Instituto Tecnológico y de Estudios Superiores de Monterrey
Campus Ciudad de México
School of Engineering and Sciences
An integral approach for the synthesis of optimum operating procedures of
thermal power plants towards better operational flexibility.
A dissertation presented by
Erik Rosado Tamariz
Submitted to the
School of Engineering and Sciences
in partial fulfillment of the requirements for the degree of Doctor of Philosophy
In
Engineering Science
Principal Advisor: Rafael Batres Prieto
Co-advisors: Alfonso Campos Amezcua and Diego Ernesto Cárdenas Fuentes
Mexico City, June 11th, 2020
Dedication
To my parents Carmelo Rosado Mojica and Teodora Tamariz González, for being the best example in life, and for all their love, trust, support, and effort. Thank you for teaching me the value of love, honesty, humility, gratitude, discipline, and hard work in life.
To my son José Alain and my daughter Christian America for being the engine that drives me, my motivation, the source of my inspiration, and my balance. For all the teachings and life experiences. For being unconditional with me, for all your support, love, and for trusting me.
To my wife Christian, my life partner, my best friend, and my accomplice. Thank you for always giving me your support, trust, and words of encouragement. Thank you for being with me and supporting me in all those moments of success, but especially in those difficult ones. Simply because without you, I don't know if I would have made it.
Live as if you were to die tomorrow. Learn as if you were to live forever.
Mahatma Gandhi
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Acknowledgements
This thesis for the Doctor of Philosophy in engineering science degree was completed thanks to the support in the tuition granted by the Tecnologico de Monterrey and thanks to the support for living granted by the Consejo Nacional de Ciencia y Tecnologia (CONACYT).
To the Tecnológico de Monterrey for allowing me to live this experience, and work with great people including colleagues, professors, teachers, and students. For allowing me to develop my research in the Project 266632 “Bi-National Laboratory on Smart Sustainable Energy Management and Technology Training”, funded by the CONACYT SENER Fund for Energy Sustainability (Agreement: S0019201401).
I would like to express a special thanks to the National Institute of Electricity and Clean Energies (INEEL) for their financial support. To the mechanical systems division and its directors Dr. José Miguel González Santaló (†) and Dr. Eduardo Preciado Delgado for trusting me and allowing me to continue growing professionally with this doctorate. To the Managers Dr. Ulises Mena Hernandez and MSc. Alonso Alvarado Gonzaléz for giving me this opportunity.
I would like to express my gratitude to my main advisor, Dr. Rafael Batres who helped me lay the basis for this research, guided me and provided me with the necessary tools to develop this research. For all your advice and your perseverance. Thanks for allowing me to work in his research group.
To my advisors at the INEEL Dr. Zdzislaw Mazur and Dr. Alfonso Campos for all their support, advice, and suggestions. For contributing all their experience of the energy sector to development and improvement of this research. To my co-advisor Dr. Diego Cardenas for promoting hard and structured work in me, for their constructive criticism and patience. To my committee member, Dr. Ricardo Ganem, for his comments and guidance on this work.
To Professor Dr. Filippo Genco for allowing me to participate in his research group during my research stay at the Universidad Adolfo Ibáñez, as well as his support and suggestions to complete and extend the scope of this research. I also appreciate the help and technical support received by the researchers of Adolfo Ibanez University and in particular of engineers Macarena Montane’ and Luis Campos.
I would like to express special gratitude to my colleagues in the research group Miguel Ángel, Luis Enrique, Sara, Emilio y Rodrigo who support me in those difficult moments and enjoying the achievements with me. Particularly to Miguel Ángel who support me in the development of the research and contributed valuable ideas to improve my research, and to Emilio for your contribution to the implementation of the optimization algorithm.
To the Agencia Chilena de Cooperacion Internacional para el Desarrollo who, through the Plataforma de Movilidad Estudiantil y Académica de la Alianza del Pacífico scholarship, provided the necessary support for conducting a doctoral research internship at the Universidad Adolfo Ibáñez, thus allow performing and successfully completing this research project.
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An integral approach for the synthesis of optimum operating procedures of thermal power plants towards a better operational
flexibility Erik Rosado Tamarizby
Abstract
To deal with the challenge of a balance between the large-scale introduction of variable renewable energies and intermittent energy demand scenarios in the current electrical systems, operational flexibility plays a key role. The electrical system operational flexibility can be addressed from different areas such as power generation, transmission and distribution systems, energy storage (both electrical and thermal), demand management, and coupling sectors. Regarding power generation, specifically at the power plant level, operational flexibility can be managed through the cyclic operation of conventional power plants which involve load fluctuations, modifications in ramp rates, and frequents startup and shutdowns. Since conventional power plants were not designed to operate under cyclic operating schemes with involve fast response times, must develop these capabilities through the design of operating procedures that minimize the time needed to take the power plant from an initial state to the goal state without compromising the structural integrity of critical plant components. This thesis proposes a dynamic optimization methodology to the synthesis of optimum operating procedures of thermal power plants which determine the optimal control valves sequences that minimize its operating times based on techniques of dynamic simulation, metaheuristic optimization, and surrogate modeling. Based on such an approach, the power plants must be increasing its operational flexibility to address a large-scale introduction of variable renewable energies and intermittent energy demand scenarios. This thesis proposes a dynamic optimization framework based on the implementation of a metaheuristic optimization algorithm coupled with a dynamic simulation model, using the modeling and simulation environment OpenModelica and a surrogate model to estimate in a computationally efficient way the structural integrity constraint of the dynamic optimization problem. Two case studies are used to evaluate the proposed framework by comparing their results against information published in the literature. The first case study focuses on managing the thermal power plant's flexible operation based on the synthesis of the startup operating procedure of a drum boiler. The second case study addresses the synthesis of an optimum operating strategy of a combined heat and power system to improve the electric power system’s operational flexibility.
