This document discusses several power system engineering concepts studied using PowerWorld simulator. It includes 10 problems analyzing topics like power flow analysis, fault analysis, unsymmetrical faults, power factor correction, transmission line diagrams, phase shifting transformers, transmission line conductor selection, transmission line evaluation, load angle estimation, and short circuit duty. The first problem analyzes real and reactive power flow between two buses under base case conditions and with an increased load. It establishes the relationships between real power and load angle and reactive power and voltage.
The document provides an overview of synchronous machines, including:
1. Their physical description with salient pole and round rotor structures.
2. Their mathematical modeling using coupled circuit equations to represent stator and rotor windings.
3. Their steady state operation with balanced sinusoidal stator and rotor magnetic fields.
This document discusses power factor and methods for improving it. It defines power factor as the ratio of active power to apparent power. Low power factor is caused by inductive devices and indicates inefficient electricity use. Correcting power factor through capacitors can provide benefits like increased plant capacity and reduced utility charges. Capacitors work by opposing inductive lagging current. They can be installed at individual equipment, equipment groups, or at the main service, with various tradeoffs to consider. Harmonic distortion from devices like variable speed drives can also impact power quality if not properly addressed.
1) Synchronous machines have a rotor supplied by an external DC source that produces a rotating magnetic field. This induces a voltage in the stator windings.
2) The rotor can have either salient or non-salient poles and is laminated to reduce eddy currents. DC power is supplied to the rotor via slip rings and brushes or a brushless exciter.
3) An equivalent circuit model represents the internal generated voltage and accounts for armature reaction, inductance, and resistance effects on the terminal voltage.
The document discusses power flow analysis, which determines the voltage, current, real power, and reactive power at points in an electrical network under normal operating conditions. It provides three key points:
1. Power flow analysis is important for planning, operations, and future expansion of power systems by studying the effects of new loads, generators, or transmission lines.
2. The analysis involves classifying buses as slack, generator, or load buses and formulating the network equations based on the bus admittance matrix.
3. Solving the load flow problem involves determining the complex voltages across all buses given the network configuration and bus demands. This provides critical information for monitoring overloads and voltage deviations.
Power system analysis material -Mathankumar.s VMKVECMathankumar S
Β
This document provides an overview of power systems, including different types of power generation sources like thermal, hydroelectric, nuclear, gas turbine, and diesel power plants. It also describes the basic components of a power system such as generators, transformers, transmission lines, and loads. Additionally, it discusses the voltage structure of electric power systems including generating stations, transmission systems, and distribution systems. Finally, it introduces the need for system analysis in planning and operating power systems, and distinguishes between steady state and transient state stability analysis.
The document provides an overview of synchronous machines, including:
1. Their physical description with salient pole and round rotor structures.
2. Their mathematical modeling using coupled circuit equations to represent stator and rotor windings.
3. Their steady state operation with balanced sinusoidal stator and rotor magnetic fields.
This document discusses power factor and methods for improving it. It defines power factor as the ratio of active power to apparent power. Low power factor is caused by inductive devices and indicates inefficient electricity use. Correcting power factor through capacitors can provide benefits like increased plant capacity and reduced utility charges. Capacitors work by opposing inductive lagging current. They can be installed at individual equipment, equipment groups, or at the main service, with various tradeoffs to consider. Harmonic distortion from devices like variable speed drives can also impact power quality if not properly addressed.
1) Synchronous machines have a rotor supplied by an external DC source that produces a rotating magnetic field. This induces a voltage in the stator windings.
2) The rotor can have either salient or non-salient poles and is laminated to reduce eddy currents. DC power is supplied to the rotor via slip rings and brushes or a brushless exciter.
3) An equivalent circuit model represents the internal generated voltage and accounts for armature reaction, inductance, and resistance effects on the terminal voltage.
The document discusses power flow analysis, which determines the voltage, current, real power, and reactive power at points in an electrical network under normal operating conditions. It provides three key points:
1. Power flow analysis is important for planning, operations, and future expansion of power systems by studying the effects of new loads, generators, or transmission lines.
2. The analysis involves classifying buses as slack, generator, or load buses and formulating the network equations based on the bus admittance matrix.
3. Solving the load flow problem involves determining the complex voltages across all buses given the network configuration and bus demands. This provides critical information for monitoring overloads and voltage deviations.
Power system analysis material -Mathankumar.s VMKVECMathankumar S
Β
This document provides an overview of power systems, including different types of power generation sources like thermal, hydroelectric, nuclear, gas turbine, and diesel power plants. It also describes the basic components of a power system such as generators, transformers, transmission lines, and loads. Additionally, it discusses the voltage structure of electric power systems including generating stations, transmission systems, and distribution systems. Finally, it introduces the need for system analysis in planning and operating power systems, and distinguishes between steady state and transient state stability analysis.
The document discusses power flow analysis, which determines bus voltages and power flows in a power system under normal steady-state operating conditions. It provides the mathematical formulation of the power flow problem as a set of nonlinear algebraic equations that must be solved iteratively. Buses are classified as slack, generator, or load buses depending on which two of four associated quantities - real power, reactive power, voltage magnitude, and voltage angle - are specified versus solved for. Solution methods like the Gauss-Seidel method are commonly used to iteratively solve the power flow equations until bus voltages converge.
Exp 3 (1)3. To Formulate YBUS Matrix By Singular Transformation.Shweta Yadav
Β
The document describes formulating a YBUS matrix for a power system network model using MATLAB. It presents the theory behind developing the bus admittance matrix YBUS using Kirchhoff's current law and singular transformation. An example 4-bus power system is given, and the student is asked to calculate the YBUS matrix with and without a dotted transmission line connected.
The document discusses capacitance on transmission lines. It explains that capacitance occurs between parallel conductors due to potential differences, similar to capacitor plates, and depends on conductor size and spacing. For short power lines under 80km, capacitance is minor but becomes important for longer, higher voltage lines. It then examines the capacitance of three-phase lines with both equilateral and unsymmetrical conductor spacing, noting calculations are simpler if the line is transposed so each conductor occupies the same positions over cycles.
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.!
Power electronics Uncontrolled Rectifiers - Diode RectifiersBurdwan University
Β
This document discusses different types of uncontrolled diode rectifiers. It begins by classifying rectifiers as controlled, half-controlled, or uncontrolled based on whether they use thyristors, thyristors and diodes, or only diodes, respectively. The document then describes various single-phase and three-phase uncontrolled rectifier circuits including half-wave, full-wave center-tap, full-wave bridge, and multiphase designs. Key parameters like efficiency, voltage, current, ripple, and frequency are defined for each rectifier type. Circuit diagrams and operating principles are provided to explain how the different rectifiers function.
The document discusses the Fast Decoupled Load Flow (FDLF) method for solving load flow problems. FDLF is based on the Newton-Raphson method but further simplifies the load flow equations by assuming that active power changes are more sensitive to voltage angle changes and reactive power changes are more sensitive to voltage magnitude changes. This allows the Jacobian matrix to be separated into two square submatrices related to voltage angle and magnitude. FDLF requires fewer iterations than Newton-Raphson, has higher reliability, and is faster and uses less storage. The method is physically justifiable and can be used in optimization studies involving multiple load flow solutions.
Generation shift factor and line outage factorViren Pandya
Β
This is animated presentation to let students have an idea about use of generation shift factor and line outage distribution factor to assess power system security by contingency analysis. Entire presentation is prepared from a very nice book authored by Wood.
The document discusses load flow studies and the Gauss-Siedel method for solving power flow equations. Load flow studies calculate voltage drops, bus voltages, and power flows under various conditions to determine if voltages remain within limits and equipment is not overloaded. The Gauss-Siedel method iteratively solves power flow equations represented by a non-linear algebraic equation using the bus admittance matrix and known real and reactive power values at buses to calculate unknown bus voltages until converging on a solution. An example applies the Gauss-Siedel method with an acceleration factor to a three bus system to calculate voltages after the first iteration.
This document discusses different types of armature windings for DC motors, including lap and wave windings. Lap winding is where successive coils overlap each other with the finishing end of one coil connected to the starting end of the next. Wave winding forms a wave pattern with coils connected in series. Lap windings use multiple parallel paths and are used for high current machines, while wave windings use two series circuits and are used for high voltage machines. Examples of winding tables for each type are provided.
This document describes receiving end circle diagrams used to visualize load flow over a transmission line. It provides the following key points:
1) Receiving end circle diagrams are derived from voltage phasor diagrams and have different centers for the voltage circles, with a common active and reactive power axis.
2) They can be used to understand how an inductive or capacitive load will affect the reactive power supplied by the source.
3) The center of the receiving end circle is located based on the receiving end voltage magnitude and angle. The radius depends on the sending and receiving end voltage magnitudes.
4) The receiving end circle allows determining the total power received based on the operating point located from the known real power received
60232804 ppt-compensation-techniques-in-ac-transmission-system-using-cABHISHEK RAI
Β
This document discusses series compensation of transmission lines and a new fault location algorithm for series compensated lines under power oscillation conditions. The key points are:
1. Series compensation is used to increase power transfer capability and improve stability by reducing transmission line reactance. It allows increased power transfer but introduces problems like sub-synchronous resonance.
2. The new fault location algorithm accounts for the influence of series capacitors on fault voltages and currents during power oscillations. It calculates corrected voltage drops across series capacitors to improve fault location accuracy under dynamic conditions.
3. The algorithm identifies whether faults occur on the left or right side of series capacitors using a criterion based on voltage and current measurements. An iterative process is
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.
- Synchronous generator excitation requires varying levels of excitation depending on the machine's size, number of poles, speed, and desired regulation. Smaller machines with many poles require proportionally more excitation, while larger machines with fewer poles require less.
- Exciters are commonly built to operate at 125 or 250 volts. Larger alternators are better suited to 250-volt exciters to decrease current.
- Common excitation systems involve a self-excited or separately excited DC shunt generator. For larger machines, a separately excited main exciter driven by a pilot exciter is often used. Automatic voltage regulators aim to maintain a constant voltage despite load changes.
automatic power factor correction reportamaljo joju e
Β
The document describes a project to develop an automatic power factor correction system using a microcontroller. Power factor is an important measure of efficiency in power systems but decreases with increasing inductive loads. The project aims to design a microcontroller-based control system that can monitor power factor and switch capacitor banks in and out to maintain a high power factor close to unity. This will reduce losses in the power system and increase efficiency for both consumers and suppliers. The system design includes current and voltage sensors, a zero-crossing detector, microcontroller calculation of power factor, and relays to switch capacitors banks to compensate for inductive loads.
A flyback converter is a type of switch mode power supply that uses a transformer to transfer energy from the input to the output. It operates by storing energy in the transformer during the on-time of the primary switch, and releasing this energy to the output during the off-time when a diode is conducting. Flyback converters provide galvanic isolation between the input and output through the use of the transformer. They can operate in discontinuous conduction mode where the transformer fully demagnetizes during each switching cycle.
DETECTING POWER GRID SYNCHRONISATION FAILURE ON SENSING BAD VOLTAGE OR FREQUE...Pradeep Avanigadda
Β
The project is designed to develop a system to detect the synchronization failure of any external supply source to the power grid on sensing the abnormalities in frequency and voltage.
There are several power generation units connected to the grid such as hydel, thermal, solar etc to supply power to the load. These generating units need to supply power according to the rules of the grid. These rules involve maintaining a voltage variation within limits and also the frequency. If any deviation from the acceptable limit of the grid it is mandatory that the same feeder should automatically get disconnected from the grid which by effect is termed as islanding. This prevents in large scale brown out or black out of the grid power. So it is preferable to have a system which can warn the grid in advance so that alternate arrangements are kept on standby to avoid complete grid failure.
