RADOEGEERG, VOL. 4, O., JE 005 9 Dgtal Power etwork Parameters Measurement Ján HRBK, Peter FCHS, Mloslav HRŠKOVC, Rastslav MCHÁLEK, Branslav LOJKO Det. of Rado Electroncs, Slovak nversty of Technology, lkovčova, 8 9 Bratslava, Slovak Reublc hrbk@kre.elf.stuba.sk, fuchs@elf.stuba.sk, hruskovc@kre.elf.stuba.sk, mchalek@kre.elf.stuba.sk, lojko@kre.elf.stuba.sk Abstract. Exact measurement of the arameters of a ower network s now ossble by dgtal methods. The descrton of the roosed and realzed nstrument based on the dgtal samlng method s gven. t can measure basc arameters of the three-hase ower network such as rms values of voltages and currents, owers, energes, ower factors and the network frequency. Questons concernng the accuracy of measurement, error sources, and error correcton are also gven. A method of calbraton based on the frequency outut s roosed and ts calculaton accuracy evaluated by MATLAB. Keywords Dgtal electrcty meter, DSP, ower measurement, measurement accuracy, error sources, calbraton.. ntroducton Electronc methods of ower and energy measurement are based on dfferent rncles, [], []. The methods sutable for use n dgtal electrcty meters may use Hall effect, [], ulse-wdth modulaton (tme-dvson multler), [4], analog multlyng C, [5], three-termnal thermoconverter (TTTC), [6], or dgtal multlcaton, [7], to menton only a few ublshed aers. The method used n electrcty meter deends on the desred accuracy and on the allowed rce of the nstrument. The followng consderatons concern dgtal electrcty meters based on dgtal multlcaton. Basc nstruments for the most accurate measurement of electrc ower and energy are dgtal electrcty meters. They use dgtal multlcaton of voltage and current samles, [], [], receved from one A/D converter wth multlexed nuts, [7], or they may use searate A/D converter for each nut sgnal, [4]. The advantages of such nstruments are obvous: hgh accuracy, short- and long-term stablty, comlex net arameters measurements, ossblty of remote automated data rocessng, auto-calbraton, selftest and many other functons resultng from the mcrorocessor-based dgtal system ossbltes. Wth today s hgh comutng ower of dgtal sgnal rocessors t s also smle to measure the reactve ower, aarent ower, hase shft, ower factor and the frequency sectrum of the ower network sgnals. Very mortant characterstc of electrcty meters s ther accuracy. t deends on the accuracy of the analog nut crcuts, the accuracy of the samlng rocess tself, [9], the accuracy of A/D converson and the accuracy of dgtal calculatons. n dgtal samlng electrcty meters the measurement error can be smly elmnated n the dgtal sgnal rocessng. n ths case the man roblem s the stablty of the arameters of these arts whch handle the measured sgnals. The analog nut crcuts must be constructed usng hghly stable comonents. sually, synchronzed or aroxmately synchronzed samlng s used, [9]. A/D converson wth multlexed nuts of A/D converter must use one of the known methods of comensaton of errors caused by tme delay between the multled voltage and current samles, [0]. Better way s to use searate A/D converter for each nut sgnal. There are many methods of error correcton n dgtal electrcty meters, []. Most of these methods use software correcton based on calbraton rocess. Dgtal electrcty meters have dfferent measurement and communcaton ossbltes and dfferent rces. The accuracy of the best nstruments s of the order 0.0 % or better.. Analog Crcuts of the Electrcty Meter Crcut dagram of the roosed nstrument for ower network arameters measurement s n Fg., []. t contans the crcuts for condtonng of the sgnals roortonal to the network voltages and currents. The rocessor art controls some crcuts of the analog art, dgtzes the sgnals, makes necessary calculatons and sgnal rocessng n dgtal form, dslays the results and generates sgnals for testng of other electrcty meters. Voltage sensors n the voltage channel scale the levels of the net voltages to the desred values. These voltage sensors are realzed as four stage resstve voltage dvders. The voltage range s from 0 V to 500 V. Sngle oututs of the voltage dvders are swtched by a range swtch whch s controlled by the rocessor system ac-
