The search for more efficiency in the production of eletrical energy, has led several countries to re- structure their eletric sectors, traditionally under control of federal, or state governments like in England, in /spain, in New Zeland, in argentina, in Chile, in Peru (object of this work), and now in Brasil. In this new structure the profit of the private enterprises ough to go tied to the efficiency of their electric systems. This thesis introduces an alternative form for optimal operation planning, and for determination of dual variables that can be used as indicators for rate-schedule structures in hydrothermal systems based on graph theory. The main advantage are simplicity, and efficiency: the algorithm for optimal search in graph is 200 to 300 times faster than the general purpose methods of linear and non- linear optimization. The operations model of the hydrothermal system considers the hydraulic constraint, historical influx scenarius, and capacity expansion projects within the study horizon.