Development of a System for Estimating and Forecasting the Rational Resource-Saving Operating Modes of TPP

The world energy crisis and environmental problems have prompted a rapid increase in the share of electricity generation by renewable sources. However, the operating modes of such energy facilities are rather uneven over 24 hours. Thus, for the energy sector of most developing countries, and as well as for part of developed countries, such fluctuations in the overall energy production balance lead to the forced limitation of the equipment capacity at TPPs or to the full shutdown of power units.<br><br>The insufficient quantity of maneuvering capacities in the overall energy generating balance is a characteristic feature of the power systems of such countries as the Russian Federation, Ukraine, Macedonia, Bulgaria, Romania, Argentina, and others. The shortage of such capacities is often compensated for by the pulverized coal units with a power of 200–300 MW, whose operation is enabled at half-peak and peak modes. This equipment is not designed for such operations. Therefore, the development of a regime method of resource management has been proposed to prevent the premature exhaustion of TPP generating equipment.<br><br>Based on technical auditing of the operational documentation of generating companies, a method has been suggested aimed at forecasting the rational resource-saving operational regimes of the high-temperature elements of power equipment by optimizing the ratio of the number of launches of the equipment from various thermal states. An optimization problem has been stated, which implies determining such a distribution of the process structural-technological parameters that would ensure the maximal preservation of equipment resource. The residual resource has been selected as the objective function of the optimization problem. The devised method has been represented in the form of a comprehensive system for estimating and forecasting the rational operational modes of the TPP high-temperature elements, which makes it possible to define individual resource indicators over the entire period of equipment operation for all possible future combinations of operational modes and to compile forecasts for thousands of different variants of power unit exploitation, implying the calculation of resource indicators for each of them.


Introduction
An important issue related to the energy systems of many countries, including parts of Europe, the CIS, Argentina, and South Africa, is the lack of peak capacities in the overall generating energy balance. As a result, there is a need to in-volve base and semi-base TPP energy units to control power in the grid. However, such equipment is not designed to operate under frequent variable modes. Violating the service regulations, caused by the necessity of excessively frequent launches and stops of power units, leads to a sharp decrease in the lifetime of the specified power units [1].
Therefore, at the current stage of the development of the energy sector in such countries, an acute and priority task is to substantiate the feasibility and possibility to prolong the service life of TPP main equipment of this type. However, a simple extension of the service life will not make it possible to ensure the high excessive operation and is not able to provide sufficient time for the technical modification of energy generation.
It is expedient to apply such methods to manage the service life-time of high-temperature elements that could slow the pace of damage accumulation by the basic metal of power equipment [2].
Consequently, there is a need to devise a methodology for analyzing the impact of the structural, technological, and regime parameters of appropriate equipment on the damageability and residual resource. The purpose is to compile recommendations on the management of a high-temperature elements' resource, both for the power units that have been in operation over a long time and for those newly installed.
There is a need to combine experimental experience and classic empirical dependences, which are conventionally used for project calculations, as well as modern information technologies [3]. The effective implementation of the procedure for analyzing the reliability and durability of the high-temperature elements' operation is largely dependent on con sidering the correlation between the structural, technological, and regime parameters of a power unit.
Given the significant number of significant factors affecting the damageability and residual resource, there is a need to determine their optimal, or at least rational, distribution. The high efficiency of the implementation of the results from forecasting optimization in power engineering has been proven in studies [4,5].
The above testifies to the relevance of studies aimed at determining the rational operational regimes for the TPP high-temperature elements.

Literature review and problem statement
It is known that in order to ensure stable operation of a power system, it is advisable that the base capacities within a structural balance of energy generating capacity should amount to 50-55 %, half-peaks -to about 30-35 %, and peak -at least to 15 % [6].
The base maneuvering peak capacities in most countries of the world are provided by gas-turbine, hydroelectric power stations (HEPS), and pumped storage power plants (PSPP). However, according to data from WEC (World Energy Council), in some regions of the world, their capacity is not enough to compensate for the fluctuations in power systems. Thus, in the Middle East, their share is only 5 %, whereas in some European countries -more than 20 %.
