Power System Analysis was a core subject for Electrical & Electronics Engineering, Based On Anna University Syllabus. The Whole Subject was there in this document.
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1. The document discusses power system stability, including classifications of power system states as steady state, dynamic state, and transient state.
2. It describes synchronous machine swing equation and power angle equation, which relate the mechanical power input to the electrical power output of a generator through the power/torque angle.
3. An example calculation is shown to find the steady state power limit of a power system with a generator connected to an infinite bus through a transmission line.
SWICTH GEAR AND PROTECTION (2170906)
DISTANCE RELAY
• There are mainly Three types of distance relay
1) Impedance Relay
2) Reactance Relay
3) Mho Relay
Unit I: Introduction to Protection System:
Introduction to protection system and its elements, functions of protective relaying, protective zones, primary and backup protection, desirable qualities of protective relaying, basic terminology.
Relays:
Electromagnetic, attracted and induction type relays, thermal relay, gas actuated relay, design considerations of electromagnetic relay.
Unit-II: Relay Application and Characteristics:
Amplitude and phase comparators, over current relays, directional relays, distance relays, differential relay.
Static Relays: Comparison with electromagnetic relay, classification and their description, over current relays, directional relay, distance relays, differential relay.
Unit-III Protection of Transmission Line:
Over current protection, distance protection, pilot wire protection, carrier current protection, protection of bus, auto re-closing,
Unit-IV: Circuit Breaking:
Properties of arc, arc extinction theories, re-striking voltage transient, current chopping, resistance switching, capacitive current interruption, short line interruption, circuit breaker ratings.
Testing Of Circuit Breaker: Classification, testing station and equipments, testing procedure, direct and indirect testing.
Unit-V Apparatus Protection:
Protection of Transformer, generator and motor.
Circuit Breaker: Operating modes, selection of circuit breakers, constructional features and operation of Bulk Oil, Minimum Oil, Air Blast, SF6, Vacuum and d. c. circuit breakers.
1. A document discusses fault analysis in power systems, including symmetrical and unsymmetrical faults. Common fault causes include insulation failure, mechanical issues, over/under voltage, and accidents.
2. Key concepts are introduced, such as different types of reactance (subtransient, transient, steady-state) and how fault current transients have both AC and DC components.
3. Two examples are provided to demonstrate how to calculate fault current and MVA for given systems using per unit calculations and reactance values.
Unit 04 Protection of generators and transformers PremanandDesai
The document discusses faults and protection methods for alternators and transformers. For alternators, common faults include failure of the prime mover, field failure, overcurrent, overspeed, overvoltage, and unbalanced or stator winding faults. Differential and inter-turn protection are described. For transformers, faults include open circuits, overheating, and winding short-circuits. Buchholz devices, earth fault relays, overcurrent relays, and differential systems provide protection. Earth fault protection for transformers uses a core-balance leakage scheme.
A three-phase transformer can be constructed as a single unit or from three individual single-phase transformers connected together. A single-unit transformer has advantages like less space, weight, and cost, and is more efficient. However, if a phase fails, the entire transformer must be removed for repair unlike with individual transformers. The document discusses different three-phase transformer connections like star-star, delta-delta, and uses of tertiary windings.
1. The document discusses power system stability, including classifications of power system states as steady state, dynamic state, and transient state.
2. It describes synchronous machine swing equation and power angle equation, which relate the mechanical power input to the electrical power output of a generator through the power/torque angle.
3. An example calculation is shown to find the steady state power limit of a power system with a generator connected to an infinite bus through a transmission line.
SWICTH GEAR AND PROTECTION (2170906)
DISTANCE RELAY
• There are mainly Three types of distance relay
1) Impedance Relay
2) Reactance Relay
3) Mho Relay
Unit I: Introduction to Protection System:
Introduction to protection system and its elements, functions of protective relaying, protective zones, primary and backup protection, desirable qualities of protective relaying, basic terminology.
Relays:
Electromagnetic, attracted and induction type relays, thermal relay, gas actuated relay, design considerations of electromagnetic relay.
Unit-II: Relay Application and Characteristics:
Amplitude and phase comparators, over current relays, directional relays, distance relays, differential relay.
Static Relays: Comparison with electromagnetic relay, classification and their description, over current relays, directional relay, distance relays, differential relay.
Unit-III Protection of Transmission Line:
Over current protection, distance protection, pilot wire protection, carrier current protection, protection of bus, auto re-closing,
Unit-IV: Circuit Breaking:
Properties of arc, arc extinction theories, re-striking voltage transient, current chopping, resistance switching, capacitive current interruption, short line interruption, circuit breaker ratings.
Testing Of Circuit Breaker: Classification, testing station and equipments, testing procedure, direct and indirect testing.
