A generator for a wind turbine has a rotor and a stator separated radially by an air gap, wherein the stator includes at least one stator segment, which includes a stack of lamination sheets and at least one stator winding, and a stator support structure supporting the at least one stator segment, wherein the generator further includes a cooling arrangement for providing cooling fluid at least to the air gap, wherein the cooling arrangement further includes a cooling fluid flow dividing element for dividing an incoming cooling fluid flow to the stator into a first partial cooling fluid flow directed to the air gap and a second partial cooling fluid flow directed to the stator support structure.