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This paper studies the impact of natural gas (NG) contracts and constraints on a GENCO's midterm risk-constrained hydrothermal scheduling problem. The NG contracts and constraints are modeled as a set of linear equations. The proposed model utilizes the stochastic price-based unit commitment (PBUC). The PBUC hourly solution considers uncertainties of market prices for energy and ancillary services, uncertainties of natural water inflows, and random NG infrastructure interruptions in Monte Carlo scenarios. Illustrative examples analyze the GENCO's risk levels when considering midterm schedules for generating units, target payoffs, and usages of water inflow, NG and other thermal resources. Simulation results show that a GENCO's midterm schedules and financial risks could be impacted significantly with the consideration of NG contracts and constraints.