The stability of 3 phase alternators synchronized to the Electrical Grid is affected by the inductive reactance of the transmission lines. Alternator voltage is controlled by an automatic voltage regulator which adjusts rotor excitation current to aid in maintaining stable synchronous operation during steady state and transient conditions.
Three phase circuits have advantages over single phase circuits. The document discusses three phase connections including delta-wye connections and how to calculate voltages and currents in three phase circuits. It also covers converting between delta and wye connections and provides an example of calculating line currents and voltages for a three phase circuit with a delta connected source and wye connected load.
1. The document discusses power factor correction by adding a capacitor to an existing load to make the power factor closer to 1.
2. It provides equations to calculate the current drawn by the original load, the supply current after adding a capacitor, and the current drawn by the capacitor.
3. As an example, it calculates the current values for a 2 kW mud pump with an original power factor of 0.5 that is corrected to 0.95 by adding a capacitor, and draws a phasor diagram to illustrate the current values and phase angles.
The document discusses three-phase circuits and their analysis. It covers balanced and unbalanced three-phase configurations, power in balanced systems, and analyzing unbalanced systems using PSpice. The objectives are to understand different three-phase connections, distinguish balanced and unbalanced circuits, calculate power in balanced systems, analyze unbalanced systems, and apply the concepts to measurement and residential wiring. Key points covered include wye-wye, wye-delta, delta-delta, and delta-wye connections for both sources and loads.
This document presents a study on dynamic modeling of flyback switching power supplies using graph modeling for application in variable speed DC drives. It first reviews DC motor speed control using a flyback switching power supply and optimal symmetric controlling method to control the converter's switch-on and switch-off times. It then introduces graph modeling as a precise, simple and efficient method to model DC-to-DC converters to reduce simulation time while maintaining accuracy. The document models a flyback converter using graph modeling and simulates it, finding the modeled simulation takes much less time than simulating the actual converter circuit. It then designs a variable speed DC drive using the flyback converter and controller and models the complete system using graph modeling, verifying the modeled
Power Circuits and Transforers-Unit 6 Labvolt Student Manualphase3-120A
This document provides instruction on analyzing balanced three-phase AC circuits connected in wye and delta configurations. It discusses the differences between line and phase voltages and currents. Formulas are presented for calculating active, reactive, and apparent power in balanced three-phase circuits. Exercises are included to measure voltages and currents in wye- and delta-connected resistive loads to verify the theoretical calculations and relationships between line and phase values.
This document provides instructions for connecting the windings of a three-phase transformer in delta-delta and wye-wye configurations. It describes verifying the phase relationships by measuring voltages before closing the secondary windings. For a delta connection, the voltage within the closed delta must be zero to avoid high currents. The procedure involves connecting the transformer, measuring voltages to check phase relationships, closing the secondary delta if voltages are correct, and measuring secondary line voltages.
Power Circuits and Transformers-Unit 2 Labvolt Student Manualphase3-120A
This document discusses alternating current (AC) and sine waves. It explains that AC voltage continually changes polarity and amplitude, and can be considered a DC voltage that is changing. The frequency of an AC voltage is the number of times per second its polarity changes. Sine waves are well-suited for electrical systems as they allow for efficient power transfer. Key parameters of sine waves include amplitude, frequency, phase, and phase shift. Circuit laws like Ohm's Law apply to AC circuits as well.
Three phase circuits have advantages over single phase circuits. The document discusses three phase connections including delta-wye connections and how to calculate voltages and currents in three phase circuits. It also covers converting between delta and wye connections and provides an example of calculating line currents and voltages for a three phase circuit with a delta connected source and wye connected load.
1. The document discusses power factor correction by adding a capacitor to an existing load to make the power factor closer to 1.
2. It provides equations to calculate the current drawn by the original load, the supply current after adding a capacitor, and the current drawn by the capacitor.
3. As an example, it calculates the current values for a 2 kW mud pump with an original power factor of 0.5 that is corrected to 0.95 by adding a capacitor, and draws a phasor diagram to illustrate the current values and phase angles.
The document discusses three-phase circuits and their analysis. It covers balanced and unbalanced three-phase configurations, power in balanced systems, and analyzing unbalanced systems using PSpice. The objectives are to understand different three-phase connections, distinguish balanced and unbalanced circuits, calculate power in balanced systems, analyze unbalanced systems, and apply the concepts to measurement and residential wiring. Key points covered include wye-wye, wye-delta, delta-delta, and delta-wye connections for both sources and loads.
This document presents a study on dynamic modeling of flyback switching power supplies using graph modeling for application in variable speed DC drives. It first reviews DC motor speed control using a flyback switching power supply and optimal symmetric controlling method to control the converter's switch-on and switch-off times. It then introduces graph modeling as a precise, simple and efficient method to model DC-to-DC converters to reduce simulation time while maintaining accuracy. The document models a flyback converter using graph modeling and simulates it, finding the modeled simulation takes much less time than simulating the actual converter circuit. It then designs a variable speed DC drive using the flyback converter and controller and models the complete system using graph modeling, verifying the modeled
Power Circuits and Transforers-Unit 6 Labvolt Student Manualphase3-120A
This document provides instruction on analyzing balanced three-phase AC circuits connected in wye and delta configurations. It discusses the differences between line and phase voltages and currents. Formulas are presented for calculating active, reactive, and apparent power in balanced three-phase circuits. Exercises are included to measure voltages and currents in wye- and delta-connected resistive loads to verify the theoretical calculations and relationships between line and phase values.
This document provides instructions for connecting the windings of a three-phase transformer in delta-delta and wye-wye configurations. It describes verifying the phase relationships by measuring voltages before closing the secondary windings. For a delta connection, the voltage within the closed delta must be zero to avoid high currents. The procedure involves connecting the transformer, measuring voltages to check phase relationships, closing the secondary delta if voltages are correct, and measuring secondary line voltages.
Power Circuits and Transformers-Unit 2 Labvolt Student Manualphase3-120A
This document discusses alternating current (AC) and sine waves. It explains that AC voltage continually changes polarity and amplitude, and can be considered a DC voltage that is changing. The frequency of an AC voltage is the number of times per second its polarity changes. Sine waves are well-suited for electrical systems as they allow for efficient power transfer. Key parameters of sine waves include amplitude, frequency, phase, and phase shift. Circuit laws like Ohm's Law apply to AC circuits as well.
Power Circuits and Transforers-Unit 5 Labvolt Student Manualphase3-120A
* Active power (P) = 3 kW = 3,000 W
* Inductive reactive power (Q) = 4 kvar
* Using the power triangle:
* Apparent power (S) = √(P^2 + Q^2)
* = √(3,000^2 + 4,000^2)
* = √(9,000,000 + 16,000,000)
* = √25,000,000
* = 5,000 VA = 5 kVA
The apparent power is 5 kVA. The answer is b.
Power systems can be modeled and analyzed using per-unit representations of components. Key models include:
1) Generator models that specify real and reactive power injection or terminal voltage and current.
2) Transformer models using an equivalent circuit with magnetizing reactance and resistance.
3) Load models like constant impedance, current, or power to represent different load characteristics.
4) Transmission lines modeled as series impedances.
The per-unit system allows analysis of different voltage levels on a common scale and simplifies modeling of components.
Calculations of a.c distributions methods & 3 phase unbalanced loads &...vishalgohel12195
This document presents information on calculations for AC distribution methods, three-phase unbalanced loads, four-wire star-connected unbalanced loads, and ground detectors. It discusses two methods for calculating AC distribution based on load power factors referred to the receiving end voltage or respective load voltages. It also describes different types of unbalanced three-phase loads including four-wire star-connected and delta-connected loads. Ground detectors are defined as devices used to detect ground faults on ungrounded AC systems.
