This document presents an analysis of transient stability in a dual-machine power system using the swing equation. It begins with introductions to stability, the swing equation, and numerical solution methods. It then discusses steady-state and transient stability analysis using the swing equation for a single machine connected to an infinite bus. Next, it extends the analysis to a multi-machine system and presents the swing equations for a dual-machine system. The document simulations transient stability in a dual-machine system for different fault clearing times and analyzes the results. It concludes that transient stability is affected by fault type and location and presents conclusions about analyzing stability in multi-machine systems.
Transient stability analysis on a multi machine system in psateSAT Journals
Abstract
Modern power system are subject to large disturbances such as three phase short circuit faults. When a fault occurs on a system
the generators rotor angle becomes unstable and thus it losses synchronism with the system and it becomes unstable. Thus
transient stability analysis can be performed on a system in order to understand the generators performance when subjected to a
short circuit fault. When the system is subjected to a fault the generator experiences transient oscillations in rotor speed and
angle which can be effectively suppressed with the incorporation of Automatic Voltage Regulator (AVR) and Power System
Stabilizer (PSS). The simulations have been performed using the MATLAB/PSAT software.
Keywords—Transient stability, Three phase fault Faults, AVR, PSS.
DYNAMIC STABILITY ANALYSIS (Small Signal Stability) – 1
Small-Signal Stability of Multi-machine Systems
Special techniques for analysis of very large systems
Characteristics of Small-Signal Stability Problems
Local problems
Global problems
DYNAMIC STABILITY ANALYSIS – 2
Introduction
Overview of the Proposed Method
Generating Unit
Synchronous Machine
Calculation of Equilibrium State Conditions
Excitation and Governor Control Systems
Excitation System
Turbine-Governor System
Combined Model of Generating Unit
The ability of the power system to maintain synchronous operation when subjected to a severe transient disturbance
faults on transmission circuits, transformers, buses
loss of generation
loss of loads
Response involves large excursions of generator rotor angles: influenced by nonlinear power-angle relationship
Stability depends on both the initial operating state of the system and the severity of the disturbance
Post-disturbance steady-state operating conditions usually differ from pre-disturbance conditions
Steady state stability analysis and enhancement of three machine nine bus pow...eSAT Journals
Abstract
Power System stability study is the important parameter of economic, reliable and secure system planning and operation. Studies
are important during the planning and conceptual design stages of the project as well as during the operating life of the plant
periodically. This paper presents the power system steady state stability analysis for IEEE- 9 bus test system and examines
influence of TCPS FACTS device based controller on test system. It is assumed that system under study has been perturbed from a
steady state equilibrium that prevailed prior to the application of the disturbance. If system is stable, we would expect that for
temporary or permanent disturbance, system will acquire initial or new operating state after a transient period. The stability
study is accessed using Lyapunov’s first method. The effectiveness of damping controller in enhancing the steady state stability is
investigated by incorporating available constraints. For analysis MATLAB software is employed. The conclusions have been
drawn here, based on theoretical and mathematical analysis so as to provide an insight and better understanding of steady state
stability of considered multi machine power system.
Key Words: Lyapunov’s first method, Steady-state stability, Phase portrait, FACTS device, supplementary modulation
controller, eigen value, synchronizing power coefficient, IEEE-9 Bus Test System, Load Flow Study, Differential
algebraic equation.
Objectives: This course will provide a comprehensive overview of power system stability and control problems. This includes the basic concepts, physical aspects of the phenomena, methods of analysis, the integration of MATLAB and SINULINK in the analysis of power system .
Course Content: 1. Power System Stability: Introduction
2. Stability Analysis: Swing Equation
3. Models for Stability Studies
4. Steady State Stability
5. Transient Stability
6. Multimachine Transient Stability
7. Power System Control: Introduction
8. Load Frequency Control
9. Automatic generation Control
10. Reactive Power Control
The control of motor rotation speed by the change of resistor resistance value in armature circuit is called ‘resistor control”. For the regulation of resistance value R0, included in armature winding circuit, we can use various technical solutions. The most used solution is the discrete variation of armature added resistance value by shunting its parts with contactors contacts. Nowadays, the change of resistor resistance in armature circuit can be realized by shunting with a given porosity γ of resistor R0 trough electronic keys. In this paper, we study the design of control system represented on figure 1.
Transient stability analysis on a multi machine system in psateSAT Journals
Abstract
Modern power system are subject to large disturbances such as three phase short circuit faults. When a fault occurs on a system
the generators rotor angle becomes unstable and thus it losses synchronism with the system and it becomes unstable. Thus
transient stability analysis can be performed on a system in order to understand the generators performance when subjected to a
short circuit fault. When the system is subjected to a fault the generator experiences transient oscillations in rotor speed and
angle which can be effectively suppressed with the incorporation of Automatic Voltage Regulator (AVR) and Power System
Stabilizer (PSS). The simulations have been performed using the MATLAB/PSAT software.
