A new system for distorted three-phase sinusoidal quantities measurement

Measurement 32 (2002) 1–6 www.elsevier.com / locate / measurement

A new system for distorted three-phase sinusoidal quantities measurement ` S. Sangiovanni*, E. Zappitelli L. Podesta, Universita degli studi di Roma, ‘ La Sapienza’, Dipartimento di Ingegneria Elettrica, Via Eudossiana 18, 00184 Rome, Italy Received 15 March 2001; accepted 23 November 2001

Abstract In recent years, due to the wide spread of electronic power components, the waveforms of voltage and current on power lines have characteristics far different from the sinusoidal conditions. In this paper, a new system based on an algorithm allowing the determination of parameters related to each harmonic in voltage and in current on three-phase power lines, practically symmetric and balanced, is proposed. This system has been verified both by simulation and by testing with an experimental set-up reproducing distorting loads.  2002 Elsevier Science Ltd. All rights reserved. Keywords: Sinusoidal quantity measurement; Distorting loads; Voltage; Current

1. Introduction Today in electric power systems, the sinusoidal condition is reached only in a very few cases. In fact, the use of electronic components to supply and to control electric engines causes a waveform distortion of the supply quantities [1,2]. In this paper a measurement system, based on a new method, is proposed to determine all the quantities related to couples of isofrequential harmonics, that appear in voltage and in current [3–5]. The results obtained with an experimental set-up that supplies non-linear loads are reported too. The results have shown the validity of the method that

*Corresponding author. Tel.: 139-06-4458-5509; fax: 139-06488-3235. E-mail address: [email protected] (S. Sangiovanni).

can be profitably utilized to obtain a complete analysis of the system. In particular the analysis results can be utilized: • to quantify the power amount of harmonics; • to minimize the residual harmonics, operating on the system control to obtain a reduction of demand limit; • to compensate the influence of current harmonics to improve the supply quality.

2. Measurement principle In this paper a measurement system, based on a new investigation method, applied to three-phase circuits, practically symmetric and balanced, with three wires, is proposed in the presence of deformed waveforms. The different electric parameters related to couples of isofrequential harmonics, that appears,

0263-2241 / 02 / $ – see front matter  2002 Elsevier Science Ltd. All rights reserved. PII: S0263-2241( 01 )00056-2

L. Podesta` et al. / Measurement 32 (2002) 1 – 6

2

at the same time, in current and voltage, are determined. This method uses the property of the sequences and it presupposes to determine by the usual way, as a preliminary, the fundamental period. To find the generic h-order harmonic, groups of three samples are acquired, and they are added together. The first sample corresponds to the first phase, the second sample to the second phase, and the third sample to the third phase; considering for the second and the third phase the samples having the characteristic phase displacement of positive and negative phase sequences, according to the harmonic order, compared to the first phase. For the h-order harmonic, h groups are added together, previously determined at constant rate 2p / h, referring to the fundamental period. The sampling is extended to an integer number ‘s’ of periods of the fundamental to remove the possible presence of noise. In this way, all the lower order harmonics will be eliminated, including the fundamental, and those of higher order, for which the frequencies ratio, related to the examined harmonic, is represented by a non integer number. Therefore it is possible to write:

OO 1 i 5] O OC sh

1 s h21 vh 5 ] C sh j 51 i 50 Vij s

(1)

The results of the sums represent, unless a suitable coefficient, the projection of voltage Vx and of current Ix on a generic x-axis. Repeating the procedure, in the same way, but considering values with a phase-displacement of p / 2 compared with the examined harmonic, two values of Vy and Iy , of voltage and current in quadrature with the previous ones will be obtained. By means of the calculated values, taking into account a suitable coefficient, it’s possible to determine for each harmonic the following quantities: ]]] V 5œV 2x 1V 2y ]] 2 2 I 5œI x 1 I y

max voltage amplitude max current amplitude

(3) (4)

F

G

real power

(5)

F

G

reactive power

(6)

