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.
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