This document proposes a modified lambda-iteration method for solving economic dispatch problems and minimizing fuel costs. It involves determining the optimal power output of each generator given constraints like load demand and transmission losses. The method is implemented in MATLAB and tested on a 6 generator system. Results found the total power was 1263.0074MW at an incremental cost of 13.2539$/MWh, close to those from a genetic algorithm solution. The proposed method provides a fast, easy to use approach for economic dispatch optimization problems.
This document provides an overview of optimization techniques applied to solve the unit commitment problem for a 10 unit power system. It describes the objective function and constraints of the unit commitment problem formulation. It then briefly introduces several common optimization techniques used to solve unit commitment, including simulated annealing, harmony search, and multi-agent evolutionary programming incorporating a priority list. The document presents cost comparisons of applying different optimization techniques to the standard 10 unit test system, including tabular and graphical summaries of results from research papers. It concludes with references.
Unit 5 Economic Load Dispatch and Unit CommitmentSANTOSH GADEKAR
This document provides information on economic load dispatch and unit commitment in power systems. It discusses the input-output and incremental cost characteristics of thermal and hydro power plants. It also describes the equal incremental cost method for economic load dispatch using Lagrange multipliers. A numerical example with two generating units is provided to illustrate solving for optimal dispatch considering varying load demand over different time periods.
The document discusses automatic load frequency control (ALFC) in a power system. ALFC aims to maintain system frequency by matching generator output to changing load. It does this through a feedback control loop involving the speed governor, hydraulic actuator, turbine, and generator. The speed governor senses deviations in frequency and power setting to adjust the hydraulic actuator. This controls the turbine output to balance generator power with load demand and regulate frequency. The control loop maintains small, slow load changes but not large imbalances. The document analyzes the static performance of the speed governor control loop under different network conditions.
This document presents an overview of economic load dispatch in power systems. It discusses the objectives of economic dispatch as generating required power at minimum cost. It describes different constraints like generator limits, transmission limits and voltage limits that need to be considered. It explains the operating costs of thermal plants using heat rate and fuel cost curves. It provides formulations for economic dispatch neglecting and including transmission losses. The document uses examples to illustrate the iterative method used to solve economic dispatch problems.
The document discusses unit commitment in power systems. Unit commitment involves determining which generating units to operate and when to operate them in order to meet the changing electricity demand at the lowest possible production cost while satisfying operational constraints. It describes the unit commitment problem and various constraints like minimum up/down times, ramp rates, reserve requirements, and start-up costs that make it more complex than economic dispatch. It provides a simple example to illustrate the concepts.
Analysis of Shunt APF (Active PowerFilter)Rajesh Dunna
The document analyzes a shunt active power filter based on instantaneous reactive power theory to compensate for harmonics from nonlinear loads. It describes the basic principle and control method of the shunt active power filter, including current tracking, PWM control, and harmonic compensation simulation. The results show the filter can detect harmonics well and enhance power quality by reducing total harmonic distortion below 5%.
Load / Frequency balancing Control systems studyCAL
In this project, the load and frequency control problem on the power generator at 'Britannia sugar factory' is investigated under different governor action. The existing system employs a Mechanical-hydraulic governor. It is desired to improve the system's response to load disturbances on the interconnected power grid.
This document discusses economic dispatch in power systems. It begins with an introduction that defines economic dispatch and optimal power flow problems. It then discusses various constraints in economic dispatch problems, including generator limits, transmission line limits, and reserve requirements. Different economic dispatch problems are examined, including ones that neglect transmission losses and include losses. The document also discusses unit commitment problems and provides an example of calculating the optimal dispatch to minimize total generation costs.
This document provides an overview of optimization techniques applied to solve the unit commitment problem for a 10 unit power system. It describes the objective function and constraints of the unit commitment problem formulation. It then briefly introduces several common optimization techniques used to solve unit commitment, including simulated annealing, harmony search, and multi-agent evolutionary programming incorporating a priority list. The document presents cost comparisons of applying different optimization techniques to the standard 10 unit test system, including tabular and graphical summaries of results from research papers. It concludes with references.
Unit 5 Economic Load Dispatch and Unit CommitmentSANTOSH GADEKAR
This document provides information on economic load dispatch and unit commitment in power systems. It discusses the input-output and incremental cost characteristics of thermal and hydro power plants. It also describes the equal incremental cost method for economic load dispatch using Lagrange multipliers. A numerical example with two generating units is provided to illustrate solving for optimal dispatch considering varying load demand over different time periods.
The document discusses automatic load frequency control (ALFC) in a power system. ALFC aims to maintain system frequency by matching generator output to changing load. It does this through a feedback control loop involving the speed governor, hydraulic actuator, turbine, and generator. The speed governor senses deviations in frequency and power setting to adjust the hydraulic actuator. This controls the turbine output to balance generator power with load demand and regulate frequency. The control loop maintains small, slow load changes but not large imbalances. The document analyzes the static performance of the speed governor control loop under different network conditions.
This document presents an overview of economic load dispatch in power systems. It discusses the objectives of economic dispatch as generating required power at minimum cost. It describes different constraints like generator limits, transmission limits and voltage limits that need to be considered. It explains the operating costs of thermal plants using heat rate and fuel cost curves. It provides formulations for economic dispatch neglecting and including transmission losses. The document uses examples to illustrate the iterative method used to solve economic dispatch problems.
The document discusses unit commitment in power systems. Unit commitment involves determining which generating units to operate and when to operate them in order to meet the changing electricity demand at the lowest possible production cost while satisfying operational constraints. It describes the unit commitment problem and various constraints like minimum up/down times, ramp rates, reserve requirements, and start-up costs that make it more complex than economic dispatch. It provides a simple example to illustrate the concepts.
Analysis of Shunt APF (Active PowerFilter)Rajesh Dunna
The document analyzes a shunt active power filter based on instantaneous reactive power theory to compensate for harmonics from nonlinear loads. It describes the basic principle and control method of the shunt active power filter, including current tracking, PWM control, and harmonic compensation simulation. The results show the filter can detect harmonics well and enhance power quality by reducing total harmonic distortion below 5%.