1 P 5 3 ](Vx Ix 1Vy Iy 2 1 Q 5 3 ](Vy Ix 2Vx Iy 2 ]]] S 5œP 2 1 Q 2 P cos w 5 ] S

apparent power

power factor

(7) (8)

h21

h

j 51 i 50

I ij

(2)

where vh and i h represent the instantaneous current and voltage values of the h-order harmonic in the three-phase system, and CVij and CIij represent the values of each above mentioned group, made of three samples, on the three phases. To suppress the higher-order harmonic, having an integer ratio in frequency m, compared with the investigated harmonic, each instantaneous value will be added to the related instantaneous value having a phase displacement, referred to the fundamental, of p a 5 ]. mh Relating to the frequency bandwidth present in most practical cases, we could consider only two m values, to eliminate the influence of all harmonics, higher than the investigated one.

3. Simulation The proposed method has been verified, by simulation, on three phase circuits with three wires, with a fundamental three-phase system of voltage (220 V) and of current (10 A), and with harmonic contributions as shown in Tables 1–3. Only values related to real power and for phase-displacements of 08, 308 and 608 have been reported. In each table, the actual value Pa and the measured value Pm of real power have been shown with their type A standard uncertainty u%, obtained by simulating A / D converters with 8, 10, 12 bits and with infinite resolution. In Table 4 the values of measured power Pm and its uncertainty u%, versus the actual power Pa , for different values of actual frequency compared with measured frequency (50 Hz), are reported.

L. Podesta` et al. / Measurement 32 (2002) 1 – 6

3

Table 1 Actual and measured value of real power in a three-phase circuit (phase displacement between V and I 5 08) Harmonic order

Pa

Pm (W)

(W)

8 bits

u%

10 bits

u%

12 bits

u%

Resol. `

u%

5 7 11 13 17

270.00 150.00 90.00 75.00 30.00

267.89 149.02 89.10 74.14 29.31

0.78 0.66 1.00 1.15 2.31

269.47 149.90 89.74 74.81 29.82

0.19 0.06 0.29 0.26 0.60

269.76 150.02 89.96 74.96 29.98

0.09 0.01 0.04 0.06 0.08

270.00 150.00 90.00 75.00 30.00

0.00 0.00 0.00 0.00 0.00

Table 2 Actual and measured value of real power in a three-phase circuit (phase displacement between V and I 5 308) Harmonic order

Pa

Pm (W)

(W)

8 bits

u%

10 bits

u%

12 bits

u%

Resol. `

u%

5 7 11 13 17

233.82 129.90 77.94 64.95 25.98

233.99 126.58 77.41 64.61 25.89

0.07 2.56 0.68 0.53 0.36

233.11 129.59 77.72 64.72 25.92

0.30 0.24 0.28 0.35 0.23

233.92 129.71 77.89 64.94 25.94

0.04 0.15 0.06 0.01 0.14

233.83 129.83 77.94 64.95 25.98

0.01 0.05 0.00 0.00 0.00

Table 3 Actual and measured value of real power in a three-phase circuit (phase displacement between V and I 5 608) Harmonic order

Pa

Pm (W)

(W)

8 bits

u%

10 bits

u%

12 bits

u%

Resol. `

u%

5 7 11 13 17

135.00 75.00 45.00 37.50 15.00

136.04 74.46 44.05 36.62 14.83

0.77 0.72 2.12 2.35 1.11

134.80 75.12 44.91 37.31 14.99

0.15 0.16 0.20 0.51 0.04

134.96 74.90 44.98 37.46 14.97

0.03 0.14 0.04 0.10 0.18

135.00 75.00 45.00 37.50 15.00

0.00 0.00 0.00 0.00 0.00

Table 4 Measured power and related uncertainty for different actual frequency values relating to the measured frequency 50 Hz Harmonic order

Pa

49.98 Hz

(W)

Pm (W)

u%

Pm (W)

49.99 Hz u%

Pm (W)

50.01 Hz u%

Pm (W)

50.02 Hz u%

5 7 11 13 17

90 50 30 25 10

89.74 49.59 30.16 25.04 10.05

0.29 0.82 0.53 0.16 0.50

89.86 49.79 30.08 25.02 10.03

0.16 0.42 0.27 0.08 0.30

90.22 50.13 29.92 24.94 9.97

0.24 0.26 0.27 0.24 0.30

90.30 50.43 29.83 24.96 9.94

0.33 0.86 0.57 0.16 0.60

L. Podesta` et al. / Measurement 32 (2002) 1 – 6

4

Fig. 1. Experimental set-up with power required by a three-phase non-linear inductive-ohmic load.