This document provides an overview of electrostatics and electric current concepts. It defines electrostatics as electricity from the Greek word for amber, where static electricity is generated by rubbing materials together. The key concepts covered include:
- Coulomb's law which describes the force between electric charges.
- The properties of electric fields and field intensity.
- How capacitors store electric charge and the differences between capacitors connected in parallel versus series.
- Definitions of electric current, resistance, voltage, and potential drop in circuits.
The document is about power system analysis and contains the following information:
1. It discusses the advantages of per unit computation such as manufacturers specifying impedance in per unit values and impedances being within a narrow range even for widely different ratings.
2. It asks questions related to load flow analysis, types of buses, Jacobian matrix, need for slack bus, and static load flow equations.
3. It covers topics like power flow solution methods, representation of loads, need for base values, and applications of bus admittance matrix in load flow analysis.
The calculation of a Triangle Voltage Stability Index (TVSI) for monitored alternating-current circuits using voltage data from a PSSE load flow study. The analysis provides TVSI values for monitored transmission circuits in the Bulk Electric System under varying power transfers and contingencies.
TVSI provides an indication of the closeness of the load voltage to potential voltage collapse. To provide situational awareness to system operators, AEP proposes monitoring the phase angle across a low loss EHV overhead circuit operating in a system environment and comparing the angle to an established phase angle loci as a proxy for TVSI.
This monitoring could be independent of the line loading or the associated line impedance.
This document summarizes key concepts about three-phase systems. It defines a three-phase system as having three sinusoidal voltages differing in phase by 120 degrees. The voltages can form a positive or negative sequence. Three-phase systems are commonly used for power generation, transmission, and distribution due to their ability to transmit more power with less material. Formulas are provided for calculating line voltages, currents, and power in balanced and unbalanced three-phase systems. Advantages of three-phase systems like constant torque and easier starting of motors are also discussed.
Power Circuits and Transforers-Unit 8 Labvolt Student Manualphase3-120A
This exercise explores connecting transformers in parallel and measuring their efficiency. Two 100-VA transformers are connected in parallel to supply a 200-VA load. Efficiency is calculated as the ratio of output power to input power. Measurements of input and output power will be taken to determine the overall efficiency and verify that the load is shared between the two transformers. Connecting transformers in parallel allows supplying power greater than the rating of a single transformer.
This document provides an overview of load flow analysis and power flow solution techniques, specifically the Gauss-Seidel and Newton-Raphson methods. It begins with an example Gauss-Seidel power flow calculation for a two bus system. It then discusses the inclusion of PV generator buses in the Gauss-Seidel iteration and accelerated Gauss-Seidel convergence. The document concludes by introducing the Newton-Raphson power flow algorithm and comparing the advantages and disadvantages of Gauss-Seidel versus Newton-Raphson.
Power Circuits and Transforers-Unit 3 Labvolt Student Manualphase3-120A
This document discusses determining equivalent capacitance for series and parallel capacitors. It explains that capacitance opposes changes in voltage across capacitor terminals and depends on factors like dielectric material and plate size/spacing. The exercise objectives are to calculate equivalent capacitance using circuit measurements and explain how capacitance values combine in series and parallel configurations.
This document discusses distance protection relay types and characteristics. It begins by explaining the principles of comparison-type distance relays using phase and impedance comparisons. It then describes several common relay characteristics including impedance, ohm, reactance, mho, and offset mho. The document also discusses power swings and loss of synchronism, explaining how to represent these phenomena on an R-X diagram using system and relay impedances.
Includes Introduction, Derivation of power flow through transmission line, Single line diagram of three phase transmission, methods of finding the performance of transmission line. 1.Analytical Method 2.Graphical method (circle diagram)., circle diagram of receiving end side and sending end side.
Power Circuits and Transforers-Unit 1 Labvolt Student Manualphase3-120A
This document discusses fundamentals of electrical circuits, including basic concepts, symbols, and terminology. It covers topics like voltage, current, resistance, and Ohm's law. The document contains detailed information and diagrams about atomic structure, electric fields, resistance of materials, and measuring voltage and current using a data acquisition system. It provides objectives and procedures for an exercise to demonstrate and apply Ohm's law using circuit measurements.
This document provides a summary of key concepts from Chapter 2 on AC circuits. It discusses instantaneous, average, and active power calculations. It defines reactive power as the oscillating component of instantaneous power. It examines power calculations for resistive, inductive, and capacitive circuits. Power triangles and complex power are introduced. Power factor correction methods are described. Complex power flow between buses is discussed. Key concepts for three-phase circuits like phase sequence, line voltages, and per-phase analysis are covered. Formulas are provided for calculating real, reactive, and complex power in balanced three-phase systems.
This document discusses delta-star and star-delta transformations of electrical networks. It provides derivations of the transformation formulas and explains that a delta network can be converted to an equivalent star network, and vice versa, using the formulas. It also discusses advantages like reduced starting current and disadvantages like reduced starting torque of star-delta connections. Additionally, it explains the relationships between line and phase voltages in star and delta networks.
EE456_NWPUD Transmission Reinforcement Planningki hei chan
The document presents two design options for upgrading the transmission system to accommodate load growth and a new wind farm. The first design connects the wind farm to bus 4 and costs $37.2 million with annual costs of $1.657 million. It requires upgrading 64.5 miles of conductors and adding 43 miles of new lines. The second design connects the wind farm to buses 14 and 27 using three transmission lines and costs $43.9 million with annual costs of $1.889 million. It requires more materials and right of way. A cost-benefit analysis determined the first design to be the most cost-effective option.
This document describes receiving end circle diagrams used to visualize load flow over a transmission line. It provides the following key points:
1) Receiving end circle diagrams are derived from voltage phasor diagrams and have different centers for the voltage circles, with a common active and reactive power axis.
2) They can be used to understand how an inductive or capacitive load will affect the reactive power supplied by the source.
3) The center of the receiving end circle is located based on the receiving end voltage magnitude and angle. The radius depends on the sending and receiving end voltage magnitudes.
4) The receiving end circle allows determining the total power received based on the operating point located from the known real power received
The document discusses how to properly parallel and synchronize DC and AC electrical systems, including:
1) DC systems are paralleled by ensuring voltages are similar before closing the breaker to avoid circulating currents.
2) Single phase AC supplies are synchronized by matching frequency, voltage, phase, and polarity between the generator and grid using a synchroscope and voltmeters before closing the breaker.
3) Three phase AC systems require matching frequency, voltage, phase, and polarity as well as ensuring consistent phase rotation (RWB) between systems to avoid damage when the breaker is closed.
This document contains a resume for Donald Shepard, who has experience working as a security personnel and law enforcement officer. He has over 5 years of experience in law enforcement and served 1 year in the US Army in Afghanistan. He has extensive training and certifications in security procedures. His work history includes over 15 years providing security at various facilities like airports, government buildings, and apartment complexes where he monitored access points and responded to security incidents. He has an Associate's degree in computer marketing and continuing education in security-related topics.
Power Circuits and Transforers-Unit 5 Labvolt Student Manualphase3-120A
* Active power (P) = 3 kW = 3,000 W
* Inductive reactive power (Q) = 4 kvar
* Using the power triangle:
* Apparent power (S) = √(P^2 + Q^2)
* = √(3,000^2 + 4,000^2)
* = √(9,000,000 + 16,000,000)
* = √25,000,000
* = 5,000 VA = 5 kVA
The apparent power is 5 kVA. The answer is b.
Power systems can be modeled and analyzed using per-unit representations of components. Key models include:
1) Generator models that specify real and reactive power injection or terminal voltage and current.
2) Transformer models using an equivalent circuit with magnetizing reactance and resistance.
