A Comparative Investigation of Electromechanical Stresses on Transformers Caused by Inrush and

Short-Circuit Currents

Neves W., Fernandes Jr. D. Electrical Engineering Department

Federal University of Campina Grande Campina Grande-PB, Brazil

waneves@dee.ufcg.edu.br, damasio@dee.ufcg.edu.br

Baltar F. J. A. Electrical Operation Studies Department

CHESF Hydroelectric Company of San Francisco Recife-PE, Brazil

fbaltar@chesf.gov.br

Rosentino Jr. A. J. P., Saraiva E., Delaiba A. C., Guimares R., Lynce M., De Oliveira J. C. Faculty of Electrical Engineering Federal University of Uberlndia

Uberlndia-MG, Brazil arnaldo@ieee.org, elise.saraiva@yahoo.com.br, delaiba@ufu.br, ronaldoguimaraes@yahoo.com.br, lynce@ufu.br,

jcoliveira@ufu.br

Abstract This paper presents the mechanical effect on transformers when subjected to one of the power quality indicators, i.e., the electromagnetic transients. A common reason for internal faults in transformers windings is the weak insulation. This effect can be caused and accelerated by the electromechanical efforts produced by the inrush and short-circuit currents. Even though the transformer energizing is considered a normal operation, it produces high currents and this phenomenon significantly reduces the transformer life expectancy and may even lead to its instantaneous or timing destruction. Moreover, taking into account the same magnitude of current, the inrush currents can produce greater forces than those caused by short-circuit currents. Therefore, this papers aims to present and compare the electromechanical effects produced by the inrush and short-circuit currents in the transformers windings. To conduct this research, FLUX software in its 3D version, based on the finite element method (FEM) will be used. To highlight the overall model and the software performance, a laboratory 15 kVA transformer is utilized. It has been built with concentric double-layer windings and ferromagnetic core with three columns.

Keywords- Power quality, Inrush currents, Short-circuit currents, Three-phase transformers, Electromechanical efforts, Finite element method.

I. INTRODUCTION It is known that high magnitude currents that occur during

transformers energizing are caused by saturation of its ferromagnetic core. These high currents, called by inrush currents, can cause a variety of adverse effects on the electrical system supplier, as well as in the transformers, such as momentary voltage sags, harmonics, electromechanical stress in the winding transformers, insulation deterioration of conductors, incorrect operation of differential and overcurrent

relays, etc. Thus, this situation can affect the power quality supplied by the power system and thus reduce the transformer life.

In general, it is very difficult to note an electromechanical defect in the transformers windings, since even with the winding deformed, equipment can operate normally. However, the transformer winding with some defect becomes less robust, reducing the equipment life expectancy. Moreover, it is noteworthy that the frequent action of forces in the windings results in a cumulative phenomenon, reducing even more the mechanical supportability of the conductors.

The electromechanical stresses characteristics in the windings caused by inrush and short-circuit current are different. While the short-circuit current causes forces involving the various windings of the transformer, the inrush current involves only its energizing. The high inrush currents cause the core saturation as well its effective permeability reduction. Thus, the components produced by the leakage flux can be neglected, as well as, if existent, the currents in the secondary. Then, in the forces analysis under inrush conditions, only the field components produced by the currents in the conductors of the primary winding are considered [1].

The inrush currents, even with peaks 30% lower than those caused by short circuit currents can produce forces with amplitudes similar to those caused by short circuit. This is due to the exposure time of the inrush currents being considerably higher than the short-circuit current. Another fact to consider is that the presence of inrush current is much more frequent as this can be considered as normal service operation [2].

This paper will make an electromechanical stresses analysis that occur in transformers windings when they are subjected to the inrush and short circuit current. Subsequently,

978-1-4673-0378-1/11/$26.00 2011 IEEE

a laboratory 15 kVA transformer made of traditional ferromagnetic core with three columns and two concentric double layered windings will be modeled in flux 3D software package, based on finite element methods and it is a very well-known product offered by CEDRAT France. Two conditions will be analyzed, i.e., inrush and short-circuit situation. Thus, electromechanical forces produced by these transient currents will be confronted.

II. ANALYSIS OF ELECTROMECHANICAL EFFECTS IN TRANSFORMERS DUE TO INRUSH AND SHORT-CIRCUIT

CURRENTS

The occurrence of electromechanical forces in the transformers windings can be explained as shown in (1), which is based on the Lorentz force [3].

BJF = (1)

Where: J is the current density in A/m2 and B is the magnetic leakage flux density in T.

The main strengths are associated with the direction of leakage flux, that is, the flux density in axial and radial direction produces forces, respectively, in the radial and axial direction.

A. Radial Force The radial forces produced by the inrush currents stretch

the energized winding [3]. On the other hand, in short-circuit condition, the radial forces compress the inner winding and stretch the other one [4].

Fig. 1 illustrates the radial forces direction resulting from the inrush and short-circuit current.

Figure 1. Radial force direction in a transformer winding under inrush (a)

and short-circuit (b) current.

