This document provides an introduction to symmetrical components analysis for power system fault analysis. It discusses key symmetrical component concepts including positive, negative, and zero sequence components. Equations are presented for transforming unbalanced three-phase systems into balanced symmetrical components as well as for analyzing and synthesizing systems from the component quantities. Various fault types are reviewed including three-phase, phase-to-phase, phase-to-ground, open phase, and examples are shown of interpreting faults using symmetrical components.
The document appears to be a technical paper on electrical engineering topics related to symmetrical components, transformer energization, and fault analysis. It includes diagrams of symmetrical component representations of faults, discussions of transformer magnetic flux and core saturation during energization, and waveform diagrams of currents and voltages under different fault conditions.
John Kretzschmar presented on advanced polyphase metering on June 20, 2017. The presentation covered the evolution of meters and loads over time, from the past to present and possibilities for the future. It also discussed changes in communications and how non-linear loads have impacted the basic computations of metering. The bulk of the presentation was focused on providing an overview of three-phase power concepts including phasors, voltage and current relationships, and different connection types for three-phase systems.
1) The document analyzes the power system connecting two towns by converting all values to per unit for easier analysis. Fault currents were calculated.
2) A fault current of -j6.76pu was found to flow through the 33kV underground cables during a fault.
3) Voltage drops during faults were calculated for buses A, B, and C. The voltages during a fault at bus A is 1.7502pu, bus B is 1.86859pu, and bus C is -0.0254pu.
This presentation describes the Voltage Source Inverter (VSI) - Six Step Switching - Pole voltages and its control - Frequency control of line voltages
1) The document discusses three-phase power theory, including basic assumptions about three AC voltage sources displaced 120 degrees in time.
2) Key concepts covered include phasors, phase rotation, resistive/inductive/capacitive loads, instantaneous and average power, and Blondel's theorem for measuring power in a multi-wire system.
3) Blondel's theorem states that the total power in an N-wire system can be determined from the readings of N-1 wattmeters.
Single-phase transformers have two adjacent coils that are not physically connected. An alternating current in the primary coil produces a changing magnetic field that induces a voltage in the secondary coil. Transformers can be connected in various configurations including wye-wye, wye-delta, delta-wye, and delta-delta to step up or step down voltages depending on the ratio of turns in the secondary coil to the primary coil.
The document discusses key components of electrical power systems including:
1. Generation stations, transmission lines, substations, distribution systems, and protection devices like circuit breakers and fuses that are used to generate, transmit, and distribute electrical power.
2. Concepts of three-phase power systems including balanced and unbalanced systems, star and delta configurations, phase and line voltages/currents, and impedances of transmission lines.
3. Review of three-phase systems including voltage and current relationships, power calculations, and Kirchhoff's laws applied to nodes.
This document describes different types of waveforms that can be generated by a function generator. It discusses how triangular, square, and sine waves are produced. For triangular waves, the function generator charges and discharges a capacitor to produce a linear ramp waveform. A square wave is created using an integrator circuit that causes the output to switch between saturation voltages. Sine waves can be approximated from triangular waves using a resistor-diode network to nonlinearly scale the output.
The document appears to be a technical paper on electrical engineering topics related to symmetrical components, transformer energization, and fault analysis. It includes diagrams of symmetrical component representations of faults, discussions of transformer magnetic flux and core saturation during energization, and waveform diagrams of currents and voltages under different fault conditions.
John Kretzschmar presented on advanced polyphase metering on June 20, 2017. The presentation covered the evolution of meters and loads over time, from the past to present and possibilities for the future. It also discussed changes in communications and how non-linear loads have impacted the basic computations of metering. The bulk of the presentation was focused on providing an overview of three-phase power concepts including phasors, voltage and current relationships, and different connection types for three-phase systems.
1) The document analyzes the power system connecting two towns by converting all values to per unit for easier analysis. Fault currents were calculated.
2) A fault current of -j6.76pu was found to flow through the 33kV underground cables during a fault.
