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A DIGITAL PHASE ANGLE METER FOR POWER FREQUENCY MEASUREMENTS BY JOHN P. GILES B.Sc., B.E. PROJECT REPORT FOR THE DEGREE OF MASTER OF ENGINEERING SCIENCE IN THE SCHOOL OF ELECTRICAL ENGINEERING UNIVERSITY OF NEW SOUTH WALES DECEMBER 1974 UNIVERSITY OF N.S.W. 46353 -2. SEP 75 LIBRARY DECLARATION It is hereby declared that the work described in this thesis has been performed by the author and has not previously been submitted for a post-graduate degree to any other University or institution. ABSTRACT A Digital phase angle meter is described which is primarily designed for power frequency phase angle measurements in the range 40 - 1000 Hz. The instrument is designed for measuring slowly changing signals of the type found in standardization or calibration of industrial phase angle indicators or transducers, where the 1 second or 10 second aperture time is of no consequence. The result is displayed digitally directly in degrees. No setting up procedures are necessary before taking a measurement. The accuracy of the instrument described is 0.5 of a degree plus or minus one digit. A frequency measuring function is also provided for measurements in the range 1 - 2000Hz. The factors which limit phase angle measure­ ment accuracy are described, together with the methods by which the induced errors are reduced or eliminated. ACKNOWLEDGMENTS This investigation was conducted as part of the require­ ments for a Master of Engineering Science in the School of Electrical Engineering of the University of New South Wales* The guidance of Associate Professor G* J. Johnson in this project is sincerely appreciated* The comments of Mr* F* Lewin on the draft copy are gratefully acknowledged* 1 CONTENTS page number ABSTRACT ACKNOWLEDGMENTS TABLE OF CONTENTS 1 1. INTRODUCTION 6 1*1 The Definition of Phase Angle 6 1*2 Analogue Phase Angle Measurement Techniques 7 1.3 Digital Phase Angle Measurement Techniques 13 2. ERRORS IN ZERO CROSSING PHASEMETERS 20 2.1 D.C. Offset 20 2.2 Noise 21 2.3 Harmonic Distortion 21 2.4 Frequency Stability 23 3. DESIGN CONSIDERATIONS 24 3«1 General 24 3«2 Input Circuits 25 3.3 Phase Angle to Pulse Width Converter 27 3*4 Gate Circuit 31 3*5 Quantising Pulse Generator 32 3*6 Timing Signals Divider 36 3«7 Control Signal Generator 38 3*8 Display Divider 39 3*9 Display and Over range Circuits 39 3«10 Phase Sign Circuit 41 3.11 Frequency Measuring Circuit 43 3*12 Power Supply 43 4. INSTRUMENT OPERATION 47 5. PERFORMANCE OF THE PHASEANGLE METER 48 5*1 Measurement Method 48 5.2 Sources of Error 50 5*3 Effect of the Variation of Ambient Temperature 52 5*4 Performance as a Phase Angle Meter 54 5*5 Performance as a Frequency Meter 56 2 Contents cont*d page number 6. EVALUATION OF THE INSTRUMENT DESIGN 57 6.1 Design Philosophy for Further Work 57 6.2 Recommended Design Changes 59 6.3 Improved Input Facilities 60 7. CONCLUDING REMARKS 6l 8. BIBLIOGRAPHY 63 9. APPENDIX 65 Contents cont'd Page number Figure 1*1 Typical patterns produced by a C.R.O. when sinusoidal voltages of different phases are applied* 7k Figure 1*2 Single phase power-factor meter - dynamometer type* 8a Figure 1*3 Equilibrium position of the moving coils for an arbitrary phase angle theta. 9A Figure l*4a Basic analogue phase angle meter* 10A Figure l*4b Waveforms associated with the basic analogue phase angle meter* 10B Figure 1*5» Basic analogue phasemeter with an extra flip-flop to remove the 0 degree, 180 degree ambiguity* 11A Figure l*5b Diagram illustrating how the 0 degree, 180 degree ambiguity arises* 11B Figure 1*6 Analogue phasemeter utilising both forward and reverse zero crossings* 12A Figure 1*7 Diagram illustrating the effect of input noise on the phase detector output* 12B Figure 1*8 Block diagram of phasemeters in which the phase angle is measured during a single period. 13A Figure 1*9 Single period phase measurement using the heterodyne principle to obtain a frequency suitable for direct display in degrees* 15® Figure 1*10 Basic multi-period digital phasemeter* 15A Figure 1*11 Diagram illustrating some of the measure­ ment periods due to the arbitrary start­ ing and stopping of the gate circuit* 17A Figure 1.12 Two wire phase angle measurement circuit* 18a Figure 1*13 Waveform for (a) lagging power factor 18a (b) leading power factor 4 Contents cont’d Page number Figure 2.1 Distortion phase errors. 22A Figure 3*1 Instrument block diagram. 25A Figure 3.2 aero crossing detector circuit. 26a Figure 3.3 Logic level translator circuit. 26A Figure 3.4 Zero-crossing detector output waveforms. 27A Figure 3*5 Special case of waveform illustrated in Figure 3*4. 27A Figure 3*6 Zero crossing detector output with Channel B shifted by 180 degrees with respect to Figure 3.5 28a Figure 3-7 Phase measuring circuit. 29A Figure 3.8a Timing diagram A. 29B Figure 3-8B Timing diagram B. 29B Figure 3.9 Gate circuit. 31A Figure 3*10 Basic MECL gate circuit. 35A Figure 3.11 Equivalent circuit of a quartz crystal. 34a Figure 3*12 Crystal oscillator circuit. 34a Figure 3.13 72MHz divider circuit. 