The document discusses electric power system operation and control. It addresses the objectives of power system operation which are to provide continuous quality service to energy users at minimum cost. This includes supplying power at acceptable voltage and frequency while minimizing environmental impact and ensuring security and reliability. The tasks of operation planning, control and accounting are described. Operation planning involves scheduling generation and transmission facilities to meet load demand at minimum cost over various time periods. Operation control functions like economic dispatch, load frequency control and operating reserve calculation aim to satisfy instantaneous load demands. Optimization of generation dispatch to minimize total operating costs is formulated as a constrained optimization problem solved using methods like Lagrange multipliers and iterative techniques. Transmission losses are also accounted for in the optimal load dispatch model
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.
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.
This document discusses the key components and types of AC power transmission systems. It begins with an introduction that describes how electrical energy generated at power plants is transmitted through transmission lines to consumers. It then provides a single line diagram showing the steps of increasing voltage for transmission and decreasing it for distribution. The main types of transmission line systems are described as single phase, two phase, and three phase AC systems, as well as DC systems. Finally, the key elements of transmission lines are outlined, including conductors, transformers, insulators, support towers, and protective devices.
Exp 3 (1)3. To Formulate YBUS Matrix By Singular Transformation.Shweta Yadav
The document describes formulating a YBUS matrix for a power system network model using MATLAB. It presents the theory behind developing the bus admittance matrix YBUS using Kirchhoff's current law and singular transformation. An example 4-bus power system is given, and the student is asked to calculate the YBUS matrix with and without a dotted transmission line connected.
This document discusses issues related to connecting renewable energy sources to the electric grid. It notes that renewable resources like wind and solar are intermittent and lack flexibility, posing challenges to balancing supply and demand. Various technical issues are explored, such as voltage fluctuations, frequency variation, power quality issues like harmonics. Solutions discussed include using inverters with voltage regulation modes, frequency ride-through systems, and distributing generation sources across three phases. The document advocates for grid-tied renewable systems and the development of new technologies to better integrate intermittent renewables at high penetration levels.
concept of resilience and self healing in smart gridKundan Kumar
The document discusses concepts related to resilience and self-healing in smart grids. It defines a smart grid as an electrical grid using communications technologies to improve efficiency. Key functions include enabling customer participation and accommodating different generation options. Self-healing is the ability of a system to automatically restore itself without human intervention. For the electrical grid, this means timely detection of issues and minimizing loss of service through reconfiguring resources. The transmission and distribution components can be modeled using graph theory to analyze resilience. Automatic meter reading is one approach for distribution grids.
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.
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.
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.
This document discusses the key components and types of AC power transmission systems. It begins with an introduction that describes how electrical energy generated at power plants is transmitted through transmission lines to consumers. It then provides a single line diagram showing the steps of increasing voltage for transmission and decreasing it for distribution. The main types of transmission line systems are described as single phase, two phase, and three phase AC systems, as well as DC systems. Finally, the key elements of transmission lines are outlined, including conductors, transformers, insulators, support towers, and protective devices.
Exp 3 (1)3. To Formulate YBUS Matrix By Singular Transformation.Shweta Yadav
The document describes formulating a YBUS matrix for a power system network model using MATLAB. It presents the theory behind developing the bus admittance matrix YBUS using Kirchhoff's current law and singular transformation. An example 4-bus power system is given, and the student is asked to calculate the YBUS matrix with and without a dotted transmission line connected.
This document discusses issues related to connecting renewable energy sources to the electric grid. It notes that renewable resources like wind and solar are intermittent and lack flexibility, posing challenges to balancing supply and demand. Various technical issues are explored, such as voltage fluctuations, frequency variation, power quality issues like harmonics. Solutions discussed include using inverters with voltage regulation modes, frequency ride-through systems, and distributing generation sources across three phases. The document advocates for grid-tied renewable systems and the development of new technologies to better integrate intermittent renewables at high penetration levels.
concept of resilience and self healing in smart gridKundan Kumar
The document discusses concepts related to resilience and self-healing in smart grids. It defines a smart grid as an electrical grid using communications technologies to improve efficiency. Key functions include enabling customer participation and accommodating different generation options. Self-healing is the ability of a system to automatically restore itself without human intervention. For the electrical grid, this means timely detection of issues and minimizing loss of service through reconfiguring resources. The transmission and distribution components can be modeled using graph theory to analyze resilience. Automatic meter reading is one approach for distribution grids.
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 emerging facts about STATCOM (Static Synchronous Compensator) controllers. It describes that a STATCOM is a voltage source converter that produces synchronized AC output voltages using a DC voltage input to compensate for reactive power. It can improve dynamic voltage control, power oscillation damping, transient stability, voltage flicker control, and control of both reactive and active power. The STATCOM structure uses encapsulated electronic converters in a small footprint to minimize environmental impact. It can independently generate or absorb reactive power depending on the magnitude of its output voltage compared to the line voltage.
This slide presents an introduction to microgrid. This is the second class for the subject 'Distribution Generation and Smart Grid'. Class wise I will provide all the discussions and analysis.
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 .
This document discusses traction motors and their control. It describes the desirable characteristics of traction motors, including high starting torque, simple speed control, and self-relieving properties. It evaluates the suitability of DC series motors, AC series motors, and linear induction motors for traction applications. It also examines speed control methods for DC traction motors like series parallel control, transition methods, regenerative braking, and the self-relieving property of DC series motors. Numerical examples are provided on series parallel control and regenerative braking.
This document presents an overview of reactive power compensation. It defines reactive power compensation as managing reactive power to improve AC system performance. There are two main aspects: load compensation to increase power factor and voltage regulation, and voltage support to decrease voltage fluctuations. Several methods of reactive power compensation are discussed, including shunt compensation using capacitors and reactors, series compensation, static VAR compensators (SVCs), static compensators (STATCOMs), and synchronous condensers. SVC and STATCOM technologies are compared, with STATCOMs having advantages of smaller components, better control, and transient response.
OVERVIEW
WHAT IS SMART GRID?
NEED OF SMART GRID IN INDIAN CONTEXT.
SMART GRID ATTRIBUTES.
INDIAN GOVERNMENT INTIATIVE TOWARDS SMART GRID
SMART GRID PROJECTS IN INDIA.
INDIAN GOVT. APPROVED PROJECTS.
PRESENT STATUS OF PROJECTS
BARRIERS TO SMART GRID IMPLEMETATION
LAYOUT OF SMARTGRID
CONCLUSION
REFRERENCES
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.