Load / Frequency balancing Control systems studyCAL
In this project, the load and frequency control problem on the power generator at 'Britannia sugar factory' is investigated under different governor action. The existing system employs a Mechanical-hydraulic governor. It is desired to improve the system's response to load disturbances on the interconnected power grid.
This document discusses economic dispatch in power systems. It begins with an introduction that defines economic dispatch and optimal power flow problems. It then discusses various constraints in economic dispatch problems, including generator limits, transmission line limits, and reserve requirements. Different economic dispatch problems are examined, including ones that neglect transmission losses and include losses. The document also discusses unit commitment problems and provides an example of calculating the optimal dispatch to minimize total generation costs.
Input output , heat rate characteristics and Incremental costEklavya Sharma
This document discusses the input-output, heat rate, and incremental cost characteristics of thermal power plants. It defines input-output characteristics as a plot of fuel input versus power output. Heat rate is the ratio of fuel input to energy output and is the slope of the input-output curve. An incremental fuel rate curve plots the incremental fuel rate, or change in input divided by change in output, versus output. The incremental cost curve multiplies incremental fuel rate by fuel cost to determine incremental cost in monetary terms per unit of output. Economic dispatch of power plants aims to minimize total incremental costs while meeting demand.
The document discusses swing equation, which is used to model rotor dynamics in power systems. It defines swing equation as a second order differential equation that relates the change in rotor angle over time to the difference between mechanical and electrical power inputs. The document outlines the derivation of swing equation from the torque-speed relationship of a synchronous generator. It also discusses swing curves, which plot electrical power output versus rotor angle, and the equal area criteria method for assessing transient stability using swing curve plots.
In microgrid, if fault occurs or any other contingency happens, then the problems would be created which are related to power flow, also there are various protection schemes are used for minimize or eliminate these problems.
Voltage control is used for reactive power balance and P-f control is used for active power control.
Various protection schemes such as, over current protection, differential protection scheme, zoning of network in adaptive protection scheme are used in microgrid system .
Fault location and correction are important in case of any power systems. This process has to be prompt and accurate so that system reliability can be improved , outage time can be reduced and restoration of system from fault can be accelerated.
Fault location calculation using Magnetoresistance sensor is described here.
Series & shunt compensation and FACTs Deviceskhemraj298
Series compensation is used to improve the performance of extra high voltage transmission lines by connecting capacitors in series with the line. It allows for increased transmission capacity and improved system stability by reducing the phase angle between sending and receiving end voltages for the same power transfer. Shunt compensation controls the receiving end voltage by connecting shunt capacitors or reactors to meet reactive power demand and prevent voltage drops or rises. Flexible AC transmission systems use high-speed thyristors to switch transmission line components like capacitors and reactors to control parameters like voltages and reactances to optimize power transfer.
This document discusses power system stability and microgrids. It defines power system stability and classifies it into several types including rotor angle stability, voltage stability, and frequency stability. It also discusses microgrids, their interconnection to main grids for availability and economic benefits, and methods for connecting microgrids using switchgear or static switches. In conclusion, it states that power system stability is important for normal operation and can be improved through devices like capacitors and FACTS controllers, and that microgrids satisfy local loads while reducing transmission losses through local renewable generation.
This document discusses static shunt compensation on transmission lines. Shunt compensation can increase steady-state transmittable power and control voltage profiles by using shunt reactors to minimize overvoltage under light loads and shunt capacitors to maintain voltage levels under heavy loads. Midpoint shunt compensation regulates voltage along line segments by exchanging only reactive power at the midpoint, significantly increasing transmittable power as the midpoint has the maximum voltage sag. End of line shunt compensation also provides voltage support to prevent instability.
Design aspects of high voltage transmission linejournalBEEI
The transmission lines are very important in the transmitted of electrical power, and the process of selecting the voltage of the line is an important task in the design and implementation process. The process of transferring electrical power from one side then onto the next place for long away. While maintaining the percentage regulation within the permissible limits is an important problem in the transfer of energy. In electrical transmission line there are important elements are resistance, inductance and capacitance. The purpose of this paper is to study and calculate economic high-tension voltage and selection of overhead line conductor ACSR.
The document discusses various methods for improving power system stability, including automatic voltage regulators (AVR), load frequency control (LFC), and power system stabilizers (PSS). AVR works to maintain generator terminal voltage at a preset value by adjusting excitation current. LFC maintains system frequency and power exchange between areas at scheduled values. PSS adds damping to generator oscillations to stabilize the grid by modulating voltage regulator setpoint based on speed.
Grid Interconnection of Renewable Energy Sources at the Distribution Level Wi...Pradeep Avanigadda
Renewable energy resources (RES) are being increasingly connected in distribution systems utilizing power electronic converters.
This project presents a novel control strategy for achieving maximum benefits from these grid-interfacing inverters when installed in 3-phase 4-wire distribution systems.
The inverter can thus be utilized as:
1) power converter to inject power generated from RES to the grid &
2) shunt APF to compensate current unbalance, load current harmonics, load reactive power demand and load neutral current.
Single area load frequency control by using pi,fuzzy logic control1SAI SREE
This paper compares PI and fuzzy logic controllers for single area load frequency control of an isolated power system. PI controllers are commonly used but have poor transient performance and require steady state error to reach zero. Fuzzy logic controllers offer improved transient performance as they are robust and nonlinear. The paper finds that while PI controllers are simpler with less required data, fuzzy logic controllers settle more quickly with changes in load and are thus better for maintaining constant frequency during transients despite being more complex.
