « 1 0 GN ~ 2 0 1Oh0 So (A2'8) Substituting(A2.4), (A2.6) into (A2.7) vN „ , G_ 3 T O ^ fo Assume = 20 logoff j3 (A2.9) 52 S ° GNdb = I G3db ( A 2 . 1 0 ) Substituting (A2.3), (A2.10) into (A2.8) 20 l o g Nout N 10 V. in _ G + 20 l o g i n G 3 3db °10 No (A 2 . l l ) A s S U m e GNodb = 2 0 1 O g 1 0 GNo ( A 2 ' 1 2 ) Substituting (A2.6) into (A2.12) GNodb ' = 2 0 l o g 1 0 ( G f o } G i (A2.13) Substituting (A2.12) into ( A 2 . l l ) an Nout -UE G + G ) 2CT3 3db Nodb 10 (A2.14) Nodb inequation (A2.13) i s independent of c i r c u i t capacitance C. It can be found i n the curves i n Figure A2.1 that G O J, at f = 0 f o r a l l curves 3db s t a r t at ̂ ^^=0. It can be also explained as the c i r c u i t Figure 3.2(f) that when the c i r c u i t i s working i n dc no e f f e c t of by-pass and feedback fo r both C a r i s e s . The G ^ Q i s measured by experiment and l i s t e d i n Table A2.1 Table A2.1 Calculated G.T (Ns=3) N o d b N 1 2 3 G -(G. ) N - G . No fo l 9.60 57.2 341 G_. =20' log. _G.T Nodb 610 No (dB) 19.64 35.14 50.6 Note: (1) Calculated: G =1.64 Experimental: G^l.61 G. =6 f o G . =5.96 f o (2) Experimental G^ ,G^ q are used 53 Equation ( A 2 . 1 4 ) i s used to cal c u l a t e the component at the measured frequency. From Table A 2 . 1 \ G30db = 5 0 ' 6 when N = 3 s u b s t i t u t i n g G ^ Q ^ = 50.6 into equation ( A 2 . 1 4 ) V V. _ 3out i n - - To ( G3db + 5 0 ' 6 ) ( A 2 ' 1 5 ) io 2 0 3 d b Example: V g o u t = 0.109 v. : output measured at t h i r d f i l t e r stage f = • 3 Hz : measured output frequency C = 1.0 uF : selected c a p a c i o r i n Figure 3.2(f) f o r a l l three f i l t e r stages We f i n d G O J, = -0.64 dB from C = 1.0 uF curve at f = 3 Hz odb i n Figure A2.1.. so that _ 0.109 V. = = 0.346 mv 1 1 1 (-0.64 + 50.6) 10 (2) When N > 3 In t h i s case the attenuator, G , e x i s t s i n the middle of f i l t e r , as ' a ' ' indicated i n Figure 3.1. The way of deri v a t i o n i s s i m i l a r to that f o r N .$ 3 except that the gain of attenuator has to be added. So G.T = (G_) N * G. • G (A2.16) N f I a where G i s the gain of the attenuator G._ = (G )^ • G. • G = (G_ ) N • G. • G (A2.17) No f o i o ao f o I a where G i s the gain G at f = 0 and G = G ao ° a ao a Equations (A2.3), (A2.5) and (A2.7 - A 2 . l l ) are s t i l l a p p l i c a b l e . 54 Substituting equation (A2.17) into (A2.12) G M = 20 l o g i n ( G . ) N ' G. • G (A2.18) Nodb °10 fo 1 a so that equation (A2.14) becomes V V. _ Nout m " : (A2.19) — (— r + r ) 1 Q 2 0 K3 ^3db Nodb' which i s s i m i l a r to equation (A2.14) except i n the c a l c u l a t i o n of G„ „ . Nodb To c a l c u l a t e G J^^J equation (A2.18), G^ may be three se l e c t i o n s G a l, G a 2 and G A 3 corresponding to switch K set i n p o s i t i o n a ^ a 2 and a 3 < r e s p e c t i v e l y . The gains of G , G and G „ simply consist of the emitter follower of gain 1 and resistance d i v i d e r , l i s t e d i n Table 3.1 f o r actual r e s i s t o r values. Therefore, G N O ^ i s obtainable through c a l c u l a t i o n of equation (A2.18) and l i s t e d i n Table A2.2. Table A2.2 Calculated G._ (N>3) N=4 N=5 N=6 a l Ga2 Ga3 a l Ga2 Ga3 a l Ga2 a3 1 1/7.4 1/206 1 1/7.4 1/206 1 1/7.4 1/206 G N O = N G i G a G f o 2031 274 9.81 12106 1636 58.5 72157 9751 350 GNodb = 2 ° - l o S l O G N o 66.15 48.75 19.8 81.7 64.2 35.4 97.16 79.8 50.9 Note : Experimental G ^ l . 6 1 , Gf-=5.96 are used The procedue to c a l c u l a t e the with N>3 through equation (A2.14) i s s i m i l a r to that used f or N$3

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