The document discusses various braking methods for induction motors, including regenerative braking, plugging, and different types of dynamic braking. Regenerative braking occurs when the rotor speed exceeds synchronous speed, causing power to flow in the reverse direction. Plugging involves reversing the phase sequence of the supply to change operation from motoring to braking. Dynamic braking disconnects one phase of the supply or connects the motor to a DC supply, causing the motor to act as a generator and dissipate energy as heat.
The document summarizes different types of excitation systems used for synchronous generators. It describes the components and operation of static excitation systems, which are now widely used. Static excitation systems provide fast acting voltage control using thyristor bridges and power electronics. They allow high response ratios of 3-5 compared to older systems like DC excitation. The key components of a static excitation system are the rectifier transformer, SCR bridges, excitation start up equipment, field discharge equipment, and regulator/control circuits.
MicroGrid and Energy Storage System COMPLETE DETAILS NEW PPT Abin Baby
A microgrid is a localized grouping of electricity generation, energy storage, and loads that normally operates connected to a traditional centralized grid (macrogrid). This single point of common coupling with the macrogrid can be disconnected. The microgrid can then function autonomously. Generation and loads in a microgrid are usually interconnected at low voltage. From the point of view of the grid operator, a connected microgrid can be controlled as if it were one entity.
Microgrid generation resources can include fuel cells, wind, solar, or other energy sources. The multiple dispersed generation sources and ability to isolate the microgrid from a larger network would provide highly reliable electric power. Produced heat from generation sources such as micro turbines could be used for local process heating or space heating, allowing flexible trade off between the needs for heat and electric power.
Role of storage in smart grid
Different types of storage technologies
USE OF BATTERIES IN GRID
TYPES OF BATTERIES
SMES {SUPERCONDUCTING MAGNETIC ENERGY STORAGE}
Communication, Measurement and Monitoring Technologies for Smart Grid
Real time pricing
Smart Meters
CLOUD Computing
cyber security for smart grid
Phasor Measurement Units (PMU)
The document discusses the basic types of FACTS (Flexible AC Transmission System) controllers, including series controllers that inject voltage in series with a line, shunt controllers that inject current, and combined series-shunt controllers. FACTS controllers are used to control power flow and improve voltage profiles by injecting currents and voltages. The choice of controller depends on the desired control over current, power flow, damping of oscillations, and improvement of voltage.
This document discusses energy efficient motors and provides details on various factors that affect their efficiency. It describes how energy efficient motors have efficiencies 4-6% higher than standard motors due to design improvements that reduce losses. These improvements include using more copper to lower resistance, thinner steel laminations, and optimized slots. The document also covers motor loading calculations, effects of voltage variations, the importance of proper maintenance during energy audits, and methods for improving power factor and controlling motor speed to match varying loads.
The document discusses power flow in transmission lines, explaining that the flow of active and reactive power can be controlled by varying factors like the voltage magnitudes at each end, the phase angle difference between the voltages, and the reactance of the transmission line. It provides diagrams to illustrate how active power flow is affected by these parameters and how controlling devices can regulate power flow through injection of voltages in series with the transmission line.
Power quality conditioners are devices used in smart grids to improve the quality of power delivered to loads. They ensure efficient power transfer, isolate grids from disturbances, convert DC to AC, and integrate with energy storage. Common types include distribution static compensators (DSTATCOMs), active power filters, and unified power quality conditioners (UPQCs). DSTATCOMs regulate voltage and compensate for reactive power. Active power filters compensate for harmonics and reactive power. UPQCs combine series and shunt filters to compensate for both voltage and current issues. Power quality conditioners are important for integrating renewable energy and ensuring loads function properly in smart grids.
The document discusses permanent magnet brushless DC motors, including their construction with a permanent magnet rotor, electronic commutation instead of a mechanical commutator, and applications in automotive, industrial, computer and small appliance uses. It provides details on the operation, classifications based on pole arc and waveform, and common controller circuits used for permanent magnet brushless DC motors.
The document discusses the electricity sector in India. It provides details on the current installed power capacity in India as of 2011-12, which includes thermal, hydro, nuclear, solar, wind, biomass and other sources. It also discusses the smart grid system which enables two-way communication between utilities and consumers to efficiently deliver power. Key components of a smart grid discussed include smart meters, distribution intelligence, and ability of appliances to communicate with the smart grid and each other. Technical issues in implementing a smart grid like proper network laying, short circuits, overloading etc. are also summarized.
input output characteristics of thermal plantmathamramesh
This document discusses key characteristics of thermal power plants, including:
1. Input-output characteristics, which is a fundamental curve that plots the plant's fuel input in Btu/hour versus power output in MW.
2. Heat rate characteristics, which is the ratio of fuel input to energy output measured in Btu/KWh, and is the slope of the input-output curve. A lower heat rate means higher fuel efficiency.
3. Incremental fuel rate and cost curves, where incremental fuel rate is the change in fuel input divided by the change in output, and incremental cost is the product of incremental fuel rate and fuel cost per unit.
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.
This document provides an overview of economic dispatch and unit commitment in power systems. It discusses:
1. Economic dispatch is the process of determining generator outputs to meet demand at minimum cost, taking into account generator costs and constraints. It can be solved graphically or using the KKT conditions.
2. Unit commitment determines which generators will operate over different time periods to meet forecasted load at minimum cost, while considering generator operating constraints like minimum up/down times. It is solved using techniques like mixed integer programming and Lagrangian relaxation.
3. Mixed integer programming and Lagrangian relaxation are commonly used optimization methods for unit commitment. Mixed integer programming formulates it as an optimization problem with discrete and continuous variables.
The document discusses the economic operation of power systems. It defines economic operation as distributing load among generating units and plants in a way that minimizes costs while meeting demand. This involves two aspects: economic dispatch, which determines the most cost-effective output of each plant; and accounting for transmission losses to minimize total delivered costs. Methods described include using incremental cost curves to distribute load optimally and representing losses as a function of outputs. The document also covers unit commitment, which determines the optimal startup and shutdown schedule of plants over time.
The document discusses emerging facts about STATCOM (Static Synchronous Compensator) controllers. It describes that a STATCOM is a voltage source converter that produces synchronized AC output voltages using a DC voltage input to compensate for reactive power. It can improve dynamic voltage control, power oscillation damping, transient stability, voltage flicker control, and control of both reactive and active power. The STATCOM structure uses encapsulated electronic converters in a small footprint to minimize environmental impact. It can independently generate or absorb reactive power depending on the magnitude of its output voltage compared to the line voltage.
This slide presents an introduction to microgrid. This is the second class for the subject 'Distribution Generation and Smart Grid'. Class wise I will provide all the discussions and analysis.
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 .
