This document describes thermo-economic functional analysis (TFA), a method for optimizing complex thermal systems. TFA combines thermodynamic and economic concepts using a systems approach. The key steps are:
1) Identifying the function of each system component/unit
2) Constructing a functional diagram showing the flow of functions between units
3) Formulating an optimization problem to minimize total cost subject to constraints
4) Solving the optimization equations to determine optimal design variables
The document then provides an example application of TFA to optimize a 4-unit thermal power plant.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
A Research on Optimal Power Flow Solutions For Variable LoaIJERA Editor
This paper presents the optimal power flow solutions under variable load conditions. In this article we present the recent trend towards non-deterministic (random) search techniques and hybrid methods for OPF and give the conclusions. These methods have become popular because they have a theoretical advantage over the deterministic methods with respect to handling of non convexity, dynamics, and discrete variables. Present commercial OPF programs can solve very large and complex power systems optimization problems in a relatively less time. In recent years many different solution methods have been suggested to solve OPF problems. The paper contributes a comprehensive discussion of specific optimization techniques that can be applied to OPF Solution methodology.
In recent times, fractional order controllers are gaining more interest. There are several fractional order controllers are available in literature. Still, tuning of these controllers is one of the main issues which the control community is facing. In this paper, online tuning of five dierent fractional order controllers is discussed viz. tilted proportional-integral-derivative (T-PID) controller, fractional order proportional-integral (FO-PI) controller, fractional order proportional-derivative (FO-PD) controller, fractional order proportional-integral-derivative (FO-PID) controller. A reference tracking method is proposed for tuning of fractional order controllers. First order with dead time (FOWDT) system is used to check feasibility of the control strategy.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
A Research on Optimal Power Flow Solutions For Variable LoaIJERA Editor
This paper presents the optimal power flow solutions under variable load conditions. In this article we present the recent trend towards non-deterministic (random) search techniques and hybrid methods for OPF and give the conclusions. These methods have become popular because they have a theoretical advantage over the deterministic methods with respect to handling of non convexity, dynamics, and discrete variables. Present commercial OPF programs can solve very large and complex power systems optimization problems in a relatively less time. In recent years many different solution methods have been suggested to solve OPF problems. The paper contributes a comprehensive discussion of specific optimization techniques that can be applied to OPF Solution methodology.
In recent times, fractional order controllers are gaining more interest. There are several fractional order controllers are available in literature. Still, tuning of these controllers is one of the main issues which the control community is facing. In this paper, online tuning of five dierent fractional order controllers is discussed viz. tilted proportional-integral-derivative (T-PID) controller, fractional order proportional-integral (FO-PI) controller, fractional order proportional-derivative (FO-PD) controller, fractional order proportional-integral-derivative (FO-PID) controller. A reference tracking method is proposed for tuning of fractional order controllers. First order with dead time (FOWDT) system is used to check feasibility of the control strategy.
Photophysical properties of light harvesting molecules: three different approaches (of increasing complexity and accuracy) to foresee the harvesting behaviour are reviewed with a highly didactic flow. Design principles are highlighted.
A supplementary document explaining the details is available among my uploads.
This set of slides collects a self-made research I did for a photochemistry course. I don't own part of the shown material and references for many public images are collected at the end of the presentation.
ADAPTIVE STABILIZATION AND SYNCHRONIZATION OF HYPERCHAOTIC QI SYSTEM cseij
The hyperchaotic Qi system (Chen, Yang, Qi and Yuan, 2007) is one of the important models of fourdimensional hyperchaotic systems. This paper investigates the adaptive stabilization and synchronization of hyperchaotic Qi system with unknown parameters. First, adaptive control laws are designed to stabilize the hyperchaotic Qi system to its equilibrium point at the origin based on the adaptive control theory and Lyapunov stability theory. Then adaptive control laws are derived to achieve global chaos synchronization of identical hyperchaotic Qi systems with unknown parameters. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive stabilization and synchronization schemes.
Dynamic Economic Dispatch Assessment Using Particle Swarm Optimization TechniquejournalBEEI
This paper presents the application of particle swarm optimization (PSO) technique for solving the dynamic economic dispatch (DED) problem. The DED is one of the main functions in power system planning in order to obtain optimum power system operation and control. It determines the optimal operation of generating units at every predicted load demands over a certain period of time. The optimum operation of generating units is obtained by referring to the minimum total generation cost while the system is operating within its limits. The DED based PSO technique is tested on a 9-bus system containing of three generator bus, six load bus and twelve transmission lines.
Reduction of Active Power Loss byUsing Adaptive Cat Swarm Optimizationijeei-iaes
This paper presents, an Adaptive Cat Swarm Optimization (ACSO) for solving reactive power dispatch problem. Cat Swarm Optimization (CSO) is one of the new-fangled swarm intelligence algorithms for finding the most excellent global solution. Because of complication, sometimes conventional CSO takes a lengthy time to converge and cannot attain the precise solution. For solving reactive power dispatch problem and to improve the convergence accuracy level, we propose a new adaptive CSO namely ‘Adaptive Cat Swarm Optimization’ (ACSO). First, we take account of a new-fangled adaptive inertia weight to velocity equation and then employ an adaptive acceleration coefficient. Second, by utilizing the information of two previous or next dimensions and applying a new-fangled factor, we attain to a new position update equation composing the average of position and velocity information. The projected ACSO has been tested on standard IEEE 57 bus test system and simulation results shows clearly about the high-quality performance of the planned algorithm in tumbling the real power loss.
Adaptive Signal Processing has been playing a key role confining itself not just to the field of communications but also had spread into the fields of embedded systems, biological instruments, astronomy, image processing and many other fields. Adaptive filters are slowly replacing traditional filters in many areas. The development of new techniques and trends of adaptation algorithms has provided us with a broader sense of understanding the adaptation phenomena. In this paper some basic algorithms such as Least-Mean-Squares, Leaky-LMS, Normalized-LMS, and Recursive-Least-Squares algorithms have been studied and the convergence of these algorithms has been studied. The study convergence of the algorithms gives us a better picture of how fast the algorithms converge to optimum values. This is an issue of consideration in real-time signal processing as the signal processor implementing these kinds of algorithms has to be converging fast enough to the optimum values to save time and memory.