Keywords—Transient stability, Three phase fault Faults, AVR, PSS.
DYNAMIC STABILITY ANALYSIS (Small Signal Stability) – 1
Small-Signal Stability of Multi-machine Systems
Special techniques for analysis of very large systems
Characteristics of Small-Signal Stability Problems
Local problems
Global problems
DYNAMIC STABILITY ANALYSIS – 2
Introduction
Overview of the Proposed Method
Generating Unit
Synchronous Machine
Calculation of Equilibrium State Conditions
Excitation and Governor Control Systems
Excitation System
Turbine-Governor System
Combined Model of Generating Unit
The ability of the power system to maintain synchronous operation when subjected to a severe transient disturbance
faults on transmission circuits, transformers, buses
loss of generation
loss of loads
Response involves large excursions of generator rotor angles: influenced by nonlinear power-angle relationship
Stability depends on both the initial operating state of the system and the severity of the disturbance
Post-disturbance steady-state operating conditions usually differ from pre-disturbance conditions
Steady state stability analysis and enhancement of three machine nine bus pow...eSAT Journals
Abstract
Power System stability study is the important parameter of economic, reliable and secure system planning and operation. Studies
are important during the planning and conceptual design stages of the project as well as during the operating life of the plant
periodically. This paper presents the power system steady state stability analysis for IEEE- 9 bus test system and examines
influence of TCPS FACTS device based controller on test system. It is assumed that system under study has been perturbed from a
steady state equilibrium that prevailed prior to the application of the disturbance. If system is stable, we would expect that for
temporary or permanent disturbance, system will acquire initial or new operating state after a transient period. The stability
study is accessed using Lyapunov’s first method. The effectiveness of damping controller in enhancing the steady state stability is
investigated by incorporating available constraints. For analysis MATLAB software is employed. The conclusions have been
drawn here, based on theoretical and mathematical analysis so as to provide an insight and better understanding of steady state
stability of considered multi machine power system.
Key Words: Lyapunov’s first method, Steady-state stability, Phase portrait, FACTS device, supplementary modulation
controller, eigen value, synchronizing power coefficient, IEEE-9 Bus Test System, Load Flow Study, Differential
algebraic equation.
Objectives: This course will provide a comprehensive overview of power system stability and control problems. This includes the basic concepts, physical aspects of the phenomena, methods of analysis, the integration of MATLAB and SINULINK in the analysis of power system .
Course Content: 1. Power System Stability: Introduction
2. Stability Analysis: Swing Equation
3. Models for Stability Studies
4. Steady State Stability
5. Transient Stability
6. Multimachine Transient Stability
7. Power System Control: Introduction
8. Load Frequency Control
9. Automatic generation Control
10. Reactive Power Control
The control of motor rotation speed by the change of resistor resistance value in armature circuit is called ‘resistor control”. For the regulation of resistance value R0, included in armature winding circuit, we can use various technical solutions. The most used solution is the discrete variation of armature added resistance value by shunting its parts with contactors contacts. Nowadays, the change of resistor resistance in armature circuit can be realized by shunting with a given porosity γ of resistor R0 trough electronic keys. In this paper, we study the design of control system represented on figure 1.
Power System Stabilizer with Induction Motor on Inter Area Oscillation of Int...IJMTST Journal
This paper describe the problem of initializing the dynamic models of the induction motor for inter area oscillation of power system studies. To further investigate the effects of dynamic loads on power systems stability, the effectiveness of conventional as well as modern linear controllers is tested and compared with the variation of loads. The effectiveness is assessed based on the damping of the dominant mode and the analysis in this paper highlights the fact that the dynamic load has substantial effect on the system damping. This paper presents an analysis to investigate the critical parameters of the induction motor like inertia and stator and rotor resistance, and reactance which effect of the stability of the system. The examination is showed on the both a standard IEEE 10-machine system with dynamic loads. To further investigate the Power System Stabilizer with Induction Motor on Inter Area Oscillation of Inter Connected by using the MATLAB/SIMLINK Model.
An Application of Ulam-Hyers Stability in DC MotorsIJAPEJOURNAL
In this paper, a generalization to nonlinear systems is proposed and applied to the motor dynamic, rotor model and stator model in DC motor equation. We argue that Ulam-Hyers stability concept is quite significant in design problems and in design analysis for the class of DC motor’s parameters. We prove the stability of nonlinear partial differential equation by using Banach’s contraction principle. As an application, the Ulam-Hyers stability of DC motor dynamics equations is investigated. To the best of our knowledge this is the first time Ulam-Hyers stability is considered from the applications point of view.
