Life Estimation of Distribution Transformers Considering Axial Fatigue in Loose Winding Conductors

Life estimation of distribution transformers considering axial fatigue in loose winding conductors

N.S. Beniwala, , , , D.K. Dwivedib and H.O. Guptaa

a Electrical Engineering Department, Indian Institute of Technology Roorkee, Roorkee 247 667, India

b Mechanical and Industrial Engineering Department, Indian Institute of Technology Roorkee, Roorkee 247 667, India

Received 13 June 2010;  revised 28 September 2010;  accepted 28 September 2010.  Available online 10 October 2010.

Abstract

This paper presents an experimental study on axial fatigue behaviour of loose winding conductors of aluminum and copper wound distribution transformers. Algorithms are presented for estimating the life and switchings withstand capability of distribution transformers by considering axial fatigue in loose winding conductors. The life and switchings withstand capability of distribution transformers have been calculated by using experimentally determined results of fatigue life cycles of winding conductors corresponding to stress. The experiments were conducted considering wire sizes and other parameters of 25 kVA distribution transformers. The outcomes of this study can be used as a guide for designing and producing reliable distribution transformers by selecting suitable conductor diameter which may has better fatigue life cycles endurance capability. This study is useful especially for frequently energized distribution transformers having insignificant protection against cold load pick up and inrush current.

Keywords: Distribution transformer; Creep; Cold load pick up; Fatigue; Inrush current

Article Outline

1. Introduction2. Axial fatigue test setup and procedures

2.1. Axial fatigue test setup2.2. Test procedures

3. Results and discussion

3.1. Fatigue results3.2. Fatigue life estimation algorithm

3.2.1. Assumptions3.3. Discussion3.3.1. High voltage winding conductor material3.3.2. Stress

4. ConclusionsAcknowledgementsAppendix A. Mathematical formulation for calculation of stress on high voltage conductors [6]

A.1. Hoop stressA.2. Internal axial forceA.3. Maximum compressive forceA.4. Resultant stress

Appendix B. Sample calculations for fatigue life

B.1. Fatigue life estimation of aluminum wound distribution transformersB.2. Fatigue life estimation of copper wound distribution transformers

References

1. Introduction

In power deficient, poorly designed and haphazardly expanded power distribution networks, many distribution transformers (having insignificant protection against cold load pick up and inrush current conditions) are failing much before reaching their design life. In some of the areas of India, the failure rate of distribution transformers (DTs) is over 25% per year. In these areas, the power outage occurs frequently due to various reasons such as planned and unplanned load shedding, maintenance, extension works and faults. Thus, repeated energization of the DTs is required for power restoration in distribution networks which in turn causes frequent cold load pick up (CLPU) and inrush current conditions in the DTs. The CLPU condition is caused by loss of diversity among thermostatically controlled electrical devices during restoration of power in distribution networks. This condition produces a load current which may be several times higher than the normal value and persists for few minutes to several hours [1]. The inrush current generates during energization of the transformer due to magnetic saturation of the core containing residual flux. The inrush current is found to be non-sinusoidal in nature and its magnitude ranges from 10 to 20 times of the rated current [2]. Owing to the slow attenuation of the transients, the effects of inrush current may persist for several seconds before attaining the steady state condition [3].

The CLPU and inrush current cause electro-magnetic and thermal stresses on the high voltage (HV) winding conductors for long duration [4] and [5]. Earlier, the authors [6] have identified and reported the elongation in the HV winding conductors owing to creep as one of the reasons for failure of repeatedly energized DTs having insignificant protection against inrush current and CLPU. Also, the authors [7] have reported the assessment of life and switchings withstand capability of frequently energized DTs

considering the creep phenomenon in the HV winding conductors. The HV winding conductors may become loose due to creep or any manufacturing defect. These loose winding conductors are susceptible to fatigue due to electro-magnetic stresses of alternating nature.