A comparative analysis for stabilize the temperature variation of a water bod...eSAT Journals
Abstract
Minimization of performance indices is very effective criteria for real time system. The process basically indicates a stable system.
Now, fixing the temperature in a water body is an important method for practical life where fuzzy logic is appl ied naturally. Here
in this paper we will try to show the method of minimization of error parameter using optimal regulator have equally effects the
fuzzy system for that the system runs towards the stable system.
Keywords - Crisp Set, Fuzzy Set, FLC, Cost Function, HJB Method
Evaluation of Vibrational Behavior for A System With TwoDegree-of-Freedom Und...IJERA Editor
Analysis of the vibrational behavior of a system is extremely important, both for the evaluation of operating conditions, as performance and safety reason. The studies on vibration concentrate their efforts on understanding the natural phenomena and the development of mathematical theories to describe the vibration of physical systems. The purpose of this study is to evaluate an undamped system with two-degrees-of-freedom and demonstrate by comparing the results obtained in the experimental, numerical and analytical modeling the characteristics that describe a structure in terms of its natural characteristics. The experiment was conducted in PUC-MG where the data were acquired to determine the natural frequency of the system. We also developed an experimental test bed for vibrations studies for graduate and undergraduate students. In analytical modeling were represented all the important aspects of the system. In order, to obtain the mathematical equations is used MATLAB to solve the equations that describe the characteristics of system behavior. For the simulation and numerical solution of the system, we use a computational tool ABAQUS. The comparison between the results obtained in the experiment and the numerical was considered satisfactory using the exact solutions. This study demonstrates that calculation of the adopted conditions on a system with two-degrees-of-freedom can be applied to complex systems with many degrees of freedom and proved to be an excellent learning tool for determining the modal analysis of a system. One of the goals is to use the developed platform to be used as a didactical experiment system for vibration and modal analysis classes at PUC Minas. The idea is to give the students an opportunity to test, play, calculate and confirm the results in vibration and modal analysis in a low-cost platform
International Journal of Engineering Research and Development (IJERD)IJERD Editor
call for paper 2012, hard copy of journal, research paper publishing, where to publish research paper,
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
On the Fractional Optimal Control Problems With Singular and Non–Singular ...Scientific Review SR
The aim of this paper is to design an efficient numerical method to solve a class of time fractional optimal control
problems. In this problem formulation, the fractional derivative operator is consid- ered in three cases with both
singular and non–singular kernels. The necessary conditions are derived for the optimality of these problems and the
proposed method is evaluated for different choices of derivative operators. Simulation results indicate that the
suggested technique works well and pro- vides satisfactory results with considerably less computational time than
the other existing methods. Comparative results also verify that the fractional operator with Mittag –Leffler kernel in
the Caputo sense improves the performance of the controlled system in terms of the transient response compared to
the other fractional and integer derivative operators.
The tensor language provides a unifying approach that simplifies notation, which leads to compact modeling of multi-way information objects in many knowledge fields, and a thought framework as well. By such a language, it is modeled a generic system that connects to environment through its boundaries.
This paper analyses the optimal power system planning with DGs used as real and reactive power compensator. Recently planning of DG placement reactive power compensation are the major problems in distribution system. As the requirement in the power is more the DG placement becomes important. When planned to make the DG placement, cost analysis becomes as a major concern. And if the DGs operate as reactive power compensator it is most helpful in power quality maintenance. So, this paper deals with the optimal power system planning with renewable DGs which can be used as a reactive power compensators. The problem is formulated and solved using popular meta-heuristic techniques called cuckoo search algorithm (CSA) and particle swarm optimization (PSO). the comparative results are presented.
Solving practical economic load dispatch problem using crow search algorithm IJECEIAES
The practical economic load dispatch problem is a non-convex, non-smooth, and non-linear optimization problem due to including practical considerations such as valve-point loading effects and multiple fuel options. An optimization algorithm named crow search algorithm is proposed in this paper to solve the practical non-convex economic load dispatch problem. Three cases with different economic load dispatch configurations are studied. The simulation results and statistical analysis show the efficiency of the proposed crow search algorithm. Also, the simulation results are compared to the other reported algorithms. The comparison of results confirms the high-quality solutions and the effectiveness of the proposed algorithm for solving the non-convex practical economic load dispatch problem.
PuShort Term Hydrothermal Scheduling using Evolutionary Programmingblished pa...Satyendra Singh
In this paper, Evolutionary Programming method
is used for short term hydrothermal scheduling which minimize
the total fuel cost while satisfying the constraints. This paper
developed and studies the performance of evolutionary programs
in solving hydrothermal scheduling problem. The effectiveness of
the developed program is tested for the system having one hydro
and one thermal unit for 24 hour load demand. Numerical results
show that highly near-optimal solutions can be obtained by
Evolutionary Programming.
ECONOMIC LOAD DISPATCH USING PARTICLE SWARM OPTIMIZATIONMln Phaneendra
In this ppt particle swarm optimization (PSO) is applied to allot the active power among the generating stations satisfying the system constraints and minimizing the cost of power generated.The viability of the method is analyzed for its accuracy and rate of convergence. The economic load dispatch problem is solved for three and six unit system using PSO and conventional method for both cases of neglecting and including transmission losses. The results of PSO method were compared with conventional method and were found to be superior.
Centralized Optimal Control for a Multimachine Power System Stability Improve...IDES Editor
this paper introduces the application of wave variable
method in reducing the effect of delay during the transmission of
control signals via large distances in a multimachine power
system. Fast response and pure control signals applied to a power
system have great importance in control process. At first we
design a centralized optimal control considering no transport
delay and then we compare them to the one considering this effect
in order to demonstrate the deteriorating effect of transmission
delay. Then we apply the wave variable method and it is shown
that performance of centralized optimal controller is improved.
