The cost of water distribution system includes cost of pipes, pumping system, civil works and
pumping energy. Out of these, cost of civil works and pumping system are nearly fixed for any specific water
supply project. The cost of pipes and pumping energy are variable and can be minimized by suitable selection
of pipe size, material of pipes and staging of elevated service reservoir. In the present work, the cost of pipes
and energy have been optimized using Particle Swarm Optimization (PSO) method for a water supply system
having large pipe network. In addition to this, the effect of swarm size and different inertia weights of PSO is
also studied on the optimized cost of the system
Cost optimization of pipeline systems using genetic algorithmIAEME Publication
This document summarizes a research paper that uses a genetic algorithm to optimize the cost of irrigation pipeline networks. The paper aims to find the lowest cost pipe diameter configuration that meets hydraulic constraints like head requirements. It first describes using a genetic algorithm to represent different pipe diameter combinations as chromosomes. It then calculates the cost of initial random configurations and checks if they meet constraints. The algorithm iteratively applies genetic operators like selection, crossover and mutation to chromosomes until optimized low-cost configurations are found that satisfy constraints like supplying required water flows and pressures.
Capacitor Placement and Reconfiguration of Distribution System with hybrid Fu...IOSR Journals
The document describes a hybrid fuzzy-opposition based differential evolution algorithm for capacitor placement and distribution system reconfiguration to minimize transmission losses and costs. The algorithm considers constraints like voltage limits and current limits while optimizing the objective function of total annual cost, which includes energy loss costs and capacitor costs. It was tested on the IEEE 33-bus distribution test system and able to reduce losses and satisfy power flow constraints.
Cost Aware Expansion Planning with Renewable DGs using Particle Swarm Optimiz...IJERA Editor
This Paper is an attempt to develop the expansion-planning algorithm using meta heuristics algorithms. Expansion Planning is always needed as the power demand is increasing every now and then. Thus for a better expansion planning the meta heuristic methods are needed. The cost efficient Expansion planning is desired in the proposed work. Recently distributed generation is widely researched to implement in future energy needs as it is pollution free and capability of installing it in rural places. In this paper, optimal distributed generation expansion planning with Particle Swarm Optimization (PSO) and Cuckoo Search Algorithm (CSA) for identifying the location, size and type of distributed generator for future demand is predicted with lowest cost as the constraints. Here the objective function is to minimize the total cost including installation and operating cost of the renewable DGs. MATLAB based `simulation using M-file program is used for the implementation and Indian distribution system is used for testing the results.
Optimizing location and size of capacitors for power loss reduction in radial...TELKOMNIKA JOURNAL
Power radial distribution systems are increasingly more and more important in transmitting the electric energy from power plants to customers. However, total loss in lines are very high. This issue can be solved by allocating capacitor banks. Determining the suitable allocation and optimal sizing of capacitor banks needs an efficient approach. In this study, the diffusion and update techniques-based algorithm (DUTA) is proposed for such reason. The efficiency of DUTA is inspected on two distribution systems consisting of 15-bus and 33-bus systems with different study cases. The solutions attained by DUTA are competed with recently published methods. As a consequence, the method is more effective than the other methods in terms of the quality of solution.
This is a resume of my master’s degree thesis where I made a Na-tech which one of the purposes was found the best technique to use in the new generation hydrogen pipelines to face an earthquake.
For further information and contributions don’t hesitate to contact me.
Multi Objective Directed Bee Colony Optimization for Economic Load Dispatch W...IJECEIAES
Earlier economic emission dispatch methods for optimizing emission level comprising carbon monoxide, nitrous oxide and sulpher dioxide in thermal generation, made use of soft computing techniques like fuzzy,neural network,evolutionary programming,differential evolution and particle swarm optimization etc..The above methods incurred comparatively more transmission loss.So looking into the nonlinear load behavior of unbalanced systems following differential load pattern prevalent in tropical countries like India,Pakistan and Bangladesh etc.,the erratic variation of enhanced power demand is of immense importance which is included in this paper vide multi objective directed bee colony optimization with enhanced power demand to optimize transmission losses to a desired level.In the current dissertation making use of multi objective directed bee colony optimization with enhanced power demand technique the emission level versus cost of generation has been displayed vide figure-3 & figure-4 and this result has been compared with other dispatch methods using valve point loading(VPL) and multi objective directed bee colony optimization with & without transmission loss.
HYDROTHERMAL COORDINATION FOR SHORT RANGE FIXED HEAD STATIONS USING FAST GENE...ecij
This paper presents a Fast genetic algorithm for solving Hydrothermal coordination (HTC) problem.
Genetic Algorithms (GAs) perform powerful global searches, but their long computation times, put a
limitation when solving large scale optimization problems. The present paper describes a Fast GA (FGA)
to overcome this limitation, by starting with random solutions within the search space and narrowing
down the search space by considering the minimum and maximum errors of the population members.
Since the search space is restricted to a small region within the available search space the algorithm
works very fast. This algorithm reduces the computational burden and number of generations to
converge. The proposed algorithm has been demonstrated for HTC of various combinations of Hydro
thermal systems. In all the cases Fast GA shows reliable convergence. The final results obtained using
Fast GA are compared with simple (conventional) GA and found to be encouraging.
Evaluation of Morphometric Parameters Derived from CartoDEM and Aster GDEM wi...Dr Ramesh Dikpal
From three different sources viz. survey of India topographic map (1:50,000), CartoDEM (10 mts) and Aster GDEM (30 mts) morphometric parameters are derived and evaluated. Manually digitized the drainage network from toposheets and extracted drainage network system from CartoDEM and Aster GDEM using ArcGIS 10.2 software. Basic, derived and shape parameters are considered for basin analysis. The mean bifurcation ratio of the given basin for CartoDEM & Aster GDEM are having nearby values and also indicates some sort of geological control, high stream frequency (Fs) is indicative of high relief and low infiltration capacity of the bedrock pointing towards the increase in stream population with respect to increase in drainage density, low drainage density (Dd) leads to coarse drainage texture, value of Lg for topographic, CartoDEM and Aster GDEM data indicating very fine texture & fine texture respectively. From the shape parameters the Kumudvathi watershed indicates it is sub-circular and elongated. The results from the high resolution data will have the nearby values and less of % variation, whereas in low resolution data % of variation is more and will not meet criteria.
Cost optimization of pipeline systems using genetic algorithmIAEME Publication
This document summarizes a research paper that uses a genetic algorithm to optimize the cost of irrigation pipeline networks. The paper aims to find the lowest cost pipe diameter configuration that meets hydraulic constraints like head requirements. It first describes using a genetic algorithm to represent different pipe diameter combinations as chromosomes. It then calculates the cost of initial random configurations and checks if they meet constraints. The algorithm iteratively applies genetic operators like selection, crossover and mutation to chromosomes until optimized low-cost configurations are found that satisfy constraints like supplying required water flows and pressures.
Capacitor Placement and Reconfiguration of Distribution System with hybrid Fu...IOSR Journals
The document describes a hybrid fuzzy-opposition based differential evolution algorithm for capacitor placement and distribution system reconfiguration to minimize transmission losses and costs. The algorithm considers constraints like voltage limits and current limits while optimizing the objective function of total annual cost, which includes energy loss costs and capacitor costs. It was tested on the IEEE 33-bus distribution test system and able to reduce losses and satisfy power flow constraints.
