Victor Manuel Jimenez-Mondragon, Juan Carlos Olivares-Galvan, Eduardo Campero-Littlewood ,

Jose Luis Hernandez -Avila, Rafael Escarela-Perez

Departamento de Energia Universidad Autonoma Metropolitana-Azcapotzalco,

Mexico, D.F.

Salvador Magdaleno-Adame

Instituto Tecnologico de Morelia Morelia, Mexico.

e-mail: smagdalenoa@hotmail.com

e-mail: vmjm@correo.azc.uam.mx

Abstract—This article analyses and presents an economic

evaluation of the impact in load losses of anti-theft metal ducts

(throats) in the low-voltage side of pole-mounted single phase

distribution transformers. Anti-theft throats are used to cover

the low voltage bushings to eliminate the possibility of an

unwanted connection to the transformer terminals. The results

presented are based on simulations, performed with a

commercial finite element program, to quantify losses caused

by currents induced in the anti-theft duct of a 167-kVA

distribution transformer. The results show that when the anti-

theft throat is added: (i) The load losses are increased and (ii)

the operation cost of the transformer is increased.

Keywords-Transformer, anti-theft duct, load losses, economic

evaluation, finite element method.

I. INTRODUCTION

The generation, transmission and distribution of electricity involve losses. While the losses involved in generation can be defined technically, transmission and distribution losses cannot be quantified precisely [1]-[3]. This is because electricity theft is present in some networks. The electricity consumption due to theft is interpreted as non-technical losses. These losses affect the quality of electricity supply, increase the load to the generating stations and have an impact in tariffs that affect the consumers who pay for the service, or in the case of governmental subsidies reduce the funding for other public services

Non-technical losses related to theft of electricity occur due to different reasons: consumers deliberately try to deceive the utility tampering the meter; illegal lines and connections bypass meters so that consumption remains unregistered; when customers systematically do no pay their arrears over a long period of time (often not recognized as no-technical losses) and last there can be billing irregularities [2], [4]-[5].

Non-technical losses caused by electricity theft comprise one of the main concerns of electric energy suppliers. This problem occurs mainly in less developed countries but also in developed countries such as USA and UK [4]. Specifically, high rates of electricity theft have been reported in developing countries where, on average, non-technical losses are 20% to 30% of the total energy generated.

Today, in some pole- mounted distribution transformers, a throat (metal part of the same material of the transformer tank but usually with reduced thickness) is used to cover the low voltage bushings to eliminate the possibility of electricity theft by consumers who make illegal connections to the distribution system. Authors have knowledge that these throats have been used only in single-phase transformers, and there is no information of its use in three phase transformers.

In distribution transformers, the load losses are a component of parasitic losses in the tank which surrounds the bushings [6]-[7]. This effect can be neglected in the high-voltage side, but in the low-voltage side the currents are high, and due to the proximity of the conductors to the tank wall, have a significant impact on the load losses [8]-[9].

The eddy currents in low frequency devices, like distribution transformers, are induced in conductive materials (tank wall and throat) due to variation of the magnetic field over time [6]. These currents generate power losses by joule effect.

In this work, the transformer in study (of 167 kVA), is simulated using the finite element program ANSYS Maxwell v15. This program allows visualization of magnetic fields and current density induced in materials conductive. This program includes a port-processor which can compute the eddy currents losses in the transformer tank and throat.

We performed a harmonic analysis. In this type of analysis currents induced by a sinusoidal current excitation in metallic structures of electromagnetic devices are calculated. To calculate the losses in the transformer tank and throat, eddy current analysis to nominal frequency (60 Hz, in the case of Mexico) is performed.

Finally, a techno-economic analysis is performed to obtain the increase in the cost of operation of the distribution transformer throughout its life-time, due to eddy currents losses in the anti-theft throat.

II. 3D MODEL

The Finite Element Method (FEM) allows finding the solution to the eddy current problem in transformers tanks, which use the formulation of magnetic and electric potential to solve the electromagnetic problem [10]-[11].

