1. Modeling the Assessment and Monitoring of Reliability of the Condensation Thermal Power Plants (Co-TPP)

The development and use of condensation thermal power plants (Co-TPP) is characterized today by great complexity, regardless of whether a technological scheme or built-in equipment is observed. On the other hand, large energy plants with new or improved solutions can be built only in case they have a high degree of safety and reliability and when they fully meet the applicable environmental criteria. Any disturbance in the operating mode of such a plant or reduction of its power also affects the electric power system (increase in the reserves of production capacities in it, uneven supply of electricity to consumers, etc.). Reliability assessment methods are mainly based on results of experiments on the set of system components based on observations of parameters of number and/or time of failure. In order to determine the reliability of components, it is necessary to either conduct some long-term and very expensive tests on a very large number of samples under special operating modes collect the data from exploitations, which is very risky. At the same time, the choice of general mathematical methods is especially important, due to the different shapes of the curves which quantitatively define the reliability with different functions of the failure rate and the great dependency of such curves on the change in the operating mode of the components and environmental conditions. In an attempt to overcome the above problems, we find that the introduction of approximate calculations gives an overview not only of the basic characteristics of the reliability of the observed system as a whole, but also insufficiently exact final parameters, due to a whole series of larger or smaller approximations, as well as the inability to take into account all the existing influences (development of new technologies, specificities of new disorders, etc.). On the other hand, the calculation of reliability of a complex system represents only the first initial phase of verification of quantitative features, that is, the very formed hypothesis in which we have more or less confidence. Their final acceptance or refusal represents the verification of reliability through the control of certain quantitative indicators of the system for the set technical conditions of operation. For these reasons, the alternative concepts, such as reliability control or hypothesis testing, have been often used in the literature to verify the reliability. Diagnostics, the evaluation of the state of elements of the facility together with tracking the progression of its aging, is very complex, responsible, and expensive task which demands educated personnel and modern diagnostic equipment. Diagnostic equipment available in the market is filled with diversity and methods used for diagnostic purposes are not generally accepted. The results of conducted diagnostic controls do not always give full answers, so that they are often limited to the monitoring of trend of change of observed diagnostic values. Consequently, experience becomes an unavoidable and immeasurable element of diagnostics. Experience itself is of course only possible to be acquired through the work and usage of diagnostic equipment, but it is also necessary to keep in mind the cost of experience acquirement in relation to a risk of investment in testing equipment. Development of diagnostic methods is intense regarding both field and laboratory methods but efforts to provide more and more cost-effective application methods are highly required. By developing new technologies and through the application of modern equipment and tools for monitoring of present state and diagnostics of the primary gear, the cost of routine maintenance that makes possible to recognize priorities of intervention maintenance can be decreased.

The methodology of maintenance regarding reliability also includes analysis of failure in the process of decision-making when maintenance is in question. A major problem in the early stage of development of maintenance strategies was analysis of reliability of complex energetic technical systems. Developing the aero-industry and introducing tracking of certain parameters during the operation (condition monitoring) was the basis of maintenance of technical systems (according to the condition).

1.2 Models for Predicting the Reliability of Complex Technical Systems

Today, the most frequently used models for predicting the reliability of technical systems are based on stochastic or statistical analysis, including Markov chains (processes), Poisson processes, Bayes method, state-based models, Monte Carlo simulations, and combinations of these models [¹,²]. As their use in the analysis of complex energy systems is accompanied by significant limitations (most of these models focus only on mean time to failure (MTTF) or the expected number of failures for a given technical system), a smaller number of models regarding imperfect preventative maintenance actions have been developed (when the maintenance action fails to increase reliability level to 100%), as well as their integration with block diagrams [3]. One model for predicting the reliability of complex systems with a block diagram is the split system approach (SSA) model [4]. The researches related to the interactions between individual parts of technical systems and their failure or reliability prediction using a very low number of data about failures are also very limited and their application is very rare. A larger number of researches have been published about the technology of maintenance and models of reliability of technical systems. Predicative maintenance strategy, that is, condition based maintenance that belongs to the third generation of maintenance, carries out maintenance actions based on the condition of the parts or the entire system. As a result, the aims of this strategy are a higher level of reliability and availability of the plant, greater safety of operation, better product quality, longer lifetime of equipment, etc. The next strategy is a proactive maintenance strategy, with the aim not only of preventing the failure of the system, but also of setting the conditions to avoid or minimize the consequences of failure itself in the event of its occurrence. Additional optimization is the goal of maintenance, while prediction of reliability and risk assessment are the basis for making optimum maintenance decisions. The philosophy and concept of maintenance relate to the effective implementation of reliability assessment models, their implementation methodology, and strategic policies at the level of business management structures. Maintenance and reliability studies published so far can be classified into one of the categories shown in Figure 1.1, which provides an overview of the research in the domain of science on the maintenance and reliability of complex technical systems (CTSs). Below is an overview of several important conceptual approaches to reliability research as a CTS.

The power plant reliability index, which is decomposed and graphically presented in the research of Nikhil Dev et al., is a solid attempt to solve a crucial problem in such CTSs that are preventively maintained in the sense that it is possible to compensate for a small number of data on failures [5]. Since the model relies heavily on the empirical experience and does not have enough objective data, its application is limited to more efficient energy systems. Exploitation systems and systems that can be decomposed into a number of components after a long period of exploitation by failure cannot be used to apply this reliability model. More importantly, interactions of failures of the system components are not predicted by the model. The result of the model is the real time reliability index (RTRI), which in fact represents the value of reliability at a time point of calculation.

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FIGURE 1.1
The overview of research in domain of maintenance and reliability science of technical systems. (Based on Sun [4] and Milovanović [11].)

A larger number of researches rely on Monte Carlo simulations, such as those of Naess et al., attempting to bypass the problems of mathematically complex or undetected rules of reliability modeling [6]. This method gives space for successful overcoming of such a task, but the models lack time dynamics and/or preventive maintenance actions. Thereby, the models have lost the possibilities of real implementation, especially when it is necessary to apply them to systems of a more complex structure.

The research of Weber and Jouffe combines several methods, such as the method of analysis of the fault tree, the Bayesian network, and the Markov chains [7]. This research is focused on modeling the reliability of production processes in CTSs. This also means higher requirements in the domain of reliability modeling, especially since this model has taken into account the existence of preventive maintenance actions as well as the time dynamics of reliability. The thing which is not complied with the real circumstances are the interactions of failures and the possibility of applying the model to CTSs decomposed into a large number of components due to the exponential increase in the number of combinations in the model, and the calculations for individual cases cannot be done within a reasonable time text.

Moazzami et al. gave assessments of the reliability of busbars in the power plant using Monte Carlo simulations; however, the time dynamics of movements of reliability assessment is missing, and no cases of repairs having a real impact on the system reliability are foreseen [8]. Also, reliability assessed based on parameters has been partially observed without an integral model.

In his dissertation, Sun developed several models relying on the existing ones such as SSA and analytical model for interactive failures (AMIF) [4]. The new developed model is the extended split system approach (ESSA) which involves the case of a small number of system failures, preventive maintenance actions, imperfect fixes, interactions of failure, and time dynamics. The model also predicts the existence of cascading failures as the possibility of applying different distributions of failures. The model is focused on making decisions on timely preventive but not corrective maintenance actions, so that the combined maintenance is excluded from the model. The model allows the reliability of each component of the system to be specifically considered, and preventive maintenance actions are defined according to each component of the system separately. The interactions of the components are defined by the matrix of interactive coefficients where the impact of the failure of one component on the failure of the other component is constant over time. After the preventive failures of components, the change of characteristics of theoretical distribution of failures of the system components where there would be no preventive maintenance actions is possible. However, the heuristic approach to determining the coefficients of interaction has remained a weak point in the model and made it more difficult for application. The ESSA model does not have clearly stated algorithms, although it is clear that they can be defined. The model also has predefined times of preventive maintenance actions and the implementation of maintenance actions in terms of reliability is not part of the model, although it is a reality in case of maintenance based on reliability [4].

The research done by Petrović et al. is based on the Markov process, whereby the optimal preventive maintenance time is established by maximization of the system availability. The model is stochastic and considers maintenance actions and their effects. The model is an applied transport system that was decomposed into two components. Such a model can easily be oriented to reliability; an answer about the times of optimal maintenance actions can be provided based on its criteria. However, in order to be applied to structurally complex technical systems with a large number of components, this model would have to undergo significant changes and many issues have to be solved. The model also neither anticipates an imperfect maintenance action nor an interaction of failures of system components [9].

Milošević, in one of the conclusions during the research within his dissertation, proposed an integral model for ensuring the reliability of CTSs, such as thermal power plants [10]. This model was based on the assumption that by decomposition every system component can be subject to the separate process of simulation, that is, a certain group of components, when necessary, are simulated together according to the reliability, which is the case with interaction of failures of components. The development of this model started from the collection, arrangement, classification of data, and decomposition of the system on the database. After the decomposition, the reliability of irreparable system components was modeled, then corrective maintenance actions were introduced, and then the preventive, so that the model included the reliability of the components that were maintained in combination. By following the assumption of perfect and imperfect maintenance actions, where after the maintenance actions the reliability follows, two models for predicting the reliability of components were developed. In case of the model of imperfectly maintained components, the problem of assessment of parameters of reliability for the theoretical distribution, to which failures of components due to successive maintenance actions are subject, appeared. Since this problem was complex, it was solved by Monte Carlo simulation on concrete examples, and a further simulation based on the parameters obtained was developed. The greatest challenge was the development of reliability models with the existence of interactive failures. It also included preventive maintenance actions, which are often more frequent than corrective, and it was necessary to develop methods for diagnosis and quantification of failure interaction. For this purpose, software solutions were used to analyze the data on system failure. Preventive maintenance actions during downtime were also included as a reality in the model itself. Regression analysis established the interdependency of some component failures with the interactions of others. It was done using a software package that identified the potential mutual interaction of failures of all components. Based on this, an interaction matrix was developed that was the basis for further modeling after calculating the extent of the change of reliability of the affected after a certain inter-failure of affecting components. This finally resulted in development of the proposed model.