4. Measurement system realization

Table 6 Voltage sensor: Chauvin Arnoux DP25

4.1. Hardware The measurement system is realized (see Fig. 1) with a workstation based on: • a Pentium III processor; • two acquisition boards, National Instruments PCI6110E, each one with four analog inputs, 12 bit A / D converters, synchronous sampling and a maximum sampling rate of 5 MHz; • three current probes, Chauvin Arnoux A100 20– 200 A, accuracy 1% in all bandwidths (up to 20 kHz) and output impedance 1 kV; the other characteristics are reported in Table 6; • three voltage probes, Chauvin Arnoux DP25, accuracy 2% and output impedance 1 MV; the other characteristics are reported in Table 5.

4.2. Software The acquisition system was controlled by a Virtual Table 5 Current sensor: Chauvin Arnoux A100 20–200 A Rated current range

From 0.5 A to 20 A

From 20 A to 200 A

Ratio Output / input

100 mV/A

10 mV/A

Attenuation

3200

350

320

Input voltage range (DC1AC peak-to-peak)

1300 V

350 V

140 V

Instrument (written in graphical programming LabVIEW by National Instruments). The algorithm processing electrical quantities was written in HiQ (by National Instruments). Electrical quantities are provided as samples from the acquisition boards.

5. Experimental verifications The first verification was performed using two arbitrary waveform generators (Yokogawa FG320). These instruments generate signals (properly synchronized) reproducing the behaviour of a strongly distorted three-phase system. The three-phase power system was obtained considering the output signals of each channel as voltage values and related in phase current. Table 7 shows, for several harmonics present in the system, the actual real power Pe , the measured power Pm , the deviation d% in percentage and the uncertainty u% in percentage. Deviation and uncertainty have been determined relating to the actual

L. Podesta` et al. / Measurement 32 (2002) 1 – 6

5

Table 7 Experimental verifications. Measured power and deviation in percentage related to each harmonic present in a highly distorted three-phase signal system, supplied by two arbitrary waveform generators (Yokogawa FG320) properly synchronized Harmonic order

Harmonic in percentage related to the fundamental

Pa (W)

Pm (W)

d%

u%

5 7 11 13 17

50% 30% 20% 20% 15%

1.041 0.375 0.166 0.166 0.094

1.042 0.376 0.167 0.165 0.095

0.09 0.27 0.60 0.60 1.06

1.41 2.35 3.51 3.51 4.69

power supplied by the two-function generators having the following accuracy in the operating range: amplitude: 6(0.8% of reading 114 mV) frequency: 620 ppm phase resolution: 0.01 deg. An experimental set-up, shown in Fig. 1, has been realized. PZ4000 is the three-phase digital wattmeter Yokogawa, with an accuracy in the operating frequencies: 6(0.1% of reading 10.025% of range). The PC and the acquisition boards implement the measurement method. The non-linear load was realized by means of resistances and inductances on iron operating in saturation. Voltage adjustment was obtained by means of three resistances to obtain downstream a three-voltage system with deformation similar to the current system. In Table 8 the real power Pw shown by the wattmeter, the real power Pm measured using the proposed method, the deviation in percentage d% between the two values and the uncertainty u% are reported, for several harmonics. The power of the 13th and 17th harmonics is negligible, relating to the Table 8 Power measured by the digital wattmeter (Yokogawa PZ 4000) and power measured by means of the proposed method, relating to each harmonic present in a three-phase system supplying an ohmic-inductive non-linear load Harmonic order

