Nitrogen interstitials (N$_mathrm{i}$) have the lowest formation energy among intrinsic defects of hexagonal boron nitride (hBN) under n-type and N-rich conditions. Using an optimized hybrid functional, which reproduces the gap and satisfies the generalized Koopmans condition, an N$_mathrm{i}$ configuration is found which is lower in energy than the ones reported so far. The (0/-) charge transition level is also much deeper, so N$_mathrm{i}$ acts as a very efficient compensating center in n-type samples. Its calculated photoluminescence (PL) at 3.0 eV agrees well with the position of an N-sensitive band measured at 3.1 eV. It has been also found that the nitrogen vacancy (V$_mathrm{N}$) cannot be the origin of the three boron electron (TBC) electron paramagnetic resonance (EPR) center and in thermal equilibrium it cannot even exist in n-type samples.
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