Symmetrical Components
Symmetrical Component Analysis
Synthesis of Unsymmetrical Phases from Their Symmetrical Components
The Symmetrical Components of Unsymmetrical Phasors
Phase Shift of Symmetrical Components in or Transformer Banks
Power in Terms of Symmetrical Components
1. The document discusses symmetrical components, which allow representation of unbalanced three-phase quantities as the sum of three balanced components.
2. It introduces the positive, negative, and zero sequence components and the transformation matrix used to relate the symmetrical components to the original unbalanced quantities.
3. Symmetrical components are useful for simplifying analysis of unbalanced conditions like single line-to-ground faults in power systems. Sequence impedances can be used to model devices and transmission lines.
The document discusses sequence impedances of transformers. It defines positive, negative, and zero sequence impedances as the impedance offered to each type of symmetrical current component. For transformers, the positive and negative sequence impedances are equal to the leakage impedance due to negligible core losses. The zero sequence impedance depends on transformer winding configuration and whether the neutral is grounded, ranging from the leakage impedance for grounded neutrals to an open circuit for isolated neutrals.
This seminar presentation discusses symmetrical components in power systems. It introduces symmetrical components and explains their use in power system analysis and protection. Specifically, it covers:
1) The need for symmetrical component analysis to protect generators from overheating during unbalanced loads and to supply sensing voltages for voltage regulators.
2) The mathematical technique of resolving an unbalanced set of phasors into balanced positive, negative, and zero sequence systems.
3) Examples of applying symmetrical component analysis to generators and transformers.
4) The conclusion that symmetrical component analysis improves power system reliability by enabling effective analysis of unbalanced fault systems.
Unit 04 Protection of generators and transformers PremanandDesai
The document discusses faults and protection methods for alternators and transformers. For alternators, common faults include failure of the prime mover, field failure, overcurrent, overspeed, overvoltage, and unbalanced or stator winding faults. Differential and inter-turn protection are described. For transformers, faults include open circuits, overheating, and winding short-circuits. Buchholz devices, earth fault relays, overcurrent relays, and differential systems provide protection. Earth fault protection for transformers uses a core-balance leakage scheme.
Per unit analysis is used to normalize variables in power systems to avoid difficulties in referring impedances across transformers. It involves choosing base values for voltage, power, impedance and current, then expressing all quantities as ratios of their actual to base values. This allows transformer impedances to be treated as single values regardless of which side they are referred to. It also keeps per unit quantities within a narrow range and clearly shows their relative values. The procedure is demonstrated through an example circuit solved first using single phase and then three phase per unit analysis with the same result.
System protection is used to detect problems in power system components and isolate faulty equipment to maintain reliable power. The key elements of a protection system include differential relays to protect generators and transformers from internal faults, overcurrent and distance relays to protect transmission lines from external faults, and bus differential relays to protect distribution buses. Protective devices are needed to maintain acceptable operation, isolate damaged equipment, and minimize harm to personnel and property.
The document discusses over current protection in electrical systems. It describes over current as a situation where excess current flows through a conductor, risking heat generation and equipment damage. Possible causes of over current include short circuits, excessive load, incorrect design, or ground faults. Over current relays protect systems by detecting excess current from current transformers and tripping circuit breakers. Relays are classified based on their time of operation as instantaneous, definite time, or inverse time relays. The document outlines various over current protection schemes used in electrical equipment like transformers and generators.
1. The document discusses symmetrical components, which allow representation of unbalanced three-phase quantities as the sum of three balanced components.
2. It introduces the positive, negative, and zero sequence components and the transformation matrix used to relate the symmetrical components to the original unbalanced quantities.
3. Symmetrical components are useful for simplifying analysis of unbalanced conditions like single line-to-ground faults in power systems. Sequence impedances can be used to model devices and transmission lines.
The document discusses sequence impedances of transformers. It defines positive, negative, and zero sequence impedances as the impedance offered to each type of symmetrical current component. For transformers, the positive and negative sequence impedances are equal to the leakage impedance due to negligible core losses. The zero sequence impedance depends on transformer winding configuration and whether the neutral is grounded, ranging from the leakage impedance for grounded neutrals to an open circuit for isolated neutrals.
This seminar presentation discusses symmetrical components in power systems. It introduces symmetrical components and explains their use in power system analysis and protection. Specifically, it covers:
1) The need for symmetrical component analysis to protect generators from overheating during unbalanced loads and to supply sensing voltages for voltage regulators.
2) The mathematical technique of resolving an unbalanced set of phasors into balanced positive, negative, and zero sequence systems.
3) Examples of applying symmetrical component analysis to generators and transformers.
4) The conclusion that symmetrical component analysis improves power system reliability by enabling effective analysis of unbalanced fault systems.
Unit 04 Protection of generators and transformers PremanandDesai
The document discusses faults and protection methods for alternators and transformers. For alternators, common faults include failure of the prime mover, field failure, overcurrent, overspeed, overvoltage, and unbalanced or stator winding faults. Differential and inter-turn protection are described. For transformers, faults include open circuits, overheating, and winding short-circuits. Buchholz devices, earth fault relays, overcurrent relays, and differential systems provide protection. Earth fault protection for transformers uses a core-balance leakage scheme.
Per unit analysis is used to normalize variables in power systems to avoid difficulties in referring impedances across transformers. It involves choosing base values for voltage, power, impedance and current, then expressing all quantities as ratios of their actual to base values. This allows transformer impedances to be treated as single values regardless of which side they are referred to. It also keeps per unit quantities within a narrow range and clearly shows their relative values. The procedure is demonstrated through an example circuit solved first using single phase and then three phase per unit analysis with the same result.
System protection is used to detect problems in power system components and isolate faulty equipment to maintain reliable power. The key elements of a protection system include differential relays to protect generators and transformers from internal faults, overcurrent and distance relays to protect transmission lines from external faults, and bus differential relays to protect distribution buses. Protective devices are needed to maintain acceptable operation, isolate damaged equipment, and minimize harm to personnel and property.
The document discusses over current protection in electrical systems. It describes over current as a situation where excess current flows through a conductor, risking heat generation and equipment damage. Possible causes of over current include short circuits, excessive load, incorrect design, or ground faults. Over current relays protect systems by detecting excess current from current transformers and tripping circuit breakers. Relays are classified based on their time of operation as instantaneous, definite time, or inverse time relays. The document outlines various over current protection schemes used in electrical equipment like transformers and generators.