This document discusses traction motors and their control. It describes the desirable characteristics of traction motors, including high starting torque, simple speed control, and self-relieving properties. It evaluates the suitability of DC series motors, AC series motors, and linear induction motors for traction applications. It also examines speed control methods for DC traction motors like series parallel control, transition methods, regenerative braking, and the self-relieving property of DC series motors. Numerical examples are provided on series parallel control and regenerative braking.
This document presents an overview of reactive power compensation. It defines reactive power compensation as managing reactive power to improve AC system performance. There are two main aspects: load compensation to increase power factor and voltage regulation, and voltage support to decrease voltage fluctuations. Several methods of reactive power compensation are discussed, including shunt compensation using capacitors and reactors, series compensation, static VAR compensators (SVCs), static compensators (STATCOMs), and synchronous condensers. SVC and STATCOM technologies are compared, with STATCOMs having advantages of smaller components, better control, and transient response.
OVERVIEW
WHAT IS SMART GRID?
NEED OF SMART GRID IN INDIAN CONTEXT.
SMART GRID ATTRIBUTES.
INDIAN GOVERNMENT INTIATIVE TOWARDS SMART GRID
SMART GRID PROJECTS IN INDIA.
INDIAN GOVT. APPROVED PROJECTS.
PRESENT STATUS OF PROJECTS
BARRIERS TO SMART GRID IMPLEMETATION
LAYOUT OF SMARTGRID
CONCLUSION
REFRERENCES
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.
The document discusses various braking methods for induction motors, including regenerative braking, plugging, and different types of dynamic braking. Regenerative braking occurs when the rotor speed exceeds synchronous speed, causing power to flow in the reverse direction. Plugging involves reversing the phase sequence of the supply to change operation from motoring to braking. Dynamic braking disconnects one phase of the supply or connects the motor to a DC supply, causing the motor to act as a generator and dissipate energy as heat.
The document summarizes different types of excitation systems used for synchronous generators. It describes the components and operation of static excitation systems, which are now widely used. Static excitation systems provide fast acting voltage control using thyristor bridges and power electronics. They allow high response ratios of 3-5 compared to older systems like DC excitation. The key components of a static excitation system are the rectifier transformer, SCR bridges, excitation start up equipment, field discharge equipment, and regulator/control circuits.
MicroGrid and Energy Storage System COMPLETE DETAILS NEW PPT Abin Baby
A microgrid is a localized grouping of electricity generation, energy storage, and loads that normally operates connected to a traditional centralized grid (macrogrid). This single point of common coupling with the macrogrid can be disconnected. The microgrid can then function autonomously. Generation and loads in a microgrid are usually interconnected at low voltage. From the point of view of the grid operator, a connected microgrid can be controlled as if it were one entity.
Microgrid generation resources can include fuel cells, wind, solar, or other energy sources. The multiple dispersed generation sources and ability to isolate the microgrid from a larger network would provide highly reliable electric power. Produced heat from generation sources such as micro turbines could be used for local process heating or space heating, allowing flexible trade off between the needs for heat and electric power.
Role of storage in smart grid
Different types of storage technologies
USE OF BATTERIES IN GRID
TYPES OF BATTERIES
SMES {SUPERCONDUCTING MAGNETIC ENERGY STORAGE}
Communication, Measurement and Monitoring Technologies for Smart Grid
Real time pricing
Smart Meters
CLOUD Computing
cyber security for smart grid
Phasor Measurement Units (PMU)
The document discusses the basic types of FACTS (Flexible AC Transmission System) controllers, including series controllers that inject voltage in series with a line, shunt controllers that inject current, and combined series-shunt controllers. FACTS controllers are used to control power flow and improve voltage profiles by injecting currents and voltages. The choice of controller depends on the desired control over current, power flow, damping of oscillations, and improvement of voltage.
This document discusses energy efficient motors and provides details on various factors that affect their efficiency. It describes how energy efficient motors have efficiencies 4-6% higher than standard motors due to design improvements that reduce losses. These improvements include using more copper to lower resistance, thinner steel laminations, and optimized slots. The document also covers motor loading calculations, effects of voltage variations, the importance of proper maintenance during energy audits, and methods for improving power factor and controlling motor speed to match varying loads.
The document discusses power flow in transmission lines, explaining that the flow of active and reactive power can be controlled by varying factors like the voltage magnitudes at each end, the phase angle difference between the voltages, and the reactance of the transmission line. It provides diagrams to illustrate how active power flow is affected by these parameters and how controlling devices can regulate power flow through injection of voltages in series with the transmission line.
Power quality conditioners are devices used in smart grids to improve the quality of power delivered to loads. They ensure efficient power transfer, isolate grids from disturbances, convert DC to AC, and integrate with energy storage. Common types include distribution static compensators (DSTATCOMs), active power filters, and unified power quality conditioners (UPQCs). DSTATCOMs regulate voltage and compensate for reactive power. Active power filters compensate for harmonics and reactive power. UPQCs combine series and shunt filters to compensate for both voltage and current issues. Power quality conditioners are important for integrating renewable energy and ensuring loads function properly in smart grids.
The document discusses permanent magnet brushless DC motors, including their construction with a permanent magnet rotor, electronic commutation instead of a mechanical commutator, and applications in automotive, industrial, computer and small appliance uses. It provides details on the operation, classifications based on pole arc and waveform, and common controller circuits used for permanent magnet brushless DC motors.
The document discusses the electricity sector in India. It provides details on the current installed power capacity in India as of 2011-12, which includes thermal, hydro, nuclear, solar, wind, biomass and other sources. It also discusses the smart grid system which enables two-way communication between utilities and consumers to efficiently deliver power. Key components of a smart grid discussed include smart meters, distribution intelligence, and ability of appliances to communicate with the smart grid and each other. Technical issues in implementing a smart grid like proper network laying, short circuits, overloading etc. are also summarized.
input output characteristics of thermal plantmathamramesh
This document discusses key characteristics of thermal power plants, including:
1. Input-output characteristics, which is a fundamental curve that plots the plant's fuel input in Btu/hour versus power output in MW.
2. Heat rate characteristics, which is the ratio of fuel input to energy output measured in Btu/KWh, and is the slope of the input-output curve. A lower heat rate means higher fuel efficiency.
3. Incremental fuel rate and cost curves, where incremental fuel rate is the change in fuel input divided by the change in output, and incremental cost is the product of incremental fuel rate and fuel cost per unit.
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.
This document provides an overview of economic dispatch and unit commitment in power systems. It discusses:
1. Economic dispatch is the process of determining generator outputs to meet demand at minimum cost, taking into account generator costs and constraints. It can be solved graphically or using the KKT conditions.