Within the framework of his dissertation, Milovanović emphasizes the importance of defining and forecasting the reliability indicators in case of preventive maintenance of complex systems [11]. Corrective actions in terms of further risks of failures and prevention of major damage are possible only if they are based on timely assessments. The optimum management of the thermal power plant system should be based on the assessment and complex optimization of the reliability indicators, depending on the way they are secured and the hierarchical level of details of the system as a whole, as well as the current stages of the life cycle of the plant. For these reasons, the optimization process includes basic structural, parametric, and constructive solutions related to the thermal power plant system through the change of its most important characteristics: energy efficiency, maneuverability, reliability, and economic efficiency as a whole. The complex of optimization goals ends with the overall selection of reliability indicators and possible manners for their provision, given the already established rules regarding the higher hierarchical level of the electric power system. The proposed modified method for assessment of optimal reliability of the system of condensation thermal power plant provides a good basis for further work on its development and improvement of the accuracy of the assessed values, with the introduction of technical diagnostics and the modern information and management system. The maintenance costs incurred are minimally possible for each specific situation. The dependency of the cost of electricity generation in the thermal power plant from the level of reliability should be considered from two aspects: thermal power plants and users. In both cases, the point of minimum costs determines the optimal reliability of both the thermal power plant and the user.

The Monte Carlo method, as a general method for solving problems in different fields of science, is based on the use of random numbers and probability theory [12]. It is used to simulate physical phenomena and solve complex problems. The final solution of a system of equations that describes the relations among particular phenomena is usually based on random sampling of relations and interactions, with a large number of repetitions or calculations. In this regard, the use of this method is one of the best examples of using computers as a research tool, in solving problems depending on their formulation in a statistical and random environment, that is, in situations where physical experiments are either impractical (risky) or too expensive. The very essence of application of the concept of the probability theory within the Monte Carlo method is to find solutions to physical problems often not related to probability or reliability. The direct simulation of the Monte Carlo method has several steps, which can be defined as follows: defining the basic settings of the problem faced by the analyst, the lack of important prerequisites for performance of necessary experiments (the technological process does not allow it, too expensive process, too risky job requiring the work on the boundaries of the criterion function, lack of time to perform the experiment, etc.), it is not possible to obtain an exact mathematical expression (mathematical model) which would adequately describe the process, and based on which a solution would be found within the limits of the allowed error; without performing an analytical solution, a random process defining the solution of the problem is defined, it is simulated on the computer, and the parameters for its solution are assessed, with the definition of allowed error and the required number of repetitions of the process itself (the distribution of parameters of different elements of a CTS selection of a random sample of each element, selection of their basic and supplementary parameters, combination of these samples and obtaining of the reliability of the technical system as a whole). For the calculation of the reliability of CTSs using the Monte Carlo method, the reliability or unreliability of each element is represented by a series of random numbers, while the choice of numbers is done in a sequence, so that each successive number is another success or a lack of success (failure). In addition, a computer, in which the database a program for generating random numbers is already installed, is used as a tool. By the appropriate combination of results obtained from the selection and interpretation for each element of the technical system, simulation of the technical system as a whole is done. The very program installed on the computer functions on the basis of logical diagram and description of operations on the system, as well as the existing functional connections of the system elements. The further course of the procedure is determined based on the previous starting condition (the condition of the system in operation and the condition of the system in failure). In the case when the number represents a success or the correct condition (operational condition), the group of random numbers for the next element in the same logical input is set at the input, and the new value of the random number is determined depending on whether the element is a success or a lack of success (failure). The process continues until the failure or breakdown occurs, which omits this path from the logic diagram and automatically returns the activity to the closest connection of the other parallel path. Thereby, the program uses the appropriate random number for the first element in the parallel path. If in this case the selection simulates success for the first element, then the random number set for the second element in a parallel path is used to determine the success or failure of that element. The process continues until a successful path is found, which indicates the success of the technical system as a whole or until the failure is simulated on all possible paths. The speed of the process depends on the number of elements of the technical system and the degree of its complexity, as well as on the reliability of the elements of the system itself. In cases where the preparation of the computer program shows certain simplicity, it is recommended to develop a mathematical model and apply certain analytical expressions and solve them. There are certain groups of factors influencing the applicability of the Monte Carlo method in order to determine the reliability of CTSs, and the three more important factors are emphasized. Redundancy of many technical systems is sequential, and in some cases it is “actively parallel,” meaning that the failure time of one element affects the reliability of its sequential redundant replacement. A set of random numbers which represents the success or failure of a redundant element is not a constant, but is a function of a special random number representing the failure time of an element in the first path. Each number of the first group, which represents the relation of the first element, also determines the group to be used for the redundant element [an alternative is that the second group of random numbers remains the same, but that the interpretation of each value as a success (operational condition) or a lack of success (failure) varies as a function of a random number in the group for the first element]. Since this is a complex task that involves several phases with individual logical diagrams, an element that is redundant in one phase can be in one or the other row, and sometimes in a different redundant configuration. The fact which applies here is that if it does not appear in one phase—it will not even appear in the following phases. The program must make it possible to draw the condition of each component from one phase to the next, until the simulation of the complete task, while the determination of one successful path per phase is not enough if more than one phase is involved. The condition of each element must be fully determined at each stage. The probabilities of setting aims for solving the complex task of determining the reliability of CTSs can be individually required, while the probabilities of security and success of tasks are most often determined and interconnected. Further decisions defining the continuation of the task depend on the number of available redundant paths for performance of critical functions. At the same time, the probability of successful achievement of other noncritical functions may require a simulation, whereby the computer program must allow simultaneous determination of all these interdependent probabilities.

The boundary method as a reliability calculation method using limit values is applied when the reliability has to be established for the technical system or for the simplest redundant configuration [2]. It is characterized by time savings in relation to considerably longer procedures with mathematical models. It is suitable for the most CTSs in which exact mathematical models cannot be developed, provided that the simulation procedures have to be previously developed. The boundary method involves calculation of the numbers of upper and lower forecasting boundaries, whereby the calculation of the probability of the operational condition or the failure condition and their combination becomes quite simple. Values of a failure event(s) are deducted from the unit (the upper limit of reliability), while the probability of successful cases is added to the unit (lower limit of reliability). By considering as many cases as possible, the area between the upper and lower limits of reliability narrows. The first calculation of the upper limit takes into account only those elements of failure that can individually cause nonperformance of the task, so serially bound blocks in the logical diagram should be considered for the boundary method. This is sufficient only for some satisfactory assessment. In the case where the reliability associated with individual blocks is not very high, for CTSs requiring high reliability in operation, it is necessary to observe parallel blocks.

The Markov process describes the future condition of the system based on the current parameters and thus makes the past and future condition of the system independent [4]. When it is not about continuous but discrete sizes, we can talk about Markov chains [3]. Markov processes are suitable for assessing the reliability of functionally complex systems and complex repairs or maintenance strategies. However, they support the monotony of functions and processes. A model based on the Markov process assumes that the system has the final space of condition and a series of possible transitions between these conditions. Functions, different failure and standby models, and various maintenance activities can be described as different conditions. If the transitions between the conditions can be approximately described by stochastic processes based on the characteristics of this model, then Markov methods can be used to estimate the reliability of the system after several conditions [13]. Thus, it is quite common to use Markov theory to model the problem of predicting the reliability of a repaired system [14]. Markov chains is applied when rates of transition, for example, malfunction or repair depending on the condition of the system, vary depending on the load, level of stress, system structure, etc. Especially, the system structure (e.g., standby conditions) and maintenance policy may create dependencies that cannot be balanced by other techniques. Markov models also have many limitations. They are often applied to repairable systems; however, it is not easy to reach the probabilities of all the transitions that are necessary, and the assumptions of the models are always very restrictive. Also, there are problems in the domain of continuous sizes, for example, Markov processes of mathematical solutions of equations can be very inaccessible, due to which the applicability of the model, as well as in many other cases, is seriously questioned.

The Poisson process was named after French mathematician Siméon Denis Poisson. It is a stochastic process in which events occur continuously and independently of each other. Poison processes are a special case of Markov chains. Poisson processes can describe various phenomena and system failures. This model assumes that the failures are independent of each other and that the number of failures in each time interval is subject to Poisson distribution [15]. There are various types of Poisson processes, such as the homogeneous Poisson process (HPP), the nonhomogeneous Poisson process (NHPP), the complex Poisson process (CPP), the doubly stochastic Poisson process (DPP), the filtered Poisson process (FPP), etc. The HPP as a model requires stationary increments while the NHPP does not require incremental increments. In many applications of the Poisson process, it is not realistic to assume that the average rate of failure is constant. This rate depends on the time, that is, the changeable t. That is why NHPP is a more suitable model for modeling repairable systems with imperfect maintenance actions and a lot of models are based on it today. Also, this model may include rates of occurrence of failures (ROCOF) when they are interdependent, and the time between failures is neither independently nor identically distributed [16]. Some researches suggest that multicomponent repair systems cannot be modeled on continuous distributions, which is logical due to the complexity of the reliability of the system being monitored [17]. Failures which appear in repairable systems could be considered as series of discrete events that appear randomly in the continuum. These situations behave as stochastic points of the process and can be analyzed by statistics of series of events. The log-linear NHPP model and power law NHPP model are two widely used models for repairable systems. Power law NHPP model is based on Weibull distribution. Pulcini applied this model to the reliability of complex repairs. Reliability is software modeled based on the Poisson process and the reliability of software based on this process is also modeled. The Poisson process is suitable for the analysis of repairable systems with more regular failures with the point stochastic nature of the process. However, the existing models on this basis are only available for random failures, but do not include growing hazards over time. Models based on the Poisson process assume that the probability of system failure follows the Poisson distribution, and the number of failures does not affect the reliability of the system. The HPP model assumes that the reliability immediately after the repair is the same as the reliability immediately before the corresponding failure, which makes the model suitable for the so-called minimum repairs, but not for repairs such as overhaul [14]. With the increase of diagnostic techniques, maintenance has got the ambition to improve the constancy of reliability prediction. The proportional risk model (PHM) developed by Cox is currently the most popular model of this type [15]. Similar is the proportional intensity model (PIM), although the first model is more flexible and as such avoids certain problems which appear with the other. Prior to the concept of a proportional hazards model, the reliability and hazard functions were mathematically defined as follows. The reliability function R(t) was used to represent the distribution of the random variable T of the homogeneous population of individuals each of which has a “failure time” [16].