Static relays use electronic components like semiconductors instead of mechanical parts to detect faults and operate. They have components like rectifiers to convert AC to DC, level detectors to compare values to thresholds, and amplifiers and output devices to trigger trips. The document discusses the components, types, and applications of various static relays like overcurrent, directional, differential, distance and instantaneous relays used in power system protection.
The document discusses unsymmetrical faults in power systems. It defines different types of unsymmetrical faults like line-to-ground, line-to-line, and double line-to-ground faults. It explains sequence components and the sequence operator a which is used to resolve unbalanced three-phase quantities into balanced sequence components. The symmetrical component transformation and inverse transformation matrices are provided to convert between phase and sequence domains. Sequence impedances for different fault types are also described.
This document discusses unsymmetrical faults in power systems. It begins by defining unsymmetrical faults as faults that result in unequal line currents and displacement. It then discusses the causes of unsymmetrical faults such as falling trees, wind, and insulation failures. The document also summarizes the effects of faults such as overcurrent, equipment loss, and electrical fires. It describes the types of unsymmetrical faults and introduces symmetrical components and Fortescue's Theorem for analyzing unsymmetrical faults using positive, negative, and zero sequence networks. Finally, it briefly discusses fault limiting devices like fuses, circuit breakers, and protective relays.
This presentation discusses various differential protection schemes including circulating current, balanced voltage, percentage differential, transmission line, and carrier aided protection schemes. The circulating current scheme is suitable for pilot wire resistances up to 1000 ohms and capacitances up to 2.5 microfarads. The percentage differential protection relay is used for protection of generators and transformers, providing about 85% earth fault protection for generator windings. Carrier aided protection is most widely used for ultra-high and extra-high voltage power line protection utilizing carrier signals of 500-700 kHz.
Commutation is the process by which the current in a short circuited coil is reversed as it crosses the MNA. During commutation, the coil is briefly short-circuited. If current reversal from positive to zero to negative is completed by the end of the short circuit period, commutation is ideal. If not completed, sparking can occur in the brushes, making commutation non-ideal. Commutation is illustrated through figures showing the current in a coil decreasing to zero and then reversing as it transitions from one side of the brush to the other during the short circuit period.
A three-phase transformer can be constructed as a single unit or from three individual single-phase transformers connected together. A single-unit transformer has advantages like less space, weight, and cost, and is more efficient. However, if a phase fails, the entire transformer must be removed for repair unlike with individual transformers. The document discusses different three-phase transformer connections like star-star, delta-delta, and uses of tertiary windings.
This document discusses power system protection settings and provides information on calculating protection settings. It covers the functions of protective relays and equipment protection, the required information for setting calculations such as line parameters and fault studies, and the process of calculating, checking, and implementing protection settings. The goal is to set protections to operate dependably, securely, and selectively during faults while meeting clearance time requirements.
Power System Analysis was a core subject for Electrical & Electronics Engineering, Based On Anna University Syllabus. The Whole Subject was there in this document.
Share with it ur friends & Follow me for more updates.!
measurement of high voltage and high currents mukund mukund.m
The document discusses various techniques for measuring high voltages and currents, including:
- Sphere gap voltmeters, which measure sparkover voltage between conducting spheres;
- Electrostatic voltmeters, which measure the attraction force between charged parallel plates;
- Generating voltmeters, which use a variable capacitor to generate a current proportional to input voltage.
Peak reading voltmeters are also summarized, which use a capacitor to measure the peak voltage of AC waveforms. The document provides details on the principles, construction, advantages, and limitations of these different high voltage and current measurement methods.
This document discusses different types of directional over current relays. It explains that directional over current relays operate when fault current flows in a particular direction and will not operate if power flows in the opposite direction. It provides details on 30 and 90 degree connections for directional relays and describes the construction and operation of non-directional over current relays and shaded pole type directional over current relays.
This power point presentation provides an overview of fault analysis and sequence networks in power systems. It defines different types of faults including open circuit faults, short circuit faults, symmetrical faults, and unsymmetrical faults. Symmetrical faults involve all three phases and remain balanced, while unsymmetrical faults involve one or two phases. Sequence networks, including positive, negative, and zero sequence networks are used for fault analysis. The presentation describes each type of fault and sequence network in detail.
1. The document discusses power system stability, including classifications of power system states as steady state, dynamic state, and transient state.
2. It describes synchronous machine swing equation and power angle equation, which relate the mechanical power input to the electrical power output of a generator through the power/torque angle.
3. An example calculation is shown to find the steady state power limit of a power system with a generator connected to an infinite bus through a transmission line.
The document provides an overview of substation protection basics. It discusses why protection is needed to detect faults and isolate faulty equipment. The main types of faults are described along with the causes of insulation failures. The types of protection principles covered include overcurrent, differential, pilot wire, and distance protection. Key elements of a protection scheme like circuit breakers, relays, batteries, and transformers are also mentioned.
This document provides an overview of symmetrical components for analyzing three-phase power systems. It introduces symmetrical components and how they can be used to simplify fault calculations. The key symmetrical components are defined as the positive, negative, and zero sequence components. Equations are presented to express the original unbalanced phase voltages and currents in terms of these symmetrical components. The significance of each component is described. Methods for calculating faults using symmetrical components are also outlined.
1) Streamer theory was proposed in 1940 by Rather, Meek and Loeb to explain phenomena not accounted for by Townsend's theory of gas breakdown, such as dependence on gas pressure and geometry.
2) Streamer theory describes how a single avalanche can develop into a spark discharge through distortion of the electric field by space charge, generating further avalanches cumulatively at the avalanche head.
3) Positive ions are left behind the rapidly advancing avalanche head, enhancing the field in front and reducing it behind, while the field is also enhanced between the tail and cathode. This leads to further space charge increase and field enhancement around the anode, forming a streamer connecting anode to cathode.
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.
Three Phase Transformer
Presented by:
Rizwan Yaseen 2017-EE-432
Zeeshan Saeed 2017-EE-414
Muhammad Hamad 2017-EE-404
Muhammad Zeeshan 2017-EE-402
A three phase transformer is made of three sets of primary and secondary windings wound around the legs of a common iron core. It allows for higher transmission voltages using lower amperage wiring. The core can be constructed as either a core type or shell type configuration. A three phase transformer works by inducing secondary voltages from the three phase primary voltages to maintain the proper phase relationships for power distribution.
Detailed presentation created on the topic of electrical power subject on the power system analysis. Shown about Ybus details, Ybus calculations, Power flow and design, Interconnected operation of power system etc.