35A Figure 3*14 Timing signals divider circuit. 35B Figure 3.15 Timing signals 36a Figure 3.16 Control signal generating circuit. 3&A Figure 3.17 Display divider circuit. 39A Figure 3*16 Block diagram of the display devices. 40A Figure 3*19 Display circuit. 40B Figure 3.20 Sign sensing circuit. 4lA Figure 3-21 Timing diagram for Figure 3*20. 4lA Figure 3*22 Channel inversion circuit. 42A Figure 3.23 Plus five volt supply circuit. 44a 5 Contents cont*d Page number Figure 3«24 Minus five point two volt supply circuit* 45A Figure 3*25 Plus or minus fifteen volt supply circuit* 46a Figure 5»1 Block diagram of test set-up* 49A Figure 5*2 Equivalent circuit of test set-up* 49A Figure 3*3 Vector diagram of test set-up. 50A Figure 3*4 Digital record of synthesizer period. Figure 5*5a Digital record of the time interval unit's output for a fixed input. 51A Figure 5»5b Analogue record of the time interval output for a fixed period. 51B Figure 5*6 Output of the 3243L showing the variation of the measured period. 52A Figure 5»7 Low frequency modulation of 3243L output. 53A Figure 5«8 Variation of error with phase angle. 55A Figure 6.1 Voltage controlled oscillator. 57A Figure 6.2 Block diagram of phase looked loop. 59A Figure 6.3 Circuit diagram of phase locked loop. 59A Figure 6.4 Suggested input circuit. 60A -6- A DIGITAL PHASE ANGLE METER FOR POWER FREQUENCY MEASUREMENT 1. INTRODUCTION This work is concerned with the description of an accurate digital phasemeter capable of operation in the power frequency range* The investigation was primarily concerned with the dev­ elopment of an instrument suitable for use in the calibration of general industrial phase angle and power factor measuring equipment* 1* 1 THE DEFINITION OF PHASE ANGLE For a phase angle to be meaningfult the two signals being invest­ igated must be two periodic signals of the same waveform, but rel­ atively displaced in time* The phase angle may then be defined as the angular separation between a pair of corresponding points selected arbitrarily* As measurements in the time domain may be made with very high resolution, it is usual to use a phase to time conversion* There are two obvious choices for the corresponding points: a) Maxima or minima b) Zero crossings In the phasemeter to be described the latter points were sel­ ected because the first derivative of a sine function is a maximum when the value of the function is zero* This means that the zero crossing point enables maximum resolution in time to be obtained* A further advantage is that the zero crossings are independant of the signal amplitude* If X is the time interval between corresponding zero crossings and u is the frequency, the phase angle 0 in radians as defined above is 0 se 2.TCX>H a —1*1 T where T is the signal period Tr 1 -1.2 V -7A- SINE 0 r JL A TYPICAL PATTERNS PRODUCED BY A C.R.O, WHEN SINUSOIDAL VOLTAGES OF DIFFERENT PHASE ARE APPLIED Fi gure 1 - 1 7- 1. 2 ANALOGUE PHASE ANGLE MEASUREMENT TECHNIQUES a) Cathode-ray-tube Methods Where a measurement of relatively low precision is required, use can be made of a cathode ray oscilloscope* To obtain the phase angle between two voltages of the same frequency, one voltage is applied to the horizontal deflecting electrodes and the other to the vertical deflectors* The resulting pattern is elliptical in nature varying according to the relative amplitude and phase of the two signals being measured* The shape of the ellipse determines the phase angle according to the formula sin © » + B “ A -1*3 where B is the y ordinate cut by the ellipse, and A is the maximum y value* (See figure 1*1) The quadrant may be determined from the orientation of the major axes of the ellipse and the direction in which the trace moves. Uncertainty as to the direction of the trace rotation may be eliminated by shifting the phase of one of the deflecting voltages in a known direction and noting the effect on the pattern* When the two voltages are in phase the resulting pattern is a straight line at 45 degrees to both axes* By utilizing this fact it is possible to insert a variable phase shifter in series with one of the signals and then vary the phase shift until the pattern becomes a line* The amount of phase shift to accomplish this result is then the desired phase shift* Obviously this method is more accurate than that obtained from equation 1*3• as the introduced phase shift can be determined more accurately than can the division of an elliptical pattern* If an oscilloscope with a circular time base is available, two further methods present themselves* The circular timebase is adjusted to have the same frequency as the input signals* Their relative phase is indicated by the angular position on the circle - one complete revolution being 3&0 degrees* In one method, the signal whose phase is to be measured is applied to the electrode controlling the beaus intensity, which is biased approximately to cutoff* The resulting pattern is a semi­ circular arc, the position of which is a function of phase.

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