List of Figures
Figure 1.1. Demand profiles of the Mexican National Electric Power System 2018-2019
based on [3]. ... 17
Figure 1.2. Comparison of baseline demand profile with respect to scenarios of shifting and shedding demand due to controllable and unexpected factors, based on [6]. ... 18
Figure 1.3. Comparison of solar photovoltaic power plant daily generation profiles for sunny and cloudy days, based on [12]. ... 19
Figure 1.4. Comparison of solar photovoltaic power plant daily generation profiles for sunny and cloudy days, based on [12]. ... 20
Figure 1.5. Demand profile for an electric power system with high variable renewable generation penetration, based on [12]. ... 21
Figure 1.6. Mexican electric power system total installed capacity distribution by technology, based on [14]. ... 22
Figure 1.7. Power plant ramp rate definition. Based on data from [24]... 25
Figure 1.8. Power plant ramp rate definition based on [24]. ... 26
Figure 1.9. Spiral model adaptation proposed, based on [29]. ... 32
Figure 2.1. World gross electricity production, by source, 2017, based on [32]. ... 36
Figure 3.1. Implementation of the framework. ... 55
Figure 3.2. Operation diagram of the mGA. ... 57
Figure 3.3. Example of a random population of four individuals. ... 58
Figure 3.4. Graphical representation of the crossover genetic operator in the mGA. .... 59
Figure 3.5. Graphical representation of the crossover genetic operator in the mGA. .... 59
Figure 3.6. The new population after the crossover and mutation operators. ... 60
Figure 3.7. An example of the fitness associated with each member of the population. 60 Figure 3.8. An example of the selection of the best individual of the population. ... 61
Figure 3.9. An example of the selection of the best individual of the population. ... 61
Figure 3.10. An example of the selection of the best individual of the population. ... 62
Figure 3.11. Operating scheme of the SATAS hybrid optimization. ... 62
Figure 3.12. Operation diagram of the seed generation algorithm. ... 63
Figure 3.13. Randomly generated procedures. ... 63
Figure 3.14. Mutation process from one to four mutations. ... 65
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Figure 3.16. Operation diagram of the SATAS hybrid optimization algorithm. ... 67
Figure 3.17. Example of five neighbors (one mutation) from an actual solution. ... 67
Figure 3.18. Probability of neighbor solution (better and worse) of becoming the new actual solution. ... 68
Figure 4.1. A drum boiler basic configuration. ... 71
Figure 4.2. A drum boiler’s basic configuration. ... 72
Figure 4.3. Drum boiler simulator in OpenModelica. ... 77
Figure 4.4. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of heat supplied. ... 78
Figure 4.5. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of the steam regulator valve position. ... 78
Figure 4.6. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of the output steam from the drum boiler. .... 79
Figure 4.7. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of the pressure in the drum boiler. ... 79
Figure 4.8. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of the steam temperature in the drum boiler. 80 Figure 4.9. Results comparison between the curve reported by Belkhir et al. [98] (blue line) and our simulator (red line) in terms of the thick-walled von Mises stresses. ... 80
Figure 4.10.A combined cycle power plant basic configuration. ... 84
Figure 4.11. Gas turbine structure. ... 85
Figure 4.12. The basic configuration of a HRSG with one pressure level. ... 86
Figure 4.13. Steam line schematic representation. ... 87
Figure 4.14. Schematic diagram of a steam turbine. ... 88
Figure 4.15. Schematic diagram of a power plant condenser. ... 89
Figure 4.16. CHP system based on hot exhaust gases, based on [127]. ... 91
Figure 4.17. CHP system based on low-pressure steam, based on [127]. ... 91
Figure 4.18. Operating scheme of a CHP system based on energy recovery from the hot exhaust gas. ... 92
Figure 4.19. The basic configuration of combined heat and power systems based on high- temperature exhaust gases. ... 94
Figure 4.20. Combined cycle power plant simulator in OpenModelica graphical environment. ... 105
Figure 4.21. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of gas turbine mechanical
power. ... 106
Figure 4.22. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of low-pressure steam turbine mechanical power. ... 106
Figure 4.23. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of intermediate pressure steam turbine mechanical power. ... 107
Figure 4.24. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of high-pressure steam turbine mechanical power. ... 107
Figure 4.25. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of gas turbine exhaust gas temperature. ... 108
Figure 4.26. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of high-pressure drum boiler level. ... 108
Figure 4.27. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of intermediate pressure drum boiler level. ... 109
Figure 4.28. Results comparison between the profile reported by Hefni et al. [52] (blue line) and the proposed simulation model (red line), in terms of low-pressure drum boiler level. ... 109
Figure 4.29. Exhaust Gas Splitter System (EGBS) proposed for the CHP system in the OpenModelica graphical environment. ... 111
Figure 4.30. Heating circuit features of the electrowinning plant based on [149]. ... 113
Figure 4.31. Combined heat and power simulation model – OpenModelica. ... 114
Figure 4.32. Splitter location feasibility in terms of energy consumption. ... 116
Figure 4.33. Splitter location feasibility in terms of flue gas temperatures. ... 116
Figure 4.34. Exhaust gases flow profiles for CCPP and CHP System. ... 119
Figure 4.35. Mechanical power profiles for CCPP and CHP System. ... 119
Figure 5.1. A superheater basic configuration [153]. ... 123
Figure 5.2. The superheater header surrogate model implementation flowchart. ... 125
Figure 5.3. Finite element model of the superheater header with mesh refinement in the vicinity of nozzles holes. ... 128
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Figure 5.4. Heat transfer boundary conditions in the superheater header nozzle’s holes
and inner surfaces. ... 130
Figure 5.5. Heat transfer boundary conditions in the external surfaces... 130
Figure 5.6. Header temperature distribution for the FEM heat transfer analysis. ... 131
Figure 5.7. Mechanical load in terms of pressure on the inner cylinder and on the surfaces of the nozzle holes of the header. ... 131
Figure 5.8. Normal von Mises stress distribution in the header under unit thermal load. ... 132
Figure 5.9. Normal von Mises stress distribution in the header under unit mechanical load. ... 133
Figure 5.10. Thermal and mechanical load curve in terms of the steam pressures and temperatures for the transient analysis. ... 135
Figure 5.11. Temperature evolution in the inner and outer surfaces of the header during heat transfer transient analysis. ... 136
Figure 5.12. Thermal and mechanical stresses evolution in the header for structural transient analysis... 137
Figure 5.13. Comparison of thermal stresses distributions between the unit static analysis and some simulation times at the beginning of the transient analysis. ... 138
Figure 5.14. Comparison of thermal stresses distributions between the unit static analysis and some simulation times at the end of the transient analysis. ... 139
Figure 5.15. Comparison of mechanical stresses distributions between the unit static analysis and some simulation times at the beginning of the transient analysis. ... 140
Figure 5.16. Comparison of mechanical stresses distributions between the unit static analysis and some simulation times at the end of the transient analysis... 141
Figure 5.17. Thermal stresses evolution in the header. A comparison is made between structural transient analysis and their corresponding stresses escalation based on the unit static analysis. ... 142
Figure 5.18. Mechanical stresses evolution in the header. A comparison is made between structural transient analysis and their corresponding stresses escalation based on the unit static analysis. ... 142
Figure 5.19. Failure-prone critical zone in the header. ... 144
Figure 5.20. Header stress response surface under unit thermal load. ... 145
Figure 5.21. Header stress response surface under unit mechanical load. ... 145
Figure 5.22. Response surface scaled according to the pressure differential in the header. ... 147
Figure 5.23. Response surface scaled according to the header differential temperature.