3) Load models like constant impedance, current, or power to represent different load characteristics.
4) Transmission lines modeled as series impedances.
The per-unit system allows analysis of different voltage levels on a common scale and simplifies modeling of components.
Calculations of a.c distributions methods & 3 phase unbalanced loads &...vishalgohel12195
This document presents information on calculations for AC distribution methods, three-phase unbalanced loads, four-wire star-connected unbalanced loads, and ground detectors. It discusses two methods for calculating AC distribution based on load power factors referred to the receiving end voltage or respective load voltages. It also describes different types of unbalanced three-phase loads including four-wire star-connected and delta-connected loads. Ground detectors are defined as devices used to detect ground faults on ungrounded AC systems.
This document provides an overview of electrostatics and electric current concepts. It defines electrostatics as electricity from the Greek word for amber, where static electricity is generated by rubbing materials together. The key concepts covered include:
- Coulomb's law which describes the force between electric charges.
- The properties of electric fields and field intensity.
- How capacitors store electric charge and the differences between capacitors connected in parallel versus series.
- Definitions of electric current, resistance, voltage, and potential drop in circuits.
The document is about power system analysis and contains the following information:
1. It discusses the advantages of per unit computation such as manufacturers specifying impedance in per unit values and impedances being within a narrow range even for widely different ratings.
2. It asks questions related to load flow analysis, types of buses, Jacobian matrix, need for slack bus, and static load flow equations.
3. It covers topics like power flow solution methods, representation of loads, need for base values, and applications of bus admittance matrix in load flow analysis.
The calculation of a Triangle Voltage Stability Index (TVSI) for monitored alternating-current circuits using voltage data from a PSSE load flow study. The analysis provides TVSI values for monitored transmission circuits in the Bulk Electric System under varying power transfers and contingencies.
TVSI provides an indication of the closeness of the load voltage to potential voltage collapse. To provide situational awareness to system operators, AEP proposes monitoring the phase angle across a low loss EHV overhead circuit operating in a system environment and comparing the angle to an established phase angle loci as a proxy for TVSI.
This monitoring could be independent of the line loading or the associated line impedance.
This document summarizes key concepts about three-phase systems. It defines a three-phase system as having three sinusoidal voltages differing in phase by 120 degrees. The voltages can form a positive or negative sequence. Three-phase systems are commonly used for power generation, transmission, and distribution due to their ability to transmit more power with less material. Formulas are provided for calculating line voltages, currents, and power in balanced and unbalanced three-phase systems. Advantages of three-phase systems like constant torque and easier starting of motors are also discussed.
Power Circuits and Transforers-Unit 8 Labvolt Student Manualphase3-120A
This exercise explores connecting transformers in parallel and measuring their efficiency. Two 100-VA transformers are connected in parallel to supply a 200-VA load. Efficiency is calculated as the ratio of output power to input power. Measurements of input and output power will be taken to determine the overall efficiency and verify that the load is shared between the two transformers. Connecting transformers in parallel allows supplying power greater than the rating of a single transformer.
This document provides an overview of load flow analysis and power flow solution techniques, specifically the Gauss-Seidel and Newton-Raphson methods. It begins with an example Gauss-Seidel power flow calculation for a two bus system. It then discusses the inclusion of PV generator buses in the Gauss-Seidel iteration and accelerated Gauss-Seidel convergence. The document concludes by introducing the Newton-Raphson power flow algorithm and comparing the advantages and disadvantages of Gauss-Seidel versus Newton-Raphson.
Power Circuits and Transforers-Unit 3 Labvolt Student Manualphase3-120A
This document discusses determining equivalent capacitance for series and parallel capacitors. It explains that capacitance opposes changes in voltage across capacitor terminals and depends on factors like dielectric material and plate size/spacing. The exercise objectives are to calculate equivalent capacitance using circuit measurements and explain how capacitance values combine in series and parallel configurations.
This document discusses distance protection relay types and characteristics. It begins by explaining the principles of comparison-type distance relays using phase and impedance comparisons. It then describes several common relay characteristics including impedance, ohm, reactance, mho, and offset mho. The document also discusses power swings and loss of synchronism, explaining how to represent these phenomena on an R-X diagram using system and relay impedances.
Includes Introduction, Derivation of power flow through transmission line, Single line diagram of three phase transmission, methods of finding the performance of transmission line. 1.Analytical Method 2.Graphical method (circle diagram)., circle diagram of receiving end side and sending end side.
Power Circuits and Transforers-Unit 1 Labvolt Student Manualphase3-120A
This document discusses fundamentals of electrical circuits, including basic concepts, symbols, and terminology. It covers topics like voltage, current, resistance, and Ohm's law. The document contains detailed information and diagrams about atomic structure, electric fields, resistance of materials, and measuring voltage and current using a data acquisition system. It provides objectives and procedures for an exercise to demonstrate and apply Ohm's law using circuit measurements.
This document provides a summary of key concepts from Chapter 2 on AC circuits. It discusses instantaneous, average, and active power calculations. It defines reactive power as the oscillating component of instantaneous power. It examines power calculations for resistive, inductive, and capacitive circuits. Power triangles and complex power are introduced. Power factor correction methods are described. Complex power flow between buses is discussed. Key concepts for three-phase circuits like phase sequence, line voltages, and per-phase analysis are covered. Formulas are provided for calculating real, reactive, and complex power in balanced three-phase systems.
This document discusses delta-star and star-delta transformations of electrical networks. It provides derivations of the transformation formulas and explains that a delta network can be converted to an equivalent star network, and vice versa, using the formulas. It also discusses advantages like reduced starting current and disadvantages like reduced starting torque of star-delta connections. Additionally, it explains the relationships between line and phase voltages in star and delta networks.
EE456_NWPUD Transmission Reinforcement Planningki hei chan
The document presents two design options for upgrading the transmission system to accommodate load growth and a new wind farm. The first design connects the wind farm to bus 4 and costs $37.2 million with annual costs of $1.657 million. It requires upgrading 64.5 miles of conductors and adding 43 miles of new lines. The second design connects the wind farm to buses 14 and 27 using three transmission lines and costs $43.9 million with annual costs of $1.889 million. It requires more materials and right of way. A cost-benefit analysis determined the first design to be the most cost-effective option.
This document describes receiving end circle diagrams used to visualize load flow over a transmission line. It provides the following key points:
1) Receiving end circle diagrams are derived from voltage phasor diagrams and have different centers for the voltage circles, with a common active and reactive power axis.
2) They can be used to understand how an inductive or capacitive load will affect the reactive power supplied by the source.
3) The center of the receiving end circle is located based on the receiving end voltage magnitude and angle. The radius depends on the sending and receiving end voltage magnitudes.
4) The receiving end circle allows determining the total power received based on the operating point located from the known real power received
The document discusses how to properly parallel and synchronize DC and AC electrical systems, including:
1) DC systems are paralleled by ensuring voltages are similar before closing the breaker to avoid circulating currents.
2) Single phase AC supplies are synchronized by matching frequency, voltage, phase, and polarity between the generator and grid using a synchroscope and voltmeters before closing the breaker.
3) Three phase AC systems require matching frequency, voltage, phase, and polarity as well as ensuring consistent phase rotation (RWB) between systems to avoid damage when the breaker is closed.
This document contains a resume for Donald Shepard, who has experience working as a security personnel and law enforcement officer. He has over 5 years of experience in law enforcement and served 1 year in the US Army in Afghanistan. He has extensive training and certifications in security procedures. His work history includes over 15 years providing security at various facilities like airports, government buildings, and apartment complexes where he monitored access points and responded to security incidents. He has an Associate's degree in computer marketing and continuing education in security-related topics.