0 J. HRBK, P. FCHS, M. HRŠKOVC, R. MCHÁLEK, B. LOJKO, DGTAL POWER ETWORK PARAMETERS MEASREMET cordng to the outut values of the A/D converters. Overvoltage rotecton s a smle way of the voltage lmtaton n case of the occurrence of nadequate voltage levels. For the sake of low leakage current and hgh seed these crcuts are realzed wth dodes. nstead of the sensed voltages t s ossble to connect calbraton values to the nuts of the buffer stages. n ths case t s ossble to check zero level shfts and to connect and measure recson DC calbraton voltage. naccurate adjustment of the voltage dvders s comensated by coeffcents ntroduced nto the calculaton of the nut voltages n the rocessor art. The hase shfts of the voltage channel were mmeasurable u to the frequency khz. controls the oeraton of the devce. t contans also an address decoder and control logc. All the crcuts (keyboard, dslay, DSP board) are maed nto ts memory what makes the communcaton very smle. For resentaton of tme and frequency characterstcs, grahcal LCD dslay wth the resoluton of 40x8 dots s used. A block of A/D converters dgtzes the sgnals from the analog art. t contans sx 8-bt A/D converters (6 bts used) wth aroxmately synchronzed samlng, [9], and samlng frequency f s 50 khz. The DSP art wth the Texas nstruments TMS0C67 rocessor makes necessary calculatons and sgnal rocessng n dgtal form. t also contans software for sgnal generaton wth the outut through a D/A converter block and a frequency outut wth the frequency roortonal to the measured ower. Fg.. Block dagram of the roosed dgtal electrcty meter. The concet of the current channel s ractcally the same as the voltage channel, Fg.. The current sensors are realzed as current transformers wth metal glass core materal followed by the current-to-voltage converson. There are sx current ranges so the total current range s from 50 ma to 0 A. naccuraces n the current channel are comensated by the calbraton rocedure for every current range searately. The hase shfts of the current channel are mmeasurable u to the frequency khz. The attemts have been made to use comensated current transformers, Fg., but the better accuracy of the converson has been overshadowed by the ncreased nose level and more comlcated constructon. Fg.. Block dagram of the comensated current transformer.. Dgtal Part of the Electrcty Meter The block dagram of the dgtal art of the desgned electrcty meter s n Fg., [], [4]. Mcrocontroller board wth the Texas nstruments TMS0F4 rocessor Fg.. Block dagram of the dgtal art of the roosed electrcty meter. The devce oerates n two modes. n the calbrator mode the followng arameters are measured and calculated: rms values of voltages and currents, actve, reactve and aarent owers, ower factors, network frequency, energy delvered nto the load and frequency sectrum of the measured sgnals. The results are dslayed contnuously on the dslay. n the regstraton mode the measured and calculated arameters are erodcally stored n the memory. As a result, tme characterstc or electrc energy consumton can be obtaned. The erod of averagng and storng the results s otonal. The shortest tme nterval of voltages, currents and owers calculaton s one erod of the network sgnals. The measured average values are dslayed on demand. All data can be transferred nto an external devce va an nfrared or RS nterface. The most mortant art of the devce s the dgtal sgnal rocessor (DSP) board wth a owerful DSP TMS0C67. Ths art makes all the necessary comutatons of the system. t controls the communcaton wth A/D converters and stores data n memory. n regstraton mode the devce takes the advantage of a large on-board memory where the measured values are stored. To vsualze the results, a communcaton ort wth the mcrocontroller has been desgned. The mcrocontroller s the master n the system and t s able to dslay any data of the DSP on the grahcal LCD dslay. The DSP board also con-