For example, according to ref. [1], in 2020, as regards the energy-generating structure of Ukraine, they make up about 10 %, in contrast to 15 % required for the steady operation of the power system.
A similar issue relates to maneuvering half-peak capacities. At present, TPP power units with a capacity of 100-150 MW, which, at sufficient efficiency [7], could be used as the half-peak maneuvering ones, constitute about 18 % against the required 30-35 %.
At the same time, the energy engineering in many countries the world is characterized by a rapid increase in the proportion of electricity generation by renewable sources [8], which is predetermined by both the economic causes [9] and environmental problems [10].
However, it should be noted that the operating modes of such energy facilities are rather uneven over 24 hours. For example, according to the daily schedule of electricity consumption by United Energy System of Ukraine (UESU) as of 07.04.2020 [11], the renewable energy sources (RES) capacity for the period from 10:00 to 16:00 was about 2.5-3.3 GW, while it decreased to 220 MW over the evening-night period. Such a fluctuation in power in the overall balance resulted in the forced equipment power limits at TPPs or their shutdown.
Given the above, the energy systems in many European countries have recently been characterized by the displacement of semi-base power units at TPPs towards the half-peak and peak regions in an electric load schedule [12].
This issue was considered in [13], reporting an approach aimed at evaluating the problems related to the maneuverable operation mode of power units, with recommendations on the operation and planning of power plants' exploitation. The research results make it possible to increase the efficiency of maneuverable thermal power plants over variable modes, but the issue of their operation duration and resource-saving was not considered.
Paper [14] estimated the maneuvering possibilities of power generating units. The authors analyzed a series of negative consequences due to the increased dynamism and mobility of TPP power units. They proposed a series of possibilities to improve the maneuverability of power units. However, the issue of reducing the resource indicators of energy equipment was disregarded.
The influence of frequent variable operation modes of the TPP pulverized coal units on the durability of their performance was investigated in paper [15]. However, the authors did not address the optimization of the operating modes of power units to prevent the premature wear of TPP generating equipment under operation at the peak and half-peak parts of load schedule.
It is worth noting the data reported by the authors of scientific work [16]. It is noted that the growing proportion of electrical power from renewable energy sources dictates the irregular operation of heat-energy plants to compensate for the energy-generating instability of renewable sources. As a consequence, due to thermomechanical fatigue, creep, and corrosion there is a reduction in the operational period of power unit nodes. The authors of [16] emphasize that a technique that could predict the residual lifetime of unit operations is necessary for managerial decisions on the operation of power plants and planning their service.
All this allows us to argue that research aimed at creating technology for estimating and forecasting the rational, in terms of prevention of premature wear, operating modes of power units could make it possible to partly compensate for the negative impact of TPP maneuvering operations.

The aim and objectives of the study
The aim of this study is to build a system for estimating and forecasting the rational resource-saving operational regimes of the high-temperature elements of energy equipment. This would make it possible to automate the process of data acquisition on the residual resource and to extrapolate the information obtained for making timely decisions regarding the operation of specific power units.
To accomplish the aim, the following tasks have been set: -to acquire and to treat statistically the data on the operation of specific energy units at TPP (the number of launches; the number of launches for the most characteristic operating regimes (CS, NCS, HS), operation under a rated mode; overall operation time; -to determine the allowable number of cycles for different types of launches based on the technological audit, as well as data on the actual operating conditions over the entire ope ration duration, and the diagnostic control of the main metal; -to construct a mathematical model for predicting the rational resource-saving regime operational modes and to implement it by software.

Materials and methods to study approaches to building an evaluation and forecasting system
Underlying the development of an evaluation and forecasting system (EFS) is the approach based on [17,18,20]: «a mathematical model -an intelligent expert system -an automated evaluation and forecasting system», which is schematically shown in Fig. 1. An EFS examines the technological process in the form of a multi-component system of the interrelated examined objects: the elements of power equipment, a heat-carrier, mechanical loads, etc.
