  We present a new event generator for the simulation of both neutral- and
charged-current deep inelastic scattering (DIS) at next-to-leading order in QCD
matched to parton showers using the POWHEG method. Our implementation builds on
the existing POWHEG BOX framework originally designed for hadron-hadron
collisions, supplemented by considerable extensions to account for the
genuinely different kinematics inherent to lepton-hadron collisions. In
particular, we present new momentum mappings that conserve the special
kinematics found in DIS, which we use to modify the POWHEG BOX implementation
of the Frixione-Kunszt-Signer subtraction mechanism. We compare our predictions
to fixed-order and resummed predictions, as well as to data from the HERA ep
collider. Finally we study a few representative distributions for the upcoming
Electron Ion Collider.