3) Voltage drops during faults were calculated for buses A, B, and C. The voltages during a fault at bus A is 1.7502pu, bus B is 1.86859pu, and bus C is -0.0254pu.
This presentation describes the Voltage Source Inverter (VSI) - Six Step Switching - Pole voltages and its control - Frequency control of line voltages
1) The document discusses three-phase power theory, including basic assumptions about three AC voltage sources displaced 120 degrees in time.
2) Key concepts covered include phasors, phase rotation, resistive/inductive/capacitive loads, instantaneous and average power, and Blondel's theorem for measuring power in a multi-wire system.
3) Blondel's theorem states that the total power in an N-wire system can be determined from the readings of N-1 wattmeters.
Single-phase transformers have two adjacent coils that are not physically connected. An alternating current in the primary coil produces a changing magnetic field that induces a voltage in the secondary coil. Transformers can be connected in various configurations including wye-wye, wye-delta, delta-wye, and delta-delta to step up or step down voltages depending on the ratio of turns in the secondary coil to the primary coil.
The document discusses key components of electrical power systems including:
1. Generation stations, transmission lines, substations, distribution systems, and protection devices like circuit breakers and fuses that are used to generate, transmit, and distribute electrical power.
2. Concepts of three-phase power systems including balanced and unbalanced systems, star and delta configurations, phase and line voltages/currents, and impedances of transmission lines.
3. Review of three-phase systems including voltage and current relationships, power calculations, and Kirchhoff's laws applied to nodes.
This document describes different types of waveforms that can be generated by a function generator. It discusses how triangular, square, and sine waves are produced. For triangular waves, the function generator charges and discharges a capacitor to produce a linear ramp waveform. A square wave is created using an integrator circuit that causes the output to switch between saturation voltages. Sine waves can be approximated from triangular waves using a resistor-diode network to nonlinearly scale the output.
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.
The document discusses three phase voltage source inverters. It begins by introducing inverters and their use in converting DC to AC power. It then classifies inverters as voltage source or current source. The main topic is the three phase voltage source inverter, which converts DC to three phase AC power using six switches in three arms delayed by 120 degrees. The inverter can operate in 180 degree or 120 degree conduction modes, which determine the output phase and line voltages. Applications of three phase inverters include DC power utilization, UPS, induction heating, variable frequency drives, and electric vehicle drives.
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.
SS9620 PV Cell Evaluation System
Overall Evaluation System Capable of Measuring
Solar Cell Dark Current
l Dark current measurement of large solar cell modules by connecting the booster unit 46015
l Precise parallel resistance measurement and bypass diode
evaluation by using the reverse polarity unit
l Maximum output power of 300W (300V/±1A, 30V/±10A)
l High speed measurement at 100 points in 5ms
l 50μs to 6s/point that supports various kinds of solar cells
l Sampling for short-pulsed, middle-pulsed and long-pulsed light
l 3-slope linear sweep function to measure finely around Isc,
Pmax and Voc
This document discusses how to calculate transformer stability by calculating primary and secondary currents. It provides data for a sample transformer, including rated voltages and currents for the HV, LV, and TV sides. It then shows calculations for expected primary and secondary currents between different sides under different conditions: injecting 380V from the LV side with the HV side shorted, the LV and TV sides shorted, and all three (HV, LV, TV) sides shorted. The calculations are done using the transformer's percentage impedance and rated voltages and currents. The document concludes by listing the calculated primary and secondary current values for each load type and side.
Alternating Current Machines-Synchronous MachinesTalia Carbis
This document provides an overview of synchronous machines including:
- Synchronous machines operate at synchronous speed and lock into the rotating magnetic field produced by the stator.
- The rotor is a magnet that is dragged along for the ride as the rotating magnetic field rotates.
- Torque is produced as the magnetic fields of the rotor and stator interact. The torque allows the motor to operate at a constant synchronous speed under varying load.