... 148 Figure 5.24. Graphical representation of the configuration of the neural net model. ... 150 Figure 5.25. Graphical representation of the neural network model of the thermal response surface. ... 153 Figure 5.26. Graphical representation of the neural network model of the mechanical response surface. ... 153 Figure 5.277. Comparison of times in minutes to assess the structural integrity constraint in the dynamic optimization problem using different models. ... 155 Figure 6.1. Comparison of the distance from the current state to the goal state overtime for the drum boiler startup optimization obtained with mGA (dotted lines) and SATAS (solid lines). ... 160 Figure 6.2. Results comparison between the curves of the operating benchmark profile developed by Åström & Bell, the optimized profiles reported by Franke et al. and Belkhir et al., and the proposed approach mGa and SATAS for the power generated. ... 161 Figure 6.3. Results comparison between the curves of the operating benchmark profile developed by Åström & Bell, the optimized profiles reported by Franke et al. and Belkhir et al., and the proposed approach mGa and SATAS for the steam that exits of the system.
... 161 Figure 6.4. Results comparison between the curves of the operating benchmark profile developed by Åström & Bell, the optimized profiles reported by Franke et al. and Belkhir et al., and the proposed approach mGa and SATAS for the pressure in the drum boiler.
... 162 Figure 6.5. Results comparison of the operating profile of the steam regulating valve between the models Åström & Bell, Franke et al. and Belkhir et al. ... 163 Figure 6.6. Results comparison of the optimized operating profile of the steam regulating valve based on the proposed approach using mGa and SATAS algorithms. ... 163 Figure 6.7. Results comparison of the operating profile of the heat flow supplied to the system between the models Åström & Bell, Franke et al., and Belkhir et al. ... 164 Figure 6.8. Results comparison of the optimized operating profile of the heat flow supplied to the system based on the proposed approach using mGa and SATAS algorithms. . 164 Figure 6.9. Results comparison between the curves of the operating benchmark profile developed by Åström & Bell, the optimized profiles reported by Franke et al. and Belkhir et al., and the proposed approach mGa and SATAS for the thick-walled von Mises stress.
... 165 Figure 6.10. Steam turbines operational data of the San Isidro II combined cycle power plant for the 2018 year. ... 169
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Figure 6.11. Normalized operating scheme of the CHP system during the cyclic operation case study. ... 171 Figure 6.12. Gas turbine exhaust gases flow regulation system in the CHP system. .. 173 Figure 6.13. Gas turbine exhaust gases flow required by the cogeneration system (blue) and flow available for the operation of steam turbines (red) in the case of a cyclic operation study. ... 176 Figure 6.14. Profiles of temperature and enthalpy of the electrolytic solution during the cyclic operation case study of the San Isidro II combined cycle power plant coupled to a cogeneration plant. ... 177 Figure 6.15. Control profiles of the regulating valve for the gas turbine exhaust gases in the electrowinning process inlet during the cyclic operation case study of the San Isidro II combined cycle power plant coupled to a cogeneration plant. ... 177 Figure 6.16. Comparison of the distance from the current state to the goal state overtime for the baseline case study (blue) and optimized profile using the SATAS optimization algorithm for the cyclic operation case study. ... 178 Figure 6.17. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the power generated in the steam turbines. ... 179 Figure 6.18. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the steam pressure at the high-pressure evaporator outlet. ... 179 Figure 6.19. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the steam temperature at the high-pressure evaporator outlet. ... 180 Figure 6.20. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the throttle valve that regulates the steam flow that enters the HP superheaters... 181 Figure 6.21. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the ramping rate of flow flue gases in the Heat Recovery Steam Generator (HRSG).
... 181 Figure 6.22. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the thermomechanical stresses in critical zone 1 that are prone to failure. ... 182 Figure 6.23. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the thermomechanical stresses in critical zone 2 that are prone to failure. ... 183
Figure 6.24. Results comparison between the curves of the operating baseline profile (blue line) and the proposed approach using the SATAS optimization algorithm (red line) for the power generated in the gas and steam turbines. ... 184
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List of Tables
Table 1.1. Operational flexibility features of thermal power plants [28]. ... 27
Table 3.1. Relation between feasibility scale and number of mutations in the operating procedure for an example of 9 genes. ... 64
Table 4.1. Electrowinning process characterization [149]. ... 113
Table 4.2. Exhaust gases operating parameters for a load change simulation. ... 115
Table 4.3. Cogeneration system operating parameters for full load gas turbine. ... 118
Table 5.1. Superheater header features. ... 127
Table 5.2. Header convection heat transfer coefficients. ... 129
Table 5.3. Structure of the inputs and outputs for ANN model. ... 151
Table 5.4. Accuracy of the ANN model for the evaluation of the structural integrity constraint in the superheater header. ... 151
Table 5.5. Comparison of times to assess the structural integrity constraint in the dynamic optimization problem using different models. ... 155
Table 6.1. Combinations of the heat flow rate and steam flow rate for each action. ... 158
Table 6.2. Comparison of the useful life consumption and fatigue damage in the drum boiler for all startup profiles evaluated in the case study 1. ... 166
Table 6.3. Combinations of the heat flow rate in the HSRG inlet and steam flow rate in the superheater for each action. ... 175
Table 6.4. Comparison of the useful life consumption and fatigue damage in the superheater header for the cyclic operation case study of the combined cycle power plant coupled to a cogeneration plant. ... 184
Contents
Declaration of Authorship ... 1
Dedication ... 2
Acknowledgements ... 3
Abstract ... 5
List of Figures ... 6
List of Tables ... 13
1. Chapter one ... 16
Introduction ... 16
1.1 Background ... 16
1.2 Problem statement ... 28
1.3 Research questions ... 29
1.4 Hypothesis ... 30
1.5 Objectives ... 31
1.6 Research methodology ... 32
1.7 Thesis outline ... 34
2. Chapter two ... 36
Literature review ... 36
2.1 Thermal power plants ... 36
2.2 Approaches to improve operational flexibility ... 38
3. Chapter three ... 53
Dynamic optimization framework ... 53
3.1 Introduction ... 53
3.2 Proposed approach ... 54
4. Chapter Four ... 69
Simulation models ... 69
4.1 Introduction ... 69
4.2 Drum boiler modeling ... 70
4.3 Modeling of Combined Cycle Power Plants (CCPP) and Combined Heat and Power Systems (CHP) ... 81
5. Chapter Five ... 121
Surrogate modeling ... 121
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5.2 The superheater... 123
5.3 Surrogate modeling ... 124
6. Chapter Six ... 156
6.1 Case study 1: Synthesis of the startup operating procedure of a drum boiler 156 6.2 Case study 2: Synthesis of an optimum operating strategy of a CHP system 168 7. Chapter Seven... 186
Conclusions and Future Work ... 186
References... 190
8. Appendix A ... 202
Published papers ... 202
Curriculum Vitae ... 207
1. Chapter one
Introduction 1.1 Background