Unit-V Apparatus Protection:
Protection of Transformer, generator and motor.
Circuit Breaker: Operating modes, selection of circuit breakers, constructional features and operation of Bulk Oil, Minimum Oil, Air Blast, SF6, Vacuum and d. c. circuit breakers.
1. A document discusses fault analysis in power systems, including symmetrical and unsymmetrical faults. Common fault causes include insulation failure, mechanical issues, over/under voltage, and accidents.
2. Key concepts are introduced, such as different types of reactance (subtransient, transient, steady-state) and how fault current transients have both AC and DC components.
3. Two examples are provided to demonstrate how to calculate fault current and MVA for given systems using per unit calculations and reactance values.
Unit 04 Protection of generators and transformers PremanandDesai
The document discusses faults and protection methods for alternators and transformers. For alternators, common faults include failure of the prime mover, field failure, overcurrent, overspeed, overvoltage, and unbalanced or stator winding faults. Differential and inter-turn protection are described. For transformers, faults include open circuits, overheating, and winding short-circuits. Buchholz devices, earth fault relays, overcurrent relays, and differential systems provide protection. Earth fault protection for transformers uses a core-balance leakage scheme.
A three-phase transformer can be constructed as a single unit or from three individual single-phase transformers connected together. A single-unit transformer has advantages like less space, weight, and cost, and is more efficient. However, if a phase fails, the entire transformer must be removed for repair unlike with individual transformers. The document discusses different three-phase transformer connections like star-star, delta-delta, and uses of tertiary windings.
This document discusses different types of distance relays used for transmission line protection. It describes impedance, reactance, and admittance relays. An impedance relay operates based on the ratio of voltage to current, with a torque proportional to current and restraining torque proportional to voltage. During a fault, the impedance ratio decreases and trips the circuit breaker if it falls below a predetermined value.
This document discusses power system protection settings and provides information on calculating protection settings. It covers the functions of protective relays and equipment protection, the required information for setting calculations such as line parameters and fault studies, and the process of calculating, checking, and implementing protection settings. The goal is to set protections to operate dependably, securely, and selectively during faults while meeting clearance time requirements.
This document contains the question bank for the subject EE 1351 Power System Analysis. It includes 18 multiple choice and numerical questions related to modeling components of a power system including generators, transmission lines and transformers. It also covers per-unit calculations, impedance and reactance diagrams, bus admittance matrices, symmetrical components and power flow analysis. Sample questions are provided on determining the per-unit impedances of components, drawing equivalent circuits, calculating sequence impedances and modeling various elements for power flow studies.
Protection of transmission lines (distance)Rohini Haridas
This gives idea about necessity of protection of transmission line and protection based on time grading as well as on current grading. Also includes three step distance protection of transmission line
The document provides an introduction to power system analysis. It discusses the components of a power system including generators, transformers, transmission lines and loads. It explains that power system analysis involves monitoring the system through load flow analysis, short circuit analysis and stability analysis in order to maintain the system safely and economically. It also discusses the need for power system analysis in planning and operating the system, and ensuring power demand is met through reliable generation and transmission of electricity.
Static relays use electronic components like semiconductors instead of mechanical parts to detect faults and operate. They have components like rectifiers to convert AC to DC, level detectors to compare values to thresholds, and amplifiers and output devices to trigger trips. The document discusses the components, types, and applications of various static relays like overcurrent, directional, differential, distance and instantaneous relays used in power system protection.
This document discusses different types of directional over current relays. It explains that directional over current relays operate when fault current flows in a particular direction and will not operate if power flows in the opposite direction. It provides details on 30 and 90 degree connections for directional relays and describes the construction and operation of non-directional over current relays and shaded pole type directional over current relays.
Protection against overvoltage
overvoltage
causes of overvoltage
lightning
types of lightning strokes
harmful effect of lightning
protection against lightning
System protection is used to detect problems in power system components and isolate faulty equipment to maintain reliable power. The key elements of a protection system include differential relays to protect generators and transformers from internal faults, overcurrent and distance relays to protect transmission lines from external faults, and bus differential relays to protect distribution buses. Protective devices are needed to maintain acceptable operation, isolate damaged equipment, and minimize harm to personnel and property.
Unit-2 Three Phase controlled converter johny renoald
This document discusses three phase controlled rectifiers. It provides equations and diagrams for a three phase half-wave converter with an RL load operating under continuous and constant load current. The average output voltage is derived as one-third the peak phase voltage multiplied by 2/π. Waveforms at different trigger angles are shown. Methods for calculating the maximum, RMS, and normalized average output voltages are also presented.