SIGNAL SPECTRA EXPERIMENT 1 - FINALS (for AGDON)Sarah Krystelle
This experiment analyzed the operation of a class A power amplifier. Key findings include:
1) The initial operating point (Q-point) was not centered on the AC load line, resulting in output clipping.
2) Adjusting the emitter resistance centered the Q-point on the AC load line, eliminating clipping and increasing the maximum undistorted output voltage.
3) A class A amplifier has low efficiency due to conduction over the entire input cycle, but provides the most linear amplification.
1. The document discusses various types of brushless DC motors (BLDC) and permanent magnet synchronous motors (PMSM), including their operation, advantages, and disadvantages.
2. It provides information on sensorless field oriented control of BLDC and PMSM motors, including current regulation using PI controllers and coordinate system transformations.
3. Mathematical models and filtering techniques like model-based observers are presented for estimating rotor position and motor states in sensorless control applications.
The document summarizes experiments on non-linear op-amp circuits, including a comparator, half-wave rectifier, and clipper. It provides the objectives, required equipment, pre-lab questions, and theoretical explanations of how each circuit works. The experiments involve assembling the circuits using op-amps and diodes, observing input and output waveforms on an oscilloscope, and analyzing the output characteristics as circuit parameters are varied. Key points covered include how comparators detect voltage levels, how rectifiers and clippers modify input signals based on reference voltages, and the roles of op-amp gain and diode properties.
Analog to Digital , Digital to Analog ConversionKunj Patel
This document discusses analog to digital and digital to analog conversion. It explains that many real-world phenomena are analog and require conversion to be processed digitally. It describes how analog to digital conversion works by taking discrete samples of an analog signal at regular time intervals. The document also discusses factors that affect conversion quality like bit depth, sampling rate, and quantization levels. It provides an overview of successive approximation analog to digital conversion and how digital to analog conversion can recreate an analog signal from digital values.
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.
The document provides information about electrical theory, AC and DC power generation and distribution, AC waveforms, RMS values, and three-phase power systems. It explains that three-phase power systems are more efficient and economical than single-phase systems as they allow for smaller conductor sizes while delivering the same power and provide constant power delivery to motors. It also describes the Y and Delta connections in three-phase systems and how the voltage and current values differ between the two configurations.
Chapter 2 ( A) - Polyphase Circuits .pptLiewChiaPing
This document discusses three phase circuits. It covers the advantages of polyphase circuits, basic configurations including delta-wye connections, and power relationships in three phase circuits. Key concepts covered include instantaneous power in balanced three phase circuits remaining constant, voltage and current relationships in wye-wye and delta connections, and how to determine line currents and voltages from given phase information. Examples are provided to demonstrate calculating values for various three phase circuit connections.
The document summarizes an experiment on characterizing a class A power amplifier. Key steps include:
1) Determining the operating point (Q-point) on the DC load line. 2) Drawing the AC load line and ensuring the Q-point is centered. 3) Measuring the maximum undistorted output voltage and input voltage to calculate voltage gain. The measured gain is compared to theoretical calculations accounting for resistances. Unbypassed emitter resistance reduces gain and stability.
This document discusses Bipolar Junction Transistors (BJTs) and their operating regions. It describes the basic components and operation of NPN and PNP BJTs. The three main operating regions for BJTs are discussed: active, cutoff, and saturation regions. Equations for calculating operating points in the active region are provided. The document also discusses biasing techniques, including using a four-resistor network to provide stable biasing and prevent variations in the operating point due to changes in transistor characteristics. An example calculation of bias points is included.
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.
The document discusses three phase voltage source inverters. It begins by introducing inverters and their use in converting DC to AC power. It then classifies inverters as voltage source or current source. The main topic is the three phase voltage source inverter, which converts DC to three phase AC power using six switches in three arms delayed by 120 degrees. The inverter can operate in 180 degree or 120 degree conduction modes, which determine the output phase and line voltages. Applications of three phase inverters include DC power utilization, UPS, induction heating, variable frequency drives, and electric vehicle drives.
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.