Bayesian methods are brought into connection with Thomas Bayes (1702–1761). There are many of these methods, for example, Bayes factor, Bayesian game, Bayesian multivariate linear regression, Bayesian network, empirical Bayes methods, etc. [10]. The Bayesian model is also used in modeling reliability and it also implies the possibility of implementing empirical experience of maintainers. Mazzuchi and Soyer expanded this model to a traditional time-based replacement policy and a policy of replacing a block with minimal repairs under the assumption that the repair costs are constant and that the parameter of scale α and parameter of shape β are initially independent [17]. Considering the cost of repair of accidental and unknown system failures, Shue developed a model of adaptive replacements using the Bayesian approach, assuming that the hazard of system is monotonous and rising [18]. Using the Bayesian approach, Percy researched the possibilities of improving preventive maintenance [19]. Apelan tried to use a completely subjective or Bayesian approach for making of maintenance decisions when objective data were insufficient [20]. The Bayesian approach is used to describe failures with a common cause. The Bayesian model allows the empirical experience of maintainers to be involved as the biggest advantage but it is not in itself appropriate for modeling the reliability. Its greatest advantage is a combination with the theoretical probability distribution, in which the Bayesian method serves to correct this distribution as the main to describe the failure of the system.

Technological advance makes it possible to use computer techniques to increase analytical capabilities and quality of research [4]. Some of the advanced methods used in the researches are the fuzzy logic, neural networks, genetic algorithms, data fusion, combinations of Monte Carlo methods or Markov chains or these techniques, etc. All these methods are attractive for maintenance since they offer new possibilities in terms of the precision of reliability prediction. Some researchers combined different models (hybrid models), such as the Bayesian method with the Poisson process, or even three models, such as Bayesian, Markov chains, and the Monte Carlo method, resulting in the creation of new specific reliability models [11,21, 22, 23, 24, and 25]. Hybrid models have a perspective in terms of scientific research, but for now they do not provide universal solutions and have a serious problem at the level of applicability. In recent times, models that relate both to improper maintenance and attempts of prediction of system reliability have been developed. However, most models have serious limitations that limit implementation, but also do not create a realistic picture of the system reliability [10].

1.3 Mathematical Models of the Growth of Reliability of System

The process of system development is a constant interaction between testing and determination of types of failures and changes, which are directed to the elimination of these failures [26, 27, 28, 29, 30, 31, 32, 33, and 34]. The analysis of the influence of the introduced changes on the system reliability, by applying appropriate mathematical models, is very important for the assessment of the development process. It entails an iterative design-develop process that includes [35] detection of failure modes, identification of root causes, feedback of problems identified, redesign based on failure mode root causes, implementation of redesign, and verification of redesign effectiveness by retesting and iterating the process, Figure 1.2. The majority of models of reliability growth provide the making of conclusions about problems related to the existing system reliability and reliability projection in the next stages of development. The largest number of reliability models examine a certain mathematical formula, which represents the reliability of the system during the development phase. It is commonly assumed that these curves are nondecreasing. When the exact shape of the reliability growth curve is known before the beginning of the development, it is a deterministic model of reliability growth. However, in most cases, the exact shape of the reliability growth curve is not known before the start of the development phase, but it is assumed that the curve belongs to a certain parameter of the curves of reliability growth. The analysis is reduced to the statistical problem of assessment of unknown parameters from experimental data. The assessments can be revised by collecting new data in further development. Assessments are used to dynamically manage the reliability of the system. Concerning the parametric models of reliability growth, Duane’s and Wieren’s models are emphasized, and concerning the nonparametric models, the Barlow and Scheuer models.

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FIGURE 1.2
Reliability growth testing process. (Based on the Page 10. “AMSAA Design for Reliability Handbook” [35].)

Duane’s mathematical model for describing the intensity of the failure is as follows:

$\begin{matrix} L (T) = β T^{- α}, for 0 \leq α \leq 1 and β > 0, \end{matrix} (1.1)$

where L(T) - cumulative intensity of the failure during the working time T, α and β - parameters.

Duane’s model is very important for the analysis of reliability growth and is characterized by the following advantages: the model is mathematically simple and, in practice, it is often applied; since the parameter α is of a dimensionless size, it is relatively easy to establish dependency on the level of effort involved, it is possible to use cumulative data for tests. The similarity of Duane’s model to the Weibull model allows the use of existing analytical methods for reliability intervals and statistical testing of the hypothesis; the model is represented by the straight line on the log-log paper of probability, which is convenient for illustrating the reliability growth curve. The limitations of Duane’s model are as follows: the assumption of the model is that the failures belong to the exponential distribution, although the attributive tests can be analyzed if Poisson approximation for the binomial distribution is used; the model assumes that the corrective actions are carried out simultaneously with continuous tests, although it is successfully applied even when testing and corrective actions are interchangeable and when there is enough time to make changes to the system which is examined; if it happens that the form of growth of reliability cannot be precisely defined by the basic Duane’s model, then the whole development period is divided into a number of parts, so a special Duane’s model is applied for each part.

Wieren’s model of reliability growth. The mathematical model of Wieren’s growth of reliability can be described by the equation:

$\begin{matrix} R = a b^{c}, \end{matrix} (1.2)$

where the parameter a represents an unknown upper limit of reliability R, which is asymptotically achieved when the development time t→∞, while 0 < b < 1 and 0 < c < 1, parameters which are assessed based on the test results. At the moment, t = 0, the reliability level is ab. Therefore, the parameter c determines the form of growth of reliability. Wieren’s reliability model implies the assessment of parameters a, b, and c, while a certain procedure is required.

Reliability model of Barlow and Scheuer. This model assumes that the changes during development do not decrease the reliability of the system, but no functional form for reliability growth is defined. In this model, each failure must be classified as an inherited failure, in which the causes of the occurrence cannot be determined, or as a causal failure, the causes of which can be determined. The development program takes place in K phases, while similar systems are tested within each phase. It is considered that one phase of development is completed when the causal failure occurs, except for the last one. At each stage of development, the number of systems whose tests have been successfully completed is recorded. According to this model, it is assumed that the probability of inherited failure of q₀ remains the same during the whole development phase, and that the probability of causal failure at q_i at i stage does not grow from one phase to another within the development program, that is, must be q₁ ≥ q₂ ≥ ⋯ ≥ q_K. In order to eliminate the cause of failure, certain reconstructions are performed, so that the tested systems differ from phase to phase, but are homogeneous within a single phase. Reliability models include some assumptions, so the question is how much they are acceptable for presenting the actual process of reliability growth. It is important that the availability of appropriate statistical procedures necessary for the assessment of the relevant characteristics must be taken into account. However, these models provide a mathematical description of the empirical and planned reliability growth, as well as the design of reliability for the next stages of development. When the characteristics of reliability growth are poorly known, nonparametric methods are used, in which the lower limit of confidence for reliability is very low. Reliability models are used to consider changes in system reliability during the program of development. Regarding the time period of use and the goals to be achieved, there are four models of reliability growth: empirical growth model, planned growth model, model of growth assessment, and the model of the projected assessment of growth.

Empirical reliability model provides an answer to the question of what kind of form of reliability can be expected. The model provides a general form of growth and is based on data from the development of similar systems. It can be graphically represented by showing some reliability characteristics (mean time between failures, probability of success, etc.). The most common form of the empirical model is given by a continuous curve, whose equation is determined by one of the mathematical models of reliability growth (often, Duane’s model). The continuous curve represents growth in the phase or part of the phase, where changes are made in the design of the system being tested and where the growth of reliability is realized in a series of jumpy changes. These jumpy changes can be negative, which is often the case at the beginning of the production process, when production is still in the process of establishment.

The planned reliability growth model is used to solve the question of what values are expected in certain periods of the development phase. The curve of the planned growth model has the same general form as the empirical curve, but passes through a determined set of points, which are determined from the characteristic phase. These determined values depend on the complexity of the system, time of testing, failure analysis, and possibilities for reconstruction. The initial reliability values are mainly determined by the synthesis of the test results of the elements and subsystems, or based on the results of prototype testing. If the initial test results in the development of the system do not match the predicted initial reliability values, the program must be carefully reexamined to assess the forecasting reality.