Worldwide, electric power systems are undergoing large structural changes. Commonly, these systems are based on centralized models in which fossil-fuel-based electric power generation prevailed. Nowadays, electric power systems are evolving towards liberalized energy markets in which part of the electricity demand tends to be met by variable renewable energy sources [1]. International commitments on climate change, development of public policies, and the increasing competitiveness of energy generation based on variable renewable energy sources have been the main drivers of the electric power systems transition [2]. In this context, it is essential to consider the whole electric power system's operational capabilities to integrate, in an efficient way the generation based on variable renewable technologies. Also, factors related to the operation of the electric power system must be taken into account, such as the variability in the electrical power demand, which can cause instabilities in the power network. Such variability in electrical power demand may be due to consumption factors since the users consume electrical power according to their needs and have no evident consumption patterns;
consumers can change their load throughout the day, week, and months of the year. An electric power system intermittence induced by the variable consumption of electricity can be exemplified by electrical power demand profiles. Figure 1.1 shows the demand profiles of the Mexican National Electric Power System (SEN) on different days for twelve months 2018-2019 [3].
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Figure 1.1. Demand profiles of the Mexican National Electric Power System 2018-2019 based on [3].
Due to current technological impediments for the storing of energy in massive quantities and the need for the electric power system to operate synchronically, the electrical power generation, and the system energy demand must be balanced in real- time (illustrated in Figure 1.1). Thus, the electric power system operator (PSO)1 is always responsible to coordinate power generation of all power units available to match energy supply with demand, guaranteeing safe, stable, and economic operation of the electric power system. In Mexico, the system operator is the Centro Nacional de Control de Energía (CENACE) [4]. Operational management of electrical power units is carried out in a planned way, following well-studied and predicted demand patterns albeit the presence of exceptional events that can induce operational variations to the system.
These events can be predictable or spontaneous. As a result, the electric power system must be able to respond to these needs efficiently without compromising the quality and continuity of electric power supply.
1 The PSO is responsible for managing and monitoring the power grid in order to anticipate and mitigate potentially dangerous and costly system problems, and when a power grid disturbance occur, its function is to restore it to safe operating conditions efficiently [5].
Other causes of variability include unforeseen failures in power units, transmission or distribution lines, substations or transformers, as well as disconnection of many electricity consumers of the power grid at the same time. Likewise, events such as a holiday, musical concerts, or high-attendance sports events can also generate significant levels of variability. Based on [6], a comparison for an electric power system baseline demand profile with respect to shifting and shedding demand scenarios due to controllable and unexpected factors is shown in Figure 1.2.
Figure 1.2. Comparison of baseline demand profile with respect to scenarios of shifting and shedding demand due to controllable and unexpected factors, based on [6].
In this way, electric power systems are provided with an inherent capability of operational flexibility, which allows them to deal successfully with the variability and uncertainty challenges in order to balance the electrical power supply and energy demand efficiently.
Another source of variability is the result of the introduction of large-scale variable renewable energy, which has its own variability in power generation. According to [7], deployment of power plants based on variable renewable sources such as wind, and solar energy are achieving a key role in new electric power systems. This because of the development of variable renewable energy technologies have reached a good
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technological level promising a bright future for electric power systems and with highly competitive generation costs [8]. Likewise, the combined effect of the energy variable demand coupled with the increasing adoption of variable renewable power plants makes it difficult to reach a supply-demand balance.
As reported by [9-11], non-conventional renewable generation or variable generation are those power generation technologies from renewable primary resources whose availability and intensity varies significantly with weather conditions and time scales. Examples are wind and solar energy, which are the most mature and widely employed technologies. Therefore, these technologies cannot operate at this time as a traditional dispatchable generator due to variable generation nature and its dependence on weather conditions. The variable and intermittent behavior of these power plants can be illustrated through their daily generation profiles for typical periods of generation.
Figure 1.3 shows the generation profiles of a solar photovoltaic power plant, produced during sunny and cloudy days (based on data available in [12]). Figure 1.4 illustrates a month of electrical power generation for a couple of onshore wind power plants currently in operation [12].
Figure 1.3. Comparison of solar photovoltaic power plant daily generation profiles for sunny and cloudy days, based on [12].
Electrical power generation in solar photovoltaic power plants is restricted by the time of day, being unable to generate energy during the night hours. Also, solar power generation is constrained by weather conditions such as cloudy days, resulting in generation profiles with repetitive patterns and frequent ramps up and down during the operation period. It should be noticed that the individual impact of these power plants is minimal for the electric power system in terms of possible imbalances between supply and demand, but their large-scale introduction could induce significant instabilities and operational risks to the system.
Figure 1.4. Comparison of solar photovoltaic power plant daily generation profiles for sunny and cloudy days, based on [12].
While daily solar photovoltaic generation profiles have slight differences in terms of shape and pattern, wind power generation has greater variability regarding its primary source intensity and availability. As shown in Figure 1.4, wind energy must deal with the challenge of intraday2 variability, as well as the contrast of maximum generation levels for each day.
2 In the intraday market, buyers and sellers can trade power close to real time to balance the supply and
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Since the generation based on variable renewable technologies cannot be controlled, they must be dispatched whenever their primary energy source is available:
this drives the electrical system operator to manage conventional generation in such a way that wind and solar energy are supplied first. This requires a higher level of electrical power system operational flexibility to guarantee a safe, stable, and economic operation of the electrical grid. In other words, conventional power-generation plants should efficiently dispatch generation to variable and uncertain demand profiles. In the operation of electric power systems involving variable renewable technologies, demand curves are usually studied as net demand profiles or residual loads, where net demand corresponds to the instantaneous difference between demand and variable renewable generation.
