The protesters claim to have closed the plant, but owner Npower says that is not the case.
Campaigners want closure of the coal-fuelled plant, saying it makes a massive contribution to climate change.
A spokesman for Npower said 15 protesters had gained entry in the early hours of Thursday. Greenpeace said 30 were present.
Laura Yates, one of the protesters, told BBC News: "One team have attached themselves to the conveyer belt which carries coal into the boilers, so they're preventing any more coal going in there."
Man arrested
A Greenpeace spokesman said: "The campaigners are demanding that the government phases out this kind of coal-fired power station and instead backs localised or decentralised power generation, which is much more efficient."
Police officers have arrested one man on the site on suspicion of aggravated trespass and are negotiating with 10 of the protesters.
An Npower spokeswoman said: "The power station has not been shut down, but protesters have chained themselves to the coal intake and have climbed a chimney.
"We are working with local police and we are investigating how they entered the site."
In July, campaigners from Reclaim Power climbed a 131ft (40m) lighting tower at the site to unveil a banner which read Climate Crime.
In August, about 600 environmental campaigners staged a mass protest at Drax power station in North Yorkshire and attempted to close the plant.
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