The reliability estimation model provides an answer to the question of the extent of existing reliability at a certain point in time. This assessment can be achieved with three possibilities: based on the results of testing of the existing system project; based on a statistical combination of the results of all previous tests, taking into account the achieved growth of reliability; based on the results of all previous tests, with a preliminary assessment of the results of previous tests. The model of the projected assessment of the growth of reliability provides an answer to the question of what is expected at the end of the development program, if certain planned activities are followed. The projected assessment can be obtained by extrapolation starting from the currently assessed value, using the empirical model for determining the general shape and the proposed program characteristics for determining the specific direction of further development.

1.4 Reliability Assessment Methods

An important step within the security analysis, and therefore the reliability of technical systems, is simply the standardization of security, that is, the formulation of the requirements for the security of system. In addition, the problem of formation of the minimally sufficient set of indicators, which characterize the observed property of certain system, is still not completely solved [36]. Depending on the observed system, the security, or reliability as its component, is the result of superposition of other more “elementary properties,” such as mechanical strength, stability, refractoriness, elasticity, etc. The existence of potential sources of danger and thus the rate of hypothetical failures can serve as a universal quantitative feature of safety or reliability of all technical systems. Thus, through this indicator, it is possible to mutually compare the technical subsystems of different purposes and operating principles, that is, “measurement” according to the scale of emergencies of different sources of danger. This represents a risk, which is characterized by the frequency of occurrence of unwanted events in the unit of time. In the dictionary of the European Quality Organization (EOQ), within the terms used in the field of general quality management, the risk is defined as “the common factor of probability of occurrence of unwanted events and their consequences” [37]. Until recently, the basic methods of analysis of reliability as a component of the broader term of security were based on the conservative concept of “absolute security,” which is not adequate to the probable nature of occurrence of failures and disorders of exploitation, caused most frequently by changing the conditions of exploitation. On the other hand, in order to avoid the occurrence of common differences between the set requirements for reliability and their dependency on the fulfillment of operational requirements, special attention should be paid to defining the analytical expressions and numerical values of reliability parameters [38]. For the realization of this task it is necessary to form an appropriate database, related not only to the system as a whole, but also to the components of the system as the basic links in the reliability chain. The intensity of failure of some of the system components depends on many factors (mechanical and thermal overload, environmental impact, exploitation conditions, the manner of repair or replacement, the influence of human factors, etc.). In addition, the reliability assessment, depending on the purpose and phase of the life cycle of the thermal power plant, is generally realized in three basic manners: estimation of reliability on the principle of similarity of equipment, on the basis of its typization or retrospective analogue information, with the correction for new forecasting project conditions, then the reliability assessment with the method of listing components, or so-called rough reliability calculation, with the formation of appropriate statistical methods and logical-credential models, as well as assessment in case of incomplete determination of information and reliability assessment by the stress analysis method, or the so-called fine calculation reliability (characteristics of possible relations of work parameters and loads), as well as assessment of probability of endurance parameters and possible deviations of constructive elements, expert correction of characteristics of durability and resources of details with the participation of harmful impacts [39,40].

The intensive development of probability methods of security analysis resulted in the formulation of a set of probability methods for analyzing the security of technical systems [8]. Further progress in improving the reliability assessment, except in the adaptation of classical methods to the specificities of the complex of the thermal power plant, lies in the need to shorten the testing time of one or more factors by selecting an optimum plan of shortened testing by automating on-line procedures of reliability assessment and its optimization based on selected criteria (most often the economic criteria) [41]. Taking into account the very structure of the thermal power plant technological system and the characteristics of reliability of certain elements, it is also necessary to provide the measure of importance and rank through it the elements from the aspects of rational distribution of resources while increasing the reliability of each of them. As a result of solving the problem, the list of the critical consequences of the consequences (effects) of the failure is determined. The conditions necessary to be fulfilled in order to get the list are the following: knowledge of the conditions of operation of the thermal power plant system, its structure and possession of the database of failure of elements. Setting the methodology and criteria, based on which the priority lists for replacements and reconstructions of individual units within the CTS of Co-TPP would be determined, results in the maintenance of satisfactory safety of the entire Co-TPP system as a whole and reduction of the operating costs of the electrical energy system (EES) as a higher hierarchical system [42]. The “weak points” in the complex system of the thermal power plant significantly affect the reliability and safety of their work and carry certain risks. An increase in the level of security and reliability of any system element is directly reflected in the system as a whole. All this requires that the considerable attention has to be paid to the issues of reliability and availability of individual components and the system as a whole. Starting from the assumption that the manners of providing reliability at different stages of lifetime can be provided through taking certain types of reserves, with the elimination of all other redundant parameters, both for the basic and the extended lifetime, the following are stated as their most frequent representatives: functional form of reserve, reserve in load, time reserve, assessment of the dependency of the reliability of plant on the adopted programs of overhaul and the contents of overhauls, and the assessments of reliability, security, and durability of the thermal power plant with the participation of the technological and information form of the reserve.

1.5 Indicators of Reliability of Co-TPP

The issue of reliability of operation of Co-TPP is of special interest, given that about 70% of total electricity production is realized on these plants. Since it is not possible to have a stock of electricity in the warehouse, it is necessary to have an adequate reserve of installed power during the operation of the Co-TPP within the EES, and any change in the consumers’ demands for electricity determines the production of electricity within the EES [43]. The work of any electric power facility is strictly defined by legislation, rules, and instructions, on the basis of which the operating conditions and safety of their exploitation are defined. Quality, reliability, safety, economy, and ecology are particularly important for the operation of electric power facilities. The reliability is the probability of realization of the required function of the objective of energy system (production of electric and heat energy and/or technological steam) in the given scope and concrete conditions of exploitation, Figure 1.3.

The energy block within the electric power system works with the adequate installed power N (set 1) according to the specified graph of load. The probability of such operating mode in specific conditions is given with P_N (set 2) in time duration $τ_{r a d}$ (set 3) [44]. The reliability of the energy block is determined by its operating ability for production (set 4) in the form

$\begin{matrix} E = N P_{N} τ_{r a d} \end{matrix} (1.3)$

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FIGURE 1.3
Illustration of the concept of reliability of the energy system for the production of electricity and heat and/or technological steam. (Based on Milovanović [44].)

which represents the state of the energy facility in which it is able to fulfill all or part of the given function (work with reduced power or production of one form of useful form of energy) in the required extent. The loss of operation ability is a failure of the system. In the process of exploitation, there are cases when there is a complete or partial loss of functional properties. The event which results in the discontinuance of the energy system operation is called failure. Failure can be complete (emergency interruption or downtime) or partial (reduction of work ability), Figure 1.4. Failures can be immediate or gradual. Immediate failure is characterized most often by breakage and devastation of individual elements or parts of the power system, which automatically by its function imply its full downtime, while a gradual failure has a time change in the state of one or more plant elements. These failures have been caused most often by the weakening of the material due to work in thermally unfavorable conditions or caused by removal of material and the reduction of walls due to corrosion, erosion, and abrasion.

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FIGURE 1.4
Overview of operation of power facility within EES [2]. (Based on Milovanović [37].)

In addition to the criteria for assessing reliability indicators, it is also necessary to define the basic and supplemental reliability indicators. The choice of basic and supplemental reliability indicators is directly related to the conditions of specific tasks [44]. There are different indicators in the stage of development and design of facility, the solution of the tasks of optimization of the power system and its components, in the stage of production of serial energy equipment and details, in the stages of installation and commissioning, as well as on the stage of exploitation. Failure and stages of recovery of operating ability represent opposite events that make up the flow (sequence) of events, Figure 1.5.

The safety of functioning of the energy system and its accompanying energy equipment is determined by the number of different (by their nature) factors, such as construction, quality of materials used, production technology, quality of installation, service and exploitation conditions, quality of steam and similar. The flow (sequence) of events can be described by the sequences of distribution of random sizes, which characterize the probability of occurrence of these events P(k), where k represents the number of failures (random events). Thus, the probability of event X

$\begin{matrix} P (X) = m * / n, \end{matrix} (1.4)$

where m* is the number of random events and n is the number of all events.

The probability of work without failures for the repaired (newly recovered) to the planned operation time T₀ is determined as follows:

$\begin{matrix} P (τ) = e^{- (λ / τ)}, \end{matrix} (1.5)$

where τ is the observed time interval and λ = 1/T₀ is the intensity of failure, Figure 1.6.

The parameter that characterizes the frequency of failure for a certain period is the parameter of flow of failure, and represents the rate of the probability of occurrence of failure of the object which is repaired, or the average number of failures of equipment which is repaired in the unit of time. The reliability of the facility of the energy system according to its function, that is, the giving of mechanical work through the connection to the generator and the production of electrical as well as thermal (and technological) energy according to a predetermined strict regime with regulated and unregulated deductions, can be characterized by appropriate complex indicators, of which the most significant is so-called coefficient of production of insurance (power, energy) [1,11,44].

FIGURE 1.5
The course of failure and its removal with the aim of restoring work ability (τ₁, τ₂, …, τ_n—operation time until the failure (time from the start of operation until the occurrence of failure; τ_rep1, τ_rep2, …, τ_repn—time of repair). (Based on Milovanović et al. [44].)

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FIGURE 1.6
Intensity of failure during service life of elements. (Based on Papić [1].)