The occurrence of some radial defect in the inner winding is more common than in the outer winding [3], since the compressive forces on the inner winding can experience a force from the core and axial supports in the opposite direction. As only the short-circuit current causes this effect, transformer energizing does not cause such damage for the

winding, because in this case the winding will be under tensile forces. Fig. 2 shows typical deformations in the inner winding due to radial compressive forces that occur in the inner winding under short-circuit current [5, 6].

Figure 2. Typical deformations in the inner winding caused by radial forces.

B. Axial Force The axial forces produced by the short-circuit and inrush

current are similar, i.e., both compress the windings. The difference is that in the presence of short-circuit, both windings will be under this compressive force, while in transformer energizing only one. Fig. 3 shows this effect.

Figure 3. Axial force direction in a transformer winding under inrush (a)

and short-circuit current (b).

The axial force caused by the radial flux at the ends of the coils is directed toward the winding midpoint.

The axial forces due to inrush current are higher than those produced by short-circuit current (both effects at the same current). Note that the magnetic flux during transformer energizing is higher than that produced by short-circuit current, under the same induction [3].

However, in general, the inrush currents are much smaller than the short-circuit current. Thus, the forces due to inrush current, which are proportional to the square of current, will also be smaller. However, the major problem of axial forces caused by inrush current is due to the fact that the transformers are connected to the electrical system more frequently than the short-circuit occurs. Then, the repeated action of axial forces may result in the accumulation of residual deformations

This work was sponsored by CHESF - Hydroelectric Company of San Francisco.

(cumulative phenomenon) [1, 3]. Fig. 4 illustrates typical deformations in the winding due the axial force [7].

Figure 4. Typical deformations in the winding caused by axial forces.

III. COMPUTATIONAL SIMULATIONS This section presents the results of electromechanical

efforts produced in the windings of a laboratory transformer, through a computer simulation based on finite element method (FEM). The transformer will be submitted to the inrush and a three-phase short circuit current. The objective is to show that the inrush current can cause electromechanical forces higher than those due to short-circuit current when both effects are of the same current magnitude.

A. Transformer constructive characteristics The equipment used for the analysis was a three-phase

transformer, star connection, 15 kVA, with two double-layer windings per phase, each with a rated voltage of 127 V. Each winding has two layers with 33 turns which leads to a total of 66 turns per coil [8]. Fig. 5 presents an actual photo of the equipment without the tank. Fig. 6 shows some physical and geometrical characteristics of the modeled transformer.

Figure 5. Picture of the transformer without the tank.

Figure 6. Geometrical and physical characteristics of the transformer

analysed (dimensions in (mm)).

This transformer was chosen because all data were available to researchers, by direct access to the equipment as well as its complete project.

B. Transformer modeling using 3D finite element method Computer simulations were performed using the software

FLUX in its 3D version. This program has pioneered the development of formulations based on FEM. The FLUX basic modules include the preprocessing (geometry, definition of physical properties, and meshes), the processing (problem solving) and post processing to results analysis.

In this way, the model implemented in software is presented in Fig. 7. It can be noted that only a quarter of the transformer was considered. This technique is widely used in applications based on finite element method because it reduces the processing time of the simulation.

Figure 7. The transformer implemented in the FLUX3D.

Based on the geometrical and physical characteristics of the transformer, two conditions were simulated. The first one considers the transformer energizing, while the second one considers a balanced three-phase short-circuit condition.

C. Case 1: Transformer energizing simulation In this case, the simulation was performed by the outer

winding energizing. Fig. 8 presents the inrush current waveform obtained by the software. The peak occurred for the phase B equal to 514.63 A. So, all the results refer to this phase.

Figure 8. Inrush current waveform obtained by the FLUX3D.

Fig. 9 shows the leakage flux distribution for phase B for this condition. It can be seen that the highest intensity of the magnetic induction is found in a layer of the outer winding and in all inner winding (yellow intensity). It occurs because of the magnetic flux directed toward the iron core.

Figure 9. Leakage flux distribution in phase B by energizing the transformer

outer winding.

Fig. 10 shows the forces direction in the outer winding of the phase B. Note that, as expected the forces tend to stretch the winding. Although there is a high intensity of magnetic flux in the inner winding, the current is almost zero, therefore the forces can be neglected.

Figure 10. Forces direction in the outer winding of the phase B for

transformer energizing condition.

Table I summarizes some results of electrical, magnetic and mechanical parameters obtained in the phase B outer winding for transformer energizing condition. These values will be compared with the next case, i.e., the short-circuit condition.

TABLE I. ELECTRICAL, MAGNETIC AND MECHANICAL VALUES IN THE PHASE B OUTER WINDING FOR TRANSFORMER ENERGIZING CONDITION.