Reactive power is necessary to maintain adequate voltage levels to transmit active power across transmission systems. It is required for system reliability and to prevent voltage collapse. Voltage is controlled by managing the production and absorption of reactive power on the system. Both insufficient reactive power and excessive reactive power can cause voltage issues and equipment problems if voltage is not properly regulated. Reactive power reserves are also required to maintain voltage stability under contingency events like generator or transmission line outages.
The document discusses planning for HVDC transmission and modern trends in HVDC technology. When planning HVDC transmission, the key factors to consider are cost, technical performance, and reliability. Modern trends aim to reduce converter station costs while improving reliability and performance. This includes advances in power semiconductors, converter control technology, development of DC breakers, conversion of existing AC lines, and operation with weak AC systems. Emerging technologies discussed are active DC filters, capacitor commutated converters, and ultra-high voltage DC transmission.
Includes Introduction, Derivation of power flow through transmission line, Single line diagram of three phase transmission, methods of finding the performance of transmission line. 1.Analytical Method 2.Graphical method (circle diagram)., circle diagram of receiving end side and sending end side.
This document provides information about substations, including:
1. Substations are facilities used to change characteristics of electric power supply like voltage, frequency, or converting AC to DC. They are located between generation/transmission and distribution.
2. Substations are classified by their function (transformer, switching, power factor correction etc.) and construction (indoor, outdoor, underground etc.).
3. Key equipment in substations includes transformers, busbars, circuit breakers, insulators, and protection devices. Instrument transformers like PTs and CTs are also used.
4. Distribution systems distribute power from substations to consumers using feeders, distributors, and service mains. Distribution systems are classified by supply type
This presentation discusses the key protection devices used in electrical substations. It introduces current transformers and potential transformers, which reduce current and voltage levels for protection relays. Relays detect faults by measuring currents and voltages. When a fault is detected, relays signal circuit breakers to isolate the faulty component. Other protection devices discussed include lightning arresters, isolators, and surge diverters. The objective of the substation protection system is to isolate only faulty parts of the network while keeping the rest operational.
Voltage Regulation and Control in Transmission LinesToshaliMohapatra
Voltage Regulation and Control in Transmission Lines includes: Importance of Voltage Control, Methods of Voltage Control, Shunt Compensator, Shunt Capacitor & Reactors, Series Compensator, Performance of Series and Shunt Compensators, Results Obtained from Graph, Synchronous Condenser, Tap Changing Transformer, Auto Transformer, Booster Transformer
The document discusses power flow analysis, which determines voltages, currents, real power, and reactive power in a power system under steady-state load conditions. It describes the different types of buses in a power system and how they are modeled. The key component of power flow is the bus admittance matrix, which relates nodal voltages to branch currents based on Kirchhoff's current law. Solving the matrix equations provides the voltage magnitude and angle at each bus.
This document provides an introduction to power system analysis. It discusses the components of an electrical power system including generators, loads, transmission lines, and transformers. It describes the need for network models to analyze power systems and mentions different types of models used, including algebraic equations, differential equations, and transfer functions. It also discusses faults and the need to analyze balanced networks as unbalanced networks during fault conditions. The document provides examples of equivalent circuits used to represent power systems and mentions some of the challenges in modeling loads and generators. Finally, it introduces the topics of network solutions, incidence matrices, faults analysis, and stability analysis that will be covered in the book.
This document discusses different types of distance relays used for transmission line protection. It describes impedance, reactance, and admittance relays. An impedance relay operates based on the ratio of voltage to current, with a torque proportional to current and restraining torque proportional to voltage. During a fault, the impedance ratio decreases and trips the circuit breaker if it falls below a predetermined value.
This document discusses power system protection settings and provides information on calculating protection settings. It covers the functions of protective relays and equipment protection, the required information for setting calculations such as line parameters and fault studies, and the process of calculating, checking, and implementing protection settings. The goal is to set protections to operate dependably, securely, and selectively during faults while meeting clearance time requirements.
This document contains the question bank for the subject EE 1351 Power System Analysis. It includes 18 multiple choice and numerical questions related to modeling components of a power system including generators, transmission lines and transformers. It also covers per-unit calculations, impedance and reactance diagrams, bus admittance matrices, symmetrical components and power flow analysis. Sample questions are provided on determining the per-unit impedances of components, drawing equivalent circuits, calculating sequence impedances and modeling various elements for power flow studies.
Protection of transmission lines (distance)Rohini Haridas
This gives idea about necessity of protection of transmission line and protection based on time grading as well as on current grading. Also includes three step distance protection of transmission line
The document provides an introduction to power system analysis. It discusses the components of a power system including generators, transformers, transmission lines and loads. It explains that power system analysis involves monitoring the system through load flow analysis, short circuit analysis and stability analysis in order to maintain the system safely and economically. It also discusses the need for power system analysis in planning and operating the system, and ensuring power demand is met through reliable generation and transmission of electricity.
