Thermoeconomic Diagnosis of anUrban District Heating System based onCogenerative Steam and Gas Turbines

The energy system diagnosis is a experimental technique applied for the detection and the location of possible anomalies. These information are obtained by comparing the values assumed by opportune variables in a operation condition with the corresponding reference values. In this thesis a procedure based on the use of thermodynamic variables, elaborated using the thermoeconomic methods, is proposed. The main originality, in comparison with other thermoeconomic diagnosis procedures, consists on the evaluation of the regulation system effects on the plant working condition; these effects can be then isolated to achieve the purpose of the malfunction location. The usefulness of such an operation is shown by applying the procedure to some cases of anomalies, obtained using a mathematical model of two thermal power plants, located in Moncalieri (Turin). Thermoeconomics is an engineering discipline born in sixties, consisting in the contemporary use of thermodynamic principles and economic concepts. It allows to associate a cost to all the productive processes taking place inside a system and in particular their products. This cost can be measured in monetary units and eventually in pure thermodynamic units. The key of the thermoeconomic analysis procedures consists on a productive model of the system, called productive structure, generally different from its physical model. Every energy transformation is represented and quantified in terms of supplied product, i.e. the useful effect obtained, resources required and possible losses. Such quantities in modern thermoeconomics are expressed using exergy fluxes. The system is first divided in some subsystems or components, in each one a significant energy transformation takes place. The grade of detail depends on the available information and on the aim of the analysis. The thermodynamic variables (mass and energy flows, temperatures, pressures etc.) required to characterize the fluxes entering and exiting the component must be known. In this way a more detailed analysis furnish more information, but it requires the measures of a larger number of physical variables. The ratio between every resource used by a component and its product is called unit exergy consumption. The values assumed by the whole of the unit exergy consumptions completely describes the thermoeconomic model of the system. This means that the description of the system based on its productive model is a simplification of the physical model. The information are summarized in the thermoeconomic parameters, which substitute the thermodynamic variables measured in correspondence of the fluxes crossing the boundaries of the control volumes. The thermoeconomic diagnosis is made by studying the temporal variation of the unit exergy consumptions, while, the methodologies usually applied in the energy systems, the variation of a whole of different quantities is analysed. The thermoeconomic diagnosis allows the use of the same procedure for all the anomalies, so it is a general methodology. On the contrary the other methodologies use a different procedure, depending on the kind of anomaly wants to be detected; the available data must be chosen and organized so that they could furnish the required information. Nevertheless the thermoeconomic diagnosis only allows to detect anomalies having sensible repercussions on the thermodynamic behaviour of the system. Moreover some information are lost when the physical structure is substitute with the productive structure, which could make the procedure unable to locate some kind of malfunctions. These considerations suggest the contemporary use of the thermoeconomic diagnosis together with other methodologies, as they are often complementary. In particular the other techniques are normally devised to prevent the anomalies which can cause, if not repaired, failures. On the contrary the aim of the thermoeconomic diagnosis consists on the detection and the location of the anomalies causing the reduction of the system efficiency. Moreover it also allows to evaluate the costs associated to the variation of the working condition, which is more significant than the simple variation of the efficiency of a single process. The same efficiency variation can in fact involves a different fuel impact depending on where it takes place. This consideration is known as principle of non equivalence of the irreversibilities. The procedures of thermoeconomic diagnosis consist on the determination of the values assumed by the unit exergy consumptions in a operation condition and a reference condition, on the calculation of opportune evaluation indices based on these quantities and on their comparison. The two states must be characterized by the boundary conditions: the environment must be characterized by the same temperature, pressure and humidity, the plant production must be the same in quality and quantity (the same electric power and, in case of thermal production, the exiting flow must be characterized by the same energy flow, temperature, pressure and thermodynamic quality) and finally the fuel quality must be the same. Due to these constraints, the reference condition is usually determined by means of a simulator. The correct anomaly location is only possible in the cases where its effect is largely concentrated in the component where it has taken place. This does not happens always. The first effect of an anomaly is the reduction of the efficiency of the component where it has occurred (intrinsic malfunction). If the component resource has been maintained constant, the anomaly causes the reduction of its product. As this product is generally resource of other components, their production is affected too and in particular it decreases. This effect is not negative, but can have a negative consequence: the efficiency of the components generally depends on the working condition, so the variation of their resources involve a variation of their efficiency too. A malfunction, called induced malfunction, takes so place in the other components, although any anomalies have occurred in them. A second consequence of the variation of the working condition consists on the variation of some control parameters. In particular the total production of the plant has varied and some set-points can have varied. The working condition originated as direct effect of the anomaly is unacceptable, so the control system intervenes to operate a regulation in order to restore the setting values of these parameters. The intervention modifies the natural effects of the anomaly, so other malfunctions and dysfunctions are induced. The location of the intrinsic malfunctions becomes more difficult once the regulation system has intervened. The thermoeconomic diagnosis procedure here proposed is based on the determination of the working condition that would have taken place if the regulation system did not intervene. This condition is fictitious, as the constraints imposed by the control system are not complied, so it must be mathematically calculated. If the anomaly is sufficiently little, the effect of the regulation parameters on the unit exergy consumptions can be calculated using a Taylor’s development. The independent variables are represented by the characteristic variables of the regulation system, i.e. a set of variables which completely individuated its positioning. In this way an artificial working condition can be built, where the effects of the regulation system are not present but the effects of the anomaly are. This condition is here called free condition. The diagnosis is made by comparison of the values assumed by the unit exergy consumptions in free and reference conditions. The thermoeconomic diagnosis procedures proposed in literature are based on the comparison between operation and reference conditions. In this comparison the contribution of the regulation system is hidden and sometimes makes impossible the correct location of the anomalies, as