ANSYS Maxwell v15 finite element program was used to determine the eddy currents in the transformer with and

Induced Current in Anti-Theft Ducts of Pole-mounted Distribution

Transformers

2012 Andean Region International Conference

978-0-7695-4882-1/12 $26.00 © 2012 IEEE

DOI 10.1109/Andescon.2012.46

141

2012 Andean Region International Conference

978-0-7695-4882-1/12 $26.00 © 2012 IEEE

DOI 10.1109/Andescon.2012.46

167

without throat. Fig. 1 and Fig. 2 show the geometry of 167 kVA transformer, with the throat in the low-voltage side.

Figure 1. Plan view of the transformer tank with anti-fraud throat (all distances are in mm).

The thickness of the transformer tank is 2.28 mm and the thickness of the throat is 1.9 mm. The conductivities and relative permeability for the materials used are: 5.8x107 S/m and �r=1 for copper conductors and 5x106 S/m and �r=500 for carbon steel tank and throat. The bushings diameter is 3.6 cm. The three holes in the transformer tank and the bottom hole of the throat were modeled using polygons of 24 sides. The tank was modeled using a polygon with 48 sides. The low-voltage conductors have a diameter of 11.938 cm.

Figure 2. Top view of the transformer throat (all distances are in mm).

The boundary conditions at the exterior surface of the

finite element model can be specified with a zero tangential magnetic field condition. However, the direct modeling of eddy current regions leads to very expensive finite element meshes and simulation time increases, since the skin depth of massive conductors is small compared with the thickness of both the tank and throat transformer. In carbon steel the skin effect factor is 1.3 mm for this reason was convenient to work with impedance boundaries [12]-[15].

In the impedance boundary a relation between the tangential magnetic field component H and the electric field E is established, using the analytic solution of the field distribution in a semi-infinite conductor bar. The implementation of this approach is done relating the tangential component Hst with the tangential component Est at the eddy-current region surface using [9]:

( )st s stZ= ×E n H (1)

Where: s

1 jZ

σδ

+= y n is a unit vector normal to the

surface of the conductor bar. The use of impedance boundary conditions requires that

the material surface is covered by finite elements which considerably reduces the simulation time on the analysis of eddy currents in a three dimensional model.

An impedance boundary was applied to the model. The eddy currents losses are obtained by [16]:

8r o

érdidas st

S

P dsωµ µ

σ= � �

stH H (2)

Where Hst

* is the conjugate of the tangential component of the magnetic field intensity, μr the relative permeability, �0 the vacuum permeability, � the electrical conductivity and � the angular frequency. The integration of (2) on the tank wall and throat, give us the total eddy current losses.

The three dimensional model of the tank front wall and

the throat of the distribution transformer analyzed in this paper is shown in Fig. 3.

Figure 3. Three dimensional model of the transformer tank with anti-fraud throat.

Fig. 4 shows the finite element mesh consisting of 275,818 elements. The height of the transformer tank is 60 cm.

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A peak nominal current at low-voltage conductors of 1968.11 A was used in the simulations.

(a)

(b)

Figure 4. Element finite mesh: a) tank wall, b) anti-fraud throat

III. EDDY LOSSES CALCULATION USING FEM

Several simulations were performed using ANSYS

Maxwell v15 to determine parasitic losses in the distribution transformer tank with and without throat. The results considered a single-phase distribution transformer of 167 kVA: a) The transformer tank without throat, b) the transformer tank with anti-fraud throat.

Fig. 5 and Fig. 6 show the magnetic field intensity distribution on the transformer tank and throat. Fig. 5 shows that the maximum magnetic field intensity is located around the low-voltage bushing holes. A maximum intensity value of 1.5x104 A/m was calculated around the two holes of 3.6 cm of diameter where the conductors are carrying currents. Total losses on the tank wall calculated by (2) were 380.77 W.