Comparison of Different Design Methods for Power System Stabilizer Design - A...ijsrd.com
In the past two decades, the utilization of supplementary excitation control signals for improving the dynamic stability of power systems has received much attention. In recent years, several approaches based on intelligent control and optimization techniques have been applied to PSS design problem. This paper introduces a review on the techniques applied on the conventional PSS design only. Power System Stabilizer (PSS) is the most cost effective approach of increase the system positive damping, improve the steady-state stability margin, and suppress the low-frequency oscillation of the power system. A PSS has to perform well under operating point variations. This paper introduces a review on the techniques applied on the conventional PSS design only. The techniques could be mainly classified into linear and nonlinear.
Design of power system stabilizer for damping power system oscillationsIOSRJEEE
The problem of the poorly damped low-frequency (electro-mechanical) oscillations of power systems has been a matter of concern to power engineers for a long time, because they limit power transfers in transmission lines and induce stress in the mechanical shaft of machines. Due to small disturbances, power systems experience these poorly damped low-frequency oscillations. The dynamic stability of power systems are also affected by these low frequency oscillations. With proper design of Power System Stabilizer (PSS), these oscillations can be well damped and hence the system stability is enhanced. The basic functions of the PSS is to add a stabilizing signal that compensates the oscillations of the voltage error of the excitation system during the dynamic/transient state, and to provide a damping component when it’s on phase with rotor speed deviation of machine. Studies have shown that PSS are designed to provide additional damping torque, for different operation point normal load, heavy load and leading to improve power system dynamic stability.
• Sensorless speed and position estimation of a PMSM (Master´s Thesis)Cesar Hernaez Ojeda
Field Oriented Control (FOC) was chosen to control the motor. A Voltage Switch Inverter (VSI) controls the machine currents using Space Vector Modulation (SVM). Back-EMF method was used to estimate the position and a Phase Locked Loop to estimate the speed. The project was tested experimentally in the laboratory using a Danfoss power converter and dSpace.
Speed Control of The Three Phase Induction Motor via changing the line voltageYazan Yousef
This report introduces a method of speed control of the three-phase induction motor driving a fan using the MATLAB. A MATLAB code and Simulink are used to propose the system and to study the speed control method. The method is to control the speed by changing the line voltage. Moreover, the motor performance especially the torque and power are studied during varying the voltage.
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.
Simulation and Analysis of Modified DTC of PMSMIJECEIAES
This research paper describes the simulation and analysis of the modified DTC for Surface mounted Permanent Magnet Synchronous Motor (SPMSM) using PI controller. Among all of the various drive systems,PMSM is widely used for accurate speed and torque control, with greater efficiency, superior torque to inertia and high power density.The Conventional DTC secheme widely used for this purpose but it is failed to achieve desirable performance of the system for which the modified DTC secheme is propsed.The modified DTC algorithm controls the voltage vectors, directly from a simple look up table depending on outcome of the torque and indirectly flux controllers.The overall drive system can be implemented in SIMULINK/MATLAB environment.The modified DTC is validated with loading conditions.The simulated results are focused on the speed, settling time at loaded conditions, torque and flux linkages ripple and THD in the phase current for modified DTC applied to SPMSM.
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.
Research on the synchronous vibration of the non-integral mechanism under the...IJRES Journal
This article proposes and designs the internal structure of the electrical cabinet which can achieve
the 3-DOF (degrees-of-freedom) motion, and making it in the horizontal vibration environment with excitation
frequency of 12.5Hz.Obtaining vibrational properties of its internal structure through the Simulink simulation
results, which is to said that manipulator and low-voltage electrical appliances are not in the synchronous
conditions. But it is necessary to make it in a state of near synchronization to ensure the accuracy of the reliability
test of the variable load load with low-voltage electrical appliances. On this issue,to achieve the desired results
through the PID feedback control to further optimize.
Speed Control System of Induction Motor by using Direct Torque Control Method...ijtsrd
Escalator is useful and act in the important part to carry passengers to the targeted floors of building. Every escalator must be driven by its own motor and this motor speed must be controled. To drive escalator with a constant speed, direct torque control technique is used to drive three phase squirrel cage induction motor. In this paper, the development of speed control system for three phase squirrel cage induction motor using a direct torque control method is presented and simulation for proposed system is done with the help of MATLAB SIMULINK. Soe Sandar Aung | Thet Naing Htun "Speed Control System of Induction Motor by using Direct Torque Control Method used in Escalator" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd27903.pdfPaper URL: https://www.ijtsrd.com/engineering/electrical-engineering/27903/speed-control-system-of-induction-motor-by-using-direct-torque-control-method-used-in-escalator/soe-sandar-aung
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.