Static relays use electronic components like semiconductors instead of mechanical parts to detect faults and operate. They have components like rectifiers to convert AC to DC, level detectors to compare values to thresholds, and amplifiers and output devices to trigger trips. The document discusses the components, types, and applications of various static relays like overcurrent, directional, differential, distance and instantaneous relays used in power system protection.
This document discusses different types of directional over current relays. It explains that directional over current relays operate when fault current flows in a particular direction and will not operate if power flows in the opposite direction. It provides details on 30 and 90 degree connections for directional relays and describes the construction and operation of non-directional over current relays and shaded pole type directional over current relays.
Protection against overvoltage
overvoltage
causes of overvoltage
lightning
types of lightning strokes
harmful effect of lightning
protection against lightning
System protection is used to detect problems in power system components and isolate faulty equipment to maintain reliable power. The key elements of a protection system include differential relays to protect generators and transformers from internal faults, overcurrent and distance relays to protect transmission lines from external faults, and bus differential relays to protect distribution buses. Protective devices are needed to maintain acceptable operation, isolate damaged equipment, and minimize harm to personnel and property.
Unit-2 Three Phase controlled converter johny renoald
This document discusses three phase controlled rectifiers. It provides equations and diagrams for a three phase half-wave converter with an RL load operating under continuous and constant load current. The average output voltage is derived as one-third the peak phase voltage multiplied by 2/π. Waveforms at different trigger angles are shown. Methods for calculating the maximum, RMS, and normalized average output voltages are also presented.
Reactive power is necessary to maintain adequate voltage levels to transmit active power across transmission systems. It is required for system reliability and to prevent voltage collapse. Voltage is controlled by managing the production and absorption of reactive power on the system. Both insufficient reactive power and excessive reactive power can cause voltage issues and equipment problems if voltage is not properly regulated. Reactive power reserves are also required to maintain voltage stability under contingency events like generator or transmission line outages.
The document discusses planning for HVDC transmission and modern trends in HVDC technology. When planning HVDC transmission, the key factors to consider are cost, technical performance, and reliability. Modern trends aim to reduce converter station costs while improving reliability and performance. This includes advances in power semiconductors, converter control technology, development of DC breakers, conversion of existing AC lines, and operation with weak AC systems. Emerging technologies discussed are active DC filters, capacitor commutated converters, and ultra-high voltage DC transmission.
Includes Introduction, Derivation of power flow through transmission line, Single line diagram of three phase transmission, methods of finding the performance of transmission line. 1.Analytical Method 2.Graphical method (circle diagram)., circle diagram of receiving end side and sending end side.
This document provides information about substations, including:
1. Substations are facilities used to change characteristics of electric power supply like voltage, frequency, or converting AC to DC. They are located between generation/transmission and distribution.
2. Substations are classified by their function (transformer, switching, power factor correction etc.) and construction (indoor, outdoor, underground etc.).
3. Key equipment in substations includes transformers, busbars, circuit breakers, insulators, and protection devices. Instrument transformers like PTs and CTs are also used.
4. Distribution systems distribute power from substations to consumers using feeders, distributors, and service mains. Distribution systems are classified by supply type
This presentation discusses the key protection devices used in electrical substations. It introduces current transformers and potential transformers, which reduce current and voltage levels for protection relays. Relays detect faults by measuring currents and voltages. When a fault is detected, relays signal circuit breakers to isolate the faulty component. Other protection devices discussed include lightning arresters, isolators, and surge diverters. The objective of the substation protection system is to isolate only faulty parts of the network while keeping the rest operational.
Voltage Regulation and Control in Transmission LinesToshaliMohapatra
Voltage Regulation and Control in Transmission Lines includes: Importance of Voltage Control, Methods of Voltage Control, Shunt Compensator, Shunt Capacitor & Reactors, Series Compensator, Performance of Series and Shunt Compensators, Results Obtained from Graph, Synchronous Condenser, Tap Changing Transformer, Auto Transformer, Booster Transformer
The document discusses power flow analysis, which determines voltages, currents, real power, and reactive power in a power system under steady-state load conditions. It describes the different types of buses in a power system and how they are modeled. The key component of power flow is the bus admittance matrix, which relates nodal voltages to branch currents based on Kirchhoff's current law. Solving the matrix equations provides the voltage magnitude and angle at each bus.
This document provides an introduction to power system analysis. It discusses the components of an electrical power system including generators, loads, transmission lines, and transformers. It describes the need for network models to analyze power systems and mentions different types of models used, including algebraic equations, differential equations, and transfer functions. It also discusses faults and the need to analyze balanced networks as unbalanced networks during fault conditions. The document provides examples of equivalent circuits used to represent power systems and mentions some of the challenges in modeling loads and generators. Finally, it introduces the topics of network solutions, incidence matrices, faults analysis, and stability analysis that will be covered in the book.
