# dynamic model for the failure replacement of aging high voltage transformers

As the electric transmission system in the U.S. ages, mitigating the risk of high-voltage transformer failures becomes an increasingly important issue for transmission owners and operators. This paper introduces a model that supports these efforts by optimizing the acquisition and the deployment of high-voltage transformers dynamically over time. We formulate the problem as a Markov Decision Process which cannot be solved for realistic problem instances. Instead we solve the problem using approximate dynamic programming using three different value function approximations, which are compared against an optimal solution for a simpliﬁed version of the problem. The methods include a separable, piecewise linear value function, a piecewise linear, two-dimensional approximation, and a piecewise linear function based on an aggregated inventory that is shown to produce solutions within a few percent with very fast convergence. The application of the best performing algorithm to a realistic problem instance gives insights into transformer management issues of practical interest. In the 1960’s and 70’s, the electric power industry underwent a major expansion requiring a signiﬁcant investment in high-voltage transformers. This investment has produced an age distribution with a bubble of older transformers that will begin failing at a higher than average rate.

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