Mathematical model analysis and control algorithms design based on state feed...hunypink
XZ-Ⅱtype rotary inverted pendulum is a typical mechatronic system; it completes real-time motion control using DSP motion controller and motor torque. In this paper, we recognize XZ-Ⅱrotational inverted pendulum and learn system composition, working principle, using method, precautions and software platform. We master how to build mathematical model and state feedback control method (pole assignment algorithm) of the one order rotational inverted pendulum system and finish simulation study of system using Mat lab. In the end we grasp debugging method of the actual system, and finish online control of the one order rotational inverted pendulum system as well.
Power System Stabilizer with Induction Motor on Inter Area Oscillation of Int...IJMTST Journal
This paper describe the problem of initializing the dynamic models of the induction motor for inter area oscillation of power system studies. To further investigate the effects of dynamic loads on power systems stability, the effectiveness of conventional as well as modern linear controllers is tested and compared with the variation of loads. The effectiveness is assessed based on the damping of the dominant mode and the analysis in this paper highlights the fact that the dynamic load has substantial effect on the system damping. This paper presents an analysis to investigate the critical parameters of the induction motor like inertia and stator and rotor resistance, and reactance which effect of the stability of the system. The examination is showed on the both a standard IEEE 10-machine system with dynamic loads. To further investigate the Power System Stabilizer with Induction Motor on Inter Area Oscillation of Inter Connected by using the MATLAB/SIMLINK Model.
An Application of Ulam-Hyers Stability in DC MotorsIJAPEJOURNAL
In this paper, a generalization to nonlinear systems is proposed and applied to the motor dynamic, rotor model and stator model in DC motor equation. We argue that Ulam-Hyers stability concept is quite significant in design problems and in design analysis for the class of DC motor’s parameters. We prove the stability of nonlinear partial differential equation by using Banach’s contraction principle. As an application, the Ulam-Hyers stability of DC motor dynamics equations is investigated. To the best of our knowledge this is the first time Ulam-Hyers stability is considered from the applications point of view.
Comparison of Different Design Methods for Power System Stabilizer Design - A...ijsrd.com
In the past two decades, the utilization of supplementary excitation control signals for improving the dynamic stability of power systems has received much attention. In recent years, several approaches based on intelligent control and optimization techniques have been applied to PSS design problem. This paper introduces a review on the techniques applied on the conventional PSS design only. Power System Stabilizer (PSS) is the most cost effective approach of increase the system positive damping, improve the steady-state stability margin, and suppress the low-frequency oscillation of the power system. A PSS has to perform well under operating point variations. This paper introduces a review on the techniques applied on the conventional PSS design only. The techniques could be mainly classified into linear and nonlinear.
Design of power system stabilizer for damping power system oscillationsIOSRJEEE
The problem of the poorly damped low-frequency (electro-mechanical) oscillations of power systems has been a matter of concern to power engineers for a long time, because they limit power transfers in transmission lines and induce stress in the mechanical shaft of machines. Due to small disturbances, power systems experience these poorly damped low-frequency oscillations. The dynamic stability of power systems are also affected by these low frequency oscillations. With proper design of Power System Stabilizer (PSS), these oscillations can be well damped and hence the system stability is enhanced. The basic functions of the PSS is to add a stabilizing signal that compensates the oscillations of the voltage error of the excitation system during the dynamic/transient state, and to provide a damping component when it’s on phase with rotor speed deviation of machine. Studies have shown that PSS are designed to provide additional damping torque, for different operation point normal load, heavy load and leading to improve power system dynamic stability.
• Sensorless speed and position estimation of a PMSM (Master´s Thesis)Cesar Hernaez Ojeda
Field Oriented Control (FOC) was chosen to control the motor. A Voltage Switch Inverter (VSI) controls the machine currents using Space Vector Modulation (SVM). Back-EMF method was used to estimate the position and a Phase Locked Loop to estimate the speed. The project was tested experimentally in the laboratory using a Danfoss power converter and dSpace.
Speed Control of The Three Phase Induction Motor via changing the line voltageYazan Yousef
This report introduces a method of speed control of the three-phase induction motor driving a fan using the MATLAB. A MATLAB code and Simulink are used to propose the system and to study the speed control method. The method is to control the speed by changing the line voltage. Moreover, the motor performance especially the torque and power are studied during varying the voltage.
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.
Simulation and Analysis of Modified DTC of PMSMIJECEIAES
This research paper describes the simulation and analysis of the modified DTC for Surface mounted Permanent Magnet Synchronous Motor (SPMSM) using PI controller. Among all of the various drive systems,PMSM is widely used for accurate speed and torque control, with greater efficiency, superior torque to inertia and high power density.The Conventional DTC secheme widely used for this purpose but it is failed to achieve desirable performance of the system for which the modified DTC secheme is propsed.The modified DTC algorithm controls the voltage vectors, directly from a simple look up table depending on outcome of the torque and indirectly flux controllers.The overall drive system can be implemented in SIMULINK/MATLAB environment.The modified DTC is validated with loading conditions.The simulated results are focused on the speed, settling time at loaded conditions, torque and flux linkages ripple and THD in the phase current for modified DTC applied to SPMSM.