Simulated Annealing for Optimal Power Flow (OPF)Anmol Dwivedi
Code available at: https://github.com/anmold-07/Optimal-Power-Flow-using-Simulated-Annealing
In this report, the algorithm is tested on standard functions like the Himmelblau’s function, Easom function, and Ackley function. Further, the algorithm is used to solve an Optimal Power Flow (OPF) with an objective to minimize the transmission line losses for an IEEE 14 bus and 30 bus systems. The proposed methodology has been tested with IEEE 14 bus and 30 bus networks and finally, the results section includes the conclusions of the work.
Photophysical properties of light harvesting molecules: three different approaches (of increasing complexity and accuracy) to foresee the harvesting behaviour are reviewed with a highly didactic flow. Design principles are highlighted.
A supplementary document explaining the details is available among my uploads.
This set of slides collects a self-made research I did for a photochemistry course. I don't own part of the shown material and references for many public images are collected at the end of the presentation.
ADAPTIVE STABILIZATION AND SYNCHRONIZATION OF HYPERCHAOTIC QI SYSTEM cseij
The hyperchaotic Qi system (Chen, Yang, Qi and Yuan, 2007) is one of the important models of fourdimensional hyperchaotic systems. This paper investigates the adaptive stabilization and synchronization of hyperchaotic Qi system with unknown parameters. First, adaptive control laws are designed to stabilize the hyperchaotic Qi system to its equilibrium point at the origin based on the adaptive control theory and Lyapunov stability theory. Then adaptive control laws are derived to achieve global chaos synchronization of identical hyperchaotic Qi systems with unknown parameters. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive stabilization and synchronization schemes.
Dynamic Economic Dispatch Assessment Using Particle Swarm Optimization TechniquejournalBEEI
This paper presents the application of particle swarm optimization (PSO) technique for solving the dynamic economic dispatch (DED) problem. The DED is one of the main functions in power system planning in order to obtain optimum power system operation and control. It determines the optimal operation of generating units at every predicted load demands over a certain period of time. The optimum operation of generating units is obtained by referring to the minimum total generation cost while the system is operating within its limits. The DED based PSO technique is tested on a 9-bus system containing of three generator bus, six load bus and twelve transmission lines.
Reduction of Active Power Loss byUsing Adaptive Cat Swarm Optimizationijeei-iaes
This paper presents, an Adaptive Cat Swarm Optimization (ACSO) for solving reactive power dispatch problem. Cat Swarm Optimization (CSO) is one of the new-fangled swarm intelligence algorithms for finding the most excellent global solution. Because of complication, sometimes conventional CSO takes a lengthy time to converge and cannot attain the precise solution. For solving reactive power dispatch problem and to improve the convergence accuracy level, we propose a new adaptive CSO namely ‘Adaptive Cat Swarm Optimization’ (ACSO). First, we take account of a new-fangled adaptive inertia weight to velocity equation and then employ an adaptive acceleration coefficient. Second, by utilizing the information of two previous or next dimensions and applying a new-fangled factor, we attain to a new position update equation composing the average of position and velocity information. The projected ACSO has been tested on standard IEEE 57 bus test system and simulation results shows clearly about the high-quality performance of the planned algorithm in tumbling the real power loss.
Adaptive Signal Processing has been playing a key role confining itself not just to the field of communications but also had spread into the fields of embedded systems, biological instruments, astronomy, image processing and many other fields. Adaptive filters are slowly replacing traditional filters in many areas. The development of new techniques and trends of adaptation algorithms has provided us with a broader sense of understanding the adaptation phenomena. In this paper some basic algorithms such as Least-Mean-Squares, Leaky-LMS, Normalized-LMS, and Recursive-Least-Squares algorithms have been studied and the convergence of these algorithms has been studied. The study convergence of the algorithms gives us a better picture of how fast the algorithms converge to optimum values. This is an issue of consideration in real-time signal processing as the signal processor implementing these kinds of algorithms has to be converging fast enough to the optimum values to save time and memory.
A comparative analysis for stabilize the temperature variation of a water bod...eSAT Journals
Abstract
Minimization of performance indices is very effective criteria for real time system. The process basically indicates a stable system.
Now, fixing the temperature in a water body is an important method for practical life where fuzzy logic is appl ied naturally. Here
in this paper we will try to show the method of minimization of error parameter using optimal regulator have equally effects the
fuzzy system for that the system runs towards the stable system.
Keywords - Crisp Set, Fuzzy Set, FLC, Cost Function, HJB Method
Evaluation of Vibrational Behavior for A System With TwoDegree-of-Freedom Und...IJERA Editor
Analysis of the vibrational behavior of a system is extremely important, both for the evaluation of operating conditions, as performance and safety reason. The studies on vibration concentrate their efforts on understanding the natural phenomena and the development of mathematical theories to describe the vibration of physical systems. The purpose of this study is to evaluate an undamped system with two-degrees-of-freedom and demonstrate by comparing the results obtained in the experimental, numerical and analytical modeling the characteristics that describe a structure in terms of its natural characteristics. The experiment was conducted in PUC-MG where the data were acquired to determine the natural frequency of the system. We also developed an experimental test bed for vibrations studies for graduate and undergraduate students. In analytical modeling were represented all the important aspects of the system. In order, to obtain the mathematical equations is used MATLAB to solve the equations that describe the characteristics of system behavior. For the simulation and numerical solution of the system, we use a computational tool ABAQUS. The comparison between the results obtained in the experiment and the numerical was considered satisfactory using the exact solutions. This study demonstrates that calculation of the adopted conditions on a system with two-degrees-of-freedom can be applied to complex systems with many degrees of freedom and proved to be an excellent learning tool for determining the modal analysis of a system. One of the goals is to use the developed platform to be used as a didactical experiment system for vibration and modal analysis classes at PUC Minas. The idea is to give the students an opportunity to test, play, calculate and confirm the results in vibration and modal analysis in a low-cost platform
International Journal of Engineering Research and Development (IJERD)IJERD Editor
call for paper 2012, hard copy of journal, research paper publishing, where to publish research paper,
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
On the Fractional Optimal Control Problems With Singular and Non–Singular ...Scientific Review SR
The aim of this paper is to design an efficient numerical method to solve a class of time fractional optimal control
problems. In this problem formulation, the fractional derivative operator is consid- ered in three cases with both
singular and non–singular kernels. The necessary conditions are derived for the optimality of these problems and the
proposed method is evaluated for different choices of derivative operators. Simulation results indicate that the
suggested technique works well and pro- vides satisfactory results with considerably less computational time than
the other existing methods. Comparative results also verify that the fractional operator with Mittag –Leffler kernel in
the Caputo sense improves the performance of the controlled system in terms of the transient response compared to
the other fractional and integer derivative operators.