shown in the proposed applications. The proposed procedure is here applied to two energy systems: a steam turbine and a gas turbine plants, both able to also provide thermal power to an urban district heating network. A mathematical model of the plants, described in the first chapter, has been built in order to simulate their behaviour. Some anomalies have been simulated by varying the values of the characteristic parameters of the components, like efficiencies, heat transfer coefficients and pressure drops. The model also takes into account the regulation system. In particular its characteristic parameters in the gas turbine plant are the fuel mass flow, the opening grades of the inlet guided vanes and of the by-pass valve and the water mass flow passing through the recuperator. The regulation parameters of the steam turbine are the fuel mass flow, the opening grade of the throttles and the mass flow of the steam extraction for the cogeneration. The effect of these variables on the productive structure fluxes has been differently evaluated for the two plants: an analytical calculation, using the mathematical model of the plant, is proposed for the gas turbine plant, while a numerical calculation, using some working conditions, is proposed for the steam turbine plant. The analytical development has been expressed in form of a constrained optimization problem, mathematically described using a Lagrangian function. Such expression is particular significant as the Lagrange multipliers coincide with the marginal costs associated to every variable. In this way a cost can be associated to the regulation parameters. The procedure is applied to some cases of single and multiple malfunctions. In all the cases it allows to locate where the anomalies have taken place. The procedure is particularly helpful in the application to the gas turbine plant, where the effects induced by the regulation system are sometimes larger than the intrinsic malfunction, so that the correct location is impossible using the ordinary thermoeconomic procedures. On the contrary, in the steam power plant the effect of the malfunctions are mainly intrinsic, so that the correct location is in most of the cases possible using both the procedures. A further develop of the diagnosis technique consists on the erasure of the contribution of the effects induced by the specific components behaviour, i.e due to the efficiency variations caused by the variation of the resources. To take into account this contribution the system can be split into its components, each one considered separately. The knowledge of different working conditions, corresponding to as many regulations, allows to build a linear thermoeconomic model of the components. The each product can be calculated as resources vary. This dependence is acceptable only if the difference between the fluxes in free and reference conditions is sufficiently low. The unit exergy consumptions of every component in a condition characterized by the same resources as in free condition can be calculated. In this condition any anomaly is present in the system, as it is built starting from the reference state. A difference between the unit exergy consumptions respect to the reference values is due to the behaviour of the components. The induced malfunctions caused by the dependence of the efficiencies on the quality and amount of resources can be so erased. The more desegregate is the productive structure and the better works this technique. The use of structures defined by splitting exergy into its components is recommended. The procedure has been applied to some gas turbine operation conditions, where single malfunctions and a triple malfunction have been simulated. In all cases it has allowed to find at the same time how many were the intrinsic effects and where they had occurred. This is an important improvement in the application to the real systems, as the number of malfunctioning components is a priori unknown. The procedure is described in the forth chapter, while the applications to the power plants is shown in chapters 5 and 6. In this last chapter an application obtained using measured data relative to the steam power plant is proposed. These results do not constitute a demonstration of the absolute validity of the methodology for the energy system diagnosis. Nevertheless an important result has been obtained: a correct thermoeconomic diagnosis is impossible without considering the regulation system. It is not a finish line, but the starting point for future studies in this field. In particular, when if more than one anomaly are present in the system, the proposed diagnosis procedure does not allow to correctly predict the technical energy saving obtained by completely removing each one. In fact, this information requires the use of a mathematical model of the system. A second aspect of the thermoeconomic analysis here studied in deep is the effect of the choice of the productive structure on the results. The definition of fuels and products is not universally accepted, although many studies and applications have allowed to achieve a certain agreement. Some grade of freedom are so available for the analyst. The choice of the productive structure has a sensible impact on the cost calculation, in particular when some losses occur in the system, i.e. some fluxes characterized by a non zero exergy exit the system without being provided (and sold) to the users. These fluxes are not products, as they do not have any usefulness, so they can not exit the system in the productive model. The components of the system must be charged for them. Different criteria allow to make this operation. A different productive structure, an so a different cost accounting, corresponds to each criterion. In the third chapter some criteria are described and applied to the Moncalieri plants. A particular emphasis is given to the choice of the productive models for the gas turbine plant. The diagnosis procedure is not sensitive to the choice of the productive structure: all the examined cases give information in coherent to indicate the components responsible for the malfunctions. Moreover a detailed structure, obtained splitting exergy into mechanical and thermal (and if necessary chemical) components to define fuels and products, also allows to obtain a more detailed information. In particular, if the gas turbine plant is considered, a more detailed structure allows to individuate the causes of pure mechanical or thermal malfunctions. On the contrary if other kinds of malfunctions occur, the location becomes more difficult, as the effects are split on terms of the unit exergy consumption matrix. Nevertheless the information does not contradict the one given by a simpler structure, so the contemporary use of both of them is suggested. The last contribution of this thesis is the evaluation of the exergy cost to be associated to the regulation system intervention. This quantity is obtained considering the fuel consumption and the total product in operation and free conditions. The unit cost is defined as the ratio between the variation of the resources and the corresponding variation of the products. This parameter allows to evaluate the incidence of internal constraints, like set-points, on the plant efficiency. If the plant does not present any anomaly this parameter is equal to the marginal cost calculated in reference condition, otherwise it assumes a different value. An higher value means that the regulation system intervention causes an increase in the cost of the products, while a lower value causes a cost decrease. negative values are associated the contemporary decrease (or increase) of the plant efficiency and the total production. From the malfunction analysis point of view, a value of the unit cost of the regulation higher than the unit cost of the plant products means that the regulation system induces malfunctions in the system. In that case the use of the proposed procedure is particularly suitable, as it allows to eliminate those malfunctions from the system.