ECNG 3015 Industrial and Commercial Electrical SystemsChandrabhan Sharma
This document discusses symmetrical components and symmetrical component networks which are used to analyze unbalanced faults in power systems. It explains that a 3-phase unbalanced system can be represented as three balanced systems known as positive, negative, and zero sequence networks. It provides details on constructing these networks for different system components like generators, transmission lines, and transformers. The networks are then used to calculate fault currents and voltages under different fault conditions.
Control of Grid- Interfacing Inverters with Integrated Voltage Unbalance Corr...IOSR Journals
This document describes a control scheme for grid-interfacing inverters to correct voltage unbalance at the point of common coupling (POC). It proposes adding a function to intentionally regulate negative sequence currents in order to minimize negative sequence voltage at the POC. The control scheme uses symmetric sequence decomposition with a multi-variable filter to detect positive and negative sequence voltages. It then determines the desired negative sequence current based on the voltage unbalance factor. Experimental results on a laboratory prototype show the inverter is able to reduce the negative sequence voltage at the POC by absorbing a small negative sequence current from the grid.
Static relays use electronic components like semiconductors instead of mechanical parts to detect faults and operate. They have components like rectifiers to convert AC to DC, level detectors to compare values to thresholds, and amplifiers and output devices to trigger trips. The document discusses the components, types, and applications of various static relays like overcurrent, directional, differential, distance and instantaneous relays used in power system protection.
The document discusses unsymmetrical faults in power systems. It defines different types of unsymmetrical faults like line-to-ground, line-to-line, and double line-to-ground faults. It explains sequence components and the sequence operator a which is used to resolve unbalanced three-phase quantities into balanced sequence components. The symmetrical component transformation and inverse transformation matrices are provided to convert between phase and sequence domains. Sequence impedances for different fault types are also described.
This document discusses unsymmetrical faults in power systems. It begins by defining unsymmetrical faults as faults that result in unequal line currents and displacement. It then discusses the causes of unsymmetrical faults such as falling trees, wind, and insulation failures. The document also summarizes the effects of faults such as overcurrent, equipment loss, and electrical fires. It describes the types of unsymmetrical faults and introduces symmetrical components and Fortescue's Theorem for analyzing unsymmetrical faults using positive, negative, and zero sequence networks. Finally, it briefly discusses fault limiting devices like fuses, circuit breakers, and protective relays.
This presentation discusses various differential protection schemes including circulating current, balanced voltage, percentage differential, transmission line, and carrier aided protection schemes. The circulating current scheme is suitable for pilot wire resistances up to 1000 ohms and capacitances up to 2.5 microfarads. The percentage differential protection relay is used for protection of generators and transformers, providing about 85% earth fault protection for generator windings. Carrier aided protection is most widely used for ultra-high and extra-high voltage power line protection utilizing carrier signals of 500-700 kHz.
Commutation is the process by which the current in a short circuited coil is reversed as it crosses the MNA. During commutation, the coil is briefly short-circuited. If current reversal from positive to zero to negative is completed by the end of the short circuit period, commutation is ideal. If not completed, sparking can occur in the brushes, making commutation non-ideal. Commutation is illustrated through figures showing the current in a coil decreasing to zero and then reversing as it transitions from one side of the brush to the other during the short circuit period.
A three-phase transformer can be constructed as a single unit or from three individual single-phase transformers connected together. A single-unit transformer has advantages like less space, weight, and cost, and is more efficient. However, if a phase fails, the entire transformer must be removed for repair unlike with individual transformers. The document discusses different three-phase transformer connections like star-star, delta-delta, and uses of tertiary windings.
This document discusses power system protection settings and provides information on calculating protection settings. It covers the functions of protective relays and equipment protection, the required information for setting calculations such as line parameters and fault studies, and the process of calculating, checking, and implementing protection settings. The goal is to set protections to operate dependably, securely, and selectively during faults while meeting clearance time requirements.
Power System Analysis was a core subject for Electrical & Electronics Engineering, Based On Anna University Syllabus. The Whole Subject was there in this document.
Share with it ur friends & Follow me for more updates.!
measurement of high voltage and high currents mukund mukund.m
The document discusses various techniques for measuring high voltages and currents, including:
- Sphere gap voltmeters, which measure sparkover voltage between conducting spheres;
- Electrostatic voltmeters, which measure the attraction force between charged parallel plates;
- Generating voltmeters, which use a variable capacitor to generate a current proportional to input voltage.
Peak reading voltmeters are also summarized, which use a capacitor to measure the peak voltage of AC waveforms. The document provides details on the principles, construction, advantages, and limitations of these different high voltage and current measurement methods.
This document discusses different types of directional over current relays. It explains that directional over current relays operate when fault current flows in a particular direction and will not operate if power flows in the opposite direction. It provides details on 30 and 90 degree connections for directional relays and describes the construction and operation of non-directional over current relays and shaded pole type directional over current relays.
This power point presentation provides an overview of fault analysis and sequence networks in power systems. It defines different types of faults including open circuit faults, short circuit faults, symmetrical faults, and unsymmetrical faults. Symmetrical faults involve all three phases and remain balanced, while unsymmetrical faults involve one or two phases. Sequence networks, including positive, negative, and zero sequence networks are used for fault analysis. The presentation describes each type of fault and sequence network in detail.
1. The document discusses power system stability, including classifications of power system states as steady state, dynamic state, and transient state.
2. It describes synchronous machine swing equation and power angle equation, which relate the mechanical power input to the electrical power output of a generator through the power/torque angle.
3. An example calculation is shown to find the steady state power limit of a power system with a generator connected to an infinite bus through a transmission line.
The document provides an overview of substation protection basics. It discusses why protection is needed to detect faults and isolate faulty equipment. The main types of faults are described along with the causes of insulation failures. The types of protection principles covered include overcurrent, differential, pilot wire, and distance protection. Key elements of a protection scheme like circuit breakers, relays, batteries, and transformers are also mentioned.
This document provides an overview of symmetrical components for analyzing three-phase power systems. It introduces symmetrical components and how they can be used to simplify fault calculations. The key symmetrical components are defined as the positive, negative, and zero sequence components. Equations are presented to express the original unbalanced phase voltages and currents in terms of these symmetrical components. The significance of each component is described. Methods for calculating faults using symmetrical components are also outlined.
1) Streamer theory was proposed in 1940 by Rather, Meek and Loeb to explain phenomena not accounted for by Townsend's theory of gas breakdown, such as dependence on gas pressure and geometry.
2) Streamer theory describes how a single avalanche can develop into a spark discharge through distortion of the electric field by space charge, generating further avalanches cumulatively at the avalanche head.
