Applying the common mathematical procedure of thermodynamic optimization the paper offers a synthesizing or generalizing modeling of power production in various energy generators, such as thermal, solar and electrochemical engines (fuel cells). Static and dynamical power systems are investigated. Dynamical models take into account the gradual downgrading of a resource, caused by power delivery. Analytical modeling includes conversion efficiencies expressed in terms of driving fluxes. Products of efficiencies and driving fluxes determine the power yield and power maxima. While optimization of static systems requires using of differential calculus and Lagrange multipliers, dynamic optimization involves variational calculus and dynamic programming. In reacting mixtures balances of mass and energy serve to derive power yield in terms of an active part of chemical affinity. Power maximization approach is also applied to fuel cells treated as flow engines driven by heat flux and fluxes of chemical reagents. The results of power maxima provide limiting indicators for thermal, solar and SOFC generators. They are more exact than classical reversible limits of energy transformation. •Systematic evaluation of power limits by optimization.•Common thermodynamic methodology for engine systems.•Original, in-depth study of power maxima.•Inclusion of fuel cells to a class of thermodynamic power systems.