The tensor language provides a unifying approach that simplifies notation, which leads to compact modeling of multi-way information objects in many knowledge fields, and a thought framework as well. By such a language, it is modeled a generic system that connects to environment through its boundaries.
This paper analyses the optimal power system planning with DGs used as real and reactive power compensator. Recently planning of DG placement reactive power compensation are the major problems in distribution system. As the requirement in the power is more the DG placement becomes important. When planned to make the DG placement, cost analysis becomes as a major concern. And if the DGs operate as reactive power compensator it is most helpful in power quality maintenance. So, this paper deals with the optimal power system planning with renewable DGs which can be used as a reactive power compensators. The problem is formulated and solved using popular meta-heuristic techniques called cuckoo search algorithm (CSA) and particle swarm optimization (PSO). the comparative results are presented.
Solving practical economic load dispatch problem using crow search algorithm IJECEIAES
The practical economic load dispatch problem is a non-convex, non-smooth, and non-linear optimization problem due to including practical considerations such as valve-point loading effects and multiple fuel options. An optimization algorithm named crow search algorithm is proposed in this paper to solve the practical non-convex economic load dispatch problem. Three cases with different economic load dispatch configurations are studied. The simulation results and statistical analysis show the efficiency of the proposed crow search algorithm. Also, the simulation results are compared to the other reported algorithms. The comparison of results confirms the high-quality solutions and the effectiveness of the proposed algorithm for solving the non-convex practical economic load dispatch problem.
PuShort Term Hydrothermal Scheduling using Evolutionary Programmingblished pa...Satyendra Singh
In this paper, Evolutionary Programming method
is used for short term hydrothermal scheduling which minimize
the total fuel cost while satisfying the constraints. This paper
developed and studies the performance of evolutionary programs
in solving hydrothermal scheduling problem. The effectiveness of
the developed program is tested for the system having one hydro
and one thermal unit for 24 hour load demand. Numerical results
show that highly near-optimal solutions can be obtained by
Evolutionary Programming.
ECONOMIC LOAD DISPATCH USING PARTICLE SWARM OPTIMIZATIONMln Phaneendra
In this ppt particle swarm optimization (PSO) is applied to allot the active power among the generating stations satisfying the system constraints and minimizing the cost of power generated.The viability of the method is analyzed for its accuracy and rate of convergence. The economic load dispatch problem is solved for three and six unit system using PSO and conventional method for both cases of neglecting and including transmission losses. The results of PSO method were compared with conventional method and were found to be superior.
Centralized Optimal Control for a Multimachine Power System Stability Improve...IDES Editor
this paper introduces the application of wave variable
method in reducing the effect of delay during the transmission of
control signals via large distances in a multimachine power
system. Fast response and pure control signals applied to a power
system have great importance in control process. At first we
design a centralized optimal control considering no transport
delay and then we compare them to the one considering this effect
in order to demonstrate the deteriorating effect of transmission
delay. Then we apply the wave variable method and it is shown
that performance of centralized optimal controller is improved.
Simulated Annealing for Optimal Power Flow (OPF)Anmol Dwivedi
Code available at: https://github.com/anmold-07/Optimal-Power-Flow-using-Simulated-Annealing
In this report, the algorithm is tested on standard functions like the Himmelblau’s function, Easom function, and Ackley function. Further, the algorithm is used to solve an Optimal Power Flow (OPF) with an objective to minimize the transmission line losses for an IEEE 14 bus and 30 bus systems. The proposed methodology has been tested with IEEE 14 bus and 30 bus networks and finally, the results section includes the conclusions of the work.
Nonlinear batch reactor temperature control based on adaptive feedback based ilcijics
This work presents the temperature control of a nonlinear batch reactor with constrains in the manipulated
variable by means of adaptive feedback-based iterative learning control (ILC). The strong nonlinearities
together with the constrains of the plant can lead to a non-monotonic convergence of the l2-norm of the
error, and still worse, an unstable equilibrium signal e(t) can be reached. By numeric simulation this
works shows that with the adaptive feedback-based ILC is possible to obtain a better performance in the
controlled variable than with the traditional feedback and the feedback based-ILC.
NONLINEAR BATCH REACTOR TEMPERATURE CONTROL BASED ON ADAPTIVE FEEDBACK-BASED ILCijcisjournal
This work presents the temperature control of a nonlinear batch reactor with constrains in the manipulated variable by means of adaptive feedback-based iterative learning control (ILC). The strong nonlinearities together with the constrains of the plant can lead to a non-monotonic convergence of the l2-norm of the error, and still worse, an unstable equilibrium signal e∞(t) can be reached. By numeric simulation this works shows that with the adaptive feedback-based ILC is possible to obtain a better performance in the controlled variable than with the traditional feedback and the feedback based-ILC.
FUZZY LOGIC Control of CONTINUOUS STIRRED TANK REACTOR ProfDrDuraidAhmed
MATLAB program version 7.6 was used to study dynamic behavior continuous stirred tank reactor and the process control implemented for different control strategies. The results of simulation were compared with experimental data and a good agreement was obtained. However, small differences between the responses were appeared. A comparison has been made between fuzzy logic controller and PID conventional control to test the effectiveness of the behavior of the system. The results showed that, a good improvement was achieved when the fuzzy logic control was used compared to the PID conventional control.
