The electrical properties and spectra of deep centers in high-resistivity undoped GaN samples used to fabricate high-power Schottky diode rectifiers with breakdown voltages exceeding 2000 V are reported. It is shown that the Fermi level in such material is pinned by defects with energy levels close to E-c-0.6 eV. Thermally stimulated current measurements revealed the presence of unidentified traps with activation energies of 0.3 and 0.7 eV. The important role of hole traps with energy levels E-v + 0.3 eV and E-v + 0.9 eV was confirmed by measurements of temperature quenching of photocurrent and by photoinduced transient current spectroscopy measurements. Prominent persistent photoconductivity was observed even for temperatures above 300 K. Imaging of the sample using microcathodoluminescence showed the existence of cellular nonuniformities with characteristic dimensions of the cells of about 3 mu m.