Figure 5. Magnetic field intensity distribution in the transformer tank

(A/m).

Fig. 6 shows that the concentration of magnetic field

occurs around the hole in the bottom of the throat. A maximum intensity value of 1x104 A/m was obtained. As can be seen this value is two thirds of the maximum intensity around the bushing hole. Even though, the two conductors that go through the throat hole have the same current circulating in opposite direction, the resultant flux intensity

is different from zero due to the fact that current trajectories are not the same in reference to the hole edges.

Figure 6. Magnetic field intensity distribution near the bottom throat hole (A/m).

Fig. 7 shows the magnetic field intensity distribution inside of the transformer throat.

Figure 7. Magnetic field intensity distribution inside of the transformer throat (A/m).

A maximum magnetic field intensity value of approximately 0.8x104 A/m is calculated in front of the throat. In the outer parts are values of 7x102 A/m. A maximum value of losses of 1.94x104 W/m2 is located around the low-voltage holes. The total losses on the throat are 41.54 W and it was calculated by (2). Table I shows the calculated losses in the transformer tank and throat. It can be seen that the losses in the throat are a significant percentage of total loss (9.83%). The losses in the tank wall are a 90.16% of total losses.

TABLE I. TOTAL LOSSES WITH ANTI-FRAUD THROAT

(kVA) Tank loss

(W)

Throat loss

(W)

Total loss

(W)

167 380.77 41.54 422.31

Note: Total loss= Tank loss + throat loss

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IV. COST COMPARISON OF EDDY CURRENT LOSSES WITH

AND WITHOUT THROAT

From the results of the simulations for the 167 kVA transformer, a techno-economic analysis was performed to evaluate the feasibility of a throat manufactured with a suitable plastic material. The use of plastic material allows zero losses in the transformer throat and prevent heating problems in the transformer. Also prevent the electricity theft in the distribution system.

Table II shows the results of operating cost by eddy current losses in the transformer with and without throat.

TABLE II. LOSS COST WITH AND WITHOUT TRANSFORMER THROAT.

(kVA) Load loss

(W)

CL

(US$)

167

Without

throat With

throat

Without

throat

With

throat

380.77 422.31 1530.69 1697.68

The parasitic losses cost are calculated with

CL= B*LL (3)

where B=US$4.02/W (load loss cost rate) which are current values for Mexican utilities [17]; LL= is the transformer load loss, CL ($) is the cost of transformer losses throughout the transformer lifetime considering 25 years. Readers con find B for 26 countries in [18].

The increase in the losses cost due to throat for the transformer is US$166.99. This is a significant amount to find a plastic material having a durability equivalent to the transformer lifetime. It is important that the plastic chosen for the throat has duration of 25 years with exposure to the same environmental conditions of the transformer. Further, the authors recommend the use of resistant plastic that can withstand a possible case of electricity theft.

V. CONCLUSION

Electricity theft is an issue of interest around the world. For this reason, many countries are implementing preventive measures to reduce electricity theft. An alternative to prevent illegal connections of consumers to the low voltage bushings is to use an anti-theft transformer throat.

The analysis in this paper compares the eddy current losses with and without transformer throat in pole-mounted single-phase distribution transformers. The technique selected to evaluate the losses was the finite element method. The losses obtained with the finite element simulations for the 167 kVA transformer show that with the throat the eddy current losses are increased by 9.83%.

The authors recommend using plastic material in the throat to eliminate the eddy current losses. The cost of plastic to create the throat should be less than the cost of reduced losses in the throat.

REFERENCES

[1] R. Depuru, and L. Wang, “Electricity theft: Overview, issues, prevention and a smart meter based approach to control theft," Elsevier., Energy Policy 39, pp. 1007-1015, 2011.