SS9620 PV Cell Evaluation System
Overall Evaluation System Capable of Measuring
Solar Cell Dark Current
l Dark current measurement of large solar cell modules by connecting the booster unit 46015
l Precise parallel resistance measurement and bypass diode
evaluation by using the reverse polarity unit
l Maximum output power of 300W (300V/±1A, 30V/±10A)
l High speed measurement at 100 points in 5ms
l 50μs to 6s/point that supports various kinds of solar cells
l Sampling for short-pulsed, middle-pulsed and long-pulsed light
l 3-slope linear sweep function to measure finely around Isc,
Pmax and Voc
This document discusses how to calculate transformer stability by calculating primary and secondary currents. It provides data for a sample transformer, including rated voltages and currents for the HV, LV, and TV sides. It then shows calculations for expected primary and secondary currents between different sides under different conditions: injecting 380V from the LV side with the HV side shorted, the LV and TV sides shorted, and all three (HV, LV, TV) sides shorted. The calculations are done using the transformer's percentage impedance and rated voltages and currents. The document concludes by listing the calculated primary and secondary current values for each load type and side.
Alternating Current Machines-Synchronous MachinesTalia Carbis
This document provides an overview of synchronous machines including:
- Synchronous machines operate at synchronous speed and lock into the rotating magnetic field produced by the stator.
- The rotor is a magnet that is dragged along for the ride as the rotating magnetic field rotates.
- Torque is produced as the magnetic fields of the rotor and stator interact. The torque allows the motor to operate at a constant synchronous speed under varying load.
SIGNAL SPECTRA EXPERIMENT 1 - FINALS (for AGDON)Sarah Krystelle
This experiment analyzed the operation of a class A power amplifier. Key findings include:
1) The initial operating point (Q-point) was not centered on the AC load line, resulting in output clipping.
2) Adjusting the emitter resistance centered the Q-point on the AC load line, eliminating clipping and increasing the maximum undistorted output voltage.
3) A class A amplifier has low efficiency due to conduction over the entire input cycle, but provides the most linear amplification.
1. The document discusses various types of brushless DC motors (BLDC) and permanent magnet synchronous motors (PMSM), including their operation, advantages, and disadvantages.
2. It provides information on sensorless field oriented control of BLDC and PMSM motors, including current regulation using PI controllers and coordinate system transformations.
3. Mathematical models and filtering techniques like model-based observers are presented for estimating rotor position and motor states in sensorless control applications.
The document summarizes experiments on non-linear op-amp circuits, including a comparator, half-wave rectifier, and clipper. It provides the objectives, required equipment, pre-lab questions, and theoretical explanations of how each circuit works. The experiments involve assembling the circuits using op-amps and diodes, observing input and output waveforms on an oscilloscope, and analyzing the output characteristics as circuit parameters are varied. Key points covered include how comparators detect voltage levels, how rectifiers and clippers modify input signals based on reference voltages, and the roles of op-amp gain and diode properties.
Analog to Digital , Digital to Analog ConversionKunj Patel
This document discusses analog to digital and digital to analog conversion. It explains that many real-world phenomena are analog and require conversion to be processed digitally. It describes how analog to digital conversion works by taking discrete samples of an analog signal at regular time intervals. The document also discusses factors that affect conversion quality like bit depth, sampling rate, and quantization levels. It provides an overview of successive approximation analog to digital conversion and how digital to analog conversion can recreate an analog signal from digital values.
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.
The document provides information about electrical theory, AC and DC power generation and distribution, AC waveforms, RMS values, and three-phase power systems. It explains that three-phase power systems are more efficient and economical than single-phase systems as they allow for smaller conductor sizes while delivering the same power and provide constant power delivery to motors. It also describes the Y and Delta connections in three-phase systems and how the voltage and current values differ between the two configurations.
