• Energy Research

Part II of this paper develops the mathematical formulations of three applications of the thermoeconomic analysis methodology described in Part I of the paper: the operation diagnosis study, including new concepts that helps to separate different contributions to those inefficiencies; the local optimization process in case of special conditions for the whole plant, and the benefit maximization (a direct application of the exergy costs accounting analysis). The operation diagnosis, which is the most complex and sophisticated application, is presented with the help of an example: the co-generation plant, as it was described in Part I.

The thermoeconomic diagnosis strategy introduced in the accompanying paper (part 1 [1]) is a zooming technique consisting of a successive localization of anomalies. At each step the required productive structure to be adopted becomes even more detailed, focusing the analysis on a more specific part of the system. The detail of a productive structure has two different levels: the number of components and the number of productive flows. The first one is selected according to the precision desired in locating the anomalies. A larger number of components (or subsystems) allows one to locate the anomalies in smaller control volumes, providing more precise indications for maintenance. The number of flows is partially dependent on the number of components. Once the number of components is fixed, the productive flows can be increased by separating exergy into its components or introducing fictitious flows, such as negentropy (see for example [2]). This decision also affects the results of the thermoeconomic analysis when it is adopted for diagnosis purposes. In this paper, the effects of the productive structure on the diagnosis results are carefully analyzed. Depending on the selected productive structure, the accuracy of the diagnosis results can be significantly improved.

Growth and development of ecosystems are subject to restrictions. Besides exergy, other properties, such as ascendency, have been described as goal functions that can inform about the health of ecosystems and synthesize information about the energy and matter flows in relation to an ideal theoretical state. Ascendency is an index that quantifies both the growth and the degree of organization in an ecosystem, in which several subsystems interact with mass and energy flows. Ascendency is quantified in terms of mass and energy exchanges among different subsystems constituting an ecosystem. Its value increases when the activity of the ecosystem increases (amount of mass and energy exchanges increase) and when the ecosystem evolves to a higher complexity of its structure (level of integration of the subsystems). Exergy provides information about the quality of energy and is therefore very appropriate for evaluating the thermodynamic efficiency of energy conversion processes. Growing concerns about energy efficiency have stimulated the development of techniques for the analysis, design, and diagnosis of complex energy systems based on the second law of thermodynamics. In this context, the set of methodologies called thermoeconomics was created, aimed at cost allocation (economic, thermodynamic, or environmental) and optimization of thermal systems based on thermodynamic concepts of system operation, which very often use exergy. Thermoeconomic analysis provides information on the interaction among the different components of energy systems and how energy resources are distributed throughout the internal mass and energy flows of the system. Herein the formulation of ascendency was adapted to industrial systems using exergy flows as the quantity of interest, employing the productive structure obtained from thermoeconomic analysis techniques to describe the production process of the system. Ascendency was then applied to a set of simple thermodynamic power systems based on the Rankine cycle to study the connection between energy (thermodynamic) efficiency and the “growth” and “development” of the power system. Four configurations with different interconnection levels between the equipment were studied, maintaining the final product of the power systems (net power) and the energy efficiency of the entire cycle constant, for comparison purposes. Moreover, different turbine efficiencies were also analyzed, maintaining a fixed system structure and constant net power produced, to obtain comparable results. It was verified that in the case of steam power plants based on the Rankine cycle, an increase in system complexity, maintaining the total plant production constant, increases ascendency as well as its potential for energy efficiency improvement. When different cases with the same interconnection level between equipment (same system structure), same net power production and different efficiencies are compared, the configuration with the highest ascendency value also presents a better potential for optimization.

These two papers resume the theoretical background supporting the main ideas of the exergy cost accounting and the thermoeconomic approach followed by Valero and co-workers. Part I introduces the basic requirements, with a simple example accompanying the dissertations, to calculate the exergy and thermoeconomic costs and to perform the thermoeconomic analysis of a complex system. The connections with other thermoeconomic approaches and schools are briefly explained. Part II presents, as an illustration of the applications of thermoeconomic analysis, some of the most interesting applications of costs to the operation diagnosis and optimization of a complex system, showing the results on the mentioned example presented in Part I.

