  Recently, Hawking radiation of the black hole has been studied using the
tunnel effect method. It is found that the radiation spectrum of the black hole
is not a strictly pure thermal spectrum. How does the departure from pure
thermal spectrum affect the entropy? This is a very interesting problem. In
this paper, we calculate the partition function by energy spectrum obtained
from tunnel effect. Using the partition function, we compute the black hole
entropy and derive the expression of the black hole entropy after considering
the radiation. And we derive the entropy of charged black hole. In our
calculation, we consider not only the correction to the black hole entropy due
to fluctuation of energy but also the effect of the change of the black hole
charges on entropy. There is no other hypothesis. Our result is more
reasonable.According to the fact that the black hole entropy is not divergent,
we obtain the lower limit of Banados-Teitelboim-Zanelli black hole energy. That
is, the least energy of Banados-Teitelboim-Zanelli black hole, which satisfies
the stationary condition in thermodynamics.