Chapter 2 ( A) - Polyphase Circuits .pptLiewChiaPing
This document discusses three phase circuits. It covers the advantages of polyphase circuits, basic configurations including delta-wye connections, and power relationships in three phase circuits. Key concepts covered include instantaneous power in balanced three phase circuits remaining constant, voltage and current relationships in wye-wye and delta connections, and how to determine line currents and voltages from given phase information. Examples are provided to demonstrate calculating values for various three phase circuit connections.
The document summarizes an experiment on characterizing a class A power amplifier. Key steps include:
1) Determining the operating point (Q-point) on the DC load line. 2) Drawing the AC load line and ensuring the Q-point is centered. 3) Measuring the maximum undistorted output voltage and input voltage to calculate voltage gain. The measured gain is compared to theoretical calculations accounting for resistances. Unbypassed emitter resistance reduces gain and stability.
This document discusses Bipolar Junction Transistors (BJTs) and their operating regions. It describes the basic components and operation of NPN and PNP BJTs. The three main operating regions for BJTs are discussed: active, cutoff, and saturation regions. Equations for calculating operating points in the active region are provided. The document also discusses biasing techniques, including using a four-resistor network to provide stable biasing and prevent variations in the operating point due to changes in transistor characteristics. An example calculation of bias points is included.
Null Bangalore | Pentesters Approach to AWS IAMDivyanshu
#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
- An overly permissive IAM role configuration can lead to privilege escalation by creating a role with administrative privileges and allow a user to assume this role.
- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
- Steps:
- Create role with administrative privileges.
- Allow user to assume the role.
- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
Design and optimization of ion propulsion dronebjmsejournal
Electric propulsion technology is widely used in many kinds of vehicles in recent years, and aircrafts are no exception. Technically, UAVs are electrically propelled but tend to produce a significant amount of noise and vibrations. Ion propulsion technology for drones is a potential solution to this problem. Ion propulsion technology is proven to be feasible in the earth’s atmosphere. The study presented in this article shows the design of EHD thrusters and power supply for ion propulsion drones along with performance optimization of high-voltage power supply for endurance in earth’s atmosphere.
Software Engineering and Project Management - Software Testing + Agile Method...Prakhyath Rai
Software Testing: A Strategic Approach to Software Testing, Strategic Issues, Test Strategies for Conventional Software, Test Strategies for Object -Oriented Software, Validation Testing, System Testing, The Art of Debugging.
Agile Methodology: Before Agile – Waterfall, Agile Development.
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...IJECEIAES
Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
scans holds profound implications for diagnosis. This study presents an ensemble convolutional neural network (CNN) with transfer learning, integrating
the state-of-the-art Deeplabv3+ architecture with the ResNet18 backbone. The
model is rigorously trained and evaluated, exhibiting remarkable performance
metrics, including an impressive global accuracy of 99.286%, a high-class accuracy of 82.191%, a mean intersection over union (IoU) of 79.900%, a weighted
IoU of 98.620%, and a Boundary F1 (BF) score of 83.303%. Notably, a detailed comparative analysis with existing methods showcases the superiority of
our proposed model. These findings underscore the model’s competence in precise brain tumor localization, underscoring its potential to revolutionize medical
image analysis and enhance healthcare outcomes. This research paves the way
for future exploration and optimization of advanced CNN models in medical
imaging, emphasizing addressing false positives and resource efficiency.
Digital Twins Computer Networking Paper Presentation.pptxaryanpankaj78
A Digital Twin in computer networking is a virtual representation of a physical network, used to simulate, analyze, and optimize network performance and reliability. It leverages real-time data to enhance network management, predict issues, and improve decision-making processes.
