Smart grids have been constructed so as to guarantee the security and stability of the power\ngrid in recent years. Power transformers are a most vital component in the complicated smart grid\nnetwork. Any transformer failure can cause damage of the whole power system, within which the\nfailures caused by overloading cannot be ignored. This research gives a new insight into overload\ncapability assessment of transformers. The hot-spot temperature of the winding is the most critical\nfactor in measuring the overload capacity of power transformers. Thus, the hot-spot temperature\nis calculated to obtain the duration running time of the power transformers under overloading\nconditions. Then the overloading probability is fitted with the mature and widely accepted Weibull\nprobability density function. To guarantee the accuracy of this fitting, a new objective function is\nproposed to obtain the desired parameters in the Weibull distributions. In addition, ten different\nmutation scenarios are adopted in the differential evolutionary algorithm to optimize the parameter\nin the Weibull distribution. The final comprehensive overload capability of the power transformer is\nassessed by the duration running time as well as the overloading probability. Compared with the\nprevious studies that take no account of the overloading probability, the assessment results obtained\nin this research are much more reliable.
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