Industry standards also address the loss of life of a transformer due to temperature and aging. The relation of insulation aging to time and temperature follows the well-known Arrhenius chemical reaction rate model.
The adaptation used in the IEEE standard [3] has the following form. Per unit life = Ae^[B/(θH 273)] where θH winding hot-spot temperature in °C, and A and B are constants.
The meaning of per unit life is illustrated as follows: If per unit life = 2, then the transformer would be expected to last twice the ‘‘normal’’ life. If per unit life = 0.5, then the transformer would be expected to last only half the ‘‘normal’’ life. Normal life for most transformers is considered to be around 30 to 40 years.
The constants A and B depend on the types of material used to insulate the windings. Since cellulose in the form of kraft paper is the most common insulation material, these constants have been worked out empirically:
Per unit life = 9.8 10 18e15000/(θH 273) (3.14.2)
The winding hot-spot design temperature to attain a normal life is 110°C. This is based on an assumed ambient temperature of 30° plus the 65°C average winding temperature gradient over ambient plus a 15°C allowance for the hotspot gradient over the average winding temperature.
Using θH = 110°C yields a per unit life = 1. The aging acceleration factor FAA is the ratio of the per unit life at the design temperature of 110°C divided by the per unit life at some operating temperature θH. The constant A then divides out:
FAA = e15000/383 15000/(θH 273) = e39.16 15000/(θH 273)
To calculate the equivalent aging of the transformer FEQA with a varying hot-spot temperature such as occurs for a cycling load or a seasonal ambient temperature, FAA is integrated over time and the integral is divided by the total time to obtain the average.
The per unit life and FAA are plotted vs. hot-spot temperature in the chart shown in Figure below.
The per unit life and the aging acceleration factor as a function of
the hot-spot temperature.
It should be stressed that most transformer failures are random events that occur for various reasons besides insulation loss of life. Therefore, the formula for per unit life cannot be used as a predictive model to determine when a given transformer will ultimately fail.
However, it is indeed certain that overloading a transformer will shorten its life, so it is a good practice from a reliability standpoint to keep the loading within the transformer’s thermal capability.
