On-line monitoring of power-plant performance, using exergetic cost techniques

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  • ~ Pergamon Applied Thermal Engineering Vol. 16, No. 12, pp. 933-948, 1996

    Copyright 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved

    1359.-4311(95)00092-5 1359-4311/96 $15.oo + o.o0



    A. Valero, M. A. Lozano and J. L. Bartolom6 CIRCE Research Center for Power Plant Efficiency, Department of Mechanical Engineering,

    University of Zaragoza, Zaragoza, Spain

    Abstract--Among the possible applications of thermoeconomics, the most promising one is perhaps the diagnosis of the operation of actual energy systems. Diagnosis can be considered as the art of discovering and interpreting signs of malfunction and of quantifying their effects in terms of additional consumption of resources. In the sphere of energy systems a good diagnosis requires: (i) the application of regulatory procedures and performance tests codes, in order to determine the state of the system with precision (clinical diagnosis) and (ii) a good theory which would provide concepts to aid the comprehension and to explain the causes of such a state (etiological diagnosis). The problem to solve can be formulated as follows: where, how and which part of the consumed resources can be saved by keeping the quantity and specifications of the final products constant? This paper briefly explains the thermoeconomic approach to solve this problem and presents a supervisory system running in a 350 MW coal power-plant which uses these ideas to diagnose in real time the causes of heat rate deviations. Copyright 1996 Elsevier Science Ltd.

    Keywords---Thermoeconomics, exergy analysis, performance tests, power-plant supervisory systems.


    Cost account ing is the field of account ing that records, measures and reports information about how much things cost. Problems generally occur because companies do not have a good understanding of their costs. Business managers use cost data for decis ion-making and performance evaluat ion and control. They have techniques for products and services costing and use differential costs for est imating how costs differ among alternatives. Manager ia l cost accounting became a profession many years ago, and almost every organizat ion uses it.

    In a paral lel to monetary cost accounting energy cost accounting for energy systems has been developed. However, energy cost accounting is something more than a manager ia l technique for keeping down the consumpt ion of energy resources. It provides a rat ionale for assessing the cost of products in terms of natural resources and their impact on the environment, and helps to optimize and synthesize very complex energy systems.

    This technique has been called thermoeconomics. It deals with costs, either monetary (S/k J) or pure energy costs (kJ of resources/kJ o f product) and it is mainly used for the cost accounting, diagnosis, improvement, design and opt imizat ion of thermal systems. In a broad sense thermoeconomics is the name of a new science in which the second law of thermodynamics meets economics. Thermoeconomic analysis techniques combine the first and second laws of thermodynamics with monetary cost balances conducted at the system component level and help understand the cost format ion process, minimize the overall product costs and assign costs to the different products produced in the processes.

    Note that no other technique ever devised can go from physics to economics at the system component level. Convent ional s imulators can answer 'what if ' questions that provide information about how many resources are needed to obtain some addit ional unit of some flow under specified circumstances but they don' t provide an integrated answer of the economic and the energy effects of any malfunction.

    The only way is thermoeconomics, because convent ional s imulators add economics as a whole


  • 934 A. Valero et al.

    and once the physical problem has been solved. The thermoeconomic approach is really very powerful and many of its applications are still in their infancy.

    The application that most attention has been paid to up to now is perhaps cost accounting; however, it leaves theoretically unsolved problems like developing criteria for a good disaggregation level. Or in other words how much accounting information is enough? What type of information provided is best? Under what criteria? The answers to these questions need additional research.

    However, the cost-accounting technique is developed enough to go one step further, to on-line cost accounting. In other words, with the rough data provided by a control room of an energy system, like pressures, temperatures, mass flow rates, electrical production, fuel consumption, oxygen excess and so on, let us convert this information plus the economic one into costs; thus giving the first real-time thermoeconomic diagnosis of a complex energy system ever made.

    This idea is quite simple, instead of using costs obtain differential costs and get them on real time, using the same conceptual procedure that costs accountants developed many years ago. In the long run the idea is to integrate the energy control of a unit with the cost-accounting department at any level of information desired.

    Suppose the goal of a plant employee is to drive the unit to the limiting conditions of materials in order to achieve as much efficiency and availability as possible. If the age of the plant is not reflected in conventional accounting, this plant employee will receive congratulations from his managers in contrast to another more prudent operator.

    Also differential exergy costs help to understand and correct the causes of malfunctions of a unit. According to the theory of exergetic cost each malfunction of a component has a cause and an impact on additional consumption of resources. If we know this information we can isolate the causes and concentrate on the important ones in order to solve them in real time wherever possible. This application of thermoeconomics is really very important in the sense that it is unique because no other technique developed until now permits one to isolate and quantify the causes of deviation of a unit from its design conditions.


    Generally speaking, the structure of energy systems can be viewed as a set of 'n' subsystems, connected among themselves and with the exterior by means of 'm' energy/mass flows (Fig. 1).

    From this representation, we can infer some obvious characteristics. There are flows which cross the boundaries of the system, taking resources, F, (flows 1 and 2), and giving up products, P, and residues, R, (flows 3 and 4), to the exterior or environment. These flows will be denoted as external, and their number is determined once the boundaries of the system have been defined. In contrast,

    I I I I 4 I

    Fig. 1. Example of the structure of a general energy system.

  • On-line monitoring of power-plant performance 935

    the number of internal subsystems and flows will depend on the disaggregation level considered, since clearly each subsystem can, in principle, be decomposed into a number of devices and processes or subprocesses which interact by means of another set of energy flows. Theoretically, this successive disaggregation appears to have no limits, but in practice, either due to the lack of data or to the excessive complexity of the analysis, or to other reasons, one reaches a reasonable disaggregation level. For example, in a conventional thermal plant, this level would go so far as to detail the basic components and/or processes making it up.