3) Positive ions are left behind the rapidly advancing avalanche head, enhancing the field in front and reducing it behind, while the field is also enhanced between the tail and cathode. This leads to further space charge increase and field enhancement around the anode, forming a streamer connecting anode to cathode.
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.
Three Phase Transformer
Presented by:
Rizwan Yaseen 2017-EE-432
Zeeshan Saeed 2017-EE-414
Muhammad Hamad 2017-EE-404
Muhammad Zeeshan 2017-EE-402
A three phase transformer is made of three sets of primary and secondary windings wound around the legs of a common iron core. It allows for higher transmission voltages using lower amperage wiring. The core can be constructed as either a core type or shell type configuration. A three phase transformer works by inducing secondary voltages from the three phase primary voltages to maintain the proper phase relationships for power distribution.
Detailed presentation created on the topic of electrical power subject on the power system analysis. Shown about Ybus details, Ybus calculations, Power flow and design, Interconnected operation of power system etc.
ECNG 3015 Industrial and Commercial Electrical SystemsChandrabhan Sharma
This document discusses symmetrical components and symmetrical component networks which are used to analyze unbalanced faults in power systems. It explains that a 3-phase unbalanced system can be represented as three balanced systems known as positive, negative, and zero sequence networks. It provides details on constructing these networks for different system components like generators, transmission lines, and transformers. The networks are then used to calculate fault currents and voltages under different fault conditions.
Control of Grid- Interfacing Inverters with Integrated Voltage Unbalance Corr...IOSR Journals
This document describes a control scheme for grid-interfacing inverters to correct voltage unbalance at the point of common coupling (POC). It proposes adding a function to intentionally regulate negative sequence currents in order to minimize negative sequence voltage at the POC. The control scheme uses symmetric sequence decomposition with a multi-variable filter to detect positive and negative sequence voltages. It then determines the desired negative sequence current based on the voltage unbalance factor. Experimental results on a laboratory prototype show the inverter is able to reduce the negative sequence voltage at the POC by absorbing a small negative sequence current from the grid.
1) A three-phase power distribution system uses a balanced three-phase configuration to transmit power from generators to loads.
2) A balanced three-phase circuit can be analyzed as an equivalent single-phase circuit. This allows determining the unknown voltages and currents by solving for a single phase.
3) For a balanced Y-Y connected three-phase circuit, the line currents are equal and differ in phase by 120 degrees, while the line voltages are √3 times the phase voltages and differ in phase by 30 degrees.
This document discusses different types of polyphase systems for generating and supplying alternating current (AC). It describes single phase, two phase, and three phase systems. In a three phase system, a generator contains three coils placed 120 degrees apart that generate three voltages equal in magnitude but out of phase by 120 degrees. Common connections of three phase systems include wye-wye, wye-delta, delta-delta, and delta-wye. Phase and line quantities are also defined.
This document discusses fault analysis in power systems using symmetrical components. It introduces symmetrical components and how they are used to represent unbalanced three-phase systems as balanced sub-systems. It describes sequence impedances for system elements and how to model them using sequence networks for positive, negative, and zero sequence currents. Sequence networks are shown for synchronous generators, power systems, and transformers to model faults.
This document discusses reactive power and voltage control. It covers topics such as the generation and absorption of reactive power, excitation systems, static and dynamic analysis, stability compensation, and various methods of voltage control including tap-changing transformers, static VAR compensators, and FACTS devices. Excitation systems are modeled and the closed-loop automatic voltage regulator model is derived. Static and dynamic analyses of the voltage regulator loop are presented to evaluate stability and response.
Three-phase power circuits consist of three-phase generators, transmission lines, and loads. Almost all electric power generation uses three-phase systems due to advantages over single-phase systems like more power per unit mass and constant power delivery to loads. A three-phase system was first patented in 1882. Three-phase generators produce three voltages 120 degrees out of phase. Loads can be connected in either a wye or delta configuration. Power quantities like real, reactive, and apparent power are defined for both phase and line quantities in balanced three-phase systems.
Three-phase systems have multiple voltages or currents that are displaced in time by 120 degrees. They provide advantages over single-phase systems like higher power capacity, self-starting motors, and more constant power output.
A 3-phase generator produces 3 voltages displaced by 120 degrees through its winding configuration. The voltages can be connected in either a star or delta configuration. In a star connection, the winding ends meet at a central neutral point. In a delta connection, the windings are connected in a closed loop.
Power in a 3-phase circuit can be measured using either 3 wattmeters connected to each phase, or 2 wattmeters connected across different phase combinations to calculate total power.
This document discusses balanced three-phase delta-connected loads. It covers calculating voltages, currents, and power in delta-connected circuits. The key learning goals are understanding basic delta connections, calculating voltages and currents in balanced delta loads, and calculating complex power. Examples are provided to demonstrate calculating phase and line currents and drawing phasor diagrams for delta loads.
Three-phase circuits use three conductors with voltages displaced 120 degrees from each other to transmit power. Balanced three-phase systems have equal voltages of the same frequency and magnitude but displaced in phase by 120 degrees. Common connections for three-phase systems include wye (Y) and delta (Δ). Power calculations can be performed for balanced and unbalanced Y-Y, Y-Δ, and Δ-Y connections. Transformations between Y and Δ configurations are also described.
This document discusses unsymmetrical faults in power systems. It defines unsymmetrical faults as faults that result in unequal line currents and phase displacements. There are three types of unsymmetrical faults: single line-to-ground faults, line-to-line faults, and double line-to-ground faults. Single line-to-ground faults are the most common, accounting for 75-80% of faults, occurring when a conductor contacts ground. Line-to-line faults occur when conductors contact each other. Double line-to-ground faults involve two lines contacting each other and ground. Symmetrical component analysis is used to analyze unsymmetrical faults by resolving currents into positive, negative, and zero sequence components.
unit-1-Three phase circuits and power systems.pptxdeepaMS4
This document provides an overview of the course "BE8254 - Basics of Electrical and Instrumentation Engineering". The objectives are to analyze three phase electrical circuits and power measurement, understand electrical machines, and learn various measuring instruments. Key topics covered include three phase power systems, electrical generators, motors, transformers, and selecting appropriate measuring instruments for applications. The document also discusses three phase power circuits, balanced and unbalanced loads, power equations, star-delta conversions, and electrical measurements.
