This paper describes an efficient implementation of a power supply meter.  The implementation is based on the Fourier Series decomposition algorithm, using CORDIC algorithm for complex mathematical computations.  It is able to calculate RMS and peak values, phase shift, power factor, and complex, active, and reactive power for two periodic waveforms up to the 25th harmonic.



Several implementation alternatives are compared pointing out the advantages and the disadvantages of each one.  Then the circuit structure at block level is described with emphasis on the advantages resulted from the use of CORDIC algorithm, followed by some considerations over precision issues

Lazarescu, MIHAI TEODOR

Sartori, M.

English

This paper describes an efficient implementation of a power supply meter.  The implementation is based on the Fourier Series decomposition algorithm, using CORDIC algorithm for complex mathematical computations.  It is able to calculate RMS and peak values, phase shift, power factor, and complex, active, and reactive power for two periodic waveforms up to the 25th harmonic.

Several implementation alternatives are compared pointing out the advantages and the disadvantages of each one.  Then the circuit structure at block level is described with emphasis on the advantages resulted from the use of CORDIC algorithm, followed by some considerations over precision issues

LAZARESCU, MIHAI TEODOR

Sartori M.

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

04 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEA high precision power supply meter / Lazarescu, MIHAI TEODOR; Sartori, M.. - ELETTRONICO. - (1996). ((Interventopresentato al convegno Mixed Design of Integrated Circuits and Systems (MIXDES 96) tenutosi a Lodz, Poland nel 30Maggio - 1 Giugno 1996.OriginalA high precision power supply meterPublisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2507489 since: 2018-09-19T18:44:53ZMIXDESA high precision power supply metering. Mihai-Teodor LZRESCUPolytechnic of Turin, Electronics departmentC.so Duca degli Abruzzi, 24, 10129 Turin, ItalyFax: + 39 (0)11 564 4134; email: lazarescu@polito.iting. Mario SARTORICOREP  LETEOC.so Duca degli Abruzzi, 24, 10129 Turin, ItalyFax: + 39 (0)11 564 4134; email: sartori@polito.itThis paper describes an ecient implementation of a power supply meter. Theimplementation is based on the Fourier series decomposition algorithm, usingCORDIC algorithm for complex mathematical computations. It is able tocalculate RMS and peak values, phase shift, power factor, and complex, active,and reactive power for two periodic waveforms up to the 25thharmonic.Several implementation alternatives are compared pointing out the advantagesand the disadvantages of each one. Then the circuit structure at block level isdescribed with emphasis on the advantages resulted from the use of CORDICalgorithm, followed by some considerations over precision issues.1 INTRODUCTIONSince the discovery of the electricity by Volta and up to our days, the electric power faced aconstantly growing utilization. The electric consumers diversify more and more and, at the sametime, they change their interaction with the power supply. Although the rational utilization of thepower distribution network becamed an issue long before the electromagnetic compatibility was anacute problem, now they have to be faced together by the electric power end user.The need to watch constantly the way that large power consumers are interacting with the supplyis a must in our days. This is accomplished by special equipments capable of performing accuratemeasurements of power supply parameters and signal or initiate corrective actions when necessary.Condential work. Published with the agreement of DTA s.r.l., Milan, ItalyWe described in this paper a circuit that can be used to perform the electric measurementsneeded for such an equipment. This circuit will be the result of a project we do in the framework ofSUMIS action for DTA s.r.l., an SME located in Milan, Italy.2 DESIGN CHOICESThe goal of the project is to build a measurement instrument for AC values. It should be ableto measure RMS values and harmonic peak values for each of its two analog inputs, and phase shift,active and reactive power, and power factor individually for each harmonic up to the 25th.First choice to be made was if an analog or a digital implementation is appropriated.The analog solution would consist mainly in putting together several switched capacitor lters.These lters should comply to very tight specications in terms of low order harmonics rejection andphase distorsion for the passband. Such lters had to be