Comparative analysis between traditional aquaponics and reconstructed aquapon...bijceesjournal
The aquaponic system of planting is a method that does not require soil usage. It is a method that only needs water, fish, lava rocks (a substitute for soil), and plants. Aquaponic systems are sustainable and environmentally friendly. Its use not only helps to plant in small spaces but also helps reduce artificial chemical use and minimizes excess water use, as aquaponics consumes 90% less water than soil-based gardening. The study applied a descriptive and experimental design to assess and compare conventional and reconstructed aquaponic methods for reproducing tomatoes. The researchers created an observation checklist to determine the significant factors of the study. The study aims to determine the significant difference between traditional aquaponics and reconstructed aquaponics systems propagating tomatoes in terms of height, weight, girth, and number of fruits. The reconstructed aquaponics system’s higher growth yield results in a much more nourished crop than the traditional aquaponics system. It is superior in its number of fruits, height, weight, and girth measurement. Moreover, the reconstructed aquaponics system is proven to eliminate all the hindrances present in the traditional aquaponics system, which are overcrowding of fish, algae growth, pest problems, contaminated water, and dead fish.
Gas agency management system project report.pdfKamal Acharya
The project entitled "Gas Agency" is done to make the manual process easier by making it a computerized system for billing and maintaining stock. The Gas Agencies get the order request through phone calls or by personal from their customers and deliver the gas cylinders to their address based on their demand and previous delivery date. This process is made computerized and the customer's name, address and stock details are stored in a database. Based on this the billing for a customer is made simple and easier, since a customer order for gas can be accepted only after completing a certain period from the previous delivery. This can be calculated and billed easily through this. There are two types of delivery like domestic purpose use delivery and commercial purpose use delivery. The bill rate and capacity differs for both. This can be easily maintained and charged accordingly.
1. Symmetrical Components I
An Introduction to Power System Fault
Analysis Using Symmetrical Components
Dave Angell
Idaho Power
21st Annual
Hands-On Relay School
2. What Type of Fault?
-25
0
25
-25
0
25
-25
0
25
-2500
0
2500
-2500
0
2500
-2500
0
2500
1 2 3 4 5 6 7 8 9 10 11
V
A
V
B
V
C
I
A
I
B
I
C
Cycles
VA VB VC IA IB IC
3. What Type of Fault?
-10000
0
10000
-10000
0
10000
-10000
0
10000
-10000
0
10000
1 2 3 4 5 6 7 8 9 10 11
I
A
I
B
I
C
I
R
Cycles
IA IB IC IR
4. What Type of Fault?
-10000
0
10000
-10000
0
10000
-10000
0
10000
1 2 3 4 5 6 7 8 9 10 11
I
A
I
B
I
C
Cycles
IA IB IC
5. What Type of Fault?
-5000
0
5000
-5000
0
5000
-5000
0
5000
-2500
0
2500
1 2 3 4 5 6 7 8 9 10 11
I
A
I
B
I
C
I
R
Cycles
IA IB IC IR
6. What Type of Fault?
-100
0
100
-100
0
100
-100
0
100
-200
-0
200
1 2 3 4 5 6 7 8 9 10 11
I
A
I
B
I
C
I
R
Cycles
IA IB IC IR
7. What Type of Fault?
-200
0
200
-200
0
200
-200
0
200
-500
0
500
1 2 3 4 5 6 7 8 9 10 11
I
A
I
B
I
C
I
R
Cycles
IA IB IC IR
8. What Type of Fault?
-250
0
250
-250
0
250
-250
0
250
-100
0
100
1 2 3 4 5 6 7 8 9 10 11
I
A
I
B
I
C
I
R
Cycles
IA IB IC IR
11. Symmetrical Component
Phasors
The unbalanced three phase system
can be transformed into three
balanced phasors.
– Positive Sequence
– Negative Sequence
– Zero Sequence
12. Positive Phase Sequence (ABC)
-1.0
-0.5
0.0
0.5
1.0
0.000 0.017 0.033 0.050
Time
Magnitude
Va Vb Vc
13. Positive Phase Sequence
Each have the
same magnitude.
Each positive
sequence voltage
or current quantity
is displaced 120°
from one another.
Va1
Vb1
Vc1
14. Positive Phase Sequence
The positive
sequence
quantities have a-
b-c, counter clock-
wise, phase
rotation. Va1
Vb1
Vc1
15. Reverse Phase Sequence (ACB)
-1.0
-0.5
0.0
0.5
1.0
0.000 0.017 0.033 0.050
Time
Magnitude
Va Vb Vc
16. Negative Phase Sequence
Each have the
same magnitude.