Variable Value Inrush current 514.63 A Axial magnetic field in the midpoint 119.76 x 10-3 T Radial force in the midpoint 33.49 N Mean radial force 523.0 N Radial magnetic field at the end 96.03 x 10-3 T Axial force at the end 36.35 N Total axial force 155.56 N

D. Case 2: Transformer under a balanced three-phase short-circuit In this case a balanced three-phase short-circuit in the

model was applied. However, the transformer was submitted to a short-circuit, where the peak in the phase B is the similar the inrush current. It was made in order to obtain results at the same reference. Fig. 11 presents the short-circuit current waveform obtained by the software. The peak value was equal to 514.67 A in the phase B. Similarly to the previous case, all results are referred to the outer winding in phase B.

Figure 11. Short-circuit current waveform obtained by the FLUX3D.

Fig. 12 illustrates the leakage flux distribution in phase B for the short-circuit condition. It can be seen that now the highest intensity for the magnetic induction is found between the windings (yellow intensity). This is the place where the greatest forces and electromechanical stresses are detected.

Figure 12. Leakage flux distribution in phase B in the outer winding for

transformer under three-phase short-circuit condition.

Fig. 13 shows the forces direction in both windings of the phase B. Note that, as expected that the forces compress the inner winding and stretch the other one.

Figure 13. Forces direction in both windings of the phase B for the

transformer under a balanced three-phase short-circuit.

Table II summarizes some results of electrical, magnetic and mechanical parameters obtained in the phase B outer winding for this analysis. Although, there are great forces in the inner winding, only the results in outer winding will be shown, in order to compare with those in previous case.

TABLE II. ELECTRICAL, MAGNETIC AND MECHANICAL VALUES IN THE PHASE B OUTER WINDING FOR TRANSFORMER UNDER A BALANCED THREE-

PHASE SHORT-CIRCUIT.

Variable Value Short-circuit current 514.67 A Axial magnetic field in the midpoint 125.89 x 10-3 T Radial force in the midpoint 35.77 N Mean radial force 534.13 N Radial magnetic field at the end 71.53 x 10-3 T Axial force at the end 28.4 N Total axial force 68.6 N

Table III shows the variation of the parameters between the both analyzed cases. Positive and negative results mean, respectively, an increase and a decrease of the variables, according to the difference between the inrush and short-circuit values.

TABLE III. PERCENTUAL DIFFERENCE OF THE VARIABLES BETWEEN THE TRANSFORMER ENERGIZING AND SHORT-CIRCUIT CONDITION.

Variable Percentual difference [%] Current -0.0078 Axial magnetic field in the midpoint -4.87 Radial force in the midpoint -6.37 Mean radial force -2.08 Radial magnetic field at the end +34.25 Axial force at the end +27.99 Total axial force +126.76

Note that the difference between the currents in the two

cases is small. In this way all results will have the same reference. Note that the radial forces due to inrush current experienced a slight reduction compared to those produced by short-circuit current. For example, at the midpoint of the winding, where the greatest radial forces are produced, a reduction of 6.37% was obtained. This small change was due to little change in the magnetic field in the axial direction, which at this point was 4.87%. Considering the mean radial force, the variation is even smaller, i.e., 2.08%. However, analyzing the results for axial forces, there is an increase in strength of approximately 28% at the end of the coil, where axial forces are the highest. This high variation was due to a great change in the magnetic field in the radial direction, which at the winding end was 34.25%. The variation is even more pronounced when comparing the axial forces directed to the midpoint of the winding. There is an increase of over 100% at this point. It is noteworthy that the total force for short-circuit condition, taking both windings, has been obtained in simulation with a value of 173.29 N. However, only 40% of this force (68.6 N) is concentrated in the outer winding. Consequently, a high variation in relation to the transformer energizing condition was obtained, as in this case, besides the radial component of magnetic field is exceeding the one in short-circuit condition, all the force is concentrated just in one winding.

IV. CONCLUSION This paper presented the differences between the electromagnetic forces imposed on the transformer windings due to one of the power quality indicators, i.e., the electromagnetic transients. The following steps were analyzed:

Characterization of the electromechanical effects that occur in the transformers windings when submitted to energizing and short-circuit current;

Computational modeling based on 3D finite element method. The equipment used was a laboratory transformer of the Federal University of Uberlndia;

Analyses of the radial and axial forces in the transformer windings caused by inrush and short-circuit current, through computer simulations.

It has been confirmed that the axial mechanical forces

caused by the inrush currents, at the same peak current, are higher than those caused by short-circuit current. It is noteworthy that transformers are frequently connected to the electrical power system, and the exposure time of the inrush currents is considerably higher than the short-circuit current. In this way, the importance of knowing the physical conditions of a given transformer arises, to prevent it from causing supply interruption of black-outs.

ACKNOWLEDGMENT This paper is a partial result of a Research and

Development project titled: "Electromechanical stress in transformer caused by the high inrush and short-circuit currents", managed by the Hydroelectric Company of San Francisco - CHESF, with support from the Federal University of Uberlandia - UFU and the Federal University of Campina Grande UFCG. Thus, the authors gratefully appreciate the Hydroelectric Company of San Francisco - CHESF for the financial support.

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