This 3-page document describes an experiment to separate the different losses in a DC shunt motor, including friction, windage, hysteresis, and eddy current losses. It provides an introduction to the theoretical background, outlines the experimental procedure and apparatus used, includes sample data collection in a table, shows calculations to determine the individual loss coefficients, and lists the conclusions. The goal is to measure the losses at different motor speeds and excitations in order to calculate the separate contributions of each loss type based on their speed and field current dependencies.
The document describes a Simulink model that was created to improve total harmonic distortion (THD) using a shunt active power filter. The model simulates a power system with a non-linear load connected to an ideal grid voltage. The shunt active power filter is connected 0.1 seconds after simulation start and works to compensate for harmonics by producing currents equal in magnitude but opposite in phase to the load harmonics. Simulation results show the THD is reduced from around 30.9% on the load side to 2.79% on the source side once the active filter is connected, below the maximum allowable limit.
Functions and Performance Requirements
Elements of an Excitation System
Types of Excitation Systems
Control and Protection Functions
Modeling of Excitation Systems
The functions of an excitation system are
to provide direct current to the synchronous generator field winding, and
to perform control and protective functions essential to the satisfactory operation of the power system
The performance requirements of the excitation system are determined by
Generator considerations:
supply and adjust field current as the generator output varies within its continuous capability
respond to transient disturbances with field forcing consistent with the generator short term capabilities:
rotor insulation failure due to high field voltage
rotor heating due to high field current
stator heating due to high VAR loading
heating due to excess flux (volts/Hz)
Power system considerations:
contribute to effective control of system voltage and improvement of system stability
This document describes a project to improve power factor using static variable compensation. It contains 5 chapters that discuss: 1) an introduction to power factor and the objectives of the project, 2) a literature review and theoretical background, 3) the main components of the project including a zero crossing detector and triac, 4) the methodology including closed and open loop control approaches, and 5) results and conclusions from testing the project. The project aims to minimize the effects of reactive power flow on transmission lines by using a thyristor switched capacitor to generate reactive power and control the power factor, providing advantages over traditional capacitor banks and synchronous condensers.
Load switches in power systems may cause oscillations in active and reactive power flow.
Such oscillations can be damped by synthetic inertia provided by smart inverters providing power
from DC sources such as photovoltaic or battery storage. However, AC current provided by inverters
is inherently non-sinusoidal, making measurements of active and reactive power subject to harmonic
distortion. As a result, transient effects due to load switching can be obscured by harmonic distortion.
An RLC circuit serves as a reference load. The oscillation caused by switching in the load presents as
a dual-sideband suppressed-carrier signal. The carrier frequency is available via voltage data but the
phase is not. Given a group of candidate signals formed from phase voltages, an algorithm based on
Costas Loop that can quickly quantify the phase difference between each candidate and carrier (thus
identifying the best signal for demodulation) is presented. Algorithm functionality is demonstrated
in the presence of inverter-induced distortion.
The document discusses power flow analysis, which determines bus voltages and power flows in a power system under normal steady-state operating conditions. It provides the mathematical formulation of the power flow problem as a set of nonlinear algebraic equations that must be solved iteratively. Buses are classified as slack, generator, or load buses depending on which two of four associated quantities - real power, reactive power, voltage magnitude, and voltage angle - are specified versus solved for. Solution methods like the Gauss-Seidel method are commonly used to iteratively solve the power flow equations until bus voltages converge.
Exp 3 (1)3. To Formulate YBUS Matrix By Singular Transformation.Shweta Yadav
Β
The document describes formulating a YBUS matrix for a power system network model using MATLAB. It presents the theory behind developing the bus admittance matrix YBUS using Kirchhoff's current law and singular transformation. An example 4-bus power system is given, and the student is asked to calculate the YBUS matrix with and without a dotted transmission line connected.
The document discusses capacitance on transmission lines. It explains that capacitance occurs between parallel conductors due to potential differences, similar to capacitor plates, and depends on conductor size and spacing. For short power lines under 80km, capacitance is minor but becomes important for longer, higher voltage lines. It then examines the capacitance of three-phase lines with both equilateral and unsymmetrical conductor spacing, noting calculations are simpler if the line is transposed so each conductor occupies the same positions over cycles.
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.!
Power electronics Uncontrolled Rectifiers - Diode RectifiersBurdwan University
Β
This document discusses different types of uncontrolled diode rectifiers. It begins by classifying rectifiers as controlled, half-controlled, or uncontrolled based on whether they use thyristors, thyristors and diodes, or only diodes, respectively. The document then describes various single-phase and three-phase uncontrolled rectifier circuits including half-wave, full-wave center-tap, full-wave bridge, and multiphase designs. Key parameters like efficiency, voltage, current, ripple, and frequency are defined for each rectifier type. Circuit diagrams and operating principles are provided to explain how the different rectifiers function.
The document discusses the Fast Decoupled Load Flow (FDLF) method for solving load flow problems. FDLF is based on the Newton-Raphson method but further simplifies the load flow equations by assuming that active power changes are more sensitive to voltage angle changes and reactive power changes are more sensitive to voltage magnitude changes. This allows the Jacobian matrix to be separated into two square submatrices related to voltage angle and magnitude. FDLF requires fewer iterations than Newton-Raphson, has higher reliability, and is faster and uses less storage. The method is physically justifiable and can be used in optimization studies involving multiple load flow solutions.
Generation shift factor and line outage factorViren Pandya
Β
This is animated presentation to let students have an idea about use of generation shift factor and line outage distribution factor to assess power system security by contingency analysis. Entire presentation is prepared from a very nice book authored by Wood.
The document discusses load flow studies and the Gauss-Siedel method for solving power flow equations. Load flow studies calculate voltage drops, bus voltages, and power flows under various conditions to determine if voltages remain within limits and equipment is not overloaded. The Gauss-Siedel method iteratively solves power flow equations represented by a non-linear algebraic equation using the bus admittance matrix and known real and reactive power values at buses to calculate unknown bus voltages until converging on a solution. An example applies the Gauss-Siedel method with an acceleration factor to a three bus system to calculate voltages after the first iteration.
This document discusses different types of armature windings for DC motors, including lap and wave windings. Lap winding is where successive coils overlap each other with the finishing end of one coil connected to the starting end of the next. Wave winding forms a wave pattern with coils connected in series. Lap windings use multiple parallel paths and are used for high current machines, while wave windings use two series circuits and are used for high voltage machines. Examples of winding tables for each type are provided.
This document describes receiving end circle diagrams used to visualize load flow over a transmission line. It provides the following key points:
1) Receiving end circle diagrams are derived from voltage phasor diagrams and have different centers for the voltage circles, with a common active and reactive power axis.
2) They can be used to understand how an inductive or capacitive load will affect the reactive power supplied by the source.
3) The center of the receiving end circle is located based on the receiving end voltage magnitude and angle. The radius depends on the sending and receiving end voltage magnitudes.
4) The receiving end circle allows determining the total power received based on the operating point located from the known real power received
60232804 ppt-compensation-techniques-in-ac-transmission-system-using-cABHISHEK RAI
Β
This document discusses series compensation of transmission lines and a new fault location algorithm for series compensated lines under power oscillation conditions. The key points are:
1. Series compensation is used to increase power transfer capability and improve stability by reducing transmission line reactance. It allows increased power transfer but introduces problems like sub-synchronous resonance.
2. The new fault location algorithm accounts for the influence of series capacitors on fault voltages and currents during power oscillations. It calculates corrected voltage drops across series capacitors to improve fault location accuracy under dynamic conditions.
3. The algorithm identifies whether faults occur on the left or right side of series capacitors using a criterion based on voltage and current measurements. An iterative process is
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.
- Synchronous generator excitation requires varying levels of excitation depending on the machine's size, number of poles, speed, and desired regulation. Smaller machines with many poles require proportionally more excitation, while larger machines with fewer poles require less.
- Exciters are commonly built to operate at 125 or 250 volts. Larger alternators are better suited to 250-volt exciters to decrease current.
- Common excitation systems involve a self-excited or separately excited DC shunt generator. For larger machines, a separately excited main exciter driven by a pilot exciter is often used. Automatic voltage regulators aim to maintain a constant voltage despite load changes.
automatic power factor correction reportamaljo joju e
Β
The document describes a project to develop an automatic power factor correction system using a microcontroller. Power factor is an important measure of efficiency in power systems but decreases with increasing inductive loads. The project aims to design a microcontroller-based control system that can monitor power factor and switch capacitor banks in and out to maintain a high power factor close to unity. This will reduce losses in the power system and increase efficiency for both consumers and suppliers. The system design includes current and voltage sensors, a zero-crossing detector, microcontroller calculation of power factor, and relays to switch capacitors banks to compensate for inductive loads.
A flyback converter is a type of switch mode power supply that uses a transformer to transfer energy from the input to the output. It operates by storing energy in the transformer during the on-time of the primary switch, and releasing this energy to the output during the off-time when a diode is conducting. Flyback converters provide galvanic isolation between the input and output through the use of the transformer. They can operate in discontinuous conduction mode where the transformer fully demagnetizes during each switching cycle.
DETECTING POWER GRID SYNCHRONISATION FAILURE ON SENSING BAD VOLTAGE OR FREQUE...Pradeep Avanigadda
Β
The project is designed to develop a system to detect the synchronization failure of any external supply source to the power grid on sensing the abnormalities in frequency and voltage.
There are several power generation units connected to the grid such as hydel, thermal, solar etc to supply power to the load. These generating units need to supply power according to the rules of the grid. These rules involve maintaining a voltage variation within limits and also the frequency. If any deviation from the acceptable limit of the grid it is mandatory that the same feeder should automatically get disconnected from the grid which by effect is termed as islanding. This prevents in large scale brown out or black out of the grid power. So it is preferable to have a system which can warn the grid in advance so that alternate arrangements are kept on standby to avoid complete grid failure.
This 3-page document describes an experiment to separate the different losses in a DC shunt motor, including friction, windage, hysteresis, and eddy current losses. It provides an introduction to the theoretical background, outlines the experimental procedure and apparatus used, includes sample data collection in a table, shows calculations to determine the individual loss coefficients, and lists the conclusions. The goal is to measure the losses at different motor speeds and excitations in order to calculate the separate contributions of each loss type based on their speed and field current dependencies.
The document describes a Simulink model that was created to improve total harmonic distortion (THD) using a shunt active power filter. The model simulates a power system with a non-linear load connected to an ideal grid voltage. The shunt active power filter is connected 0.1 seconds after simulation start and works to compensate for harmonics by producing currents equal in magnitude but opposite in phase to the load harmonics. Simulation results show the THD is reduced from around 30.9% on the load side to 2.79% on the source side once the active filter is connected, below the maximum allowable limit.
Functions and Performance Requirements
Elements of an Excitation System
Types of Excitation Systems
Control and Protection Functions
Modeling of Excitation Systems
The functions of an excitation system are
to provide direct current to the synchronous generator field winding, and
to perform control and protective functions essential to the satisfactory operation of the power system
The performance requirements of the excitation system are determined by
Generator considerations:
supply and adjust field current as the generator output varies within its continuous capability
respond to transient disturbances with field forcing consistent with the generator short term capabilities:
rotor insulation failure due to high field voltage
rotor heating due to high field current
stator heating due to high VAR loading
heating due to excess flux (volts/Hz)
Power system considerations:
contribute to effective control of system voltage and improvement of system stability
This document describes a project to improve power factor using static variable compensation. It contains 5 chapters that discuss: 1) an introduction to power factor and the objectives of the project, 2) a literature review and theoretical background, 3) the main components of the project including a zero crossing detector and triac, 4) the methodology including closed and open loop control approaches, and 5) results and conclusions from testing the project. The project aims to minimize the effects of reactive power flow on transmission lines by using a thyristor switched capacitor to generate reactive power and control the power factor, providing advantages over traditional capacitor banks and synchronous condensers.