Several configurations of polygeneration systems, conceived for a dairy industry requiring cold, heat, power and water for its operation, are presented. For these systems, a single fuel is used to produce cold, steam (heat), electricity and water from a combined cycle integrated and optimized with heaters, absorption units and desalination plants. The proposed systems are the result of minimizing a multi-objective function of energy (cold, heat and power) and water consumption in order to reach a more efficient and sustainable management of the installation. The industry covers its internal demand for energy and water and reaches important overall energy savings thanks to the integration of all the systems. Different configurations are analyzed in which, depending on the required demands, thermal desalination or reverse osmosis are considered. An economic analysis was also performed. The overall system was modeled by means of data provided by manufacturers and also by means of efficiency curves available in the literature.

In this paper the Structural Theory of Thermoeconomics is proposed as a standard and common mathematical formulation for all thermoeconomic methodologies employing thermoeconomic models that can be expressed by linear equations. In previous works it has been demonstrated that the Exergy Cost Theory (ECT), the AVCO approach and the Thermoeconomic Functional Analysis (TFA) can be dealt with the Structural Theory. In this paper, it is demonstrated that the Last-in-First-Out (LIFO) approach, a thermoeconomic cost accounting method, can also be reproduced with the Structural Theory. The LIFO and the Structural Theory are both applied to a combined cycle plant and it is shown that the equation systems obtained from both methods are the same. Moreover, a procedure to develop the productive structure representing the thermoeconomic model of LIFO (i.e. from which the same costing equations are obtained as with the LIFO approach) is explained in detail, which provides the tools to reproduce the costs obtained from LIFO with the Structural Theory for complex energy systems. This paper concludes a series of research works where it has been demonstrated that the most developed thermoeconomic optimization and cost accounting methodologies, as all of them employ thermoeconomic models that can easily be linearized, can be dealt with by the mathematical formalism of the Structural Theory.

Integration of thermoeconomics and Life Cycle Analysis was carried out within the framework of an Environmental Management Information System. This combined approach identified where environmental loads were generated and tracked environmental loads throughout the system, allowing for a more precise understanding of operational activities. A trigeneration system was modeled, providing electricity, heat, and cooling to a building. The trigeneration system consists of a cogeneration module, auxiliary boiler, absorption chiller and electrical chiller. The trigeneration system model is flexible, as it allows electricity from/to the electric grid to be purchased/sold, and part of the cogenerated heat to be wasted. Umberto software is specifically designed to analyze the distribution of material and energy resources throughout a productive system. The software is based on Petri networks, double-entry bookkeeping and cost accounting, allowing the setup of complex systems and also a combined material, energy and inventory calculation. An assistant was built to include the tracking of emissions through the application of algebra and rules similar to those used in thermoeconomic analysis. It is possible to evaluate the environmental impact in terms of the consumption of natural resources and generation of emissions in the system, from the input of natural resources to the output of the final products. Network parameters were used to calculate the emissions associated with the operation of the system. The issue of allocating environmental loads was introduced and two scenarios for each operational mode were compared: the trigeneration system vs. a conventional energy supply system in which electricity was produced in a representative coal power plant. In this case the trigeneration system operated with significant reduction of the CO"2 emitted into the atmosphere.

Thermoeconomic diagnosis of complex energy systems is probably the most developed application of thermoeconomic analysis [NATO ASI on thermodynamics and optimization of complex energy systems, 1999, p. 117]. It is applied to diagnose the causes of the additional fuel consumption of a steadily operating plant, due to the inefficiencies of its components. In this paper, a new method based on the structural theory and symbolic thermoeconomics [Energy 19 (13) (1994) 365] is introduced. It integrates the thermoeconomic methodologies developed until now, such as fuel impact and technical exergy saving [Flowers 94, Florence World Energy Research Symposium, Florence, Italy, 1994, p. 149] and let us to compute the additional fuel consumption as the sum of both the irreversibilities and the malfunction costs of the plant components. Furthermore, it will be able to quantify the effect of a component malfunction in the other components of the plant. As result, new concepts are included in the diagnosis analysis: intrinsic malfunction, induced malfunction and dysfunction. The key of the proposed method is the construction of the malfunction/dysfunction table which contains, in a very compact form, the information related with the plant inefficiencies and their effects on each component and on the whole plant. This methodology is not only a theoretical advance but also it enhances the thermoeconomic diagnosis applications, based on performance tests or simulation models. Some of them are presented in this paper using a simple example. The application of the methodology is shown in the second part of the paper.