  The well-known $(2+1)$-dimensional Reissner-Nordstrom (BTZ) black hole can be
generalized to three dimensional Einstein-nonlinear electromagnetic field,
motivated from obtaining a finite value for the self-energy of a pointlike
charge. Considering three types of nonlinear electromagnetic fields coupled
with Einstein gravity, we derive three kinds of black hole solutions which
their asymptotic properties are the same as charged BTZ solution. In addition,
we calculate conserved and thermodynamic quantities of the solutions and show
that they satisfy the first law of thermodynamics. Finally, we perform a
stability analysis in the canonical ensemble and show that the black holes are
stable in the whole phase space.
