  The fundamental issue in the energetic performance of power plants, working
both as traditional fuel engines and as combined cycle turbine (gas-steam),
lies in quantifying the internal irreversibilities which are associated with
the working substance operating in cycles. The purpose of several irreversible
energy converter models is to find objective thermodynamic functions that
determine operation modes for real thermal engines and at the same time study
the trade off between energy losses per cycle and the useful energy. As those
objective functions, we focus our attention on a generalization of the
so-called ecological function in terms of an $\epsilon$--parameter that depends
on the particular heat transfer law used in the irreversible heat engine model.
In this work, we mathematically describe the configuration space of an
irreversible Curzon-Ahlborn type model. The above allows to determine the
optimal relations between the model parameters so that a power plant operates
in physically accessible regions, taking into account internal
irreversibilities, introduced in two different ways (additively and
multiplicatively). In addition, we establish the conditions that the
$\epsilon$--parameter must fulfill for the energy converter works in an optimal
region between maximum power output and maximum efficiency points.