Thus, a net demand profile helps to visualize the combined variability due to both the demand and the variable renewable generation.
Figure 1.5 shows a net demand curve based on data from [12], which highlights some challenges that arise when the demand variability coexists in an electrical system with a high contribution of variable renewable generation (wind and solar energy).
Figure 1.5. Demand profile for an electric power system with high variable renewable generation penetration, based on [12].
As shown in Figure 1.5, different levels of adjustment between the electric power system demand (in red) and variable renewable generation (in green) can lead to more abrupt variations in the electric power system's net demand (in blue). Therefore, achieving a net demand profile balance safely and at a minimum cost is the main challenge for integrating systems based on variable renewable generation. In accordance with the increasing incorporation of variable renewable generation technologies in the electric power systems, variations in net demand are growing, giving rise to unprecedented ramp requirements and even risks variable renewable overgeneration.
The National Electric System in Mexico for 2018 had 6,585 MW installed of variable renewable energy generation, of which 4,485 MW correspond to wind power plants and 1,820 MW to solar photovoltaic generation. The variable renewable technologies represent 9.4% of the total installed capacity of the electric power system of 70,053 MW total [14]. The distribution of the total installed capacity of the Mexican electric power system by technology is shown in Figure 1.6.
Figure 1.6. Mexican electric power system total installed capacity distribution by technology, based on [14].
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1.1.1 Operational flexibility
The inherent intermittency of power generation based on variable renewable energy sources coupled with the electric power demand variability leads to improved response and adjustment capabilities of the electric power systems. According to [15–17], these capabilities are known as “power system operational flexibility”, which describe the ability of the power system to achieve a balance between generation and demand at all times.
In other words, the electric power system should have the ability to respond properly under short-term operational uncertainties and variabilities to avoid substantial instabilities and economic losses.
As reported by the International Renewable Energy Agency (IRENA) [18], to effectively manage large-scale variable renewable energy, flexibility sources must be analyzed and planned in all-electric power system components. In this way, all potential sources of flexibility should be investigated, and all energy systems must be considered.
In this sense, power generation, transmission and distribution systems, thermal and electrical storage, demand management, and coupling systems are considered.
In the context of power generation, operational flexibility can be achieved through unit commitment and plant-level operations. Unit Commitment [19] consists of finding the optimal operational schedule of each generating unit under different constraints and environmental conditions. Electric power is managed by solving an optimization problem that answers the fundamental questions of when, how, and how much energy must be generated in each power unit according to the electrical grid needs and interactions with the power plants set managed at the time. Also, power system operational flexibility can be managed using a power plant level approach [20]. In this approach, the problem is addressed as an operational design strategy using advanced optimization and control techniques that focus to minimize the operating times and maximizing the system’s capabilities to work under cyclic operating conditions3 and peak loads. Plant-level operations aim at deciding in real-time how much, when and under what operating conditions it is suitable to generate electricity to increase its competitiveness and
3 Cyclic operation or cycling refers to the operation of electric generating units at varying load levels (power demand), including on/off and low load variations, in response to changes in system load (demand) requirements. Every time a power plant is turned off and on, the boiler, steam lines, turbine, and auxiliary components go through unavoidably large thermal and pressure stresses, which cause damage [21].
profitability, according to energy market conditions and electrical grid requirements. Cyclic operation is the most common way to achieve operational flexibility [21].
Power plants suitable for more flexible operation generally correspond to hydropower plants, gas turbines, internal combustion, and combined cycle power plants.
Hydropower plants have one of the greatest capacities for cyclic operation and have been a leading actor providing operational flexibility in worldwide electric power systems.
However, they are limited to favorable hydrology scenarios and water resource availability, which are closely related to climate change. Regarding the most efficient conventional thermal power plants, these were generally designed to operate at baseload. Nevertheless, the growing development of variable renewable generation in the last decades has promoted radical modifications to their operating regime to provide operational flexibility to electrical systems with encouraging results [22].
Thermal power plants can provide flexibility as a function of its installed capacity and according to the next constraints:
– Which are the loads in which it can operate the plant in a stable and efficient way?
– How fast can the plant modify its load or generate power at partial load?
– How fast can the plant startup or shutdown?
There are two main operation regimes that determine the capacity of thermal power plants to operate under a cyclic operation regime to provide operational flexibility to the electric power system turndown and ramping: turndown and plant ramping.
The turndown is an operation regime in which the plant is at a low load condition.
The turndown ratio determines the operational range of the plant and it is defined as the ratio of the maximum capacity Pmax to minimum capacity Pmin [23]. Thus, a power plant with a higher operating range can be operated in a greater range of feasible dispatches, providing greater flexibility to the electric power system [24]. These limits are important because any load change should occur without compromising the integrity of any of the components of the plant and within the established flexibility limits.
Power plant ramping instead is an operation regime in which the plant generation changes from an initial load to a final load. The rate of change of plant load is determined by its ramp rate [24]. This parameter is expressed in terms of power per time (MW/min).
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In other words, the ramp rate describes the maximum speed with which the power plant can change the power load at a new level (higher or lower). Thus, a power plant offers greater flexibility to the system when having a greater ramp capacity as it can respond more quickly to surges in the system: the higher the power plant’s ramp rate, the higher its potential to meet fluctuating demand [25]. Therefore, the ramp rates determine the power plant startup and shutdown times. The power plant ramp rate capacity is illustrated graphically in Figure 1.7.
Figure 1.7. Power plant ramp rate definition. Based on data from [24].
The startup time is defined as the transition period when the plant is taken from a non-operating state to an operating state. Conversely, shutdown refers to the process in which the plant is taken from operational to non-operational state [26]. Thermal power plants startup and shutdown are limited mainly by the minimum times that a power plant must keep operating after startup or remain out of operation after a shutdown, in order not to compromise the integrity of its components. These periods are known as the minimum uptime and minimum downtime, respectively [24]. Startup and shutdown are dynamic processes that are strongly related to state variables of the working fluid.
According to [27], thermal power plants startup procedures can be mainly defined as a
function of three downtime states preceding the re-start of the unit, which are listed as follow:
Hot startup: less than 8 hours after shutdown.
