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Transmission planning studies in hydrothermal systems deal with complex issues. Two include 1) the need for a robust grid that can accommodate a large number of economic dispatch patterns caused by differing hydrological conditions in the river basins and 2) the high cost of grid reinforcements due to the large distance from hydro plants to load centers and the required N-l security criterion. It is thus necessary to consider the tradeoff between supply reliability and reinforcement cost. The resulting planning problem is formulated as a large-scale mixed integer nonlinear optimization model. The objective function is to minimize the sum of investment costs and expected load-shedding costs. The constraints include linearized power flow equations, limits on circuit flows for all combinations of economic dispatch points (which capture hydrological variation), and circuit contingencies (which capture supply reliability). This paper describes a new solution scheme for this problem that is based on two techniques: 1) the extension of a binary disjunctive technique, which transforms the integer nonlinear problem into a linear one and 2) screening strategies, which allow a judicious choice of contingencies and candidate circuits. Planning studies for Brazil and Bolivia are presented and discussed.