Load switches in power systems may cause oscillations in active and reactive power flow.
Such oscillations can be damped by synthetic inertia provided by smart inverters providing power
from DC sources such as photovoltaic or battery storage. However, AC current provided by inverters
is inherently non-sinusoidal, making measurements of active and reactive power subject to harmonic
distortion. As a result, transient effects due to load switching can be obscured by harmonic distortion.
An RLC circuit serves as a reference load. The oscillation caused by switching in the load presents as
a dual-sideband suppressed-carrier signal. The carrier frequency is available via voltage data but the
phase is not. Given a group of candidate signals formed from phase voltages, an algorithm based on
Costas Loop that can quickly quantify the phase difference between each candidate and carrier (thus
identifying the best signal for demodulation) is presented. Algorithm functionality is demonstrated
in the presence of inverter-induced distortion.
Hybrid Power Quality Compensator for Traction Power System with Photovoltaic ...IJMTST Journal
Β
A hybrid power quality compensator (HPQC) is proposed for comprehensive compensation under minimum
dc operation voltage in high-speed traction power supplies. Reduction in HPQC operation voltage can lead to
a decrease in the compensation device capacity, power consumptions, and installation cost. The parameter
design procedures for minimum dc voltage operation of HPQC are being explored. It is shown through
simulation results that similar compensation performances can be provided by the proposed HPQC with
reduced dc-link voltage level compared to the conventional railway power compensator. The system rating
thus can be reduced. The co phase traction power supply with proposed HPQC is suitable for high-speed
traction applications. In this study, the renewable energy sources are used as the supply to the proposed
concept. Since the solar radiation is abundant thought the world, we can use these systems any way.
Renewable energy resources (RES) are being increasingly connected in distribution systems utilizing power
electronic converters. The compensation performance of the proposed active power filter and the associated
PV system generation scheme with new control scheme is demonstrated to improve the power quality
features is simulated using MATLAB/SIMULINK.
This document describes several alternative dual-bridge matrix converter topologies that have a reduced number of switches compared to a conventional matrix converter. It discusses how the dual-bridge topology avoids commutation problems of the conventional design. It then introduces several dual-bridge topologies with fewer switches, including 18-, 15-, 12-, and 9-switch variations. It analyzes the characteristics and operation of these topologies, and presents simulation and experimental results for the 9-switch design to validate its feasibility.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and DevelopmentIJERD Editor
Β
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
This document is a study report on reactive power compensation using STATCOM. It includes an introduction to reactive power and compensation techniques like shunt and series compensation. It discusses FACTS devices used for compensation with a focus on STATCOM. The report studies load flow analysis, phase angle control of STATCOM, and includes acknowledgments and an abstract analyzing the effects of implementing STATCOM on a six bus system.
Iirdem mitigation of voltage collapse at davanagere receiving stationIaetsd Iaetsd
Β
The document discusses voltage stability issues at the Davanagere Receiving Station power grid in India. Experiments were conducted at three locations - Punabhgatta, Chickjajur, and Davanagere receiving stations - to analyze the impact of capacitor banks on reactive power compensation and voltage regulation. The results showed that connecting capacitor banks provided 0.942 MVAR, 1.02 MVAR, and 9.46 MVAR of reactive power compensation at the three locations respectively, improving the voltage profile and power factor. Simulations were also conducted to analyze performance up to 125% overload conditions, showing that flexible AC transmission systems (FACTS) devices like SVC and STATCOM could further improve voltage stability.
Load Flow and PV Curve Analysis of a 220kV SubstationIRJET Journal
Β
This document discusses load flow analysis and PV curve analysis of a 220kV substation. It presents the methodology used, which includes collecting data from the substation, developing a bus network model, performing load flow analysis using the Newton-Raphson method in MATLAB, and generating PV curves in PowerWorld simulator. The analysis was conducted on two cases with different circuit configurations. The results show voltages, power flows, line losses and identify the knee point of PV curves. Capacitor compensation is also analyzed, showing it can improve voltage stability. The study highlights the importance of load flow analysis for maintaining power system stability and performance.
IRJET- Facts Device for Voltage Regulation in Micro Grid ApplicationsIRJET Journal
Β
This document describes an enhanced controller for an integrated Unified Power Quality Conditioner (iUPQC) that expands its functionality for power quality compensation and microgrid applications. The iUPQC can act as a Static Synchronous Compensator (STATCOM) on the grid side to regulate grid current while supplying conventional UPQC power quality features like sag/swell compensation on the load side. The proposed enhanced controller allows the iUPQC to also provide reactive power support to control current on both the grid and load side buses, providing benefits over conventional STATCOM and UPQC configurations. Simulation results demonstrate the iUPQC's ability to regulate current under no load and nonlinear load conditions.
This document discusses power factor improvement through the use of capacitors. It begins with definitions of key terms like active power, reactive power, and apparent power. It then discusses how inductive loads cause low power factors and the disadvantages of low power factors, such as increased current and line losses. The document presents methods for calculating the capacitance needed to improve the power factor of an inductive load. It also provides examples of typical power factors for various equipment and industries. Overall, the document provides an overview of power factors and how capacitors can be used to improve power factors.
A photovoltaic integrated unified power quality conditioner with a 27-level i...TELKOMNIKA JOURNAL
Β
This paper presents a Unified Power Quality Conditioner (UPQC) with a 27-level inverter based on
an asymmetric H-bridge topology. Each phase of the inverter is composed of three H-bridges, supplied by
three DC sources scaled in the power of three. The output of the multilevel inverter is connected directly to
the point of common coupling (PCC) without the need to a transformer or a filter. The calculation of the Shunt
Active Power Filter (SAPF) compensation current is based on the generalized theory of synchronous frame
(d-q theory) while the calculation of a series active filter voltage is based on Instantaneous Reactive Power
(p-q theory). The control of the SAPF is achieved by using a closed-loop vector control followed by a new
multilevel modulation technique. In addition to the capability of harmonic elimination of both current and
voltage drawn from the source, the UPQC can produce real and reactive power to feed the loads during
prolonged voltage outages or source shortage. Batteries pack are used as a dc link, which is charged from
photovoltaic array connected to the battery through a maximum power point tracker and charge controller.
The injection of real and reactive power depends on the state of charge (SOC) of batteries, the frequency of
the system, real and reactive power of the load, and power factor at the point of PCC. The proposed UPQC
strategy is simulated in MATLAB SIMULINK and the results have shown a significant improved in Total
Harmonics Distortion (THD) of both the voltage and currents.
High Performance of Matrix Converter Fed Induction Motor for IPF Compensation...IOSR Journals
Β
This document discusses a new direct space vector modulation (DSVM) method to improve the input power factor of a matrix converter fed induction motor drive system. The new DSVM method allows control of the displacement angle between the input voltage and current of the matrix converter to maximize the input power factor. Two input power factor compensation algorithms using the new DSVM method are proposed. Simulation and experimental results are presented to validate the effectiveness of the proposed compensation algorithms in improving the input power factor under different load conditions. The document also provides background on the structure and operation of matrix converters, induction motors, and the issues caused by input filters in matrix converter systems that the new DSVM method aims to address.
ER Publication,
IJETR, IJMCTR,
Journals,
International Journals,
High Impact Journals,
Monthly Journal,
Good quality Journals,
Research,
Research Papers,
Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
Science Journals,
Engineering Research Publication
Best International Journals, High Impact Journals,
International Journal of Engineering & Technical Research
ISSN : 2321-0869 (O) 2454-4698 (P)
www.erpublication.org
Power Quality Improvement in Microgrids using STATCOM under Unbalanced Voltag...mohammad hossein mousavi
Β
The document describes a method for improving power quality in microgrids using a static synchronous compensator (STATCOM) under unbalanced voltage conditions. A double synchronous reference frame (DDSRF) control scheme is proposed for the STATCOM to independently control the positive and negative sequence components of voltage. This helps compensate for unbalanced voltage at the point of common coupling and reduces oscillating interactions between the positive and negative sequences. Simulation results show the proposed DDSRF control strategy effectively balances voltage and improves power quality under unbalanced conditions compared to conventional control methods.
Micro-controller based Automatic Power Factor Correction System ReportTheory to Practical
Β
This project report discusses the design of a microcontroller-based automatic power factor correction system. It begins with an introduction to power factor and different correction methods. Static capacitors are used to improve power factor and will be controlled by a microcontroller. Multiple small capacitors can be connected in parallel and switched on or off according to the microcontroller's instructions to maintain a reference power factor close to unity. The system aims to provide effective automatic power factor correction at low cost.
This MATLAB program performs power flow calculations to determine the voltage magnitudes and angles at each bus in an electric power system network. It calculates a Y-bus matrix using line impedance values, then uses the Newton-Raphson method in an iterative process to minimize mismatches between calculated and expected active/reactive power values until reaching an acceptable tolerance. The program was tested on two sample systems and the results, including Jacobian matrices and bus voltage/angle plots, are reported to analyze convergence behavior and power flows. Potential solutions like adding lines or reactive sources are discussed to improve low bus voltages.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
- The document analyzes various transient events in power systems using EMTP-RV simulation software, including capacitor bank switching, back-to-back switching, transformer switching, and transient recovery voltages.
- Simulations of capacitor bank switching show transient overvoltages up to 1.5 times the rated voltage. Back-to-back capacitor switching results in high-frequency transients.
- Transformer switching simulations demonstrate high inrush currents that could damage windings or cause insulation failure without controlled switching.
- Interrupting a ground fault by a circuit breaker leads to high transient recovery voltages that risk re-ignition if above breakdown thresholds.
1) The document presents a technical summary of a power flow analysis for a system consisting of 5 generating stations providing power to a collector substation through a 34.5 KV cable.
2) An initial case with 0 load found no contingency violations, allowing further analysis. A case with assumed loads of 2.5 MVA for the wind turbine and 100 MVA for other equipment found 10 contingency violations.
3) Upgrading the transformer connecting the wind turbine to 25.5 MVA eliminated contingency violations and overloads, providing a solution to safely operate the system within equipment ratings.
This document provides details about the Hydro-QuebecβNew England Multi-Terminal HVDC transmission line project. The project transports power from Quebec, Canada to New England, USA using a bi-polar HVDC transmission line with three terminals - Radisson, Nicolet, and Sandy Pond. The line has a total transmission capacity of 2690MW and was constructed in two phases in 1987 and 1992. It is operated using current source converter technology with Β±450kV transmission voltage.
This proposal suggests installing a tidal and wave power plant off the coast of Southern California to supply electricity to 100,000 customers. The plant would use Deep Green tidal stream generators and WaveNet wave energy converters. 30 Deep Green DG-12 devices, rated at 500 kW each, would generate 15 MW from tidal energy. 141 WaveNet Series 24 devices, rated at 750 kW each, would harness wave power to generate 100 MW. The combined plant is expected to have a total installed capacity of 115 MW.
The document is a project report analyzing power system design options for the Metropolis Light and Power utility following the retirement of the SANDERS69 power plant. It details the initial base case analysis which found system losses of 13.54 MW. Various transmission line upgrade options are available. The goal is to determine the most cost effective upgrade design that meets voltage, line flow, and reliability requirements.
The document is a project report analyzing power system upgrades needed after retirement of the SANDERS69 power plant in Metropolis. It summarizes the initial base case with losses of 13.54 MW and notes all bus voltages and line flows are within limits. It then outlines steps taken to analyze available new transmission line rights-of-way and identify the most economical system upgrades to ensure secure and compliant operation after plant retirement.
This document is an experiment report for a course on computer control of mechanical systems. It describes two main experiments conducted using an ECP software and Model 210 Rectilinear Plant. The first experiment involves PD control of a rigid body, including system identification, designing PV control with different damping ratios, and analyzing the effects of sampling period and integral gain. The second experiment is on controlling a 2DOF mechanical drive system, including system identification, designing a notch filter, and comparing simulation and experimental results. For each part of the experiment, the document analyzes and discusses the results from step responses, sine sweep responses, and simulations in MATLAB. It concludes by discussing the effects of control methods, sampling periods, and integral gains on the system response.