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.
Research on the synchronous vibration of the non-integral mechanism under the...IJRES Journal
This article proposes and designs the internal structure of the electrical cabinet which can achieve
the 3-DOF (degrees-of-freedom) motion, and making it in the horizontal vibration environment with excitation
frequency of 12.5Hz.Obtaining vibrational properties of its internal structure through the Simulink simulation
results, which is to said that manipulator and low-voltage electrical appliances are not in the synchronous
conditions. But it is necessary to make it in a state of near synchronization to ensure the accuracy of the reliability
test of the variable load load with low-voltage electrical appliances. On this issue,to achieve the desired results
through the PID feedback control to further optimize.
Speed Control System of Induction Motor by using Direct Torque Control Method...ijtsrd
Escalator is useful and act in the important part to carry passengers to the targeted floors of building. Every escalator must be driven by its own motor and this motor speed must be controled. To drive escalator with a constant speed, direct torque control technique is used to drive three phase squirrel cage induction motor. In this paper, the development of speed control system for three phase squirrel cage induction motor using a direct torque control method is presented and simulation for proposed system is done with the help of MATLAB SIMULINK. Soe Sandar Aung | Thet Naing Htun "Speed Control System of Induction Motor by using Direct Torque Control Method used in Escalator" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd27903.pdfPaper URL: https://www.ijtsrd.com/engineering/electrical-engineering/27903/speed-control-system-of-induction-motor-by-using-direct-torque-control-method-used-in-escalator/soe-sandar-aung
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.
Mathematical model analysis and control algorithms design based on state feed...hunypink
XZ-Ⅱtype rotary inverted pendulum is a typical mechatronic system; it completes real-time motion control using DSP motion controller and motor torque. In this paper, we recognize XZ-Ⅱrotational inverted pendulum and learn system composition, working principle, using method, precautions and software platform. We master how to build mathematical model and state feedback control method (pole assignment algorithm) of the one order rotational inverted pendulum system and finish simulation study of system using Mat lab. In the end we grasp debugging method of the actual system, and finish online control of the one order rotational inverted pendulum system as well.
Infinite bus bar is one which keeps constant voltage and frequency although the load varies. Thus it may behave like a voltage source with zero internal impedance and infinite rotational inertia.
Transient stability analysis and enhancement of ieee 9 bus system ecij
System stability study is the important parameter of economic, reliable and secure power system planning and operation. Power system studies are important during the planning and conceptual design stages of the project as well as during the operating life of the plant periodically. This paper presents the power system stability analysis for IEEE- 9 bus test system. The fault is created on different busses and transient stability is analyzedfor different load and generation conditions. The critical clearing time (CCT) is calculated by
using time domain classical extended equal area criterion method. The system frequency and voltage variation is observed for different fault locations and CCT. The IEEE-9 bus test system is simulated and stability is analyzed on ETAP software
Tutorial: Introduction to Transient Analysis with PowerFactory. This tutorial is a simple introduction to transient simulation using DIgSILENT PowerFactory
Classification Of Power System StabilityAravind Shaji
The Slide Deals With Power System Stability. Contents Include
Power System Stability Overview
Power System Stability: A Proposed Definition
Need of Stability Classification
Classification of stability
Power System Stability Classification
Rotor Angle Stability
Voltage Stability
Frequency Stability
Rotor Angle Stability vs. Voltage Stability
References
Transient Stability Assessment and Enhancement in Power SystemIJMER
Power system is subjected to sudden changes in load levels. Stability is an important concept
which determines the stable operation of power system. For the improvement of transient stability the
general methods adopted are fast acting exciters, circuit breakers and reduction in system transfer
reactance. The modern trend is to employ FACTS devices in the existing system for effective utilization
of existing transmission resources. The critical clearing time is a measure to assess transient instability.
Using PSAT, the critical clearing time (CCT) corresponding to various faults are calculated. The most
critical faults were identified using this calculation. The CCT for the critical faults were found to change
with change in operating point. The CCT values are predicted using Artificial Neural Network (ANN) to
study the training effects of ANN. TCSC is selected as the FACTS device for transient stability
enhancement. Particle Swarm Optimization method is used to find the optimal position of TCSC using
the objective function real power loss minimization. The result shows that the technique effectively
increases the transient stability of the system
In electric power systems that serve the load continuously should the voltage and frequency must remain constant, but if there is interference on one of the generators or the rail, then it is undeniable there will be disruption to the power supply. It is necessary to conduct a Research on the Stability of Power Systems relating to the Determination of Critical Breaking Angle and Critical Breaker Time on the generator, to find out how much the Critical Breaker Angle and how much
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.