The document discusses various objectives and applications of static shunt compensation on transmission lines. Shunt compensation can increase steady-state transmittable power, control voltage profiles, minimize line overvoltage under light loads using shunt reactors, and maintain voltage levels under heavy loads using shunt capacitors. Midpoint shunt compensation significantly increases transmitted power and is best located at the midpoint where voltage sag is maximum. End of line shunt compensation effectively increases voltage stability limits and regulates terminal voltages to prevent voltage instability. Shunt compensation can also improve transient stability and damp power oscillations on transmission lines.
This document discusses distributed generation, which refers to small-scale power generation located near the end users. It can include sources like solar panels, wind turbines, fuel cells, and cogeneration. Distributed generation has advantages like reduced transmission losses and improved supply security. However, it also presents challenges like impacts on power quality from issues such as voltage regulation, grounding, harmonics, and islanding effects. The document outlines different distributed generation technologies and concludes that its integration into the power system is possible if interconnection designs adequately address power quality and safety considerations.
This program solves the economic dispatch problem using the lambda iteration method for a system with three generating units, both with and without considering transmission losses.
It defines the cost curves and operating limits of each generator. The problem is solved by minimizing total generation cost subject to the load demand constraint, using MATLAB's fsolve function to solve the coordination equations.
Without losses, it calculates the optimal dispatch, total cost and verifies load balance. With losses, it iteratively solves the coordination equations including loss coefficients to determine the optimal dispatch that minimizes total cost including losses, calculating total losses and resulting load supplied.
The load dispatch center monitors and controls the power system to ensure reliable power supply. It collects data using a SCADA system and oversees elements like generators, transformers, and transmission lines. The load dispatch center performs economic and secure operation of the power system, and works to restore power lines after faults. It is responsible for functions like load forecasting, outage monitoring, voltage regulation, load scheduling, and coordination between grids.
This document discusses unit commitment in power systems. Unit commitment aims to schedule generating units to meet forecasted load at minimum cost while maintaining reliability. It considers startup costs, operating costs, and shutdown costs over a daily load cycle. Dynamic programming is used to solve the unit commitment problem by evaluating combinations of generating units at each time interval and carrying minimum costs backward from the final interval to find the overall lowest-cost solution. The objective is to determine the optimal set of units to operate at each time period to supply predicted load economically.
This document discusses hydrothermal scheduling, which involves optimally scheduling hydroelectric and thermal power plants together to minimize generation costs. Hydrothermal scheduling is classified as either long-range (months or years) or short-range (days or weeks). The key aspects are using low-cost hydroelectric generation where possible to reduce reliance on more expensive thermal plants. Mathematical optimization techniques are used to determine the optimal dispatch of hydro and thermal plants while meeting demand and respecting water availability constraints. While hydrothermal coordination can lower costs, the variable nature of hydro inflows makes the optimization problem complex.
These slides presents the different challenges and issues related to DG integration to Micro-grid distribution systems. The possible solutions are also presented. Later of the class I will try to upload the mathematical presentations and simulation results related to each protection scheme. However, your suggestions are always welcome.
This document provides instructions for a MATLAB assignment with two parts. Part I involves constructing Lagrange interpolants for a given function. Students are asked to create MATLAB function files for Lagrange interpolation and for defining a test function, as well as a script file to test the interpolation. Part II involves solving a system of linear ordinary differential equations and constructing the solution at discrete time points. Students are asked to create a function file to solve the ODE using eigenvalues and eigenvectors, and a script file to test it on a sample problem. Detailed hints are provided for both parts.
Genetic Algorithm for Solving the Economic Load DispatchSatyendra Singh
In this paper, comparative study of two approaches, Genetic Algorithm
(GA) and Lambda Iteration method (LIM) have been used to provide
the solution of the economic load dispatch (ELD) problem. The ELD
problem is defined as to minimize the total operating cost of a power
system while meeting the total load plus transmission losses within
generation limits. GA and LIM have been used individually for solving
two cases, first is three generator test system and second is ten
generator test system. The results are compared which reveals that GA
can provide more accurate results with fast convergence characteristics
and is superior to LIM.
Input output , heat rate characteristics and Incremental costEklavya Sharma
This document discusses the input-output, heat rate, and incremental cost characteristics of thermal power plants. It defines input-output characteristics as a plot of fuel input versus power output. Heat rate is the ratio of fuel input to energy output and is the slope of the input-output curve. An incremental fuel rate curve plots the incremental fuel rate, or change in input divided by change in output, versus output. The incremental cost curve multiplies incremental fuel rate by fuel cost to determine incremental cost in monetary terms per unit of output. Economic dispatch of power plants aims to minimize total incremental costs while meeting demand.
The document discusses swing equation, which is used to model rotor dynamics in power systems. It defines swing equation as a second order differential equation that relates the change in rotor angle over time to the difference between mechanical and electrical power inputs. The document outlines the derivation of swing equation from the torque-speed relationship of a synchronous generator. It also discusses swing curves, which plot electrical power output versus rotor angle, and the equal area criteria method for assessing transient stability using swing curve plots.
In microgrid, if fault occurs or any other contingency happens, then the problems would be created which are related to power flow, also there are various protection schemes are used for minimize or eliminate these problems.
Voltage control is used for reactive power balance and P-f control is used for active power control.
Various protection schemes such as, over current protection, differential protection scheme, zoning of network in adaptive protection scheme are used in microgrid system .
Fault location and correction are important in case of any power systems. This process has to be prompt and accurate so that system reliability can be improved , outage time can be reduced and restoration of system from fault can be accelerated.
Fault location calculation using Magnetoresistance sensor is described here.
Series & shunt compensation and FACTs Deviceskhemraj298
Series compensation is used to improve the performance of extra high voltage transmission lines by connecting capacitors in series with the line. It allows for increased transmission capacity and improved system stability by reducing the phase angle between sending and receiving end voltages for the same power transfer. Shunt compensation controls the receiving end voltage by connecting shunt capacitors or reactors to meet reactive power demand and prevent voltage drops or rises. Flexible AC transmission systems use high-speed thyristors to switch transmission line components like capacitors and reactors to control parameters like voltages and reactances to optimize power transfer.