2. Unit commitment determines which generators will operate over different time periods to meet forecasted load at minimum cost, while considering generator operating constraints like minimum up/down times. It is solved using techniques like mixed integer programming and Lagrangian relaxation.
3. Mixed integer programming and Lagrangian relaxation are commonly used optimization methods for unit commitment. Mixed integer programming formulates it as an optimization problem with discrete and continuous variables.
The document discusses the economic operation of power systems. It defines economic operation as distributing load among generating units and plants in a way that minimizes costs while meeting demand. This involves two aspects: economic dispatch, which determines the most cost-effective output of each plant; and accounting for transmission losses to minimize total delivered costs. Methods described include using incremental cost curves to distribute load optimally and representing losses as a function of outputs. The document also covers unit commitment, which determines the optimal startup and shutdown schedule of plants over time.
Advanced Optimization of Single Area Power Generation System using Adaptive F...IRJET Journal
This document summarizes research on optimizing a single area power generation system using adaptive fuzzy logic and PI control. It first describes modeling an uncontrolled single area power system in state space representation and simulating its output response. It then discusses adding a PI controller combined with an adaptive fuzzy logic controller to improve the system's steady state output response in terms of undershoot, settling time, and steady state error. Simulation results show this combined controller approach optimizes the system effectively by achieving a settling time of 2.5 seconds, zero steady state error, and 0.03% undershoot.
Iaetsd design of fuzzy self-tuned load frequency controller for power systemIaetsd Iaetsd
This document describes a self-tuning fuzzy controller designed for load frequency control (LFC) in a multi-machine power system. Conventional PID gains are first obtained using ant colony system optimization. These gains are then used to design fuzzy controller gains to solve the LFC problem under different loading conditions and non-linearities like generation rate constraints. The proposed self-tuning fuzzy controller is tested on a practical thermal and hydel power system and shown to perform better than conventional integral and ACS-PID controllers in dealing with system uncertainties and changing operating conditions.
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.
This document presents a traditional approach called the lambda iteration method to solve the economic load dispatch (ELD) problem considering generator constraints. The ELD problem aims to minimize the total fuel cost while meeting demand and generator constraints. The lambda iteration method is implemented on a three-unit and six-unit system, with and without transmission losses, in MATLAB. The results show that considering transmission losses provides a more accurate solution to the ELD problem compared to ignoring losses. The lambda iteration method provides an effective traditional technique for solving the ELD problem.
This document summarizes a study that optimizes PID controller parameters for load frequency control in a four-area interconnected power system using particle swarm optimization. The four-area system includes thermal, thermal with reheat, hydro, and gas power plants. PID controllers are used for each area. Particle swarm optimization is used to minimize the integral of squared error performance index by optimizing the PID parameters. Simulation results in MATLAB/Simulink demonstrate improved regulation of frequency deviations and tie-line power flows with the optimized PID controllers.
Optimal Unit Commitment Based on Economic Dispatch Using Improved Particle Sw...paperpublications3
The document presents an improved particle swarm optimization (IPSO) algorithm for solving the optimal unit commitment problem in power systems. The IPSO algorithm extends the standard PSO algorithm by using additional particle information to control mutation and mimic social behaviors. The algorithm was implemented on the IEEE 14 bus test system in MATLAB. Results showed the IPSO approach committed units to meet load demand over 24 hours while satisfying constraints, with bus voltages maintained between 1.0017 and 1.0751 per unit. Total costs including fuel, startup, and shutdown costs were minimized at each hour.
Parallel distribution compensation PID based on Takagi-Sugeno fuzzy model app...IJECEIAES
This paper presents a new technique for a Takagi-Sugeno (TS) fuzzy parallels distribution compensation-PID'S (TSF-PDC-PID'S) to improve the performance of egyptian load frequency control (ELFC). In this technique, the inputs to a TS fuzzy model are the parameters of the change of operating points. The TS fuzzy model can definite the suitable PID control for a certain operating point. The parameters of PID'S controllers are obtained by ant colony optimization (ACO) technique in each operating point based on an effective cost function. The system controlled by the proposed TSF-PDCPID’S is investigated under different types of disturbances, uncertainty and parameters variations. The simulation results ensure that the TSF-PDC-PID'S can update the suitable PID controller at several operating points so, it has a good dynamic response under many types of disturbances compared to fixed optimal PID controller.
Comprehensive Approach Towards Modelling and Simulation of Single Area Power...IRJET Journal
This document describes modeling and simulation of a single area power generation system using MATLAB. It begins by developing a state space model of the open loop system. Simulation shows large undershoot, long settling time, and steady state error. Then, a PI controller is added to improve the response. The controlled system is stabilized using LQR design. Simulation results show the PI controlled system has a settling time of 0.7 seconds, zero steady state error, and 5.45% undershoot, meeting control objectives.
The document describes using a Proportional Integral Derivative (PID) controller tuned with Internal Model Control (IMC) technique for Automatic Load Frequency Control (LFC) of a two area power system. It presents the system model of a two area power system and derives the control equations. It then discusses designing an IMC-PID controller for LFC by first designing an IMC controller and transforming it into an equivalent PID structure. Simulation results show the IMC-PID controller provides better stability and dynamic response for LFC compared to a conventional integral controller.
1) The document presents a framework for automatic generation control (AGC) in a two-area restructured power system with non-linear governor characteristics, including hydro-hydro systems.
2) It models the addition of a frequency stabilizer equipped with an energy storage system to stabilize frequency and tie-line power oscillations under disturbances.
3) The gains of controllers and parameters of the stabilizer are optimized using genetic algorithms. Simulations show the response of the optimized load frequency controller under different transactions in the restructured electricity market.
This chapter deals with the power system operation of different power system parts which includes the generation, transmission and distribution systems. This slide is specifically prepared for ASTU 5th year power and control engineering students.
IRJET- Speed Control of Induction Motor using Hybrid PID Fuzzy ControllerIRJET Journal
This document presents a study on using a hybrid PID fuzzy controller with a BAT optimization algorithm to control the speed of an induction motor. It begins with background on PID controllers and fuzzy logic controllers. It then proposes using a BAT algorithm to select the Kp and Ki parameters of a PI controller to regulate motor speed. The results show that the proposed BAT-PID controller reduces speed fluctuations and settling time compared to a traditional PID controller. In conclusion, the hybrid fuzzy-PID controller with BAT optimization improves induction motor speed control.
This document provides an overview of power system analysis and components. It discusses:
1. The key components of a power system including generation, transmission, distribution, and utilization.
2. The advantages of an interconnected power system such as increased reliability and reduced reserve capacity requirements.