Over the period from 2004 to 2019, significant work has been made to accumulate and statistically treat data on the operation duration of specific TPP power units in Ukraine. There is a data array on the number of launches, the number of launches for the most characteristic modes of operation (CS, NCS, HS), the duration of operation under a rated mode, the total equipment operation duration. As an example, Tables 1, 2 give data on the DTEK Vostokenergo Luhansk TPP and the DTEK Vostokenergo Kurakhiv TPP.  Based on the concluded agreements with DTEK Vostokenergo, we conducted a set of estimation studies on determining the acceptable number of cycles for different types of launches. The studies were based on data about the actual operational conditions over the entire period of work, as well as the results of technical auditing and diagnostic control of the main metal, conducted at the Laboratory of Metals and Welding of the separate enterprise Luhansk TPP from DTEK Vostokenergo.
Calculations of the total projected and existing damageability (static, cyclic), as well as a residual resource, were carried out for the protocols of equipment operating under the basic modes of operation and under the potentially most difficult maneuvering regime (daily start-stop). The calculation studies and their results are described in detail in papers [15,21,22].
It should be noted that the greatest proportion of the damage to the rotors and casings of steam turbines belongs to launches from the hot (HS) and cold (CS) states. The smallest proportion to rotors damage belongs to launches from the non-cooled state (NCS) at a metal temperature at the launch onset of 250 °C. As an example, Tables 3, 4

Constructing a mathematical model for an evaluation and forecasting system
In analogy to work [17], a procedure for constructing a mathematical model can be represented by a sequence of the following steps [18]: 1. Define the analytical dependences containing parameters that describe the estimated pattern of the examined object. These ratios should take the form of a closed system of equations describing the behavior of the object of study in real spatially-temporal coordinates (the boundary problem of mathematical physics).
2. Solve the stated problem and develop a sequence of actions (algorithm) for the conversion of input parameters to the output parameters.
3. Implement the constructed algorithm in the form of software aimed at enabling the automation of computational experiments.
Each of the above stages is a separate, sometimes a rather complicated, problem. The result of each stage would be the construction, accordingly, of three interconnected modelsanalytical, algorithmic, and digital.
Thus, a mathematical model implies a theoretical construct in the form of analytical, algorithmic, and digital models. It reflects all the properties of the examined object within the created estimated scheme and enables its automation for practical application by using computer technologies.
An analytical model defines the properties of the examined object and the problematic aspect of the set problem [19].
The structure of an analytical model is as follows: 1. Description of the patterns necessary for the comprehensive assessment of the residual energy equipment resource.
The boundary problem of the non-stationary thermal conductivity: where λ, с, γ are the functions of temperature and coordinates at the initial conditions T T x y z f x y z In solving the problem on thermal conductivity, it is necessary to specify the non-stationary boundary condition of the I-IV kind: -I kind -when the temperature of an object's surface is known at a certain time: -II kind -at the isolated surfaces, the boundary conditions are set by a heat flow: -III kind -the regularities of heat exchange between a hot heat-carrier and the equipment metal: -IV kind -corresponds to the perfect contact of solids, in the cases when both bodies at the interface of their contact have the same temperature and heat flows: The stressed-strained state of power equipment was calculated when solving the equilibrium equations jointly, which, in a tensor form, take the following form: where σ i are the normal and tangent stresses in equipment elements, X i is the mass force operating in the elements, р i are the external distributed stresses, ρ i is the density of an element's material. We also added the equations characterizing the simultaneous action of deformations and the elasticity law, which, in a matrix form, take the following form: where ε ij ΔT is the vector of temperature deformations, β is the coefficient of linear expansion; ΔT is the change in temperature during operation.
A Neuber's method was used to account for the patterns of influence of the stressed-deformed state of TPP high-temperature elements on the accumulated damage. The calculation followed the mechanism of low-cycle fatigue and long-term durability based on the amplitudes of the intensity of the local elastic-plastic deformations at the estimated temperature in this region.