Cost Aware Expansion Planning with Renewable DGs using Particle Swarm Optimiz...IJERA Editor
This Paper is an attempt to develop the expansion-planning algorithm using meta heuristics algorithms. Expansion Planning is always needed as the power demand is increasing every now and then. Thus for a better expansion planning the meta heuristic methods are needed. The cost efficient Expansion planning is desired in the proposed work. Recently distributed generation is widely researched to implement in future energy needs as it is pollution free and capability of installing it in rural places. In this paper, optimal distributed generation expansion planning with Particle Swarm Optimization (PSO) and Cuckoo Search Algorithm (CSA) for identifying the location, size and type of distributed generator for future demand is predicted with lowest cost as the constraints. Here the objective function is to minimize the total cost including installation and operating cost of the renewable DGs. MATLAB based `simulation using M-file program is used for the implementation and Indian distribution system is used for testing the results.
Optimizing location and size of capacitors for power loss reduction in radial...TELKOMNIKA JOURNAL
Power radial distribution systems are increasingly more and more important in transmitting the electric energy from power plants to customers. However, total loss in lines are very high. This issue can be solved by allocating capacitor banks. Determining the suitable allocation and optimal sizing of capacitor banks needs an efficient approach. In this study, the diffusion and update techniques-based algorithm (DUTA) is proposed for such reason. The efficiency of DUTA is inspected on two distribution systems consisting of 15-bus and 33-bus systems with different study cases. The solutions attained by DUTA are competed with recently published methods. As a consequence, the method is more effective than the other methods in terms of the quality of solution.
This is a resume of my master’s degree thesis where I made a Na-tech which one of the purposes was found the best technique to use in the new generation hydrogen pipelines to face an earthquake.
For further information and contributions don’t hesitate to contact me.
Multi Objective Directed Bee Colony Optimization for Economic Load Dispatch W...IJECEIAES
Earlier economic emission dispatch methods for optimizing emission level comprising carbon monoxide, nitrous oxide and sulpher dioxide in thermal generation, made use of soft computing techniques like fuzzy,neural network,evolutionary programming,differential evolution and particle swarm optimization etc..The above methods incurred comparatively more transmission loss.So looking into the nonlinear load behavior of unbalanced systems following differential load pattern prevalent in tropical countries like India,Pakistan and Bangladesh etc.,the erratic variation of enhanced power demand is of immense importance which is included in this paper vide multi objective directed bee colony optimization with enhanced power demand to optimize transmission losses to a desired level.In the current dissertation making use of multi objective directed bee colony optimization with enhanced power demand technique the emission level versus cost of generation has been displayed vide figure-3 & figure-4 and this result has been compared with other dispatch methods using valve point loading(VPL) and multi objective directed bee colony optimization with & without transmission loss.
HYDROTHERMAL COORDINATION FOR SHORT RANGE FIXED HEAD STATIONS USING FAST GENE...ecij
This paper presents a Fast genetic algorithm for solving Hydrothermal coordination (HTC) problem.
Genetic Algorithms (GAs) perform powerful global searches, but their long computation times, put a
limitation when solving large scale optimization problems. The present paper describes a Fast GA (FGA)
to overcome this limitation, by starting with random solutions within the search space and narrowing
down the search space by considering the minimum and maximum errors of the population members.
Since the search space is restricted to a small region within the available search space the algorithm
works very fast. This algorithm reduces the computational burden and number of generations to
converge. The proposed algorithm has been demonstrated for HTC of various combinations of Hydro
thermal systems. In all the cases Fast GA shows reliable convergence. The final results obtained using
Fast GA are compared with simple (conventional) GA and found to be encouraging.
Evaluation of Morphometric Parameters Derived from CartoDEM and Aster GDEM wi...Dr Ramesh Dikpal
From three different sources viz. survey of India topographic map (1:50,000), CartoDEM (10 mts) and Aster GDEM (30 mts) morphometric parameters are derived and evaluated. Manually digitized the drainage network from toposheets and extracted drainage network system from CartoDEM and Aster GDEM using ArcGIS 10.2 software. Basic, derived and shape parameters are considered for basin analysis. The mean bifurcation ratio of the given basin for CartoDEM & Aster GDEM are having nearby values and also indicates some sort of geological control, high stream frequency (Fs) is indicative of high relief and low infiltration capacity of the bedrock pointing towards the increase in stream population with respect to increase in drainage density, low drainage density (Dd) leads to coarse drainage texture, value of Lg for topographic, CartoDEM and Aster GDEM data indicating very fine texture & fine texture respectively. From the shape parameters the Kumudvathi watershed indicates it is sub-circular and elongated. The results from the high resolution data will have the nearby values and less of % variation, whereas in low resolution data % of variation is more and will not meet criteria.
This document presents a data-driven approach to establish relationships between the microstructure and hydraulic conductivity of packed soil particles. Soil particle packings were generated numerically and their microstructures characterized using 2-point statistics. Hydraulic conductivity was estimated using finite volume simulations. Principal component analysis was used to reduce the microstructural data, and regression analysis was employed to correlate hydraulic conductivity with the principal components, establishing a structure-property relationship. Leave-one-out cross validation was used to assess the regression models.
CFD investigation of coal gasification: Effect of particle sizeIRJET Journal
This document presents a computational fluid dynamics (CFD) investigation of the effect of coal particle size on coal gasification in a fluidized bed. The CFD model uses Eulerian-Eulerian two-fluid modeling approach with kinetic theory of granular flow to simulate gas-solid flow behavior. Simulations were performed with two particle sizes - 0.00062 m and 0.001 m - at fluidization velocities ranging from 0.16 to 1 m/s. The results show that smaller particle size leads to better solid distribution, easier generation of bubbles, and faster fluidization. At high velocities, particle size has little effect other than on bed height expansion. The study provides insights into how particle size impacts hydrodynamics in fluid
Optimization techniques for water supply network a critical reviewIAEME Publication
This document provides a critical review of optimization techniques that have been used for water supply network design. It discusses various methods that have been developed over the past few decades to analyze and optimize pipe networks, including Newton Raphson, linear theory, genetic algorithms, particle swarm optimization, and ant colony optimization. The review examines literature on applying these techniques to optimize network design factors like cost, reliability, and water quality. Overall, the document surveys extensive research on using mathematical and computational optimization methods to develop more efficient and cost-effective water distribution systems.
A MULTIPURPOSE MATRICES METHODOLOGY FOR TRANSMISSION USAGE, LOSS AND RELIABIL...ecij
In the era of power system restructuring there is a need of simplified method which provides a complete allocation of usage, transmission losses and transmission reliability margin. In this paper, authors presents a combined multipurpose matrices methodology for Transmission usage, transmission loss and transmission reliability margin allocation. Proposed methodology is simple and easy to implement on large power system. A modified Kirchhoff matrix is used for allocation purpose. A sample 6 bus system is used to demonstrate the feasibility of proposed methodology.
Cost Optimal Design of a Single-Phase Dry Power Transformerijeei-iaes
The Dry type transformers are preferred to their oil-immersed counterparts for various reasons, particularly because their operation is hazardless. The application of dry transformers was limited to small ratings in the earlier days. But now these are being used for considerably higher ratings. Therefore, their cost-optimal design has gained importance. This paper deals with the design procedure for achieving cost optimal design of a dry type single-phase power transformer of small rating, subject to usual design constraints on efficiency and voltage regulation. The selling cost for the transformer has been taken as the objective function. Only two key variables have been chosen, the turns/volt and the height: width ratio of window, which affects the cost function to high degrees. Other variables have been chosen on the basis of designers’ experience. Copper has been used as conductor material and CRGOS as core material to achieve higher efficiency, lower running cost and compact design. The electrical and magnetic loadings have been kept at their maximum values without violating the design constraints. The optimal solution has been obtained by the method of exhaustive search using nested loops.
