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Register a new userLocal and global stability analysis of a Curzon-Ahlborn model applied to power plants working at maximum $k$-efficient power
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Added by
Gabriel Valencia-Ortega
Publication date
2020
fields
Physics
and research's language is
English
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The analysis of the effect of noisy perturbations on real heat engines, working on any steady-state regime has been a topic of interest within the context of Finite-Time Thermodynamics (FTT). The study of their local stability has been proposed through the so-called performance regimes: maximum power output, maximum ecological function, among others. Recently, the global stability analysis of an endoreversible heat engine was also studied taking into account the same performance regimes. We present a study of local and global stability analysis of power plant models (the Curzon-Ahlborn model) operating on a generalized efficient power regime called maximum k-efficient power. We apply the Lyapunov stability theory to construct the Lyapunov functions to prove the asymptotically stable behavior of the steady-state of intermediate temperatures in the Curzon-Ahlborn model. We consider the effect of a linear heat transfer law on the phase portrait description of real power plants, as well as the role of the $k$ parameter in the evolution of perturbations to heat flow. In general, restructured operation conditions show better stability in external perturbations.
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In order to establish better performance compromises between the process functionals of a heat engine, in the context of finite time thermodynamics (FTT), we propose some generalizations for the well known Efficient Power function through certain variables called <<Generalization Parameters>>. These generalization proposals show advantages in the characterization of operation modes for an endoreversible heat engine model. In particular, with introduce the k-Efficient Power regime. For this objective function we find the performance of the operation of some power plants through the parameter k. Likewise, for plants that operate in a low efficiency zone, within a configuration space, the k parameter allow us to generate conditions for these plants to operate inside of a high efficiency and low dissipation zone.
The Curzon-Ahlborn (CA) efficiency, as the efficiency at the maximum power (EMP) of the endoreversible Carnot engine, has significant impact in finite-time thermodynamics. In the past two decades, a lot of efforts have been made to seek a microscopic theory of the CA efficiency. It is generally believed that the CA efficiency is approached in the symmetric low-dissipation regime of dynamical models. Contrary to the general belief, without the low-dissipation assumption, we formulate a microscopic theory of the CA engine realized with an underdamped Brownian particle in a class of non-harmonic potentials. This microscopic theory not only explains the dynamical origin of all assumptions made by Curzon and Ahlborn, but also confirms that in the highly underdamped regime, the CA efficiency is always the EMP irrespective of the symmetry of the dissipation. The low-dissipation regime is included in the microscopic theory as a special case. Also, based on this theory, we obtain the control scheme associated with the maximum power for any given efficiency, as well as analytical expressions of the power and the efficiency statistics for the Brownian CA engine. Our research brings new perspectives to experimental study of finite-time microscopic heat engines featured with fluctuations.
Power-to-gas (P2G) can be employed to balance renewable generation because of its feasibility to operate at fluctuating loading power. The fluctuating operation of low-temperature P2G loads can be achieved by controlling the electrolysis current alone. However, this method does not apply to high-temperature P2G (HT-P2G) technology with auxiliary parameters such as temperature and feed rates: Such parameters need simultaneous coordination with current due to their great impact on conversion efficiency. To improve the system performance of HT-P2G while tracking the dynamic power input, this paper proposes a maximum production point tracking (MPPT) strategy and coordinates the current, temperature and feed rates together. In addition, a comprehensive dynamic model of an HT-P2G plant is established to test the performance of the proposed MPPT strategy, which is absent in previous studies that focused on steady states. The case study suggests that the MPPT operation responds to the external load command rapidly even though the internal transition and stabilization cost a few minutes. Moreover, the conversion efficiency and available loading capacity are both improved, which is definitely beneficial in the long run.
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.
Several recent theories address the efficiency of a macroscopic thermodynamic motor at maximum power and question the so-called Curzon-Ahlborn (CA) efficiency. Considering the entropy exchanges and productions in an n-sources motor, we study the maximization of its power and show that the controversies are partly due to some imprecision in the maximization variables. When power is maximized with respect to the system temperatures, these temperatures are proportional to the square root of the corresponding source temperatures, which leads to the CA formula for a bi-thermal motor. On the other hand, when power is maximized with respect to the transitions durations, the Carnot efficiency of a bi-thermal motor admits the CA efficiency as a lower bound, which is attained if the duration of the adiabatic transitions can be neglected. Additionally, we compute the energetic efficiency, or sustainable efficiency, which can be defined for n sources, and we show that it has no other universal upper bound than 1, but that in certain situations, favorable for power production, it does not exceed 1/2.
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