Each negative
sequence voltage
or current quantity
is displaced 120°
from one another.
Va2
Vc2
Vb2
17. Negative Phase Sequence
The negative
sequence
quantities have a-
c-b, counter clock-
wise, phase
rotation. Va2
Vc2
Vb2
19. Zero Phase Sequence
Each zero
sequence quantity
has the same
magnitude.
All three phasors
with no angular
displacement
between them, all
in phase.
Va0
Vb0
Vc0
20. Symmetrical Components
Equations
Each phase quantity is equal to the
sum of its symmetrical phasors.
Va = Va0 + Va1 +Va2
Vb = Vb0 + Vb1 +Vb2
Vc = Vc0 + Vc1 +Vc2
The common form of the equations
are written in a-phase terms.
21. The a Operator
Used to shift the a-phase terms to
coincide with the b and c-phase
Shorthand to indicate 120° rotation.
Similar to the j operator of 90°.
Va
22. Rotation of the a Operator
120° counter clock-wise rotation.
A vector multiplied by 1 /120° results in
the same magnitude rotated 120°.
Va
aVa
23. Rotation of the a2 Operator
240° counter clock-wise rotation.
A vector multiplied by 1 /240° results in
the same magnitude rotated 240°.
Va
a2Va
24. B-Phase Zero Sequence
We replace the
Vb sequence
terms by Va
sequence terms
shifted by the a
operator.
Vb0 = Va0
Va0
Vb0
Vc0
25. B-Phase Positive Sequence
We replace the Vb
sequence terms by
Va sequence terms
shifted by the a
operator
Vb1 = a2Va1
Va1
Vb1
Vc1
26. B-Phase Negative Sequence
We replace the Vb
sequence terms by
Va sequence terms
shifted by the a
operator
Vb2 = aVa2 Va2
Vc2
Vb2
27. C-Phase Zero Sequence
We replace the
Vc sequence
terms by Va
sequence terms
shifted by the a
operator.
Vc0 = Va0
Va0
Vb0
Vc0
28. C-Phase Positive Sequence
We replace the Vc
sequence terms by
Va sequence terms
shifted by the a
operator
Vc1 = aVa1 Va1
Vb1
Vc1
29. C-Phase Negative Sequence
We replace the
Vc sequence
terms by Va
sequence terms
shifted by the a
operator
Vc2 = a2Va2
Va2
Vc2
Vb2
30. What have we produced?
Va = Va0 + Va1 + Va2
Vb = Va0 + a2Va1 + aVa2
Vc = Va0 + aVa1 + a2Va2
37. Symmetrical Components
Analysis Equations - 1/3 ??
Va1= 1/3 (Va + aVb +
a2Vc)
