PLL AND NUMBER OF SAMPLE SYNCHRONISATION TECHNIQUES FOR ELECTRICAL POWER QUALITY MEASURMENTS

 Harvey Morris
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1 XX IMEKO World Congress Metrology or Green Growth September 9 14, 2012, Busan, Republic o Korea PLL AND NUMBER OF SAMPLE SYNCHRONISATION TECHNIQUES FOR ELECTRICAL POWER QUALITY MEASURMENTS Richárd Bátori Department o Electrical and Electronic Engineering, University o Miskolc, Miskolc, Hungary, Abstract: Today and in the uture the measuring and analysing o electrical energy is a signiicant topic because its quality and consumption has more and more importance in scientiic means and also practical. Since power requency is luctuating measurements must be synchronised to the network requency to avoid spectral leakage error. In this paper two synchronisation methods are shown and compared. Keywords: electrical power measuring, power quality, synchronisation techniques, PhaseLocked Loop 1. INTRODUCTION Today electrical energy is a signiicant energy source or industrial and commercial applications, and it will continue to be so in the uture. Providing a standard quality o electrical energy at the utilisation site is not an easy task, because nonstandard energy cannot be removed rom the network and consumers can also disturb each other s usage. The power supplier would like to know who contaminates its power network, while the consumers want to know whether they receive the appropriate quality. Examination o the quality and study o the eiciency o the energy consumption o companies is o economic signiicance. One o the most signiicant problems in power quality analyses is the power requency luctuation. The correctly executed Fourier transorm demands analysis o integral cycles o the time signal. The duration o cycles will be dierent i network requency changes. There is a widely used solution to eliminate this problem, when PhaseLocked Loop (PLL) is applied [13] but there are some less requently used methods involving synchronisation as well [4, 5], which are mainly classiied in sotware solutions based on signal spectral analysis techniques. In this paper yet another method is used: a synchronisation method ensuring analysis o integral cycles is proposed. This new method was also built in a power quality measuring instrument. Details o PLL and a new synchronisation method called synchronisation with number o samples are also discussed and compared. 2. SPECTRAL LEAKAGE ERROR AND FREQUENCY FLUCTUATION The network s requency luctuation makes it more diicult to analyse the power quality. When using a rectangular window to analyse power quality, it is important to synchronise the measurement window with the power system requency to avoid spectral leakage error (Fig. 1) [6]. Fig. 1. Spectral leakage error ( signal =50.25Hz T reg cycles) According to the standard EN :2008 [7], exactly 10 cycles (or a 50 Hz power system) must be used or analysis as a rectangular window. When the power requency changes, the width o this window changes as well. The measurement window T reg can be calculated rom the number o samples or 10 cycles N 10cycles and the sample rate : N 10 cycles Treg (1) The measurement window is also equal to the time o 10 power network periods: 10 T reg (2) pn Since power network requency luctuates (igure 2 and igure 3) the measurement window is not constant. Fig. 2. Fluctuation o power requency
2 Fig. 3.Statistic o power requency luctuation From the ormulae 1 and 2 the power requency can be expressed as: 10 pn (3) N 10cycles Thus during the measurement sample rate or number o samples must be changed to ensure synchronisation and avoid spectral leakage error. 3. PHASELOCKED LOOP (PLL) Synchronisation is solved by a PLL circuit. PLL generates a requency on its output that is a multiple o the input requency. Instead o the onboard clock o the acquisition card the output o the PLL is used as a clock. In this case it is sure that 10 cycles will be analysed while the network requency is changing. A slight disadvantage o PLL is that an additional time measurement is required because time intervals between samples are not known. A more signiicant disadvantage o PLL is the predeined sample rate. The system can measure only with constant requency, which is a eature o PLL. I the multiplier o PLL is 100 then the sample rate is about 5 khz (it is not exactly 5 khz because the power requency is not a constant 50 Hz either). Fig 4. Simple structure o PLL