E NERGY D EGREE D ISTANCE C LUSTERING A LGORITHM FOR W Snsijwmn
This document summarizes a new Energy-Degree Distance (EDD) Clustering Algorithm for wireless sensor networks. The algorithm aims to minimize energy consumption and balance energy usage among nodes. Key aspects of the EDD algorithm include electing cluster heads based on a node's remaining energy, degree, and distance to the base station. Simulation results show the EDD algorithm outperforms the LEACH algorithm in terms of network lifetime and energy efficiency. Both dynamic and static clustering methods are evaluated, with dynamic clustering showing better performance overall.
A tool was developed for optimizing 3D marine structures subjected to fluid forces and stresses. It was used to optimize a NACA 0009 hydrofoil, leading to a 12.4% efficiency increase, 7.3% weight reduction, and 45% higher cavitation inception speed, while satisfying stress and cavitation constraints. The tool can optimize complex marine propellers and turbines to reduce fuel use and emissions in maritime transport, responsible for 90% of world trade.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
This 3 sentence summary provides the high level and essential information from the document:
The document discusses optimal assembly plans and control policies for networks of parallel queues with finite buffer sizes. It presents a cost model that considers both the quality of service cost and server holding cost. The problem is formulated as determining the number of processors for each queue and a routing policy to minimize the total cost, with the goal of maximizing the probability that all queues have a certain minimum number of occupied processors.
An Effectively Modified Firefly Algorithm for Economic Load Dispatch ProblemTELKOMNIKA JOURNAL
This paper proposes an effectively modified firefly algorithm (EMFA) for searching optimal solution of economic load dispatch (ELD) problem. The proposed method is developed by improving the procedure of new solution generation of conventional firefly algorithm (FA). The performance of EMFA is compared to FA variants and other existing methods by testing on four different systems with different types of objective function and constraints. The comparison indicates that the proposed method can reach better optimal solutions than other FA variants and most other existing methods with lower population and lower maximum iteration. As a result, it can lead to a conclusion that the proposed method is potential for ELD problem.
Electric potential energy fractal dimension for characterizing permo carbonif...Khalid Al-Khidir
1) The document analyzes fractal dimensions calculated from electric potential energy and capillary pressure measurements on sandstone samples from the Permo-Carboniferous Shajara Formation in order to characterize heterogeneity.
2) Equations relating water saturation, electric potential energy, and fractal dimension were derived and used to calculate electric potential energy fractal dimensions from logarithmic plots.
3) Capillary pressure fractal dimensions were also calculated from logarithmic plots and found to be similar to the electric potential energy fractal dimensions.
4) Fractal dimensions generally increased with increasing permeability and grain size, indicating more interconnected pore spaces in less compacted samples.
Laboratory Assessment of Energy Efficiency in Vibraotry Compaction of Granula...Garrett Osborne
This document describes a laboratory test method for assessing the energy efficiency of vibratory compaction of granular materials. The method tracks material density and energy consumption during compaction using a vibratory hammer. Density-energy curves are produced to evaluate both the maximum achievable density and the compactibility, or rate of density increase with energy. Testing of a granular concrete mix found that higher compactibility leads to more energy-efficient compaction by reaching the target density with less total energy. This approach can guide selection of optimal compaction variables like frequency to improve sustainability of earthworks construction.
MINIATURIZATION OF BRANCH-LINE COUPLERS USING OPEN STUBS AND STEPPED IMPEDANC...csijjournal
The document summarizes two proposed structures for compact branch-line couplers (BLCs) using miniaturization techniques. The first structure uses open stubs and meandering transmission lines, reducing the area to 61.8% of a conventional design. The second uses open stub and stepped impedance unit cells, reducing the area to 50.8%. Simulation results show the first structure achieves return losses and isolation of -27.8 dB and -27.9 dB respectively with a 312 MHz bandwidth. The second structure achieves comparable performance to previously published measured results. Both miniaturized designs achieve good size reduction while maintaining BLC performance compared to a conventional design.
Multi Area Economic Dispatch Using Secant Method and Tie Line MatrixIJAPEJOURNAL
In this paper, Secant method and tie line matrix are proposed to solve multi area economic dispatch (MAED) problem with tie line loss. Generator limits of all generators in each area are calculated at given area power demands plus export (or import) using secant method and the generator limits of all generators are modified as modified generator limits. Central economic dispatch (CED) problem is used to determine the output powers of all generators and finally power flows in all tie lines are determined from tie line matrix. Here, Secant method is applied to solve the CED problem. A modified tie line matrix is used to find power flow in each tie line and then tie line loss is calculated from the power flow in each tie line. The proposed approach has been tested on two-area (two generators in each area) system and four-area (four generators in each area) system. It is observed from various cases that the proposed approach provides optimally best solution in terms of cost with tie line loss with less computational burden.
- The document proposes grey-box models that combine physics-based Morison's equation and data-based Gaussian process models to improve prediction of wave loading on offshore structures.
- Morison's equation is used as the physics component to predict wave loading from assumed wave particle velocities and accelerations. Gaussian process NARX models are used as the data-based components.
- Two approaches are presented for combining the white-box and black-box components: 1) simple summation, and 2) using the white-box prediction as additional input to the black-box. The best approach was found to be a residual modelling GP-NARX.
Capacitor Placement Using Bat Algorithm for Maximum Annual Savings in Radial ...IJERA Editor
This paper presents a two stage approach that determines the optimal location and size of capacitors on radial distribution systems to improve voltage profile and to reduce the active power loss. In first stage, the capacitor locations can be found by using loss sensitivity method. Bat algorithm is used for finding the optimal capacitor sizes in radial distribution systems. The sizes of the capacitors corresponding to maximum annual savings are determined by considering the cost of the capacitors. The proposed method is tested on 15-bus, 33 bus, 34-bus, 69-bus and 85-bus test systems and the results are presented.
Determining optimal location and size of capacitors in radial distribution ne...IJECEIAES
In this study, the problem of optimal capacitor location and size determination (OCLSD) in radial distribution networks for reducing losses is unraveled by moth swarm algorithm (MSA). MSA is one of the most powerful meta-heuristic algorithm that is taken from the inspiration of the food source finding behavior of moths. Four study cases of installing different numbers of capacitors in the 15-bus radial distribution test system including two, three, four and five capacitors areemployed to run the applied MSA for an investigation of behavior and assessment of performances. Power loss and the improvement of voltage profile obtained by MSA are compared with those fromother methods. As a result, it can be concluded that MSA can give a good truthful and effective solution method for OCLSD problem.
techTransmission usage and cost allocation using shapley value and tracing me...elelijjournal
In the deregulated power system, transmission pricing has become a very important task because it is necessary to develop an efficient, feasible and reliable pricing scheme that can generate the useful economic signals to network users such as generating companies, transmission companies, distribution companies and customers. The objective of this paper is to compare transmission usage and cost allocation scheme to loads (and/or generators) based on Shapley value method and power flow tracing method.Modified Kirchhoff matrix is used for power flow tracing. A comparison is done between the both methods.
A case study based on sample 6 bus power system is applied to check the feasibility and reliability of the proposed usage and cost allocation methodology.
Effect of inertia weight functions of pso in optimization of water distributi...IAEME Publication
The document summarizes research that optimized a water distribution network using Particle Swarm Optimization (PSO) with different inertia weight functions. Eight inertia weight functions were tested to study their effect on network cost. The minimum cost solution of Rs. 419,000 was obtained using a logarithmic inertia weight function with a swarm size of 50 over 15 runs. Results closely matched those from a previous study that optimized the same benchmark network, validating the developed PSO program.
