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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 of both the original already existing power transformers and the new parallel connected additional transformer. The independant 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 transformers and the new one. Any condition yielding overloading of either of them is to be excluded. The results will strongly depend on the electrical and magnetic loadings assumed. It is shown that for a certain value of the new transformer core flux density, an absolute minimum for the total substation annual cost exists, whereas increasing the current density will result a monotonous decrease of the objective cost function. The new method is applied to a practical example, and several checks for its validity are given.