  We define a kind of heat engine via three-dimensional charged BTZ black
holes. This case is quite subtle and needs to be more careful. The heat flow
along the isochores does not equal to zero since the specific heat $C_V\neq0$
and this point completely differs from the cases discussed before whose
isochores and adiabats are identical. So one cannot simply apply the paradigm
in the former literatures. However, if one introduces a new thermodynamic
parameter associated with the renormalization length scale, the above problem
can be solved. We obtain the analytical efficiency expression of the
three-dimensional charged BTZ black hole heat engine for two different schemes.
Moreover, we double check with the exact formula. Our result presents the first
specific example for the sound correctness of the exact efficiency formula. We
argue that the three-dimensional charged BTZ black hole can be viewed as a toy
model for further investigation of holographic heat engine. Furthermore, we
compare our result with that of the Carnot cycle and extend the former result
to three-dimensional spacetime. In this sense, the result in this paper would
be complementary to those obtained in four-dimensional spacetime or ever
higher. Last but not the least, the heat engine efficiency discussed in this
paper may serve as a criterion to discriminate the two thermodynamic approaches
introduced in Ref.[29] and our result seems to support the approach which
introduces a new thermodynamic parameter $R=r_0$.