Effect of inertia weight functions of pso in optimization of water distributi...IAEME Publication
Water distribution in adequate quantity at required pressure is the prime requirement of design of network. It is found from the literature, that stochastic methods gives better results in optimizing the water distribution network (WDN) than deterministic methods. The optimize solution obtained from any stochastic method depends on the parameter values associated with that method. In the present work a program is developed in MATLAB environment to optimize the water distribution system using Particle Swarm Optimization (PSO) tech nique. The analysis is carried out using finite element method. The validity of developed program i s demonstrated by comparing results with a benchmark water distribution network. Different values of inertia weight function in Partial swarm optimization has been used to study the effect of t his variant on the cost of water distribution network.
Effect of inertia weight functions of pso in optimization of water distributi...IAEME Publication
The document summarizes research that optimized a water distribution network using Particle Swarm Optimization (PSO) with different inertia weight functions. Eight inertia weight functions were tested to study their effect on network cost. The minimum cost solution of Rs 419,000 was obtained using a logarithmic inertia weight function with a swarm size of 50 over 15 runs. Results closely matched those from a previous study that optimized the same benchmark network, validating the developed PSO program.
Optimizing pumping rate in pipe networks supplied by groundwater sourcesMedhat Elzahar
This document presents an analytical solution for determining the optimal pumping rate in pipe networks supplied by groundwater wells. The solution is based on maximizing economic benefit from the produced water. It utilizes a case study of a pipe network supplied by two wells connected to an elevated tank and distribution pipes. Cost functions are developed that consider pipe network costs, pumping and pump costs, well and tank costs, and operation and maintenance costs. An optimization technique called the gradient method is applied to these cost functions to derive an analytical solution for optimal pumping rate. The solution is verified against graphical solutions and prior studies on the example pipe network, demonstrating the reliability of the analytical approach.
A suggestion of optimization process for water pipe networks designMedhat Elzahar
This document proposes a process for optimizing the design of water pipe networks. It suggests including all cost parameters, such as pipe, pump, and energy costs, in the optimization process to determine the most cost-effective pipe diameters. The study compares results from a genetic algorithm software (GANEO) that optimizes based on pipe costs only, to a derivative method that considers total costs. While GANEO found smaller pipe diameters with minor pipe cost savings, the total costs were much higher due to increased pumping requirements. Excluding pump costs from the optimization process slightly reduced pipe diameters and costs. However, the best approach is to include all relevant cost parameters to obtain the most reliable cost-optimized solution.
This document presents a data-driven approach to establish relationships between the microstructure and hydraulic conductivity of packed soil particles. Soil particle packings were generated numerically and their microstructures characterized using 2-point statistics. Hydraulic conductivity was estimated using finite volume simulations. Principal component analysis was used to reduce the microstructural data, and regression analysis was employed to correlate hydraulic conductivity with the principal components, establishing a structure-property relationship. Leave-one-out cross validation was used to assess the regression models.
CFD investigation of coal gasification: Effect of particle sizeIRJET Journal
This document presents a computational fluid dynamics (CFD) investigation of the effect of coal particle size on coal gasification in a fluidized bed. The CFD model uses Eulerian-Eulerian two-fluid modeling approach with kinetic theory of granular flow to simulate gas-solid flow behavior. Simulations were performed with two particle sizes - 0.00062 m and 0.001 m - at fluidization velocities ranging from 0.16 to 1 m/s. The results show that smaller particle size leads to better solid distribution, easier generation of bubbles, and faster fluidization. At high velocities, particle size has little effect other than on bed height expansion. The study provides insights into how particle size impacts hydrodynamics in fluid
Optimization techniques for water supply network a critical reviewIAEME Publication
This document provides a critical review of optimization techniques that have been used for water supply network design. It discusses various methods that have been developed over the past few decades to analyze and optimize pipe networks, including Newton Raphson, linear theory, genetic algorithms, particle swarm optimization, and ant colony optimization. The review examines literature on applying these techniques to optimize network design factors like cost, reliability, and water quality. Overall, the document surveys extensive research on using mathematical and computational optimization methods to develop more efficient and cost-effective water distribution systems.
A MULTIPURPOSE MATRICES METHODOLOGY FOR TRANSMISSION USAGE, LOSS AND RELIABIL...ecij
In the era of power system restructuring there is a need of simplified method which provides a complete allocation of usage, transmission losses and transmission reliability margin. In this paper, authors presents a combined multipurpose matrices methodology for Transmission usage, transmission loss and transmission reliability margin allocation. Proposed methodology is simple and easy to implement on large power system. A modified Kirchhoff matrix is used for allocation purpose. A sample 6 bus system is used to demonstrate the feasibility of proposed methodology.
Cost Optimal Design of a Single-Phase Dry Power Transformerijeei-iaes
The Dry type transformers are preferred to their oil-immersed counterparts for various reasons, particularly because their operation is hazardless. The application of dry transformers was limited to small ratings in the earlier days. But now these are being used for considerably higher ratings. Therefore, their cost-optimal design has gained importance. This paper deals with the design procedure for achieving cost optimal design of a dry type single-phase power transformer of small rating, subject to usual design constraints on efficiency and voltage regulation. The selling cost for the transformer has been taken as the objective function. Only two key variables have been chosen, the turns/volt and the height: width ratio of window, which affects the cost function to high degrees. Other variables have been chosen on the basis of designers’ experience. Copper has been used as conductor material and CRGOS as core material to achieve higher efficiency, lower running cost and compact design. The electrical and magnetic loadings have been kept at their maximum values without violating the design constraints. The optimal solution has been obtained by the method of exhaustive search using nested loops.
E NERGY D EGREE D ISTANCE C LUSTERING A LGORITHM FOR W Snsijwmn
This document summarizes a new Energy-Degree Distance (EDD) Clustering Algorithm for wireless sensor networks. The algorithm aims to minimize energy consumption and balance energy usage among nodes. Key aspects of the EDD algorithm include electing cluster heads based on a node's remaining energy, degree, and distance to the base station. Simulation results show the EDD algorithm outperforms the LEACH algorithm in terms of network lifetime and energy efficiency. Both dynamic and static clustering methods are evaluated, with dynamic clustering showing better performance overall.
A tool was developed for optimizing 3D marine structures subjected to fluid forces and stresses. It was used to optimize a NACA 0009 hydrofoil, leading to a 12.4% efficiency increase, 7.3% weight reduction, and 45% higher cavitation inception speed, while satisfying stress and cavitation constraints. The tool can optimize complex marine propellers and turbines to reduce fuel use and emissions in maritime transport, responsible for 90% of world trade.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
This 3 sentence summary provides the high level and essential information from the document:
The document discusses optimal assembly plans and control policies for networks of parallel queues with finite buffer sizes. It presents a cost model that considers both the quality of service cost and server holding cost. The problem is formulated as determining the number of processors for each queue and a routing policy to minimize the total cost, with the goal of maximizing the probability that all queues have a certain minimum number of occupied processors.
An Effectively Modified Firefly Algorithm for Economic Load Dispatch ProblemTELKOMNIKA JOURNAL
This paper proposes an effectively modified firefly algorithm (EMFA) for searching optimal solution of economic load dispatch (ELD) problem. The proposed method is developed by improving the procedure of new solution generation of conventional firefly algorithm (FA). The performance of EMFA is compared to FA variants and other existing methods by testing on four different systems with different types of objective function and constraints. The comparison indicates that the proposed method can reach better optimal solutions than other FA variants and most other existing methods with lower population and lower maximum iteration. As a result, it can lead to a conclusion that the proposed method is potential for ELD problem.