designed by hand, with a very accuratelayout. Long and extensive electric simulations in transient mode and the layout complexity wouldmade the design last too long and would give very few guaranties for a rst time working product.Moreover, this solution would rise the problem of nding an available technology providing SC ltersfor very low frequencies (as low as 50Hz).Moving the analog solution to a digital implementation leads mainly to a DSP machine actingvery much as the analog lters. This solution is not less expensive in terms of area but the design owis much more simplied allowing a VHDL description and synthesis approach.Given that we had to do a harmonic analysis, we looked toward the FFT (DFT) algorithm asan optimized DSP approach for this task. We noted that a RAM buer is required to store the inputsamples for processing and that a lot of multiplications are to be done in the DFT algorithm. Wenoted also that DFT works for any kind of input signals.As we had to measure only periodic waves, we decided to implement a particularization of theFourier transform, the Fourier series development, only for the harmonics of interest. This solutionhas the following main advantages over the DFT: the computation eort is much lower; real time processing can be done avoiding input samples storage on board; the algorithm is simpler to implement resulting in a smaller area; the resulting DSP machine is more observable and easier to debug.In general, all digital implementations oer larger exibility in postprocessing the results forobtaining derived values from the direct measured ones, that are the harmonic peak value and phase.They can also be interfaced with a microprocessor system and can be much easier integrated into aremote measurement or control equipment.-100-80-60-40-2000 1 2 3 4 5 6 7 8 9 10Filter gain [dB]Normalized frequencyFourier series transfer functionFigure 1: Fourier series transfer characteristicThe DFT and Fourier series implementations are by far more accurate and ecient than theanalog or the digital implementation of general purpose lters. The Fourier series algorithm in factacts like a passband lter for the selected harmonic while having transmission zeroes for all otherharmonics of the fundamental. In gure 1 is shown the theoretical transfer characteristic of a Fourierseries that selects the second harmonic.3 CIRCUIT STRUCTUREOur aim was to keep the circuit structure as simple and small as possible while avoiding timingproblems.The block schematic we choose is presented in gure 2. For sake of simplicity we decided that amicroprogrammed machine is the most suited. This way we keep the Control block simple and small.A part of the ROM is used for storing the microcode and is in tight interaction with the Control block.In order to avoid timing problems due to the high clock frequency required by the real timeprocessing, we used two separate real time processing paths, one for current samples and one forvoltage samples. For this purpose, there are two distinct A/D converters that sample synchronouslythe voltage and current lines for one fundamental period. Real time processing is no more required inthe postprocessing part, so this part uses only one bus.The computational part of the circuit is done using two implementations of the CORDIC algo-1rotationangle/module x(-1) Xu AuXi AiCORDIC ΣΣproductCORDICproductCORDICBu16616 66 6 6 6616Data Bus for Current ProcessingCommand BusData Bus for Voltage Processing and for PostprocessingA/D1016A/D1016A/D1061ControlROM10 51086i(t)u(t)T(t)Bi13 7SerialI/OI/Octrl1661282816 19 2819 2828 28 28 28 28 28282828Figure 2: Block schematicrithm: CORDIC angle/module/rotation and CORDIC product .The rst implementation performs essentially vector rotations. Thus, with slight algorithmchanges it is able to compute in one step the vector module and the vector angle using vector X andY components as input. In another operation mode, the same block is able to rotate a vector witha given angle, returning vector X and Y components for the new position. This operation mode isused to compute the cosine trigonometric function for a given angle for power factor measurement orto compute the active and reactive powers as X and Y components for the complex power.The second CORDIC implementation, CORDIC product , is optimized for real time productcalculation. There are two such blocks, one for the current processing path and one for the voltagepath.The Control bus is used in common by the two paths in the processing phase. It will carrymainly microcode instructions that are peeked by the Control block from the ROM and that will bedecoded by