1. 1 | Page
Akshay Nerurkar
nerurkar@usc.edu
Abstract
Studyof differentparametersof electrical engineeringusingpowerworldsimulator
PROBLEM SET
EE 443 PROF. CASTRO
3. 3 | Page
Table of Contents PG
NO.
1. The study of Power flow analysisβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ 2
2. Fault analysisβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦. 19
3. Unsymmetricalfault in a circuitβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ 36
4. Power factor correctionβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.54
5. Power circle diagram for a transmission lineβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.. 61
6. Phaseshifting transformerβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ 66
7. Choice of conductor for a transmission lineβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦. 81
8. Transmission line evaluationβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ 86
9. Load angle estimation for a power lineβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦. 96
Shortcircuit dutyβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦. 101
4. 4 | Page
10.
PROBLEM#01 THE STUDY OF POWER FLOWANALYSIS
In this problemwe are going to study about real and reactive power flow and its
relationship with voltage and angle Ξ΄.
VS/Ξ΄o
VR/0O
SS=PS + jQS TRANSMISSIONLINE SR=PR + jQR
LOAD
GENERATING STATION
#A TWO-BUS POWER SYSTEM
A power flow study (load-flow study) is a steady-stateanalysis whosetargetis to
determine the voltages, currents, and real and reactive power flows in a system
under a given load conditions. The purposeof power flow studies is to plan ahead
and accountfor various hypotheticalsituations. For example, if a transmission line
is be taken off line for maintenance, can the remaining lines in the systemhandle
the required loads withoutexceeding their rated values. In the given diagramVR is
the receiving end voltage and VS is the sending end voltage and SS and SR are the
sending end and receiving end MVAβs. And we shall see an relation between real
and reactive power flow with voltage and angle Ξ΄.
APPROACH
1. The motive here is to analyzethe flow of real and reactive power. I have
decided to study the flow of power between buses NICOL69 and DAVIS69.
G
5. 5 | Page
2. Then, I am going to measurethe voltage levels and load angles at each of
the buses. And then calculate the direction of real and reactive power flow
direction in the circuit.
3. And I am going to establish the relation between real power and load angle
and voltage and reactive power.
4. And then I am going to simulate for the same in the power world analysis.
Figure1.1 shows the Power World example of Metropolis Light and Power
Problem 1
6. 6 | Page
The following figure is a zoomed view of the buses NICOL69 and DAVIS69. (Figure
1.2)
I am going to consider two cases. Onewith base caseand the other one with the
load increased one of the buses.
CASEI
Let us consider the basecase for the buses DAVIS69 and NICOL69.
DAVIS69
We can look at the Real and Reactive power levels on the bus DAVIS69by right
clicking on the bus and selecting the Quick Power Flow List option. This is what
appeared when I selected the Quick Power Flow Option for the bus, DAVIS69.
(Figure1.3)
FIG 1.3
7. 7 | Page
Q= 12.72MVAR
As can be seen from the Quick Power Flow List for the bus, DAVIS69, theReal
Power Flow at the bus is 38 MW and the reactive power flow is 12.72 MVAR.
P = 38 MW, Q = 12.72 MVAR
Figure1.4 gives the power triangle for the bus, DAVIS69.
P= 38 MW
Figure1.4
There is a lagging power factor at the bus.
Power factor = pf = cosΞΈ
π‘π‘π‘ π‘=
38
12.72
This gives,
Ξ1 = 71.44β°(lagging)
NICOL69
We can look at the Real and Reactive power levels on the bus NICOL69 by right
clicking on the bus and selecting the Quick Power Flow List option. This is what
appeared when I selected the Quick Power Flow Option for the bus, NICOL69.
(Figure1.5)
8. 8 | Page
FIG 1.5
As can be seen from the Quick Power Flow List for the bus, NICOL69, theReal
Power Flow at the bus is 28 MW and the reactive power flow is 6 MVAR.
P = 28 MW, Q = 6 MVAR
Figure1.4 gives the power triangle for the bus, NICOL69.
Q= 6MVAR
P= 28 MW
Figure1.4
There is a lagging power factor at the bus.
Power factor = pf = cosΞΈ
tanΞΈ =28/6
This gives,
9. 9 | Page
Ξ2 = 77.90β°(lagging)
Ξ΄ = ΞΈ1 β ΞΈ2
Ξ΄ =-71.44 β°+77.90β°
Ξ΄ = 6.46β°
Thus, theoretically the Real Power should flow from NICOL69 to DAVIS69.
Now,
VNICOL = 1.01 pu. (Base= 69 KV)
VDAVIS =1.02 pu. (Base = 69 KV)
Therefore, the Reactive Power mustflow from the bus DAVIS69 towards NICOL69.
We know that the value of the real power, P is given by the formula,
P = (VA+VB/X)*π‘π‘π‘ π‘
We know the value of VA, VB and Ξ΄. We need to find the value of X to find the
value of P.
The base voltage at the buses is 69 KV. The base MVA can be obtained by right
clicking on the generator on the bus DAVIS69 and selecting the generator
information dialog
11. 11 | Page
VNICOL=69*1.01 KV
VNICOL=69.69 KV
VDAVIS=69*1.02 KV
VDAVIS=70.38 KV
P= 69.69*70.38 π‘π‘π‘6.46
47.61
PTHEOROTICAL=11.61 MW.
Now that we have theorotical figures and predictions, I can simulate the model
and verify my calculations in the power world model.
FIG. 1.6
In the given figure the green arrow representthe active power flowing in the
systemand he blue arrow indicate the reactive power flowing in the system.
Fromthe FIG.1.6itis evident that the real power flows fromNICOL69 toDAVIS69
and the reactive power flows fromDAVIS69 to NICOL69.To calculatethe total Real
Power flow, right click on the transmission lines between the two buses and
select the Line Information Dialog. Add the Real Power flows for both the
transmission lines and get the total flow.
12. 12 | Page
FIG 1.7
As can be seen from figure1.7, the total real power flow between the bus
NICOL69 and DAVIS69comes outto be 9.51 MW. Thus the total power flow is
PActual = 9.51 MW fromthe NICOL69 to DAVIS69 bus.
There is a loss of 19.5% in the calculation of the theorotical and actual power
measurement sincethe theorotical power and the actual power have a diffrence
of 2.24 MW due to the losses in the other branches.
CASE2
In this caseim adding a 30 MVARcapacitor to the systemand weare going to see
its effect on the real and reactive power hence on the load angle and voltage.
13. 13 | Page
FIG 1.8
DAVIS69
We can look at the Real and Reactive power levels on the bus DAVIS69by right
clicking on the bus and selecting the Quick Power Flow List option. This is what
appeared when I selected the Quick Power Flow Option for the bus, DAVIS69.
(Figure1.9)
FIG 1.9
14. 14 | Page
P=38 MW
Q= 4.2 MVAR
As can be seen from the Quick Power Flow List for the bus, DAVIS69, theReal
Power Flow at the bus is 38 MW and the reactive power flow is -4.2 MVAR.
P = 38 MW, Q = -4.2 MVAR
Figure1.10 gives the power triangle for the bus, DAVIS69.
FIG 1.10
There is a leading power factor at the bus.
Power factor = pf = cosΞΈ
π‘π‘π‘ π‘=
4.2
38
This gives,
Ξ1 = 6.30β°(leading)
NICOL69
We can look at the Real and Reactive power levels on the bus NICOL69 by right
clicking on the bus and selecting the Quick Power Flow List option. This is what
appeared when I selected the Quick Power Flow Option for the bus, NICOL69.
(Figure1.11)
15. 15 | Page
P=28 MWQ=25.78 MVAR
P=28 MW
FIG 1.11
As can be seen from the Quick Power Flow List for the bus, NICOL69, theReal
Power Flow at the bus is 28 MW and the reactive power flow is 25.78 MVARas
there is shuntcapacitor.
P = 28 MW, Q = 31.78-6.00 MVAR
Q=25.72 MVAR
Figure1.11 gives the power triangle for the bus, NICOL69.
FIG 1.11
16. 16 | Page
There is lagging power factor at NICOLA69 bus.
Power factor = pf = cosΞΈ
tanΞΈ =28/25.72
This gives,
Ξ2 = -42.56β°(lagging)
Ξ΄ = ΞΈ1 β ΞΈ2
Ξ΄ =6.30 β° + 47.43β°
Ξ΄ = 53.73β°
Thus, theoretically the Real Power should flow from NICOL69 to DAVIS69.
Now,
VNICOL = 1.03 pu (Base= 69 KV)
VDAVIS =1.02 pu (Base = 69 KV)
Therefore, the Reactive Power mustflow from the bus NICOL69 towards DAVIS69.
We know that the value of the real power, P is given by the formula,
P = (VA+VB/X)*π‘π‘π‘ π‘
We know the value of VA, VB and Ξ΄. We need to find the value of X to find the
value of P.
The base voltage at the buses is 69 KV. The base MVA can be obtained by right
clicking on the generator on the bus DAVIS69 and selecting the generator
information dialogue box.
18. 18 | Page
P=VNICOL*VDAVIS π‘π‘π‘ π‘
X
VNICOL=69*1.03 KV
VNICOL=71.07 KV
VDAVIS=69*1.02 KV
VDAVIS=70.38 KV
P= 71.07*70.38 π‘π‘π‘53.46
47.61
PTHEOROTICAL=80.36MW.
Now that we have theorotical figures and predictions, I can simulate the model
and verify my calculations in the power world model.
19. 19 | Page
FIG 1.13
As can be seen from figure1.7, the total real power flow between the bus
NICOL69 and DAVIS69comes outto be 10.73 MW. Thus the total power flow is
PActual = 10.73 MW fromthe NICOL69 to DAVIS69 bus.
There is a loss of 80.5% in the calculation of the theorotical and actual power
measurement sincethe theorotical power and the actual power have a diffrence
of 70 MW due to the losses in the other branches. Bt stil due to the changein the
load angle there is changein the real power for the system.
Hence fromthe given example the relationship between real power and load
angle and reactive power and voltage is proved.
20. 20 | Page
Real powerACTUAL
MW
Load angle δο
Reactive
powerBRANCH
MVAR
Bus Voltage
KV(NICOL69&DAVIS69
)
9.51 6.46 12.40 69.69&70.31
10.73 53.43 4.04 71.07&70.38
I would also like to put forth my results via the matlab analysis for the equation.
DISCUSSION:
Fromthe abovecalculations and simulations we can safely correlate the real
power flows with the load angle and the reactive power flows with the voltage
levels. Real power flows fromhigher to lower load angle bus and the reactive
power flows fromhigher voltage to lower voltage level bus. We also were able to
predict the amountof amount of real power that might flow from say bus A to
bus B. Fromthe 2 cases I can also make a statement that when the reactive power
flow flow between two buses is almost nil, it becomes easier to predict accurate
values of real power flows.
PROBLEM#02 FAULTANAlYSIS
21. 21 | Page
Itis not practical to design and build electrical equipment or networks so as to
completely eliminate the possibility of failure in service. Itis therefore an
everyday factof life that different types of faults occur on electrical systems,
however infrequently, and at randomlocations. Faults can be broadly classified
into two main areas which have been designated βActiveβ and βPassiveβ.