3. Common symbols used to represent power system components like generators, transformers, and transmission lines.
4. Concepts involved in power system analysis including per unit systems, impedance and reactance diagrams, and bus admittance matrices.
This document summarizes the principles of economic dispatch and unit commitment in power systems. Economic dispatch determines the optimal power output of each generating unit to minimize the overall fuel costs while meeting the system load. The key points are:
1) The output of each generating unit is determined such that all units have equal incremental costs, as this minimizes total generation costs for a given load.
2) The incremental cost curve of each unit is derived from its input-output curve and fuel cost function.
3) Mathematical techniques like Lagrangian multipliers are used to solve the economic dispatch problem of allocating load between multiple units to equalize incremental costs while meeting the total demand.
This project was developed for an Embedded systems class: we implemented a PID controller for a mechanical inverted pendulum. It was very interesting to experiment in practice with a simple control plant.
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2. ELECTRIC POWER SYSTEM OPERATION
Operational objectives of a power system have been to provide a continuous
quality service with minimum cost to the user. These objectives are:
First Objective: Supplying the energy user with quality service, i.e., at
acceptable voltage and frequency
Second Objective: Meeting the first objective with acceptable impact upon the
environment.
Third Objective: Meeting the first and second objectives continuously, i.e.,
with adequate security and reliability.
Fourth Objective: Meeting the first, second, and third objectives with
optimum economy, i.e., minimum cost to the energy user.
The term “continuous service” can be translated to mean “secure and reliable
service”. 2
3. INTEGRATED OBJECTIVES
Interrelated objectives of operation of a power system
The direction of the arrows indicates the priority in which the objectives are
implemented
Economically constrained operation of a power system.
3
4. ELECTRIC POWER SYSTEM OPERATIONS
Task division:
Operations planning
Operations control
Operations accounting
Interrelated tasks of planned scheduling operation 4
5. OPERATION PLANNING
The facilities of a large power system consist of many generating units,
transmission lines, transformers, circuit breakers, DC/DC converters & DC/ AC
converters which are to scheduled for orderly operation & maintenance.
The energy resources of a large power system consist of hydro, nuclear, fossil
power and renewable energy sources such as wind farm, photovoltaic and
micro turbines.
These facilities are to be managed and utilized to satisfy load demand of a
power system.
The load demand of a power system is cyclic in nature and has a daily peak
demand over a week period, weekly peak demand over a month period, and
monthly peak demand over a year period.
Overall objectives of planned scheduling operation are to manage facilities and
optimize resources for satisfying the peak demand of each load cycle, such that
the total cost of operation is minimized. 5
6. OPERATION CONTROL
The primary functions of operations control are satisfying the instantaneous load
on a second-to-second and minute-to-minute basis.
Some of the functions are:
Economic Dispatch Calculation (EDC)
Load Frequency Control
On-Line Load Flow
Operating Reserve Calculation (ORC)
6
7. OPERATION CONTROL Contd…
Economic Dispatch Calculation:
Economic dispatch calculation of a power system determines the loading of
each generator on a minute-by-minute basis so as to minimize the operating
costs.
Load Frequency Control (LFC):
This function is also referred to as governor response.
As the load demand of the power system increases, the speed of generators will
decrease and this will reduce the system frequency.
Similarly, as system load demand decreases, the speed of the system generators
would increase and this will increase the system frequency.
The power system frequency control must be maintained for the power system
grid to remain stable. 7
8. OPERATION CONTROL Contd…
Online Load Flow (OLF):
This function generally utilizes the output of network topology.
It is the real time network model, and the bus injections from state estimation
for purpose of security monitoring, security analysis and penalty factor
calculations.
This function performs “if then condition” to determine the possible system
states (voltages) in face of system outages such as loss of a line due to weather
condition or sudden loss of a generator.
Operating Reserve Calculation:
The objective of operating reserve calculation is to calculate the actual reserve
carried by each unit and to check whether or not there is a sufficient reserve in
a system.
The operating reserve consists of spinning reserve (synchronized), non-
spinning reserve (non-synchronized), and interruptible load. 8
9. UNIT-1:ECONOMIC LOAD DISPATCH(ELD)
Difference between LFA & ELD:
In Load Flow Analysis (LFA), for a particular load, generation is fixed at all
generators except slack bus.
In Economic Load Dispatch, for a particular load, generation is not fixed for all
the generators but they operated under certain limits.
Scheduling:
It is the process of allocation of generation among different generating units.
Economic Scheduling:
It is a cost effective mode of generation in such a way that the overall cost of
generation should be minimum.
9
10. UNIT-1: SYSTEM CONSTRAINTS
The economic power system operation needs to satisfy the following types of
constraints.
Equality constraints: The sum of real power generation of all the various units
must always be equal to the total real power demand on the system.
Inequality constraints: These are classified as two types
1. According to the nature:
i) Hard-type and
ii) Soft-type
10
11. UNIT-1: SYSTEM CONSTRAINTS Contd…
2. According to power system parameters the inequality constraints are.
i) Output power,
ii)Voltage,
iii)Spare Capacity,
iv) Transformer tap position,
v) Transmission line and
vi) Security constraints.
System Variables:
i) Control variables(PG & QG),
ii) Disturbance variables (PD & QD)
iii) State variables (V & δ) 11
12. UNIT-1: STEAM UNIT
A typical boiler-turbine-generator unit is shown in Figure 1.
This unit consists of a single boiler that generates steam to drive a single turbine-
generator set.
The electrical output of this set is connected not only to the electric power
system, but also to the auxiliary power system in the power plant.
A typical steam turbine unit may require 2-6% of the gross output of the unit for
the auxiliary power requirements.
The necessary to drive boiler feed pumps, fans, condenser circulating water
pumps, and so on.
12
Fig. 1 Boiler-turbine-generator unit
13. UNIT-1: CHARACTERISTICS OF STEAM UNIT
Input-Output Characteristics:
Figure 2 shows the input-output characteristic of a steam unit in idealized form.
The input to the unit shown on the ordinate may be either in terms of heat
energy requirements [millions of Btu per hour (MBtu/hr)] or in terms of total
cost per hour (Rs/ hr).
The output is normally the net electrical output of the unit. The characteristic
shown is idealized in that it is presented as a smooth, convex curve.
13
Fig. 2 Input-output curve of a steam turbine generator
14. UNIT-1: CHARACTERISTICS OF STEAM UNIT
Cost Curves:
To convert the input-output curves into cost curves, the fuel input per hour is
multiplied with the cost of the fuel(expressed in Rs./million kCal).
