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Abstract: In this paper power limits and other performance indicators are investigated in various power generation systems with downgrading or upgrading of resources. Energy flux (power) is created in a power generator located between a resource fluid (‘upper’ fluid 1) and the environmental fluid (‘lower’ fluid, 2). Transfer phenomena, fluid properties and conductance values of dissipative layers or conductors influence the rate of power yield. While temperatures T i of participating media are only necessary variables to describe purely thermal systems, in the present work both temperatures and chemical potentials μ k are essential. This case is associated with engines propelled by fluxes of both energy and substance (chemical and electrochemical engines). Optimization methods are applied to determine power generation limits which are important performance indicators for various energy converters, such as thermal, solar, chemical, and electrochemical engines. Methodological similarity is shown when analysing power limits in thermal machines and fuel cells. Numerical approaches are based on the methods of dynamic programing (DP) or Pontryagin’s maximum principle. In view of the limitation of DP to systems with low dimensionality of state vector, we focus here on the Pontryagin’s method, which involves discrete canonical algorithms derived from the process Hamiltonian. Some new or relatively unknown properties of these algorithms are described in the context of their application to power systems. In fuel cells and other electrochemical systems downgrading or upgrading of resources may also occur. However, we restrict here to the steady-state fuel cells. An approximate (topology-ignoring) analysis shows that, in linear systems, only at most 1/4 of power dissipated in the natural transfer process can be transformed into mechanical or electric power. This indicator may be viewed as a new form of the second law efficiency. The relevant experimental data obtained at the institute of Power Engineering are also presented in this paper. [Copyright &y& Elsevier]