Large-amplitude deep surge instabilities are studied in a turbocharger compression system with a one-dimensional (1D) engine simulation code. The system consists of an upstream compressor duct open to ambient, a centrifugal compressor, a downstream compressor duct, a large plenum, and a throttle valve exhausting to ambient. As the compressor mass flow rate is reduced below the peak pressure ratio for a given speed, mild surge oscillations occur at the Helmholtz resonance of the system, and a further reduction in flow rate results in deep surge considerably below the Helmholtz resonance. At the boundary with mild surge, the deep surge cycles exhibit, for the particular system considered, a long cycle period containing four distinct flow phases, including quiet (stable), instability growth (mild surge), blowdown (reversal), and recovery. Further reductions in flow rate decrease the deep surge cycle period, eliminate the quiet flow phase, and shorten the duration of the instability growth phase. Simulated oscillations of nondimensional flow rate, pressure, and speed parameters show good agreement with the experimental results available in literature, in terms of deep surge cycle flow phases along with the amplitude and frequency of the resulting fluctuations. The predictions illustrate that the quiet and instability growth phases, exhibited by this compression system, disappear as the plenum volume is substantially reduced.