The amplitude of deformations was determined based on the values of strain intensity over a load cycle (initial stateloading -rated mode -unloading -initial state) according to: where ε i max , ε i min are the maximal and minimum value of deformation intensity per cycle.
The number of loading cycles until the occurrence of cracks was determined based on the experimental curves of low-cycle fatigue, obtained from testing the samples for stretching-compression under a severe symmetrical cycle and at a constant temperature. The allowable number of cycles at the estimated temperatures below 480 °C for heat-resistant steel, below 420 °C for alloyed steel, and below 350 °C for carbon steel, was selected based on the experimental curves of low-cycle fatigue by adopting the least of the two values: where N 1 , N 2 is the number of cycles that correspond in the curve of fatigue to the amplitudes ε a.r. and n ε ·ε а.r. ; n N , n ε are the strength reserve coefficients for the number of cycles and deformation; ε a.r. is the amplitude of deformation intensity reduced to the symmetric cycle of loading, taking into consideration the effective coefficient of stress concentration K T . The amplitude of deformation intensity, reduced to the symmetric loading cycle, was calculated as follows: σ B is the tensile strength of steel; r is the coefficient of loading cycle asymmetry; K T is the effective coefficient of stress concentration: where p is the coefficient of steel sensitivity to the concentration of stresses. At elevated temperatures, when there occurs the creep of material under the rated mode of operation, the number of cycles was determined as follows: The amplitude of deformation intensity reduced to the symmetric isothermal loading cycle at the estimated temperature: where where ′′ Π pred is the averaged annual damage projected for the period of operation following the estimation.
2. Constructing an analytical pattern between the reduced deformation ε a red and the acceptable number of cycles N p based on the mathematical-statistical analysis of experimental data.
It should be noted that significant difficulties in calculating the damage and residual operation duration of the TPP high-temperature elements, operation duration are caused by the inaccuracy or complete lack of information in reference literature on the behavior of special heat-resistant alloyed steels (brands 25Cr1Mo1V, 20Cr3MoWV, 15Cr1Mo1V, etc.) at the high operating temperatures of 400-550 °C. Similarly, there are no experimental data on the low-cycle fatigue of the above materials.
To solve this problem, we conducted a series of experimental studies into the prolonged strength and degradation in the static and cyclic strength of these steels after long-term exploitation in order to clarify the coefficients of strength reserve and determine the residual resource.
Experimental studies were carried out at the Pisarenko Institute for Problems of Strength of the National Academy of Sciences of Ukraine, using the laboratory installation AIMA-5-2, which is designed for the testing of metals for creep and long-term durability at constant temperature and load. The tests [23] aimed to establish a dependence between stress and time before destruction at the predefined constant temperature. The initial experimental results from studying the creep and prolonged strength of steels were analyzed based on a basic charting method. The basic charting method is based on a clear specification of the features of separate experimental sections and design diagrams of prolonged durability. Two problems are solved within the framework of this method: experimental data are analyzed; based on the analysis results, forecasting is implemented.
Based on data from the experimental studies and by using, as the base approximation function, the modified Steinhart-Hart equation, we derived the dependence between the reduced deformation ε a red and the allowable number of cycles N p in the range of operating temperature of 400-550 °C, which, in a general case, takes the following form: A detailed methodology of experimental research and the results obtained are described in detail in [23].
3. Stating a problem on the optimal distribution of the technological (mode) parameters for the operation of energy equipment based on the mathematical programming methods.
For the adopted structurally-technological scheme of a power unit, it is possible to distinguish the following basic parameters defining the course of the process: the geometric sizes of main nodes and parts of equipment, the thermal and aerodynamic parameters of a heat-carrier, as well as the mode starting parameters.
We propose solving the optimization problem, which implies determining such a distribution of the structurally-technological process parameters that would ensure maximum preservation of the equipment resource. Residual resource G was chosen as the objective function of the optimization problem: The solution to the set optimization problem is such where G is the objective function;  x is the vector of the structural-technological parameters that affect G; X is the area of the existence of vector  x; N X (min) , N X (max) are the boundaries of the existence of the vector  x components. Thus, the problem of maximizing the residual resource G requires finding such combinations of values of the vector  x, components whose implementation produces the extreme value of the objective function G.