RADOEGEERG, VOL. 4, O., JE 005 tans software for sgnal generaton wth the outut through a D/A converters block and a frequency outut wth the frequency roortonal to the measured ower. The frequency sectra of the measured voltages and currents u to th the 50 harmonc are calculated usng the FFT algorthm. The roertes of the DSP board: owerful floatng-ont Texas nstruments TMS0C67 DSP for comutaton of multle FFTs and for calculaton of measured quanttes, hgh seed temorary data memory (8 MByte SDRAM), large low-cost rogram and data memory (4 MByte flash ROM), smle control of sgnals and data transfer from the three A/D converters at samlng rate u to 00 khz, smle communcaton between the DSP and the mcrocontroller (HP nterface), watch-dog securty system, JTAG emulaton for software develoment. To set the arameters of the devce, calbraton rocedure must be run. The nstrument s calbrated usng known values of the nut quantty. Durng the calbraton a dgtal rocessor n the nstrument calculates correcton coeffcents or correcton functons whch are used to get the correct values of the measured quantty durng the measurement. n the roosed nstrument the least squares method s used but ths rocedure s not user accessble. The followng equatons have been used to calculate the ower network arameters, [5]: k k S u u, (), (), () kuk P Q S P u, (4), (5) P PF, (6) S f f s where k u and k are voltage and current range constants, resectvely. The maxmum value of the data from the A/D converter (6 bt) s u max ± 5. At the mnmum ower network frequency f 45 Hz, the number of samles er (7) erod s f s / f 50 khz / 45 Hz. The maxmum ossble value of the sum n equaton () s max (u max) and gves the necessary number of bts B 40.. Because the nut voltage s not rectangular, the summaton s accomlshed by a 40-bt regster. The averagng of samles s accomlshed durng more than one erod. The default number of erods s 50. Equatons () and () reresent starcase aroxmaton of the nut sgnals. 4. Error Sources n Electrcty Meters As mentoned earler, there are ractcally four man error sources n dgtal samlng electrcty meters: errors of the analog nut crcuts, errors of the samlng rocess, errors of A/D converson and errors of dgtal calculatons. n recse nstruments, recautons must be used to overcome or elmnate these errors. The errors caused by the analog nut crcuts are manly naccurate adjustments of voltage and current sensors, nstablty and nose of crcuts handlng the nut sgnals. The samlng of the real waveform usually aroxmates the waveform by a starcase or a ecewse lnear functon. The rms value and the ower are calculated n starcase aroxmaton by equatons () [or ()] and (4), aroxmately. n ecewse lnear aroxmaton these equatons are more comlcated, [6]: 0 ( u u u u ), (8) P ( ) u u u u. (9) 0 The aroxmaton ncreases the error of measurement but because of the symmetry of sne and cosne functons ths error may be small. Often, smler equatons (), () and (4) may gve lower errors than equatons (8) and (9). The error ncreases f the waveform s dstorted. Another roblem concernng the samlng rocess s the synchronzaton of samlng wth the nut sgnals. Asynchronous samlng s not ractcally used because of ts hgh error or very long averagng tme (summaton nterval), [9]. Smle