This presentation begins with a discussion of the generator as a source feeding a very large remote system (the "single-machine infinite-bus" representation).
Delve into the heart of power system dynamics with our comprehensive PowerPoint presentation on the "Swing Equation." If you're involved in power system operation and control, an electrical engineering student, or simply intrigued by the complexities of managing the electric grid, this presentation is a must-see.
Introduction to Power System Stability: Gain a fundamental understanding of why power system stability is crucial for reliable electrical energy supply.
The Swing Equation Explained: Learn what the Swing Equation is and why it plays a central role in power system stability analysis.
Synchronous Machines: Explore the role of synchronous machines in power generation and their critical impact on system dynamics.
Rotational Inertia and Angular Velocity: Understand the concepts of rotational inertia and angular velocity and how they relate to power system behavior.
Generator Response to Disturbances: Discover how generators respond to faults, load changes, and other disturbances, affecting system stability.
Equations and Formulas: Get a detailed look at the mathematical representations and formulas behind the Swing Equation.
Numerical Simulations: Witness practical examples and numerical simulations to grasp the real-world application of the Swing Equation.
Impact on Control Strategies: Understand how power system operators use the Swing Equation to develop control strategies for maintaining stability.
Case Studies: Explore real-world case studies where the Swing Equation has played a critical role in power system control and protection.
Future Challenges and Developments: Peek into the evolving landscape of power system operation and control, and how the Swing Equation adapts to modern challenges.
Transient Stability Analysis of IEEE 9 Bus System in Power World SimulatorIJERA Editor
It is widely accepted that transient stability is an important aspect in designing and upgrading electric power
system.
The objective of this paper was to investigate and understand the stability of power system
In this paper, modelling and transient stability analysis of IEEE 9 bus system was performed using POWER
WORLD SIMULATOR. The load flow studies were performed to determine pre-fault conditions in the system
using Newton-Raphson method. With the help of three-phase balanced fault, the variations in power angle and
frequency of the system were studied. Frequency is a reliable indicator if deficiency condition in the power
systems exists or not. For three-phase balanced fault, fast fault clearing time was analysed to bring back the
system to the stability. Further, comparison between Runga method and Euler method for better results was
performed. Hence, impact of load switching on system was also computed so as to bring system to steady state.
Transient Stability Analysis of IEEE 9 Bus System in Power World SimulatorIJERA Editor
It is widely accepted that transient stability is an important aspect in designing and upgrading electric power
system.
The objective of this paper was to investigate and understand the stability of power system
In this paper, modelling and transient stability analysis of IEEE 9 bus system was performed using POWER
WORLD SIMULATOR. The load flow studies were performed to determine pre-fault conditions in the system
using Newton-Raphson method. With the help of three-phase balanced fault, the variations in power angle and
frequency of the system were studied. Frequency is a reliable indicator if deficiency condition in the power
systems exists or not. For three-phase balanced fault, fast fault clearing time was analysed to bring back the
system to the stability. Further, comparison between Runga method and Euler method for better results was
performed. Hence, impact of load switching on system was also computed so as to bring system to steady state.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
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.
Hybrid T-I-D and Fuzzy Logic Based SVC Controller for Transient Stability Enh...IJERA Editor
This paper presents a new approach to solve the transient stability problem. The conventional PI based SVC controller has simple functioning and is economical in operation but has sluggish performance with non-linear characteristics. so, in order to circumvent this problem, fuzzy based T-I-D controller has been designed to improve the transient stability of 2 machine 3 bus power system using MATLAB/SIMULINK software.
International Journal of Engineering and Science Invention (IJESI)inventionjournals
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F05113439
1. IOSR Journal of Engineering (IOSRJEN) www.iosrjen.org
ISSN (e): 2250-3021, ISSN (p): 2278-8719
Vol. 05, Issue 01 (January. 2015), ||V1|| PP 34-39
International organization of Scientific Research 34 | P a g e
Solution of Swing equation for Transient Stability Analysis in
Dual-machine System
S. Padhi, B.P.Mishra
Department of Electrical Engg., OEC
Department of Electronics & Telecomm Engg., DRIEMS
Abstract: - The stability of an interconnected power system is its ability to return to normal or stable operation
after having been subjected to some form of disturbance. With interconnected systems continually growing in
size and extending over vast geographical regions, it is becoming increasingly more difficult to maintain
synchronism between various parts of the power system. Modern power systems have many interconnected
generating stations, each with several generators and many loads. So our study is focused on multi-machine
stability .