Electric potential energy fractal dimension for characterizing permo carbonif...Khalid Al-Khidir
1) The document analyzes fractal dimensions calculated from electric potential energy and capillary pressure measurements on sandstone samples from the Permo-Carboniferous Shajara Formation in order to characterize heterogeneity.
2) Equations relating water saturation, electric potential energy, and fractal dimension were derived and used to calculate electric potential energy fractal dimensions from logarithmic plots.
3) Capillary pressure fractal dimensions were also calculated from logarithmic plots and found to be similar to the electric potential energy fractal dimensions.
4) Fractal dimensions generally increased with increasing permeability and grain size, indicating more interconnected pore spaces in less compacted samples.
Laboratory Assessment of Energy Efficiency in Vibraotry Compaction of Granula...Garrett Osborne
This document describes a laboratory test method for assessing the energy efficiency of vibratory compaction of granular materials. The method tracks material density and energy consumption during compaction using a vibratory hammer. Density-energy curves are produced to evaluate both the maximum achievable density and the compactibility, or rate of density increase with energy. Testing of a granular concrete mix found that higher compactibility leads to more energy-efficient compaction by reaching the target density with less total energy. This approach can guide selection of optimal compaction variables like frequency to improve sustainability of earthworks construction.
MINIATURIZATION OF BRANCH-LINE COUPLERS USING OPEN STUBS AND STEPPED IMPEDANC...csijjournal
The document summarizes two proposed structures for compact branch-line couplers (BLCs) using miniaturization techniques. The first structure uses open stubs and meandering transmission lines, reducing the area to 61.8% of a conventional design. The second uses open stub and stepped impedance unit cells, reducing the area to 50.8%. Simulation results show the first structure achieves return losses and isolation of -27.8 dB and -27.9 dB respectively with a 312 MHz bandwidth. The second structure achieves comparable performance to previously published measured results. Both miniaturized designs achieve good size reduction while maintaining BLC performance compared to a conventional design.
Multi Area Economic Dispatch Using Secant Method and Tie Line MatrixIJAPEJOURNAL
In this paper, Secant method and tie line matrix are proposed to solve multi area economic dispatch (MAED) problem with tie line loss. Generator limits of all generators in each area are calculated at given area power demands plus export (or import) using secant method and the generator limits of all generators are modified as modified generator limits. Central economic dispatch (CED) problem is used to determine the output powers of all generators and finally power flows in all tie lines are determined from tie line matrix. Here, Secant method is applied to solve the CED problem. A modified tie line matrix is used to find power flow in each tie line and then tie line loss is calculated from the power flow in each tie line. The proposed approach has been tested on two-area (two generators in each area) system and four-area (four generators in each area) system. It is observed from various cases that the proposed approach provides optimally best solution in terms of cost with tie line loss with less computational burden.
- The document proposes grey-box models that combine physics-based Morison's equation and data-based Gaussian process models to improve prediction of wave loading on offshore structures.
- Morison's equation is used as the physics component to predict wave loading from assumed wave particle velocities and accelerations. Gaussian process NARX models are used as the data-based components.
- Two approaches are presented for combining the white-box and black-box components: 1) simple summation, and 2) using the white-box prediction as additional input to the black-box. The best approach was found to be a residual modelling GP-NARX.
Capacitor Placement Using Bat Algorithm for Maximum Annual Savings in Radial ...IJERA Editor
This paper presents a two stage approach that determines the optimal location and size of capacitors on radial distribution systems to improve voltage profile and to reduce the active power loss. In first stage, the capacitor locations can be found by using loss sensitivity method. Bat algorithm is used for finding the optimal capacitor sizes in radial distribution systems. The sizes of the capacitors corresponding to maximum annual savings are determined by considering the cost of the capacitors. The proposed method is tested on 15-bus, 33 bus, 34-bus, 69-bus and 85-bus test systems and the results are presented.
Determining optimal location and size of capacitors in radial distribution ne...IJECEIAES
In this study, the problem of optimal capacitor location and size determination (OCLSD) in radial distribution networks for reducing losses is unraveled by moth swarm algorithm (MSA). MSA is one of the most powerful meta-heuristic algorithm that is taken from the inspiration of the food source finding behavior of moths. Four study cases of installing different numbers of capacitors in the 15-bus radial distribution test system including two, three, four and five capacitors areemployed to run the applied MSA for an investigation of behavior and assessment of performances. Power loss and the improvement of voltage profile obtained by MSA are compared with those fromother methods. As a result, it can be concluded that MSA can give a good truthful and effective solution method for OCLSD problem.
techTransmission usage and cost allocation using shapley value and tracing me...elelijjournal
In the deregulated power system, transmission pricing has become a very important task because it is necessary to develop an efficient, feasible and reliable pricing scheme that can generate the useful economic signals to network users such as generating companies, transmission companies, distribution companies and customers. The objective of this paper is to compare transmission usage and cost allocation scheme to loads (and/or generators) based on Shapley value method and power flow tracing method.Modified Kirchhoff matrix is used for power flow tracing. A comparison is done between the both methods.
A case study based on sample 6 bus power system is applied to check the feasibility and reliability of the proposed usage and cost allocation methodology.
Effect of inertia weight functions of pso in optimization of water distributi...IAEME Publication
The document summarizes research that optimized a water distribution network using Particle Swarm Optimization (PSO) with different inertia weight functions. Eight inertia weight functions were tested to study their effect on network cost. The minimum cost solution of Rs. 419,000 was obtained using a logarithmic inertia weight function with a swarm size of 50 over 15 runs. Results closely matched those from a previous study that optimized the same benchmark network, validating the developed PSO program.
Effect of inertia weight functions of pso in optimization of water distributi...IAEME Publication
Water distribution in adequate quantity at required pressure is the prime requirement of design of network. It is found from the literature, that stochastic methods gives better results in optimizing the water distribution network (WDN) than deterministic methods. The optimize solution obtained from any stochastic method depends on the parameter values associated with that method. In the present work a program is developed in MATLAB environment to optimize the water distribution system using Particle Swarm Optimization (PSO) tech nique. The analysis is carried out using finite element method. The validity of developed program i s demonstrated by comparing results with a benchmark water distribution network. Different values of inertia weight function in Partial swarm optimization has been used to study the effect of t his variant on the cost of water distribution network.
Effect of inertia weight functions of pso in optimization of water distributi...IAEME Publication
The document summarizes research that optimized a water distribution network using Particle Swarm Optimization (PSO) with different inertia weight functions. Eight inertia weight functions were tested to study their effect on network cost. The minimum cost solution of Rs 419,000 was obtained using a logarithmic inertia weight function with a swarm size of 50 over 15 runs. Results closely matched those from a previous study that optimized the same benchmark network, validating the developed PSO program.
Optimizing pumping rate in pipe networks supplied by groundwater sourcesMedhat Elzahar
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A suggestion of optimization process for water pipe networks designMedhat Elzahar
This document proposes a process for optimizing the design of water pipe networks. It suggests including all cost parameters, such as pipe, pump, and energy costs, in the optimization process to determine the most cost-effective pipe diameters. The study compares results from a genetic algorithm software (GANEO) that optimizes based on pipe costs only, to a derivative method that considers total costs. While GANEO found smaller pipe diameters with minor pipe cost savings, the total costs were much higher due to increased pumping requirements. Excluding pump costs from the optimization process slightly reduced pipe diameters and costs. However, the best approach is to include all relevant cost parameters to obtain the most reliable cost-optimized solution.