Warm startup: between 8 and 60 hours after shutdown.
Cold startup: more than 60 hours after shutdown.
Thereby, by decreasing the power plant startup times, greater flexibility of the electric power system can be achieved. A characteristic thermal power plant startup and shutdown profiles are illustrated in Figure 1.8.
Figure 1.8. Power plant ramp rate definition based on [24].
A comparison of the thermal power plant's operational flexibility capabilities based on the evaluation of the three main technological parameters of cyclic operation (turndown, ramp rate, and operating times) is presented in Table 1 [28].
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Table 1.1. Operational flexibility features of thermal power plants [28].
Technology Minimum power
output (% Pmax) Ramp rate
(% Pmax/min) Hot startup time (min)
RE Geothermal 15 5 90
Bioenergy 50 8 180
Concentrating Solar Power 25 6 150
Dispatchable Non-RE
Coal fired 30 6 180
Lignite 50 4 360
Steam plants (fuel oil, gas) 30 7 180
Simple cycle gas turbine 15 20 10
Gas turbine combined cycle 20 8 120
From these results, it can be noticed that gas turbines and combined cycle power plants are better suited to operate in a cyclic operation regime since they operate with higher ramping rates and lower minimum loads that are the main features of cyclic operation schemes in conventional thermal power plants.
1.2 Problem statement
This thesis focuses on how the plant’s generation changes from an initial load to a final load in a minimum time possible to meet a fluctuating demand worsen by the accelerated growing penetration of variable renewable energies and intermittent energy demand conditions into the market.
Methodologies that involve both the development of advanced control strategies, as well as coupled simulation and optimization systems are proposed to guide and facilitate the design of thermal power plants operating profiles. Some representative studies are described in Chapter 2. Such research is based on thermodynamic modeling to determine the startup profiles that maximize plant efficiency. However, these optimization problems do not deal with how power plant control valves must be operated to take the power plant to the desired goal state in minimum time. Likewise, these works do not address load changes in operating conditions or sudden energy supply scenarios due to electrical grid requirements.
The main limitation to design faster thermal power plants operating profiles is related to the structural integrity of power plant critical components due to sudden changes in the state variables. To avoid hazardous scenarios in which the proposed profiles could result in a decrease in material useful life, the steam temperature, and steam pressure must be monitored. It is important to note that temperature and pressure variations must be held within the given limits to avoid high thermomechanical stresses on the thick-walled devices which in turn cause an increment of alternating tension- compression stresses leading to fatigue or even material failures. The different methods and techniques focused on quantifying the thermomechanical stress and estimate the useful life consumption of these components are described in Chapter 2. These research studies are mainly based on well-known methods that usually not consider complex geometrical effects nor advanced numerical computational techniques, as they can be computationally expensive in dynamic optimization problems. Therefore, an accurate and computationally efficient evaluation method plays an important role in the optimal design of a thermal power plant´s operating procedures.
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1.3 Research questions
How to carry out the synthesis of optimum operating procedures of thermal power plants taking into account the process control valve's actions and in a computationally efficient way to improve the electric power system flexibility to deal with the challenge of large- scale introduction of variable renewable energies and intermittent energy demand scenarios?
To answer this research question in a comprehensive manner, some specific issues must be addressed:
– How to synthesize operating procedures of thermal power plants that minimize startup times without compromising the structural integrity of critical components?
– How to synthesize operating procedures of thermal power plants that minimize load change times without compromising the structural integrity of critical components?
The last research question triggers the following related question:
– Assuming a dynamic optimization approach, what is the best way to evaluate the structural integrity of critical components in a computationally efficient way?
To efficiently address these research questions, the operational parameters of the thermal power plant that realizes the electric power system's operational flexibility must be identified first.
1.4 Hypothesis
A computational framework implementing a dynamic optimization approach that is computationally efficient can synthesize optimum operating procedures of thermal power plants that minimize startup and load-change times without compromising the structural integrity of critical components.
To develop this proposed approach, the following concepts are addressed:
– Simulation models: mathematical representations capable to emulate the dynamic behavior of a drum boiler, a combined cycle power plant, and a cogeneration system.
– Optimization algorithm: The optimization algorithm is responsible for finding the valve sequences that minimize the time it takes the plant to move from an initial load to a final load. In order to do so, it interacts with the simulation model.
– Surrogate modeling: The creation of machine learning models that minimize the computational time for the evaluation of structural integrity of critical components during the optimization processes. Surrogate models will be constructed from finite element model simulations. The evaluation of structural integrity will be based on the estimation of stresses distribution and lifetime consumption induced by operational changes proposed by the optimization algorithm.
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1.5 Objectives
The main objective of this research is to develop a computationally efficient approach for the synthesis of optimum operating procedures of thermal power plants which finding the optimal control valves sequences that minimize its operating times based on techniques of dynamic simulation, metaheuristic optimization, and surrogate modeling. The proposed approach aims at improving the electric power system operational flexibility to address a large-scale introduction of variable renewable energies and intermittent energy demand scenarios. To do this, it is necessary to:
– Develop and validate dynamic simulation models of a drum boiler, combined cycle power plant, and combined heat and power system.
– Implement an optimization algorithm for the synthesis of the startup operating procedure of a drum boiler.
– Retrofit a cogeneration system to supply thermal energy to a continuous industrial process with high energy demand.
– Develop and validate a finite element model of the steam generator critical components.
– Develop and validate a computationally efficient model to estimate stresses distribution and lifetime consumption induced by operational changes proposed by the optimization algorithm.
– Implement an optimization algorithm for the synthesis of an optimum operating strategy of a combined heat and power system to improve the electric power system’s operational flexibility.
1.6 Research methodology
This research has been developed based on an adaptation of the spiral design process proposed by Boehm [29]. The proposed model consists of repetitive spiral-shaped cycles that begin in the center and each loop or iteration represents a set of activities to be developed.
The model starts from an issue identification and in each iteration, the model must consider the research objectives, proposed approach solution alternatives, implementation and validation of the proposed solution, as well as feedback from previous loops. If the proposed solution does not solve the issue, improvements and functionalities must be implemented. The proposed spiral model focuses on two control mechanisms that measure its effectiveness, which is known as radial and angular dimensions. In the proposed adaptation, the angular dimension represents the research progress within a cycle, while the proposed approach complexity is quantified in the radial dimension. The spiral model adaptation proposed is shown in Figure 1.9.
