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Anonymous Poster #1

# How to Calculate Transformer Temperature Rise

06/06/2011 8:25 PM

Can anyone provide me with the calculation for transformer temperature rise?

I understand that I2R is one of the main factors to determine this parameter but again, for every ventilation ducting that i create between the windings will reduce the temperature significantly which means that this factor plays an important role to reduce the temperature rise.

Thank you in advance.

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#1

### Re: How to Calculate Transformer Temperature Rise

06/06/2011 11:59 PM

Yes. Maybe.

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#2

### Re: How to Calculate Transformer Temperature Rise

06/07/2011 1:04 AM

Please, you are confusing two issues here. The capacity design, cooling design and protection design of a transformer are all different issues that are separately delt with. There are three losses in a transformer as follows: 1) Iron Losses (Pi). 2) Copper Losses (Pc). 3) Eddy current losses. The third can be reduced by good design of the magnetic circuit. The three are the major determinant of TX design. What you are doing now is designing the cooling system of your TX, the losses in the TX remains the same, the heat extraction can be reduced by providing more cooling fins. DICKSON.

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#3
In reply to #2

### Re: How to Calculate Transformer Temperature Rise

06/07/2011 2:22 AM

Pardon me, but i always thought that the losses are (A) Iron losses consisting of (a1) Hysteresis losses and (a2) Eddy current losses, and (B) Copper losses. Hysteresis is minimised by using good magnetic material like silicon steel, while eddy currents are reduced by using laminated cores.

Temperature rise is due to these losses all right, but then the rise depends on how effectively the heat is dissipated using conduction, convection and radiation. Forced convection sometimes.

i have not come across any simple formulae, but have seen expensive FEA packages which are used for this analysis.

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#4
In reply to #3

### Re: How to Calculate Transformer Temperature Rise

06/07/2011 3:19 AM

GA for me.

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#5

### Re: How to Calculate Transformer Temperature Rise

06/07/2011 4:38 AM

The temperature rise of a transformer is due to the power loss dissipated by the transformer in the form of heat. The power loss of a transformer consists of core loss and of winding coil losses.

Core losses:

Significantly contribute to the temperature rise of a transformer. Hysteresis loss, eddy current loss and residual loss all contribute to the total core loss.

Winding coil losses:

Contribute to a transformer's total loss. Copper losses (I2R losses) are easy to understand.Winding coil losses due to skin effect, proximity effect, effect of eddy
currents in the windings, effects from fringing flux intersecting windings near the core gap, edge effects and extraneous conductor effects may be significant and should be considered. For simplicity, we'll ignore these additional winding losses and consider only I2R copper losses.

The resistance of each winding can be calculated by multiplying the mean length turn of the winding by the copper resistance for the appropriate wire size and by the total turn count.
Rp or Rs= MLT * RCU * N
Where:
Rp = primary coil resistance in Ω
Rs = secondary coil resistance in Ω
MLT = mean length turn in cm
RCU = copper resistance in μΩ/cm
N = turn count

The copper losses for each winding are calculated with the following
formula:
Pcu = I2 R
Where:
Pcu = copper loss in watts
I = current in amps
R = resistance in Ω

Sum the primary and all the secondary winding losses to obtain the total winding losses, and then sum the total winding losses with the core losses to obtain the total transformer losses (PΣ).

Temperature rise of a transformer is hard to predict with precision. One approach is to lump the winding losses together with the core losses and assume that the thermal energy is dissipated uniformly throughout the surface area of the core and winding assembly at all ambient temperatures. This isn't a bad assumption, because
the majority of the trans-former's surface area is ferrite core area rather than
winding area, and the thermal conductivity of ferrite (~40 mW/cm/°C) ispoor at any temperature. With these assumptions, the temperature rise of a transformer can be estimated by the following formula:

ΔT = (PΣ/AT)0.833

Where:

ΔT = temperature rise in °C.

PΣ = total transformer losses (power lost and dissipated as heat) in mW;

AT = surface area of transformer in cm2.

The exponent (0.833) used in the above formula to estimate temperature rise has been derived from empirical data with the use of the following formula:

x=ln(PΣ@1stΔT/PΣ@2ndΔT)/ln(1stΔT/2ndΔT)

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#6
In reply to #5

### Re: How to Calculate Transformer Temperature Rise

06/08/2011 1:36 AM

Resistance of copper winding will also increase with temp. Rt=Ro(1+alpha(delta t)), where Rt is resistance at temp. t, alpha is the coefficient of temp. ( for copper ) & delta t is increase in temp. Though alpha is again temp. dependent but for the permissible operating temp. range of copper winding, same is very neglible & can be considered constant for all practical purposes.

Thus as winding temp. rises, resistance also increases resulting in further increase in power loss ( Isquared r). Simultaneously the rate at which heat is being dissipated also increases, due to increase in difference of temp. between winding & surrounding. This makes it very difficult to exactly predict thermal behaviour.

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#9
In reply to #6

### Re: How to Calculate Transformer Temperature Rise

06/08/2011 2:08 AM

Winding losses also vary with loading level:

About 90%of the load losses as measured by short circuit test are due to I2R losses in the windings.
They vary with the square of the current and also with winding temperature.
Load Losses = [(Per Unit Loading)2 X Load Losses at full Load X {(F+Top)/(F+Tref)}]

F = Temperature coefficient = 234.5 for Copper and 227 for Aluminium.