EFFECT OF DIMPLES ON FLOW PERFORMANCE OF ENHANCED SURFACE TUBESIRJET Journal
The document presents a numerical study investigating the effects of dimples on the heat transfer and flow characteristics inside a tube. Computational fluid dynamics simulations are performed for smooth tubes and tubes with inward- and outward-facing dimples at Reynolds numbers of 2500, 5000, and 7500. The simulations analyze the velocity streamlines, temperature distributions, and heat transfer coefficients. Preliminary results show that maximum velocity occurs in the center of all tube types, while temperature is highest near the walls. Tubes with dimples demonstrate enhanced heat transfer compared to smooth tubes. Further analysis of heat transfer and pressure drop characteristics is needed to assess the influence of dimples.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
The document describes using a non-linear programming model to optimize the design of a water distribution network in Mumbai, India. A traditional branch software method was first used to design the network. Then, a non-linear programming model was formulated in MS Excel to minimize total pipe costs while ensuring minimum pressure requirements are met at each node. The optimized design reduced total pipe costs by 5.08% compared to the original design. The non-linear programming model provides a simpler optimization approach than other complex algorithms that require more technical knowledge.
Optimal design of storm sewer networksBhanu Pratap
This document provides a review of past, present and future approaches to optimal design of storm sewer networks. It discusses how optimization techniques have been used since the 1960s to minimize construction costs while ensuring system performance, moving from linear programming and non-linear programming to more advanced techniques like dynamic programming and discrete differential dynamic programming. The document also outlines key advantages of optimal design over traditional design methods.
This academic article discusses numerical flow simulation of an elbow draft tube using STAR-CCM+ software. It summarizes the steps taken which include geometric modeling of the draft tube, mesh generation, specification of parameters like material properties and boundary conditions, and setting up the implicit unsteady simulation. Results of the simulation like pressure and velocity variations along the draft tube over different time steps are presented. Key findings are that pressure and velocity distributions are affected by time step size, with smaller time steps showing more uniform distributions. Performance metrics like head recovery and efficiency of the draft tube are computed and seen to decrease initially with time step before leveling off.
The document summarizes research applying genetic algorithms to optimize the design of large water distribution networks. It describes using a genetic algorithm to minimize the total cost of a real network in Suez City, Egypt with 341 nodes and 389 pipes. The genetic algorithm optimizes pipe diameters to meet hydraulic constraints like minimum pressure levels at nodes. It presents the formulation of the optimization problem and genetic algorithm approach. The case study applies the method to the Suez City network, demonstrating the approach's ability to solve large-scale, real-world optimization problems.
IRJET- An Investigation of Axial Hydrofoil Tidal TurbineIRJET Journal
This document summarizes an investigation into the performance of an axial tidal turbine. Initial experimental tests on a turbine model with helical blades showed that the turbine did not rotate properly due to issues with blade orientation and shape. Computational fluid dynamics (CFD) simulations were then conducted to analyze different blade profiles. CFD simulations of airfoils NACA 0018 and NACA 0024 were performed and lift and drag coefficients were calculated and compared to experimental data to validate the CFD approach. The simulations showed that blade profile and operating parameters like solidity and tip speed ratio can impact turbine performance. Further CFD analysis of different profiles and parameters will help optimize tidal turbine design.
Optimization of Closure Law of Guide Vanes for an Operational Hydropower Plan...Dr. Amarjeet Singh
This paper addresses the optimization of twostage closure law of guide vanes in an operational
hydropower plant of Nepal. The mathematical model
has been established in commercial software Bentley
Hammer, whose correctness has been validated by
comparing the results with the data of experimental
load rejection test. The validated mathematical model
has been employed to find the parameters of optimum
closure pattern, which minimizes the non-linear
objective function of maximum water pressure and
maximum rotational speed of turbine.
Cost Optimization of Elevated Circular Water Storage Tanktheijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Cost Optimization of Elevated Circular Water Storage Tanktheijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
This document summarizes a numerical study of microchannels with internal fins for cooling electronic equipment. Three types of microchannels were studied: square channels with conventional and cross fins, and rectangular channels with conventional fins. Constant heat flux boundary conditions and laminar flow were assumed. Results for average local Nusselt number distribution along the channel length were obtained as a function of fin height ratio. An optimum fin height ratio that maximized heat transfer was found for each microchannel type. Grid independence testing was performed to select the appropriate mesh for the numerical simulations.
Distribution network reconfiguration for loss reduction using PSO method IJECEIAES
In recent years, the reconfiguration of the distribution network has been proclaimed as a method for realizing power savings, with virtually zero cost. The current trend is to design distribution networks with a mesh network structure, but to operate them radially. This is achieved by the establishment of an appropriate number of switchable branches which allow the realization of a radial configuration capable of supplying all of the normal defects in the box of permanent defect. The purpose of this article is to find an optimal reconfiguration using a Meta heuristic method, namely the particle swarm optimization method (PSO), to reduce active losses and voltage deviations by taking into account certain technical constraints. The validity of this method is tested on a 33-IEEE test network and the results obtained are compared with the results of basic load flow.
Numerical simulations have been undertaken
for the benchmark problem in a Square cavity by using
computational fluid dynamics software. This work aims at
discussing the fundamental numerical and computational
fluid dynamic aspects which can lead to the definition of
the following meshing methods and turbulence models.
The meshes used for the simulation are hexahedral,
hexahedral cell with near wall refinement, tetrahedral
grid, polyhedral, tetrahedral with near wall refinement
and polyhedral mesh with prism layer cells based the near
wall thickness of Y+ less than one. The turbulence models
used for the simulation work are AKN K-Epsilon Low-Re,
Realizable K-Epsilon, Realizable K-Epsilon Two-Layer,
standard K-Epsilon, standard K-Epsilon Low-Re,
Standard K-Epsilon Two-Layer, V2F K-Epsilon,
SST(Menter) K-Omega, and Standard(Wilcox) K-Omega.
From these meshes and turbulence models, we will
conclude the suitable mesh and turbulence for the
recirculation flow by the grid independent test. These
analytical values of results are compared with reference
data which gives an optimization of experimental work.
Unsteady simulation was ran for all the Grid Independent
mesh with the SST k omega model with the time step of
0.01 sec for 40 seconds. The flow nature is studied with
and without the temperature for Reynolds number, 1000
and 10000.
EFFECT OF DIFFUSER LENGTH ON PERFORMANCE CHARACTERISTICS OF ELBOW DRAFT TUBE ...IAEME Publication
The hydraulic turbines extract the energy of flowing water and converts into mechanical energy. The reaction turbine has components namely casing, stay ring, guide vane, runner and draft tube. Each component plays some role in performance of turbine. Out of above component casing, stay ring and distributor guide the flow while in runner and draft tube energy transfer and conversion takes place. In reaction turbine, significant part of input energy goes out of runner unutilized in form of kinetic energy. Draft tube are provided at exit of runner to connect turbine and tail race providing closed conduit flow of varying cross sectional area.
This document analyzes the effect of diffuser length on the performance of an elbow draft tube with a dividing pier using computational fluid dynamics (CFD).
The numerical simulation was performed for three diffuser lengths (L/D1=5, 10, 15) and 13 whirl velocities from -3 to 3 m/s. Pressure and velocity contours at different sections show higher pressure and lower velocity at the outer side of the elbow and dividing pier. As diffuser length increases from L/D1=5 to 15, the pressure variation decreases and becomes more uniform throughout the draft tube. The study aims to optimize diffuser length for maximum head recovery and efficiency of the draft tube.