and often used method s to start samlng n the nstant of zero crossng of the nut voltage or current (aroxmately synchronzed samlng). Better accuracy can be acheved f the samlng starts n the nstant of crossng the rms value of the samled sgnal, [7]. t s dffcult to realze n a three-hase system or f there s a hase shft between the voltage and the current. The error here s caused by the random oston of the last samle comared wth the nstant of the end of erod, mssng or exceedng samle (from the next erod). The best accuracy, from ths ont of vew, needs synchronzaton of the
J. HRBK, P. FCHS, M. HRŠKOVC, R. MCHÁLEK, B. LOJKO, DGTAL POWER ETWORK PARAMETERS MEASREMET samlng frequency wth the frequency of the nut sgnal, []. f the number of samles,, used to get the average value s low then the error of measurement ncreases, [9]. Ths error deends on the samlng rate and on the averagng tme. Hgh samlng rate makes t ossble to average the samles wth good accuracy even durng one erod of the ower network sgnal. t s then ossble to regster even short transtons n ower consumton and to change the frequency outut after every erod of the sgnal. The errors caused by A/D converson deend on the number of A/D converters used and on the resoluton of A/D converters. Errors n one A/D converter wth multlexed nuts are caused by tme delay between the multled voltage and current samles. Low-resoluton A/D converters (low number of bts) cause unaccetable quantzaton errors. Even very fast DSP s not able to make correctons of every samle accordng to the correcton functon (for the three-hase system sx samles must be corrected er one samlng erod and all other calculatons and oeratons must be also done). n ths case, usually, only the fnal calculated values are corrected and, thus, addtonal errors are ntroduced. 5. Error Correcton n Electrcty Meters n dgtal samlng electrcty meters the measurement errors of the analog nut crcuts can be smly elmnated n the dgtal sgnal rocessng. n ths case the man roblem s the stablty of the arameters of these arts whch handle the measured sgnals. The analogue nut crcuts must be constructed usng hghly stable comonents. For the sake of calculaton smlcty, manly starcase aroxmaton s used. n symmetrcal sgnals the errors of samlng n one quarter of erod are artly comensated n another quarter. Aroxmately synchronzed samlng wth the startng ont n the nstant of zero crossng of the samled sgnal s the usual case n dgtal electrcty meters. f the number of samles used n one summaton nterval s suffcently hgh, then the error of such samlng s low. Precse nstruments use sgma-delta A/D converters wth hgh resoluton (over 6 bts) and hgh samlng rate (tens ksps). All the measured quanttes are then calculated durng one erod but, usually, the results are averaged agan durng longer summaton ntervals to get hgher accuracy. To fnd out the error of calculaton when only the fnal calculated values were corrected, smlfed calculatons of the corrected rms values of the net voltage, current and the actve ower P were comared wth the calculatons where every samle was corrected, [8]. The selected correcton functon was a lnear functon of the tye y ax b, where the constant a reresents the gan error and the constant b s the offset error. 000 samles of the voltage and current er erod were calculated usng the equatons: u a m sn( π /000) a m sn( /000) b, (0) π b () where,,...,000. For smlcty, the values m and m were set to unty. The followng equatons show the correct use of the correcton functon: P b u a a b a a u a a a a b, (), () b. (4) The smlfed calculaton of the corrected values s gven by the equatons: u a a P u a a b b, (5), (6) bb a a. (7) Because of hgher calculaton errors of and n [8], equatons (5) and (6) are modfed. The dfferences of the corresondng values are the calculaton errors gven by equatons: δ u 00, (8) δ 00, (9) δ P P P P 00. (0) These errors were lotted n Fg. 4 and Fg. 5 for dfferent values of the coeffcents a, a (gan) and b, b (offset). The offset s relatve, referenced to the amltude m or m. t can be seen that the results of calculaton of the corrected