β’ Active Faults
The βActiveβ fault is when actual current flows fromone phaseconductor to
another (phase-to-phase) or alternatively fromone phase conductor to earth
(phase-to-earth). This type of fault can also be further classified into two areas,
namely the βsolidβ fault and the βincipientβ fault. The solid fault occurs as a result
of an immediate complete breakdown of insulation as would happen if, say, a pick
struck an underground cable, bridging conductors etc. or the cable was dug up by
a bulldozer. In mining, a rockfallcould crush a cable as would a shuttle car. In
these circumstances the fault current would be very high, resulting in an electrical
explosion. This type of fault must be cleared as quickly as possible, otherwise
there will be: Greatly increased damage at the fault location. (Fault energy = 1Β² x
Rf x t wheret is time). Danger to operating personnel(Flash products). Danger of
igniting combustiblegas such as methane in hazardous areas giving riseto a
disaster of horrendous proportions. Increased probability of earth faults
spreading to other phases. Higher mechanical and thermal stressing of all items of
plant carrying the current fault. (Particularly transformerswhosewindings suffer
progressiveand cumulative deterioration becauseof the enormous
electromechanical forces caused by multi-phase faults proportionalto the current
squared). Sustained voltage dips resulting in motor (and generator) instability
leading to extensive shut-down atthe plant concerned and possibly other nearby
plants. The βincipientβ fault, on the other hand, is a fault that starts fromvery
small beginnings, fromsay some partial discharge(excessiveelectronic activity
often referred to as Corona) in a void in the insulation, increasing and developing
over an extended period, until such time as it burns away adjacentinsulation,
eventually running away and developing into a βsolidβ fault.
β’ Passive Faults
22. 22 | Page
Passivefaults are not real faults in the true senseof the word but are rather
conditions that are stressing the systembeyond its design capacity, so that
ultimately active faults will occur. Overloading - leading to overheating of
insulation (deteriorating quality, reduced life and ultimate failure). Overvoltage -
stressing the insulation beyond its limits. Under frequency - causing plant to
behave incorrectly. Power swings - generators going out-of-step or synchronism
with each other.
β Types of Faults on a Three PhaseSystem
The types of faults that can occur on a three phaseA.C. systemare as follows:
Types of Faults on a Three PhaseSystem.
(A) Phase-to-earth fault
(B) Phase-to-phasefault
(C) Phase-to-phase-to-earth fault
(D) Three phase fault
(E) Three phase-to-earth fault
(F) Phase-to-pilotfault *
(G) Pilot-to-earth fault *
* In underground mining applications only
23. 23 | Page
Itwill be noted that for a phase-to-phasefault, the currents will be high, because
the fault currentis only limited by the inherent (natural) series impedance of the
power systemup to the point of faulty (refer Ohms law). By design, this inherent
series impedance in a power systemis purposely chosen to be as low as possible
in order to get maximum power transfer to the consumer and limit unnecessary
losses in the network itself in the interests of efficiency. On the other hand, the
magnitude of earth faults currents will be determined by the manner in which the
systemneutral is earthed. Solid neutral earthing means high earth fault currents
as this is only limited by the inherent earth fault (zero sequence) impedance of
the system. Itis worth noting at this juncturethat it is possibleto control the
level of earth fault current that can flow by the judicious choice of earthing
arrangements for the neutral. In other words, by the useof Resistance or
Impedancein the neutral of the system, earth fault currents can be engineered to
be at whatever level is desired and are therefore controllable. This cannot be
achieved for phase faults.
β Transient & PermanentFaults
Transient faults are faults which do not damage the insulation permanently and
allow the circuit to be safely re-energised after a shortperiod of time. A typical
example would be an insulator flashover following a lightning strike, which would
be successfully cleared on opening of the circuit breaker, which could then be
automatically reclosed. Transientfaults occur mainly on outdoor equipment
whereair is the main insulating medium. Permanent faults, as the name implies,
are the resultof permanent damage to the insulation. In this case, the equipment
has to be repaired and reclosing mustnot be entertained.
β Symmetrical & AsymmetricalFaults
A symmetricalfault is a balanced fault with the sinusoidalwaves being equal
about their axes, and represents a steady state condition. An asymmetricalfault
displays a d.c. offset, transient in nature and decaying to the steady state of the
symmetricalfault after a period of time:
Amongstthese faults assosiated with power systemsystemim gonna discuss in
shortabout symmetricsland asymmetricslfaults and discuss its effects with help
of the power world simulator:
1. Symmetrical Faults
24. 24 | Page
2. AsymmetricalFaults
Symmetrical Faults
When there is a 120o
equalphase shiftbetween the conductor due to thid
symmetry it is refered to a symmetricla fault.When there is shortcircuit condition
on a 3 phaseline such kind of fault occurs. This fault condtion rarely occurs most
of the time asymmetricla fault condition occuring but symmetricalcondition
impose moredamage on the breakers and are more severe.
Asymmetrical Faults
This is the frequently occuring fault on a power line an asymmetric or unbalanced
fault does not affect each of the three phases equally. Common types of
asymmetric faults, and their causes:
β line-to-line - a shortcircuit between lines, caused by ionization of air, or
when lines come into physicalcontact, for example due to a broken
insulator.
β line-to-ground - a shortcircuit between one line and ground, very often
caused by physicalcontact, for example due to lightning or other storm
damage
β double line-to-ground - two lines come into contact with the ground (and
each other), also commonly due to stormdamage.
The following is the curverepresenting the symmetricaland asymmetrical
faults in a system.
25. 25 | Page
In this problemim going to show with power world how a symmetricalas well as
a symmetricalfault might occour and affect the characteristic impedence of a
power line. For this im going to assumea fault on the bus and line fromSLACK345
to TIM345.
APPROACH:
1. Firstim going to find the sequence impedencevalue for a given line in our
case it is the line between buses SLACK345 and TIM345fromthebranch
information option by double clicking on the branch.
2. Then im going go to the Run option and then choose the Fault analysis
option and Choosethe single fault options
3. Then im going to choosethe fault location and fault types and its effect on
the line impeadance.
4. Then we are going to find the effects of the differenttypes of fault using
ETAP softwareas a tool.
Firstwe are going to choosea case Design case_6.1
26. 26 | Page
Design case_6.1
FIG. 2.1
The branch between buses SLACK345 and TIM345is the branch weare going to
analyzefor the effects of the different kinds of faults.
Firstdouble click on the branch SLACK345 and TIM345 and record the
characteristic impedance of the branch
27. 27 | Page
FIG 2.2
Fromthe FIG_xx
Z=R+jX=0.02+j0.03 pu;
Y=G+
π‘
π‘
=0+
π‘
0.18
pu;
Now we go to the tool ribbon and click on the fault analysis and choosethe Fault
location in our case we will choosethe in-line fault now we choosethe single line
to ground fault and calculate the fault currentvalue and the characteristic
impedance value
28. 28 | Page
FIG 2.3
Fromthe FIG 2.3
Z=R+jX=0.015+j0.022;
Y=G+
π‘
π‘
=0+
π‘
0.13
;
If
β
=44 p.u.=7833A.
WE CAN ALSO SET THE LOATIONOF THEFAULTON THE LINE.
29. 29 | Page
FROM THE FIG 2.4 LOCTIONOF THEFAULTFROM THE FARBUS.
Now we go to the tool ribbon and click on the fault analysis and give the location
% for the fault on the line we can vary it from1% to 100%.
NOW WE CAN CAN CALCULATE THE CHANGE OF CHARACTERISTICIMPEDANCE
AND ITS AFFECTONTHE LONG TRANSMISSIONLINEPARAMETER
WE CAN CALCULATE THE INITIAL LOSSLESS AND FAULTLESS PARAMETERS
FIRSTWEKNOW THAT FORA TRANSMISSIONLINETHESENDING END AND
RECEIVING END VOLTAGES AREGIVENAS-
β VS=AVR+BIR
β IS=CVR+DIR
THE EXACT MODEL GIVENFORTHE LONG LINEIS GIVENAS
β VS=AVR+BIR
β IS=CVR+DIR
BUT A=D=π‘π‘π‘π‘ π‘π‘ & C=
1
π‘ π‘
π‘π‘π‘π‘ π‘π‘ & B=ZC π‘π‘π‘π‘ π‘π‘
Firstwe have to find the receiving end current
30. 30 | Page
P=β3VIπ‘π‘π‘ π‘
INITIALLYWEASSUMETHATITβS A LOSSLESS YSTEMHENCE WE ASSUME A UNITY
POWERFACTOR
HENCE FROMTHE FIG 2.4
FIG 2.5
TIM345 BUS THEPOWER IS 122 MW AND REACTIVEPOWERIS 18 MVAR
AND V=345 KV WE HAVETO CONVERTITINTO PHASEVOLTAGEV=
345
β3
=200KV
31. 31 | Page
FIG 2.6
IR=
122π‘π‘
β3β200β1
=0.325Μ· 0O
Fromthe fig 2.6 wecan see that the impedance and admittance for the line in
ohms/mile and mhos/miles which we requirefor our calculation.
Z=0.2+J3.5=3.6Μ· 86O
ohms/mile
Y=
π‘
15.28
=0.065Μ· 90O
mhos/miles
ΟL=π‘π‘π‘π‘π‘π‘ π‘π‘ π‘π‘π‘ π‘π‘π‘π‘ π‘π‘ π‘π‘π‘π‘π‘βZY=10 β β3.600Μ· 86O
*0.065/ 90O
ΟL=0.4805Μ· 88O
ΟL=0.013+j0.485
Cosh(Ξ±l+Ξ²l)=
1
2
(eΞ±l
/Ξ²l+e-Ξ±l
/-Ξ²l)
32. 32 | Page
/Ξ²l=0.48 radians=/27.06o
e0.013
/ 27.06o
=1.01/ 27.06o
=0.89+j0.46
e-0.13
/ -27.06o
=0.98/-27.06=0.87-j0.445
Hence,
cosh ΟL=0.88+j0.02=0.88/1.30o
similarly, sinh ΟL=0.01+j0.455=0.455/88.72o
Zc=β
π‘
π‘
=7.44/-2.0o
A=D=cosh ΟL=0.88/1.30o
B=Zcsinh ΟL=3.236/86.72o
C=sinh ΟL/Zc=0.061/91o
Now,
β VS=AVR+BIR
β IS=CVR+DIR
Vs=0.88/1.30 *200/0 + 3.236/86.72*0.325/0
=176/1.30+1.051/86.72
=176.61+j5.097
=176/1.67KV
IS=0.061/91*200/0+0.88/1.30*0.325/0
=12.2/91+0.3/1.30
=0.087+j12.20
=12.20/90kA
The power factor of the line is=cos(90-4)=0.07 leading which is way of the unity
power factor we assumed therefore there is a error in the systemdue to other
interconnection in the system.
33. 33 | Page
FIG 2.7
FIG 2.8
You can see fromthe FIG 2.8 that receiving end of the transmission line receives
122 MW real power and 33 MVARreactive power fromthe fault pint instead of
the sending end bus because of fault on the line there is no power flow between
the buses SLACK345 and TIM345 henceweare going to assumethat the fault
34. 34 | Page
point is the sending end bus instead of the SLACK35 bus which is are actual
sending end bus.
FIG 2.8
Fromthese two figures we can calculate the sending end voltage and sending end
currentfor the system. And we know fromFIG_xxthe reactance,resistanceand
capacitance values.So calculating the following we get,
TIM345 BUS THEPOWER IS 122 MW AND REACTIVE POWERIS 22 MVAR
AND V=345 KV WE HAVETO CONVERTITINTO PHASEVOLTAGEV=
345
β3
=200KV
IR=
122π‘π‘
β3β200β1
=0.325Μ· 0O
36. 36 | Page
Hence,
cosh ΟL=0.93+j0.04=0.93/2.46o
similarly, sinh ΟL=0.11+j0.365=0.38/73.22o
Zc=β
π‘
π‘
=6.15/-17o
A=D=cosh ΟL=0.93/2.46o
B=Zcsinh ΟL=0.019/55.72o
& C=sinh ΟL/Zc=0.16/91o
Now,
β VS=AVR+BIR
β IS=CVR+DIR
Vs=0.93/2.46*200/0+0.019/55.72*0.325/0
=186/2.46+0.019/55.72
=185.83+j7.9
=185/2.44KV
IS=0.16/91*200/0+0.93/2.46*0.325/0
=32/91+0.3/2.46
=-0.26+j32.19
=32.20/90kA
The power factor of the line is=cos(90-4)=0.07 leading which is 7% of the unity
power factor we assumed at the receiving end bus therefore there is a error in
the system dueto other interconnection in the systemand we cannot assumea
power factor for large systemto be one as a systemcannot be lossless.And also
the sending end currenthas been affected by the change in the characteristic
impedance of the circuit.
