Let $G/H$ be a spherical homogeneous variety, where $G$ is a complex semisimple group. Assume that the subgroup $H$ is self-normalizing, i.e., $\mathcal{N}_G(H)=H$. Then by results of Brion and Pauer and Knop there exists a wonderful compactification of $G/H$. Is this wonderful compactification always projective, or in some cases it can be complete, but not projective?

Feel free to vote to close this elementary question.