Harnham is a specialist recruitment firm focused on recruiting for data and analytics roles. They have experience recruiting for roles across multiple sectors in the UK, US, and Europe. Harnham understands the challenges that clients face with recruitment and can help supplement clients' needs. They work to offer the best specialist recruitment service for the data and analytics sector through their dedicated teams focused on areas like credit risk, data science, digital marketing and more. Recent customer surveys found that 92% of clients use Harnham for their industry knowledge and 90% said Harnham makes their recruitment process easier.
(1) A generator's output is limited by rotor heating, stator winding heating, stability, core end heating, and stator core heating. Exceeding these thermal limits reduces insulation life.
(2) The document explains each limitation, how they are shown on capability curves, and the consequences of exceeding them. Rotor temperature impacts insulation life while stability issues cause dangerous power surges.
(3) For a generator at rated speed, MW output is limited by turbine output and stator heating, MVar (lag) by rotor heating, MVar (lead) by core heating and stability, and voltage by stator core heating.
The agenda outlines a day-long GIS Users Group Meeting taking place on September 14, 2016 in Martinsburg, WV. It includes sessions on implementing parcel fabric in WV, using GIS in regional development, tools and trends in GIS, integrating survey data into GIS, local contributions to state/federal datasets, evaluating riparian buffers, GIS for field mobility, high accuracy data collection, and stream delineation. The meeting runs from 8:30am to 4:00pm at The Purple Iris restaurant. RSVPs were requested by September 13, 2016.
El documento describe el desarrollo del periodismo digital en México. Comienza con los pregoneros del siglo XVI que anunciaban noticias en las calles de la Nueva España. Luego, la imprenta llegó a México en 1539 e impulsó la circulación de hojas volantes con noticias. Una de las primeras publicaciones fue el Mercurio Volante en 1693. Finalmente, en 1722 se fundó la Gaceta de México, considerado el primer periódico de México, que publicaba diferentes tipos de información.
El documento describe el Cuadro Integral de Mando como una metodología para traducir un plan estratégico a acciones concretas mediante cuatro perspectivas: financiera, clientes, procesos internos e innovación y aprendizaje. Sirve como herramienta para alinear objetivos organizacionales con las personas y medir el progreso hacia metas definidas, ayudando a los gerentes a lograr los objetivos estratégicos.
ANALISE DOS FATORES E IMPACTOS NO CRESCIMENTO DA PSIDIUM GUAJAVA – MYRTACEAE – POPULAR GOIABEIRA. E RELACIONAMENTO DOS FATORES QUE CONTRIBUEM OU NÃO PARA ESSE ACONTECIMENTO.
This document is a seminar report submitted by Ganesh Hegde to Visvesvaraya Technological University that discusses wireless systems and challenges in 5G networks. It provides an overview of the evolution of wireless technologies from 1G to 5G networks, describing the key features and capabilities of each generation. The report highlights that 5G networks will require significantly more advanced self-organizing capabilities to handle the immense complexity and scale compared to 3G/4G networks. It proposes a framework for empowering self-organizing networks with big data analytics and machine learning to address the challenges of deploying and managing 5G networks.
This SQL query selects all properties from the alf_node_properties table where the actual type is 21 and there is no matching content data in the alf_content_data table for the long value property. It performs a left join to check for null values in the alf_content_data table id field.
Se trata de un documento que con base en un ejemplo se desarrolla el tema de Gestión de calidad, aseguramiento de calidad, sistemas de gestión de calidad y control de calidad.
This document summarizes a project for a Bachelor of Computer Applications degree submitted by Mehul Jain and Hardik Bhandari in 2013-2014. The project is for an Apartment Management system developed under the guidance of Deepti Shrimal at University College of Science. The system was developed using HTML, DHTML, JavaScript, JSP, CSS, MySQL database and Apache Tomcat server. It allows users to manage apartment information and transactions online. The project was tested using white box and black box testing methods to ensure all functions and requirements were met.
Here are the answers to the questions on DC generator characteristics:
1. The external characteristic gives the relation between terminal voltage and load current.
2. The three most important characteristics or curves of a DC generator are: the no-load saturation characteristic (E0/If), internal or total characteristic (E/Ia), and external characteristic (V/I).
3. Critical speed of a shunt generator means the speed for which the given shunt field resistance represents critical resistance.
4. One condition necessary for the build-up of a self-excited shunt generator is that there must be some residual magnetism in the generator poles.
5. Some other factors which affect the voltage building of
This document discusses power flow in transmission lines and how FACTS (Flexible AC Transmission System) controllers can be used to control power flow. It begins by describing the basic model of power flow on a transmission line connected between two buses and defines key variables. It then discusses different types of FACTS controllers - series controllers that inject voltage in series with the line, shunt controllers that inject current at the point of connection, and combined configurations. The key points are that series controllers can provide powerful control of active power flow by varying the line reactance or angle, while shunt controllers are more effective for reactive power control by varying bus voltages. Combined configurations allow control of both active and reactive power.
This document discusses power factor improvement. It begins by defining power factor as the cosine of the angle between the voltage and current in an AC circuit. Power factor can be lagging if the current lags the voltage in an inductive circuit, or leading if the current leads the voltage in a capacitive circuit. Low power factor is undesirable as it results in higher equipment ratings, conductor sizes, copper losses and poorer voltage regulation. Power factor can be improved by adding capacitors in parallel with inductive loads to provide a leading reactive current. This reduces the phase angle between voltage and current, increasing the power factor. Other methods of power factor improvement include using synchronous condensers and phase advancers. Improving power factor is important for both
This document contains notes on power supply circuits and rectifiers. It includes questions and answers on half wave and full wave rectifiers, their circuit diagrams, working principles and waveforms. Filter circuits and types of filters are discussed. Voltage regulators including shunt, series and zener diode regulators are also covered. Comparisons are made between different rectifier and regulator circuits. Applications and working principles are explained through diagrams.
This document discusses sending and receiving end power circle diagrams in a transmission line experiment. It explains that active and reactive powers depend on the voltage magnitudes and phase angles at the sending and receiving ends as well as the line impedance. The document also defines complex, active, and reactive power flows and derivations. It notes that maximum active power transfer occurs at a specific power or load angle and that stability depends on if the derivative of power to the load angle is positive or negative. Typical power transfers correspond to angles below 30 degrees to ensure stability.
Capacitive voltage and current induction phenomena in GIS substationIOSR Journals
This document summarizes a study that simulated capacitive voltage and current induction in a 420kV GIS substation. The substation and transmission lines were modeled in EMTP-RV software. Single-phase and three-phase faults were applied to lines to observe induced voltage and current. For a single-phase fault, the maximum induced current was 0.41A and maximum voltage matched measured substation values. For a three-phase fault, the maximum induced current was 0.48A and maximum voltage also matched measured substation values. The results validate the accuracy of the substation and transmission line models used in the study.
This document discusses the operation and analysis of a three phase fully controlled bridge converter. Some key points:
- The converter uses six thyristors instead of diodes to allow control of the output DC voltage through phase control. There are six possible conduction modes with each thyristor conducting for 120 degrees.
- The output voltage waveform consists of segments of the input AC line voltages. The input current contains only odd harmonics of the supply frequency.
- Analysis shows the output voltage is proportional to the cosine of the firing angle. The displacement power factor is equal to the cosine of the firing angle. Total power factor is the displacement factor multiplied by the distortion factor.
- Closed form expressions are derived
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
The document discusses electrical transmission lines and their key components. It describes how transmission lines can be modeled as 2-port networks and discusses the ABCD constants that characterize different types of transmission lines from short to long. It also covers how power flow is affected by load power factor, with received voltage decreasing for lagging loads and increasing for leading loads. The power handling capability and limits of transmission lines are also summarized.