Tref = 75 °C usually, or as prescribed in the test certificates

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#7

### Re: How to Calculate Transformer Temperature Rise

06/08/2011 1:54 AM

The temperature rise of any electrical equipment depends on method of cooling. There are numerous methods of cooing the equipment. First one should have the knowledge of the losses and their distribution (how much loss is generated in which part.). Then one should know what is the type of insulation in each part of the active material is used in the design. This would decide the permissible temperature of the part. Then depending upon the various ambient conditions (like maximum ambient temperature, cooling water temperature, etc.) permissible temperature RISE can be arrived at. Then the process of design of cooling system can be taken up. As other replies have stated, knowledge of iron losses and the copper losses is the starting point.

Do you intend to design the cooling system for an existing transformer or want to know the process followed by the designer? If you want to design the cooling system for the existing transformer, then knowledge of existing cooing ducts, (number and size), dimensions of tank, and lot more information would be required.

If one is not aware about the type of losses generated in transformer, then it would be prudent to leave this work to the specialist in the field

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#8

### Re: How to Calculate Transformer Temperature Rise

06/08/2011 2:04 AM

thank you very much to all of you for helping me out on this issue.

As i understand, the formula provided by Ninu for temperature rise which i believe have not taken into the consideration of winding ductings. if i want to further reduce the temeprature rise by adding ventilation ductings where appropriate within the windings, how can i incorporate this factor into the formula to provide the final temperature rise of the transformer..or is there another formula for such calculation

?

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#10

### Re: How to Calculate Transformer Temperature Rise

06/08/2011 5:17 AM

Consider these facts Steven.

I wanted to demonstrate the effect of cooling on an electric three phase motor to some students struggling with ratings. I drilled a hole in the cast iron casing of a 0.55 kW motor and connected it to the compressed airline at 100 psi. We overloaded the motor with a generator and load bank to twice it's nominal rating, it didn't get slightly hot.

We were given a 40% increase in transformer rating by ABB after fitting fans at the base of the cooling fins. Large distribution trandformer have several ratings for natural oil circulation, forced air and pumped oil.

A few watts generated inside a pile of straw, wood or coal will accumulate and burst into flame in what is known as spontaneous combustion. Put a blanket around your PC and it will last just a few hours.

It's all a matter of how quickly you can get rid of the heat.

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#11
In reply to #10

### Re: How to Calculate Transformer Temperature Rise

06/08/2011 6:23 AM

EngineerTony,

i agree with your comment. However, without carrying out actual test on the transformer in-order to know the temperature rise, is there any way we can pre-determine the temperature rise of a transformer during design stage.

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#12

### Re: How to Calculate Transformer Temperature Rise

06/08/2011 2:21 PM

Hi Steven,

So complex, you would be calculating the heat produced by the above losses, pretty straightforward result in watts. Then what? Finally all this heat is going to the air because the frame, windings, stampings, even oil, settles at a steady working temperature for a given load.

So given the specific heat of air, i.e. joules per degree per kg (or other units), you could calculate how much air needs to come in at the ambient temperature and go out at some higher temperature. This is so complex, convection through a certain air duct, I have seen formulas for natural convection, say a light bulb, a cooker element, but a vented box or set of vanes, bit tricky. Maybe you could get some radiation loss to add in as well, that's even more complex.

Somewhere there are guidelines for dry and oil-filled transformers, no need to go to first principles, manufacturers worldwide are doing this. If this is a college project I would lose the teacher in complex maths, but give a general approximate design guide, if it's real life I would buy from a reputable manufacturer.

Last point, I2R is the main factor with modern magnetic materials and it is what it says current squared times the resistance of the copper winding(s), just like any resistance it produces watts, which is a waste of heat and a loss for the power company.

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#13
In reply to #12

### Re: How to Calculate Transformer Temperature Rise

06/08/2011 8:10 PM

hi engineerTony,

appreciate very much for the comments and recommendations. will consider. thanks

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#14

### Re: How to Calculate Transformer Temperature Rise

06/09/2011 12:21 PM

Mr. Chang, it's none of my business but why do you want to know the effects of ducts on transformer temperature rise?

If you are working for a transformer manufacture, you should have formulas and curves for ducts.

If you don't work for a transformer manufacture, then you are going to have SEVERE problems when you try to have the transformer manufactured and tested.

Above said, there is considerable difference in the design procedure for liquid cooled transformers, air/gas cooled transformers, forced liquid cooled transformers and forced air cooled transformers.
What type transformer are you interested in?

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#15
In reply to #14

### Re: How to Calculate Transformer Temperature Rise

06/09/2011 10:46 PM

Hi Mr. Carl Pugh,

i am working for a LV transformer manufacuring company and we manufacture dry type transformers from 5kVA to 500kVA mainly for OEM where clients will provide their design specificaitons and we produce accordingly. there are times that the tested result did not meet the design specificaitons and found that the specificaiton provided is incorrect like air ducting channels size was wrongly specified..and it is usual that client do not provide their calculations to us. this is for me to precheck the design.

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#16
In reply to #15

### Re: How to Calculate Transformer Temperature Rise

04/22/2013 2:09 AM

Hi

Hope you have managed to find some answers by now. I need your help with the formula to calculate Winding temperatures in a Layer wound Transformer. Taking into consideration the effect of ducts as well. Thank you

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### Comments rated to be Good Answers:

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### Users who posted comments:

Arham (1); ashoktoshniwal (1); Carl Pugh (1); Dickson (1); engineertony (2); Kudzanai (1); kvsridhar (1); lyn (1); pcchatur (1); Steven Chang (4); Vinu_Answers (2)

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