From Wikipedia
On June 27, 1954, the USSR's Obninsk Nuclear Power Plant became the world's first nuclear power plant to generate electricity for a power grid, and produced around 5 megawatts of electric power.
Later in 1954, Lewis Strauss, then chairman of the United States Atomic Energy Commission (U.S. AEC, forerunner of the U.S. Nuclear Regulatory Commission and the United States Department of Energy) spoke of electricity in the future being "too cheap to meter." Strauss was referring to hydrogen fusion- which was secretly being developed as part of Project Sherwood at the time - but Strauss's statement was interpreted as a promise of very cheap energy from nuclear fission. The U.S. AEC itself had issued far more conservative testimony regarding nuclear fission to the U.S. Congress only months before, projecting that "costs can be brought down... [to]... about the same as the cost of electricity from conventional sources..." Significant disappointment would develop later on, when the new nuclear plants did not provide energy "too cheap to meter."
In 1955 the United Nations' "First Geneva Conference", then the world's largest gathering of scientists and engineers, met to explore the technology. In 1957 EURATOM was launched alongside the European Economic Community (the latter is now the European Union). The same year also saw the launch of the International Atomic Energy Agency (IAEA).
The world's first commercial nuclear power station, Calder Hall in Sellafield, England was opened in 1956 with an initial capacity of 50 MW (later 200 MW). The first commercial nuclear generator to become operational in the United States was the Shippingport Reactor (Pennsylvania, December, 1957).
One of the first organizations to develop nuclear power was the U.S. Navy, for the purpose of propelling submarines and aircraft carriers. It has a good record in nuclear safety, perhaps because of the stringent demands of Admiral Hyman G. Rickover, who was the driving force behind nuclear marine propulsion as well as the Shippingport Reactor. The U.S. Navy has operated more nuclear reactors than any other entity, including the Soviet Navy, with no publicly known major incidents. The first nuclear-powered submarine, USS Nautilus (SSN-571), was put to sea in December 1954. Two U.S. nuclear submarines, USS Scorpion and USS Thresher, have been lost at sea. These vessels were both lost due to malfunctions in systems not related to the reactor plants. Also, the sites are monitored and no known leakage has occurred from the onboard reactors.
The United States Army also had a nuclear power program, beginning in 1954. The SM-1 Nuclear Power Plant, at Ft. Belvoir, Va., was the first power reactor in the US to supply electrical energy to a commercial grid (VEPCO), in April 1957, before Shippingport.
Enrico Fermi and Leó Szilárd in 1955 shared U.S. Patent 2,708,656 for the nuclear reactor, belatedly granted for the work they had done during the Manhattan Project.