This study deals with the active control of the dynamic response of a string with fixed ends and mass
loaded by a point mass. It has been controlled actively by means of a feed forward control method. A point mass of a
string is considered as a vibrating receiver which be forced to vibrate by a vibrating source being positioned on the
string. By analyzing the motion of a string, the equation of motion for a string was derived by using a method of
variation of parameters. To define the optimal conditions of a controller, the cost function, which denotes the dynamic
response at the point mass of a string was evaluated numerically. The possibility of reduction of a dynamic response
was found to depend on the location of a control force, the magnitude of a point mass and a forcing frequency
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
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Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
An Approach to Detecting Writing Styles Based on Clustering Techniquesambekarshweta25
An Approach to Detecting Writing Styles Based on Clustering Techniques
Authors:
-Devkinandan Jagtap
-Shweta Ambekar
-Harshit Singh
-Nakul Sharma (Assistant Professor)
Institution:
VIIT Pune, India
Abstract:
This paper proposes a system to differentiate between human-generated and AI-generated texts using stylometric analysis. The system analyzes text files and classifies writing styles by employing various clustering algorithms, such as k-means, k-means++, hierarchical, and DBSCAN. The effectiveness of these algorithms is measured using silhouette scores. The system successfully identifies distinct writing styles within documents, demonstrating its potential for plagiarism detection.
Introduction:
Stylometry, the study of linguistic and structural features in texts, is used for tasks like plagiarism detection, genre separation, and author verification. This paper leverages stylometric analysis to identify different writing styles and improve plagiarism detection methods.
Methodology:
The system includes data collection, preprocessing, feature extraction, dimensional reduction, machine learning models for clustering, and performance comparison using silhouette scores. Feature extraction focuses on lexical features, vocabulary richness, and readability scores. The study uses a small dataset of texts from various authors and employs algorithms like k-means, k-means++, hierarchical clustering, and DBSCAN for clustering.
Results:
Experiments show that the system effectively identifies writing styles, with silhouette scores indicating reasonable to strong clustering when k=2. As the number of clusters increases, the silhouette scores decrease, indicating a drop in accuracy. K-means and k-means++ perform similarly, while hierarchical clustering is less optimized.
Conclusion and Future Work:
The system works well for distinguishing writing styles with two clusters but becomes less accurate as the number of clusters increases. Future research could focus on adding more parameters and optimizing the methodology to improve accuracy with higher cluster values. This system can enhance existing plagiarism detection tools, especially in academic settings.
Literature Review Basics and Understanding Reference Management.pptxDr Ramhari Poudyal
Three-day training on academic research focuses on analytical tools at United Technical College, supported by the University Grant Commission, Nepal. 24-26 May 2024
Online aptitude test management system project report.pdfKamal Acharya
The purpose of on-line aptitude test system is to take online test in an efficient manner and no time wasting for checking the paper. The main objective of on-line aptitude test system is to efficiently evaluate the candidate thoroughly through a fully automated system that not only saves lot of time but also gives fast results. For students they give papers according to their convenience and time and there is no need of using extra thing like paper, pen etc. This can be used in educational institutions as well as in corporate world. Can be used anywhere any time as it is a web based application (user Location doesn’t matter). No restriction that examiner has to be present when the candidate takes the test.
Every time when lecturers/professors need to conduct examinations they have to sit down think about the questions and then create a whole new set of questions for each and every exam. In some cases the professor may want to give an open book online exam that is the student can take the exam any time anywhere, but the student might have to answer the questions in a limited time period. The professor may want to change the sequence of questions for every student. The problem that a student has is whenever a date for the exam is declared the student has to take it and there is no way he can take it at some other time. This project will create an interface for the examiner to create and store questions in a repository. It will also create an interface for the student to take examinations at his convenience and the questions and/or exams may be timed. Thereby creating an application which can be used by examiners and examinee’s simultaneously.
Examination System is very useful for Teachers/Professors. As in the teaching profession, you are responsible for writing question papers. In the conventional method, you write the question paper on paper, keep question papers separate from answers and all this information you have to keep in a locker to avoid unauthorized access. Using the Examination System you can create a question paper and everything will be written to a single exam file in encrypted format. You can set the General and Administrator password to avoid unauthorized access to your question paper. Every time you start the examination, the program shuffles all the questions and selects them randomly from the database, which reduces the chances of memorizing the questions.
Tutorial for 16S rRNA Gene Analysis with QIIME2.pdf
1987 . thermo economic functional analysis and optimization [frangopoulos]
1. Energy Vol. 12, No. 7, pp. 563-571, 1987 0360-5442187 $3.00 + 0.00
Printed in Great Britain Pergamon Journals Ltd
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THERMO-ECONOMIC FUNCTIONAL ANALYSIS AND
OPTIMIZATION
CHRISTOS A. FRANGOPOULOS
Department of Naval Architecture and Marine Engineering, National Technical University of
Athens, Athens 106 82, Greece
(Received 18 August 1986)
Abstract-Thermo-economic functional analysis is a method for optimal design or improvement
of complex thermal systems. Thermodynamic concepts are combined with economic considerations
in a systems approach. Units are the basic elements of the system; each unit has a particular
quantified function (purpose or product). The distribution of functions establishes inter-relations
between units or between the system and the environment and leads to a functional diagram of
the system. The optimization minimizes the total cost of owning and operating the system, subject
to constraints revealed by the functional diagram and analysis. The general formulation and a
numerical example are presented.