Cost Curves=(kCal*10^6/hr)*(Rs./million kCal)=Rs./hr
Incremental Fuel Cost Curve (IFC):
The IFC is defined as the ratio of a small in the input to the corresponding small
change in the output and it is expressed in Rs./MWh.
14
Fig. 3 Incremental heat (cost) rate characteristic
15. UNIT-1: CHARACTERISTICS OF STEAM UNIT
Incremental Fuel Cost Curve (IFC):
Mathematically, the IFC curve expression can be obtained from the expression
of the cost curve.
cost curve expression is, (2nd degree polynomial)
The IFC is, (linear approximation)
Heat Rate Curve :
The Thermal unit is most efficient at a minimum heat rate
15
2
1
2 i
i
i i i G i
G
C a P b P d
( ) i i
i
i
i i G i G
G
dc IC a P b P
dP
Fig. 4 Net heat rate characteristic of a steam turbine generator unit
16. UNIT-1: OPTIMIZATION PROBLEM
MATHEMATICAL FORMULATION (Neglecting The Transmission Losses):
An optimization problem consists of :
1. Objective function.
2. Constraint equations
Assumptions:
1. Each unit does not violate the inequality constraints
2. Let the Transmission losses are neglected (PL =0)
3. Cost of ith unit is,
The objective function is minimize the overall cost(CT) of production of electrical
energy , let n be the number of units in the system and Ci be the cost of ith unit .
Objective: Min CT = (1) 16
2
1
2 i
i
i i i G i
G
C a P b P d
1
( )
i
n
i G
i
C P
17. UNIT-1: OPTIMIZATION PROBLEM Contd…
The cost is to be minimized subject to the equality constraints.
Subject: (2)
This is a constrained optimization problem that may be attacked formally using
advanced calculus methods that involve the Lagrange function.
In order to establish the necessary conditions for an extreme value of the
objective function, add the constraint function to the objective function after
the constraint function has been multiplied by an undetermined multiplier.
This is known as the Lagrange function and is shown in Eq. 3.
(3)
Take the first derivative of the Lagrange function with respect to each of the
independent variables and set the derivatives equal to zero (variables are N+1)
(4)
Condition for optimality is (5)
Eq.(5) is called an approximate co-ordination equation because losses are neglected.17
1
0
i
n
G D
i
P P
'
1
[ ]
i
n
G D
T
i
P P
C C
'
0
i
G
C
P
i
i
G
C
P
18. UNIT-1: COMPUTATIONAL METHODS
Different types of computational methods for solving the optimization problem.
1. Analytical method when the no of units are small (either 2 or 3)
2. Graphical method
3. Using a digital computer method or λ-iterative method for more no of units.
Algorithm for λ-iterative method :
i) Guess the initial value of λ0 with the use of cost curve equations.
ii) Calculate PGi according to equation (5).
iii) Calculate
iv) Check whether
v) If , set a new value of λ, i.e., and repeat from step (ii)
vi) If , set a new value of λ, i.e., and repeat from step (ii)
vii) Stop . 18
1
i
n
G
i
P
1
i
n
G D
i
P P
1
i
n
G D
i
P P
1 0
1
i
n
G D
i
P P
1 0
19. FLOWCHART WITHOUT LOSSES
19
Increase λ by Δλ
i.e., (λ = λ + Δλ )
Set PGi=PGi(Max)
START
Read n, ai, bi, di, ԑ, PGi(Min), PGi(Max), and Δλ
Choose a suitable value of λ
Set generator count i=1
Compute PGi
Is
PGi > PGi(Max)
Is
PGi < PGi(Min)
Set PGi=PGi(Min)
Yes
Yes
Increment i=i+1
1
A
B
Compute ΔΡ= | ΣΡGi-ΡD|
No
Yes
Check
if i=n?
1
Yes
A
Check
if
ΔΡ<Ԑ
Print power
generations of
all units and
compute cost of
generation
No
Check
if
ΣΡGi> Ρ D
B
Decrease λ by Δλ
i.e., (λ = λ -Δλ )
No
Yes
No
No
20. UNIT-1: OPTIMAL LOAD SHEDDING INCLUDING
TRANSMISSION LOSSES
The mathematical formulation is now stated as:
Objective: Min CT = (1)
The cost is to be minimized subject to the equality constraints.
Subject: (2)
Lagrange function is (3)
The minimum point is obtained when,
(4)
Therefore the condition for optimality is (5)
Eqn(5) is modified as (6)
Eqn(6) is called exact co-ordination equation because losses are co-ordinate the
ITL with IFC .
20
1
( )
i
n
i G
i
C P
1
0
i
n
G L D
i
P P P
'
1
[ ]
i
n
G L D
T
i
P P P
C C
'
(1- ) 0; i=1......n
i i i
i L
g
G G G
C P
C
P P P
i i
i L
G G
C P
P P
i
i
i
G
C L
P
21. UNIT-1: OPTIMAL LOAD SHEDDING Contd…
The term is called the penalty factor of plant i
The minimum operation cost is obtained when the product of the incremental
fuel cost and the penalty factor of all units is the same, when losses are taken.
The approximate expression for loss PL is given by, (7)
Where, Bij is called loss coefficients and the unit is MW-1
The incremental transmission loss (ITL) is given by, (8)
The incremental fuel cost (IFC) is given by, (9)
Substitute Eqn’s (8)&(9) in Eqn(5);we get, (10)
To solve this allocation problem use λ-iterative method with losses considered.
21
1
1-
i
i
L
G
L
P
P
1 1
i j
n n
L G ij G
i j
P P B P
1
2 j
i
n
L
ij G
G j
P B P
P
2 i
i
i
i G i
G
C a P b
P
1( )
1 2
2
j
i
n
i
ij G
j j i
G
i
ii
b
B P
P
a B
22. UNIT-1: OPTIMAL LOAD SHEDDING Contd…
Algorithm for λ-iterative method when losses are considered:
i) Assume a suitable value of λ0 . This value should be more than the largest
intercept of the incremental cost characteristics of the various generators.
ii) Calculate generations (PGi) based on approximate co-ordination Eqn (5).
iii) Calculate generations (PGi) at all buses using Eqn (10), and check if the
difference in power at all generations (PGi) between two consecutive
iterations is less than pre-specified(Ԑ) value. If not repeat from step (ii).
iv) Calculate loss value using Eqn (7), and calculate
v) Check whether change in power ΔΡ ≤ Ԑ, stop the process and calculate the
cost of generations with their values of powers. Otherwise go to next step.
vi) If ,set a new value of λ, i.e., and repeat from step (ii)
vii) If ,set a new value of λ, i.e., and repeat from step (ii)
viii) Stop the process.