Keywords: – Stability, Swing Equation, Transient Stability, Synchronous machine, Numerical Methods
I. INTRODUCTION
Successful operation of a power system depends largely on the engineer's ability to provide reliable and
uninterrupted service to the loads. The reliability of the power supply implies much more than merely being
available. Ideally, the loads must be fed at constant voltage and frequency at all times. The first requirement of
reliable service is to keep the synchronous generators running in parallel and with adequate capacity to meet the
load demand. Synchronous machines do not easily fall out of step under normal conditions. If a machine tends
to speed up or slow down, synchronizing forces tend to keep it in step. Conditions do arise, however, such as a
fault on the network, failure in a piece of equipment , sudden application of a major load such as a steel mill, or
loss of a line or generating unit., in which operation is such that the synchronizing forces for one or more
machines may not be adequate, and small impacts in the system may cause these machines to lose synchronism.
A second requirement of reliable electrical service is to maintain the integrity of the power network.
The high-voltage transmission system connects the generating stations and the load centers. Interruptions in this
network may hinder the flow of power to the load. This usually requires a study of large geographical areas
since almost all power systems are interconnected with neighboring systems.
Random changes in load are taking place at all times, with subsequent adjustments of generation.
One may look at any of these as a change from one equilibrium state to another. Synchronism frequently may be
lost in that transition period, or growing oscillations may occur over a transmission line, eventually leading to its
tripping. These problems must be studied by the power system engineer and fall under the heading "power
system stability".
II. STUDY OF SWING EQUATION
2.1 STABILITY
The tendency of a power system to develop restoring forces equal to or greater than the disturbing forces to
maintain the state of equilibrium is known as “STABILITY”.
The problem of interest is one where a power system operating under a steady load condition is
perturbed, causing the readjustment of the voltage angles of the synchronous machines. If such an occurrence
creates an unbalance between the system generation and load, it results in the establishment of a new steady-
state operating condition, with the subsequent adjustment of the voltage angles. The perturbation could be a
major disturbance such as the loss of a generator, a fault or the loss of a line, or a combination of such events. It
could also be a small load or random load changes occurring under normal operating conditions. Adjustment to
the new operating condition is called the transient period. The system behavior during this time is called the
dynamic system performance, which is of concern in defining system stability. The main criterion for stability is
that the synchronous machines maintain synchronism at the end of the transient period.
So we can say that if the oscillatory response of a power system during the transient period following a
disturbance is damped and the system settles in a finite time to a new steady operating condition, we say the
system is stable. If the system is not stable, it is considered unstable. This primitive definition of stability
requires that the system oscillations be damped. This condition is sometimes called asymptotic stability and
means that the system contains inherent forces that tend to reduce oscillations. This is a desirable feature in
many systems and is considered necessary for power systems. The definition also excludes continuous
2. Solution of Swing equation for Transient Stability Analysis in Dual-machine System
International organization of Scientific Research 35 | P a g e
oscillation from the family of stable systems, although oscillators are stable in a mathematical sense. The reason
is practical since a continually oscillating system would be undesirable for both the supplier and the user of
electric power. Hence the definition describes a practical specification for an acceptable operating condition.
The stability problem is concerned with the behavior of the synchronous machines after a disturbance. For
convenience of analysis, stability problems are generally divided into two major categories-steady state stability
and transient state stability and transient state stability.
2.2 SWING EQUATION
Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic
field axis is fixed. The angle between the two is known as the power angle or torque angle. During any
disturbance, rotor will decelerate or accelerate with respect to the synchronously rotating air gap mmf, a relative
motion begins. The equation describing the relative motion is known as the swing equation.
Synchronous machine operation:
Consider a synchronous generator with electromagnetic torque Te running at synchronous speed ωsm..
During the normal operation, the mechanical torque Tm = Te.
A disturbance occur will result in accelerating/decelerating torque Ta=Tm-Te (Ta>0 if accelerating, Ta<0 if
decelerating).
By the law of rotation –
Where J is the combined moment of inertia of prime mover and generator .
θm is the angular displacement of rotor w.r.t. stationery reference frame on the stator
θm = ωsmt+δm, ωsm is the constant angular velocity .
Swing equation in terms of inertial constant M
Relations between electrical power angle δ and mechanical power angle δm and electrical speed and
mechanical speed
where P is the pole number .
Swing equation in terms of electrical power angle δ
Converting the swing equation into per unit system
where H is the inertia constant .
III. STEADY STATE STABILITY
The ability of power system to remain its synchronism and returns to its original state when subjected to small
disturbances. Such stability is not affected by any control efforts such as voltage regulators or governor.
3.1 Analysis of steady-state stability by swing equation
Starting from swing equation:-
Introduce a small disturbance Δ δ
3. Solution of Swing equation for Transient Stability Analysis in Dual-machine System
International organization of Scientific Research 36 | P a g e
Derivation is from δ=δ0+Δδ
Simplify the nonlinear function of power angle δ
Analysis of steady-state stability by swing equation
Swing equation in terms of Δδ
3.2 Damping torque:
Phenomena: when there is a difference angular velocity between rotor and air gap field, an induction torque
will be set up on rotor tending to minimize the difference of velocities.