For a given case, we have: Preprocessor unit: -a power unit operation duration; -the number of launches of a power unit; -the percentage ratio of launch types from different thermal states; -the results of the estimated assessment of SSS in a nonstationary statement.
Solver unit: -the functional dependence of the allowable number of cycles N p on the reduced deformation ε a red and the temperature of the metal; -patterns in the SSS influence on the accumulated damage in line with the mechanism of low-cycle fatigue and long-term strength; -the gradient (by Newton abo Levenberg-Marquardt) algorithms to search for extreme values.
Postprocessor unit: -a unit to display values of the residual resource in the form of three-dimensional surfaces; -a unit to display the rational range of values for the mode-operational parameters; -optimal distribution of the mode-operational parameters.

Results of evaluating the residual resource of power units' elements
Using the above system of estimating and forecasting the rational operating regimes of high-temperature elements, we studied certain typical equipment at TPP. The study involved the equipment for a power unit with a capacity of 200 MW, which exhausted its projected resource of 220,000 hours. The number of launches of the equipment corresponds to a park value of 800, of which 50 % are the launches from the hot state of the metal, 20 % -non-cooled, 30 % -cold. The obtained results in the form of contour charts are shown in Fig. 2-4.
For the intermediate-pressure rotor of the turbine K-200-130, the most rational mode of operation that could provide the highest durability and resource-saving is a semi-basic mode (Fig. 2). The rational values of the operating parameters are: the number of hours of work per year is 3,000-4,400 h, the number of launches-stops over a year is 48-64, with the following distribution for different types: CS -28-52 %, NCS -0-20 %, HS -28-48 %. In this case, there is an evident optimum distribution of mode parameters: 3,660 hours of work per year at 57 launches, of which 40 % -from the cold state, 60 % -from the hot state.
For some equipment, there is a clear region of the irrational operating parameters. Thus, for hot intermediate overheating steam pipelines, when increasing the number of hours per year, the residual resource decreases (Fig. 3). That is, for such equipment, the rational mode of operation in the peak part of an electrical load diagram is: 2,000 hours of work per year, 75 launches during the year, 90 % of which are the launches from the hot state, 10 % -cold. This is due to that the exhaustion of long-term strength for such equipment has a dominant effect on the rate of decrease in the residual resource.
Specific equipment has several ranges in the rational operation modes. This is typical for equipment, which is equally damaged both by the mechanism of exhaustion of long-term strength and due to the accumulation of low-cycle fatigue. For example, a drum in the boiler TP-109 has two rational regions of mode parameters (Fig. 4).
The first region of rational values is the basic mode involving 6,100-6,500 hours of work per year at the minimum number of launches (25-32) per year, 90 % of which are launches from the cold state, the rest -from the hot and non-cooled states. The second region is the peak mode implying 2,000 hours of work per year and the number of launches of 70-75, of which 67-90 % -launches from HS, 0-15 % -NCS, 10-18 % -CS.

Discussion of results of developing a system of estimating and forecasting the rational modes of operation and its application
The reported system for estimating and forecasting the rational resource-saving regimes of operation of the TPP high-temperature elements makes it possible to determine the individual resource indicators over the entire time of equipment operation for all possible combinations of operation modes. Numerous studies of the resource indicators of Ukraine's TPP power equipment performed earlier have been summarized and treated statistically. That has made it possible to detect the most typical modes of power units' operation, as well as to determine the main mechanisms for the accumulation of damage by the main metal of the equipment, as well as the factors leading to its destruction. This has allowed us to establish regularities in the influence exerted by each of the typical modes of operation on the rate of exhaustion of the residual resource of the equipment, in order to determine the dominant factors of TPP exhaustion.