Generally, the fatigue causes approximately 90% of all failures during service due to mechanical causes [8], [9] and [10]. The fatigue behaviour is affected by the material geometry and chemical properties, stress range, load frequency and atmospheric conditions [11], [12] and [13]. Many researchers have proposed the different theories to explain the fatigue phenomenon. Orowan [14] has explained the attaining of yield strength stresses under elastic loading conditions using model of plastic inhomogenity in an elastic surrounding. The repetition of loading leads to plastic deformation at the inhomogenity which in turn causes a crack to form. Freudenthal and Dolan [15] gave a model for crack formation by crumbling of crystallites. Shanley [16] proposed a model for progressive failure on slip planes as a consequence of the unbonding upon repetitive cycling. Marin et al. [17] presented a study on fatigue damage in wind turbine blades. Silva [18] presented a collection of various case studies on fatigue in engine pistons. Li et al. [19] proposed the assessment of fatigue life of a rubber mount by using finite element method and material properties. Petracconi et al. [20] simulated the fatigue life of a rear tow hook assembly of a passenger car. Leslie and Eliasi [21] estimated the fatigue life of a cannon barrel.

It is expected that fatigue may be one of the causes of failure of frequently energized DTs as all necessary conditions for fatigue in loose winding conductors exist under CLPU and inrush current conditions. The influence of the fatigue phenomenon on the life and switchings withstand capability of the DTs during service has not been appreciably reported in the literature. Therefore, in the present investigation attempts have been made to study the effect of cyclic stresses developed by electro-magnetic forces (due to CLPU and inrush current) on fatigue performance of aluminum (Al) and copper (Cu) wound DTs. Further, the fatigue in loose HV winding conductors has been related to failure tendency of DTs by calculating their life and switchings withstand capability. It is based on the theoretical analysis of fatigue performance and kinds of stress conditions generated due to frequent switchings of the DTs.

In this study, fatigue behaviour of the Al wire (electric conductor grade aluminum alloy 1350) of diameter 0.8 mm and electrolytic Cu wire of diameter 0.62 mm has been investigated. These wires are used as the HV winding conductor in the 25 kVA DTs. The chemical compositions of the wires under study are given in [Table 1] and [Table 2].

Table 1. Chemical composition of the aluminum wire (electric conductor grade aluminum alloy 1350) under study.

Content Fe Si Cu Mg Mn Cr Al

Weight% 0.23 0.11 0.03 0.01 0.01 0.01 99.6

Table 2. Chemical composition of the copper wire (electrolytic copper) under study.

Content Pb Ni Al Fe Cu

Weight% 0.004 0.016 0.006 0.004 99.97

2. Axial fatigue test setup and procedures

2.1. Axial fatigue test setup

An indigenously designed and fabricated system was used for fatigue studies of Al and Cu wires [22] and [23]. The fatigue test setup consisted of a speed controlled motor and an eccentric that is attached mechanically with the motor’s shaft. A circular disc was fixed with the eccentric through a rod with a ball bearing in between. The bearing was used for giving joggling free linear motion to the test wire. The circular disc was welded with a well finished pulley. The pulley was used for fixing upper end of the test wire. The test wire was wrapped over whole the diameter of the pulley before fixing at one end. The diameter of the pulley was kept large enough to eliminate the stress concentration at any point on the test wire.

The force on the test wire was applied on the lower end of the test wire through the dead-weights placed in a container having a lever arm. The weight of the container was also taken into account for calculating the force on the test wire. A platform with spring underneath was used for providing the zero stress on the test wire. The spring was immersed in damping liquid oil to reduce the jerks on the test wire when the wire was resting on the platform and again stressing from this position. The other end of the spring was fixed. Guidance (almost negligible friction with the spring) was provided to dead-weight container for making straight motion of the test wire. The schematic diagram of the axial fatigue test setup is shown in Fig. 1.

Fig. 1. 

Axial fatigue test setup: (a) Test wire at stressed position. (b) Test wire at zero stress position.

