  We compute the deformations in the sense of generalized complex structures of
the standard classical complex structure on a primary Kodaira surface and we
prove that the obtained family of deformations is a smooth locally complete
family depending on four complex parameters. This family is the same as the
extended deformations (in the sense of Kontsevich and Barannikov) in degree
two, obtained by Poon using differential Gerstenhaber algebras.