Design And Simulation Of Distributed Statcom Controller For Power Factor Impr...IJERA Editor
The STATCOM is a static reactive power compensator. It is connected to the grid through ac side reactors and
has a capacitor on the DC-link side. This DC-link capacitor is maintained at a given voltage under closed-loop
control while a set amount of reactive current is fed according to load requirements. The operating frequency of
the VSC is also controlled in a PLL (phase locked loop) manner. Hence, it is essential to have a closed-loop
feedback control operation of the STATCOM. The state space model of the STATCOM is non-linear. The nonlinear
model of the STATCOM is linearized. A linear model of the STACOM is proposed. In this model, the
grid voltage and the fundamental component of the STATCOM VSC terminal voltage are assumed to be inphase
and the modulation index is kept within unity. PI-controllers for the active and reactive currents as well as
the DC-link voltage of the STATCOM have been designed. The model, with PI controllers has been simulated
in MATLAB/SIMULINK environment with variation of the pre-charge voltage on the DC-link capacitor with
linear loads (inductive). Improvement of the power factor of the grid current is achieved for linear loads.
International Journal of Engineering Research and DevelopmentIJERD Editor
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Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
International Journal of Computational Engineering Research(IJCER)ijceronline
This document summarizes a research paper about using an inverter to correct voltage unbalance in a power grid. It describes how the inverter can absorb a small amount of negative sequence current from the grid to reduce the negative sequence voltage at the point of connection. It presents the circuit diagram and control scheme for the inverter. The control scheme uses symmetrical component analysis and a multiple variable filter to determine the negative sequence current reference. It generates current references in the stationary frame using the voltage unbalance factor and delivers them using a double loop controller with proportional resonant controllers. Simulation results are shown to verify the proposed control method.
unit-1-Three phase circuits and power systems.pdfdeepaMS4
This document outlines the objectives and topics covered in a course on basics of electrical and instrumentation engineering. The objectives are to analyze operation of three phase electrical circuits, deal with principles of electrical machines, and understand various measuring instruments. Key topics covered include three phase power supply, balanced and unbalanced loads, power equations, star delta conversions, and electrical measurements. Outcomes include understanding concepts of three phase power circuits and measurement, electrical generators/motors/transformers, and choosing appropriate measuring instruments for applications.
This document discusses fault current calculation methods. It covers symmetrical and asymmetrical faults, and describes analyzing power systems under both normal and abnormal operating conditions. The infinite bus method and per unit methods for calculating fault current are introduced. Synchronous machine response to asymmetrical faults is examined, including the subtransient, transient, and steady state stages. Fault current envelopes are presented.
Ekeeda Provides Online Electrical and Electronics Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree.
This document discusses different types of computer monitors and video cards. It describes CRT and LCD monitors, explaining how each displays images using electrons or liquid crystals. It also covers monitor resolution and refresh rates. The document then discusses video cards, their role in offloading graphics processing from the CPU, and how they improve output quality. Finally, it briefly introduces sound systems and sound cards.
Number systems
A manner of counting
Several different number systems exist
Decimal number system
Used by humans to count
Contains ten distinct digits
Digits combine to make larger numbers
A synchronous motor is electrically identical with an alternator or AC generator.
A given alternator ( or synchronous machine) can be used as a motor, when driven electrically.
Some characteristic features of a synchronous motor are as follows:
1. It runs either at synchronous speed or not at all i.e. while running it maintains a constant speed. The only way to change its speed is to vary the supply frequency (because NS=120f/P).
2. It is not inherently self-starting. It has to be run up to synchronous (or near synchronous) speed by some means, before it can be synchronized to the supply.
3. It is capable of being operated under a wide range of power factors, both lagging and leading. Hence, it can be used for power correction purposes, in addition to supplying torque to drive loads.
The single-phase motor, which are designed to operate from a single-phase supply, are manufactured in a large number of types to perform a wide variety of useful services in home, offices, factories, workshops and in a business establishments etc.
Small motors, particularly in the frictional kW sizes are better known than any other. In fact, most of the new products of the manufacturers of space vehicles, aircrafts, business machines and power tools etc. have been possible due to of the advances made in the design of frictional kW motors. Since the performance requirements of the various applications differ so widely, the motor manufacturing industry has developed many different types of such motors, each being designed to meet specific demands.
Single-phase motors may be classified as under, depending on their construction and method of starting:
1. Induction Motors (split-phase, capacitor and shaded-pole etc.)
2. Repulsion Motors (sometime called inductive-series motor)
3. AC Series Motor, and
4. Un-excited Synchronous Motors
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Two digits combine to make data
Older computers were analog
A range of values made data
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The measure of performance varies with:
Cooling Water Temperature
Shape of load duration curve
Total output
Quality of fuel
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NATURE OF DEFECTS
Microscopic Defects
Macroscopic Defects
ORIGIN OF DEFECTS
Inherent Defects
Processing Defects
Service Defects
DETERIORATES PHYSICAL and MECHANICAL PROPERTIES of MATERIALS
DETECTION of DEFECTS
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CoVID-19 sprang up in Wuhan China in November 2019 and was declared a pandemic by the in January 2020 World Health Organization (WHO). Like the Spanish flu of 1918 that claimed millions of lives, the COVID-19 has caused the demise of thousands with China, Italy, Spain, USA and India having the highest statistics on infection and mortality rates. Regardless of existing sophisticated technologies and medical science, the spread has continued to surge high. With this COVID-19 Management System, organizations can respond virtually to the COVID-19 pandemic and protect, educate and care for citizens in the community in a quick and effective manner. This comprehensive solution not only helps in containing the virus but also proactively empowers both citizens and care providers to minimize the spread of the virus through targeted strategies and education.
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means of transport, a railway is the cheapest means of transport. The maintenance
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• Guru Hargobind's succession ceremony took place on 24 June 1606. He was barely
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• As ordered by Guru Arjan Dev Ji, he put on two swords, one indicated his spiritual
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• He had a long tenure as Guru, lasting 37 years, 9 months and 3 days
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Symmetrical components
1. Symmetrical Components
Symmetrical Component Analysis
Synthesis of Unsymmetrical
Phases from Their Symmetrical
Components
The Symmetrical Components of
Unsymmetrical Phasors
Phase Shift of Symmetrical
Components in or
Transformer Banks
Power in Terms of Symmetrical
Components
Y Y
2. Symmetrical Components
Unsymmetrical Series
Impedance
Sequence Impedance and
Sequence Network
Sequence Networks of
Unloaded generators
Sequence Network
Zero-Sequence Network
4. Synthesis of Unsymmetrical Phases from
Their Symmetrical Components 1
“An unbalanced system of n related phasors can be resolved into
n systems of balanced phasors called the symmetrical components
of the original phasors. The n phasors of each set of components
are equal in lengths , and the angles between adjacent phasors of
the set are equal.”