RADOEGEERG, VOL. 4, O., JE 005 rms values are the same f the offset coeffcent s zero. For nonzero offset coeffcent the error ncreases wth the ncreased offset. On the other hand, hgher errors can be seen for lower values of the gan coeffcent. The results of calculaton of the corrected ower values are also the same f the offset coeffcents are zero. For smlcty, the values of a and a (b and b ) are equal. For nonzero offset coeffcents the error ncreases wth the ncreased offsets. Hgher errors can be also seen for lower values of the gan coeffcents. Fg. 4. RMS value correcton error of the smlfed calculaton rocedure. Fg. 5. Power correcton error of the smlfed calculaton rocedure. Fg. 4 and Fg. 5 show that the errors of such smlfed - calculatons are of the order 0 er cent. They are small enough to use them nstead of much more comlcated and tme-consumng exact calculatons. 6. Calbraton Problems Calbraton rocedure s used to set the arameters of the devce and to correct the errors of measurement. The smlest error correcton s only the offset correcton, whch s done by measurng the value of the nut quantty wth short-crcuted nut and storng ths value n the memory for use as the correcton constant. To correct the gan error multlcaton coeffcent must be evaluated. Ths needs some reference value of the nut quantty to be connected to the nut and measured by the nstrument. The nonlnear characterstc of such an nstrument needs more values of the nut quantty to be connected to the nut and measured by the nstrument. n such case, a nonlnear correcton functon or a table of correcton values must be calculated. n electrcty meters, three calbraton rocedures must be run, [9]: voltage calbraton, current calbraton and arastc hase shft correcton. The best way s to carry out the calbraton rocess automatcally, usng a comuter. The comuter controls a sgnal source (sets the desred measured values), reads the necessary values from the calbrated and reference nstrument n the same nstant, calculates the calbraton constants and stores them n the memory of the calbrated nstrument. Manufacturers of electrcty meters usually have such ossblty. The desgned nstrument contans an algorthm for voltage calbraton usng the least squares method. The current calbraton can be done usng the same algorthm but usually the measured current s not stable. n ths case t s necessary to synchronze the measurng tme erod of the calbrated and the reference nstrument or to use mean values. t s also ossble to use frequency outut of the nstrument wth the outut frequency roortonal to the aarent or actve ower. The frequency roortonal to the measured ower s comared wth the correct value n the recse reference comarator. n ths way, the calculated aarent ower, S, s comared wth the correct ower value, S. As the voltage s correct (calbrated already) the mean value of the aarent ower relatve error s the same as the mean value of the current relatve error. These errors n a few onts over the calbrated current range can be used to calbrate the current by the least squares method. Smle, lower accuracy electrcty meters sometmes do not have the frequency outut based on the aarent ower. They have only the frequency outut based on the actve ower. n ths case the current calbraton rocedure must be reeated because of ts deendence on the hase shft correcton. A method was carred out to calculate the current and the arastc hase shft at the same tme, [0]. The measured owers P, P φ for two dfferent hase shfts 0, φ are comared wth the correct values P, P φ, resectvely, usng the frequency outut of the nstrument. The mean values of the relatve errors yeld the mean values of the calculated owers: δ δ P P( ), P ( ). () P 00 00 The equatons to be solved to get the mean values of the measured current and arastc hase shft are, [9]:
