Catalysis of the reaction: (5Z,13E)-(15S)-11-alpha,15-dihydroxy-9-oxoprost-13-enoate + NAD+ = (5Z,13E)-11-alpha-hydroxy-9,15-dioxoprost-13-enoate + NADH + H+.
(5Z,13E)-(15S)-11alpha,15-dihydroxy-9-oxoprost-13-enoate:NAD+ 15-oxidoreductase activity