Table 1.1 gives an overview of the planned operation time to the failure T₀ and time of repair $T_{p o p}$ for 200, 300, and 800 MW power blocks and their most important elements (boiler and turbine plant). As specially performed cases of coefficient $π$ , in the literature there is often also a coefficient of technical exploitation $K_{t i}$ and a coefficient of readiness $K_{g}$ . The coefficient of readiness is characterized by the probability of a state of work ability at an arbitrarily selected time for the element characterized by alternative conditions “work (exploitation)—repair (recovery),” calculated on the basis of the following equation:

$\begin{matrix} K_{g} = T_{0} / (T_{0} + T_{r e p}) = μ / (λ + μ), \end{matrix} (1.6)$

where λ = 1/T₀ and μ = 1/T_rep are appropriate intensities of failure and repair

TABLE 1.1
Overview of the Planned Operation Time to the Failure T₀ and Time of Repair T_rep, h

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The frequency of failure of an element is evaluated by the number of damage resulting in the exit from the plant in the unit of time and is determined as the ratio of the number of elements with the failure for the period $Δ τ$ compared to the total number of one-type equipment, that is, it is applicable:

$\begin{matrix} ω = n_{0} / (n Δ τ) = 8760 (8784) / T_{0} = 8760 (8784) λ . \end{matrix} (1.7)$

The time of repair of the element is determined as the time of overhaul increased by the duration of the diagnosis for the purpose of finding the defect.

The technical exploitation coefficient represents the ratio of the expected value of the time during which the facility was in operational condition for a period of exploitation and expected values of the total working state of the equipment of steam turbine, technical maintenance, and overhaul time. It should also be noted that the coefficient of readiness is a probability that the individual equipment and turbine as a whole will be ready to work at any given moment, except for the planned periods for performing planned overhauls and technical maintenance tasks.

Elements can be connected within the energy system either serially or in parallel or combined in series and parallel. An example of a serial connection is the connection of elements within the main power facility (MPF) of a thermal power plant (TPP), where the failure of any of the three elements means a failure of the system as a whole, Figure 1.7. The following equations apply to this connection) [44]:

$\begin{matrix} ω = Σ ω_{i}, \end{matrix} (1.8)$

$\begin{matrix} t_{r e p} = Σ ω_{i} T_{r e p i} / Σ ω_{i} . \end{matrix} (1.9)$

The parallel connection of the elements is characteristic for boiler plants connected to the common collector, from which fresh steam is supplied to the turbine plants or to the facilities that are reserved within the higher hierarchical EES. In energetics, for a quantitative assessment of reliability, a number of complex indicators are used, from which the factor of power of block, factor of utilization of block capacity, factor of exploitation, factor of stoppage, etc. are used. The factor of power of block K_R is defined as the amount of realized and nominal (computational) power, and is calculated according to the formula K_R = R₀/R_N, where R₀ is the achieved mean power in exploitation, and R_N is the nominal power (for new blocks the power factor is 1 and for the elderly 0.95–0.98, where deviations to 5% are allowed).

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FIGURE 1.7
Presentation of serial connection of elements of MPF to TPP. (Based on Milovanović [36].)

The factor of utilization of capacity of the block K_ik, which is determined based on the generated electricity and is defined as the quotient between the amount of generated electricity and the theoretically maximum possible generation with 100% used capacities of the facility of the block of the thermal power plant, is calculated according to the formula K_ik = E₀/E_m, where the generated electricity of the block of the thermal power plant is E₀ = R₀ T_e, that is, E_m = R_N T_k, theoretically maximum possible generation of the block of the thermal power plant. The following parameters are applicable: R₀—the realized mean power in exploitation in MW, T_e—the realized exploitation time in hours, R_N—the calculated nominal power in MW and T_k—the calendar time in hours.

Next (it is applicable) [44]:

$\begin{matrix} K_{i k} = R_{0} T_{e} / R_{n} T_{k} . \end{matrix} (1.10)$

Since the power factor is K_R = R₀/R_N and the exploitation factor is K_E = T_e/T_k, the capacity utilization factor of the block is obtained:

$\begin{matrix} K_{i k} = K_{R} K_{E} . \end{matrix} (1.11)$

This coefficient is in the range of 0.40–0.80 depending on the age of the block, its performances, and operational readiness. The exploitation factor is one of the indicators of the time exploitation of the block of the thermal power plant and can be defined in two manners: the most commonly used in literature is the definition of the block through exploitation time—the work of the block on the network (T_e) and the calendar time (T_k) for the observed period (monthly, annually, etc.), that is, is K_e = T_e /T_k. For the new block, the annual exploitation factor is 0.8, while for the old blocks it ranges from 0.6 to 0.75. In this way, a certain coefficient of exploitation is used in analyses, since the overhaul time is not excluded from the calendar time, which is important in comparative analyses. The other manner for determination of the annual exploitation coefficient is through the time of exploitation and the difference between the calendar time and the time determined for the annual overhaul, K_e¹ = T_e /(T_k− T_r). This manner of calculation is more used at the local level and in the preparation of annual plans. In most thermal power plants, the duration of overhauls is not standardized, and for a detailed analysis, the other manner of determination is not reliable for the evaluation and comparison of the quality of the operation of the thermal power plant.

Stoppages of thermal power plants are caused due to disturbance in the technological process resulting from nonstationary operating modes caused by the failures of the plants and the vital parts of plants. The failures which condition the stoppage violate the secure and safe operation of plants by the impossibility of maintenance of technological parameters according to technological instructions and technical regulations of exploitation. Some failures, which require urgent termination of the power plant block, may endanger the safety and security of personnel at exploitation and maintenance. That is the reason of existence of protection and blockages for immediate disconnections after the occurrence of such cases. Failures of plants and equipment of the thermal power plant block which condition the stoppage and shutdown due to recovery can be classified into two basic groups: the emergency ones, due to which protections automatically act and exclude the block and the nonemergency ones, because of which the work for some time can be extended and technical regulations on exploitation and security and environmental safety will not be endangered. That is why the stoppages are grouped into two basic groups—unplanned and planned stoppages. Unplanned stoppages happen as a result of failure in operation of the block caused by abrasion of the material, aging and loss of functional properties, thermal overload, improper exploitation and maintenance failure, noncompliance with technical instructions and regulations, inadequate overhaul, weariness, deteriorated quality of basic fuels, etc. Since the thermal power blocks are complex units, and are made up of a large number of dependent technological units and complex plants, thereby the possibilities for unplanned stoppages are higher, especially if the blocks are older. Planned stoppages include annual overhauls and overhauls for care of plant. Analysis of quality of exploitation and maintenance can be carried out through the thermal power plant failure factor. Factors of stoppage include: failure factor, factor of planned stoppages (care), factor of overhaul, and factor of suppression from the network.

The factor of failure or exclusion is defined as the quotient of time duration of removal of failure due to which the outage or exclusion of block from the network happened immediately after its occurrence and the calendar time for the observed time interval. It is most often calculated at annual level, and can be calculated for other requested time period of exploitation of thermal power plant. It is calculated according to the formula K_KV = T_KV/T_K, where T_KV is the time duration of the shutdown due to the failure in hours or exclusion in the observed time interval. In fact, this is the time period from exclusion of the block from the network to re-inclusion or synchronization to the network. If there are more stoppages, then these times are aggregated depending on the period for which the analysis are done, that is, applies to

$\begin{matrix} T_{K V} = T_{K V 1} + T_{K V 2} + \dots + T_{K V n} . \end{matrix} (1.12)$

The value of this factor is in the range 0.1–0.15, calculated on an annual basis. Lower values are for new blocks and larger for old blocks. Planned shutdowns are introduced as preventive measures in order to achieve greater operational readiness and risk reduction, and prevent emergency cases in the work of the blocks of thermal power plants. The size is important while planning the investments in older blocks or solving the problematic cases in exploitation that do not endanger safe work, and they need to be annulled in a certain period of time.

For the planning of shutdowns of old blocks, which are at the end of their service life, the factor of planned shutdowns is the most commonly used, whose values are most often defined on the basis of monitoring of the exploitation data of the thermal power plant and similar thermal power plants. It is defined as the quotient of the time duration of the planned shutdown and the calendar time for the observed time interval. It is calculated according to the formula K_PZ = T_PZ/T_K, where T_PZ gives the time duration in hours of the planned shutdowns in the observed time interval, and it is defined from the disconnection from the network to the re-synchronization. In fact, this is the time period for which the failure has been removed due to which the block has been suspended or the planned investment has been made on the block of the thermal power plant or the sum of more such time periods, if any, during the year. It is most often determined at annual level and is rarely applied in planning. It is used in special cases with older blocks and larger investments, and at the end of the service life of thermal power plants.

The overhaul factor defines current and capital annual overhauls. It is defined as the quotient of the overhaul duration and calendar time at the level of the year. It is calculated according to the formula K_R = T_R/T_K, where T_R is the duration of the overhaul in hours, that is, the stoppage of block for performance of planed overhaul, and is defined as the exclusion from the network to the re-synchronization. The overhaul factor is determined at the year level and has different values depending on whether the blocks of thermoelectric power plants are older, of higher power and the extent of planned overhaul work (whether it is current or capital annual overhaul). The values of this factor for older blocks range from 0.08 to 0.16. Higher values refer to capital, and less to current overhauls.

In the practice of exploitation of the thermal power plant blocks, there are cases when the power system network due to reduced consumption or for some other reasons, the production increase which is not covered by the consumption. In that case, the dispatching service must maintain the balance of the system and exclude the individual blocks from the plant, that is, suppress the block of the thermal power plant from the grid. This occurs most frequently when the water supply in hydroelectric power plants is uncontrollable large or in cases where the reductions in consumption are unplanned, that is, there is no known electricity purchaser. These cases are rare, but they happen in practice. They are defined by factors of suppression and are not of planned size. The suppression factor is defined as the amount of time of depression and calendar time. It is determined at the level of the year by the formula K_P = T_P/T_K, where T_P is the duration of the suppression in hours, that is the blockage of the block from the exclusion from the network to the re-synchronization, and T_K(h)—calendar time on an annual level.