4 J. HRBK, P. FCHS, M. HRŠKOVC, R. MCHÁLEK, B. LOJKO, DGTAL POWER ETWORK PARAMETERS MEASREMET P cos( ), P cos( ) () where φ s a hase shft between the voltage and the current caused by the nut crcuts of the nstrument and, are the measured voltage and current, resectvely. sng mathematcal formula for the cosne of the sum of two hase angles, [], and takng nto account that φ s a small hase shft t s ossble to smlfy ths equatons. The smlest soluton follows from the well known fact that f x s small then sn(x) x [rad] and cos(x) : P P sn ( ) sn ( ) [ P cos( ) P ], () P cos( ) P. (4) P sn( ) For hase shfts φ u to 5 o the error of ths soluton s of the order of tenth er cent as shown n Fg. 6. Here, for startng values of and φ the exact values of owers P and P φ are calculated from equatons (), the values of and φ are calculated agan from equatons () and (4), resectvely, and comared wth the startng values. The o values 00 V and φ 60 were used. P ( ) D 6 (8) and substtuton of equaton (8) nto (7) leads to the cube equaton: [ P cos( ) P ] 6[ P cos( ) P ] 0 P sn( ) 6 P sn( ). (9) The number of real roots of ths equaton deends on the sgn of the exresson: [ P cos( ) P ] P sn ( ) For D < 0 equaton (9) has three real roots.. (0) To solve equaton (9) three new exressons have been ntroduced: q [ P cos( ) P ] P sn ( ) [ P cos( ) P ], () r ±, () P sn ( ) q cos( α). () r Fg. 6. Errors of the aroxmate current and hase shft correctons. Hgher recson of the soluton s obtaned usng, []: sn( x) x x x, cos( x). (5) 6 n ths case equatons () change to: P ( ), (6) P cos( )( ) Extracton of from equaton (6) yelds: sn( )( ). (7) 6 The sgn of r must be the same as the sgn of q. f the hase angle φ s ostve, then q s negatve and vce versa. Three roots of equaton (9) are now gven by the exressons: α r cos P cos( ) P P sn( ) α P cos( ) P r cos 60 P sn( ), (4), (5) α P cos( ) P r cos 60. (6) P sn( ) Because the exected value of φ s near to zero, the roer root must be selected. After fndng the value of φ from one of equatons (4) to (6) the value of the current s calculated from equaton (8). The soluton of equaton (9) was carred out also n MATLAB under the same condtons as gven for the solutons () and (4). Fg. 7 shows the calculated error of such soluton of the current from equaton (8), and Fg. 8 shows the error of the soluton of the arastc hase shft φ drectly from equaton (9).
RADOEGEERG, VOL. 4, O., JE 005 5 Ths rocedure enables to calculate the correct values of the current and the hase shft at the same tme, thus overcomng the reeatng of the current calbraton after the hase shft correcton. These correct values can now be used n the current calbraton and arastc hase shft correcton rocedures. The errors of smlfed soluton are - of the order of 0 er cent for the current calculaton but of the order of tenths er cent for the arastc hase shft calculaton. Hgher recson method of such calculaton was roosed and MATLAB calculatons were used to verfy ths method. The errors of such calculatons are of -4 the order of 0 er cent. Fg. 7. The calculated error of the current soluton. Acknowledgements Ths work s suorted by the Slovak Grant Agency GAT under the grant o. 0/VTP/000. Fg. 8. The calculated error of the arastc hase shft soluton. t s evdent that for φ u to 5 o the error of such soluton s of the order of 0-4 er cent. The error s ndeendent on the current value. The results of the soluton gven by the drect calculaton from equatons (8), (4), (5), (6) are smlar. 