This document discusses power system stability and microgrids. It defines power system stability and classifies it into several types including rotor angle stability, voltage stability, and frequency stability. It also discusses microgrids, their interconnection to main grids for availability and economic benefits, and methods for connecting microgrids using switchgear or static switches. In conclusion, it states that power system stability is important for normal operation and can be improved through devices like capacitors and FACTS controllers, and that microgrids satisfy local loads while reducing transmission losses through local renewable generation.
This document discusses static shunt compensation on transmission lines. Shunt compensation can increase steady-state transmittable power and control voltage profiles by using shunt reactors to minimize overvoltage under light loads and shunt capacitors to maintain voltage levels under heavy loads. Midpoint shunt compensation regulates voltage along line segments by exchanging only reactive power at the midpoint, significantly increasing transmittable power as the midpoint has the maximum voltage sag. End of line shunt compensation also provides voltage support to prevent instability.
Design aspects of high voltage transmission linejournalBEEI
The transmission lines are very important in the transmitted of electrical power, and the process of selecting the voltage of the line is an important task in the design and implementation process. The process of transferring electrical power from one side then onto the next place for long away. While maintaining the percentage regulation within the permissible limits is an important problem in the transfer of energy. In electrical transmission line there are important elements are resistance, inductance and capacitance. The purpose of this paper is to study and calculate economic high-tension voltage and selection of overhead line conductor ACSR.
The document discusses various methods for improving power system stability, including automatic voltage regulators (AVR), load frequency control (LFC), and power system stabilizers (PSS). AVR works to maintain generator terminal voltage at a preset value by adjusting excitation current. LFC maintains system frequency and power exchange between areas at scheduled values. PSS adds damping to generator oscillations to stabilize the grid by modulating voltage regulator setpoint based on speed.
Grid Interconnection of Renewable Energy Sources at the Distribution Level Wi...Pradeep Avanigadda
Renewable energy resources (RES) are being increasingly connected in distribution systems utilizing power electronic converters.
This project presents a novel control strategy for achieving maximum benefits from these grid-interfacing inverters when installed in 3-phase 4-wire distribution systems.
The inverter can thus be utilized as:
1) power converter to inject power generated from RES to the grid &
2) shunt APF to compensate current unbalance, load current harmonics, load reactive power demand and load neutral current.
Single area load frequency control by using pi,fuzzy logic control1SAI SREE
This paper compares PI and fuzzy logic controllers for single area load frequency control of an isolated power system. PI controllers are commonly used but have poor transient performance and require steady state error to reach zero. Fuzzy logic controllers offer improved transient performance as they are robust and nonlinear. The paper finds that while PI controllers are simpler with less required data, fuzzy logic controllers settle more quickly with changes in load and are thus better for maintaining constant frequency during transients despite being more complex.
The document discusses various objectives and applications of static shunt compensation on transmission lines. Shunt compensation can increase steady-state transmittable power, control voltage profiles, minimize line overvoltage under light loads using shunt reactors, and maintain voltage levels under heavy loads using shunt capacitors. Midpoint shunt compensation significantly increases transmitted power and is best located at the midpoint where voltage sag is maximum. End of line shunt compensation effectively increases voltage stability limits and regulates terminal voltages to prevent voltage instability. Shunt compensation can also improve transient stability and damp power oscillations on transmission lines.
This document discusses distributed generation, which refers to small-scale power generation located near the end users. It can include sources like solar panels, wind turbines, fuel cells, and cogeneration. Distributed generation has advantages like reduced transmission losses and improved supply security. However, it also presents challenges like impacts on power quality from issues such as voltage regulation, grounding, harmonics, and islanding effects. The document outlines different distributed generation technologies and concludes that its integration into the power system is possible if interconnection designs adequately address power quality and safety considerations.
This program solves the economic dispatch problem using the lambda iteration method for a system with three generating units, both with and without considering transmission losses.
It defines the cost curves and operating limits of each generator. The problem is solved by minimizing total generation cost subject to the load demand constraint, using MATLAB's fsolve function to solve the coordination equations.
Without losses, it calculates the optimal dispatch, total cost and verifies load balance. With losses, it iteratively solves the coordination equations including loss coefficients to determine the optimal dispatch that minimizes total cost including losses, calculating total losses and resulting load supplied.
The load dispatch center monitors and controls the power system to ensure reliable power supply. It collects data using a SCADA system and oversees elements like generators, transformers, and transmission lines. The load dispatch center performs economic and secure operation of the power system, and works to restore power lines after faults. It is responsible for functions like load forecasting, outage monitoring, voltage regulation, load scheduling, and coordination between grids.
This document discusses unit commitment in power systems. Unit commitment aims to schedule generating units to meet forecasted load at minimum cost while maintaining reliability. It considers startup costs, operating costs, and shutdown costs over a daily load cycle. Dynamic programming is used to solve the unit commitment problem by evaluating combinations of generating units at each time interval and carrying minimum costs backward from the final interval to find the overall lowest-cost solution. The objective is to determine the optimal set of units to operate at each time period to supply predicted load economically.
This document discusses hydrothermal scheduling, which involves optimally scheduling hydroelectric and thermal power plants together to minimize generation costs. Hydrothermal scheduling is classified as either long-range (months or years) or short-range (days or weeks). The key aspects are using low-cost hydroelectric generation where possible to reduce reliance on more expensive thermal plants. Mathematical optimization techniques are used to determine the optimal dispatch of hydro and thermal plants while meeting demand and respecting water availability constraints. While hydrothermal coordination can lower costs, the variable nature of hydro inflows makes the optimization problem complex.
These slides presents the different challenges and issues related to DG integration to Micro-grid distribution systems. The possible solutions are also presented. Later of the class I will try to upload the mathematical presentations and simulation results related to each protection scheme. However, your suggestions are always welcome.