Pw (W)

Pm (W)

d%

u%

5 7 11

16.35 4.93 0.14

16.15 4.63 0.17

1.22 6.08 24.43

0.81 1.42 43.64

total system power, causing values much lower than the measurement uncertainty. The value of the power Pm is very different from the value Pw , however it is inside the uncertainty range of the wattmeter relating to the chosen range. The total real power required by the load and shown by the wattmeter is 383.17 W and the value of the fundamental is 361.32 W. Furthermore the experimental set-up shown in Fig. 2 has been realized, including a PWM electronic drive with its brake, the Yokogawa digital threephase wattmeter and PC plus acquisition board implementing the measurement method. The electronic drive characteristics are as follows: Omron Sysdrive 3G3MVA4015: 380 / 460 VAC three-phase, 50 / 60 Hz, maximum allowed motor output 1.5 kW, PWM control, carrier frequencies from 2.5 to 10 kHz, resolution of frequency 0.01 Hz. It is possible to brake the motor injecting a DC current. In this way it is possible to control the motor during starting and braking with adjustable times. Motor: three-phase asynchronous squirrel-cage, 220 / 380 VAC, absorbed current 4.3 / 2.5 A, power in continuous operating mode 1.1 kW, rated frequency 50 Hz. The motor has a brake with DC supply provided by a generator supplied at 220 VAC, that produces a direct current, flowing through the motor braking electromagnets. Measurements have been compared with the Yokogawa wattmeter. Since the wattmeter provides voltage and current values for each harmonic, the current values have been considered, because the drive introduces a little harmonic contribution on the voltage and then on the power. Hence, in Table 9, only the values related to current are reported and not the ones referring to

L. Podesta` et al. / Measurement 32 (2002) 1 – 6

6

Fig. 2. Experimental set-up with the following load: an electronic drive, a three-phase asynchronous motor and a brake.

Table 9 Current measured by the digital wattmeter (Yokogawa PZ 4000) and current measured by means of the proposed method, relating to each harmonic present in a three-phase system with a PWM inverter. The rated line current is 0.880 A Harmonic order

Iw (A)

Im (A)

d%

u%

5 7 11

0.079 0.016 0.019

0.082 0.018 0.016

3.79 12.50 15.79

2.27 7.67 9.38

Several tests and measurements have been performed, to demonstrate the principle validity. The realized system can be used for the quality analysis of a supply system and it could be implemented in a compensation system for the improvement of power quality and the reduction of demand limit. In fact it is possible to act on the electrical system, harmonic by harmonic.

References power, because they are much lower than the measurement uncertainty. In Table 9 the current Iw shown by the wattmeter, the current Im measured using the proposed method, the deviation in percentage d% between the two values and the uncertainty u% are reported, for several harmonics.

6. Conclusions A new measurement system, based on a new principle for the determination of power, voltage, current and power factor for each harmonic present in a three-phase deformed power system, was realized.

[1] H. Swart, M.J. Case, J.D. van Wyk, On techniques for localization of sources producing distortion in electric power networks, ETEP 4 (6) (1994) 485–490. [2] N. Mohan, T.M. Undeland, W.P. Robbins, Power Electronics, John Wiley, New York, 1995. ` S. Sangiovanni, E. Zappitelli, Non-conventional [3] L. Podesta, technique for power measurement in three phase systems under non-sinusoidal condition, in: IMTC / 98, Maggio, St. Paul, Minnesota, 1998. ` S. Sangiovanni, E. Zappitelli, Misure di potenza [4] L. Podesta, sotto condizioni non sinusoidali per circuiti monofasi e trifasi, in: XV Congresso Annuale del GMEE, 16 Settembre, 1998, pp. 217–220. ` S. Sangiovanni, E. Zappitelli, Sistema di misura [5] L. Podesta, per circuiti trifasi in regime non sinusoidale, in: XVII Congresso Annuale del GMEE, 14–16 Settembre, 2000.