NOMENCLATURE
cost coefficients (constants) Greek letters
annual fixed charge rate ‘111 second-law efficiency
price of electricity (%/kJ) ‘lu = w/(,%?Ah) for the turbine-generator
price of fuel ($/kJ) = niAh/wfor the pump-motor
specific heat of water ). vector of all the Lagrange multipliers
chemical essergy of fuel 0 number of units
pump material factor (constant) T number of units and junctions
enthalpy per unit mass specific volume
number of outputs from unit r ; maintenance factor
mass w number of units, junctions and branching
number of inputs to unit r points
hours of operation per year
number of transfer units of condenser
number of decision variables for unit r
pressure
parameter
overall heat transfer resistance of condenser
entropy
negentropy
entropy per unit mass
temperature
velocity
power
vector of decision variables
contraint function
Subscripts
i the ith decision variable
0 reference state
r the rth unit (r = 0 is for the environment)
W water
Overmarks
per unit time
reference quantity (constant)
fixed value of an otherwise variable quantity
vector of all the inputs and outputs
the product of unit r
the kth output from r
thejth input to r
1. INTRODUCTION
Earlier work by Tribus, Evans and El-Sayed on thermo-economics’,’ led to the concept
of thermo-economic isolation (TI) introduced by Evans.3 In order to approach thermo-
economic isolation, Tribus’ and Evans et ~1.~made use of the functions or purposes of
thermal system components, but the conditions for approaching TI remained to be derived.
The attempt to derive formally the complete set of conditions for TI has led us to the
development of a new and generally applicable method for optimal design or improvement
of complex thermal systems, which we call thermo-economic functional analysis (TFA).’
2. FUNCTIONAL ANALYSIS
2.1 Concepts and definitions
A thermal system (thermal power plant, refrigeration plant, chemical plant, etc.) consists
of a set of inter-related units.6 Each unit has one particular function (purpose or product).
563
FRANGOPOULOS, Christos A. Thermo-economic functional analysis and optimization.
Energy, v. 12, n. 7, p. 563-571, 1987.
2. 564 CHRISTOSA. FRANGOPOULOS
Functional analysis is “the formal, documented determination of the function of the
system”7 as a whole and of each unit individually.5
2.2 The functional diagram ofa system
The picture of a system will be composed of small geometrical figures representing the
units and a network of lines representing the distribution of the unit functions. This is the
functional diagram of the system. Junctions (where the functions of two or more units
merge) and branching points (where the function of a unit is distributed to more than one
unit) are considered to be fictitious units, unless they correspond to real components of
the plant.
3. THERMO-ECONOMIC FUNCTIONAL OPTIMIZATION
The optimization objective is the minimization of the total cost of owning and operating
the system, with income included as a negative cost.
3.1 Total optimization
The system is considered to be operating at the steady state with products of a specific
type, but not necessarily of predetermined quantity. The objective function is
min P = i i, + lo? tO.k,
x r=l k=l
(1)
where p = cost rate of owning and operating the whole system, Z, = amortized capital
cost rate of unit r including fixed charges and maintenance, rO,k = cost rate associated
with yO.k. For 1 < k d 8O,p O,kis positive and represents expenditure corresponding to
services purchased by the system from the environment; penalties for environmental
pollution or other social hazards can be quantified and included. For
e,, + 1 Q k < !, + m,, rO,k is negative and represents profit from selling products.
Costs are functions of decision variables and quantities purchased or sold as follows:
z =Z,(X,,Yl,l) = z,, (24
pO.k = rO.k(YO.k) = rO.k, GW
P = F(x,y) = F. (W
Both sides of Eqs. (2) are expressions for cost rate, but the left hand side (e.g. Z,) represents
the cost rate quantity itself, while the right hand side (e.g. Z,) represents the mathematical
functional operation which generates its numerical value.
In view of Eqs. (2), the objective function takes the form
T$ F = i z,(x,? Y,.l) + “so rO.k(YO.k)~
r=l k=l
(3)
The equality constraints are
Y,,j = Y,,j(X,,Y,,l) E Y,,j (r = O,l,...,W i = L&...,m,L (4)
Y,~,~= yl,j (r’= O,l,..., w, k = 1,2,..., e,). (5)
The constraints (4) give the inputs to the unit I as functions of the product Y,.~and the
decision variables x, of the unit. The constraints (5) represent interconnections between
3. Thermo-economic functional analysis and optimization 5h5
units or between a unit and the environment, which are revealed by the functional diagram
of the system.
Inequality constraints would not alter the basic principles of the method, but they will
not be considered.
For the solution of the optimization problem, the method of Lagrange multipliers has
been chosen, which leads readily to the special cases of decomposition and thermo-
economic isolation.s The Lagrangian is
r=l k=l r=Oj=l
+ f f$A'.k(Yr,j- Yr’.k). (6)
r'=Ok=l
The necessary conditions for an extremum are
v,w, Y, J-1= 0, t7a)
V&(x, y,v =0, (7b)
V*L(x, y, k) = 0. (7c)
It is proved in Ref. 5 that the Lagrangian takes the convenient form
where
L= f err- i ir.kyr.k)+ f"i?rO.k - ju0.ky0.k)3
r=l k=l k=l
(8)
I-, = z, + t 4,jY.j.
j=I
(9)
The conditions (7~) lead to a restatement of the constraints given in Eqs. (4) and (5). The
conditions (7a, b) lead to
8
( >
i r, /fJX,i = 0 (r = 1,2,...,a, i = 1,2, ..., n,),
r=l
I 0.k= arO.k/dYO.k (k = 1,2 ,...) to + mo), (11)
&k = w~y,.k (r = 1,2 )“‘, 0, k = 1,2 ,..., t,). (12)
The concept of internal economy introduced by El-Sayed and Evans’ and the correspond-
ing interpretation of Lagrange multipliers as economic indicators of prices are maintained
here. According to Eqs. (1 I), (12), each Lagrange multiplier can be viewed as the marginal
price of the corresponding function (product) y.
The optimization problem is solved by using the following procedure: (a) select a set of
values for the decision variables x; (b) solve Eqs. (4), (5) for the dependent variables y; (c)
determine the Lagrange multipliers from Eqs. (1 l), (12). We stop when Eq. (10) is satisfied
to an acceptable approximation. Otherwise, we select a new set for x and repeat the
procedure.
4. 566 CHRISTOSA. FRANGOPOULOS
3.2 Fixed-product optimization
This case arises when the income functions FO,(yc,J,
known, but the products are fixed and known quantities:
~O+l<k<to+mo, are not
Y0.k = 90,j (k = to+.i i = lg2,...,mo),
The objective function in such a situation is
(13)
minF = i Z,~,Y~J + ? ro.k(~o.k).