This document presents the analysis and design of an electronically adjustable three-phase AC load for testing AC systems. The load uses a voltage source converter (VSC) and buck converter topology to emulate various impedance combinations, including purely active and reactive loads. Simulation results are provided that demonstrate the load accurately adjusting between different power levels, such as inductive, resistive, and capacitive loads. The control system regulates the DC bus voltage and generates reference currents to achieve the desired active and reactive power emulation. This electronic variable load allows precise adjustment of power for equipment testing applications.
International Refereed Journal of Engineering and Science (IRJES)irjes
The core of the vision IRJES is to disseminate new knowledge and technology for the benefit of all, ranging from academic research and professional communities to industry professionals in a range of topics in computer science and engineering. It also provides a place for high-caliber researchers, practitioners and PhD students to present ongoing research and development in these areas.
This document discusses various types of three-phase transformer connections including:
- Delta-delta, which produces no phase shift between input and output voltages.
- Delta-wye, which produces a 30 degree phase shift.
- Wye-delta, which also produces a 30 degree phase shift with primary and secondary connections reversed from delta-wye.
- Wye-wye requires special precautions like connecting the neutral or using a tertiary winding to prevent voltage distortion.
- Open-delta can transform voltage using only two transformers in an emergency situation but has lower capacity.
- Autotransformers are more economical than conventional transformers for moderate voltage changes between 0.5-2 times.
The document discusses continuation power flow analysis, which is used to analyze power systems near voltage stability limits. It begins by defining voltage stability and factors that affect it, such as reactive power limits of generators and transmission lines. It then explains the basic principles of continuation power flow, which finds successive load flow solutions according to a load scenario using prediction and correction steps. This allows it to determine the voltage stability limit, which is the critical point where the Jacobian matrix becomes singular. Parameterization techniques are used to select the continuation parameter at each step.
1) The document discusses the history and operation of transformers, including their use in power distribution systems to step up voltage for transmission and step down voltage for distribution to loads.
2) A transformer consists of coils wrapped around a common core and works by electromagnetic induction to convert AC voltages from one level to another while maintaining the same frequency.
3) An ideal transformer is analyzed, and equations are provided showing how it transforms voltages and currents while maintaining power, reactive power, and power factor between windings. Impedance transformation is also discussed.
A Single-Stage High-Frequency Isolated Secondary- Side Controlled AC-DC Conve...IDES Editor
This paper presents a new single-stage highfrequency
isolated ac-dc converter that uses a simple control
circuit. It is well suitable for wide input variation power
sources. The circuit configuration combines a diode rectifier,
boost converter and half-bridge dc-dc resonant converter. A
high power factor is achieved by discontinuous current mode
(DCM) operation of the front-end integrated power factor
correction circuit. The output voltage is regulated by fixedfrequency,
secondary-side phase-shift active rectifier. Softswitching
operation is achieved for all the switches. This
converter operates in three modes, which is classified
according to conduction of different switches and diodes. The
intervals of operation and steady-state analysis are presented
in detail. Design example of a 100 W proposed converter is
given together with its simulation and experiment results for
wide variation in input voltage.
This paper proposed a new sparce matrix converter with Z-source network to provide unity voltage transfer ratio. It is an ac-to-ac converter with diode-IGBT bidirectional switches. The limitations of existing matrix converter like higher current THD and less voltage transfer ratio issues are overcome by this proposed matrix converter by inserting a Z-source. Due to this Z-source current harmonics are totally removed. The simulation is performed for different frequencies. The simulation results are presented to verify the THD and voltage transfer ratio and compared with the existing virtual AC/DC/AC matrix converter. The experimental output voltage amplitude can be varied with the variable frequencies.
This document discusses direct current (DC) and alternating current (AC) circuits. It covers Ohm's law, power dissipation, Kirchhoff's laws, capacitive and inductive reactance, phasors, and RLC circuits. Key points include:
- Ohm's law defines the relationship between current, voltage and resistance in a DC circuit.
- Kirchhoff's laws allow analysis of voltage and current in series and parallel circuits.
- Inductive and capacitive reactance define how inductors and capacitors respectively impede alternating current in an AC circuit.
- Phasors represent AC voltages and currents using complex numbers to facilitate circuit analysis.
- RLC circuits combine resistors,
This document provides a formula and example for calculating the capacitance needed for power factor correction of an induction motor. It explains that adding a capacitor in parallel with a single phase motor reduces the current supplied by the grid. This connection decreases power loss in the supply wires and voltage drop, increasing the voltage at the motor terminals. Power factor correction of an induction motor from 0.8 to unity can reduce wire losses by 36%.
1) Electrical loads that consume only active power have current and voltage waves that are in phase. Loads that consume reactive power have current and voltage waves that are out of phase.
2) Reactive power is measured in vars and is supplied by inductive and capacitive loads. It does not do useful work but requires extra current.
3) Connecting a capacitor of the correct size in parallel with an inductive motor can supply the motor's reactive power needs, improving the power factor to 1.
(1) A generator's output is limited by rotor heating, stator winding heating, stability, core end heating, and stator core heating. Exceeding these thermal limits reduces insulation life.
(2) The generator's MW output is limited by turbine output and stator heating, while Mvar output (lagging) is limited by rotor heating and (leading) by core heating and stability. Terminal voltage is limited by stator core heating.
(3) Increasing gas pressure raises thermal limits but not stability limits. The generator normally operates within limits to maintain insulation life.
(a) When a generator is connected to an infinite grid, its terminal voltage remains constant regardless of changes in load or excitation.
(b) If excitation is increased for a constant MW load, the generator will operate at a lagging power factor. If excitation is decreased, it will operate at a leading power factor.
(c) For a generator with constant excitation, increasing the MW load will cause its power factor to become leading while decreasing load will cause its power factor to become lagging.
1. The document discusses the behavior of a generator when loaded onto a finite bus system, as opposed to an infinite bus. It describes how the governor and automatic voltage regulator (AVR) control the generator's output to maintain stable frequency and voltage.
2. Governors have a droop characteristic to automatically adjust the generator's output based on frequency changes. The AVR keeps terminal voltage constant despite load variations.
3. Safety is important when operating a generator without an AVR, as load changes can cause overexcitation, increasing voltage beyond safe levels and potentially damaging equipment. Proper excitation adjustment is required if the AVR fails.
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
Communicating effectively and consistently with students can help them feel at ease during their learning experience and provide the instructor with a communication trail to track the course's progress. This workshop will take you through constructing an engaging course container to facilitate effective communication.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
Liberal Approach to the Study of Indian Politics.pdf
(10) stability
1. GENERATOR AND TRANSMISSION LINE STABILITY
OBJECTIVES:
1. Explain, with the aid of equivalent circuits and phasor diagrams, how the load angle
varies with load in each of the following:
a) A generator
b) A transmission line,
c) A generator and transmission line.
2. Explain each of the following using the “power transfer curve”:
a) The relationship between active power transfer and load angle,
b) The relationship between load angle and steady state stability.
3. List and explain:
a) The factor influencing steady state stability.
b) The problem caused by steady state instability,
c) One precaution and two actions that can be taken to minimize the risk of steady state
instability occurring.
4. a) Explain the difference between steady state stability and transient stability.
b) List and explain the three factors which can cause transient instability in the generator
and the four factors which can cause transient instability in the transmission lines.
c) List and explain the precautions or actions taken to minimize the risk of transient
instability occurring for each of the factors in objective 4 b).
5. Explain the consequence of transient instability.
6. Using single or multiple power transfer curves, explain generator behavior during a
transient.