7. Conclusons Bref descrton of the desgned dgtal three-hase electrcty meter s gven. Modern Texas nstruments TMS0F4 rocessor and TMS0C67 DSP were used to get a owerful measurng system. Four man error sources n dgtal samlng electrcty meters, namely errors of the analog nut crcuts, errors of the samlng rocess, errors of A/D converson and errors of dgtal calculatons are brefly exlaned. Error correcton recautons are also descrbed and accuracy results of smlfed correcton calculatons are gven. Because of low calculaton errors (of the order of 0 er cent), valdty of such - smlfed calculatons s roved. Calbraton roblems n the roosed electrcty meter are descrbed. A calbraton rocedure for the correctons of the measured current and arastc hase shft between the measured voltage and current based on the actve ower measurement s gven. References [] KAHMA, M. Elektrsche Energe elektronsch gemessen: Meβgerätetechnk, Prüfmttel, Anwendungen. Berln-Offenbach: vde-verlag, 994. [] WEBSTER, J. (ed.) Wley Encycloeda of Electrcal and Electroncs Engneerng Onlne. nstrumentaton and Measurement, ew York: John Wley & Sons, 999. [] RAPAT, Š., BABARÍK, P. Electrcty Meters Semens Constructed after Lands & Gyr Dalog of Seres ZMD0AS and ZMD0Ass. Časos EE, 00, vol. 8, no.,.. (n Slovak) [4] KS, S., AGA, T. A Sngle-Phase Three-Wre Watt-to-Pulse Frequency Converter sng Smle PWM and ts Accuracy Analyss. EEE Transactons on nstrumentaton and Measurement, 994, vol. 4, no. 5,. 770 774. [5] HASHMOTO, A., YAS, K., KS, S. Self-Calbratng Standard Watthour Meter. n Proceedngs of the Conference Meterng and Tarffs for Energy Suly. Brghton (K), 996,. 94 98. [6] LALSKÝ, T., HAŠČÍK, Š., MOZOLOVÁ, Ž., BRA, E., DRŽÍK, M. The mroved erformance of GaAs mcromachned ower sensor mcrosystem. Sensors and Actuators, 999, vol. 76,. 4 46. [7] SCHWEDTER, M. F. Dgtal Measurement System for Electrcty Meters. n Proceedngs of the Conference Meterng and Tarffs for Energy Suly. Brghton (K), 996,. 90 9. [8] K006 Three-Phase Comarator. Oeratonal Manual. EMH, Brackel MTE, Zug, 00. [9] STEBAKE, D.., DOLEV, A. Hgh-Accuracy Samlng Wattmeter. EEE Transactons on nstrumentaton and Measurement, 99, vol. 4, o. 6,. 974 978. [0] PERERA, J., POSTOLACHE, O., GRAO, P., RAMOS, H. Mnmsng Errors Due to on-smultaneous Samlng of Voltage and Current n Dgtal Power Measurement Systems. n Proceedngs th of the MEKO TC4 nternatonal Symosum Electrcal Measurements and nstrumentaton, Part, Zagreb (Croata), 00,. 07 0. [] ĎAĎO, S., VEDRAL, J. Analog and Dgtal Measurng nstruments. Prague: Edční středsko ČVT, 98. (n Czech) [] HRŠKOVC, M., HRBK, J. Voltage and Current Channel of Dgtal Calbraton Electrcty Meter. n Proceedngs of the
6 J. HRBK, P. FCHS, M. HRŠKOVC, R. MCHÁLEK, B. LOJKO, DGTAL POWER ETWORK PARAMETERS MEASREMET Conference ew Trends n Sgnal Processng V, Ltovský Mkuláš (Slovaka), 000,. 8. [] FCHS, P., FERAEC, R., GÁBOR, P., HRBK, J., HRŠKOVC, M., POVAŽAEC, D. Dgtal Three-Phase Regstraton/Calbraton Electrcty Meter. n Proceedngs of the rd nternatonal Conference on Measurement Measurement 00, Smolence (Slovaka), 00,. 66 69. [4] FCHS, P., HRBK, J., HRŠKOVC, M., LOJKO, B., MCHÁLEK, R. Dgtal Power and Energy Measurement. n CD ROM Proceedngs of the 6 th nternatonal Conference Control of Power Systems 04, Štrbské Pleso (Slovaka), 004, 4. [5] MCHÁLEK, R., GÁBOR, P., FCHS, P., HRBK, J., HRŠKOVC, M. Dgtal Part of Dgtal Electrcty Meter. n Proceedngs of the th nternatonal Czech-Slovak Scentfc Conference Radoelektronka 00, Bratslava (Slovaka), 00,. 45 48. [6] SEDLÁČEK, M., HAASZ, V. Electrcal Measurement and nd nstrumentaton, ed. Prague: Vydavatelství ČVT, 000. [7] MCHÁLEK, R., GÁBOR, P., LOJKO, B., FCHS, P., HRBK, J., HRŠKOVC, M. Dgtal Electrcty Meter. n Proceedngs of the th nternatonal Czech-Slovak Scentfc Conference Radoelektronka 00, Brno (Czech Reublc), 00,. 