each block in part. The same bus carries also busy/ready feedbacks from the blocks thatneed several clock cycles for completing their task.The Serial I/O interface will implement a slave I2C protocol and will be used to read commandsfrom an external digital system and to output measurement results.A third A/D converter is provided for temperature measuring. This is a customer's request.4 PRECISION CONSIDERATIONSAll mathematical operations are done using integers represented in 2 complement. By using thisxed point representation we considerably simplied the operation of the mathematical blocks.The drawback with respect to using a oating point representation is that more attention shouldbe paid to overows and underows.To dimension the internal busses, ROM words, and recursive algorithms iteration count we usedthe precision specications and the maximumallowable precision on output. In fact, system constraintsimposed an output size of 16 bits for measurement results that limits the results precision. Thus westart dimensioning backward, evaluating the output truncation error and following all data ows inthe algorithm up to the inputs. We imposed that all intermediate errors be at most a tenth of thelargest allowable error on output for that measurement.We have done also a theoretical worst case error estimation by cumulating in the algorithm theeects of the maximum input quantization error, internal operands truncation error, recursive algo-rithms truncation error, etc. These error estimations are very pessimistic and may never happen in realmeasurements. Moreover, when operating with real input waveforms, several errors may compensateeach other during the same measurement, leading to a much smaller error on output results.On the other hand, even in the worst case estimations described above we still did not takeinto account several important error sources as: integral approximation using a nite term sum, A/Dconverter errors, A/D signal conditioning errors (noise, phase shift, DC oset), that may heavilyinuence the overall precision of the measurements.In order to validate the algorithm and the precision performance we developed a C languageprogram that emulates most part of the hardware behavior as: operands truncations, input samplesquantization approximation, controller operation, etc. The standard test consisting in 2  86= 524288distinct input waves and calculating all the output values for the fundamental and each harmonic upto the 25thneeds about 2 weeks to complete on a SUN SPARCstation 20 workstation.5 CONCLUSIONSWe found that using the Fourier series decomposition and the CORDIC algorithm for the taskof harmonic analysis for periodic waveforms is very eective both as computational eort and circuitsize. The estimated precision class of the instrument is better than 0.5 for full scale input waves using10 bit A/D converters, without taking into account the analog part errors.The microprogrammed architecture we chosed is very exible allowing easy algorithm change toadd or eliminate postprocessing operations, to change the number of input samples per fundamentalperiod, bus size scaling for improving precision, etc.The circuit size may be further reduced by eliminating the second processing path. The currentand voltage samples may be processed in sequence using the same blocks and the same bus by doublingthe clock frequency and changing accordingly the microcode sequencing.The circuit is designed using SYNOPSYS VHDL synthesis for the AMS 0:8m digital CMOStechnology.References[1] Burrus, T.W. Parks, DFT  FFT and convolution algorithms: theory and implementation, NewYork, Wiley, 1985[2] Douglas G. Myers, Digital signal processing: ecient convolution and Fourier transform tech-niques, New York, Prentice Hall, 1990[3] E. Oran Brigham, The fast Fourier transform and its applications, London, Prentice-Hall, 1988[4] Peter Henrici, Applied and computational complex analysis, New York, Wiley, 1986[5] R.D. Harding, Fourier series and transforms, Bristol and Boston, Hilger, 1985[6] R.E. Edwards, Fourier series: a modern introduction, vol. 1, 2, New York, Springer, 1979, 1982[7] Robert W. Ramirez, The FFT fundamentals and concepts, Englewood Clis, Prentice-Hall, 1985[8] Ed. by Bede Liu, Digital lters and the fast Fourier transform, Stroudsburg, Dowden - Hutchinsonand Ross, 1975[9] Letizia Lo Presti, Valutazione numerica della Trasformata di Fourier DFT  FFT , course notes,Politecnico di Torino, May 1988

A high precision power supply meter

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A high precision power supply meter

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