-1-
2. INTRODUCTION
Generator off load and on load operation has been considered, and diagrams were
drawn showing the effects of armature reaction. In the first part of this module, the
following conditions are examined:
a) how the load angle in a generator varies with load,
b) how the load angle in a transmission line varies with load,
c) how the composite load angle for the generator and line varies with load,
d) the relationship between load angle and active power transfer,
e) the relationship between load angle and steady state stability.
The second part of this module deals with transient where the behaviour of the
generator and lines are considered under fault conditions.
STEADY STATE STABILITY
Variation of generator load Angle with the Load
A previous lesson showed that as a generator is loaded, the load angle increases. The
magnitude of the load angle depends upon the generator load current, the generator
reactance and the power factor. Since internal reactance of the generator remains
unchanged it will not be a variable.
-2-
3. Figure 1a) shows the equivalent circuit for a generator directly connected to a
resistive (pf=1) load. The product of the load current Ia and the generator internal
reactance Xd produces the internal voltage drop Ia Xd. For a given load current Ia and
terminal voltage VT, a load angle of δg, is produced in the generator. Figure1b) shows the
resulting phasor diagram.
a)
b)
Figures la) & b): Equivalent Circuit for a Generator Operating at pf = 1 and Phasor
Diagram.
From this diagram we can see the relationship between Ia Xd and the load angle.
For example, if the load current Ia is increased (all else constant), the Ia Xd product
increases, causing the load angle to increase. (Recall the effect of armature reaction — ie
the increase in stator current causes an increase in magnetic flux around these windings.
Since this increase in flux opposes rotor flux, the terminal voltage will drop, requiring an
increase in field current to maintain terminal voltage - ie Eg must also increase to
compensate for an increase in internal voltage drop Ia Xd.).
-3-
4. Figures 2a) and b) show the conditions when the same generator is connected to a 0.9 pf
lag load while delivering the same value of active current (MW load) as in the previous
example. Thus the active power and the terminal voltage VT are the same as those in
Figures 1 a) and b). But as the power factor is now 0.9 lag the load current has increased
(it now has both active and reactive components). By increasing the load current, the
product Ia Xd has increased with the results shown in Figure 2b). From this diagram, we
can clearly see that the load angle δg, has decreased. (As in the previous example an
increase in load current causes more armature reaction, which. requires AVR action to
restore the terminal voltage VT)
Figures 2a) & b) Equivalent Circuit for a Generator Operating at 0.9 pf Lagging
and Phasor Diagram.
Diagrams can be drawn to show that, when operating with a leading power factor
and delivering the same active current, the Ia Xd component will also increase (current
again has active and reactive components), but the load angle δ will Increase. (In this
case, rotor current may require a decrease to maintain terminal voltage. This is because
the magnetic field produced around the stator windings will provide less weakening of
the field flux.)
—4—
5. Variation of Transmission Line Load Angle With Load
When a transmission line is loaded, a load angle δL is produced across the line.
Figure 3 a) shows the equivalent circuit for a line having a reactance of XL ohms and load
is operating with a pf of cos θ lag. The resistance of the line is very small compared with
its reactance, and will be neglected in this lesson. When the line is operating at 0.9 pf lag
the supply voltage has to be considerably larger than the load voltage (which is kept
constant). This is shown in the phasor diagram Figure 3 b). Note that a large load current
Ia on the line having a large value of XL will give a large load angle δL
(a) (b)
Figures 3a) & b): Equivalent Circuit for a Transmission Line Operating at 0.9 Lag
with Phasor Diagram
From the diagram, we can also see the result of changes in load angle caused by
changes in load power factor (changes in θ). As θ becomes more lagging (increases
clockwise) δL decreases. And conversely, as θ becomes more leading δL increases.
Remember that this is only true in this example if the MW load remains constant.
—5—
6. Variation of Generator and Line Load Angle with Load
Figure 4 a) shows an equivalent circuit of a generator feeding a load via a
transmission line. The generator operates with a load angle of δg and the line
operates with a load angle of δL. The load is operating with a pf of cos θ.
b)
Figures 4a) & b): Equivalent Circuit for a Generator, Line and Load with Phasor
Diagram
Note that:
a) the generator operates at a power factor angle of θgen which is greater than θload
b) the generator and line operate together at an angle of δT, which is the sum of δg, and δL
Any change in the load angle of the line or the generator, will result in a change in the
total load angle for the generator/line.
—6—
7. SUMMARY OF THE KEY CONCEPTS
• The load angle in a generator increases with increasing load current Ia
• The load angle in a generator increases with operation at a more leading pf (decreasing
excitation) if the MW load is held constant.
• Conversely the load angle decreases with a decrease in load and/or operation at a more
lagging pf (increasing excitation) if the MW load remains constant.
• The load angle for a transmission line increases as the load on the line increases. As the
load power factor for a transmission line becomes more leading the load angle will
increase.
• The total load angle for a generator/line is the sum of the individual load angles.
The Relationship Between Load Angle and Active Power Transfer.
In the system shown in Figure 4 a), the resistance of the generator and the lines is
neglected, and consequently the system can be taken to be Loss free. ie there will be no
active power loss between the generator terminals and the load.
As losses are neglected Pgen = Pload
If the line has reactance XL the true power flowing through the reactance to the load will
be P = VT Vload sin δL /XL (1)
And, for the generator: P = EgVT sinδg /Xd (2)
The power transfer equation for the generator and line is:
P = Vload Eg sin( δg + δL ) / (Xd + XL) (3)
Equation 3 shows that for maximum active power transfer P:
a) Xd and XL should be kept as small as possible. A generator has a value of Xd which
cannot be altered. However, XL can be kept low by having short transmission lines or
using many lines in parallel.
b) Eg and VT and Vload should be kept at rated values. If they decrease load angle
increases.
c) The composite load angle should not exceed 90°.
—7—
8. Transmission Line Steady State Stability Characteristics
In the case of a loss free power line, the power at both ends of the line will be the
same.
Pin = Pout = VTVload sinδ/XL
Pmax = VTVload /XL which occurs at δ = 90° and sinδ = 1
Pin = Pout = Pmax sinδ
Therefore the power transmitted or transferred from one end of the line to the other is a
function of sinδ and a power transfer curve can be drawn, which has a sine wave shape.
Figure 5 shows curves & power P transmitted between two ends of a line having
reactance XL, and voltages VT at one end and VL at the other. Generator characteristics
are not included in this curve. When 100% power is being transmitted and the line is
operating on curve 1 the line will have a load angle of δ1. If the sending end voltage VT is
increased, then the power transfer capability for the line will be increased. When this
happens, we shift to curve number 2 and the line will operate at an angle δ2 which is less
than δ1. If the line voltage is decreased, the power transfer capability of the line will shift
to curve 3 and angle δ3 and if the voltage is reduced further the line will operate on curve
4 and angle δ4.
Figure 5: STEADY STATE STABILITY PTC FOR TRANSMISSION LINES
—8—
9. When δ4 is reached, the line is operating at a 90° load angle. Any further
reduction of the height of the curve or any further increase in power to be transferred will
result in the power input exceeding the power that can be transferred. Assuming the
mechanical power output from the turbine is constant, and line voltage decreases further,
the generator will not be able to convert the mechanical power into electrical power.
There will now be an excess of mechanical power produced over the electrical power
being transferred. This excess power will cause the turbine generator shaft to accelerate.
The net result is that the two ends of the line will no longer remain in synchronism and
instability will result.
Applying these curves to a generator, as soon as the load angle exceeds 90° the
power input to the generator will be greater than the power it can convert or transfer into
electrical active power. Therefore the generator rotor will start to accelerate and, unless
corrective actions are immediately taken, the generator will pole slip. The pole slip is the
result of excessive mechanical input power causing the magnetic link between the
generator and the electrical system to stretch excessively causing synchronism to be
broken. The stronger the magnetic link between the generator and the electrical system,
the more difficult pole slipping will be.