22
1
i
n
G L D
i
P P P P
1 0
1 0
0
P
0
P
23. FLOWCHART WITH LOSSES
23
Increase λ by Δλ
i.e., (λ = λ + Δλ )
Set PGi=PGi(Max)
START
Read n, ai, bi, di, ԑ, PGi(Min), PGi(Max), and Δλ
Choose a suitable value of λ
Set generator count i=1
Compute PGi
Is
PGi >
PGi(Max)
Set PGi=PGi(Min)
Yes
Yes
Increment i=i+1
1
B
D
Compute Transmission loss,
PL and check in power
change, ΔΡ= | ΣΡGi- ΡL-ΡD|
No
Yes
Check
if i=n?
Yes
Check
if
ΔΡ<Ԑ
Print power
generations of
all units and
compute cost of
generation
No
Is
ΔΡ>0
Decrease λ by Δλ
i.e., (λ = λ -Δλ )
No
Yes
No
No
Is
PGi <
PGi(Min)
Determine PGi corresponding to IPC
Set iteration count k=1
C
Check if
|Pgi
k –Pgi
k-1|
< Ԑ
Yes
Increment
iteration count k,
k=k+1
A
C
D B A 1
24. UNIT-2: HYDROTHERMAL SHEDULING
The hydrothermal co-ordination is classified into :
i) Long-Term Co-ordination
ii) Short-Term Co-ordination
Long-Range Hydro-Scheduling:
The long-range hydro-scheduling problem involves the long-range forecasting
of water availability and the scheduling of reservoir water releases (i.e.,
“drawdown”) for an interval of time that depends on the reservoir capacities.
Typical long-range scheduling goes anywhere from 1 week to 1 year or several
years.
For hydro schemes with a capacity of impounding water over several seasons,
the long-range problem involves meteorological and statistical analyses.
24
25. UNIT-2: HYDROTHERMAL SHEDULING Contd…
Short-Range Hydro-Scheduling:
Short-range hydro-scheduling (1 day to 1 week) involves the hour-by-hour
scheduling of all generation on a system to achieve minimum production cost
for the given time period.
In such a scheduling problem, the load, hydraulic inflows, and unit
availabilities are assumed known.
A set of starting conditions (e.g., reservoir levels) is given, and the optimal
hourly schedule that minimizes a desired objective, while meeting hydraulic
steam, and electric system constraints, is sought .
25
26. UNIT-2: HYDROTHERMAL SHEDULING Contd…
The factors on which the economic operation of a combined hydro-thermal system
depends on:
i) Load cycle.
ii) Incremental fuel costs (IFC) of thermal power stations.
iii) Expected water inflow in hydro-power stations.
iv) Water head that is a function of water storage in hydro-power stations.
v) Hydro-power generation.
vi) Incremental transmission loss (ITL).
The few important methods for short-term hydro-thermal co-ordination:
i) Constant hydro-generation method.
ii) Constant thermal-generation method.
iii) Maximum hydro-efficiency method.
iv) Kirchmayer’s method. 26
27. UNIT-2: SHORT RANGE HYDRO SHEDULING
Kirchmayer’s method:
In this method equivalent cost of water is used.
Let there be α thermal power stations and (n- α) hydro power stations in a
power system.
Let γj be the equivalent cost in Rupees of one cubic meter of water, and wj be
the water used in cubic meters per hour in power generation in jth hydro station.
Let ci be the cost of power generation in Rs/hr in thermal ith power station.
Then the total cost of power generation would be.
Object: Min CT= (1)
In this total cost CT is minimized subject to the equality constraint.
Subject: (2)
27
1 1
( ) Rs/hr
i
n
i T j j
i j
C P w
1 1
0
i j
n
T H L D
i j
P P P P
28. UNIT-2: SHORT RANGE HYDRO SHEDULING
Contd…
The optimal operating state is determined by the Lagrange method.
The augmented cost function is, (3)
Carrying out the differentiation of Eqn(3), we get conditions for optimality as
W.r.t, Thermal power generation the condition is, (4)
W.r.t, Hdro power generation the condition is, (5)
Solution of Eqn’s(4-5), yields the economically optimum thermal and hydro
power generations.
If transmission losses are neglected the Eqn’s(4-5) reduced to
28
*
1 1
[ ]
i j
n
T H L D
T
i j
P P P P
C C
i i
i L
T T
C P
P P
j j
j L
j
H H
w P
P P
j i
j i
j
H T
w c
P P
29. UNIT-2: LONG RANGE HYDRO SHEDULING
To mathematically formulate the optimal scheduling problem in a hydro-
thermal system.
Few assumptions are to be made for a certain period of operation T (several
years)
i) The storage of a hydro reservoir at the beginning and at the end of period of operation T are
specified.
ii) After accounting for the irrigation purpose, water inflow to the reservoir and load demand on
the system are known deterministically as functions of time with certainties.
The optimization problem here is to determine the water discharge rate q(t) in
m3/sec, so as to minimize the cost of thermal generation.
Object: Min CT= (1)
29
0
( )
t
i
c t dt
30. UNIT-2: LONG RANGE HYDRO SHEDULING Contd…
Subjected to three constraints:
i) The real power balance equation: (2)
ii) Water availability equation: (3)
iii) The real power hydro-generation: (4)
Solution of problem-discretization principle:
This problem is solved by dividing the total time interval T into M subintervals
each of time, ΔT=T/M.
To simplify the analysis, assume that during each subinterval all the variables
remain fixed.
The problem is therefore, redefined as
Objective: (5)
30
( ) ( ) ( ) ( ) 0
T H L D
P t P t P t P t
0 0
'( ) '(0) ( ) ( ) 0
T T
i
W T W W t dt q t dt
( ) ( '( ), ( ))
H
P t f W t q t
1
C ( )
M
m m m
i
T T
m
Min C P
31. UNIT-2: LONG RANGE HYDRO SHEDULING Contd…
Subject to the operating constraints are redined as:
i) Power balance equation is, (6)
ii) Water availability equation is, (7)
iii) Hydro generation in any subinterval can be expressed as:
(8)
where, h0=9.81x10-3h׳0, h׳0 is the height of the storage tank, 0.5(wm-wm-1) is the
average additional height due to storage of water, e is the water head correction
factor and ρ is the no-load discharge of water.
The sum of discharges during (M-1) intervals will give the desired available
discharge and one of the discharges is taken as dependent variable.
31
0
m m m m
T H L D
P P P P
1
0
m
m m m
i q
w w w
1
0{1 0.5 ( )}( )
m m m m
H
p h e w w q
32. UNIT-2: LONG RANGE HYDRO SHEDULING Contd…
Usually q1 is chosen as dependent variable and hence Eqn(7) corresponding to
water availability can be rewritten as
(9)
The problem of economic hydro-thermal scheduling is handled by making use
of Lagrangian multiplier.