2.2. Test procedures

The test wires of Cu (diameter 0.62 mm) and Al (diameter 0.8 mm) of 150 mm length were taken for fatigue test. The force was applied on the lower end of the test wire using dead-weight. Tensile stress cycle was achieved by alternatively stressing and relaxing the test wire. The total weight (dead-weight and container’s weight) was taken corresponding to the calculated tensile stress which is produced in the DTs under inrush and CLPU conditions. The time up to the fracture of the test wire was recorded with the help of stop watch. The total fatigue life cycles (corresponding to the particular stress) till the fracture of the test wire were calculated by multiplying the speed of the eccentric with the time up to wire’s fracture. This procedure was repeated for both Al and Cu wires at different stress values and graphs between stress (S) and corresponding fatigue life cycles (N) were plotted.

3. Results and discussion

3.1. Fatigue results

The fatigue tests were performed on 150 mm long Al and Cu wires of diameter 0.8 and 0.62 mm, respectively which are used as the HV winding conductors in 25 kVA DTs.

Each test was carried out at constant axial tensile stress corresponding to the calculated values of stress produced on HV winding conductors of the DTs at different magnitudes of CLPU and inrush current. The mathematical formulae for calculating the magnitude of stresses under CLPU and inrush current conditions have been given in Appendix A. Analysis showed that the magnitudes of the stresses under severe CLPU and inrush current conditions are in range of 8–20 MPa.

The fatigue life cycles (N) for Al and Cu winding conductors have been determined experimentally corresponding to the particular stress (S) and S–N curves have been plotted accordingly (Fig. 2). The S–N curves can also provide the approximate value of the fatigue life cycles for stress between the stress ranges of S–N curve. These S–N curves can be used for estimating the fatigue life cycles of winding conductors for different values of the stress corresponding to various ratings of the DTs.

Fig. 2. 

S–N curves for: (a) Aluminum wire of 0.8 mm diameter. (b) Copper wire of 0.62 mm diameter.

3.2. Fatigue life estimation algorithm

The fatigue life of the DTs is hereby defined as the time taken by loose HV winding conductor up to fracture due only to axial fatigue. The fatigue life (TfL) of DTs can be calculated as given under the equation:

(1) where TfL is the fatigue life of the DTs, Nsn the fatigue life cycles corresponding to particular stress which is determined using experimentally obtained S–N curves and Nd is the number of fatigue cycles per day for which the particular stress conditions develop on the HV winding conductor.

The frequency of vibration of electro-magnetic stresses produced in the DT windings is twice of the applied power frequency. Thus, the average fatigue cycles per day (Nd) to which the HV winding conductors of DTs subjected to high stress during energization or switching can be estimated as follows:

(2)Nd=2×f×Ns×Tswhere Nd is the fatigue cycles per day to which the HV winding conductors subjected to high stress during energization, f the power frequency, Ns the number of energization of DTs per day and Ts is the duration per energization for which vibrations persist in the DTs HV windings.

The number of switchings of DTs per day may vary according to power distribution network conditions which in turn affect the DT’s fatigue life. The number of switchings which a DT can withstand before failure is constant because fatigue damage is a cumulative in nature. Therefore, in addition to the fatigue life, the number of switchings which a DT can withstand in the whole life (before fatigue failure) has also been estimated as given follows:

(3)NfL=TfL×Nswhere NfL is the switchings withstand capability of the DTs.

3.2.1. Assumptions

It has been observed in power deficient areas, poorly designed and haphazardly expanded power distribution networks that approximately 15 switchings of the DTs occur per day. During each switching, the vibrations in the HV winding conductors by the CLPU and inrush current may be assumed to damp out approximately in 3–4 s. The vibrations are significant only in the early phase of CLPU and inrush current. In this study, the duration of the vibrations has been taken 3 s. By considering the axial fatigue under such conditions, the sample calculations of fatigue life and the switchings withstand capability of the 25 kVA DTs at different stress values have been given in Appendix B and the results are summarized in Table 3.

Table 3. Life and switchings withstand capability of distribution transformers considering axial fatigue in loose winding conductors.