Try to visualize the magnetic link between the generator rotor and the electrical
system as an elastic band. As the torque on the generator rotor increases, the elastic band
connecting the rotor and the electrical system stretches, and the “load angle” between the
rotor and the stator rotating magnetic field (RMF) increases. When the torque exceeds
the strength of the elastic band (exceeds magnetic field strength), the band breaks, and the
load angle continues to increase (pole slip). The stronger the elastic band, the harder it
will be to break it (pole slip).
Steady state stability deals with slow changes in system conditions. This means
that the movement between operating curves is a “slow” process, and load angle changes
are small and slow. Thus, the “worst case” steady state condition will occur when the
operating point moves to the peak of an operating curve, with δ = 90° (eg curve 4 shown
in Figure5). Instability, as described above, will result if conditions change. The
corrective actions that can be taken to avoid steady instability in this situation are:
a) Reduction in turbine power Input.
b) An increase in field current which will increase the flux and Eg (ie. cause the operating
point to move to a “higher” curve)
Instability can be prevented by operating with total load angles well below
stability limits. Maintaining a reasonable “operating margin” of load angle will ensure
unstable conditions are not reached, even if transmission lines are removed from service.
This will be shown in the examples below.
—9—
10. Examples
Practically, we can apply the above information to examples of transmission
line/generator systems.
Example 1: A generator is operating at a load angle of 30° and transmitting power over
two parallel lines. The load angle across the lines is 10°. If all the load is slowly shifted
to one power line, will the line and generator remain stable?
Answer: Using the power transfer equation for the line
P = VTVL sinδL/XL
Transposing gives:
sinδL = PXL / VTVL
If P, VT and VL remain constant then sinδL is proportional to XL.
When δL is 10° sin δL = 0.173 with reactance XL. When XL increases to 2 XL sin δL will
increase to 2(0.173) = 0.347.This gives a new value δL2 for the line load angle where δL2 =
arc sin 0.347 = 20.3°, ie the line load angle is approximately doubled.
The combined load angle for the generator and line is 30° + 20.3° = 50.3° which is
considerably less than 90° and so the generator and line will remain stable.
Example 2:
A generator is operating at a load angle of 30° and transmitting power over 2 parallel
lines. The load angle across the lines is 25°. If the load is slowly transferred to one line
will the system remain stable?
Answer: Using the same power transfer equations as before and assuming P, VL and VT
remain constant then sin δL is proportional to XL.This gives a new value of δL2 for the line
load angle where δL2 = arc sin 0.845 =57.6°, this gives a combined load angle for the
generator and line of (30° + 57.6°) = 87.6°. Under this condition the generator and line
are operating at just less than 90° and will therefore remain sable. Any slight change in
generator output or other conditions will cause the system to become unstable. It would
be most undesirable to operate under these conditions.
Steady state stability deals with slow changes in the system. Rapid changes in the
system will cause large swings in load angles. This is discussed in the following portion
of the module.
—10 —
11. SUMMARY OF THE KEY CONCEPTS
• Active power transfer across power lines varies with the sine function of the total load
angle δ.
• Steady state stability is affected by total load angle, which is the sum of the generator
load angle and line load angle.
• If the load angle exceeds 90° stability will be lost, resulting in pole slipping.
• To prevent steady state instability the mechanical power (input) must not exceed the
power transfer capability of the generator and transmission line. Increased field flux
increases internal voltage E and terminal voltage and causes a shift to a higher power
transfer curve.
• Operating without excessive load angles will ensure that stability limits are not reached,
even under upset conditions.
—11 —
12. TRANSIENT STABILITY
Transient stability examines the behaviour of the generator and lines when faults or rapid
changes occur. Remember that steady state stability involved gradual changes only.
Transient stability can result in large swings of load angles, and possible instability (pole
slipping).
GENERATORS
Figure 6 shows two power transfer curves. Curve 1 is the power transfer curve
used when the generator supplies the load with normal excitation. When the excitation is
reduced the power transfer capability is reduced to curve 2. The shape and height
(amplitude) of the curves were discussed in a previous section of this module. There air
two ways of modeling the generator response to a transient, the two curve, and the one
curve method.
Figure 6: POWER TRANSFER CURVES FOR A GENERATOR
— 12 —
13. Generator Behaviour During A Transient: Two Curve Method
Figure 6 above shows the power transfer curves for a generator before and after a
transient. At the instant before the excitation is reduced, the generator is operating at
point “C” on curve 1 with a load angle of δ1. Power input (mechanical) equals the power
output or power transferred (electrical). At the instant that excitation is reduced the
generator cannot operate at point C on curve 1 because the height of the sine curve 2 has
been reduced. (lower excitation). The generator is still operating with the same load angle
δ1, but the operating point has moved to point “D”. Examining the conditions at point D
on curve 2, we see that the power transfer capability is only P0 . Because P1 is
considerably more than P0., there is more mechanical power input to the generator rotor
than electrical power output from the stator. This difference in power (P1- P0) will cause
the generator rotor to accelerate.
As the rotor accelerates, the magnitude of its load angle will increase from δ1 to δmean at
point X. see Figure 6 where the mechanical input power to the generator equals the
electrical power sent out. But as the speed of the generator rotor is now greater than
synchronous, the magnitude of its load angle will continue to increase until the rotor is
slowed down by the output power being greater than the mechanical input power. This
occurs at point “Y”. At point “Y”, as the generator output power is greater than the input
power, the rotor speed will decrease, the rotor angle will reduce to δmean. At this point, the
rotor speed is less than synchronous, causing the rotor angle to decrease to near δ1. The
rotor will start to accelerate once more, resulting in oscillation of the rotor angle. The
rotor will continue to oscillate back and forth about δmean until the oscillation is damped
out, see Figure 7.
— 13 —
14. Figure 7: HOW ROTOR AND ROTOR ANGLE IN A GENERATOR
OSCILLATE FOLLOWING A TRANSIENT FAULT
The location of point Y is critical and depends on the equal area criteria where (refer to
Figure 8):
a) Area “A” represents the excess in energy produced by the turbine over the energy sent
out by the generator. This area is often known as the accelerating area and represents
kinetic energy gain for the rotor.
b) Area “B” represents the excess in energy sent out over the energy produced. This area
is also known as the braking area and represents kinetic energy sent out into the load.
— 14 —
15. When area “A” = area “B”, the equal area criteria is satisfied, ie, the energy gained
during acceleration is balanced by the energy sent out during braking.
Figure 8: EQUAL AREA CRITERIA WHERE AREA “A EQUALS AREA “B”
— 15 —
16. Figure 9 shows the condition where curve 2 has been reduced, by lowered excitation, to
the level where the whole of the area between curve 2 and the P1 line is used for braking.
Point “z” shows the critical stability angle for the rotor. If this load angle is exceeded, the
generator will become unstable.
Figure 9: CRITICAL STABILITY UNDER TRANSIENT CONDITIONS
— 16—
17. Figure10(a) shows the condition where a generator remaims stable and
Figure 10(b) shows the condition where a generator will become unstable.
There is insufficient braking energy in this second case.
(a) (b)
Figure 10: TRANSIENT CONDITIONS SHOWING GENERATOR STABILITY
AND INSTABILITY
Generator Behaviour During a Transient: One Curve Method.