Adding the phases yields
3 Va.
Divide by the 3 and now
Va = Va1
a2
Vc
Va
aVb
Vc
Va
Vb
42. The Synthesis Equation Results
in the Original Unbalanced
Voltage
Va2
Vb2
Vc2
Va0
Vb0
Vc0
Va1
Vb1
Vc1
Va
Vc
Vb
43. Symmetrical Components
Present During Shunt Faults
Three phase fault
– Positive
Phase to phase
fault
– Positive
– Negative
Phase to
ground fault
– Positive
– Negative
– Zero
44. Symmetrical Component
Review of Faults Types
Let’s return to the example fault
reports and view the sequence
quantities present
45. Three Phase Fault, Right?
-25
0
25
-25
0
25
-25
0
25
-2500
0
2500
-2500
0
2500
-2500
0
2500
1 2 3 4 5 6 7 8 9 10 11
V
A
V
B
V
C
I
A
I
B
I
C
Cycles
VA VB VC IA IB IC
49. Single Line to Ground Fault
Voltage
– Negative and zero sequence 180 out of
phase with positive sequence
Current
– All sequence are in phase
50. A to B Fault, Easy?
-10000
0
10000
-10000
0
10000
-10000
0
10000
1 2 3 4 5 6 7 8 9 10 11
I
A
I
B
I
C
Cycles
IA IB IC
51. A Phase Symmetrical Component
View of an A to B Phase Fault
Component Magnitude Angle
Ia0 3 -102
Ia1 5993 -81
Ia2 5961 -16
Va0 1 45
Va1 99 0
Va2 95 -117
0
45
90
135
180
225
270
315
I1
I2
V1
V2
52. C Phase Symmetrical Component
View of an A to B Phase Fault
Component Magnitude Angle
Ic0 3 138
Ic1 5993 279
Ic2 5961 104
Vc0 1 -75
Vc1 99 0
Vc2 95 2.5
0
45
90
135
180
225
270
315
I1
I2
V1
V2
53. Line to Line Fault
Voltage
– Negative in phase with positive
sequence
Current
– Negative sequence 180 out of phase
with positive sequence
54. B to C to Ground
-5000
0
5000
-5000
0
5000
-5000
0
5000
-2500
0
2500
1 2 3 4 5 6 7 8 9 10 11
I
A
I
B
I
C
I
R
Cycles
IA IB IC IR
55. A Symmetrical Component View
of a B to C to Ground Fault
Component Magnitude Angle
Ia0 748 97
Ia1 2925 -75
Ia2 1754 101
Va0 8 351
Va1 101 0
Va2 18 348
0
45
90
135
180
225
270
315
I0
I1
I2
V0
V1
V2
56. Line to Line to Ground Fault
Voltage
– Negative and zero in phase with positive
sequence
Current
– Negative and zero sequence 180 out of
phase with positive sequence
57. Again, What Type of Fault?
-100
0
100
-100
0
100
-100
0
100
-200
-0
200
1 2 3 4 5 6 7 8 9 10 11
I
A
I
B
I
C
I
R
Cycles
IA IB IC IR
59. One Phase Open (Series)
Faults
Voltage
– No zero sequence voltage
– Negative 90 out of phase with positive
sequence
Current
– Negative and zero sequence 180 out of
phase with positive sequence
60. What About This One?
-200
0
200
-200
0
200
-200
0
200
-500
0
500
1 2 3 4 5 6 7 8 9 10 11
I
A
I
B
I
C
I
R
Cycles
IA IB IC IR
68. Sequence Operating Quantities
Zero and negative sequence currents
are not present during balanced
conditions.
Good indicators of unbalanced faults
69. Sequence Polarizing Quantities
Polarizing quantities are used to
determine direction.
The quantities used must provide a
consistent phase relationship.
71. Learning Check
Given three current sources
How can zero sequence be produced
to test a relay?
How can negative sequence
produced?
72. How can zero sequence be
produced to test a relay?
A single source provides positive,
negative and zero sequence
– Note that each sequence quantity will
be 1/3 of the total current
Connect the three sources in parallel
and set their amplitude and the
phase angle equal to one another
– The sequence quantities will be equal to
each source output
73. How can negative sequence
produced?
A single source provides positive, negative
and zero sequence
– Each sequence quantity will be 1/3 of the total
current
Set the three source’s amplitude equal to
one another and the phase angles to
produce a reverse phase sequence (Ia at
/0o
, Ib at /120o
and Ic at /-120o
)
– Only negative sequence will be produced
74. Advanced Course Topics
Sequence Networks
Connection of Networks for Faults
Per Unit System
Power System Element Models
75. References
Symmetrical Components for Power
Systems Engineering, J Lewis
Blackburn
Protective Relaying, J Lewis Blackburn
Power System Analysis, Stevenson
Analysis of Faulted Power System, Paul
Anderson
76. Conclusion
Symmetrical components provide:
– balanced analysis of an unbalanced
system.
– a measure of system unbalance
– methods to detect faults
– an ability to distinguish fault direction