DISCUSSION:
37. 37 | Page
β Fromthe firstpart of the problem we simulated the value of the impedance
and calculated the sending end voltage and current for a stedy state
lossless mediumi.e. the long transmission line.
β For the second part still assuming the line to be lossless wesimulated a
fault at 25% fromthe bus SLACK345 and calculated the impedance anf
hence the values of the sending end voltage and current
β Fromthe calculation and simulation we can clearly see that the
characteristic impedance of the systemhas reduced hence the sending end
currentfor the systemhas increased .
β Therefore for the given systemthe fault alters the characteristic values of
impedance and therefore the circuit parameters.
β And hence for a systemif the characteristic impedance is reduces the
currentin the circuit increases and vise-versa.
β In this way the characteristic impedance influences the currentflowing in
the circuit. We can also compare the characteristic impedances to the line
impedance. Itappears to me that characteristic impedance Z0 is a
transmission line parameter, depending only on the transmission line
values R, G, L, and C. Whereas line impedance is Z depends on the
magnitude and phaseof the two propagating wavesV ( ) z + and V (z ) β --
values that depend not only on the transmission line, but also on the two
things attached to either end of the transmission line.
PROBLEM#03 UNSYMMETRICAL FAULTS IN POWER SYSTEM
38. 38 | Page
Intent of the problem: This problem we deduces the zero sequence network of the
system and hence calculate the fault in the sequence network.
What is a sequence network why is it necessary?
In symmetricalcomponent analysis (e.g. for unbalanced faults), a balanced three-
phaseelectrical network can be broken down into three sequence networks,
which are independent, de-coupled sub-networks comprising only quantities in
the samesequence, i.e. the positive sequence network contains only positive
sequence quantities, the negative sequencenetwork contains only negative
sequence quantities and the zero sequencenetwork contains only zero sequence
quantities.
The phase faults are unique since they are balanced i.e. symmetrical in three
phase, and can be calculated fromthe single phase positive sequenceimpedance
diagram. Therefore three phase fault currentis obtained by,
Where IF is the total three phasefault current, v is the phase to neutral voltage z1
is the total positive sequence impedance of the system; assuming that in the
calculation, impedance are represented in ohms on a voltage base.
Symmetrical ComponentAnalysis
The above fault calculation is made on assumption of three phase balanced
system. The calculation is made for one phaseonly as the currentand voltage
conditions are same in all three phases. When actual faults occur in electrical
power system, such as phaseto earth fault, phaseto phase fault and double
phaseto earth fault, the systembecomes unbalanced means, the conditions of
voltages and currents in all phases are no longer symmetrical. Such faults are
solved by symmetricalcomponent analysis. Generally three phase vector diagram
may be replaced by three sets of balanced vectors. Onehas opposite or negative
phaserotation, second has positivephase rotation and last one is co-phasal. That
means these vectors sets are described as negative, positive and zero sequence,
respectively.
39. 39 | Page
For any location in the system, the sequence networks can be reduced to
Thevenin equivalent circuits for illustration of the application of thevenin theorem
for determing the equivalent sequencenetworks, consider a simple power
systemshown in the FIG 3.1
Fig 3.1
1. The impedances are all constantand independent of currents.
2. The synchronous generator is a salient pole type which may generate under
faiult condition, negative and zero-sequenceemfs which are small and are
negligible. Thus for all purposes the machine is assumed togenerate only
positive sequenceemfs.
The network under such conditions can be represented by 3 independent
single phasesequence network.
Approach:
1. I will firstdo the calculation by hand to find the fault currentat 50% line using
the selected circuit shown in Figure _xx and draw the sequence network for the
circuit.
40. 40 | Page
2. Using the Power World software, I willthen find the fault currentat line at 50%
given by Power World.
3. With the fault current calculated by hand and through Power World, I will find
the error and hypothesizepossiblereasons for such an error.
Figure
FIG 3.2
Solution:
FirstI need to select the base MVA value. I can do this by right clicking on the
generator information dialog and obtaining the baseMVA value. (Figure 3.2)
41. 41 | Page
FIG 3.3
Itcan be seen from the Generator Information Dialog that the base MVA value for
the generator is 20 MVA. Thus, I am going to use this MVA value as the base MVA
value for the fault calculations.
The following circuit is obtained for the selected buses in figure3.4. (Figure3.4)
BASEMVA =20 MVA BASEKV =16 KV
45. 45 | Page
FIG 3.7
We have the transmission line reactance as X=0.10 p.u. fromthe FIG 3.7 as we
know the value in p.u. we donβthave to calculate the value manually.
46. 46 | Page
FIG 3.8
XT, NEW= 0.12*(
138
138
)2
*(
20
20
) = 0.12 π‘.π‘.
Now we draw the sequence network for the systemand evaluate the fault current
manually.
WE ASSUMETHE POSITIVE, NEGATIVEAND ZERO SEQUENCEREACTANCES FOR
THE GENERATOR TO BE SAME X2=X1=X0=0.1 P.U.
47. 47 | Page
FIG 3.9
THE FAULT CURRENT FOR THE SYSTEMAT MIDPOINTOF THETRANSMISSIONLINE
IS
IF=
3βπ‘ π‘
π‘2+π‘1+π‘0
=
3
0.10+0.10+0.155
=8.51 P.U.
AS THE FAULTCURRENT IS OCCURING INZONE2,
IF=8.51*ZB2=8.51*84=720A
NOW WE EVALUATE FORPOWERWORLD ANALYSIS TO FIND THEFAULT
CURRENT.
WE WILL TRY WITH ALL FOURFAULT TYPES AND FIND THEP.U AS WELL AS
AMPERE FAULT CURRENT FOR THE SYSTEM.FIRSTSETTHELOCATION AT50% OF
THE TRANSMISSIONLINE.
48. 48 | Page
FIG 3.10
NOW WE CAN ASSUME THE DIFFERENTTYPES OF FAULTS ONE BY ONE
1. SINGLELINETO GROUND FAULT
49. 49 | Page
FIG 3.11
AS YOUCAN SEE FROM THE FIG 3.11 THATTHIS NOTTHETYPE OF FAULTTHAT IS
OCCURING INOURGIVENCIRCUIT.
2. 3-PHASEBALANCED FAULT
I. INPER UNIT
II. INMAGNITUDEORAMPERES
50. 50 | Page
3. LINETO LINEFAULT
I. INPER UNIT
FIG 3.13
II. INAMPERES
52. 52 | Page
FROMTHE POWERWORLD ANALYSIS WESEE THAT THERE IS A ERROR OF 50% IN
THE SYSTEM THAT DUETO OUR ASSUMPTIONAND POSSIBLEERRORINTHE
CIRCUITITSELF
FROMTHE ANALYSIS INTHEPOWERWORLD WE ALSO CAN CLERLY SEE THAT
SINGLELINETO GROUND AND DOUBLELINET GROUND DOESNβTOCCURINOUR
CIRCUITONLYTHE3-PHASEBALANCED AND LILETO LINEFAULT CAN OCCURIN
OUR CIRCUIT
DISCUSSION
β We have obtained a substantial error in our calculation and simulated
results due to our assumptions and possiblesmall error in the circuit. Thus
Power World has emerged as an effective tool in helping engineers to
simulate complicated models and get accurate results. Wewere also
successfulin determining that the 3 phase fault currentis the highest. Thus
all protection schemes are designed with this 3 phasefault currents in
mind.
53. 53 | Page
PROBLEM#04 Power Factor Correction
Intent of the problem: This problem calculates the Power factor of a system and
the power factor improvement techniques so as to improve the total power quality
of the system.
WHAT IS POWER FACTOR AND WHY DO WE NEED TO IMPROVE IT?
Firstof all whatis power factor and how do we measure it.
β’ In an AC circuit, power is used mostefficiently when the currentis aligned
with the voltage.Efficient AC Current
β’ However, mostequipment tend to draw currentwith a delay, misaligning it
with the voltage. What this means is more currentis being drawn to deliver
the necessary amountof power to run the equipment. And the more an
equipment draws currentwith a delay, the less efficient the equipment
is.InefficientAC Current
54. 54 | Page
β’ Power factor is a way of measuring how efficiently electrical power is being
used within a facility's electrical system, by taking a look at the relationship
of the components of electric power in an AC circuit. These components are
referred to as Real Power, Reactive Power and ApparentPower:
β’ Real power (kW) β the work-producing power thatis used to actually run
the equipment
β’ Reactive power (kVAr) βthe non-work producing power thatis required to
magnetize and startup equipment
β’ Apparentpower (kVA) βthe combination of real power and reactive
power
The purposeof power factor improvement is simply to reduce the load current
drawn fromthe supply. This allows conductors of smaller cross-sectionalarea to
be utilised, reducing the amount(and cost) of copper used in those conductors
and other supply plant. In the caseof larger commercial and industrialloads,
power factor is part of the tariff, and loads with low power factors may be
financially penalised, so higher power factors aredesirable as a means of reducing
utility bills.
There are many practical ways to do so The following devices and equipments are
used for Power Factor Improvement.
β’ Static Capacitor
β’ Synchronous Condenser
β’ PhaseAdvancer
In this problemwe are going to show the effect of a power factor improvement
on a systemusing power world analysis.
Approach:
55. 55 | Page
Step 1: Firstwe are going manually calculate the power factor of circuit for buses
SANDER69 to BOB69 and note down its effect on the circuit parameters.
Step 2: Then we are going to add a shuntcapacitor to the circuit and calculate the
power factor of the circuit for the samebuses and note down its effect on the
circuit parameters
Step 3: We are going to comparethe results and using power world we are going
to simulate the results for the design case.
Solution:
Firstright click on the bus DAVIS69 and then choosethe quick power flow option
FIG 4.1
Now we note down the real power and reactive power at the bus and calculate
the power factor for the given bus.
P = 75 MW, Q = 50 MVAR
Figure1.11 gives the power triangle for the bus, DAVIS69.
56. 56 | Page
The power factor at DAVIS69bus.
Power factor = pf = cosΞΈ
tanΞΈ =50/75
This gives,
Ξ = 34β° (leading)
Pf=cos Ξ=0.82
Now we to improvethe power factor to 0.95 so we are going to calculate the
shuntcapacitor required for the system
Cos Ξ=0.95
Ξ=π‘π‘π‘β1
π‘=18.19o
P = 75 MW, Q = X MVAR
Figure1.11 gives the power triangle for the bus, DAVIS69.
FIG 1.11
Assuming the real power to be constantthe MVARrequired for the systemis
tan18.19 =X/75
This gives,
57. 57 | Page
X=24.64 MVAR
Therefore the new shuntreactance to be added should be
XNEW=25 MVAR
Adding this new shuntreactance we get new MVAR value for the system
therefore consideing the values and calculating the new power factor we get,
FIG 4.2
As can be seen from the Quick Power Flow List for the bus, SANDER69, the Real
Power Flow at the bus is 28 MW and the reactive power flow is 6 MVAR.
P = 75 MW, Q = 33 MVAR
Figure1.4 gives the power triangle for the bus, SANDER69.
Q= 33MVAR
P= 75 MW
58. 58 | Page
The power factor at SANDER69 bus.
