What happens if all off-site power is lost for an extended period of time?  Are  the spent fuel and  the reactor core protected from overheating?

The NuScale Nuclear Power Modules sit submerged in the reactor pool. The spent nuclear fuel is submerged in the spent fuel pool, which is fluid and thermally connected to the reactor pool. Upon loss of power, passive cooling systems on the NuScale Power Modules are automatically placed in service to transfer core decay heat to the reactor pool via natural circulation. No operator action, AC or DC power, or additional water is required. Assuming conservative initial conditions, adequate water will remain in the pool to cool all the Nuclear Power Modules and to keep the spent fuel pool covered in excess of 100 days with no operator actions. The NuScale plant response to an extended loss of AC power will be detailed in the Design Certification Application and supporting technical documentation.