Figure 1.9. Spiral model adaptation proposed, based on [29].
Each cycle of the spiral comprises four phases: 1) problem analysis, 2) solution proposal, 3) proposal implementation and validation, and 4) evaluation and analysis of results. The first phase involves the problem analysis through literature review and the
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research scope is established. In the second phase, the approach and solution alternatives are proposed according to the scope established in phase one of the corresponding cycle. For the third phase, one of the proposed solutions is selected and implemented. In the last phase, a results evaluation is carried out to determine if the research results have been achieved and the process is completed. Otherwise, the process continues, and potential research issues are identified that were not initially recognized, which will enrich the proposed research. The main advantage of the spiral model lies in its iterative development, and that the improvements and functionalities can be implemented progressively.
In this context, the spiral model allowed for an incremental development approach, since in each phase the opportunity areas were identified, and the process was fed back to address efficiently the current issues. The development of the research in the analysis phase is quantified in terms of the research scope expansion, which initially focused on finding the problem solution for the operationally critical components of thermal power plants, and next for full thermal power plants until reaching combined heat and power systems. For the solution proposals phase, a two-phase methodology described in [30]
was originally used, consisting of a conceptual phase and a detailed phase. The conceptual phase focused on finding the state variables profile that minimizes the power plant operating time without compromising the structural integrity of critical components, while the detailed phase takes the optimal operating procedure developed in the conceptual phase stage and generates the optimal sequence of valve operations. This evolves into a dynamic optimization framework like the one described in [31], addressing the problem of finding the optimal control valve sequences that minimize the startup time using a dynamic optimization framework based on metaheuristic optimization algorithms coupled with a dynamic simulation model. Regarding the implementation of the proposed research approach, an interface based on the C# code was developed to connect the power plant simulator with the framework optimization modules. Then, as a means for the evaluation of the constraints of the dynamic simulation problem, surrogate models based on finite element analysis were developed to estimate thermomechanical stresses in power plant critical components. Finally, the proposed approach should be evaluated through case studies and precise comparisons.
1.7 Thesis outline
The main contribution of this research work is the development of a computationally efficient approach for the synthesis of optimum operating procedures of thermal power plants which determine the optimal control valves sequences that minimize its operating times based on techniques of dynamic simulation, metaheuristic optimization, and surrogate modeling. Based on such an approach, the power plants must be increasing its operational flexibility to address a large-scale introduction of variable renewable energies and intermittent energy demand scenarios. This thesis is organized as follow:
Chapter 1 describes the problem that motivated this research work. Then the background, problem statement, research questions, hypothesis, objectives, research methodology, and the thesis outline are explained.
Chapter 2 presents a literature review and background of thermal power plants modeling, simulation, and optimization to provide a context within which the contributions of this thesis can be evaluated. Likewise, methods and techniques currently used to evaluate the structural integrity of power plant critical components in dynamic optimization problems are described. Finally, a review of thermal power plants retrofitting alternatives focused on improving their operational flexibility is presented.
Chapter 3 covers the first topic of the proposed research approach in this thesis, which focuses on the development of a framework for the synthesis of operating procedures based on dynamic simulation and metaheuristic optimization.
Chapter 4 presents the formulation, development, and validation of the dynamic simulation models required to implement and validate the proposed dynamic optimization framework and the integrated approach for the synthesis of optimum operating procedures of thermal power plants. Dynamic simulation models for a drum boiler power plant, an existing combined cycle power plant, and a combined heat and power system were developed and validated.
Chapter 5 describes a surrogate model based on artificial neural networks (ANN) and finite element method (FEM) to estimate in a computationally efficient way the structural integrity and life consumption in a thermal power plant superheater. The model developed is compared against analytical models, as well as sub-models, and rigorous and simplified finite-element models.
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Chapter 6 addresses the validation of the proposed integrated approach for the synthesis of optimum operating procedures. The proposed dynamic optimization framework is validated according to a power plant drum boiler startup optimization based on a startup reference sequence published in the literature. Likewise, the optimal operating procedures design of a Combined Heat and Power system based on a retrofitting existing combined cycle power plant retrofitted, which are focused on the efficient supply of electrical power to the system and useful thermal energy for an industrial process is also compared with the case study used to validate the proposed integrated approach.
Chapter 7 summarizes the accomplishments and main conclusions of this research work, and finally, some suggestions for future works are provided.
Appendix A presents the different papers generated as part of this research work.
2. Chapter two
Literature review
This chapter reviews the state of the art of the current methodologies and approaches on modeling, simulation, and optimization related to operational flexibility.
2.1 Thermal power plants
Most of the installed power generation capacity worldwide is based on thermal power plants. According to data from the International Energy Agency (IEA), electrical power generation from thermal power plants in 2017 accounted for 78.9% of total world gross electricity production, of which 74.7% corresponds to conventional power plants and the 4.2% remaining to renewable power plants [32]. World gross electricity production by source for 2017 is shown in Figure 2.1.
Figure 2.1. World gross electricity production, by source, 2017, based on [32].
In conventional thermal power plants, electric power is generated by transforming chemical energy stored in a primary energy source such as fossil fuels or nuclear energy into thermal energy, which is, in turn, converted into mechanical energy, and finally transformed into electrical energy [33]. The conversion process of thermal to mechanical energy is carried out through power plants using steam turbines (ST) or gas turbines (GT), whereas mechanical energy conversion into electrical power is performed by an alternator or electric generator [34]. In the case of steam-turbine power plants, it is in the furnace of the steam generator (boiler) where the chemical energy is converted into thermal energy,
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while for gas-turbine power plants this process occurs in a combustion chamber [35]. The behavior of ST and GT power plants are based on two thermodynamic cycles. The operation of a gas turbine is described by the Brayton cycle, while the Rankine cycle describes the thermodynamics of the water-steam cycle of the steam power plant.
Regarding operability, both technologies present advantages and drawbacks.
Both, ST and GT plants can reach up to 40% thermal efficiency. An essential difference is that for the same power, GT installations are smaller since they have a simple design in contrast to ST plants, which require extra equipment such as boilers, condensers, and their auxiliary piping and equipment. However, ST plants will provide electric power in significantly larger amounts than GT plants for turbines of the same size.
The overall efficiency of electric power plants can be increased by combining the Brayton cycle with the Rankine cycle to recover and use the residual heat energy in hot exhaust gases. Such process-combination is realized in combined-cycle power plants (CCPP). Compared to ST and GT plants, CCPP’s have larger operational ranges and efficiencies.