    One vital question we can now ask ourselves is: what is the cost of producing any given flow of our now-defined energy system? Let us solve the problem by successive approximations. First, let us set the maximum aggregation level, the overall system in Fig. 1. To produce the plant's product, P, identified as flow 3, it is necessary to consume resources, F, identified as flows 1 and 2, and to dispose of residues or byproducts, R, identified as flow 4.

    The cost of producing P will be the cost of the resources, F, minus what we get from selling R, as a byproduct, or alternatively, plus what we must pay to dispose of R as a residue to the environment. In either case, the cost of R will have a sign. For this simple analysis we do not consider amortization costs.

    The specific or unit consumption of producing P is commonly defined as:

    Kp- - F- R physical units

    P physical units

    The physical units which define the numerator and denominator can vary in practice: energy/mass, mass/mass, energy/energy, etc.

    We see that the unit cost of producing P is intimately linked to the concept of specific consumption, since if we have the unit prices of F and R (say CF and cR), we can get it from

    Cp m CF'F- cR'R monetary units

    P physical units "

    From this simple study we can now draw some important conclusions. The price of energy flows is something which is formed in the exchange, in the market, and it will never have any bearing on our analyses, simply because we are not interested in it. What we are interested in is the objective search for the production costs. Prices are external to the system.

    The internal reasons for the production cost are due exclusively to the quality of the production process, defined by the specific consumption, or its inverse, the efficiency:

    P 1 q-F -R

    For our analysis, it is necessary and reasonable that ~c or r/should be dimensionless, and that they should objectively express the degree of quality of a process in a way which allows processes to be compared. For this purpose F, P and R must be evaluated in terms of a property which quantifies thermodynamic equivalence.

    Obviously, the second law of thermodynamics gives us that property: exergy, or availability, which measures the amount of useful energy contained in a given flow with respect to specific exhausted environment conditions.

    Using exergy to define F, P and R also guarantees that (F -- R) -- P -- I > 0 defining I as the process' irreversibility (i.e. the number of units of useful energy destroyed by its inefficiency). Alternatively, it also guarantees that in any real process, the following holds: K > 1 or t /< 1.

    To define efficiency, it is first necessary to identify fuels or resources, products and residues. We cannot just associate the fuels with the input flows, nor the products with the output flows. We need to have a clear idea of what we want to produce, before defining efficiency.

    In an Aristotelian sense, F is the 'causa materialis', or that from which something else arises, and P is the 'causa finalis', or the end, the reality towards which something tends. The principle of change, or 'causa efficiens' is in the inexorable degradation of natural resources, quantified in the term I.

  • 936 A. Valero et al.

    These ideas lead to another no less important one: to know the costs, it is not enough to know the objective values of the exergies of the flows entering and leaving the system, together with the price of resources. Correct cost assignment will need our concept of efficiency.

    Thus, we can construct the following chain of reasoning. The second law gives a function which quantifies, in an objective and general way, the thermodynamic importance of a plant's flows: their exergy. This allows us to define the true efficiency of processes in the plant, once we have identified the flows we wish to produce, and those which will consequently be consumed. The accumulated performance over the production process will measure the exergy expense required in the plant in order to produce a given flow in it. Finally, we can interpret the prices as weighting factors which externally modify the thermodynamic importance of the different flows. Thus, we naturally lead from exergy expense to economic costs. That is

    Second law ~ Efficiency (unit consumption) --, Expense --* Cost.

    Therefore, our,hypothesis is that the irreversibilities in the system, together with the subjective concept of production which we have for each and every one of the subsystems making up our plant, are what generate costs. Although to calculate this we will need extra information, such as the price of resources, the cost of amortization, maintenance, etc., for the subsystems, these data are external to the system, and do not alter the intrinsic physical processes.

    When the flow is internal, it will leave one subsystem and enter another. The efficiency of these subsystems can also be defined such that the physical units of exergy consumed to produce this flow can be found, as before, but now by accumulating all the unit exergy consumptions of the previous processes, all the way back to the external flows.

    Since 1986, Prof. A. Valero et al. [1-3] from CIRCE, University of Zaragoza, have been developing the Theory of Exergetic Cost and the Structural Theory of Thermoeconomics for assigning costs to plants and systems.

    The concept of exergetic cost is still only within thermodynamics, but it already shares many of the characteristics of economics. It is clearly a conceptual link between these two disciplines. Thus the isomorphism between exergetic cost and economic cost let us straightforwardly convert thermodynamic costs into thermoeconomic costs, simply by adding the prices or resources (or) and the plant's depreciation costs (Z) (amortization costs) to the matrices found in calculating the costs:

    Cp ~-

    ~crF + Z monetary units P physical units "

    Note that vector Z can contain not only amortization costs but any depreciation cost incurred by the system due to bad operation maintenance costs as well as overheads. In other words, once we have a good costs structure we can charge to the costs scheme any type of direct and indirect costs, depending upon the controller who decides what information to get from the developed system.

    Using the exergetic costs, it is also possible to find out which subsystems are malfunc- tioning, and to what extent they are doing so; how their failure affects other subsystems, to what extent these subsystems increase the plant's production cost and also what effect an improvement would have on the overall behaviour of the plant. Furthermore, by this approach it is possible to provide a tool for controlling economic costs and for plant management and maintenance.


    Given an energy system [4], the manner in which its productive structure is defined is a key point in the thermoeconomic analysis of the system. The causal or productive structure is a way of disaggregating systems focusing on causes of irreversibilities rather than identifying actual physical

  • On-line monitoring of power-plant performance 937

    flows and devices (flow diagram). What is important in this representation is the amount which each local resource contributes to the formation of each product, since the cost...


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