Power factor = pf = cosΞΈ
tanΞΈ =33/75
This gives,
Ξ = 23β° (leading)
Pf=cos Ξ=0.92
Now we to improvethe power factor to 0.92 so we have an error in the
calculation due to the presenceof other interconnection to the buses wedidnβt
consider.
Now we connect an load to the systemand see the changes in the system
FIG 4.3
P = 75 MW, Q = 43 MVAR
Figure1.4 gives the power triangle for the bus, SANDER69.
59. 59 | Page
Q= 43MVAR
P= 75 MW
The power factor at SANDER69 bus.
Power factor = pf = cosΞΈ
tanΞΈ =43/75
This gives,
Ξ = 30β° (leading)
Pf=cos Ξ=0.86
Due to the additional load to the systemthere is a MVAR addition to the system
and the power factor decreases to improveit to 95% i.e. 0.95 weincrease the
shuntreactance value the value required we first are going to calculate manually
Cos Ξ=0.95
Ξ=π‘π‘π‘β1
π‘=18.19o
P = 75 MW, Q = X MVAR
Figure1.11 gives the power triangle for the bus, DAVIS69.
FIG 1.11
Assuming the real power to be constantthe
60. 60 | Page
MVAR required for the systemis
tan18.19 =X/75
This gives,
X=24.64 MVAR
Therefore the new shuntreactance to be added should be
XNEW=25 MVAR
Adding this new shuntreactance or increasing the value of the existing shunt we
get new MVAR value for the systemthereforeconsidering the values and
calculating the new power factor we get,
Figure1.4 gives the power triangle for the bus, SANDER69.
P = 75 MW, Q = 17 MVAR
The power factor at SANDER69 bus.
Power factor = pf = cosΞΈ
tanΞΈ =17/75
This gives,
Ξ = 15β° (leading)
Pf=cos Ξ=0.97
Q= 33MVAR
P=75 MW
61. 61 | Page
Now we to improvethe power factor to 0.97 i.e. 97% so we havean error in the
calculation due to the presenceof other interconnection to the buses that we
didnβt consider.
DISCUSSION:
I was unable to incorporate the effect of the other parts of the circuit in
improving the power factor at the selected bus. Thus, Power World has once
again proved its worth as a simulator which can provide moreaccurate results
than manual calculations. When adding the load, additional real and reactive
power came from the rest of the circuit since the values of the other generators
changed. Since some reactive power and real power were used in the
transmission lines, I had to depend on the real and reactive power values given in
Power World to calculate accurate values.
64. 64 | Page
Locate point N having coordinates-1.21 cmand -5.48 cmand draw load line OP at
an angle π‘π‘π‘β1
0.8 i.e. 36.9o
inclined to the horizontaland to represent
β3βπ‘ π‘π‘βπ‘ π‘
1000
MVAR i.e.
β3β275β504
1000β100
cm=2.4 cm
Draw circle diagramwith N (-1.21 cm, - 5.48 cm) as center and NP as radius.
Fromcircle diagram NP= 7.6 cmβ¦β¦β¦..(fromMeasurement)
β΄ NP=
π‘ π‘π‘βπ‘ π‘π‘
π‘
=100*7.6=760MVA.
β΄ VSL=
760βπ‘
π‘ π‘π‘
=
760β122.38
275
=338 kV
Ξ-Ξ±=64o
Ξ=Ξ²-64o
=78.69o
-64=14.69o
For sending end power circle diagram
Horizontalcoordinate=-
π‘
π‘
VSL π‘π‘π‘(π‘ β π‘)=-
0.9075
122.38
π‘π‘π‘(78.69 β 1.17) *3382
=183
MW
Vertical coordinate=-
π‘
π‘
VSL π‘π‘π‘ (π‘β π‘) =-
0.9075
122.38
π‘π‘π‘(78.69 β 1.17)*3382
=827
MW
Radius of circle=
π‘ π‘π‘βπ‘ π‘π‘
π‘
=7.6 cm
Draw a circle diagram with N (1.83 cm, 8.27 cm) as center and 7.6 cm as radius.
Draw NP inclined at angle Ξ²+Ξ΄ i.e. 78.68 + 14.69 =93.38o
to the horizontalcutting
the arc of sending-end power circle at P. Join OP
Sending-end power factor angle=Ξ¦S=15o
(frommeasurement)
Sending-end power factor=π‘π‘π‘ π‘ π‘ =π‘π‘π‘15=0.966.
OP=2.4 cm= 2.4*100=240 MVA
β΄OP=
β3βπ‘ π‘π‘βπ‘ π‘
1000
MVAR
β΄IS=
π‘π‘β1000
β3βπ‘ π‘π‘
=410 A
65. 65 | Page
Discussion
β Hence we have drawn the circle diagram for the sending end and receiving
end power and we can see that a circle diagramgives the results which are
sufficient accuratefor practical purpose, despitethe fact that an
approximate equivalent circuit is used in a circle diagramand provides a
panoramic view of how operating characteristics areaffected by changes in
the machines parameters, voltage, frequency etc.
β We also can see that for a long transmission linewe have assumed a Ο-
configuration
β And this can be done becauseit generates very low discrepancies in the
solution but a shorttransmission line solution might fail in this case and
hence cannot be assumed for the case.
PROBLEM#06 Phase shifting transformer
66. 66 | Page
Intent of the problem: This problem calculates the Sending end and Receiving end
power and we draw and explain these parameters via the power circle diagram.
What is a PST & Why is it required?
A Phase-Shifting Transformer is a device for controlling the power flow through
specific lines in a complex power transmission network.
The basic function of a Phase-Shifting Transformer is to change the effective
phasedisplacement between the input voltage and the output voltage of a
transmission line, thus controlling the amount of active power that can flow in the
line.
APPROACH
1.Firstweare going to simulate a circuit in a power world simulator for a
transmission line and evaluate the power flowing through a line and the total
losses in a line.
2. Then we aregoing to add a phaseshifting transformer to the same
transmission line.
3. We are going to controlthe phasebetween the transmission line with the
help of the PSTand thereby evaluate the power flow.
SOLUTION:
Firstwe are going to consider the case3.60 for the question we evaluating,
67. 67 | Page
FIG 6.1
In the given FIGURE6.1 weare assuming a two bus systemfor evaluation, the
values of the generator parameters are:
FIG 6.2
68. 68 | Page
We set the limiting Max value for the generator and for the given generator
parameter we set the value of the load to 500 MW and 100 MVAR. And with help
of the load field we can controlthe value of the generator load.
FIG 6.3
The load field is given set the value of the delta or cahnge in the input power with
respect to the output power to 50 MW per click.
69. 69 | Page
FIG 6.4
We can see fromthe simulator for that for the output of 500 W and 100 MVAR
the input power being generated is 534 MW and 236 MVAR fromFIG 6.1. And the
voltage angle set at the generating bus is 0O
for refrence hence the voltage angle
at the receiving end bus is
70. 70 | Page
Vreceving end=297/-14o
kV
The phase angle at the receiving end is -14o
, now weare going to add a phase
shifting transformer to the circuit and set the phasevalue for the transformer to
0o
.
71. 71 | Page
Now we can see from the FIG_xxthat the total power being transmitted to the
output has an alternate path and the reactive and active power are divided into
the total seprate paths to the load without the load being affected. We have set
the the degree field to th phaseshift of the load bus.
72. 72 | Page
We are going to set the limit for thr phase shiftwe are applying to the circuit we
are considering.
FIG 6.8
For the circuit we havegiven a max and min phaseangle value to +/- 30o
for the
phaseshifting transformer. Now weare going to phaseshift a transformer by 10o
and evalute the change in the power transfer value.
73. 73 | Page
FIG 6.9
Fromthe figureyou can see that the bulk of the power is flowing fromthe phase
shifting transformer and hence by changing the output power phasewe have
managed to reduce the power flow fromthe transmission line.
Now we change the phasefrom10o
to 20 o
and take a look at the change,
FIG 6.10
As the phaseis changed to 20o
the power flow fromthe transmission line is
further reduced and the power transmitted fromthe transformer is further
74. 74 | Page
enhanced. We can also see that the transformer produces power morethan what
is required at the load and hence the direction of this residual power is changed
and now it flows fromthe load to the generator. You can see the change in the
phaseangle at the receiving end too.
FIG 6.11
Vreceving end=326/2o
kV
You can see that there is positivephase angle at the receiving end and now its
leads the sending end power line voltage.
Now we change the phaseto the maximum value of the phase shifting
ttansformer i.e.
75. 75 | Page
FIG 6.12
Fromthe figureyou can see that the a significantamount of the power is being
transmitted fromthe load to the generator. Hence with the useof the phase
shifting transformer wehave managed to change the flow of power through a
circuit.
76. 76 | Page
Vreceving end=319/6o
kV
You can see that there is increased value of positive phaseangle at the receiving
end and now its leads the sending end power line voltage.
Now we make a negative phasechange and evalute the circuit, now that the
phaseis reversed
77. 77 | Page
FIG 6.14
Since the phaseis reversed the excess power of the load flows fromthe
transformer instead of the power line and reactive power is reversed to and it
flows fromthe power line as the MVAR at the sendinf end and receiving end have
little diffrencethe magnitude is small and there is no significantreactive power
flowing in the power line. Now we reversethe phasefurther and evalute the
circuit.
Now we reversethe phaseto the minimum limit of the transformer and evaluate
the changein the circuit
78. 78 | Page
Since the phaseis reversed further the a significant excess power of the load
flows fromthe transformer instead of the power line and the reactive power
flows frombus 2 to bus 1 but as there is still no significant diffrencein the sending
end and receiving end voltage angle.
FIG 6.15
Vreceving end=319/-20o
kV
Hence we conclude that through a useof a phase shifttransformer wemanaged
to control the power flow in the circuit either through the transformer or the
power line.
79. 79 | Page
DISCUSSION:
β A PST is a usefulmeans of control of active power flow, as is proved by
hands-on experience obtained from the varied applications. A simulation in
a power world simulator illustrates the ability to regulate the active power
transmitted over a line.
FIG 6.16
80. 80 | Page
FIG 6.18
β But a draw back of a PSTis the reactive power losses which are significantly
high for positive as well as negative phasechanges. So its high power
applictaions are limited. Or they require really expensivecompensators.
PROBLEM#07 Choice of TransmissionLine Conductor
81. 81 | Page
Intent of the problem: To calculate the impedance and admittance for a
transmission line using two different conductors and make a choice depending on
the losses for same input parameters.
Why do we need to differentiate between conductors?
WE need to because of the costof the conductors fora long transmission line to be
laid this might help reduce the infrastructure costand also minimization of losses
as one of the important factors as different conductorshave different conductivity
and losses margin for the different type of transmission lines.
Approach:
Step 1: First we are going to choose two conductors which we are going to
differentiate for our case study
Step 2: Then we are going to manually calculate the impedances and admittances
for the conductors.
Step 3: Then we are going to insert these values into the power world simulator
and for the same circuit we are going to evaluate the total loss in the system and
make a choice for the conductor to be best suited for the circuit.
For our case study we are going to choose BLUEBIRD and OSTRICH
Technical considerations
I will first assumethat the conductors arearranged in an couple fashion with a
distance of 15 feet between each of the conductors.
Firstwe consider BLUEBIRD conductor.
I will also assumethe GMR for thr circuit i.e. GMR=β(π‘ π‘ β
6")=3.33β/Ξ¦=0.2775β/Ξ¦
0.788*radius of theconductor
83. 83 | Page
FIG 7.2
We can see that on the right side we havethe per unit values for the given actual
values.
Now we go to the run mode and run the simulation and now we note the loss
value for the line. first we go to the line information box option on right clicking
the line we are using for us line between the buses DEMAR69 and SANDER69.
84. 84 | Page
FIG 7.3
We can see that the losseare 0.385 MW and 0.025 MVARfor the BLUEBIRD
conducter.
