  Based on $K$-band integral-field spectroscopy, we analyze four Wolf-Rayet
stars of the nitrogen sequence (WN) found in the inner part of the Quintuplet
cluster. All WN stars (WR102d, WR102i, WR102hb, and WR102ea) are of spectral
subtype WN9h. One further star, LHO110, is included in the analysis which has
been classified as Of/WN? previously but turns out to be most likely a WN9h
star as well. The Potsdam Wolf-Rayet (PoWR) models for expanding atmospheres
are used to derive the fundamental stellar and wind parameters. The stars turn
out to be very luminous, $\log{(L/L_\odot)} > 6.0$, with relatively low stellar
temperatures, $T_* \approx$ 25--35\,kK. Their stellar winds contain a
significant fraction of hydrogen, up to $X_\mathrm{H} \sim 0.45$ (by mass). We
discuss the position of the Galactic center WN stars in the Hertzsprung-Russell
diagram and find that they form a distinct group. In this respect, the
Quintuplet WN stars are similar to late-type WN stars found in the Arches
cluster and elsewhere in the Galaxy. Comparison with stellar evolutionary
models reveals that the Quintuplet WN stars should have been initially more
massive than 60\,$M_\odot$. They are about 2.1 to 3.6\,Million years old, and
might still be central hydrogen burning objects. The analysis of the spectral
energy distributions of the program stars results in a mean extinction of $A_K
= 3.1 \pm 0.5$\,mag ($A_V = 27 \pm 4$\,mag) towards the Quintuplet cluster.
