  We study real ternary forms whose real rank equals the generic complex rank,
and we characterize the semialgebraic set of sums of powers representations
with that rank. Complete results are obtained for quadrics and cubics. For
quintics we determine the real rank boundary: it is a hypersurface of degree
168. For quartics, sextics and septics we identify some of the components of
the real rank boundary. The real varieties of sums of powers are stratified by
discriminants that are derived from hyperdeterminants.
