چنانکه بیان فرموده اند، منظور از k واحد سنجش دمای کلوین است و چون صحبت از افزایش دما است، می توان آنرا درجه سانتیگراد نیز در نظر گرفت.
میزان توان نامی یک ترانس بر حسب مقادیر فوق تعریف می شود. با عدول از این مقادیر عمر بخشهای مختلف ترانس کاهش می یابد. در جدول زیرضرایب باردهی ترانس به ازای گرادیانهای دمایی مختلف نشان داده شده است.
به دلیل ارتباط فاکتورهای فوق با سلامت ترانس و طول عمر آن، می باید در تنظیمات حفاظتی و هشدار دهنده ترانس ملحوظ گردند. در زیر شرحی بر این موارد بر گرفته از کتب مرجع آمده است.
For normal ambient conditions, which are defined in IEC 60076-2, as air never below -25˚C and never hotter than +40˚C, not exceeding +30˚C average during the hottest month and not exceeding +20˚C yearly average, or water never exceeding 25˚C at the inlet to oil/water coolers, permitted temperature rises are as follows:
Temperature rise of top oil 60 K
Average winding temperature rise by resistance
– for transformers identified as ON.. or OF.. 65 K
– or transformers identified as OD.. 70 K
No tolerances are permitted on the above values.
In all except the smallest transformers cooling of the oil will be by some external means, tubes or radiators mounted on the side of the tank, external banks of separate radiators or even oil/water heat exchangers. If the oil is required to circulate through these coolers by natural thermosiphon, that is,
ON.. type cooling is employed, then a fairly large thermal head will be required to provide the required circulation, possibly of the order of 25 K. If the oil is pumped through the coolers, that is, OF.. or OD.. type cooling is employed, then the difference between inlet and outlet oil temperatures might be, typically,
10–15 K. Thus temperatures within designs of each type of transformers, using the second of the two alternative derivations identified above, might typically be:
The setting of alarms is dependent on local ambient and loading conditions, but is usually based on the EN maximum oil temperature rise of 60˚C. Alarm thermometers, which depend upon oil temperature, might be set at 85˚C and 90˚C respectively to take account of the inherent time lag between maximum and top oil temperatures. Winding temperature indicators, which more closely follow variations of winding temperature, are used for all large transformers and might have a warning alarm set at 105˚C and a trip at 110˚C: these values are similarly subject to local ambient and loading conditions. It must be borne in mind that there will be a temperature gradient between the actual maximum temperature of the copper conductors and that registered in the top of the oil, the former, of course, being the higher. This accounts for the differences suggested between the permissible continuous temperature and the alarm temperatures.
Protection settings may be set to a lower level than the recommended permanent settings for the initial energization.
In all of the foregoing discussion load capability has been related to hot-spot temperature. The effect on hot-spot temperature at rated load of variation in ambient is simple to deduce; one degree increase or reduction in ambient will result, respectively, in one degree increase or reduction in hot-spot temperature.
The question which is less simple to answer is, how does hot-spot temperature vary with variation in load at constant ambient? To consider the answer to this it is necessary to examine the thermal characteristics of a transformer.
Hot-spot temperature is made up of the following components:
- Ambient temperature.
- Top oil temperature rise.
- Average gradient.
- Difference between average and maximum gradient of the windings.
In IEC 76 the last two terms are on occasions taken together to represent maximum gradient. Maximum gradient is then greater than average gradient by the ‘hot-spot factor’. This factor is considered to vary between 1.1 for distribution transformers to 1.3 for medium-sized power transformers. The last term thus varies between 0.1 and 0.3 times the average gradient.
Effect of load on oil temperature rise
Mean oil rise is determined by the dissipation capability of the cooling surface and the heat to be dissipated. The heat to be dissipated depends on the losses.
At an overload k times rated load the losses will be increased to:
Fe + k2
where Fe and Cu are the rated no-load and load losses respectively.
As the excess temperature of the cooling surface above its surroundings increases, cooling efficiency will tend to be increased, that is the oil temperature will increase less than pro rata with the increased losses to be dissipated. This relationship may be expressed in the form:
is the oil temperature rise, with suffixes 1 and 2, respectively, indicating the rated and the overload conditions.
IEC 76, Part 2, which deals with temperature rise, gives values for the index x which are considered to be valid within a band of +/-20% of the rated power, these are:
0.8 for distribution transformers having natural cooling with a maximum rating of 2500 kVA.
0.9 for larger transformers with ON.. cooling.
1.0 for transformers with OF.. or OD.. cooling.
The inference to be drawn from the above values is that with OF.. and OD.. cooling, the coolers are already working at a high level of efficiency so that increasing their temperature with respect to the surroundings cannot improve the cooler efficiency further.
Effect of load on winding gradients
The heat transfer between windings and oil is considered to improve in the case of ON.. and OF.. transformers for increased losses, that is the increased heat to be dissipated probably increases the oil flow rate, so that the winding gradient also increases less than pro rata with heat to be dissipated, which is, of course, proportional to overload factor squared. IEC 76, Part 2, gives the following values:
is the winding/oil differential temperature, or gradient, with additional suffixes 1 and 2, respectively, to indicate the rated and overload conditions.
The index y is then:
1.6 for ON.. and OF.. cooled transformers.
2.0 for OD.. cooled transformers.
IEC 76, Part 2, places limits on the accuracy of the above as within a band of
+/-10% of the current at which the gradient is measured; however, it does state that this limitation, and that placed on the formula for extrapolation for oil temperature indicated above, should be applied where the procedure is used for the evaluation of test results subject to guarantee. In other circumstances the method may give useful results over wider ranges.
The above method may be used to estimate the hot-spot temperature of a 30/60 MVA, 132/33 kV ONAN/ODAF transformer when operated at, say, 70 MVA. The transformer has losses of 28 kW at no-load and load losses of 374 kW on minimum tapping at 60 MVA. On temperature rise test the top oil rise was 57.8°C and the rise by resistance was LV, 69.2°C, HV, 68.7°C on minimum tapping. The effect of changes in ambient can also be included. Let us assume that the ambient temperature is 10°C.
The transformer temperature rise test certificate should indicate the value of the mean oil rise and the winding average gradients. If this information is not available, for example if no temperature rise test was carried out, these values will have to be estimated. Top oil rise at 60 MVA can be measured by a thermometer placed in the top tank pocket. Oil temperature rise on return from the cooler can be similarly measured at the tank oil inlet. Mean oil temperature rise is the average of these two figures. Let us assume that either from the test certificate or by measurement, mean oil rise is found to be 49.8°C. Then,
By reference to above Table, it can be seen that this overload may be carried for up to one and a half hours per day with the remainder of the time at a load which is low enough to cause minimal loss of life. Alternatively, provided this daily overload is only imposed for a matter of a few weeks, normal load may be carried for the remainder of the day with only negligible loss of life.
Normally a transformer such as the one in the above example would have pumps and fans controlled from a winding temperature indicator which would mean that these would not be switched in until a fairly high winding temperature was reached; however, if the overload is anticipated, pumps and fans can, with advantage, be switched in immediately. This will delay the time taken to reach maximum hot-spot temperature and, although cooler losses will be incurred, these will to some extent be offset by the lower transformer load loss resulting from the reduction in winding copper temperature.