Short-term energy storage systems, e.g., batteries, are becoming one promising option to deal with flexibility requirements in power systems due to the accommodation of renewable energy sources. Previous work using medium-and long-term planning tools has modeled the interaction between Short-term energy storage systems and seasonal storage (e.g., hydro reservoirs). Despite these developments, opportunity costs considering the impact of short-term energy storage systems signals in stochastic hydrothermal dispatch models have not been analyzed. This paper proposes a new formulation to include short-term energy storage systems operational decisions in a stochastic hydrothermal dispatch model, which is based on Linked Representative Periods approach that allows an analysis of both short-and long-term storage at the same time. This represents the main contribution in this research because it uses intra-and inter-period dual information from the energy storage balance constraint, which has not been proposed before and it is not possible in the classic Load Duration Curve model. This advantage is also reflected in the case study results. For instance, the proposed Linked Representative Periods obtains operating decisions of short-term energy storage systems with errors between 5% to 10%, while the classic Load Duration Curve approach fails by an error greater than 100%. Moreover, the Load Duration Curve model cannot determine opportunity costs on an hourly basis and underestimates the water value by 6% to 24% for seasonal hydro reservoirs. On the other hand, the proposed Linked Representative Periods model produces an error on the water value lower than 3% and can determine hourly opportunity costs for short-term energy storage systems using dual variables from both intra-and inter-period storage balance equations. Therefore, hourly opportunity costs in the Linked Representative Periods model successfully internalize long-term signals due to seasonality in hydro reservoirs.