X,Y r=l k=l
(14)
Equation (6) is vaiid if the upper limit PO+ m, of the summation over I0.k is replaced by
lo, while Eq. (8) takes the form
>
+ ; (r0.k - l-O.kYO.k) + jtl ‘0.jfO.j
k=l
(15)
The procedure to solve the optimization problem is similar to the one described in Sec.
3.1.
3.3 Main actions for TFA and 0
In summary, the thermo-economic functional analysis and optimization of a thermal
system consists of the following actions: (1) identifying the functions of the system as a
whole and of each individual unit; (2) constructing the functional diagram of the system;
(3) formulating the optimization problem, i.e. (a) selecting the decision variables,(b) deriving
the cost functions ZI(x,, Y,.~)and &,k(yo.k), (c) deriving the constraint functions YI,Axr,y,,r),
(d) deriving the explicit form of the optimization equations; (4) solving the system of
optimization equations. Parametric study and sensitivity analysis may follow.
4. APPLICATION OF TFA AND 0 TO A FOUR-UNIT THERMAL POWER PLANT
4.1. Description of the plant and main assumptions
The method will now be applied to a simplified thermal power plant. The system is
considered to be made up of four units: (1) boiler, (2) turbine-generator, (3) condenser and
condensing supply works (e.g. cooling towers, coolinggwater-circulating pumps etc.), and
(4) boiler feed pump (see Fig. 1).
A distinction must be drawn between a unit and a component. The cooling tower or
cooling-water-circulating pump are components. However, in this example, they are not
considered to be separate units but are instead combined with the condenser in a unit
having one function. The number of units in a system is not unique and depends on the
available information and desired results. The designer may select high (many units) or
low resolution (a few units), depending on the objectives.
It is assumed that the plant produces only electrical power at a specified rate I& The
power required by the pump is supplied from outside the system. All of the components
are well insulated and losses through the pipes connecting the components are negligibly
small.
4.2. The functional diagram of the system
The function of each unit will be measured by means of essergy (as defined by Evans’)
and entropy. To identify the functions and their distribution, the following procedure is
used: a closed loop of an essergy-carrying stream is considered, Fig. 2. The units take from
this stream or from outside the system the amount of essergy required for their operation,
5. Thermo-economic functional analysis and optimization 567
Fuel
Ex.Gases Air
1.
I
C
1 - 1
I. _ -__-a
(a) *'"I
ti
w
Fig. 1. A four-unit thermal power plant (B = boiler, T = turbine, G = generator, C = condenser, P = pump).
and give their product either back to the stream or to the environment. The operation of
the units creates entropy, which is rejected to the environment through the condenser. In
other words, the condenser is supplying the system with the negative ofentropy, (negentropy,
as introduced by Brillouin’ and used by Smith” to quantify the function of the condenser).
A negentropy-carrying stream runs parallel to the essergy stream but in the opposite
direction (see Fig. 2).
yil.1
1,
r-
___---_--_-- -___
y1,1
1
y1,2
-J
1
y1,3
:
q.Yl.1
- _m5-*
r-- ,
s4
II
I . I,
1
.%,t .
5, 1
1 'IV1
I y2,1 /
y2.1
L2-2< 0
yod
Y2
I'
I
I
152
I
-_-_-
System Boundary
Fig. 2. The power plant with essergy and negentropy streams.
I
6. 568 CHRISTOSA.FRANGOPOULOS
I
i I t *5.1
L-,
I
i *2,i /
__~ r-;-eJ
y2.1
2-
----_ -L
" v
y2,2
7
L- -l-*3,2
_-____
-7---------
I l-*n :, System Boudary
Fig. 3. Functional diagram of a four-unit thermal power plant
Essergy and negentropy balances along each stream lead to expressions for the yr,j,
which are given in Appendix A. The concepts introduced in Sec. 2.2 and the procedure
described here lead to the functional diagram of the system (see Fig. 3).
An arrow pointing toward a unit does not necessarily represent a stream (of mass,
energy, essergy, etc.) entering the unit. For example, exhaust gases of a boiler form a stream
exiting the boiler; but, the service of getting rid of exhaust gases is provided to the boiler
by an other unit (not shown in Fig. 3, because of the resolution level selected). Similarly,
if the boiler is to be penalized for environmental pollution, then the corresponding
expenditure will depend on an appropriate measure of pollution, to be represented by an
arrow, say y1.4 pointing toward the unit.
4.3 Optimization of the system
Among the many quantities involved, the decision variables are selected to be
x = (q,rtrrl, T2, Gr~wt1,14). (16)
The remaining quantities are either dependent variables or parameters. The objective
function is given by Eq. (14) with CJ= 4 and /, = 3.
The procedure described at the end of Sec. 3.1 has been used to solve the optimization
problem for ri/= 20 MW. Figures 4 and 5 show the influence of fuel and electricity prices
on optimum values of decision variables. The effect of parameter uncertainties on the
optimum solution may be obtained by using sensitivity anaIysis. The change (uncertainty)
in the objective function due to a change (uncertainty) in a particular parameter may be
estimated from
AF = (dF/apj)Apj. (17)
7. Thermo-economic functional analysis and optimization 569
-6,Tb -h
(K) (K)
320 830
310
300
820
810
1.0 1.5 2.0 2.5 3.0 35 4.0
cF
(106$/d
Fig. 4. Effect of fuel price on optimum values of decision variables.
2.0 - - 0.84
;i
I%
'; 18- - 0.62 c2
>*
1.6 - - 0.60
1.4 - - 0.70
2 3 4 5 6 7
C,(C/kWhr)
Fig. 5. EfFect of electricity price on optimum values of decision variables.
The maximum possible uncertainty in the objective function caused by uncertainties in a
set of parameters is
AF,,, =
while the most probable uncertainty is
AF prob = J~C(aFlaPjWPjl’. (19)
(18)
As an example, sensitivity analysis results are presented in Table 1. Primarily economic
parameters have been selected, because of the inherent uncertainty in deriving or predicting
values of these parameters. Cost data found in the literature are only accurate to +25-
30%.