99 0. [8] FCHS, P., MCHÁLEK, R., GÁBOR, P., LOJKO, B., HRBK, J., HRŠKOVC, M. Dgtal Electrcty Meter. n Proceedngs of the 4 th nternatonal Conference on Measurement Measurement 00, Smolence (Slovaka), 00,. 4 44. [9] HRBK, J., FCHS, P., HRŠKOVC, M., MCHÁLEK, R., LOJKO, B. Dgtal Power and Energy Measurement. n Proceedngs of the 4 th nternatonal Czech-Slovak Scentfc Conference Radoelektronka 004, Bratslava (Slovaka), 004,. 60 6. [0] FCHS, P., HRBK, J., HRŠKOVC, M., LOJKO, B., MCHÁLEK, R. Dgtal Power and Energy Measurement. n Proceedngs of the th nternatonal Symosum on Measurements for Research and ndustry Alcatons and 9 th Euroean Worksho on ADC Modellng and Testng, Athens (Greece), 004, vol.,. 49 497. [] BROŠTEJ,.., SEMEĎAJEV, K. A. Mathematcs Handbook, rd ed. Bratslava: SVTL, 964. (n Slovak) About Authors... Ján HRBK (Doc. ng. PhD.) was born n 948. He graduated from the Slovak Techncal nversty, Faculty of Electrcal Engneerng n Bratslava n 97. Snce 97 he has been wth the Faculty of Electrcal Engneerng and nformaton Technology, Slovak nversty of Technology n Bratslava. Here he also receved the CSc. (PhD.) scentfc degree n Electronc Engneerng n 98. n 989 he was aonted Assocated Professor. Hs rofessonal actvtes concern electronc measurements and analog electronc crcuts, namely n the feld of ntegratng AD converson, esecally current-to-frequency converson. Snce 996 hs actvtes concern manly electrc ower and energy measurement. Peter FCHS (ng. PhD.) was born n 959. He graduated from the Slovak Techncal nversty, Faculty of Electrcal Engneerng n Bratslava, Slovaka, n 98. n the years 98-985 he was wth VRSE. Snce 985 he has been wth the Faculty of Electrcal Engneerng and nformaton Technology, Slovak nversty of Technology n Bratslava. Here he also receved the CSc. (PhD.) scentfc degree n Electronc Engneerng n 994. Snce 995 he has been grant rojects head and snce 996 he has been the head of the Euroean Tranng Center for T sgnal rocessors. Hs rofessonal actvtes are concentrated on frequency synthess, mcrocontrollers and ther alcaton and dgtal sgnal rocessors and rocessng. Mloslav HRŠKOVC (Doc. ng. PhD.) was born n 94. He graduated from the Slovak Techncal nversty, Faculty of Electrcal Engneerng n Bratslava, Slovaka, n 968. Here he also receved hs PhD. scentfc degree n the feld of Electronc Engneerng n 98. He has been wth the Faculty of Electrcal Engneerng and nformaton Technology, Slovak nversty of Technology snce 969. n 990 he was aonted Assocated Professor. Hs rofessonal actvtes concern crcut theory, nose evaluaton and ulse ower suly sources. Hs actvtes n the last years have ncluded research n the feld of electrc ower and energy measurement. Rastslav MCHÁLEK (ng.) was born n Malacky, Slovaka, n 977. He receved the BSc. and MSc. degrees n Electrcal Engneerng from the Slovak nversty of Technology, Faculty of Electrcal Engneerng and nformaton Technology n Bratslava, n 999 and 00, resectvely. He s currently workng on hs PhD. degree at the Deartment of Rado Electroncs at the same unversty. He s rmarly engaged n dgtal sgnal rocessng, electrc ower and energy measurement and electronc systems wth mcrocontrollers. Branslav LOJKO (ng.) was born n Bratslava, Slovaka, n 977. He receved the BSc. and MSc. degrees n Electrcal Engneerng from the Slovak nversty of Technology, Faculty of Electrcal Engneerng and nformaton Technology n Bratslava, n 000 and 00, resectvely. He s currently a PhD. student at the Deartment of Rado Electroncs at the same unversty. He s rmarly engaged n dgtal sgnal rocessng n electrc ower and energy measurement and n electronc systems wth frequency control focused on syntheszers based on frequency locked loos for wreless communcatons.