This document provides instructions for a MATLAB assignment with two parts. Part I involves constructing Lagrange interpolants for a given function. Students are asked to create MATLAB function files for Lagrange interpolation and for defining a test function, as well as a script file to test the interpolation. Part II involves solving a system of linear ordinary differential equations and constructing the solution at discrete time points. Students are asked to create a function file to solve the ODE using eigenvalues and eigenvectors, and a script file to test it on a sample problem. Detailed hints are provided for both parts.
Genetic Algorithm for Solving the Economic Load DispatchSatyendra Singh
In this paper, comparative study of two approaches, Genetic Algorithm
(GA) and Lambda Iteration method (LIM) have been used to provide
the solution of the economic load dispatch (ELD) problem. The ELD
problem is defined as to minimize the total operating cost of a power
system while meeting the total load plus transmission losses within
generation limits. GA and LIM have been used individually for solving
two cases, first is three generator test system and second is ten
generator test system. The results are compared which reveals that GA
can provide more accurate results with fast convergence characteristics
and is superior to LIM.
Economic/Emission Load Dispatch Using Artificial Bee Colony AlgorithmIDES Editor
This paper presents an application of the
artificial bee colony (ABC) algorithm to multi-objective
optimization problems in power system. A new multiobjective
artificial bee colony (MOABC) algorithm to
solve the economic/ emission dispatch (EED) problem is
proposed in this paper. Non-dominated sorting is
employed to obtain a Pareto optimal set. Moreover, fuzzy
decision theory is employed to extract the best
compromise solution. A numerical result for IEEE 30-bus
test system is presented to demonstrate the capability of
the proposed approach to generate well-distributed
Pareto-optimal solutions of EED problem in one single
run. In addition, the EED problem is also solved using the
weighted sum method using ABC. Results obtained with
the proposed approach are compared with other
techniques available in the literature. Results obtained
show that the proposed MOABC has a great potential in
handling multi-objective optimization problem.
Reverse Piezoelectric Effect is the theory used to explain how KETM power optimization system works well in every conditions. KETM increases the environment condition of electric current and allows the current flow in maximum capacity.
Economics is the study of production, distribution, and consumption of goods and services. It is divided into microeconomics and macroeconomics. Microeconomics deals with supply and demand at the individual level, while macroeconomics examines concepts at the national level like economic growth and monetary policy. Rational decision making in economics involves identifying feasible options, assessing the consequences, ranking alternatives based on priorities, and choosing the highest priority option.
Business economics production analysisRachit Walia
The document discusses several key concepts in production analysis:
1. It defines production functions, marginal product, average product, and the law of diminishing returns. Marginal product refers to the change in output from a small change in one input.
2. It explains the relationships between total, average, and marginal productivity and how marginal productivity initially increases and then decreases.
3. There is a distinction made between short and long run periods of production - in the short run some inputs can be varied, while in the long run all inputs can be varied.
4. The concepts of economies of scale, isoquants, and marginal rate of technical substitution are also introduced at a high level.
Many traditional optimization methods have been successfully used from years to deal with ELD problem. However these techniques have limitations in many aspects as they provide inaccurate results. The objective is to minimize total fuel cost of power generation so as to meet the power demands to satisfy all constraints. In present paper, the parameters of the fuzzy logic are tuned using genetic algorithms. By using GA with fuzzy logic leads to an intelligent dimension for ELD solution space to obtain an optimum solution for ELD
Economic Load Dispatch (ELD) is a process of scheduling the required load demand among available generation units such that the fuel cost of operation is minimized. The ELD problem is formulated as a non-linear constrained optimization problem with both equality and inequality constraints. In this paper, two test systems of the ELD problems are solved by adopting the Cuckoo Search (CS) Algorithm. A comparison of obtained simulation results by using the CS is carried out against six other swarm intelligence algorithms: Particle Swarm Optimization, Shuffled Frog Leaping Algorithm, Bacterial Foraging Optimization, Artificial Bee Colony, Harmony Search and Firefly Algorithm. The effectiveness of each swarm intelligence algorithm is demonstrated on a test system comprising three-generators and other containing six-generators. Results denote superiority of the Cuckoo Search Algorithm and confirm its potential to solve the ELD problem.
Umts Radio Interface System Planning And OptimizationDavid Rottmayer
The document discusses planning and optimizing UMTS radio networks. It begins with an overview of UMTS network architecture and the differences between UMTS and GSM radio system planning. Key aspects of UMTS planning include coverage and capacity planning occurring simultaneously, as capacity requirements influence coverage. The document then covers WCDMA air interface specifications, propagation environments, and the UMTS radio system planning process. It discusses challenges such as varying traffic levels and distributions. The document provides a typical link budget example and explains transmitter, receiver, and channel parameters considered in UMTS coverage planning.
This document provides an overview of the Artificial Bee Colony (ABC) algorithm. It describes how ABC was inspired by the foraging behavior of honey bees. The core components of the ABC algorithm are introduced, including the initialization phase, employed bee phase, onlooker bee phase, and scout bee phase. Pseudocode and a flowchart depicting the steps of the ABC algorithm are presented. Applications of ABC in areas such as optimization, bioinformatics, scheduling, clustering, and engineering are discussed. Finally, the advantages of ABC like simplicity and flexibility are contrasted with limitations such as high computational cost.
The document summarizes the artificial bee colony (ABC) algorithm, which was introduced in 2005 and is inspired by the foraging behavior of honeybee swarms. The ABC algorithm simulates three groups of bees - employed bees, onlookers, and scouts - to solve optimization problems. It involves phases of employed bee search, onlooker bee choice, and scout bee recruitment to balance exploration and exploitation. The ABC algorithm has few parameters and fast convergence but is limited by its initial solutions. Variations include multi-objective ABC algorithms and parameter studies on swarm size, limit, and dimension.
