Clark turned down an appeal by developer FCC Environment against Cumbria County Council’s February 2014 decision to refuse planning permission for the scheme near Workington.
The minister ruled that planning impacts identified by communities local to the site had not been addressed, and thus the proposal fell foul of arrangements set out in a written ministerial statement (WMS) in June.
A decision letter sent on behalf of Clark said: "Having applied the transitional provision set out in the June 2015 WMS, the secretary of state is not satisfied that the planning impacts identified by affected local communities have been addressed.
"These include concerns about the cumulative impacts on the character of the landscape as well as the impacts on residential amenity."
FCC Environment originally applied to the council for permission to install four 2.3MW turbines with blade tip heights of up to 99 metres, as well as associated infrastructure. The firm then removed one of the turbines when amending its scheme at appeal stage.
Planning inspector Jessica Graham found that the development would cause "substantial cumulative harm" to the character of the landscape. She added that it would result in adverse visual impacts on nearby residents and users of roads and public rights of way.
Graham said these impacts would "clearly and convincingly" outweigh the benefits of the renewable energy scheme. Clark acted in line with her advice when dismissing the appeal.
The June WMS has been cited by the minister in a number of wind power planning rejections recently, including schemes in Yorkshire and Cumbria last month.