S. no.

Stress (MPa)

Fatigue life TfL (years) of DTs

Switchings withstand capability NfL (numbers) of DTs

Al wound DTs

Cu wound DTs

Al wound DTs Cu wound DTs

1 8 2 12 10,950 66,300

2 10 1.5 11 8700 64,125

3 12 1 10.5 5850 60,675

S. no.

Stress (MPa)

Fatigue life TfL (years) of DTs

Switchings withstand capability NfL (numbers) of DTs

Al wound DTs

Cu wound DTs

Al wound DTs Cu wound DTs

4 14 0.75 10 4125 57,675

5 17 0.5 9.5 2400 53,400

6 19 0.25 9 1050 50,400

7 20 0.13 8 705 48,300

3.3. Discussion

From Table 3, it is evident that the life and switchings withstand capability of the DTs are significantly affected by the fatigue in the loose HV winding conductors. In the present study, the calculated fatigue life and switchings withstand capability of the DTs does not include the time elapsed in loosening of the HV winding conductors. The life of the DTs depends upon the number of switchings per day but the switchings withstand capability of DTs before failure is constant due to cumulative nature of fatigue.

The fatigue life cycles for winding conductors corresponding to particular stress can be predicted between stress ranges of the experimentally determined S–N curves. The S–N curves of the winding conductors may therefore be incorporated during design for producing trustworthy DTs of improved life by choosing winding conductors of higher fatigue stress cycles endurance capacity.

The effect of the HV winding conductor material and the stress on the life and switchings withstand capability of DTs considering axial fatigue has been discussed in the following sections:

3.3.1. High voltage winding conductor material

The life of the DTs is found proportional to the fatigue life cycles of the HV winding conductors. The fatigue life of Cu wound DTs has been found more than Al wound DTs. At higher stress, the life of the Cu wound DTs has been determined to affect lesser than Al wound DTs (Table 3). For example, at stress of 8, 12 and 20 MPa, the life of Cu wound DTs are 6, 10, and 61 times, respectively more than Al wound DTs. The switchings withstand capability of the DTs considering axial fatigue is found to be in the same proportion as their fatigue life.

3.3.2. Stress

The fatigue life cycles of the winding conductors reduce by increasing magnitude of axial tensile stress (Table 3). The effect of axial tensile stress on the life of the DTs can easily be observed from the Table 3. For example, the life of Al wound DTs reduces by approximately 25% and 48% by increasing the stress from 8 to 10 MPa and from 19 to 20 MPa, respectively. The life of the Cu wound DTs decreases only by about 8% and 11% by increasing the stress from 8 to 10 MPa and 19 to 20 MPa, respectively. These facts suggest that at higher stress levels, the fatigue life of Al wound DTs reduces more drastically than Cu wound DTs.

A fatigue failure is very dangerous as it occurs without any obvious warning. The fractured surface due to fatigue often appears to be quite brittle, with very slight deformation occurring before fracture. Specimens loaded to failure in static tension shows substantial deformation before fracture but a specimen fractures under repeated loadings displays very small overall deformation. The SEM images of some of the fatigue fractured surfaces of the Cu and Al wires under study have been shown in [Fig. 3] and [Fig. 4], respectively. It can be observed that the fracture surface is usually normal to the direction of the principal tensile stress. The crack forms at a nucleus, such as an internal flaw or metallurgical discontinuity, and continues to grow during the repetition of loading with very little plastic deformation. Eventually, the crack grows to such an extent that the stress is significantly amplified by the reduced cross section, and unstable crack growth (fracture) occurs. The EDAX analysis showing chemical composition of the fractured surfaces of the wires under study has been shown in [Fig. 5] and [Fig. 6].

Fig. 3. 

SEM images of fatigue fractured surfaces of copper wire under study.

Fig. 4. 

SEM images of fatigue fractured surfaces of aluminum wire under study.

Fig. 5. 

EDAX analysis of fatigue fractured surface of copper wire under study.

Fig. 6. 

EDAX analysis of fatigue fractured surface of aluminum wire under study.

The literature also reveals that the Al and Cu have no endurance limit i.e., the stress below which no fatigue fracture can take place. Hence, fatigue failure in Al and Cu can occur at any stress level. Therefore, fatigue in loose HV winding conductors can cause failure of the DTs even in their normal operating conditions. However, the time required to fail may be large enough under such operating conditions due to low magnitude and duration of stress developed on the HV winding conductors. The effect of fatigue on the life of the DTs during short circuits can also not be ignored but such occurrences are very less in life time of the DTs.

