Zinc Phosphide ($Zn_3P_2$) could be the basis for cheap and highly efficient solar cells. Its use in this regard is limited by the difficulty in n-type doping the material. In an effort to understand the mechanism behind this, the energetics and electronic structure of intrinsic point defects in zinc phosphide are studied using generalized Kohn-Sham theory and utilizing the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional for exchange and correlation. Novel 'perturbation extrapolation' is utilized to extend the use of the computationally expensive HSE functional to this large-scale defect system. According to calculations, the formation energy of charged phosphorus interstitial defects are very low in n-type $Zn_3P_2$ and act as 'electron sinks', nullifying the desired doping and lowering the fermi-level back towards the p-type regime. This is consistent with experimental observations of both the tendency of conductivity to rise with phosphorus partial pressure, and with current partial successes in n-type doping in very zinc-rich growth conditions.