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Multi-objective optimization of water distribution system using particle swarm optimization
1. IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE)
e-ISSN: 2278-1684,p-ISSN: 2320-334X, Volume 12, Issue 6 Ver. I (Nov. - Dec. 2015), PP 21-28
www.iosrjournals.org
DOI: 10.9790/1684-12612128 www.iosrjournals.org 21 | Page
Multi-objective optimization of water distribution system using
particle swarm optimization
Minakshi Shrivatava1
, Dr. Vishnu Prasad2
, Dr. Ruchi Khare3
1, 2, 3
(Department of Civil Engineering, M.A. National institute of technology Bhopal- 462003, India)
Abstract: The cost of water distribution system includes cost of pipes, pumping system, civil works and
pumping energy. Out of these, cost of civil works and pumping system are nearly fixed for any specific water
supply project. The cost of pipes and pumping energy are variable and can be minimized by suitable selection
of pipe size, material of pipes and staging of elevated service reservoir. In the present work, the cost of pipes
and energy have been optimized using Particle Swarm Optimization (PSO) method for a water supply system
having large pipe network. In addition to this, the effect of swarm size and different inertia weights of PSO is
also studied on the optimized cost of the system.
Key words: Water supply system, Particle swarm optimization, Inertia weight function
I. Introduction
Water is a vital commodity for all living beings on earth surface next to air [15]. Therefore water
supply systems are the most important public utility for safe supply of potable water. To supply the adequate
amount of water at desired pressure with minimum cost is a big challenge for researchers. The pipe and energy
cost involved in the water supply contribute major share of any water supply project [7]. These two cost are
variable and depend on the commercial pipe sizes, pipe material available and the staging of service reservoir.
Many investigators have worked on the minimization of pipe cost taking constant height of reservoir. In this
process, the pipes sizes selected for optimization may not be hydraulically efficient. The pipes selected may be
either oversized or undersized to give minimum cost. Various deterministic as well as stochastic methods have
been used for optimization of water distribution system [3]. Literature reveals that stochastic method are faster
and gives good results for optimizing water distribution system.[1]
Particle swarm optimization is one of the best stochastic techniques for optimizing water distribution
system as it has very simple features and has very fast rate of convergence. It is developed by James Kennedy
and Russell Eberhart in 1995[2]. The inertia weighted function ‘w’ is very important parameter in PSO [5, 6].
In the present work, height of service reservoir is also minimized along with pipe cost after putting constraints
on hydraulic gradient. It is seen that most of optimization of pipe network using PSO has been done using a
single inertia weight function. The effect of different inertia weights on network optimization has also been
presented in this paper. A computer program has been developed for the optimisation of network and analysis
has been done by finite element method. The code developed is validated with existing optimised network
given in literature with fixed tank staging and results are closely matching.
II. Problem formulation
The optimisation has been achieved by minimisation of pipe cost as well as energy cost by
minimising height of service reservoir using following two objective functions:
2.1 Minimization of pipe cost:
The commercially available ductile iron pipes are used in design of network and objective function
for minimization of pipe cost is:
mi
i
ii
DLCZMin
1
1
),( (1)
2.2 Minimization of energy cost:
The pumping energy required to lift water to service reservoir depends on height of service reservoir
for specific flow rate and annual energy cost is given by
2. Multi-objective optimization of water distribution system using particle swarm optimization
DOI: 10.9790/1684-12612128 www.iosrjournals.org 22 | Page
1000/3652 p
TEQYMinZ (2)
In this equation, the energy cost minimized by optimizing the staging of service reservoir ‘Y’.
The present worth of optimized energy cost for the design period of 20 years is computed using annuity
method as:
t
t
r
r
r
Z
Z
)1(
1)1(2
3
(3)
2.3 Constraints and bounds:
2.3.1 Constraint 1: Diameter constraint
The commercial pipe sizes are to be used in network design optimization and the diameter chosen for
design of network must be commercially available. Hence
Dj Є [Dk] (4)
where Dk is the diameter of commercial available pipe set.
2.3.2 Constraint 2: Head constraint
Head at each junction must be greater than the minimum head required at each junction.
Hk ≥ Hmin (5)
2.3.3 Constraint 3: Reservoir height
The staging of elevated reservoir must be within the minimum and maximum specified heights of
reservoir
Ymin ≤ Y ≤ Ymax (6)
III. Partical swarm optimization
Partical swarm optimization is Meta heuristic technique for optimization. It is developed by James
Kennedy and Russell Eberhart in 1995 [10]. After each iteration, the objective function is evaluated and pbest
and gbest are updated to move towards optimal solution.
In this method the initially swarm sizes are generated randomly. If the initial position of the particle is
xi(t), then after the next iteration it will move to the next position of xi(t+1). The particle moves toward the
best optimal solution using velocity update from vi(t) to vi(t+1) as in equation 7 and equation 8.[8].
vi(t+1) = w*vi(t) +C1*R1*(pbest- xi(t))+C2*R2*(gbest- xi(t)) (7)
xi(t+1) = xi(t)+ vi(t+1) (8)
Where C1 and C2 are the positive constants termed as cognitive learning rate and social learning rate
respectively and accelerate the particle towards the optimal solution. It is found from the literature that
C1=C2=2 gives the best results for optimization and same is taken for in present work. R1 and R2 are the
uniform random number ranging from 0 to 1. ‘pbest’ is the best solution obtained by the individual particle
and 'gbest' is the best value of objective function from the entire swarm size. ‘w’ is the inertia weight
function.[4] The different form of inertial weight functions used in PSO are tabulated in Table -1.
3. Multi-objective optimization of water distribution system using particle swarm optimization
DOI: 10.9790/1684-12612128 www.iosrjournals.org 23 | Page
Table 1: Different inertia weight functions of PSO [6,11]
S. No. Inertia weight function Function Equation
1 Constant inertia weight ω1=.7
2 Random inertia weight
1
(1)
.5
2
ra n d
w
3 Linear decreasing inertia weight ( w - w )
m a x m in
w = - [ ] itera tio nw m a x1 m a xitera tio n
4 Logarithmic inertia weight
1
1
.5 (1 )
1 lo g ( )
w
itera tio n
5. Natural exponent inertia weight strategy e-1
m a x
1 0
( ) . e1 m in m a x m in
ite r
ite r a tio n
w w w w
6 Natural exponent inertia weight strategy e2 2
m a x
4
( ) . e1 m i n m a x m i n
i t e r
i t e r a t i o n
w w w w
7. Simulated annealing inertia weight
1 m in m ax m in
( ) ^ ( 1)w w w w iter
Here ƛ = 0.95
8. Time varying inertia weight (m a x )
[( ) ]
1 m a x m in m inm a x
ite r a tio n ite r
w w w w
ite r a tio n
IV. Network design data
A residential colony developed in Bhopal, Madhya Pradesh, India with plot size 1000-1200 sqft. is
taken for optimization. There is 3 floor building on each plot. The demand for network has been computed for
4 people per floor. The per capita demand per day is taken 150 liters. The ductile iron pipes are to be used for
network. The layout of pipes is shown in fig.1. The complete network consists of 107 pipes and 75 nodes. The
minimum head to be maintained at each junction is 17 m. Total supply hour is taken as 6 hours and pumping is
done for 16 hours. The total length of pipes of network is 3796 m.
Fig1: Water distribution network .