Power system analysis material -Mathankumar.s VMKVECMathankumar S
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.
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.
The document discusses the key elements of a power system, including generation, transmission, distribution, and load. It describes the different types of power generation such as fossil, hydro, and nuclear. It then explains the transmission system, how power is transmitted through overhead lines or underground cables. Finally, it discusses power distribution to load through lower voltage networks.
POWER SYSTEM SIMULATION LAB-1 MANUAL (ELECTRICAL - POWER SYSTEM ENGINEERING )Mathankumar S
This document discusses the computation of parameters for single and double circuit transmission lines. It provides the theoretical background on line parameters such as resistance, inductance, capacitance. Formulas are given for calculating inductance and capacitance based on the geometric mean distance and radius for different conductor arrangements including single circuit, three phase symmetrical, asymmetrical transposed lines and double circuit transposed lines. Sample exercises are given to calculate the inductance and capacitance of given transmission line configurations and verify the results using software.
This document describes a special project on using an artificial neural network (ANN) for load flow studies of the MSU-IIT electrical system. The objectives are to model the power system as a 5-bus system, evaluate bus voltages using a power flow program under different loads, train an ANN using the power flow results, and validate the ANN's accuracy by comparing its results to the power flow program. The document reviews literature on load flow studies, numerical methods, ANNs, and discusses how ANNs could provide faster and more accurate solutions to complex load flow problems compared to numerical methods.
The document discusses key concepts in per unit representation systems for power systems analysis. It defines per unit values as the ratio of an actual value to a base value, and explains that per unit systems simplify analysis by eliminating factors of √3 and 3. The document also outlines advantages of per unit systems like providing relative magnitude information, simplifying analysis with different voltage levels/transformer ratios, and allowing assumed values when specific data is unavailable. Base values are needed to convert different components to common reference values for unified analysis of the entire power system.
Assignment 1 170901 interconnected power systemVara Prasad
Planning and operation of a power system requires studies of load, faults, protection from surges and short circuits, and stability. A disturbance causes changes in system parameters moving it from steady to transient state. Small disturbances can be analyzed linearly while large disturbances require nonlinear analysis. Transient stability means generators remain synchronized after a disturbance and steady state stability means the system returns to the pre-disturbance steady state after a small disturbance. Per unit representations use common base values for analysis and allow easy conversion between different bases.
Assignment 1 170901 interconnected power systemVara Prasad
1. The document discusses power system analysis and modeling of various components in a power system. It provides definitions, equations, and examples related to topics like load flow analysis, bus types, transformer modeling, and transmission line modeling.
2. Key aspects covered include defining the three main bus types - PQ bus, PV bus, and slack bus - and explaining the quantities specified for each. Equations are given for calculating base values like current and impedance as well as transforming values between bases.
3. Modeling of components like transformers and transmission lines is also summarized, along with advantages of per-unit systems. Factors affecting stability and methods to improve it are briefly mentioned.
This document contains details about the Power System Analysis course offered at Muthayammal Engineering College. It includes 5 units that cover topics like power flow analysis, fault analysis of balanced and unbalanced faults, and power system stability. The course aims to impart knowledge of power system modeling and numerical methods for solving power flow and stability problems. It also covers analysis of faults using methods like symmetrical components. The document lists the course faculty, objectives, outcomes, textbooks, and topics to be covered in each unit.
1. A one-line diagram is a simplified diagram that uses standard symbols to represent a three-phase power system using a single line for each phase.
2. The document discusses per-unit representation, which allows quantities in a power system with multiple voltage levels to be normalized and analyzed more easily.
3. The key advantages of per-unit representation are that impedances can be directly compared between different voltage levels and components, and systems can be easily modeled and simulated on computers.
The document discusses power system modeling and analysis techniques. It covers topics like single line diagrams, commonly used component symbols, impedance diagrams, per-unit quantities, and their advantages. It also includes two practice problems on drawing impedance diagrams and converting impedances to per-unit values using different bases.
This document summarizes a study that simulated a grid-connected photovoltaic (PV) system incorporating an efficient maximum power point tracking (MPPT) algorithm. The study used PSIM software to model the PV module, boost converter with Perturb and Observe MPPT control, and inverter connecting the PV array to the grid. Simulation results showed the model achieved the MPPT function and improved the inverter output by reducing voltage ripple.
This document contains information about power system components and fault analysis. It includes:
- An introduction to one-line diagrams and their use in representing power systems through standardized schematic symbols. One-line diagrams simplify three-phase systems and are useful for power flow studies.