The document discusses power optimization using a six phase transmission system. It begins with an introduction to high phase order transmission and implementations of six phase systems. It then covers topics like power transmission optimization techniques, constructing a six phase system using transformers, feasibility analysis in terms of transfer capability, electric field, and lightning performance. Additional sections discuss economic considerations, faults and protection schemes for six phase systems, and considerations for future six phase design. The document concludes that six phase transmission can optimize power transfer but is currently not economically viable at most distances.
This document outlines some basic economic concepts. It discusses how every society has four factors of production - land, labor, capital, and entrepreneurs - which are used along with resources to produce goods and services. However, resources are limited while human wants are unlimited, creating an economic problem of scarcity. This scarcity means societies must make choices about what goods and services to produce, how to produce them, and who will consume them, establishing an economic system. These choices involve trade-offs and opportunity costs.
Production involves transforming inputs into outputs. There are three types of transformation: change in form, place, or time. A production function relates the maximum output to a given quantity of inputs. There are three stages of production based on diminishing returns. In the short run, one factor is fixed while in the long run all factors are variable, leading to different types of returns to scale. Isoquants represent combinations of inputs that produce the same output level, with their properties determining the optimal input mix.
Power system planning & operation [eceg 4410]Sifan Welisa
The document discusses power load forecasting and substation planning. It explains that accurate load forecasting is important for power system planning and operation. Several load forecasting methods are described, including those based on historical load data, economic factors, and standardized load curves. Load forecasts can be short, medium, or long-term. The document also discusses factors to consider in substation planning and design, such as location, equipment requirements, and configuration. Feasibility studies are important for assessing potential hydroelectric and substation projects.
This document provides an overview of microeconomics concepts including:
1. Economics is defined as the study of how scarce resources are allocated among alternative uses.
2. Key concepts in microeconomics include rational choice, incentives, marginal analysis, and opportunity cost.
3. Economic systems must answer questions about what to produce, how to produce it, and who receives it given the constraints of scarce resources.
This document contains the question bank for the subject EE 1351 Power System Analysis. It includes 18 multiple choice and numerical questions related to modeling components of a power system including generators, transmission lines and transformers. It also covers per-unit calculations, impedance and reactance diagrams, bus admittance matrices, symmetrical components and power flow analysis. Sample questions are provided on determining the per-unit impedances of components, drawing equivalent circuits, calculating sequence impedances and modeling various elements for power flow studies.
This document discusses fault level calculations in electric power systems. It explains that fault level calculations are necessary to select protective devices, circuit breakers, and equipment that can withstand short circuit currents. The document outlines the procedure for calculating fault levels, which involves representing the system with a single line diagram, choosing a base MVA, calculating per unit reactances, determining the equivalent reactance to the fault point, and using formulas to calculate fault MVA and current. It also discusses how current limiting reactors can be used to insert additional reactance and reduce short circuit currents to match circuit breaker ratings.
This document provides an introduction to power system fault analysis. It discusses the importance of accurately analyzing fault conditions and their effects on the power system. Various types of faults are described, including short circuits, open circuits, simultaneous faults, and winding faults. Factors that affect fault severity are also outlined. The document then discusses methods for calculating faults, including using symmetrical components and sequence networks. An example fault calculation is provided to illustrate the process. Fault analysis is necessary for proper power system design, operation, and protection.
This document provides an introduction to genetic algorithms (GAs) including:
- GAs are inspired by Darwin's theory of evolution and use techniques like inheritance, mutation, selection, and crossover to find solutions to optimization problems.
- The document discusses key GA components like populations of individuals, fitness functions, selection, crossover, and mutation.
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HYBRID PARTICLE SWARM OPTIMIZATION FOR SOLVING MULTI-AREA ECONOMIC DISPATCH P...ijsc
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environment for practical multi-area cases with tie line constraints. Our objective is to generate allocation
to the power generators in such a manner that the total fuel cost is minimized while all operating
constraints are satisfied. This problem is NP-hard. In this paper, we propose Hybrid Particle Swarm
Optimization (HGAPSO) to solve MAEDP. The experimental results are reported to show the efficiency of
proposed algorithms compared to Particle Swarm Optimization with Time-Varying Acceleration
Coefficients (PSO-TVAC) and RCGA.
Hybrid Particle Swarm Optimization for Solving Multi-Area Economic Dispatch P...ijsc
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A Decomposition Aggregation Method for Solving Electrical Power Dispatch Prob...raj20072
This document proposes a decomposition/aggregation method to solve large-scale economic dispatch problems with many generators. It decomposes a power system into areas, each containing generators and loads. An evolutionary programming technique optimizes dispatch in each area locally. The area solutions are then aggregated to solve the overall system problem while minimizing total cost. The method is demonstrated on 5-bus and 26-bus test systems decomposed into two areas each. Local area problems are solved as subproblems, while the overall system solution is the "master problem". Results are compared to a centralized approach. The decomposition/aggregation method shows promise in solving economic dispatch with large numbers of generators.
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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.
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This document describes using particle swarm optimization (PSO) to solve the economic load dispatch (ELD) problem of optimizing the operation of six interconnected generating units. ELD aims to minimize total generation costs while satisfying constraints. PSO is applied to find optimal unit outputs that minimize cost, accounting for transmission losses. The proposed PSO approach is compared to genetic algorithms and conventional methods on a test system, showing PSO provides better solutions faster. Key steps of the PSO algorithm for ELD are initializing particles, evaluating fitness at each iteration, and updating personal and global best positions to iteratively improve solutions.