by C.L Fortescue , 1918
5. Synthesis of Unsymmetrical Phases from
Their Symmetrical Components 2
1. For positive- sequence
components
2. For negative-sequence
components
(1) Positive- sequence components (2) Negative-sequence components
1a 1b
1c
2a
2c
2b
n n
6. Synthesis of Unsymmetrical Phases from
Their Symmetrical Components 3
(3) Zero-sequence components
0aV
0bV
0cV
0 For zero-sequence components
7. Synthesis of Unsymmetrical Phases from
Their Symmetrical Components 4
021 aaaa VVVV
021 bbbb VVVV
021 cccc VVVV
0aV
2aV
aV
1aV
1bV
2bV
0bV
1cV
bV
0cV cV
2cV
8. Synthesis of Unsymmetrical Phases from
Their Symmetrical Components 5
Use a to designate the operator that causes a rotation of in the
counterclockwise direction ,
13601
866.05.02401
866.05.01201
03
02
0
a
ja
ja
0
120
2
a
3
,1 a
2
a a
3
,1 a
a
10. The Symmetrical Components of
Unsymmetrical Phasors 2
02
2
1021
021
2
021
021
aaacccc
aaabbbb
aaaa
VVaVaVVVV
VaVVaVVVV
VVVV
2
1
0
2
2
1
1
111
a
a
a
c
b
a
V
V
V
aa
aa
V
V
V
11. The Symmetrical Components of
Unsymmetrical Phasors 3
2
2
1
1
111
aa
aaA
aa
aaA
2
21
1
1
111
3
1
c
b
a
a
a
a
V
V
V
aa
aa
V
V
V
2
2
2
1
0
1
1
111
3
1
* When three phase phasors are balanced , only the
positive-sequence component exists .
12. The Symmetrical Components of
Unsymmetrical Phasors 4
1.Sequence component representation of L-L voltage
ca
bc
ab
ab
ab
ab
V
V
V
aa
aa
V
V
V
2
2
2
1
0
1
1
111
3
1
2.Sequence component representation of current
c
b
a
a
a
a
I
I
I
aa
aa
I
I
I
2
2
2
1
0
1
1
111
3
1
13. The Symmetrical Components of
Unsymmetrical Phasors 5
)(
3
1
)(
3
1
)(
3
1
0
0
0
cbaa
cabcabab
cbaa
IIII
VVVV
VVVV
No zero-sequence components exist if the sum of the three
phasors is zero.
14. The Symmetrical Components of
Unsymmetrical Phasors 6
)(
3
1
0 cbaa VVVV
00 aV
00 aV 3When is balanced
When 0)( cba VVV
* If then is unbalanced.
* Unbalanced does not guarantee .
00 aV 3
3 00 aV
15. The Symmetrical Components of
Unsymmetrical Phasors 7
)(
3
1
0 cabcabab VVVV
is always zero whether the three phase system
is balanced or not.
)( cabcab VVV is always zero (form closed loop)
0abV
a
b
c
16. The Symmetrical Components of
Unsymmetrical Phasors 8
aI
bI
cI
aI
bI
cI
aI
bI
cI
nI
0)(
3
1
0 cbaa IIII
( ungrounded Y )
0)(
3
1
0 cbaa IIII
nacba IIIII 03)(
Y with a path to neutral
0)(
3
1
0 cbaa IIII
connected
VECTOR
SOFTWARE
17. The Symmetrical Components of
Unsymmetrical Phasors 9
example : One conductor of a three-phase line is open. The current flowing to the
-connected load through line a is 10 A. With the current in line a as
reference and assuming that line c is open, find the symmetrical components
of the line currents
Z Z
Z
a
c
b
ampIa
0
010
ampIb
0
18010
0cI
AIa
0
010
AIb
0
18010
AIc 0
The line currents are :
18. The Symmetrical Components of
Unsymmetrical Phasors 10
0)018010010(
3
1 00
0 aI
)012018010010(
3
1 000
1 aI
Aj 0
3078.589.25
)024018010010(
3
1 000
2 aI
Aj 0
3078.589.25
AIb
0
1 15078.5
AIb
0
2 15078.5
00 bI
AIc
0
1 9078.5
AIc
0
2 9078.5
00 cI
Since there no neutral current involved ,
should be zero .
0aI
19. Phase Shift of Symmetrical Components
in or Transformers Banks 1Y Y
The American standard for designating terminal and on or
transformer requires that the positive-sequence voltage drop from to
neutral leads the positive-sequence voltage drop from to neutral by ,
regardless of whether the or winding is on the high tension side .
Similarly, the positive-sequence voltage drop from to neutral leads the
voltage drop from to neutral by and the positive-sequence voltage
drop from to neutral leads the voltage drop from to
neutral by .
1H
1X Y1H
1X 0
30
0
30
3H
2X
3X
2H
0
30
Y
Y
20. Phase Shift of Symmetrical Components
in or Transformers Banks 2Y Y
Example :
A
B
C a
c
b1H
3H
2H 2X
1X
3X
A
B
C
a
b
c
1H
3H
2H
1X
2X
3X
1AV 1bV 0
30leads by 1aVleads by1AV 0
30
21. Phase Shift of Symmetrical Components
in or Transformers Banks 3Y Y
The American standard for designating terminal and on or
transformer requires that the negative-sequence voltage drop from to
neutral lags the negative-sequence voltage drop from to neutral by ,
regardless of whether the or winding is on the high tension side .
Similarly, the negative-sequence voltage drop from to neutral lags
the voltage drop from to neutral by and the negative-sequence
voltage drop from to neutral lags the voltage drop from to neutral
by .
