A Case Study: Optimization and Standardization of ...ijaerd.com/papers/special_papers/ME060.pdf · In IS 2062,2006[6] complete specification of hot rolled low, medium and hightensile

International Journal of Advance Engineering and Research Development

Scientific Journal of Impact Factor (SJIF): 4.72 Special Issue SIEICON-2017,April -2017

e-ISSN : 2348-4470 p-ISSN : 2348-6406

@IJAERD-2017, All rights Reserved 1

A Case Study: Optimization and Standardization of Conservator for Oil

Filled Power Transformer

Mr.Vishal M. Solanki1, Mr.Dhaval V. Patel2

1Assistant Professor, Department of Mechanical Engineering, Sigma Institute of Engineering, Vadodara 2Assistant Professor, Department of Mechanical Engineering, Nirma University, Ahmedabad

__________________________________________________________________________________________

Abstract: A transformer is a vital component in any industry. If the transformer fails, theelectric supply fails. So

it is very necessary that the transformer must work without anyinterruption. Transformer has many components

and all are essential for its smoothworking. So every component in transformer is critical. One of the critical

components is a Conservator. It acts as an oil reservoir, which allows expansion and contraction of

transformeroil to prevent the damage to the tank. So, the problem to optimizethe weight and also to reduce the

variety of the sizes available with the industry hasbeen taken. The problem has been solved and the design for

the same has beenoptimized for reduction in weight using classical optimization technique called

LagrangeMultiplier.

__________________________________________________________________________________________

Keywords: Conservator, Oil Filled Transformer, Optimization, Transformer, Lagrange Multiplier.

I. INTRODUCTION

Figure 1. Conservator

Conservator is a small tank fitted to the main oil tank. Its main purpose is toprovide extra space for the

change of volume of oil due to variations of temperaturedue to atmospheric changes and current _owing through

the winding. So, it is verycritical equipment which prevents the damage to the transformer main tank due to

thepressure rise resulted from change in density of insulating oil.Presently the industry is having many variety of

conservator which they have todesign according to the requirement. This is time consuming process, so

reduction andstandardization in variety is needed. Apart from this there is necessity to reduce weightof mild

steel used to reduce the overall cost of a transformer.The optimization of conservator considering the weight

reduction as criteria is to becarried out. Also the varieties of the conservator will be reduced by making designstandardize.

II. LITERATURE REVIEW

A conservator is very essential component of oil filled power transformer. The conservator is mounted on

the top of the transformer such that it would allow the oil to expand or contract without causing damage to the

tank. But when the transformer catches in fire, the oil is fed to the fire from conservator because of the gravity.

Mr.Thomas C. Lenox, the inventor from US, invented an alternative arrangement “conservator for liquid

International Journal of Advance Engineering and Research Development (IJAERD)

Special Issue SIEICON-2017, April -2017,e-ISSN: 2348 - 4470 , print-ISSN:2348-6406


immersed apparatus”[1] for transformer. He mounted the conservator vertically parallel to the tank. The top of

the conservator is always below the top cover of the transformer tank. This arrangement is useful for the control

of fire.

Another inventor Mr.Shinji NakazavaEtal from Japan had done very goodinvention for conservator. In his

patent “Conservator for oil immersed transformer”[2]he introduced an arrangement for prevention of moisture addition in thetransformer oil through the conservator. As the conservator is open to atmosphere toallow the

change in volume of transformer oil, the moisture from atmosphere is addedand it will affect the functionality of

transformer. So an oil-proof, gas-tight flexiblerubber bag is placed in the conservator. This bag allows the

expansion and contractionof oil and eliminates the direct contact of oil to the atmosphere. Now-a-days this bagis

known as an „air cell‟ in transformer industry.

Author S.S.Rao explained various optimization techniques for solving problem of optimization in

engineering practice in his book titled “Engineering Optimization - Theory and Practice”[3]. This is a very good

book of optimization. In this bookdetailed procedure of classical optimization techniques are explained. Various

classicaloptimization techniques are given which are very useful to solve optimization problemshaving different

conditions. Lagrange Multiplier technique to solve the problem ofmultiple design variables with equality

constraints is very accurate technique. Thistechnique may be applied on almost every optimization problem and gives satisfactoryresults.

“Manual on Transformers”[4]contains complete criteria to design the transformer according to various

Indian Standards. This book is very useful for transformerdesign in transformer industry. One can get idea about

complete procedure of erection,commissioning and maintenance of transformer.