8. 570 CHRISTOSA. FRANGOPOULOS
Table 1. An example of sensitivity analysis
Parameter (pj)
j. aF
aPj
LIP!*’
3
AF.
Symbol Nominal Units 3
Value
1
=f
2.0x10-a B/kJ 7.7378x10C 2.0x10-' 1.5476x10-'
2 'e
8.33x1O-6 B/kJ 2.3541~10' 8.33x10-' 1.9610x10-'
3 bll 740. $/(kW)".8 3.7912x1o-5 74. 2.8055x10-'
4 b12 0.8 2.8941x10-1 0.08 2.3153x10-'
5 b21 3000. $/(kW)"*7 7.2855x10-' 300. 2.1857x10-:
6 b22 0.7 2.1645x10-l 0.07 1.5152x10-'
7 b31 217. S/m’ 1.2885~10-~ 21.7 2.7961x10-*
8 b32 577. S/(kg/s) 5.7447x1o-6 57.7 3.3147x1o-u
9 b41 378. $/(kW)".71 6.4086x10-' 37.8 2.4225x10-5
to b42 0.71 - 1.1835~10-~ 0.071 8.4O29x1O-5
Ll fm 1.06 - 5.3079x10-* 0.106 5.6264x10-'
L2 c 18.2 % 3.o914x1o-3 1.82 5.6264x10-j
AFmax
= 7.0940~10-* AF
prob
= 1.0813x10-'
(*) for Apj/pj = 0.10
Acknowledgements-The author expresses his sincere gratitude to R. B. Evans for advice and encouragement.
Support provided by the Georgia Institute of Technology and the National Technical University of Athens is
gratefully acknowledged.
REFERENCES
1. M. Tribus and R. B. Evans, A Contribution to the Theory of Thermoeconomics, UCLA Report No. 62-36,
University of California at Los Angeles, Los Angeles, Calif. (1962).
2. Y. M. El-Sayed and R. B. Evans, .I. Engng Power 92, 27 (1970).
3. R. B. Evans, Energy 5, 805 (1980).
4. R. B. Evans, W. A. Hendrix and P. V. Kadaba, Essergetic functional analysis for process design and synthesis,
in Ejiciency and Costing: Second Law Analysis ofProcesses (Edited by R. A. Gaggioli), p. 239. ACS Symposium
Series No. 235, Washington, D.C. (1983).
5. C. A. Frangopoulos, Thermoeconomic Functional Analysis: A Method for Optimal Design or Improvement
of Complex Thermal Systems. Ph.D. Thesis, Georgia Institute of Technology, Atlanta, Ga (1983).
6. N. J. T. A. Kramer and J. Smit, Systems Thinking: Concepts and Notions. Martinus Nijoff Social Sciences
Division, Leiden, The Netherlands (1977).
7. S. L. Dickerson and J. E. Robertshaw, Planning and Design. Lexington Books, Lexington, Mass. (1975).
8. R. B. Evans, A Proof that Essergy is the only Consistent Measure of Potential Work. Ph.D. Thesis, Dartmouth
College, Hanover, N.H. (1969).
9. L. Brillouin, Science and Information Theory, 2nd ed. Academic Press, New York (1962).
IO. M. S. Smith, Effect of Condenser Design upon Boiler Feedwater Essergy Costs in Power Plants. M.S. Thesis,
Georgia Institute of Technology, Atlanta, Ga (1981).
11. R. M. Garceau, Thermoeconomic Optimization of a Rankine Cycle Cogeneration System. M.S. Thesis,
Georgia Institute of Technology, Atlanta, Ga (1982).
12. J. G. Singer ed., Combustion: Fossil Power Systems, 3rd ed. Combustion Engineering Inc., Windsor, Conn.
(1981).
13. H. Popper, Modern Cost Engineering Techniques. McGraw-Hill, New York (1970).
14. R. S. Hall, J. Matley and K. J. McNaughton. Chem. Engng 89, 80 (1982).
9. Thermo-economic functional analysis and optimization 571
APPENDIX A
Expressions for the Functions of Fig. 2 and 3
The essergy flows related to the environment are:
y,., = $3 Y3.2 = fi,v,(P, - Pb)lVMW
~4.1 = ri/, = h(k, - hA/r7Md. y2, = ri/= ?/M*14?(hl- h2).
Other essergy flows are:
Y1.2 = fiv,(P* - PI), Y2.1 = M11/1 - (LA Y3.1 = Mti1 - $3).
Y4.1 = M+a - ti3)? L, = +, + Y4 , - Y1.2 = Mi, - v4(P4 - P,)l.
y, , ==9, - 9, = nicI(I1- $4)+ v4(P4 - P,)l,
where $ is the flow essergy per unit mass:
The negentropy flows are:
where:
$ = h - h, - T,(s - s,,) and 9” = ti$.
Y3.1 = $2 - $3 + y, 1 = Wl(s, - sj),
Y1.3 = $1 - $4 -+ y1.3 = ‘WAS, - &A
Y2,2 = $2 - $1 -+ y2.z = n;lT,(s, - s,),
Y4.2 = $4 - $3 -+ y4.2 = n;lT,(s, - s3).
S, = -nisi(i = 1,2,3,4)
The last forms of y3,,.y1 3,y2,2, and y4 z are obtained by multiplying negentropy flows by the reference
temperature To and changing the sign. This convenient procedure is used in order to obtain all functions as
positive quantities in the same units.
APPENDIX B
Cost Functions
The following equations have been derived in Ref. 5 by using information from several sources (e.g. Refs. 1I
14):
where:
i,, = (C/3.6 x 10SN)+,h,i, gP = expl(P, - ~,).!b,,l,
RI, = 1+ C(O,45 - ri,,,)/(O, 45 - %,P.
R,~= 1+ b,,exp[(T, - T,)/bJ(r = 1.2).
R,, = 1 + ~(1 - sdm - r7diVr = 2,4).