1.6 Failures and Damages during the Operation of Co-TPP

The failure of a part of the thermal power station system or the thermal power station as a whole is defined as the termination of the possibility of some system element or the system as a whole to perform the functions they have been designed for [11]. The reduction or the loss of the technical system working capacity in the course of exploitation is a consequence of the effect of various factors (embedded, random or time), which change initial system parameters, causing alongside also a different level of damage. For reducing unplanned jams, preventing breakdowns, and increasing reliability in the work of the individual parts of thermal power stations or the thermal power station as a whole, it is necessary to strictly apply the regulations for quality insurance in the course of their lifetime, starting from the phase of preparation and design and all the way to the end of exploitation and its withdrawal from the operation. During the exploitation period, the degradation of the condition of both the elements and the thermal power station as a whole is necessary. Monitoring of the condition in a specified time period or continuous monitoring represents a process of constant inspections or supervisions of the equipment operation for the purpose of ensuring a proper functioning and detecting the abnormalities that announce a forthcoming failure. It is suitable for the equipment for which it is not possible to predict the wear-out trend by the periodic checks. The very modeling of the system conduct most frequently depends on the specific operational research, application of the mathematical statistics method (definition and selection of distribution, assessment of observed parameters, hypothesis test, definition of the scope, and estimation of characteristics), as well as on the application of the probability theory method (different mathematical models) [38]. The functions that the technical diagnostic system should realize are given in the form of specific checks of the system technical condition, checks of the working capacity, checks of the functionality, location of the failure position at the lowest possible hierarchical level, as well as estimation of the remaining period of use or trend of the malfunction occurrence, Figure 1.8. The application of technical diagnostics opens up new possibilities of managing electrical power stations, which creates all preconditions for a significant decrease of corrective and preventive activities related to maintenance, along with preserving the same or realizing a higher level of reliability of the plant as a whole. By introducing maintenance according to the condition, along with the application of the technical diagnostics and proper determination of the remaining operational lifetime (reliability management), it is possible to decrease the number of failures of the system of the steam turbine and electrical generator) [1]. Of course, this has to be followed also by the application of the computer technique, as well as the database both at the level of the thermal power stations and at the power utility level. Besides, the diagnostics enables a good quality assessment of the aging progression and the remaining lifetime, and specification and planning of the restoration, the replacement of the old equipment, as well as optimal correction, that is, it is tightly related to the maintenance strategy according to the equipment condition, which makes it directly affect reduction of the costs originating from the cuts in production, transmission and distribution of the electric power [37]. The supervision over the equipment implies an automated and continuous determination of its status, along with following the values of several parameters within the plant. Depending on the number and type of the controlled parameters, we differ partial (following one or several related values) and complete monitoring systems (following a hundred different parameters of a certain plant element). Here, it is important to mention that the complete monitoring systems often also contain the expert subsystem, which based on the collected data and the diagnostics relying upon the embedded expert knowledge and algorithms at an early stage warns the operator about the forthcoming problems and recommends necessary actions. It is not difficult to show that the purposes of diagnostics and monitoring are identical—increase of the plant cost-effectiveness and equipment availability. We can say that the automated diagnostics “with no time tensions” is in fact a synonym for the system monitoring [38,46].

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FIGURE 1.8
Functions of technical diagnostic and monitoring related to condition of certain parts of thermal power plant. (Based on Milovanović [38].)

The most common classification of failures in TPP includes their grouping into the failures due to structural defects (defects of technical documentation, errors in calculations and mathematical modeling, wrongly applied methods of calculations, etc.) and low quality of production, errors in exploitation (noncompliance with the operating mode of EES, noncompliance with production guidelines and instructions, accidental mistakes of the workers), low quality of assembly work, and defects of overhaul. Design and assembly errors are detected in the period up to 30,000 h of operation. Figure 1.9 shows the distribution of the failures in TEP. Physical and chemical processes in the steam boiler during exploitation are the most complex (steam tract, smoke tract, material of certain elements of the steam boiler), and result in a change in the properties and characteristics of the material. The processes of combustion, heat exchange, corrosion, and formation of deposits on the heat exchanger surfaces determine the reliability of boilers to a great extent.

Characteristic failures caused due to design defects on boilers result in large heat deformations on the heating surfaces caused by the high speed of ash consumption. The distortions of the characteristics of elasticity, casting, with thermal treatment of heat-resistant parts made of steel, welded parts, etc., are widespread. The deviation of real charcoal characteristics from the calculated ones leads to deviation from the given volumes of combustion products and temperature of flue gas at the boiler output, and the consequence is the disturbance in the work of the boiler’s convective part, the increase in ash extraction. The low quality of steam and water leads to a sudden increase in deposits, with the rise of the temperature of the steel tubes and their overheating.

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FIGURE 1.9
Distribution of failure on TPP as a whole. (Based on Milovanović [44].)

Table 1.2 gives the intervals for distribution of failures of boiler, depending on their capacity. The intensity of failures of the energy equipment of the boiler plant is not the same, Table 1.3.

During the exploitation, the pipe screens are exposed to the effect of radiation energy, the corrosive active environment of the fuel combustion products, which, at low circulation speeds and disturbance in the water regime of the boiler, results in their damage and failure in the operation of the boiler. It should be noted that the quality of water and steam has a decisive influence on the damages of the heating surfaces of the steam boiler.

TABLE 1.2
Distribution of Failure on Steam Boiler

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TABLE 1.3
Share of Failure of Power Equipment of Boiler Plant

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An uneven field of temperatures along the height of the smoke duct, which has a steam superheater (the heat load of the upper and lower parts of the coils can vary up to 20% and the smoke channel width up to 30%), has significant influences on the change in thermal deformations. Steam heaters are also damaged by prolonged operation at temperatures higher than 500°C, where the metal structure suffers significant changes. The curves on most of the pipelines are damaged due to corrosion-fatigue processes, and due to the lack of compensation for uninterrupted thermal expansion. The main damage to the stop and the control valves are defects in valve housings and valves, deterioration of density, and similar. Compared to the boilers, the failures during the operation of turbines are significantly less frequent. However, physical and chemical processes leading to the reduction in reliability levels of turbine components have much in common with the processes occurring on boiler elements (change of properties of metal over long service life, erosion processes, etc.). Emergency situations happen in the case of breakage of blades, then in the failures in the automatic control system, as well as during damage to the bearings (increased vibration). They are caused by the imperfection of technology of commissioning, disconnection from the drive, and unloading. Damaged blades due to the action of the flow of wet steam are characteristic for the last levels of the part of low pressure of turbine. Rotor damage happens most often due to insufficient quality of manufacturing and disturbance in the operating mode of commissioning and exclusion from the drive, which can lead to the occurrence of residual deviation. Figure 1.10 shows the characteristic distribution of the turbine failure.

The number of failures can be prevented by the application of organizational and technical measures (by ensuring that the observed plant works only on the project fuel, by selecting the optimal operating regimes, carrying out measures and maintenance activities, etc.). Other failures can only be prevented by timely replacement of equipment or some of its elements (preventive maintenance). Timely overhauls of the high technical level with the participation of normative technical documentation and diagnostic methods provide reliable long-lasting operation of the equipment, Table 1.4.

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FIGURE 1.10
Overview of main causes of failure at turbine plants from 200 to 500 MW per years (1, …, 6—years). (Based on Milovanović [44].)

TABLE 1.4
Orientation Indicators of Reliability of Energy Blocks by Years after 200,000 h of Work

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1.7 Modified Method for Assessment of the Optimal Reliability of Co-TPP

Possible criteria for the selection and formulation of the contents of mathematical models and methods for calculating the reliability of the thermal power systems during the life cycle, depending on the choice of its principled scheme, variants of construction and parameters, methods and character of the predicting the reserves, system for overhaul-technical maintenance, diagnostics, and protection, are as follows: forms of connections in terms of reliability, operating modes of basic and auxiliary equipment, as well as other conditions defining the manners for ensuring the reliability of facilities as a whole and its constituents; the procedure of processing the condition of the working and nonworking activities of the elements and the system as a whole, their interconnection and possible forms of representation of their change in time; defining criteria, basic and additional reliability indicators for solving optimization tasks by elements, and the system of thermal power plant as a whole; defining the limitations and additional requirements of the tasks for assessing the optimal reliability, as well as the additional conditions, the prescribed norm or possible forms of their presentation; scope and characteristics of the initial information (parameters), with the assessment of their completeness, presentation form, accuracy, etc.; the possibility of applying existing programs of computer technology, volume, periodicity, calculation speed, and limitations of existing methods. Analyses of the complex system of the thermal power plant from the aspect of expected reliability and preventive engineering have the task not only to find and remove the “bad spots” in the plant, but also to assess the moment and justification of its revitalization. A timely decision on revitalization will result in the appropriate reconstruction and modernization of both the plant and the system as a whole. In this case, the appropriate economic savings will be achieved in the work of the power plant, and the funds invested will be returned through increasing the reliability indicators, that is, increasing the time in operation, and reducing the time of failures. The algorithm of the modified method for assessing the optimum reliability, shown in Figure 1.11, based on the system of technical diagnostics and condition-based maintenance, will significantly improve the procedure for making such a decision in terms of larger unification of the method on blocks whose nominal power is different from the referent. The starting database was developed as a result of many years of research carried out for the basic configuration of the thermal power plant for solid fuel (coal), with a nominal reference power of 300 MW. Due to the specificity of the work of the considered systems of different thermal power plants, the lower minimum values of the interval estimation of the reliability characteristics of the basic referent block are defined. Any change of a particular project-forecasting condition requires additional consideration of other forms of information sources, mainly from lower hierarchical levels and a greater degree of details of the objects and processes that occur there. It is also necessary to complete the basic method of structural calculation for the reliability indicators for the working and nonworking condition of work with the corresponding additional correction factors (two-step correction system). The rapid and efficient applicability of this method on a range of energy blocks with different installed nominal power, the position within the power system and a specific maintenance system, is enabled by the use of a simple empirical equation [11,43]:

$\begin{matrix} C_{A} = {(A / 300)}^{m} B_{300}, \end{matrix} (1.13)$

where A is the nominal power of the thermal power plant, MW; B₃₀₀ is the indicator of reliability for a 300 MW thermal power plant system; C_A is the an indicator of the reliability of a thermal power plant with a power different than 300 MW; m is the value of the exponents obtained on the basis of statistical data processing from exploitation during the life cycle of the thermal power plant.