- Descriptions of impedance diagrams and reactance diagrams, which represent power system components through equivalent circuits by replacing elements like generators, transformers, and transmission lines with their impedances or reactances.
- Examples of drawing one-line, impedance, and reactance diagrams for given power system configurations. Resistances are often omitted from reactance diagrams for fault analysis calculations.
- Explanations of symmetrical components and their use
This document summarizes a study on modelling and automating a Controllable Network Transformer (CNT). The CNT augments an existing load tap-changing transformer with an AC chopper to control voltage magnitude and phase angle. The study models the CNT using MATLAB and automates its response to system voltage variations. Simulation results demonstrate the CNT's ability to dynamically control output voltage between taps by varying the chopper's pulse width. An automatic tap and pulse selector subsystem chooses the appropriate tap and pulse width based on the required voltage. The automated CNT model proves CNT is a valuable solution for future grid network links by providing flexible voltage matching and bidirectional power flow control.
Augmentation of Real & Reactive Power in Grid by Unified Power Flow ControllerIJERA Editor
In this paper, a Power Flow Control in transmission line with respect to voltage condition (L-G, L-L-G, L-L)
over come by using unified power flow controller. The existing system employs UPFC with transformer less
connection with both series and shunt converter. This converter have been cascaded with multilevel inverters
which is more complicated to enhance the performance of UPFC.A proposed system consist of three terminal
transformer for shunt converter and six terminal transformer for series converter. Shunt converter & series
converter is coupled with common DC capacitor. DC link capacitor voltage is maintained using PID controller
and synchronous reference frame theory (SRF) is used to generate reference voltage & current signal.
Simulation studies are carried out for (L-G, L-L-G, L-L real & reactive power compensation results will be
shown in this paper)
The document provides information about a course on power systems analysis and protection. It includes:
1. An overview of topics covered in the course including per-unit systems, power flow analysis, fault analysis, stability, and protection schemes.
2. Expected learning outcomes including analyzing balanced and unbalanced faults, demonstrating power flow software, and expressing suitable protection schemes.
3. A lecture plan outlining the contents to be covered each week.
4. Assessment details including oral exams, written tests, assignments, and a final exam.
This document discusses per unit systems used in power systems analysis. It defines single line diagrams, impedance diagrams, and reactance diagrams used to represent power systems. It then explains the per unit method for simplifying calculations by expressing all values relative to a common base. Key advantages are simplified calculations, consistent representation of components between different rated systems, and elimination of ideal transformers in diagrams. Some equations are modified in per unit systems and equivalent circuits become more abstract.
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 discusses per unit calculations in power systems. It defines per unit quantities as actual quantities normalized by a base quantity. Common base quantities used are voltage (Vbase), apparent power (Sbase), and impedance (Zbase). The document provides formulas for calculating base impedance and converting impedances to different bases. It includes an example of calculating the per unit impedances of components in a sample power system diagram and drawing the equivalent impedance diagram.
This slide aims to impart knowledge to the learners about the modelling of the power system components using per unit analysis, construction of Y bus and Z bus, different methods of power flow analysis. This also enables the students to analyse the stability of the system using different methods for power system planning and operation.
Small Signal Modeling Of Controller For Statcom Used In Distribution System F...IJERA Editor
This document presents a small signal model of a STATCOM (Static Synchronous Compensator) used for reactive power management in a distribution system. A PI controller is designed for the reactive current component of the STATCOM. The model linearizes the nonlinear STATCOM model and performs small signal modeling of the phase angle and modulation index. Simulation results in MATLAB/Simulink show the model with PI controllers can improve the power factor of the grid current for linear inductive loads by adjusting the reactive power output of the STATCOM.
Simulation And Hardware Analysis Of Three Phase PWM Rectifier With Power Fact...IOSR Journals
This document summarizes a research paper on simulating and analyzing a three-phase PWM rectifier with power factor correction. The paper describes the design of a three-phase PWM rectifier circuit to convert AC power input into DC power output at unity power factor. Simulation results show that the rectifier controls input currents to be sinusoidal and in phase with voltages, improving power quality. Hardware testing also demonstrates unity power factor with voltage and current waveforms in phase. The rectifier design and simulation aim to improve power quality by controlling reactive power and achieving unity power factor.
Grid Interfaced 3-phase Solar Inverter with MPPT by using Boost ConverterIJMTST Journal
This document describes a grid-interfaced 3-phase 750VA solar inverter system with maximum power point tracking (MPPT). It uses a boost converter with a perturbation and observation MPPT algorithm to extract maximum power from the solar panels. The boost converter output is fed to a 3-phase inverter to regulate the voltage and frequency for supplying AC loads or grid integration. Simulation results in MATLAB/Simulink show the MPPT algorithm effectively tracks maximum power and the voltage controller with SPWM regulates the inverter output voltage. The inverter can supply 1kW of power to the grid with output voltages and currents as required.