ECONOMIC LOAD DISPATCH USING GENETIC ALGORITHMIJARIIT
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Operation cost reduction in unit commitment problem using improved quantum bi...IJECEIAES
Unit Commitment (UC) is a nonlinear mixed integer-programming problem. UC used to minimize the operational cost of the generation units in a power system by scheduling some of generators in ON state and the other generators in OFF state according to the total power outputs of generation units, load demand and the constraints of power system. This paper proposes an Improved Quantum Binary Particle Swarm Optimization (IQBPSO) algorithm. The tests have been made on a 10-units simulation system and the results show the improvement in an operation cost reduction after using the proposed algorithm compared with the ordinary Quantum Binary Particle Swarm Optimization (QBPSO) algorithm
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Optimal Unit Commitment Based on Economic Dispatch Using Improved Particle Sw...paperpublications3
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Hybrid method for achieving Pareto front on economic emission dispatch IJECEIAES
In this paper hybrid method, Modified Nondominated Sorted Genetic Algorithm (MNSGA-II) and Modified Population Variant Differential Evolution(MPVDE) have been placed in effect in achieving the best optimal solution of Multiobjective economic emission load dispatch optimization problem. In this technique latter, one is used to enforce the assigned percent of the population and the remaining with the former one. To overcome the premature convergence in an optimization problem diversity preserving operator is employed, from the tradeoff curve the best optimal solution is predicted using fuzzy set theory. This methodology validated on IEEE 30 bus test system with six generators, IEEE 118 bus test system with fourteen generators and with a forty generators test system. The solutions are dissimilitude with the existing metaheuristic methods like Strength Pareto Evolutionary Algorithm-II, Multiobjective differential evolution, Multiobjective Particle Swarm optimization, Fuzzy clustering particle swarm optimization, Nondominated sorting genetic algorithm-II.
This paper proposes a hybrid approach using fuzzy logic and genetic algorithms to solve the economic load dispatch (ELD) problem. The ELD problem aims to minimize generation costs while meeting load demands and generator constraints. The proposed method combines fuzzy logic and genetic algorithms to adaptively adjust crossover and mutation rates during optimization. Testing on 3-generator and 10-generator systems shows the hybrid approach finds more accurate and economically optimal solutions faster than genetic algorithms or traditional lambda iteration methods. The hybrid approach proves effective for solving the ELD problem in power systems.
International Journal of Engineering Research and DevelopmentIJERD Editor
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This document presents a hybrid Gravitational Search Algorithm and Sequential Quadratic Programming (GSA-SQP) approach to solve economic emission load dispatch (EELD) problems in power systems. The approach aims to minimize both fuel costs and emission levels simultaneously while satisfying operational constraints. It formulates EELD as a multi-objective optimization problem involving non-linear, non-convex objectives and constraints. Numerical results on three test power systems show the proposed GSA-SQP hybrid approach provides better performing solutions compared to other evolutionary algorithms like NSGA-II and SPEA2.
IRJET- Solving Economic Load Dispatch Problem with Valve Point EffectIRJET Journal
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Economic Dispatch of Generated Power Using Modified Lambda-Iteration Method
1. IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE)
e-ISSN: 2278-1676,p-ISSN: 2320-3331, Volume 7, Issue 1 (Jul. - Aug. 2013), PP 49-54
www.iosrjournals.org
www.iosrjournals.org 49 | Page
Economic Dispatch of Generated Power Using Modified Lambda-
Iteration Method
Damian Obioma Dike, Moses Izuchukwu Adinfono, George Ogu
(Electrical and Electronic Engineering Department, School of Engineering and Engineering Technology,
Federal University of Technology, Owerri (FUTO), Nigeria)
Abstract: In practical situations and under normal operating conditions, the generating capacity of power
plants is more than the total losses and load demand. Also, power plants have different fuel costs and are not
the same distance from the load centers. Hence the need for developing improved methods of economic dispatch
of generated power from mostly remote locations to major load centers in the urban cities. Most methods
adopted for optimal dispatch are either cumbersome in their computational approaches. This work proposes a
fast and easy to use generic MATLAB syntax to aid in solving economic dispatch problems. The software
component proposed in this work will try to estimate the optimal value of real power to be generated with the
least possible fuel cost. This will be based on the assumption of equal incremental cost and the result compared
to genetic algorithm simulation.
Keywords: Economic Dispatch, Equal Incremental Cost, Modified Lambda-Iteration, Genetic Algorithm
I. Introduction
Economic Dispatch is “the operation of generation facilities to produce energy at the lowest cost to
reliably serve consumers, recognizing any operational limits of generation and transmission facilities [1].” The
objective of economic dispatch is to determine the power output of each generating unit under the constraints of
load demands and transmission losses that will give minimal cost on fuel or operation of the whole system [2].
Over the years, many research works have been published on many and various efforts made to solve
Economic Load Dispatch (ELD) problems, employing different kinds of constraints, mathematical programming
and optimization techniques. The classical or conventional methods include Lambda-iteration method [2],
Gradient Projection Algorithm, Interior Point Method [3], Linear Programming, Lagrangian relaxation [4] and
Dynamic Programming. The heuristic methods include Evolutionary Programming (EP) [5], [35], Differential
Evolution (DE) [6-10], [29], Particle Swarm Optimization (PSO) [11-24], Genetic Algorithm (GA) [25-27],
Simulated Annealing [28-29], Tabu Search (TS) [30-31], Artificial Immune System [32-33] and Artificial Bee
Colony Method [34].
II. Problem Formulation
The economic dispatch problem will now be mathematically described. We will be considering the
operation of generating units.
The variation of the fuel cost of each generator ( ) with real power output ( ) is given by a Second
order smooth fuel cost function [57]. The total fuel cost of the plant is the sum of the costs of the individual
units:
(1)
Where, is the input-output cost function, is the total number of units, is the index of dispatchable units,
, , are coefficients of the quadratic fuel cost function and is the generated power of unit .
With losses neglected, the fuel cost will be subjected to the power balance equation given as (2);
(2)
This can be rewritten as:
(3)
Where,
is the sum of all demands at load nodes in the system
Each unit has its maximum and minimum generating limit. This will also serve as a form of constraint.