1H
1X Y1H
1X 0
30
0
30
3H
2X
3X
2H
0
30
Y
Y
22. Phase Shift of Symmetrical Components
in or Transformers Banks 4Y Y
A
B
C a
c
b1H
3H
2H 2X
1X
3X
A
B
C
a
b
c
1H
3H
2H
1X
2X
3X
2aV(b) lags by2AV 0
30
2bV(a) lags by2AV 0
30
Example :
23. Phase Shift of Symmetrical Components
in or Transformers Banks 5Y Y
A
B
C a
c
b1H
3H
2H 2X
1X
3X
2B
2A
2C
2b
2c
2a
1B
1A
1C
1b
1a
1c
1AVleads by1aV 0
90
2AVlags by2aV 0
90
1bVleads by1AV 0
30
2bVlags by2AV 0
30
Y
24. Phase Shift of Symmetrical Components
in or Transformers Banks 6
Example 11.7. The resistive Y-connected load bank of Example 11.2 is supplied from the low-voltage
Y-side of a Y- transformer. The voltages at the load are the same as in that example. Find the line
voltages and currents in per unit on the high-voltage side of the transformer.
unitperI a
0)1(
6.439857.0
unitperI a
0)2(
3.2502346.0
)(6.439857.0 0)1(
basevoltageneutraltolineunitperV an
)(3.2502346.0 0)2(
basevoltageneutraltolineunitperV an
9456.02785.06.739857.0306.439857.0 000)1(
jV A
1517.01789.03.2202346.0303.2502346.0 000)2(
jV A
unitperjVVV AAA
0)2()1(
8.828.07939.00994.0
7138.06798.04.469857.0 0)1(2)1(
jVaV AB
Y Y
25. Phase Shift of Symmetrical Components
in or Transformers Banks 7
0791.02209.07.192346.0 0)2(2)2(
jVaV AB
unitperjVVV BBB
0)2()1(
4.4120.17929.09007.0
2318.09581.06.1939857.0 0)1(2)1(
jVaV AC
2318.00419.03.1002346.0 0)2(2)2(
jVaV AC
unitperjVVV CCC
0)2()1(
1800.100.1
5868.18013.07929.09007.07939.00994.0 jjjVVV BAAB
)(8.11678.1 0
basevoltagaeneutrallineunitper
)(8.116
3
78.1 0
basevoltagaelinetolineunitper
Y Y
27. Phase Shift of Symmetrical Components
in or Transformers Banks 9
A
B
C a
c
b1H
3H
2H 2X
1X
3X
A
B
C
a
b
c
1H
3H
2H
1X
2X
3X
(b) leads by 0
30aV )1(
(a) leads byAV )1( 0
30 AV )1(
aV )1(
Figure 11.23
labeling of lines connected to a three-phase Y- transformer.
Y Y
28. Power in terms of Symmetrical Components
ccbbaa IVIVIVjQPS ***
*
012012
*
AIAV
I
I
I
V
V
V
S
T
c
b
a
T
c
b
a
*
012012
*
012
*
012 3 IVIAAV
TTT
*
2
1
0
2103
a
a
a
aaa
I
I
I
VVV
)(3 2
*
21
*
10
*
0 aaaaaa IVIVIV
IAAT
3, *
29. Unsymmetrical Series Impedance 1
a
b
c '
c
'
b
'
a
cZ
bZ
aZ
aI
bI
cI
caZ
acZ
abZ
c
b
a
ccbca
bcbba
acaba
cc
bb
aa
I
I
I
ZZZ
ZZZ
ZZZ
V
V
V
'
'
'
30. Unsymmetrical Series Impedance 2
2
1
0
2
1
0
'
'
'
a
a
a
ccbca
bcbba
acaba
cc
bb
aa
I
I
I
A
ZZZ
ZZZ
ZZZ
V
V
V
A
2
1
0
1
2
1
0
'
'
'
a
a
a
ccbca
bcbba
acaba
cc
bb
aa
I
I
I
A
ZZZ
ZZZ
ZZZ
A
V
V
V
Z
34. Unsymmetrical Series Impedance 6
Case 2 . If
0)( jiijZ
cba ZZZ
aaaa
ZIV 11' aaaa
ZIV 22' aaaa
ZIV 00'
Symmetrical components of unbalanced currents flowing in a balanced- load
or in balanced series impedances produce voltage drops of the same sequence ,
provided no coupling exists between phases.
If the impedances are unequal, the voltage drop of any one sequence is dependent on the
current of all three sequences.
If coupling such as mutual inductance exists among the three impedances, then the
formula will become more complicated.
Y
1.
2.
Complete transportation assumed
35. Unsymmetrical Series Impedance 7
Assume:
1. No coupling
2.
Positive-sequence currents produce positive-sequence voltage drops.
Negative-sequence currents produce negative sequence voltage drops.
zero-sequence currents produce zero-sequence voltage drops.
cba ZZZ
36. Sequence Impedance and Sequence Network 1
The impedance of circuit when positive- sequence
current alone are flowing is called positive-sequence
impedance.
The impedance of circuit when negative-sequence
currents alone are flowing is called negative
sequence impedance.
When only zero-sequence currents are present, the
impedance is called zero sequence impedance.
37. Sequence Impedance and Sequence Network 2
The single-phase equivalent circuit composed of the impedance to
current of any one sequence only is called the sequence network.
Positive-sequence network contains positive sequence current and
positive sequence impedance only.
Negative-sequence network contains negative sequence current
and negative sequence impedance only.
38. Sequence Impedance and Sequence Network 3
Sequence network carrying the individual currents ,
and are interconnected to represent various
unbalanced fault condition.
1aI 2aI
0aI
Zero-sequence network contains zero sequence current and
zero sequence impedance only.
39. Sequence Impedance and Sequence Network 4
Sequence Impedance of Various Devices
Positive Negative Zero
Line same same different
Transformer same same same
Machine different different different**
* Usually they are assumed to be the same
40. Sequence Networks of Unloaded Generators 1
The generator voltage
are of positive sequence only,
since the generator is designed
to supply balanced three-phase
voltage.
aI
bI
cI
nI
cE
bE
aE
bc
a
++
+
-
--
nZ ),,( cba EEE
41. Sequence Networks of Unloaded Generators 2
2aI
2cI
2bI
a
c
b
2Z
2Z
2Z 2aV
2aI
a
2Z
+
-
Negative-sequence
network
+
-
1aV
aE
1aI
a
1Z
+
-
Positive-sequence
network
Reference
Reference
1aI
1bI
cE
bE
aE
bc
a
+
++
-
--
1Z
1Z1Z
aI
111 ZIEV aaa
222 ZIV aa
42. Sequence Networks of Unloaded Generators 3
1cI
0aI
0aI
0aI
a
c
b
0gZ
0gZ 0gZ
0aI
0aV
a
0gZ
+
-
nZ3
0Z
Zero-sequence
network
Reference
only appears in the zero-sequence
network
nZ
000 ZIV aa nZ
03 aI
)3( 00 nga ZZI
na II 03
43. Sequence Networks of Unloaded Generators 4
Example 11.6. A salient-pole generator without dampers is rated 20 MVA, 13.8kV and has a
direct=axis subtransient reactance of 0.25 per unit. The negative-and-zero-sequence reactance
are, respectively, 0.35 and 0.10 per unit. The neutral of the generator is solidly grounded. With
the generator operating unloaded at rated voltage with , a single line-to-
ground fault occurs at the machine terminals, which then have per-unit voltages to ground,
Determine the subtransient current in the generator and the line-t0-line voltages for subtransient
conditions due to the fault.
