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Due to the increasing demand for electrical energy, the transmission capacity of existing power transformer substations must be correspondingly increased to prevent their overloading. This paper represents a new method for the optimal expansion for such substations. The optimized objective function includes the total annual cost for the original already existing transformers and the new parallel connected additional transformer. The independent variables for the optimization process are the power rating and the main geometrical dimensions of the new transformer. These variables affect not only the electrical parameters of the new transformer, but also govern the load-sharing between the original and new transformers. Any condition yielding overloading of either of them is to be excluded. The results will strongly depend on the assumed electrical and magnetic loadings. It is shown that for a certain value of the new transformer core flux density, an absolute minimum for the total annual substation cost exists, whereas increasing the current density will result in a monotonous decrease of the cost function. The new method is applied to a practical example, and several checks for its validity are given.