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FIGURE 1.11
Block diagram of modified method for reliability evaluation of condensation thermal electric power plant. (Based on Milovanović [11].)

The values obtained represent the estimated value of the reliability indicator, the accuracy of which is further improved by the iterative process to a certain, previously defined, level of accuracy. For simplicity, the initial use of data in the form of diagrams of analogue objects (the first iteration) is recommended, and, then in the next phase, it is necessary to make the necessary corrections from the aspect of participation of functional and reservation of, as well as participation of time reservation, etc. We should not forget the correction of the assessment of dependency of reliability indicators in relation to the overhaul programs, as well as the contents of the overhaul cycles. At the level of development and design, previous calculation comparisons of the mono and double block structure, as well as the parameters of the selection of operational stocks, fuel, and heat carrier, are realized. Additional research should be carried out in case of poor results for some of the reliability characteristics (e.g., testing with and without material destruction, additional analysis of data related to the exploitation of the observed system or its analogues, etc.). Since the given procedure has iterative character, it is interrupted after confirming the initial hypothesis related to the agreement of the result of prognosis and actual exploitation data. The following is the process of developing a time plan for specific activities in order to achieve a higher level of reliability, using one of the standard methods (the method of network plan—Program Evaluation and Review Technique or PERT, the Gantt diagram or linear chart-chart, etc.), phase III of the process shown in Figure 1.11. Optimization according to the proposed algorithm of the modified method is based on the indirect method and internally in advance orientated specific range of variation of certain characteristics of reliability. This manner allows for certain simplification of a large part of the undetermined impacts and conditions of exploitation, that is, the very accuracy of this method is limited by the accuracy of the optimal results with properly given starting data, with the possibility of its continuous correction on the stage of exploitation of the object. Methods and programs for solving the reliability of certain parts of the technological scheme or the system as a whole, with adequate planning of the program, content, and duration of planned overhauls, are based mainly on statistical analysis and the use of analogue-based results. Models and methods for solving optimization tasks can be conditionally classified into several subgroups:

Increase of the influence of the basic technological scheme of the plant on the mono and double block structure without its detailing and analysis of losses in the structure of equipment, through analysis based on nominal power
Variant assessment of the scheme of plant through the application of the FMEA/FMECA analysis and the tree of failure of the most critical drive (obtained by the method of ranking), combined with the analysis of semi-Markov or Markov processes of failure according to the criterion of the condition without failures or without occurrence of breakdown or the readiness.
Variant assessments of a complex set of reliability indicators for the corresponding principled scheme and structural reservation of the plant based on previously performed assessment of reservation of a higher hierarchical level of the EES, with simplified or detailed analysis (depending on the predefined precision).

1.8 System of Maintenance with Entries and Exits Toward Environment

Reinforcement of connections between technical and technological complexity of thermal power plant (TPP) (in the form of a high initial price of the plant and equipment and more rational exploitation—production and economic factors, effect of breakdown on the reduction of production of electric and thermal energy, as well as technological gas on one side and ecological requirements on the other side) conditions a complex dependency of the maintenance function on a large number of factors. Reduction of possibilities in realizing the goal function set in the form of certain criteria is followed by the appropriate change of the status of system and its elements, being most often a consequence of wear, fatigue, corrosion, abrasion, pressure, heating, ageing, etc. The maintenance system of TPP is linked with the environment through certain entry parameters presented in Figure 1.12:

Characteristics of TPP as an overall system and its consisting elements and accessory equipment (kind of TPP, place and status of TPP within electro energetic system (EES), manner of connections through transmission network, place and role within the system of South East Europe, estimated status, manner of exploitation, status of the level of applied technical diagnostics, etc.)

FIGURE 1.12
Presentation of the system of maintenance of TPP and ties with the environment. (Based on Milovanović [38].)
Available maintenance resources (available personnel for operations, possibility of use of services of external specialized companies for individual segments of maintenance and individual actions in maintenance, operating tools for maintenance, spare parts and possibility of producing spare parts on its own, materials, tools, etc.)
Economic-social factors (place and status of maintenance in the organization of TPP, customer’s culture, management of the system of TPP, tradition, etc.).

On the other hand, the system of maintenance of TPP with its organization structure, adopted strategy, and applied technologies of maintenance should satisfy planned objectives of maintenance (exit toward environment), defined within several groups:

Technical-technological objectives (maintenance and increase of working capacity up to the required level of efficiency of the system of TPP and its higher hierarchical system of EES, realization of planned basic and extended revitalized operating period of the plant and equipment of TPP, qualitative and quantitative improvement of the process of production of useful forms of energy, along with meeting general and special quality standards and service safety in the continuous supply of energy for the customer, increase of the production capability of TPP as a whole, continuous work on reconstruction, modernization and improvement of individual segments of TPP, with the goal of increasing technological, economic and ecological acceptability, etc.)
Economic-financial goals (reasonable use of the plant and equipment from the aspect of expenditure of spare parts, materials, tools and accessories, services of external specialized companies in individual maintenance jobs, then purchase of raw materials, available human potential, investment in maintenance in function of raising rentability, productivity and efficiency, decrease of costs with retaining the required level of maintenance in the value of TPP and its final product in the form of useful energy, etc.)
Social-sociological goals (development of the local community and broader region through the compensations linked with the work of TPP, reasonable use of primary energy resources through an optimal management of TPP within EES, rational use of human capacities, preservation and growth of psychological stability of employees, increase of motivation for work by raising the reliability of the system as a whole, ecological risk in order to protect environment, risk at work in order to protect the personnel at TPP and population that lives and works in the closer and broader environment of TPP, etc.).

The concept of maintenance organization within TPP should provide a comprehensive approach to all maintenance activities, with the goal of realizing the defined goal function in the form of continued production of useful energy, along with a safe and sustainable work with regard to the personnel and environment. Concerning its dynamic character, the system of maintenance of TPP prepares and implements the maintenance function in the form of organized forms by individual groups of equipment and plants. Therefore, modern strategies for maintenance of TPP should in practice represent most optimally integrated group of adequate data bases (subsystems), like the system of equipment components (German Kraftwerk Kennzeichen System—KKS system), determined significance of individual systems or components for a reliable and safe plant of TPP as a whole (analysis of causes and consequences of failures, analysis of the failure tree, analysis of importance with regard to reliability of the system as a whole, methods for assessment of reliability and determination of significance, along with defining “bottlenecks” or “critical points,” etc.), and system of potential mechanism of defects of individual components (CEN documents, e.g., CWA 15740:2008, etc.) and potential drive (operating) problems with TPP (statistics according to: API, ASME, OREDA, NERC, CEN, etc.). After defining the maintenance strategy (approach to maintenance), it is necessary to also define the technological maintenance processes (maintenance technology), with the goal of realizing set goals by an adequate maintenance strategy [45]. This implies elaboration of the maintenance technology itself, adoption of the known principles of performing recording of failures and repairs themselves, determination and diagnostics of different parameters that define the status of the system of TPP, as well as definition of appropriate repair technologies for the repair of damaged parts, lubrication, anticorrosive protection, etc. The decision on the type of maintenance of TPP is taken based on the criterion of company expenditures referring to maintenance and exploitation. In this manner it is possible to determine economically most acceptable activities of maintenance, which are necessary to be realized by applying an appropriate type of maintenance. In doing so, it is also not allowed to neglect the activities of maintenance technology linked with the control and diagnostics in maintenance, the repair technologies of maintenance themselves, as well as the activities connected with lubrication and anticorrosive protection of technical systems [46]. Among the procedures that are most frequently used for repairing broken or worn-out parts on TPP, those used are as follows: welding, built-up welding, metallization, electrolytic application, electromechanical processing, Metalock procedure of connecting broken parts, gluing technique, patented technologies for repair welding, application of material on the surface by the techniques of Plasma Spraying and Flame Spraying, etc.

1.9 Overview of Maintenance Activities in TPP

Important elements when determining the strategy for the maintenance and the scale and methodology of inspection of certain elements and the equipment in TPP are understanding and systematics of possible operative problems during exploitation (disturbance or complete loss of function), so as systematics of possible mechanisms of damage emergence (damaging or degradation of the material). In that light, according to the modified classification in the system OREDA or NERC, disturbances or deviations and problems related to structure materials in thermal power plant consist of several subgroups: fouling and deposits without fluid flow disturbances, fluid flow disturbances, like high or low fluid flow (HFF/LFF), no fluid flow (NFF), so as other fluid flow problems (OFFP), noise (NOIS), and vibrations (VIB), improper dimensioning and improper clearances, man-made disturbance, like deliberate disturbance, disturbance to insufficient training, etc., accidents, like fires, explosions and similar, improper start or stop—failed to start or stop (FTS), failed while running (FWR), external leakage (EXL) and overheating, thermal overheating (OHE), and other problems (OTH). Also, there are classifications regarding problems of installed material, Table 1.5. This kind of systematization enables grouping and marking cases of failures or possible damages, what as a consequence have easier statistical processing of the data on the level of individual parts or elements of the power plant (inside electro energetic system). Besides the history of operation (statistically processed data regarding past operation of the plant), for practical determining state of the system, it is necessary to create the plan of inspection by using convenient methods of technical diagnostics. Determining the scale of the damage and predicting its further progress together with following evaluation of risk and safety in the plant operation demands additional optimization of choosing the component and location of possible damage, type of the method for detection of the damage, but also the method for further estimation of scale and degree of the damage.