Introduce a damping power by damping torque :
Introduce the damping power into swing equation.
Characteristic equation:
Solution of the swing equation :
Roots of swing equation :
Fig.3.1 Diagram for Steady State Problem
IV. TRANSIENT STABILITY
The transient stability studies involve the determination of whether or not synchronism is maintained
after the machine has been subjected to severe disturbance. This may be sudden application of load, loss of
generation, loss of large load, or a fault on the system. In most disturbances, oscillations are of such magnitude
that linearization is not permissible and the nonlinear swing equation must be solved.
4.1 NUMERICAL SOLUTION OF SWING EQUATION
The transient stability analysis requires the solution of a system of coupled non-linear differential
equations. In general, no analytical solution of these equations exists. However, techniques are available to
obtain approximate solution of such differential equations by numerical methods and one must therefore resort
to numerical computation techniques commonly known as digital simulation. Some of the commonly used
numerical techniques for the solution of the swing equation are:
Point by point method
Euler modified method
Runge-Kutta method
In our analysis, we have used Euler modified method and Point-by Point Method.
The swing equation can be transformed into state variable form as :
4. Solution of Swing equation for Transient Stability Analysis in Dual-machine System
International organization of Scientific Research 37 | P a g e
We now apply modified Euler’s method to the above equations as below :
Then the average value of the two derivatives is used to find the corrected values.
This is illustrated in the Simulink design.
Fig.4.1 Diagram for Transient State Stability design
V. MULTI-MACHINE SYSTEM
Multi-machine system can be written similar to one-machine system by the following assumptions:
Each synchronous machine is represented by a constant voltage E behind Xd (neglect saliency and flux
change) .
Input power remain constant .
Using pre-fault bus voltages, all loads are in equivalent admittances to ground .
Damping and asynchronous effects are ignored
δmech = δ
Machines belong to the same station swing together and are said to be coherent, coherent machines can
equivalent to one machine .
Solution to multi-machine system:
Solving initial power flow and determine initial bus voltage magnitude and phase angle
Calculating load equivalent admittance
Nodal equations of the system
Electrical and mechanical power output of machine at steady state prior to disturbances.
5. Solution of Swing equation for Transient Stability Analysis in Dual-machine System
International organization of Scientific Research 38 | P a g e
Classical transient stability study is based on the application of the three-phase fault
Swing equation of multi-machine system
Yij are the elements of the faulted reduced bus admittance matrix
State variable model of swing equation
`
Fig.5.1 Diagram for Dual-machine Stability
VI. SIMULATION
For our simulation we have taken a Power System Network of a electrical company shown in fig.5.1 .
The values of load data, voltage magnitude, generation schedule and the reactive power limits for the regulated
buses are suitably taken. Bus 1 of the system is carefully considered with a specified value and is taken as slack
bus . The data for basemva, accuracy, mailer, bus data, line data and gendata are suitably taken in matrix form .
The whole process of simulation is carried out by using MATLAB-7.0.
Fig.6.1 Dual-machine Stability for Fault cleared at Fig.6.2 Dual-machine Stability for Fault cleared at
0.4Sec . 0.8Sec .
6. Solution of Swing equation for Transient Stability Analysis in Dual-machine System
International organization of Scientific Research 39 | P a g e
Fig.6.3 Dual-machine Stability for Fault cleared at 0.697Sec .
VII. RESULT ANALYSIS
Phase angle differences, after reaching a maximum of δ21=123.90 and
δ31=62.950 will decrease, and the machines swing together.
Hence, the system is found to be stable when fault is cleared in 0.4 second.
The swing curves shown in figure show that machine 2 phase angle increases without limit.
Thus, the system is unstable when fault is cleared in 0.5 second.
The simulation is repeated for a clearing time of 0.45 second which is found to be critically stable.
VIII. CONCLUSIONS
It can be seen that transient stability is greatly affected by the type and location of a fault so that a
power system analyst must at the very outset of a stability study decide on these two factors. Thus we saw that a
two-machine system can be equivalently reduced to a one machine system connected to infinite bus bar. In case
of a large multi-machine system, to limit the computer memory and time requirements, the system is divided
into a study subsystem and an external subsystem. The study subsystem is modelled in details whereas
approximate modelling is carried out for the rest of the subsystem. The qualitative conclusions regarding system
stability drawn from a two-machine or an equivalent one-machine infinite bus system can be easily extended to
a multi-machine system. It can be seen that transient stability is greatly affected by the type and location of a
fault so that a power system analyst must at the very outset of a stability study decide on these two factors. The
solution of swing equation in Small Signal Stability Including Effects of Rotor Circuit Dynamics in synchronous
machine will be the future work.
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