2. Economic Dispatch of Generated Power Using Modified Lambda-Iteration Method
www.iosrjournals.org 50 | Page
(4)
Where,
is the minimum generation limit of unit
is the maximum generation limit of unit
For optimal dispatch, we assume that the incremental cost of running each unit is equal i.e.:
(5)
(6)
Where,
is the incremental cost
The optimality condition from (6) reduces to:
(7)
(8)
From the (8), the power generated in unit can be gotten as:
(9)
Now accounting for transmission losses, from kron’s loss formula:
(10)
Where,
is the transmission losses
are the transmission line coefficients
The power balance constraint, (3), becomes:
(11)
Also, the optimality condition, (6), becomes
(12)
(13)
Where is the incremental loss of unit
Putting (7) and (13) into (12), we have:
(14)
From Equation 14, the power generated in unit can be gotten as:
(15)
This can be simplified as:
(16)
The net power can then be calculated as:
(17)
3. Economic Dispatch of Generated Power Using Modified Lambda-Iteration Method
www.iosrjournals.org 51 | Page
III. Implementation
1.1. Algorithm for Economic Dispatch
1. Initialization:
Input data such as; number of plants, total load demand, generator limits, cost curve coefficients, iteration limit
and tolerance.
2. Start counter.
3. Calculate power value for each plant using Equation 15.
4. Check if iteration limits is exceeded.
If yes, inform user of non-convergence and stop.
Else, go to step 5.
5. Check if Power value for plant is less then set limit.
If yes, set power value to lower limit, increment counter and go to 4.
Else, go to 6.
6. Check if Power value for plant is more than set limit.
If yes, set power value to upper limit, increment counter and go to 4.
Else go to 7.
7. Sum up Power for all plants and calculate the power loss using Equation 10.
8. Calculate net power from Equation 17.
9. If absolute value for net power is less than set tolerance level,
Display calculated power value, incremental cost value and stop.
10. If net power is greater than zero,
Reduce the value of the incremental cost, increment counter and go to 4.
Else, increase the value of the incremental cost, increment counter and go to 4.
The flow chat of which is shown in Fig. 1.
1.2. Matlab Program
%N = iteration count limit
%e = iteration tolerance
%lamda = Lagrange multiplier (Lambda)
%del_lamda = change in lambda
%PD = Power Demand
%Pmin & Pmax = minimum and maximum power limits
n=1; lamda=0; del_lamda=0; e=0.01; P=0;
Psum=0;
4. Economic Dispatch of Generated Power Using Modified Lambda-Iteration Method
www.iosrjournals.org 52 | Page
m=input('Input total number of thermal unit:')
for k=1:m
disp('plant')
disp(k)
Pmin(k)=input('insert minimum power:')
Pmax(k)=input('insert maximum power:')
end
disp('Input cost coefficients per plant in the form below:')
disp('[alpha1 beta1 gamma1;alpha2 beta2 gamma2;...]')
C=input('Insert Cost Coefficients:')
for k=1:m
P(k)=(lamda-C(k,2))/(2*C(k,3));
if P(k)<Pmin(k)
P(k)=Pmin(k);
elseif P(k)>Pmax(k)
P(k)=Pmax(k);
end
Psum=Psum+P(k);
end
if n>N
disp('Solution non-convergence');
disp('Number of Iterations:')
disp(n-1)
else
Pnet=Psum-PD;
del_lamda=abs(Pnet)/P(k);
if abs(Pnet)<e
disp('final value for lamda:')
disp(lamda)
disp('Power for plants 1 to m:')
disp(P)
disp('number of iterations:')
disp(n)
disp('iteration tolerance:')
disp(e)
elseif Pnet>0
lamda=lamda-del_lamda;
else
lamda=lamda+del_lamda;
end
end
Psum=0;
%n=n+1;
1.3. Implementation Data
Table 1: Fuel Cost Coefficients
Generator No.
1 0.0070 7.0 240
2 0.0095 10.0 200
3 0.0090 8.5 220
4 0.0090 11.0 200
5 0.0080 10.5 220
6 0.0075 12.0 190
5. Economic Dispatch of Generated Power Using Modified Lambda-Iteration Method
www.iosrjournals.org 53 | Page
Table 2: Real Power Limits for the Generators
Generator No. Generator Limits (MW)
1 100 500
2 50 200
3 80 300
4 50 150
5 50 200
6 50 120
IV. RESULTS AND DISCUSSION
An economic load dispatch is performed on a 26 bus system with six generators. The six generators are
connected to bus1, bus2, bus3, bus4, bus5, and bus26 respectively. The operating costs of the generators are in
$/h. The optimal scheduling of the generators has to be within the maximum and minimum limits of each of the
generators. The total load demand of the system is 1263MW. The fuel cost coefficients are shown in TABLE 1.
Table 3: Result
Generator No.
Power Generated (MW)
Proposed Method Genetic Algorithm [25]
1 446.7087 454.7141
2 171.2591 147.5434
3 264.1068 269.7175
4 125.2179 144.7849
5 172.1201 170.7478
6 83.5948 92.0970
0
100
200
300
400
500
Gen.
1
Gen.
2
Gen.
3
Gen.
4
Gen.
5
Gen.
6
MW
Proposed Method
Genetic Algorithm
Figure 1: bar chart showing result
The proposed method gave a total power value of 1263.0074MW with incremental cost of
13.2539$/MWh, while the genetic algorithm gave an incremental cost of 13.6445$/MWh with total power value
of 1263.8809 and transmission loss of 15.7238MW. Successive Approximation is used to calculate the
incremental costs of the generators, based on equal incremental cost principle. This is done with the help of the
proposed MATLAB syntax. The following results are gotten from a 3GB RAM, 2.1GHz, and Pentium Dual-
Core CPU.
V. Conclusion
A new approach to solving Economic Dispatch Problem (EDP) s using modified lambda-iteration is
proposed. This paper demonstrates the feasibility of the proposed technique for efficient solving of EDPs with
generator constraints. The technique was implemented with the help of MATLAB programming.
The loss formula and loss coefficients were not fully employed in the examples used in the paper. However,
there is no problem in implementing the changes, because it has been incorporated in the flow chart.
Computational results reveal that the proposed method gave fairly improved results when compared
with that obtained from Genetic algorithm Method, in most of the geneators.
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