  In this paper we have studied two non-linear black holes in 2+1 dimensions.
They are regular and could have two horizons for chosen values of the
parameters in the theory. Thermodynamics of the two black holes are studied in
the extended phase space where the pressure P = -{\Lambda}/8{\pi}. In order to
satisfy the Smarr formula and the first law of thermodynamics, a
renormalization parameter is introduced. Hence there is an additional
thermodynamical parameter for the black hole. We have also studied the two
black holes in the context of heat engines. A thermodynamical cycle, consisting
of two isobaric and two isochoric is considered. Efficiency is computed by
varying the non-linear parameter and the electric charge of the black hole. It
is observed that when the non-linear parameter and the charge increases, the
efficiency increases. When compared to the charged BTZ black hole, the
efficiency for the rectangle cycle is smaller for the regular black holes.
