Local stability analysis of a thermo-economic model of an irreversible heat engine working at different criteria of performance

In recent works [1, 2], we reported a local stability analysis of a thermo-economic model of an irreversible heat engine working at maximum power conditions. In those works, we calculated the relaxation times in terms of τ, f and R (a parameter which comes from the Clausius inequality and measures the degree of the internal irreversibilities). Besides τ=T₂/T₁ , with T₁ > T₂, being the temperatures of the external heat reservoirs and the parameter f is the fractional fuel cost, which is associated to several energy resources considering energy sources where de investment is the preponderant cost (f = 0), until energy sources where the fuel is the predominant cost (f = 1). In those works, we showed that, after a small perturbation the system decays exponentially to the steady state determined by two different relaxation times. In this work, we extend the local stability analysis considering other regimes of performance: The Maximum Efficient Power and the Ecological Function regime. We show that the relaxation time under maximum ecological function conditions is lesser than the relaxation times under both maximum power and maximum efficient power, that is, under maximum ecological conditions we have better stability conditions than for the other two regimes. Besides, we observe that the stability of the system improves as τ increases whereas the steady-state energetic properties of the engine declines for all cases of energy sources.