circuit Source o sample rate is the voltagecontrolled oscillator (VCO) which gives the clock rate or the acquisition card (Fig. 4.). The most important part o the PLL is the phase detector which compares phases o the input signals (signal o reerenceoscillator and output signal o VCO) and provides the error signal, which is iltered by the lowpass ilter. Filtered voltage signal controls VCO to reduce phase dierent thereore the output signal o VCO will be the same as the network requency [2]. So phaselocked loop tracks an input requency, or i there is a requency divider in the loopback PLL generates a requency that is a multiple o the input requency, thereore it solves the synchronization problem in power analysing systems. A similar method to PLL which modiies sample rate as well during the measuring is another method. I we know exactly the power requency and the number o samples is constant, the sample rate can be acquired: pn 10cycles N (4) 10 This synchronisation method is not a good choice because acquisition cards do not support a change in changing sampling rate without stopping the measuring, and data loss is not allowed, either. Consequently this method requires special data acquisition hardware that can modiy the sample rate during the measurement without any data loss. 4. SYNCHRONISATION WITH NUMBER OF SAMPLES Synchronisation with number o samples is a sotware solution which doesn t need any special hardware. Using this method the sample rate is always constant and the synchronisation can be solved with the number o sample changing only. The number o samples is computed continuously while the sample rate is constant. The value o the actual power requency is required (5). N 10 10cycles (5) pn Using this solution at low sample rates, calculation errors are high because the number o samples must be an integer, but at higher sample rate errors are much lower. Since the number o samples must be an integer, Eq. (5) is altered to: 10 N 10cycles 0. 5 (6) pn According to the standard [7], the maximum deviation (H Treg ) rom 10 cycles o the 50 Hz power system is ±0.03%, which is 60 μs at 50 Hz and 52 μs at 57.5 Hz. The worst situation is at 57.5 Hz because the permissible error is the smallest. Fig. 4. Maximum deviation [μs] at 10 cycles using number o samples synchronisation In Fig. 4 synchronisation with number o samples meets the standard requirements i the sample rate is higher than 10 khz, because the maximal possible error decreases as the sample rate increases (7).
3 1 HT reg 2 (7) Synchronisation with the number o samples is a soar unutilised method to eectively solve synchronisation to the power requency. The advantage o synchronisation with number o samples over PPL is that there is no need or additional time measurement because time intervals between samples are well deined by the constant sample rate. The disadvantage o the method is the changing numbers o samples in the dierent 10cycle, which has to be solved rom the sotware side. An advantage o the method is avoiding special hardware use. Since the FFT (Fast Fourier Transorm) algorithm requires a constant number o samples and the number must be two to the power o n where n is an integer, DFT (Discrete Fourier Transorm) must be used instead. 5. EFFECTS OF VOLTAGE DISTORTION ON SYNCHRONISATION Voltage distortions can weaken the eiciency and accuracy o both synchronisation methods. Let s see them in details. Comparators o PLL circuit are triggering the square wave signals to the zerocrossings o the power network s sine wave. In ideal case the power requency changes only so zerocrossings are synchronised with power requency. Unortunately distortions o power network, e.g. THD or voltage sag and dip can cause incorrect zerocrossings at unchanged requency which disturb the correct operation o PLL. Output requency will be luctuating and spectral leakage error will appear. 