Over the last years, sustainable development policies related to environmental protection and the need to improve the efficiency of electric power systems have led to more and more efficient solutions and productivity improvements of power plants. In this sense, solutions with high-efficiency cycles such as CCPP that provide performances considerably higher than conventional units with efficiencies of about 60-63%, are the trend of new liberalized markets [36]. Moreover, combined cycle technologies have lower rates of greenhouse gas emissions [37,38]. However, most CCPP base their electric power generation on the availability of fossil fuels such as diesel and natural gas, whose long-term reserves costs are uncertain.
As explained in Chapter 1, thermal power plants must be operationally flexible to meet fluctuations in demand levels, as well as to fulfill the residual load induced by non- conventional renewable energy generation.
Therefore, one of the main challenges of electric power systems is to guarantee high operational flexibility and reliability of the electrical grid while reducing environmental impact and maximizing efficiency.
Although deregulated power markets aim at a generation matrix mostly based on renewable sources [39], in short, and medium terms, these technologies will not be able to replace conventional thermal power plants on a massive scale. Thus, conventional thermal power plants will continue to play a key role in the electrical power generation for a long period. In this context, CCPP will most likely have strong growth in the coming years due also to relatively cheap costs provided by North American shale gas.
2.2 Approaches to improve operational flexibility
Researchers have focused their attention on studying dynamic simulation and optimization to improve flexible generation capabilities of thermal power plants.
2.2.1 CCPP Simulations models
Dynamic modeling represents one of the most powerful methods to study, evaluate, and design operational strategies of power plants. Usually, these models are based on differential and algebraic equations systems. Reliable models can predict accurately the power plant dynamic behavior, enabling the development of simulators for testing and proposing new operational strategies. Such models have been developed using different techniques, methods, and tools.
Previous works such as those by [40-45], have shown that applications based on theoretical and simplified models can accurately predict the power plant dynamic behavior. For example, a simplified method based on fundamental physics laws to predict the CCPP steam cycle under different temperatures and exhaust gases mass flow boundary conditions was developed by Gülen and Kim [40]. Improved models have also been developed, including those proposed by Mello [41] and Ahner [42], in which the GT dynamic behavior is described by first-principle models based on fundamental thermodynamic equations of mass and energy balances, based on the simplified model of a gas turbine presented by Rowen [43]. Likewise, Shin et al. [44], proposed a model based on the transient form of mass and energy balances for each CCPP component combined with lumped heat capacitance and the use of a well-known correlation equation to determine heat transfer coefficients of water and steam. Validation case studies were
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performed using transients driven by step and sinusoidal variations in the gas turbine load. An adapted model for the optimization process, which considers not only transient mass and energy balance equations but also dynamic heat transfer phenomena such as condensation, and steam turbine metal temperature profiles is described by Faille et al.
[45]. It must be noted that in most of these works, the block function diagram is used in MATLAB or Simulink environments system modeling.
Plant-wide models have been developed based on object-oriented modeling languages such as Modelica [46], and modeling environments such as Dymola, OpenModelica, ASPEN Plus Dynamic, EBSILON, EcoSimPro, APROS, among others.
For example, Alobaid et al. [47,48] used ASPEN Plus Dynamic and APROS to predict the CCPP dynamic behavior under operational conditions of partial loads, off-design and warm startup. Simulation models were validated against a power plant's real operational data and both simulation environments produced reliable results, but the authors preferred APROS for its accuracy. Similarly, Wojcik and Wang [49], conducted a feasibility study for the integration of a CCPP with an Adiabatic Compressed Air Energy Storage (ACAES) using EBSILON® Professional software environment. Based on the hybrid model simulations, they determined the optimal connection point for the CCGT and ACAES models and the minimum load time to charge the ACAES system: it was found that CAES discharging process is fully independent of CCGT process and provides an additional 47.5% of power boost over the registered capacity of CCGT plant during peak times.
A CCPP dynamic behavior model under real operating conditions was developed by Benato et al [50]. The dynamic model of a three-pressure level combined cycle power plant was developed in Dymola. In this work, simulations were carried out in steady-state and partial load simulating also the dynamic behavior of the power plant under thermal fatigue with the main focus onto the heat recovery steam generator. All models developed include simplifications and assumptions such as neglecting pressure drops, friction effects, heat loss, and similar.
The CCPP models developed by Tică et al. [51] and Hefni and Bouskela [52] were developed and tuned with data obtained existing power plants. According to [51], the solution of design and optimization problems based on large-scale power plant models
involve powerful algorithms, which impose some constraints for the model formulation.
Therefore, a method to transform a CCPP physical model in a simulation and optimization-oriented model, which can be coupled with efficient algorithms to improve startup performances were presented. The authors demonstrate the model consistency and its applicability for optimization and control purposes.
In [52], the authors present the ThermoSysPro library for the OpenModelica software for the modeling and simulation of power plants. They use this library to simulate a dynamic model of a combined cycle power plant for a load change scenario. The model comprises the flue gas side and the full thermo-dynamic water/steam cycle closed through the condenser. Simulation results show that the ThermoSysPro library is complete and robust enough for the modeling and simulation of power plants.
However, these models are limited as they can calculate ST metal temperature evolution but cannot evaluate mechanical stresses in the steam turbine and steam generator components.
2.2.2 CCPP operational constraints
The main barrier to the design of faster CCPP operational strategies is the presence of thermal stress-induced fatigue damage in the steam cycle. A broad variety of research has been done to find those components that are more prone to failure due to severe changes in operating conditions. In this context, the work carried out by Shirakawa et al.
[53], Lind et al. [54], Alobaid et al. [55], Kim et al. [56] and Mertens et al. [57] consider the high-pressure drum as the most critical component of the power plant. Meanwhile, the work of Alobaid et al. [58], Mirandola et al. [59], Farragher et al. [60], Hentschel et al. [61], Taler et al. [62] and Angerer et al. [63] identify the high-pressure superheater header as a component even more critical than the high-pressure drum. Likewise, Shirakawa et al.
[53], Casella et al. [64], Spelling et al. [65], Born et al. [66], Moroz et al [67] and Ji et al.
[68] consider the steam turbines as the most critical component.
An accurate and computationally efficient evaluation of stress levels and life consumption in critical components plays a critical role in the optimal design of CCPP operating procedures. In the literature, different methods and techniques have been developed to quantify the thermomechanical stress in the critical components under