unitperEan
0
00.1
0aV 0
25.102013.1 cV0
25.102013.1 bV
0cI
aI
0bI
na II
cnE
bnE
anE
bc
a
++
+
-
- -
nZ
n
Figure 11.15
44. Sequence Networks of Unloaded Generators 5
Figure 11.15 shows the line-to-ground fault of phase a of the machine.
unitperjVb 990.0215.0
unitperjVc 990.0215.0
unitper
j
j
j
j
j
aa
aa
V
V
V
c
b
a
0500.0
0643.0
0143.0
990.0215.0
990.0215.0
0
1
1
111
3
1
2
2
)0(
)0(
)0(
unitperj
j
j
Z
V
I
go
a
a 43.1
10.0
)0143.0()0(
)0(
45. Sequence Networks of Unloaded Generators 6
unitperj
j
jj
Z
VE
I
aan
a 43.1
25.0
)0643.0()00.1(
1
)1(
)1(
unitperj
j
j
Z
V
I
a
a 43.1
35.0
)0500.0(
2
)2(
)2(
29.43 )0()2()1()0(
jIIIII aaaaa
There, the fault current into the ground is
The base current is and so the subtransient current in line a isA837)8.133(000,20
AjjIa 590,383729.4
46. Sequence Networks of Unloaded Generators 7
Line-to-line voltage during the fault are
unitperjVVV baab
0
7.7701.1990.0215.0
unitperjVVV cbbc
0
270980.1980.10
unitperjVVV acca
0
7.7701.1990.0215.0
kVVab
00
7.7705.87.77
3
8.13
01.1
kVVbc
00
27078.15270
3
8.13
980.1
kVVca
00
3.10205.83.102
3
8.13
01.1
47. Sequence Networks of Unloaded Generators 8
Before the fault the line voltages were balanced and equal to 13.8kV. For comparison with the line
voltages after the fault occurs, the prefault voltages, with as reference, are given asanan EV
kVVab
0
308.13 kVVbc
0
2708.13 kVVca
0
1508.13
Figure 11.6 shows phasor diagrams of prefault and postfault voltages.
Figure 11.6
(a) Prefault (b) Postfault
anV
caVcaV
bcV
bcV
abVabV
aa
n
b
b
c c
48. Sequence Networks of Unloaded Generators 9
The positive-sequence diagram of a generator is
composed of an emf in series with the positive-sequence
impedance of the generator.
The negative and zero-sequence diagrams contain no
emfs but include the negative and zero-sequence
impedances of the generator respectively.
49. Sequence Networks 1
The matching reactance in positive-sequence network is the subtransient ,transient,
or synchronous reactance, depending of whether subtransient , transient, or
steady- state condition are being studied.
The reference bus for the positive and negative sequence networks is the neutral
of the generator. So for as positive and negative sequence components are
concerned , the neutral of the generator is at ground potential even if these is
connection between neutral and ground.
The reference bus for the zero sequence network is the ground (not necessary
the neutral of the generator).
nZ
50. Sequence Networks 2
Convert a positive sequence network to a negative sequence
network by changing, if necessary, only the impedance
that represent rotating machine , and by omitting the emf.
The normal one-line impedance diagram plus the induced emf is the
positive sequence network.
Three-phase generators and motors have internal voltage of positive
sequence only.
51. Example of Positive and Negative-Sequence Network 1
Example: Draw the positive and negative-sequence networks
for the system described as below . Assume that the
negative-sequence reactance of each machine is
equal to its subtransient reactance .Omit resistance.
1T
1M
T
r
p
m nk l
2M
52. Example of Positive and Negative-Sequence Network 2
++
+
--
-
0857.0j 0915.0j0815.0j
5490.0j
02.0j
2745.0j
2mE1mE
gE
k l m n
p r
0857.0j 0915.0j0815.0j
5490.0j
02.0j 2745.0j
Reference bus
k l m n
p q
(Positive)
(Negative)
53. Zero sequence Network 1
1 . Zero-sequence network currents will flow only if a return path exists.
2 . The reference bus of the zero-sequence network is the ground.
ZZ
Z
N
Z
Z
Z
N
Z N
R
N
Reference
55. Zero sequence Network 3
Zero-sequence equivalent circuit of three phase transform banks.
Symbols Connection Diagrams
Zero-Sequence
Equivalent Circuit
p
p
p
p p p
Q
Q
Q
Q Q
0Z
0Z
Reference bus
Reference bus
56. Zero sequence Network 4
Symbols Connection Diagrams Equivalent Circuit
Zero-Sequence
p
p
p
p
p
p
Q
Q
Q Q
0Z
0Z
Reference bus
Reference bus
57. Zero sequence Network 5
Symbols Connection Diagrams Equivalent Circuit
Zero-Sequence
p
p
p
Q Q
0Z
Reference bus
58. Zero sequence Network 6
nZ3
0gZ Q
R
S
T
M N
P
(Zero-Sequence)
Example:
nZ
Q S
P
R T
M N
59. Zero sequence Network 7
1gZ
Q S
R T
M
NP
2gZ
1gE 1gE
++
--
Q
R T
M
N
P
S
(Positive-Sequence)
(Negative-Sequence)
SEQUENCE
NETWORK
SOFTWARE
60. Zero sequence Network 8
Example 11.9. Draw the zero-sequence network for the system described in Example 6.1. Assume
zero-sequence network for the generator and motors of 0.05 per unit. A current-limiting reactor of
is in each of the each of the neutrals of the generator and the large motor. The zero-sequence
reactance of the transmission line is
4.0
km5.1
Generator:
Motor 1:
Motor 2:
unitperX 05.00
unitperX 0686.0)
8.13
2.13
)(
200
300
(05.0 2
0
unitperX 1372.0)
8.13
2.13
)(
100
300
(05.0 2
0
333.1
300
)20( 2
ZBase
635.0
300
)8.13( 2
ZBase
61. Zero sequence Network 9
unitperZn 900.0)
333.1
4.0
(33
unitperZn 890.1)
635.0
4.0
(33
unitperZ 5445.0
3.176
645.1
0
The zero-sequence network is shown in Fig. 11.28
05.0j
900.0j
0857.0j 5445.0j 0915.0j
l m
k
n
p r
0686.0j
890.1j
1372.0j
reference