6. FREQUENCY ESTIMATION Accurate power requency value is needed during measuring when synchronisation with number o samples is used. Power requency is changing continuously thereore requency has to be estimated continuously as well. In literature there are several methods to measure requency o the electrical network [8], e.g. zerocrossing detection, interpolated discrete Fourier transorm, chirpz transorm, Kalman iltering, GaussNewton method and advanced signal processing methods are used to requency estimation. Nevertheless the most commonly used method is the simple counting o zero crossing. This algorithm is also used by the IEC power quality measurement standard [7]. According to the standard the undamental requency output is the ratio o the number o integral cycles counted during the 10 s time interval, divided by the cumulative duration o the integer cycles. This standard also says beore each assessment, harmonics and interharmonics shall be attenuated to minimise the eect o multiple zero crossing. In order to ulil this requirement 3 th order lowpass Butterworth digital ilter was used. Unortunately the time varying amplitude o the signal would have adverse impact on the estimation result since ilter was applied. Shiting o zerocrossing is the problem again as in case o PLL (Fig. 5). At irst let s see the requency estimation with zero crossing detection then the developed algorithm to avoid alse zerocrossing detection. Fig. 6. Linearisation method at zerocrossing X 1 (8) u1 X u2 Fig. 5. Shiting o zerocrossing i ilter is in used because the voltage increased (dashed line is the iltered signal) Harmonics can be eliminated with a lowpass ilter so PLL gets only the undamental component. Applying ilter brings new problem. Voltage dips and swells shit the place o zerocrossing i ilter is applied (Fig. 5.) This phenomenon cases again alse synchronisation but only caused by sudden voltage increase or decrease. When synchronisation with number o samples is applied the same problem arises at voltage dip or swell. A new algorithm was developed to solve this phenomenon which is introduced in the next chapter. X u1 1 Yu1 (9) Y Y u1 Number _ o _ Cycles c (10) 1 LastREdge FirstREdge X X u1 u2 Linearisation method was used which increases the accuracy o this calculation. The sampled data usually do not exactly a value o zero. In most cases the signal jumps across the zero value and doesn t hit that thereore the location o the zero crossing should be estimated or interpolated. I we could ind the exact location where the signal would have the zero value, the estimated requency would be more accurate. Figure 6 shows how works a more u2
4 accurate method or requency estimation. Y u1 and Y u2 are the samples next to the zerocrossing. X u1 and X u2 can be calculated using Eqs. (8) and (9). Sum o X u1 and X u2 is the reciprocal o the sample rate so these values can be easily calculated by ollowing equation. The actual calculated power network requency ( c ) is obtained with Eq. (10). Digital ilter must ollow the varying voltage amplitude. I the order number o digital ilter is higher, ilter needs more time to catch amplitude change. Figure 5 shows ilter needed one and hal cycle to catch the input voltage signal. Samples in this interval are unusable or zerocrossing detection. At the beginning o the measuring these samples can be dropped but samples ater amplitude change are part o the continuous measurement. Higher voltage amplitude changes aect only the next one or two zerocrossing i the order o digital ilter is not higher than 5. Whereas accurate place o the irst and last zerocrossings are necessary only it is enough to know the number o zerocrossings during the interval. So the problem can be caused only either by the irst or the last zerocrossing. In power networks signiicant voltage amplitude changes are not occurring so oten. It means during one second there are no more than 23 amplitude changes. One second voltage signal contains 100 zerocrossings. In this case there are a lot o zerocrossing which is not shited by amplitude changes. I alse zerocrossings can be determined right requency estimation will be provided. To ind alse zerocrossings is not an easy tank thereore other way was chosen to solve this problem. Let s chose an interval, e.g. one second and estimate requency value or this interval. This interval will be shited with hal cycle then new requency estimation will be executed or the new interval. This shiting and requency calculation is executed repeatedly n times. Result o the algorithm is n requency values. Some o them will signiicantly deviate rom the real requency in consequence o amplitude changes. Most o value will be correct because there are not amplitude changes in the power network at every cycle. Frequency values are sorted and correct power requency () is obtained using ormula 11. i 2n /3 pn i i n /3 (11) n / 3 Simulations were perormed where amplitude changes were generated every hal second. I the chosen interval or requency estimation was not shorter than 0.4 