Similarly the “Transformers”[5] published by BHEL, Bhopal is another good book on transformer. In this

book one can get practical knowledge as well as theoretical knowledge about the transformer. In this book one

learns about principles of transformer, material used in transformer, electrical accessories used in transformer,

cooling arrangement, design procedure, testing, standards used, erection commissioning and maintenance of a

transformer.

In IS 2062,2006[6] complete specification of hot rolled low, medium and hightensile structural steel is

given. From this various mechanical and chemical propertiesof steel of various grades used in industry can be

referred.

Insulating oil is the most essential part of any oil filled transformer. The quality of this oil must be

maintained according to standards. In India most of transformer industries follows IS 335 - 1993 “Insulating Oil

Specification”[7]. This standard gives complete specification of insulating mineral oil. In oil filled transformers,

oil is used according to the properties given in this standard.

“Standard terminology for power and distribution transformers”[8], standard terminology for power and

distribution transformers are given in this standard. This is known as IEEE C57.12.80 _ 2010.

III. METHODOLOGY

Two classical optimization techniques for solving problem of multiple design variableswith equality

constraint are applied.

By method of Lagrange Multipliers

By method of Constrained Variation

Among these two methods, Lagrange Multipliers is very effective method. It gives veryaccurate results.

Constraint Variation method is used in order to support the resultgiven by Lagrange Multipliers.

IV. IMPLIMENTATION OF WORK

The industry previously had 135 varieties of conservator. Then they revised list andreduced it to 59

varieties. But still the reduction in variety and optimization in weightis needed.

4.1. Material properties - According to IS:2062-2006




Table 1. Material Properties

Material of conservator Mild Steel

Density 7850 kg/m3

Grade St 42 W (Industrial Term)

E250 (According to IS 2062-2006)

Tensile Strength 410 MPa

Yield Stress 250 MPa (thickness <20mm)

240 MPa (thickness 20-40mm)

230 MPa (thickness >40mm)

Internal Bend Diameter 2 x Thickness (thickness <=25mm)

3 x Thickness (thickness >25mm)

4.2. Solution: By Lagrange Multipliers

Figure 2. Simplified Diagram of a Conservator

Where;

𝐷 = 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟𝑜𝑓𝑎𝐶𝑜𝑛𝑠𝑒𝑟𝑣𝑎𝑡𝑜𝑟

𝐿 = 𝐿𝑒𝑛𝑔𝑡𝑕𝑜𝑓𝑎𝐶𝑜𝑛𝑠𝑒𝑟𝑣𝑎𝑡𝑜𝑟

𝑇 = 𝑇𝑕𝑖𝑐𝑘𝑛𝑒𝑠𝑠𝑜𝑓𝐶𝑜𝑛𝑠𝑒𝑟𝑣𝑎𝑡𝑜𝑟𝑆𝑕𝑒𝑙𝑙 Consider,

𝐷 = 𝑥1

𝐿 = 𝑥2

𝑇 = 5𝑚𝑚

2𝑇 = 10𝑚𝑚

Design Variables:

𝑋 = 𝐷𝐿 =

𝑥1𝑥2

Objective Function: To minimize the weight

𝑊𝑒𝑖𝑔𝑕𝑡 = 𝜋 × 𝐷 × 5 × 𝐿 + 𝜋

4× 𝐷2 × 10 × 2

𝑓 𝑋 = 5 × 𝜋 × 𝐷 × 𝐷 + 𝐿 𝑓 𝑋 = 5 × 𝜋 × 𝑥1 × 𝑥1 + 𝑥2

Constraint:

𝑉𝑜𝑙𝑢𝑚𝑒 = 𝑣 =𝜋

4× 𝐷2 × 𝐿




𝑔 𝑋 = 𝑣 =𝜋

4× 𝐷2 × 𝐿

𝑔 𝑋 = 𝑣 =𝜋

4× 𝑥12 × 𝑥2

Lagrange Function is,

𝐿 𝑥1, 𝑥2, 𝜆 = 𝑓 𝑋 + 𝜆 × 𝑔 𝑋

The necessary condition to satisfy Lagrange Function is, 𝜕𝐿

𝜕𝑥1=

𝜕𝐿

𝜕𝑥2=

𝜕𝐿

𝜕𝜆= 0

By satisfying necessary condition, the optimum values are obtained,

𝑥1∗ = 2 × 𝑣

𝜋

1

3

𝑥2∗ = 16 × 𝑣

𝜋

1

3

𝜆∗ =

−20

2×𝑣

𝜋

1

3

𝑓∗ = 15 × 𝜋 × 2 × 𝑣

𝜋

2

3

Take value of „v‟ as unity. Now the sufficient condition is,

𝜕2𝐿

𝜕𝑥12

𝜕2𝐿

𝜕𝑥1𝜕𝑥2

𝜕2𝐿

𝜕𝑥1𝜕𝜆𝜕2𝐿

𝜕𝑥1𝜕𝑥2

𝜕2𝐿

𝜕𝑥22

𝜕2𝐿

𝜕𝑥2𝜕𝜆𝜕2𝐿

𝜕𝑥1𝜕𝜆

𝜕2𝐿

𝜕𝑥2𝜕𝜆

𝜕2𝐿

𝜕𝜆2

= 0

So the matrix will become,

−10𝜋 − 𝑧 −5𝜋 4𝜋1

3

−5𝜋 0 − 𝑧𝜋

2

1

3

4𝜋1

3𝜋

2

1

30

= 0

On solving above matrix, the optimum value of „z‟ becomes 6.28. As the value is positive, x1* and x2*

will give the minimum value of the function.

So,

𝐿

𝐷=

16

𝜋

1

3

2

𝜋

1

3

= 2

Now the L/D graph is,




Figure 3. L/D Vs. M/V Graph

Where,

M = Weight of a Conservator V = Inside volume of a Conservator

V. RESULTS AND DISCUSSION

Optimum length to diameter ratio of Conservator for minimum weight by keeping the inside volume

constant is „2‟. But due to maintain the electrical clearances to keep theconservator supporting structure size

less, it is not possible to take this ratio equal to „2‟ in actual practice.

Figure 4. Minimum Electrical Clearance in Air

As shown in figure 4; phase to phase clearance and phase to earth clearance areto be maintained.

The list of clearances according to various voltage classes is as given in table 2.




Table 2. Minimum Electrical Clearance in Air

By applying other technique of classical optimization “Constrained Variation” the same result is

obtained.

Now it is decided to take this ratio `2.5', `3' and `3.5' in actual and to prepare a standard for industry.

The conservator is vacuum and pressure tested at maximum of 0.11772 MPa. So, each conservator is

checked for maximum vacuum and pressure of 0.11772 MPa and found the hoop stress within the safe

limit of 162 MPa.

By applying same methodology, the variety of the conservator model has been reduced from 135 to 27,

which has helped the industry to save their expenses in managingvarious inventories.

VI. CONCLUSION

Optimum length to diameter ratio of Conservator for minimum weight by keeping theinside volume

constant is `2'. But due to maintain the electrical clearances to keep theconservator supporting structure size less,

it is not possible to take this ratio equal to`2' in actual practice. Now it is decided to take this ratio `2.5', `3' and

`3.5' in actualand to prepare a standard for company.

The industry previously had 135 varieties of conservator. Then they revised list and reduced it to 59

varieties. Now after this optimization and standardization, the _nalsizes of conservator are standardized and

reduced to 27 varieties.

An excel program for calculation of weight of conservator, conservator support,conservator supporting structure, oil in conservator and to check the shear stress ineach bolt of supporting structure is also prepared.

REFERENCES

[1] Thomas C. Lenox; “Conservator for liquid immersed apparatus” ; USPatent no.2622122; Year 1952.

[2] Shinji NakazavaEtal; “Conservator for oil immersed transformer”; USPatent no.3253081; Year 1966.

[3]Singiresu S. Rao; “Engineering Optimization - Theory and Practice”; Page no. 66-79; New Age International

Publications; Third edition,2010.

[4] “Manual on Transformers”; Central Board of Irrigation and Power, NewDelhi; March 2006.

[5] “Transformers”; Bharat Heavy Electricals Ltd, Bhopal; Tata McGrawHill Publications Ltd.; Second Edition

- 2002. [6] Ammendment 1- IS 2062,2006; “Hot rolled low, medium and high tensile structural steel”.

[7] IS 335 - 1993; “Insulating Oil Specification”.

[8] IEEE C57.12.80 - 2010; “Standard terminology for power and distribution transformers”.

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A Case Study: Optimization and Standardization of ...ijaerd.com/papers/special_papers/ME060.pdf · In IS 2062,2006[6] complete specification of hot rolled low, medium and hightensile