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. Several irreversible models of energy converters have been studied under different contexts of non-equilibrium thermodynamics, their purpose is to find objective thermodynamic functions that determine more realistic bounds for real energy converters and at the same time reduce energy losses per cycle. As these objective functions characterize specific operation regimes, we focus our attention in one generalization of the so-called ecological function in terms of a generalizing parameter ( ) which can be related not only to a large number of accessible operation modes, but also to parameters representing both internal and external irreversibilities in models of power plants. In this work, we conclude the characteristic loops in the power output-efficiency space can be sketched, for either of the two irreversible heat engine models considered with heat leak. We found out that from a set of loops related to the physical constraints, the above systems work as heat engines and their operating conditions lie in 3 particular zones. The optimum zone featured by high power output and high efficiency is characterized through a relation between the irreversibility degrees and the constraints-parameters.