Power systems can be modeled and analyzed using per-unit representations of components. Key models include:
1) Generator models that specify real and reactive power injection or terminal voltage and current.
2) Transformer models using an equivalent circuit with magnetizing reactance and resistance.
3) Load models like constant impedance, current, or power to represent different load characteristics.
4) Transmission lines modeled as series impedances.
The per-unit system allows analysis of different voltage levels on a common scale and simplifies modeling of components.
Numerical Methods was a core subject for Electrical & Electronics Engineering, Based On Anna University Syllabus. The Whole Subject was there in this document.
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Digital Signal Processing (DSP) from basics introduction to medium level book based on Anna University Syllabus! This is just a share of worthfull book!
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Object Oriented Programming For Engineering Students as well as for B.Tech -IT. Covers Almost All From The Basics.
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The document discusses electrical drives and converters used in electric drive systems. It describes controlled rectifiers, switched-mode converters, and various types of converters including two-quadrant and four-quadrant converters. It also discusses DC motor drives, induction motor drives, and field-oriented control of induction motors. Simulation examples using Simulink are provided for different drive systems.
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The document describes experiments to be performed on an 8-bit microprocessor and microcontroller. It includes aims, block diagrams, flowcharts and assembly language programs for arithmetic operations, sorting an array, and interfacing experiments. Experiments cover topics like addition, subtraction, multiplication, division, ascending/descending order, maximum/minimum values, and interfacing components like ADCs, DACs, stepper motors. Similar experiments are outlined for an 8-bit microcontroller.
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1. POWER SYSTEM ANALYSIS
UNIT I THE POWER SYSTEM – AN OVERVIEW AND MODELLING
Structure of electric power system – Current scenario – Complex power – Concepts of real
and
reactive power – Per phase analysis – Modeling of generator, transformer with off-nominal
tap
ratio, transmission line – Per unit system – One-line, Impedance and reactance diagrams –
Change
of base – Primitive network and network matrices – Y-bus formulation by direct inspection
and
singular transformation methods.
UNIT II POWER FLOW ANALYSIS
System model – The power flow equations (PFE) – System variables – PFE in real form –
Basic
problems, modified specification – Bus classification – Solution technique – Gauss-seidel
method
– Newton-raphson method – Fast-decoupled method – Comparison of solution techniques.
UNIT III SYMMETRICAL FAULT ANALYSIS
Internal voltages of loaded machines under fault conditions – Balanced three phase fault –
Fault
calculations using bus impedance matrix – Algorithm for formation of the impedance matrix
–
Selection of circuit breakers.
UNIT IV SYMMETRICAL COMPONENTS AND UNBALANCED FAULT
ANALYSIS
Symmetrical component analysis of unsymmetrical faults – LG – LL – LLG faults – Open
conductor faults – Unbalanced fault analysis using bus impedance matrix.
UNIT V POWER SYSTEM STABILITY
Rotor dynamics and swing equation – Stability classification – Small signal stability – Large
signal
stability – Equal area criterion and solution of SMIB system problems – Solution of swing
equation – Point-by-point method, R-K method and modified euler method – Techniques for
stability improvement.
L: 45 T: 15 Total: 60
TEXT BOOKS
1. Grainger, J.J. and William D. Stevenson Jr., “Power System Analysis”, Tata McGraw Hill,
2. 2005.
2. Gupta, B.R., “Power System Analysis and Design” S.Chand and Co., Ltd, 2005.
REFERENCES
1. Gupta, J.B., “A Course in Electrical Power”, S.K.Kataria and Sons, 2002.
UNIT I
THE POWER SYSTEM – AN OVERVIEW AND MODELLING
Structure of electric power system – Current scenario – Complex power –
Concepts of real and
reactive power – Per phase analysis – Modeling of generator, transformer with
off-nominal tap
ratio, transmission line – Per unit system – One-line, Impedance and reactance
diagrams – Change
of base – Primitive network and network matrices – Y-bus formulation by direct
inspection and
singular transformation methods.
Power system
A Power system consists of Generation, Transmission and Distribution.
Power system analysis
The evaluation of power system is called as power system analysis
Functions of power system analysis
To monitor the voltage at various buses, real and reactive power flow
between buses.
To design the circuit breakers.
3. To plan future expansion of the existing system
To analyze the system under different fault conditions
To study the ability of the system for small and large disturbances
(Stability studies)
Components of power system
The components of power system are Generators, Power transformers,
Transmission lines, Distribution lines, Loads and compensating devices like shunt,
series, and static VAR compensator.