The established analytical dependence (21) of the lowcycle fatigue of heat-resistant turbine steels makes it possible to automate the estimation process while studying the residual resource of energy equipment. An issue related to such calculations is that when forecasting residual operation duration, cyclic damage of the metal is estimated based on experimental curves of low-cycle fatigue for a particular combination of operating modes. When a different distribution of regimes is involved, it is necessary to «manually» recalculate. Therefore, typically, when forecasting the residual resource, the condition was accepted that the po wer unit would continue to operate in the same mode as at the time of calculation. The derived analytical dependence makes it possible to automate the estimation of a metal cyclic damage for many different combinations of TPP operation modes.
The constructed estimating and forecasting system makes it possible to consider all possible intermediate modes of operation of power units within two diametrically opposite variants. Namely, a fully basic one (under which annual operation duration approaches maximum T→max while the number of launches per year is minimum n→min), as well as a full peak one (T→min, n→max). Additionally, different ratios of the number of launches from the typical thermal state conditions (CS, NCS, HS) are considered. At the same time, certain logical conditions of operations are taken into consideration. For example, for a variant with a large annual operation duration, most of the launches must be from the hot state as, in this case, the downtime is small and the equipment would not have time to cool down to the non-cooled or cold states.
Thus, the EFS makes it possible to build forecasts for thousands of different variants of the power unit operation, with the calculation of resource indicators for each of them. This makes it possible to choose a convenient mode of operation from the region of rational values, thereby providing for the sufficient durability of the equipment operation. This information is useful for generating companies when planning a strategy for their operations in the power system.
At the current stage, the key drawback of a given estimating and forecasting system is that it can provide information about the rational mode of operation for a particular type of equipment, not the entire power unit. Fig. 2-4 show that, for various equipment of the same unit with a capacity of 200 MW, the regions of rational operating modes differ. This is due to that each piece of equipment is not equally sensitive to certain mechanisms of damage; therefore, the influence of different combinations of operating modes varies.
In the future, we plan to construct an integrated system for predicting rational modes of operation, which would be able to provide recommendations for the entire power unit. They would be established on the basis of the partial distributions of optimum operating modes taking into account the range of change in the residual resource for the specified equipment, its cost, the complexity of repair, consequences of emergency failure, etc.
The ultimate implementation of the further advancement of the reported EFS is to consider its integration into a single complex with registration instruments (sensors) of basic parameters, with a controller, a computer of appropriate power, and, directly, a power unit. That would enable dynamic tracking of change in the resource parameters; in other words, the creation of a power unit resource counter.

Conclusions
1. We have accumulated and treated statistically the data on the operation duration of specific power units at TPPs (the number of launches, the number of launches for the most characteristic modes of operation (CS, NCS, HS); operation under a rated mode; overall operation duration, hours).
2. Based on the mathematical-statistical analysis of experimental data, we have established a pattern between the reduced deformation ε a red and the acceptable number of cycles N p for special heat-resistant alloyed steels (brands 25Cr1Mo1V, 20Cr3MoWV, 15Cr1Mo1V, etc.); the chosen basic approximation function was the modified Steinhart-Hart equation. The results of experimental studies into the creep and prolonged strength of the steels were analyzed on the basis of a basic charting method. The data were acquired at high operating temperatures (400-550 °C) of the metal.
3. An estimating and forecasting system has been proposed for the rational resource-saving regimes of operation of the high-temperature elements in TPP power equipment. For the EFS, we have determined an acceptable number of cycles of the power plants' energy equipment for different types of launches. Our study was based on data on the actual operating conditions over the entire period of work, as well as the results from technical auditing and diagnostic control of the principal metal in the high-temperature elements of power units. A mathematical model has also been constructed to forecast the rational resource-saving regimes of TPP power units' operation; it has been implemented as software. The reported estimating and forecasting system of the rational modes of operation of the TPP high-temperature elements makes it possible to provide individual (separately for each node in a specific power generating unit at a specific TPP) recommendations on the appropriate operation modes of equipment in order to ensure the maximum residual operation duration of a power unit. An increase in the residual operation duration when using the above-described EFS could reach 30 % depending on the level of accumulated damage and the type of energy equipment.