4. Conclusions

This paper has presented estimation of the life and switchings withstand capability of distribution transformers by considering axial fatigue in loose HV winding conductors. The distribution transformers considered under study were operating in power deficient areas, poorly designed and haphazardly expanded power distribution networks. And, these transformers had inadequate protection against cold load pick up and inrush current. Following conclusions can be made from the present investigation:

i. The effect of fatigue in loose winding conductors has been investigated on failure tendency of the aluminum and copper wound 25 kVA distribution transformers.

ii. The life and switchings withstand capability of the distribution transformers considering fatigue have been estimated lesser than their designed life.

iii. Both the life and switchings withstand capability of distribution transformers considering fatigue depend upon the winding conductor material in terms of fatigue life cycles.

iv. The magnitude and duration of the stress experienced by the loose winding conductors influence the performance of the distribution transformers.

v. The fatigue causes failure of the aluminum wound distribution transformers earlier than copper wound distribution transformers of the same kVA ratings.

vi. The fatigue life cycles of winding conductors can be found from the experimentally determined S–N curve corresponding to the particular stress. Thus, S–N curves of the winding conductors may also be included at the design stage to decide the conductor diameter for having more fatigue stress cycle survival potential. This will help in manufacturing the reliable distribution transformers of enhanced life.

Acknowledgement

The authors wish to thank Mr. Pradeep Kumar, MIED, IIT Roorkee for help and suggestions throughout the experimental work.

References

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Appendix A. Mathematical formulation for calculation of stress on high voltage conductors [6]

The winding conductors of the transformer are subjected to stress which are placed in magnetic leakage flux. According to Fleming’s left-hand rule, these stresses act perpendicular to the current and leakage flux. If the current in the winding conductors has the same direction then they get attracted otherwise these are repelled from each other. For a two winding core type transformer having concentric winding, the stress on winding conductors due to cold load pick up and inrush current can be calculated as follows:

A.1. Hoop stress

Hoop stress is a mechanical stress which acts circumferentially i.e., perpendicular both to the axis and to the radius of the conductor.

(A1) where Iph is the per phase current, Rdc the DC resistance of winding, hw the window height and Zpu is the per unit impedance of winding.

K for , K for and is the asymmetric factor whose value is decided on the basis of X/R ratio with reference to IS: 2006, part -1-1977, Clause 16.11.2.

A.2. Internal axial force

Axial forces may bend the winding conductors in vertical direction which in turn increase the pressure on spacers between windings. It can be calculated as follows:

(A2) where Sn is the kVA rating of the DT. The negative sign indicates that force is acting towards the center of the winding.

A.3. Maximum compressive force

The compressive force on the winding conductors can be calculated as follows:

(A3) where A is the total supported area of the radial spacer (in cm2).

A.4. Resultant stress

The maximum value of the hoop stress is two times of the mean value and it is on the inner layer of the high voltage windings. Therefore, the resultant stress on the conductor of the inner layer of most stressed winding can be calculated as follows:

(A4) where 40 kg/cm2 is the tightening force.

The resultant stress due to CLPU current on the inner layer conductors of high voltage windings of the 25 kVA DTs have been calculated between 8 and 20 MPa.

Appendix B. Sample calculations for fatigue life

B.1. Fatigue life estimation of aluminum wound distribution transformers

At stress 8 MPa

Nsn ≈ 3.27 × 106, Ns ≈ 15

Nd ≈ 2 × 50 × 15 × 3 ≈ 4500

(B1)

(B2)

B.2. Fatigue life estimation of copper wound distribution transformers

at stress 8 MPa

Nsn ≈ 1.99 × 107, Nd ≈ 4500, Ns ≈ 15

(B3)

(B4)

Corresponding author. Tel.: +91 9415 179843; fax: +91 1332 273560.

Engineering Failure AnalysisVolume 18, Issue 1, January 2011, Pages 442-449