The augmented cost function is given as
(10)
The Lagrangian multipliers can be obtained by differentiating the augmented
function w.r.t, dependent variables (PT
m,PH
m ,wm and q1) and equating it to zero.
For minimization of the augmented function, differentiate the augmented
function w.r.t, independent variable (qm) and obtain the gradient vector which
should be zero. 32
1 0
1 2
M M
M m m
i
m m
w q
q w w
* 1
1 2
1
0
3
( ) ( )
{ [1 0.5 ( )( )]}
m m m m m m m
m m m
T i
T H L D
m m m m m
H
c c P P P P w w w q
P h e w w q
33. UNIT-2: LONG RANGE HYDRO SHEDULING
Contd…
The coordination equations are given as:
Where, α is a positive scalar value with a range of 0.4-0.8.
*
1 1 1
(1 ) 0 or (11)
m m
T L T L
m m m
m m m m m
T T T T T
P P
c c
c
P P P P P
*
3 1 1 1 3
(1 ) 0 or (12)
m m
L L
m m m m m
m m m
H H T
P P
c
P P P
* 1 1 1
0 0
2 2 3 3
0( )
[0.5 ( )] [0.5 ( )] 0 (13)
m m m m
m m
m m orM
c h e q h e q
w
* 1 1 1
0 1
0
2 3
1
[1 0.5 (2 2 )] 0 (14)
i
c h e w w q
q
*
1
0
2 3
1
[1 0.5 (2 2 )] (15)
m m m
m m
i
m
m
c h e w w q
q
*
1
(1 ) (16)
m m
new old
m
m
c
q q
q
34. UNIT-2: LONG RANGE HYDRO SHEDULING
Contd…
Algorithm for Long-Term Co-ordination:
i) Assume initial set of independent variables, qm for all sub-intervals except the
first sub-interval.
ii) Obtain the values of dependent variables PT
m,wm , PH
m and q1 using Eqn’s (6),
(7), (8), and (9) respectively.
iii) Obtain the Lagrangian multipliers λ1
m, λ3
m, λ2
1 and λ2
m using Eqn’s(11), (12),
(14), and (13) respectively.
iv) Obtain the gradient vector using equation (15) and check whether all its
elements are close to zero within a specified tolerance, if so the optimal value is
reached; if not, go to the next step.
v) Obtain the new values of control variables using the equation (16), then go to
step (ii) and repeat the process.
35. UNIT-3: UNIT COMMITMENT
The total load of the power system is not constant but varies throughout the day
and reaches a different peak value from one day to another.
Therefore, it is not advisable to run all available units all the time.
So, it is necessary to decide in advance which generators are to
startup/shutdown, and for how long.
The computational procedure for making such decision is called unit
commitment.
Unit commitment means to ‘commit’ a generating unit to ‘turn it on’
In the case of ELD all the available units should be turned on for all the time.
In the case of UC only a best of available units to be turned on to supply the
forecast load of the system over a future time period.
36. UNIT-3: UNIT COMMITMENT
Need for UC:
The plant commitment and unit ordering schedules.
Weekly patterns can be developed from daily schedules, likewise monthly and
annual schedules.
A great deal of money can be saved by turning off the units when they are not
needed for the time.
Constraints in UC:
i) Spinning reserve:
1. low/high frequency
2. islands
3. fast/slow responding units
37. UNIT-3: UNIT COMMITMENT
ii) Thermal unit constraints:
1. Minimum up/down time
2. crew constraints
3. start-up cost: Two approaches are there
Start-up cost when cooling=Cc(1-e-t/α) F+Cf
Start-up cost when banking=Ct × t × F+Cf
Where Cc is cold start cost(MBtu), F is fuel cost, Cf is fixed cost, α is thermal
time constant for the unit, Ct is cost (Mbtu/h) of maintaining unit at operating
temperature, and t is time (h) the unit was cooled
iii) Hydro unit constraints:
1. Must run constraint
2. Fuel constraints
38. UNIT-3: UNIT COMMITMENT
Cost function formulation:
1. Running cost.
2. Start-up cost.
3. Shut-down cost.
The total expression for the cost function is given as:
Unit commitment solution methods:
1. Priority list (PL) schemes.
2. Dynamic programming (DP) method.
3. Lagrange’s relaxation (LR) method.
1 1 1 1 1
t ij i t i t
t
y
N k x
T
T ij G sc i sd i
t i j i i
F C P C C
39. UNIT-3: UNIT COMMITMENT
Priority list method:
The simplest unit commitment solution method consists of creating a priority
list of units.
In this method a simple shut-down rule or priority-list scheme could be obtained
after an exhaustive enumeration of all unit combinations at each load level.
The priority list could be obtained by noting the full-load average production
cost of each unit.
where the full-load average production cost is simply the net heat rate at full
load multiplied by the fuel cost.
The most efficient unit (least average production cost) is loaded first to be
followed by the less efficient units in order as the load decrease.
40. UNIT-3: UNIT COMMITMENT
Dynamic programming approach:
Assumptions in the DP approach:
1. A state consists of an array of units with specified units operating and the rest off-line.
2. The start-up cost of a unit is independent of the time it has been off-line.
3. There are no costs for shutting down a unit.
4. There is a strict priority order, and in each interval a specified minimum amount of
capacity must be operating.
Mathematical representation:
is called recursive relation.
Where, FN(x) be the min cost in Rs,/hr of generation of ‘x’ MW by N no. of units.
and, fN(y) be the cost of generation of ‘y’ MW by Nth unit.
and, FN-1(x-y) be the min cost of generation of ‘x-y’ MW by remaining N-1 units.
1
( ) min{ ( ) ( )}
N N N
y
F x f y F x y
41. UNIT-3: UNIT COMMITMENT
Procedure for preparing the UC table using the DP approach:
Step 1: Start arbitrarily with considerations of any two units.
Step 2: Arrange the combined output of the two units in the form of discrete
load levels.
Step 3: Determine the most economical combination of the two for all the load
levels.
Step 4: Obtain most economical cost curve in discrete form for the two units
and that can be treated as the cost curve of a single equivalent unit.
Step 5: Add the third unit and repeat the procedure to find the cost curve of the
three combined units.
Step 6: Repeat the process till all available units are exhausted.
Advantage of DP approach:
The main advantage is that having obtained the optimal way of loading ‘K’ units, it
is quite easy to determine the optimal way of loading (K+1) units.