[2] R. Depuru, L. Wang, V. Devabhaktuni, and N. Gudi “Measures and Setbacks for Controlling Electricity Theft”

[3] L. J. Hernandes Jr., L. C. Duarte, F. O. Morais, E. C. Ferreira, J. A. Siqueira, “Optimizing the Inspection Routine for the Detection of Electrical Energy Theft in AES Eletropaulo in São Paulo, Brazil," WSEAS Transactions on Power Systems, issue 2, Vol. 7, pp. 81-89, April 20011

[4] M. M. Badjian, J. NAgi, S. K. Tiong, K. S. Yap, S. P. Koh, and F. Nagi, “Comparison of supervised learning techniques for non-technical loss detection in power utility”.

[5] S. Nunoo and J. Attachie, “A methodology for the design of an Electricity theft monitoring system," Journal of Theorical and

Applied Information Technology, Vol. 26, No. 2, pp. 112-117, April 2011.

[6] I. Nathan and J.P.A. Bustos., Electromagnetics and Calculation of

Fields, Springer-Verlag New York, Inc, 1992. [7] J. C. Olivares-Galván, P. S. Georgilakis, and R. Ocon-Valdez, “A

review of transformer losses," Elec. PowerCompon. Syst., Vol. 37, No. 9, pp. 1046-1062, Septembre 2009.

[8] D. H. Kim, and S. Y. Hahn, “Improved design of cover plates of power transformers for lower eddy current losses," IEEE Trans.

Magnet., Vol. 35, No. 5, pp. 2529-3531, September 1999. [9] Juan C. Olivares-Galvan, Salvador Magdaleno-Adame, Eduardo

Campero-Littlewood, Rafael Escarela-Perez, and Pavlos S. Georgilakis, “Techno-economic evaluation of reduction of low voltage bushings diameter in single-phase distribution transformers," Electric Power Components and Systems, 39:1388–1402, 2011.

[10] O. Bíro and K. Preis, “On the use of the magnetic vector potential in the finite element analysis of three-dimensional Eddy currents," IEEE Trans. Magn., 1989, Vol 2, pp. 3145-59.

[11] N. A. Golias, C. S. Antonopoulos, T. D. Tsiboukis and E. E. Kriezis “3D Eddy currents computation with edge elements in terms of the electric intensity," Int. Journal for computation and mathematics in

electrical and electronic engineering (COMPEL), MCB university

press, Vol. 1, No. 5/6, pp. 667-673,1998. [12] R. V. Sabariego, P. Dular, C. Geuzaine, and J. Gyselinck, “Surface-

impedance boundary conditions in dual time-domain finite-elements simulations," IEEE Trans. Magnet., Vol. 46, No.8, pp.3524-3531.August 2010”

[13] J. Sakellaris, G. Meunier, C. Gurin, and J.C. Sabonnadiere, ‘‘Application of the impedance boundary condition in a finite element environment using the reduced potential formulation," IEEE Trans.

Magn., vol. 27, no. 6, pp. 5022---5024, Nov. 1991. [14] S. A. Holland, G. P. O’Connell, and L. Haydock, “Calculating stray

loss in power transformers using surface impedance with finite elements," IEEE Transactions on Magnetics, Vol. 28, No. 2, March 1992, pp.1355-1358.

[15] D. Rodger and H. C. Lai H. ‘‘A surface impedance method for 3-D time transient problems," IEEE Trans. Magn., vol. 35, no. 3, pp. 1369---1371, May 1999.

[16] R. M. Del Vecchio, B. Poulin, P. T. Feghali, D.M. Shah, and R. Ahuja, Transformer Design Principles. Taylor & Francis, New York, NY, 2002, pp. 412-418.

[17] J.C. Olivares-Galván, de F. León, P. S. Georgilakis, and R. Escarela-Perez, “Selection of copper versus aluminum windings for distribution transformers," IET Elect. Power Appl.Vol. 4, No. 6, pp. 474–485, 2010.

[18] R. Baehr, “Transformer technology state-of-the-art and trends of future development," ElectraNo. 198, October 2001.

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