Lifetime characterization via lognormal distribution of transformers in smart grids: design optimization

In this paper, the problem of the optimal rating of transformers in smart grids is properly discussed with respect to the specific load characteristics. The design is based on the accurate prediction of the lifetime degradation of mineral-oil-immersed transformers subject to highly intermittent loads. In fact, by investigating the nature of the loads in the smart grid scenario, it clearly appears that the intermittent nature of the power demand increases drastically. In this context, specific tools for the characterization of the lifetime duration are required, since severe reduction of the transformer’s life can be observed due to overloads, even in the case of short-duration overloads. The classical approaches based on using the equivalent thermal current to predict the transformer’s lifetime might result in incorrect estimates, thus requiring advanced models that can deal with the time variability of the load. In this paper, the randomness of the load powers is addressed in terms of stochastic processes. In particular, the Wiener process is demonstrated to provide robust modeling of load variability. By starting from this assumption, it was demonstrated analytically that the hot-spot temperature, which is a major contributor to the degradation of the transformer’s lifetime, also is a stochastic process. Then, in spite of the nonlinearity of the thermal model, the hot-spot temperature can be represented as a Wiener process, the robustness of which has been verified adequately. By taking into account the nonlinear relationship between the hot-spot temperature and the lifetime, the authors verified that the transformer’s lifetime is modeled as a lognormal, stochastic process. Hence, a novel, closed-form relationship was derived between the transformer’s lifetime and the distributional properties of the stochastic load. The usefulness of the closed-form expression is discussed for sake of design, even if a few of the considerations also are performed with respect to operating conditions. The aim of the numerical application was to demonstrate the feasibility and the easy applicability of the analytical methodology.