If only the normal operating curve and the maximum angle of swing are
known, then an examination of the curve and the conditions occurring at the maximum
swing angle can determine whether the generator will remain stable. Figure11 shows the
condition where a system transient caused the generator load angle to swing from δ1, to a
maximum angle “A”. A transient increase in input power and/or a transient decrease in
power transfer capability must have occurred. This could have been due to a transmission
line fault or some other cause. At point “A”, the generator rotor angle has reached its
maximum angle of swing and it is once more operating on the curve shown. At point
“A”, there is an excess of power being transferred over the power being produced by the
turbine. Consequently the rotor angle will decrease. A minimum angle will be reached
before the angle increases again producing an angular oscillation which will decay after a
short time. The generator will remain stable, see Figure 11.
— 17—
18. Figure11: GENERATOR REMAINS STABLE
If the swing angle shown at “B” is now considered, see Figure 12, The transient
has caused the rotor load angle to exceed the critical angle δc and there is an excess of
turbine power over the power being transferred. Consequently there is a resultant
accelerating force and the load angle δ wIll continue to grow. The generator will pole slip
and become unstable.
— 18—
19. Figure 12: GENERATOR BECOMES UNSTABLE
Factors Affecting Generator Transient Stability
An adequate stability margin must be allowed. This is to ensure stability under transient
conditions. To achieve this, the following should be noted:
a) Under normal loading the generator load angle should not be allowed to exceed a
specified low value (about 30°). This is achieved by not exceeding the generator MW
rating, and by keeping sufficient excitation on the rotor. (The reactance Xd which affects
the load angle will by design be kept to a minimum. This will keep the internal voltage
drop and hence the load angle to a minimum.)
b) A fast acting AVR is required to ensure that, under fault conditions, Eg, and VT are not
allowed to decrease excessively.
c) Faults on transmission lines and on other parts of the system must be cleared quickly
by protective relaying and breakers. This will prevent the system from operating on
“low” transfer curves for an appreciable time. It follows that protection schemes and
breakers must have fast operating times (2 cycles). Figure 13) shows how the load angle
increases during fault conditions.
—19—
20. d) Another factor to be considered is that generators should have large inertias, which
will slow the rate of increase in load angle under transient conditions. This is a design
constant over which we have no control. We will ignore this factor’s contribution from a
stability viewpoint.
Figure13: HOW LOAD ANGLE INCREASES DURING A FAULT
The upper curve in Figure 13) represents power transfer under healthy conditions. For
this example, let’s assume that this represents power transfer through three parallel lines
transmission lines, If a line is temporarily lost due to a lightning strike, power transfer is
shifted to the capacity of the two remaining lines. This shifts the operating point to “B”
on the lower curve. Since the power produced is still at P0, which is greater than the
power that can be transferred the turbine generator rotor will accelerate, and the load
angle increases. When the fault clears and the line is restored, the power transfer will
return to the upper curve. The maximum swing of the load angle after the fault clears will
again be determined by the equal area criteria (area A-B-C-D = area D-E-F-G). It follows
that the longer the fault persists the longer the generator is operating on the lower curve
and the greater the load angle becomes with a greater risk of instability.
-20-
21. Transient Stability: Transmission Lines
The power transfer capability of a transmission line is proportional to the product
of the supply and load end voltages. To keep the power transfer capability to its
maximum, and for the line to remain stable under transient conditions, the following
features are employed:
a) Fast acting AVRs are used on the generators at the supply end. This keeps the supply
voltage constant.
b) Synchronous condensers and capacitors are used to keep the load end voltages almost
constant. Having an interconnected system will also aid in keeping the load voltage
constant
c) The reactance XL in ohms per kilometer for a line is essentially constant and the only
way of reducing XL is to operate with short transmission lines, and using more lines in
parallel. Although we cannot change the distance to the loads, we can control the number
of lines.
d) As with generators, fast acting protection schemes and breakers are
required to minimize the time that transient conditions exist.
Examples
A generator and transmission system are operating at point P1 on curve 1 shown
in Figure14. Between the generator and the load are two transmission lines. Due to a
lightning strike, one line trips and the generator and. remaining line operate on curve 2.
Explain whether the generator and line will remain stable. If the generator remains stable,
show the maximum and mean angles of swing and sketch in any oscillations in load
angle.
Figure14: PTC FOR A GENERATOR AND TRANSMISSION LINES
22. -21-
Answer:
The equal area criteria must be satisfied for stability. Figure15 shows the power transfer
curves for a generator and two lines (Curve 1), and a generator and one line (Curve 2).
Area “A” represents the condition where the power input from the turbine is greater than
the power being transferred and the generator rotor accelerates. The rotor speed and
hence load angle δ increases. Area “B” represents the condition where the output power
is greater than the turbine power and the generator rotor brakes or slows down, this
causes δ to decrease. The equal area criteria are satisfied and stability is maintained.
Figure 15: TRANSIENT STABILITY
When the line trips, the rotor and line load angle will increase to δmax,
because the input power is greater than the power being transferred. But, at the δmax point,
because the power output is greater than the power input, the load angle will begin to
reduce (eventually to a value near δ1). The load angle will oscillate and finally stabilize at
a steady value of δmean (see diagram). The braking energy available was greater than the
accelerating energy so the critical angle was not attained and the generator and line
remain stable.
23. -22-
Question:
The power transfer curve for a generator is shown in Figure16. Due to a transient
system disturbance the load angle δ increases. A, B and C on the diagram, are maximum
angles of swing for the three different system disturbances. For each disturbance explain
whether the generator would remain stable or unstable. If the generator remains stable,
show on your diagram the angle at which the generator will stabilize; if it is unstable
show how the angle continues to increase.
Figure16: POWER TRANSFER CURVE FOR A GENERATOR
Answer:
Only one power transfer curve is given together with the maximum load angle for
each condition. Therefore assume that the generator only operates on this curve.
The Input power to the generator, P1 is constant. When the power being supplied by the
generator is greater than P1, the generator rotor brakes or decelerates. When the power
being supplied by the generator is less than P1 the generator rotor accelerates. It is this
acceleration /deceleration that produce the change in load angle δ. Figure 17 shows that
when P1 is less than the power being transferred (point “A’, which is less than the critical
angle δc, on the PTC), the excess power transferred over that supplied by the turbine
creates a braking force and the generator rotor will decelerate. Therefore δ decreases and
after oscillating, will return to its original angle of δ1. The generator will remain stable.
24. -23-
Figure 17: CONDITION “A” SHOWING GENERATOR REMAINS STABLE
For condition B, Figure 18 shows that when the maximum swing angle becomes δ = B,
which is less than the critical angle δc, the braking force is greater than the power
supplied by the turbine so the rotor will, after oscillating, return to its original angle of δ1.
25. Figure 18: CONDITON “B” SHOWING GENERATOR REMAINS STABLE
-24-
For condition C, Figure19 shows that when the maximum swing angle becomes δ = C,
which is greater than the critical angle δc the braking force is less than the turbine force
(P1 is greater than the power being transferred) so the rotor will not return to its original
angle of δ1. The rotor angle will continue to increase and the generator rotor will pole
slip.
Figure 19: CONDITION “C” SHOWING GENERATOR BECOMES UNSTABLE
26. -25-
SUMMARY OF THE KEY CONCEPTS
* Transient instability can result in pole slipping.
For the generator:
* Control of generator load angle will help ensure transient stability. Exceeding
generator MW rating should be avoided.
* AVRs are used to keep generator terminal volts VT constant and improve stability.
* Protection schemes and breakers must rapidly clear faults to prevent large swings in
load angles during transient conditions.
* Preventive maintenance and testing are important to ensure that protection schemes
are operational.
For the transmission line:
* Multiple power lines are used in parallel ( keep XL low).
* Automatic voltage regulation is used to keep supply end voltage
constant. * Synchronous condensers and interconnections are used to keep
load end volts constant. This minimizes voltage drops reducing chances of
transient instability.
* Protection schemes and breakers must rapidly clear faults.