4. Multi-objective optimization of water distribution system using particle swarm optimization
DOI: 10.9790/1684-12612128 www.iosrjournals.org 24 | Page
V. Computational procedure
i. Input network parameters like pipe length, junction demand and elevation, commercial pipe sizes, cost,
design period and rate of interest, unit energy cost.
ii. Choose the swarm size and generation random number for diameter of pipes between given range of
commercially available pipe diameter set.
iii. Replace the random number to nearest commercial pipe diameter by considering the permissible hydraulic
gradient.
iv. Carry out network analysis by finite element method.
v. Find out pbest, gbest and fitness cost.
vi. Update the tank height.
vii. Update diameter set.
viii. Repeat steps (iii) to (viii) till the solution converges to specified accuracy for pbest, gbest and reservoir
staging for all inertia weights of PSO and gives same optimized cost for at least 60 iterations.
The commercial ductile iron pipes used in present network optimization are 100mm, 125mm,
150mm, 200mm, 250mm, 300mm, 350mm, 400mm, 450mm, 500mm and their corresponding unit costs are
Rs.775, Rs.948, Rs.1120, Rs.1550, Rs.2100, Rs.2900, Rs.2900, Rs.3445, Rs.4015, Rs.4853, 5753[13]. The
design period, rate of interest and unit energy cost are taken as 20 years, 10 % and Rs.5 respectively.
VI. Result and discussions
The analysis has been carried out for 6 swarm size ranging from 150 to 250 at interval of 20 for 8
different inertia weight function of PSO. The optimized cost of pipes, energy and sum of these two cost as
total cost are presented in form of bar chart for different swarm size in fig.2 to fig.7.
It is observed from the minimum cost obtained with different swarm size and inertia weight functions
that the ratio of average energy cost to pipe cost is about 45:35. It indicates that energy cost minimization is
more important for economic design of pipe network however the energy cost is also dependent on the energy
charges and rate of interest and design period.
It is seen from the cost variation in fig.2 to fig.7 that minimum energy cost is nearly same and found
to be independent of weight function and swarm size. The lowest value of minimum cost achieved is Rs.45.01
lakhs for 5
swarm size and weight functions and highest value is Rs.45.31 lakhs at swam size 170 (fig.3) and constant
weight functions. The maximum difference between the optimized energy cost from different inertia weight
functions and swarm size is 8.12% at swarm size 170 while minimum difference is 0.29% at swam size 190.
The overall standard deviation is 2.93
There is large variation in the minimum pipe cost obtained from optimization for different swarm size
and weight functions. The highest value of optimized pipe cost is Rs.38.76 lakhs at 210 swarm size for
logarithmic weight function (fig.5) while lowest cost is Rs.34.10 lakhs at swarm size 170 and random weight
function (fig.3). The maximum difference between highest and lowest minimum cost is 9.21% at swarm size
210 and minimum difference is 3.82% at swarm size 230 with overall standard deviation of 2.07.
The minimum optimized total cost is again achieved at swarm size and weight functions other than
where minimum optimized pipe and energy cost is obtained. The highest value of minimum cost is Rs.83.95
lakhs for logarithmic weight function at swam size 170, while lowest value is Rs.79.85 lakhs for natural
exponent e-1 weight function at same swarm size 170 (Fig.3). The percentage variations in highest and lowest
optimized cost at different weight function and swarm size are 5.13 % and 1.49 % respectively. The standard
deviation of the percentage cost variation is 1.33.
5. Multi-objective optimization of water distribution system using particle swarm optimization
DOI: 10.9790/1684-12612128 www.iosrjournals.org 25 | Page
Fig 2: Variation of costs for different variant at swarm size 150
Fig 3: variation of costs for different variant at swarm size 170
Fig. 4: Variation of costs for different variant at swarm size 190
6. Multi-objective optimization of water distribution system using particle swarm optimization
DOI: 10.9790/1684-12612128 www.iosrjournals.org 26 | Page
Fig. 5: Variation of costs for different variant at swarm size 210
Fig. 6: Variation of costs for different variant at swarm size 230
7. Multi-objective optimization of water distribution system using particle swarm optimization
DOI: 10.9790/1684-12612128 www.iosrjournals.org 27 | Page
Fig. 7: Variation of costs for different variant at swarm size 250
Table 2: Highest and lowest values of optimised cost at different inertia weight functions
Table 3: Highest and lowest values of optimised cost at different swarm size
Swarm
size Energy cost (Rs. in Lakhs) Pipe cost (Rs. in Lakhs) Total cost(Rs. in Lakhs)
Highest Lowest Difference
(%)
Highest Lowest Difference
(%)
Highest Lowest Difference
(%)
150 45.47 45.01 1.02 37.50 35.64 5.21 82.51 80.65 2.31
170 48.99 45.31 8.12 36.88 34.10 8.15 83.95 79.85 5.13
190 45.14 45.01 0.29 37.14 35.35 5.06 82.15 80.47 2.09
210 45.36 45.01 0.78 38.76 35.49 9.21 83.77 80.85 3.61
230 45.75 45.01 1.64 36.06 34.73 3.82 81.16 79.97 1.49
250 45.62 45.01 1.36 36.83 34.95 5.37 81.94 80.17 2.21
Standard
deviation
2.93 2.07 1.33
Inertia weight
function
Energy cost (Rs. in Lakhs) Pipe cost (Rs. in Lakhs) Total cost (Rs. in Lakhs)
Highest Lowest Difference
(%)
Highest Lowest Difference
(%)
Highest Lowest Difference
(%)
Constant 45.75 45.01 1.64 37.89 34.84 8.75 83.1 80.59 3.11
Random 47.19 45.01 4.84 36.92 34.10 8.27 82.06 80.65 1.75
Linear
decreasing
45.36 45.01 0.78 35.88 34.86 2.93 80.86 80.07 0.99
Logarithmic 48.99 45.01 8.84 39.47 34.96 12.90 83.95 80.98 3.67
Natural
exponent
strategy e-1
45.47 45.01 1.02 36.28 34.71 4.52 81.84 79.98 2.33
Natural
exponent
strategy e-2
45.42 45.01 0.91 36.47 34.43 5.93 81.85 79.85 2.50
Simulated
annealing
47.56 45.01 5.67 39.77 34.53 15.18 82.49 80.58 2.37
Time varying 45.36 45.01 0.78 35.88 34.86 2.93 80.89 80.07 1.02
8. Multi-objective optimization of water distribution system using particle swarm optimization
DOI: 10.9790/1684-12612128 www.iosrjournals.org 28 | Page
VII. Conclusions
It is observed from the results of optimization of pipe network that total cost and pipe cost are
affected by both swarm size and PSO variant. The optimized lowest cost energy of is nearly independent of
swarm size and weight function. The capitalized energy cost over the design period is more than pipe cost and
affect the optimization to large extent. The minimum optimized cost of energy is Rs.45.01Lakhs at all weight
function and swarm size except swarm size 170 but optimized cost of pipe is Rs.34.10 Lakhs for swarm size
170 and random weight function . The minimum optimized total cost is Rs.79.85 Lakhs at swarm size 170 and
natural exponent strategy e-2 weight function. The for maximum difference of 9.21% between highest and
lowest optimized cost is seen for the pipe cost while the minimum difference 0.29% is there for energy cost.
The swarm size and weight function to be chosen for optimization will depend on the size of network.
Notations:
Ep - Unit energy cost (Rs.)
Hk - Head available at each junction
Hmin
-
Minimum required head at every junction
K - Total no. of junctions
hf - Head loss (m)
f - Friction factor
L - Length of the pipe (m)
V - Velocity in the pipe (m/s)
D - Diameter of the pipe (m)
r - Rate of interest
T - Design period (Years)
Y - Staging of over head tank(m)
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