Now we choose the OSTRICH conductor and calculate the the parameters.
Firstwe consider OSTRICH conductor.
I will also assumethe GMR for thr circuit i.e. GMR=β(π‘ π‘ β
6")=3.33β/Ξ¦=0.2775β/Ξ¦
0.788*radius of theconductor
GMD=β π‘3
β π‘ β 2π‘
86. 86 | Page
We can see that the losseare 0.4 MW and 0.023 MVARfor the OSTRICH
conducter.
DISCUSSION:
We can say fromour calculations and assumption that for the same line between
the buses SANDER69 and DEMAR69 for the OSTRICH conductor wehavehigher
losses due to are assumption thses losses arenot high enough but we still
consider them with the error that the BUEBIRD conductor is better suited for the
given line.
87. 87 | Page
PROBLEM#08 TransmissionLine Evaluation
Intent of the problem: This problem calculates the parameters of a short, medium
and long transmission line and compare the result to see whether their models are
compatible with a different transmission line for e.g. short can be used on a long
line.
CASE: Power World Design Case 9
Approach:
Step 1: First we are going to assume the appropriate values needed or our
calculation
Step 2: Then we are going to calculate manually the different parameters for the
short, medium and long transmission lines.
Step 3: Then we are going to insert these values into the power world case we are
assuming and simulate it
Step 4: Then we are going to compare the results and for accurate answers.
SOLUTION:
Firstwe are going to assumea case for our case study
FIG 8.1
90. 90 | Page
Sending end power factor=15.3-6.2=9.1o
=0.987 lagging
Sending end power =β3 β 237.23 β 0.164 β 0.980=52.15 MW.
Now that we have calculated the value of the parameters manually we will use
power world to do so as well and compre the values.
FIG 8.2
Fromthe figurewe can see that the we have set the value according to our
assumptions
93. 93 | Page
FIG 8.5
We can also see that the MW value for the systemis different fromthe value we
calculated i.e. 58 MW for simulation and 52 MW for calculated value.
Now we insert the the values of medium and long transmission line and observe
the changes in the circuit
FIG 8.6
94. 94 | Page
We can see that fromassumption and the values we have inserted that the
currentvalue we calculated and the current value wesimulated arevery close
and the our assumptions arerightbut wealso see that the power in MW i.e. 57
MW is quite away fromour calculated values due to the discrepensies in the
circuit. Hence for a long line our sjortline assumptions produces errors and hence
it cannot be applied for a long transmission lineassumptions buta medium
transmission line assumptions havethe same currentvalue at the sending end for
our assumptions.so wecan usemedium transmission lineassumption for a long
line.
95. 95 | Page
DISCUSSION:
We have calculated the transmission line parameter for assumptions wehave
made manually and then we have simulated the results with the help power
simulator through which we haveconcluded that for a long transmission line we
can apply medium line mdel but we cannot apply the shortline model because of
its discrepensies in the circuit.
PROBLEM#09 Load Angle EstimationFor a Power Line
96. 96 | Page
Intent of the problem: This problem we calculate the load angle for system and
introduces a concept called equal area criterion to do so.
What is EQUAL AREA CRITERION?
Firstwe will consider a Power Transfer Equation Single Machine-InfiniteBus
System. For a simple lossless transmission lineconnecting a generator and infinite
bus as shown in Figure
Figure9.1: One machine against infinite bus diagram.
If V1 = U1, V2 = U2cos Ξ΄ + j U2 sin Ξ΄,
Z = R + j X;
Itis well known that the active power P transferred between two generators for
a lossless line can be expressed as:
P= | U2 | | U1| *sinΞ΄
X
Where,
V1 is the voltage of the infinite bus (reference voltage), volt
V2 is the voltage of the generator bus Ξ΄ is the angle difference between the
generator and infinite bus, rad
X is the total reactance of the transmission lineand generator, ohm
The impedance is reduced to the reactance of the line becausethe resistanceis
often small and gives little contribution to the
The Power Angle Curve
97. 97 | Page
FIG 9.2
The generator in Figure is in stable operation at a phaseangle of Ξ΄ compared to
the infinite bus, i.e. the voltage at the generator bus U2 is leading the voltage at
the infinite bus U1 by an angle Ξ΄. The mechanical power input Pm and the
electrical power output Pe drawn in Figure describes the power balance of the
generator. The curves intersectat two points, the stable equilibrium point and the
unstable equilibrium point.
Approach:
1. We will consider a casefor the of a generator connected to an infinite bus
via interconnected two line system. Then we will find the maximum delta
angle for the systemin a fault condition
2. We are going to make necessary assumption to provethe same. This
maximum delta angle will dtermine the stability of the system.
SOLUTION:
98. 98 | Page
β For a systemE=1.2 pu.;V=1 pu;Xβd=0.2 pu,X1=X2=0.4 pu. Initialpower
supply of the systemis 1.5 pu.
Determine Max delta angle for a fault condition on one of the two
interconnnected lines.
FIG 9.3
For the power angle curve;
FIG 9.4
For the curveA i.e. when oth the lines are in operation,
Transfer reactances X=Xβd+
π‘1
2
99. 99 | Page
=0.4 pu.
Steady state power limit, PMAX=
π‘π‘
π‘
=3 pu.
For initial condition Po=1.5 pu.
Initial load ange=π‘π‘π‘β1 π‘0
π‘ π‘π‘π‘
=30o
For curveB i.e. when one of the line trips due to fault conditions
Transfer reactances X=Xβd+X1(or X2)
=0.6 pu.
Steady state power limit, PMAX=
π‘π‘
π‘
=2 pu.
Electrical power Developed PβE=Pβmax=2π‘π‘π‘ π‘
Initial load ange=π‘π‘π‘β1 π‘ π‘
π‘β² π‘π‘π‘
=48.6o
And load angle Ξ΄m=180-48.6=131.4
The area A is given as;
A=β«
π‘ π‘
π‘ π‘
( π‘ π‘ β π‘
β²
π‘) π‘π‘=β«
0.848
0.524
(1.5 β 2π‘π‘π‘ π‘) π‘π‘=0.0769
The systemstability depends on whether there is enough negative area B in the
interval Ξ΄c<Ξ΄<Ξ΄m to match the area A
B=β«
π‘ π‘
π‘ π‘
( π‘ π‘ β π‘
β²
π‘) π‘π‘=β«
2.293
0.848
(1.5 β 2π‘π‘π‘ π‘ ) π‘π‘=-0.4777
Since B is greater in magnitude then in A,the systemis stable
The maximum angle Delta for the systemis given by the conditon A=B
β«
π‘ π‘
π‘ π‘
( π‘ π‘ β π‘
β²
π‘) π‘π‘==0.0769
orβ«
π‘ π‘
0.848
(1.5 β 2π‘π‘π‘ π‘ ) π‘π‘ = β0.0769
or 1.5 β 2π‘π‘π‘ π‘=-0.0769+1.5*2cos0.848=2.158
The equation is non-linear and by solving this equation weget;
100. 100 | Page
ΞM=69.8o
Discussion:
We conclude that for a stable system we have managed to find the Maximum
delta angle for a system using our own assumptions. And we know that fo stable
system the maximum delta value is 90o
but for a fault condition an delta
maximum value can never be 90o
.
PROBLEM#10 SHORT CIRCUIT DUTY
Intent of the problem: This problem calculates the Short Circuit Duty (SCD) of
generator connected in SERIES with a transformer. It also uses the concept of fault
analysis shown in previous problems. This SCD can be extended to be used in fault
analysis when calculating fault current from and for different areas/zones.
101. 101 | Page
What is SHORT CIRCUIT DUTY?
Short circuit duty is a description of the severity of overcurrent that a device can
reasonably be expected to withstand transformer windings must be stout enough to
absorb the heat and withstand the magnetic forces during such an event, circuit
breaker contacts must be robust enough to not melt, and in big ones there must be
nonconductive vanes surrounding the contacts to break up the arc cut open a big
round industrial fuse and you'll probably find it stuffed with sand to quench the arc.
CASE: Power World Design Case 6
Approach:
Step 1: First we are going to divide the area we are considering for the given case
to be divided into zone 1 and zone 2. Given the MVA rating of the generators and
KV rating of the generators and transformer, we are able to find out the zone
currents and zone impedances. Assuming the rated MVA value, we will find out
the per unit equivalent reactance on base of 100 MVA in terms of individual
reactance of the generators and transformer. The equivalent reactance and the
system reactance we will add to the system and the fault current will give us the
short circuit duty of generator.
Step 2: Using power world simulator, the fault current at bus SANDER69 can be
calculated.
Step 3: Another generator of the same rating will be added to the bus and 3-phase
fault current will be calculated using power world. Since we assume the values of
reactance of all the generators to be same, the fault current can be verified by
manual calculation.
Now we select a power world design case 6
102. 102 | Page
Design power world case_6 _FIG 10.1
Firstwe have to find the generators and transformer value. We can find this from
the power world example.
β’ To effectively calculate all these values for the generators, transformers
and the transmission lines, I need to obtain these values using Power World
simulator. The data for the generator can be obtained using the Generator
103. 103 | Page
Information Dialog. The data for the transmission lines and the transformer
can be obtained using the Branch Information Dialog. Thus I obtained the
reactance and MVA value for all the generators, transformers and
transmission lines using the information dialogues.
FIG 10.3
104. 104 | Page
FIG. 10.4
Fromthe two figures FIG 10. 2. And FIG 10. 3. To effectively calculate all these
values for the generators, transformers and thetransmission lines, I need to
obtain the MVA, KV and reactance values using Power World simulator. The data
for the generator can be obtained using the Generator Information Dialog. The
data for the transmission lines and the transformer can be obtained using the
Branch Information Dialog. Thus I obtained the reactance and MVA value for all
the generators, transformersand transmission lines using the information
dialogues.
Hence I have obtain the data for all the elements.
106. 106 | Page
XG2, NEW=0.05 p.u
Now using power world simulator we calculate the fault at the bus SANDER69.
We must firstgo to the run mode then select fault analysis then choosesingle
fault and then bus fault fromfault location then we can choosethe bus wherewe
want to calculate the fault then in our casewhich is SANDER69 then we choose
fault type i.e. phase fault in our case. Then we click on calculate fromthe top left
then we get the fault at the given bus in p.u and in amps
FIG .10.6
107. 107 | Page
FIG. 10.7
The bus currents are-
IP.U=47 p.u
IAMP=391 KA
Ibus=ibus*Ib1;
FIG 10.8
110. 110 | Page
We can clearly see the risein the fault current.
Ip.u=54 p.u;
Imagnitude=440KA
DISCUSSION:
Hence the solution demonstrates the following:
1. The fault currentdue to a new generator increases. This means that the
generator will add to the fault currentand the added current depends on the
MVA rating of the generator as well as the reactance. Itcan be seen that the fault
currentis directly proportionalto the SCD and the p.u. reactance of the
generator. Hence the systemreactance can be modeled for the generator fault
duty for a specific value of SCD or shortcircuit current.
2. Short circuit duty is an important parameter for modeling the shortcircuit
currentthat a generator can kick-off at a given voltage. Oncewe determine SCD,
we can calculate the shortcircuit current at any voltage- base, rated or operating.
Itgives a tie link between voltage, shortcircuit currentand SCD. Ittells us the
maximum currentthe generator can produce in case of a fault, hence helping in
determining the ratings of fuseand circuit breakers.
3. Practical application of SCD is when power systemengineers need to model
large and heavily interconnected systems. Itis usefulwhen the network is divided
into certain areas with separatecharacteristics, but since they are
interconnected, they cannot be ignored in analysis problems. This is wherethe
ShortCircuit Duty comes into play. When the SCD for an area is known, it can be
easily modeled for large systems and complicated analysis doneby power
engineers.