s than requency estimation was accurate with this algorithm. Below 0.4 s dropping o highest and lowest requency values was not enough to eliminate the wrong requency value which results wrong estimation. This extended zerocrossing detection algorithm can estimate requency about at every 0.4 s but it is suicient when synchronisation with number o samples is applied. estimation can be provided by the method introduced in latest chapter. Unortunately power requency is luctuating continually because load o the power network is changing. Thereore requency can change signiicantly during the measuring interval or requency estimation which causes inaccurate synchronisation. 10 s time interval which suggested by the standard [7] is too wide to estimate requency or synchronisation with number o samples. I the power requency luctuation is more than 10 mhz in the time interval then the synchronisation will not be accurate and suit standard requirements [9]. Power requency luctuation has to be measured to get how wide time interval is necessary to ensure less then 10 mhz requency luctuation within the interval. Frequency was calculated at every 0.5 s or 1 week with the estimation method introduces in this paper. During 10 s 20 requency values were estimated and dierent ( 10s ) o maximum ( max ) and minimum ( min ) value is calculated or this interval (12) so requency luctuation is estimated or 10 s. (12) 10 s max min Figure 7 shows probability o requency changes during 10 s. In several cases the requency luctuation was more than 10 mhz, thereore estimation o requency at ever 10 s is not acceptable when synchronisation with number o samples are used. Fig. 7. Probability o requency changes during 10 s I the requency values are obtained rom 5 s time interval than the requency luctuation is much lower (Fig. 8.). 98% o the requency deviations during the 5 s time intervals were lower than 10 mhz but it is also not adequate or synchronisation with samples. 7. MEASURING FLUCTUATION OF POWER NETWORK FREQUENCY Synchronisation with number o samples works properly i the estimation o power requency is accurate. Accurate Fig. 8. Probability o requency changes during 5 s
5 Using 2 s time interval % o the deviations were lower than 10 mhz which means there are only ew 2 s time intervals where the deviation is higher than 10 mhz which can cause wrong synchronisation (Fig. 9.). than 4000 samples are required in order to avoid spectral leakage error. Application instead o 4000 acquires 4002 samples to provide the required synchronisation which suits standard requirements. Hence spectral leakage phenomenon doesn t appear in igure 12. Fundamental harmonic is Hz in this example. Fig. 11. Ten integrals cycles rom threephase voltage signal Fig. 9. Probability o requency changes during 2 s Consequently power requency has to be estimation at least every 2 s rom the 2 s time interval to ensure right synchronisation when synchronisation with number o samples is used. According to additional measurements it is worth using 1 s time interval or estimation because synchronisation will be more accurate but lower interval is not recommended because requency estimation is increasingly unreliable when interval decreases using algorithm introduced in chapter USING SYNCHRONISATION WITH THE NUMBER OF SAMPLES IN MEASUREMENTS Our department are continuously developing a complex measurement system which can measure our threephase systems and solve real time measuring [10]. Fig. 12. Amplituderequency spectrum o one phase voltage signal in igure 11. Our network analyser system has already used to analyse several industrial network. During the more weeks long measurement all power parameters (RMS, THD, power actor, active power, reactive power, distortion power, etc.) are being calculated in realtime and all samples and calculated parameters are being saved in repository o hard disk drive. Fig. 13 Evaluation o the measurements Fig. 10. Complex measuring instrument Actual device (Fig. 10.) provides synchronized power network measurement without PLL circuit because in its sotware realisation synchronisation with number o samples is applied. During measurements waveorms o voltage and current are displayed in realtime. Commonly 20 khz sample rate is used by the device to measure power network thereore in case o 50 Hz power requency 4000 samples will be acquired rom 10 cycles. Figure 11 shows threephase voltage signals where the actual power requency is Hz. In this case cycles are longer thereore more Analyser application was developed [11] where saved values can be displayed and examined (Fig. 13). This sotware is capable to process those measurements which were measured by the instrument using synchronisation with number o samples. This application can display the ollowing values and changes o these values in time according to IEC and IEC where all parameters here except the requency and licker are synchronized by samples: Frequency o the voltages to be measured RMS values or all channels (voltages, currents); Flicker values or voltage channels Supply voltage unbalance
