# Contributions concerning the oscilloscopic method, for checking the clock-hour figure of the vector group of a three phase, 50 VA electric transformer.

I. Introduction

To identify the clock-hour figure of the vector group, for the group of connections of a three-phased transformer, the literature presents the voltmeters (the electricians), the phase indicator, the DC power supply and, the oscilloscopic method [1], [4]-[6]. In this paper our attention is focused on the last method.

The oscilloscopic method principle is based on the comparison of the primary voltages oscillograms with the second one, measured between the homologous terminals [1]. Also, it includes the identification of the phase difference between the curves corresponding to the two voltages. Figure 1 presents an experimentally fitting necessary for a proper investigation of oscilloscopic method principle.

The stand above includes the verified transformer, three measuring instruments for voltage, an autotransformer and an oscilloscope, useful to visualize the waveforms of compared voltages.

In this case, the waveforms of the two voltages are in opposition of phase. The phase difference between primary voltage and secondary, homologous, is in the clock-hour figures of the vector group 6.

II. THEORETICAL ASPECTS FOR THE CLOCK-HOUR FIGURE IDENTIFICATION

The clock-hour figure of the vector group of a power transformer can be expressed by a mathematical model [1], [2], represented as appropriate, by a code matrix or by a code equation given as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (2)

where [[eta].sub.jk] designate the electrical signals, which according to the polarity, are denoted by "0", "1" or "-1"; [M.sub.100], [M.sub.10], and [M.sub.1] represent the matrices of following configuration.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (3)

In (2), sgn T = 1, when the transformer T does not reverse the polarity pulse applied to the input, sgn T = -1, when the transformer T reverses the polarity pulse applied to the input and, sgn T = 0, when the transformer T blocks the transmission of the pulse applied to the input.

The smaller equivalent schemes and the phase diagrams, corresponding to the possible 12 clock-hour figures of the vector group, are shown in Fig. 2. Based on these findings, it is concluded that, any three-phased transformer may be represented by a modelling scheme, consisting of nine transformers with a single-phase, connected properly [1], [2], [7].

The conclusion that the phase difference [phi], which corresponds to a clock-hour figure of the vector group, can be obtained by a simplified scheme, consisting only of three transformers, equivalent with one of the outputs ab, bc, ca, can be reached by complete equivalent diagram mentioned above (extended--Fig. 3).

In [1] the author explains how the wiring diagrams for the transformers were obtained.

III. CONTRIBUTIONS TO THE OSCILLOSCOPIC METHOD PRINCIPLE

Considering a multiple switch with 12 positions and multiple sections, which makes all the 12 schemes, presented in the Fig. 2, it is possible to obtain, at the output, a voltage which has a different phase from the supply voltage of the transformer group, with an angle [phi]. This angle corresponds, depending on the position of the switch, to one of the 12 possible clock-hour figures of the vector group.

In Fig. 4 we present a schematic diagram of a device in order to identify the clock-hour figure of the vector group, for a three-phased transformer [3]. This is designed based on the oscilloscopic method principles and no less important on the compensation method principles.

The device for identifying the clock-hour figure of the vector group, for the three-phase transformer (Fig. 4 and Fig. 5) consists mainly of group transformers 1, composed on three single-phase transformers [T.sub.a], [T.sub.b], [T.sub.c].

The transformer connections are modified using a switch with 12 positions and several sections. The phase equilibrium of the tensions obtained at the switch output (2) and, at the homologous terminals of the tested transformer 5, is compared with a phase discriminator 4 and a null indicator 6.

In another version, the device for identifying the clock-hour figure of the vector group for a three-phase transformer can be made by replacing the phase discriminator mentioned above, by a two-channel oscilloscope. If, when we start the experiment, the two compared voltages are not in phase (Fig. 6), we will have to successively modify the switch position, until the two oscillograms overlap (Fig. 7).

In the mentioned situation, the number indicated on the knob switch with 12 positions, represents the searched clock-hour figure of the vector group. The installation used to investigate this version is presented in Fig. 8.

This installation is achieved, as can be seen in Fig. 8, in a group transformer, a transformer verified, a multiple switch with 12 positions and an oscilloscope, necessary to compare the waveforms of the voltages from those two transformers.

IV. CONCLUSIONS

The solution presented in this paper leads to a considerable simplification of the oscilloscopic method, which, although bears the name used in the literature, does not use an oscilloscope, considered expensive and complicated.

By using the proposed solutions we obtain a higher precision of the measurements, limiting the risk of errors, which can occur in case of small phase displacements. Obviously, the risk of error increases when the two curves of checked voltage have different variation laws.

Another important aspect refers to easily accessible and low-cost components, used to achieve the described installations.

http://dx.doi.Org/10.5755/j01.eee.19.8.1929

Manuscript received June 18, 2012; accepted September 17, 2013.

This research was funded by the project "Progress and development through post-doctoral research and innovation in engineering and applied sciences-PRiDE--Contract no. POSDRU/89/1.5/S/57083 ", project co-funded from European Social Fund through Sectorial Operational Program Human Resources 2007-2013.

REFERENCES

[1] D. Cernomazu, Etudes sur le modele mathematique de l'indice horaire d'un transformateur triphase. Editions de l'Universite Suceava, 1997, p. 149.

[2] C. Prodan, "Theoretical and experimental contributions regarding the connections and the groups of connections at the electric force transformers", Ph.D. dissertation, Dept. Elect. Faculty of Electrical Engineering and Computer Science, "Stefan cel Mare" Univ., Suceava, Romania, 2008.

[3] D. Cernomazu, C. David, M. R. Milici, L. D. Milici, M. Rata, I. Nitan, "Aparat pentru identificarea indicelui orar la transformatoarele electrice", Bulletin Oficial de Proprietate Industriala, OSIM Bucursti, no. 2, p. 47, 2012.

[4] R. Radvan, B. Dobrucky, M. Frivaldsky, P. Rafajdus, "Modelling and Design of HF 200 kHz Transformers for Hard- and Soft- Switching Application", Elektronika ir Elektrotechnika (Electronics and Electrical Engineering), no. 4, pp. 7-12, 2011.

[5] M. Jamali, M. Mirzaie, S. Asghar Gholamian, "Calculation and Analysis of Transformer Inrush Current Based on Parameters of Transformer and Operating Conditions", Elektronika ir Elektrotechnika (Electronics and Electrical Engineering), no. 3, pp. 17-20, 2011.

[6] A. Koochaki, S. M. Kouhsari, G. Ghanavati, "Transformer Internal Faults Simulation", Advances in Electrical and Computer Engineering, no. 2, pp. 23-28, 2008.

[7] D.Cernomazu, Ph. Delarue, M. R. Milici, "Le schema equivalent pour la modelisation de la matrice de code de l'indice horaire d'un transformateur triphase", Analele Universitatii "Stefan cel Mare" Suceava Anul III--Editura Universitatii Suceava, no. 5, pp. 39-49, 1996.

C. Prodan (1), D. Cernomazu (1), V. Chatziathanasiou (2)

(1) Department of Electrotechnics, Faculty of Electrical Engineering and Computer Science, "Stefan cel Mare" University of Suceava, University St. 13, 720229 Suceava, Romania

(2) Faculty of Engineering, School of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki 541 24, Greece

cristinap@eed.usv.ro
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