1.10 Unsolved Tasks and Directions of Further Developing Models for Forecasting Reliability of CTSs

The display of the developed reliability models mostly relies on the probability theory, with one part, to a greater or lesser extent, reflecting the experiences from practice or experimental researches. Other researches include empirical experience and experiment, but also have serious shortcomings despite the tendency to get closer to realistic conditions. For example, models that calculate a system reliability after preventative maintenance actions are inadequate and difficult to be applied, while models based on the reliability assessment of complex repair systems often do not decompose the system, while considering the reliability of individual system components, and the system is viewed integrally giving a simplified and imprecise assessment of system reliability. On the other hand, the interaction between the failures of system components is not adequately modeled, and the existing models related to dependent failures consider mainly the one-way effects of failure (models with continuous interactions between components have not been sufficiently developed yet). There are no adequate models developed to evaluate the reliability of the system based on a small number of failures or in cases where they do not exist. This means, as with any model, that certain assumptions also create some limitations of the model, but the flexibility of the model can be a way that it can be applied to as many technical systems as possible, and that its limiting assumptions can be corrected in accordance with the needs of modeling the reliability of the concrete technical system. Previous researches have some yet unsolved tasks in front of them. For example, there is a very large inconsistency between theoretical research and applied models in practice. The majority of models have been developed by scientists in the form of theoretical, mathematical, statistical, informatics or other problematics which cannot be implemented and solve a practical problem in the industry. The task for the next period is to develop models that can be implemented to solve practical problems in the industry, as well as to create models that can be applied in the case of a small number of available system data, and especially a small number of failures (the reality for many technical systems and the fact that when there is no alternative). The accuracy of the reliability model is something that still provides great opportunities for improvement. This is especially important when it comes to reliability prediction, which is the basis of planning and decision-making on optimal maintenance actions according to the given criteria. The reliability models relating to the CTSs have not been developed yet as sufficiently precise, applicable, and they do not include important real factors (further work in these directions is necessary).

TABLE 1.5
Systematics of Problems and Damages by CEN CWA 15740:2008

Images

For engineering application it is necessary to know the methods of calculating, testing, and installing the reliability of complex systems, which include software (so-called software systems) in the development phase, on one side, but the knowledge of methods of increasing the reliability of such systems in the period of use is also required on the other side. The reliability of a complex system depends on the level of reliability of each of its components. There are mathematical relationships that show the dependency of the reliability of the complex system on the reliability of the components. The reliability of the system is installed in the development phase, and it is therefore called inherent reliability. If the system is well designed, tested in details, well maintained, with proper use, a high level of reliability in use is expected. However, the reliability of the system is significantly influenced by the environment. Reliability is measured and has a practical interpretation. The exact value of reliability is never known, but its numerical estimate of close real value can be obtained. Such an estimate can be obtained with stochastic methods based on data obtained by measuring at a particular set. The reliability estimate based on a certain number of data sets is expressed by the reliability level, which represents the mathematical probability and connects the estimated and actual (but unknown) value of reliability. The level of reliability is the probability that a certain value of reliability will be between the lower and upper bounds.

During the development of CTSs and artificial intelligence systems, it is often necessary to make decisions in terms of indeterminacy. Because of the nature of indeterminacy, it is basically impossible to predict the consequences of certain activities, technical solutions, failures, etc. with absolute reliability. The application of quantitative models is focused on the use of the notion of probability to describe the indeterminacy of a different nature. The so-called Bayesian approach for assessment of reliability and security proved to be very perspective. In Bayesian approach, the indeterminacy is seen as a probability that can be interpreted as a relative frequency, as a level of conviction or in some other way. To solve the problem of indeterminacy in this approach, it is necessary to provide a set of a priori probabilities that describe the basic set. The a priori probabilities can be determined by means of frequencies or statistical analyses. Such statistical analyses start in advance from the fact that the relevant data for describing the basic set are available. If such data are not available, then the a priori probabilities are given as subjective assessments by the experts. The result of the analysis represents a set of a posteriori probabilities. On the other hand, the theory of fuzzy sets is a convenient mathematical apparatus for the treatment of indeterminacy. A fuzzy set represents such a set (interval) of values with the corresponding function of belonging to the given in this interval. There is on one translation for the term fuzzy, and in many works, the fuzzy is translated as: blurry, unsharp, papery, fluffy, fibrous, imprecise set. However, most often this term is not translated, but used in its original form, that is, as a fuzzy set. In the case when the starting data for reliability analysis are not given point-to-point, the problem of estimating the degree of criticality can be successfully solved by setting the change interval with the corresponding belonging functions. This approach can be implemented in expert systems designed for reliability analysis and failure analysis.

1.11 Conclusion

The database of input data, in addition to basic data about plant, has to contain relevant data on the process of previous exploitation and maintenance. The most important feature of these data is the truth, because based on the subsequent statistical processing of the basic indicators a further strategy for the operation on this plant is determined. In order to monitor the functioning of the reference system and define its reliability indicators, power events in the EES over a specific time period (usually the previous period of operation) are monitored and recorded. On the basis of data from exploitation, the total duration of the units outside the plant is calculated, and on the level of the entire observed time period the following basic data: the number of failures and stoppages, the average time of stoppage, the causes of failures and stoppages, the unavailability of the components and the TPP as a whole, the total unsupplied electric energy. The reliability indicators of the observed TPP, as well as its individual units are calculated by statistical processing of the recorded data. A set of data developed by recording of driving events and the results of statistical processing of the same are referred to as “statistics of driving events.” The statistics of driving events are also used for comparison with other analogue systems and the evaluation of performance of company that manages the TPP, as well as for studies of planning and probabilistic simulations of the operation of the system as a whole. Stoppage of units and components of TPP can be considered as random events joined by certain probability. Maintenance of machinery, equipment, and CTSs, from the aspect of the amount of necessary investments during their lifespan, is directly a function of defining and realizing the wanted efficiency (reliability, readiness, and suitability for maintenance), both at the level of their projecting and in the course of their exploitation itself. A well-chosen concept of maintenance, with a correct organization, programming, and realization of individual maintenance activities during exploitation, along with well-trained personnel and provided maintenance control, also affects improvement of economic results of the given organization or company. On the other hand, with the increase of complexity of technical systems there also occurs a problem of their optimal functionality, particularly if we know that such systems may often cause big economic losses or endanger security of a broader macro region and people serving them. Each CTS carries within it a big potential danger of possible occurrence of failures and break-downs dangerous for a broader environment. Reliability of complex systems, designed such as to successfully perform the function, determines lasting of the time interval in which the system will function without a failure. The research directed toward the increase of the reliability level and management of reliability during the lifespan of the object aims at defining the system of protection measures and their optimization from the aspect of simultaneous provision of exploitation efficiency and realization of complex regulations linked with the environment protection and safety of both micro and macro region. Special tasks of maintenance technology are provision of the process of maintenance optimization and advancement of principles for achieving higher quality, reliability, and efficiency of the CTS and its own production. The decision on the type and activities of maintenance may be taken also on the basis of expenditures of the company referring to maintenance and exploitation and chosen methods for maintenance. The order of development steps, which need to be implemented, affects both efficiency and effectiveness of the maintenance system. The formulation of tasks related to the optimization of the reliability of the thermal power plant system can in general be defined as the minimization of the loss on the construction and application of a serial unified power plant, which consists of losses associated with the installation itself and losses due to its connection to the ESS, depending on the reliability indicators and the possible manners for their provision for the given takas at each stage of the life cycle, as well as the taken system parameters and the known minimum necessary functional structure of the plant. For these reasons, all limitations of operation of the thermal power plant within the electric power system are also valid. Solving this problem is, taking all the given limitations and the overall analysis of the interconnection and overlapping of certain expressions, pretty complex from the aspect of the totality of the equation system, and for these reasons considerable simplification is done for the level of assessment of reliability indicators. Sometimes, in the process of optimization, the costs related to the hierarchical connection of the thermal power plant with the environment and the measures for implementing its supplementary protection, as well as the occurrence of possible restrictions, are included. The next step is the grouping of the said costs per objects, life cycle stages, and purpose of resources. This system should be supplemented with costs related to providing reliability for each of the phases of the life cycle of the thermal power plant system.

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Table of Contents for
1. Modeling the Assessment and Monitoring of Reliability of the Condensation Thermal Power Plants (Co-TPP)

1

Modeling the Assessment and Monitoring of Reliability of the Condensation Thermal Power Plants (Co-TPP)

CONTENTS

1.1 Introduction

1.2 Models for Predicting the Reliability of Complex Technical Systems

1.3 Mathematical Models of the Growth of Reliability of System

1.4 Reliability Assessment Methods

1.5 Indicators of Reliability of Co-TPP

1.6 Failures and Damages during the Operation of Co-TPP

1.7 Modified Method for Assessment of the Optimal Reliability of Co-TPP

1.8 System of Maintenance with Entries and Exits Toward Environment

1.9 Overview of Maintenance Activities in TPP

1.10 Unsolved Tasks and Directions of Further Developing Models for Forecasting Reliability of CTSs

1.11 Conclusion

References

Table of Contents for 1. Modeling the Assessment and Monitoring of Reliability of the Condensation Thermal Power Plants (Co-TPP)

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Table of Contents for
1. Modeling the Assessment and Monitoring of Reliability of the Condensation Thermal Power Plants (Co-TPP)