6 , Amplitude  requency spectrum (voltage harmonics and interharmonics) and THD values or all channels; Power actor and undamental power actor (cosφ) or channelpairs (voltage  current) Apparent, active and reactive power or channelpairs (voltage  current) Fundamental and nonundamental apparent, active and reactive power or channelpairs (voltage  current) Voltage, current and harmonic distortion power or channelpairs (voltage  current) Application also can recognise voltage interruptions, voltage dips and swells and create statistical distribution o any properties or any time interval. Ater the tests and laboratory measurements power network analysing system are used in industrial environment. We are continuously perorming evaluation o power networks with this product and give advices to companies where they can decrease their electricity bill. 9. SUMMARY Two synchronisation methods were introduced. PLL have been using decades but synchronisation with number o samples is new and works only at high sample rate. At low sample rate only PLL can ensure the synchronisation but at high sample rate synchronisation with number o samples is a better solution because about 10 khz there is no limitation in sample rate and no need o special hardware. Voltage distortion can disturb synchronisation but a new requency estimation method was developed which eliminate this problem. Power requency has to be estimated between 1 and 2 s time interval to ensure the right synchronisation when synchronisation with number o samples is applied. This synchronisation method was build in an own developed power network analysing instrument which has already analysed several power networks successully in industrial environments. [3] F. D. Freijedo, J. DovalGandoy, O. Lopez and J. Cabaleiro: Robust Phase Locked Loops Optimized or DSP Implementation in Power Quality Applications, Proc. IECON 2008, 34th Annual Conerence o the IEEE Industrial Electronics Society, FL, Orlando, [4] M. Aiello, A. Cataliotti, V. Cosentino, S, Nuccio, Synchronization Techniques or Power Quality Instruments, IEEE T. Instrum. Meas., vol. 56, no. 5, pp , October 2007 [5] A. Nagliero, R. A. Mastromauro, M. Liserre, A. Dell Aquila, Monitoring and Synchronization Techniques or SinglePhase PV Systems, Proc. SPEEDAM 2010, International Symposium on Power Electronics, Electrical Drives, Automation and Motion, Pisa, [6] Math H.J. Bollen, Irene Y.H. Gu, Signal Processing o Power Quality Disturbances, Processing o Stationary Signals, IEEE Press Series on Power Engineering, New York, pp , 2006 [7] Standards IEC :2008: Testing and measurement techniques Power quality measurement methods [8] Pedro M. Ramos, A. Cruz Serra: Comparison o requency estimation algorithm or power quality assessment, Measurement 42, pp , 2009 [9] A. V. Szarka, Measuring harmonic distortion in electrical power networks New approach, Measurement 43 pp , 2010 [10] R. Bátori, Electrical Power Quality and Eiciency Diagnostic System, XIX IMEKO, 2009, Lisbon [11] R. Bencs, R. Bátori, Development o a measurement data processing application in Measurement Studio to analyse electrical networks, XII. ENELKO, ClujNapoca, Romania, pp , ACKNOWLEDGEMENT The described work was carried out as part o the TÁMOP B 10/2/KONV project in the ramework o the New Hungarian Development Plan. The realisation o this project is supported by the European Union, co inanced by the European Social Fund. 11. REFERENCES [1] A. Cataliotti, V. Cosentino, S. Nuccio, A new Phase Locked Loop Strategy or Power Quality Instruments Synchronisation, Proc. IMTC 2005 Instrumentation and Measurement Technology Conerence, Ottawa, Canada, [2] L. Kazup, G. Z. Marcsák, Application o PhaseLocked Loop Circuit in Electrical Network Diagnostic Systems, 21 th International Conerence on Computers and Education, Cluj, Romania, pp , 2011