Nuclear power plants are commonly operated in a "baseload" mode at maximum rated capacity whenever online. However, nuclear power plants are technically capable of flexible operation, including changing power output over time (ramping or load following) and providing frequency regulation and operating reserves. At the same time, flexibility is becoming more valuable as many regions transition to low-carbon power systems with higher shares of variable renewable energy sources such as wind or solar power. We present a novel mixed integer linear programming formulation to more accurately represent the distinct technical operating constraints of nuclear power stations, including impacts of xenon transients in the reactor core and changing core reactivity over the fuel irradiation cycle. This novel representation of nuclear flexibility is integrated into a unit commitment and economic dispatch model for the power system. In a case study using representative utility data from the Southwest United States, we investigate the potential impacts of flexible nuclear operations in a power system with significant solar and wind energy penetration. We find that flexible nuclear operation lowers power system operating costs, increases reactor owner revenues, and substantially reduces curtailment of renewables.