Modern power system
A modern power system can be subdivided into four major parts: Generation,
Transmission and Sub transmission, Distribution and Loads.
Per phase analysis.
A balanced three phase system is always analyses on per phase basis by
considering one of the three phase lines and neutral.
Infinite bus bar
A large system whose voltage and frequency remain constant, independent of
the power exchange between synchronous machine and bus, and independent of the
excitation of the synchronous machine.
Single line diagram
A single line diagram is diagrammatic representation of power system in
which the components are represented by their symbols and interconnection between
them are shown by a straight line9eventhough the system is three phase system0.The
ratings and the impedances of the components are also marked on the single line
diagram.
Purpose of using single line diagram
The purpose of the single line diagram is to supply in concise form of the
significant information about the system.
Impedance diagram & approximations made in impedance diagram
The impedance diagram is the equivalent circuit of power system in which the
various components of power system are represented by their approximate or
simplified equivalent circuits. The impedance diagram is used for load flow studies.
Approximation:
(i) The neutral reactances are neglected.
(ii) The shunt branches in equivalent circuit of transformers are neglected.
Reactance diagram & approximations made in reactance diagram?
The reactance diagram is the simplified equivalent circuit of power system in
which the various components of power system are represented by their reactances.
The reactance diagram can be obtained from impedance diagram if all the resistive
components are neglected. The reactance diagram is used for fault calculations.
4. Approximation:
(i) The neutral reactances are neglected.
(ii) The shunt branches in equivalent circuit of transformers are neglected.
(iii) The resistances are neglected.
(iv) All static loads are neglected.
(v) The capacitance of transmission lines are neglected.
Per unit value.
The per unit value of any quantity is defined as the ratio of the actual value of
the any quantity to the base value of the same quantity as a decimal.
Advantages of per unit system
i. Per unit data representation yields valuable relative magnitude information.
ii. Circuit analysis of systems containing transformers of various transformation
ratios is greatly simplified.
iii. The p.u systems are ideal for the computerized analysis and simulation of
complex power system problems.
iv. Manufacturers usually specify the impedance values of equivalent in per unit
of the equipments rating. If the any data is not available, it is easier to assume
its per unit value than its numerical value.
v. The ohmic values of impedances are refereed to secondary is different from
the value as referee to primary. However, if base values are selected properly,
the p.u impedance is the same on the two sides of the transformer.
vi. The circuit laws are valid in p.u systems, and the power and voltages
equations are simplified since the factors of √3 and 3 are eliminated.
vii.
Need for base values
The components or various sections of power system may operate at different
voltage and power levels. It will be convenient for analysis of power system if the
voltage, power, current and impedance rating of components of power system are
expressed with reference to a common value called base value.
Equation for per unit impedance if change of base occurs.
A generator rated at 30MVA, 11KV has a reactance of 20%.Calculate its per unit
reactance for a base of 50 MVA and 10KV.
MVA new = 50 ; KV new = 10 ; MVA old = 30 ; KV old = 11
X p.u = 20% = 20/100 = 0.2 p.u
5. New p.u impedance if the new base MVA is twice the old base MVA
Draw the per unit reactance diagram for the power systems shown below. Neglect
resistance and use a base of 100MVA, 220KV in 50 ohms line. The ratings of the
generator, motor and transformers are
G: 40MVA, 25KV, X’’ = 20%
M: 50MVA, 11KV, X’’ = 30%
T1: 40MVA, 33 Y/ 220Y KV, X = 15%
T2: 30MVA, 11 Δ / 220Y KV, X = 15%
Load: 11KV, 50MW+j68 MVAR
Solution:
Base MVA, MVAb, new = 100MVA
Base KV, KVb, new = 220KV
j 50Ω
G1 M
T1 T2
6. Reactance of the transmission line:
Actual reactance =50Ω
Reactance of the Transformer T1:
;
; =?
= 33 KV
Reactance of the Generator G:
;
; = 33
Reactance of the Transformer T2:
;
; =?
7. = 11 KV
Reactance of the Motor M:
;
; = 11
Reactance Diagram
1. Draw the reactance diagram using a base of 50MVA and 13.8KV on generatorG1
j 0.287
j 0.375 j 0.1033 j 0.5
j 0.6
Eg
Em
G1 G3
G2
T1 T3
T2
Line 1 Line 2
j80Ω j100Ω
8. G1: 20MVA, 13.8KV, X’’=20% ; G2: 30MVA, 18.0KV, X’’=20%
G3: 30MVA, 20.0KV, X’’=20% ; T1: 25MVA, 220/13.8 KV, X =10%
T2:3Single phase unit each rated 10MVA, 127/18 KV, X =10%
T3: 35MVA, 220/22 KV, X =10%
Solution:
Base MVA, MVAb, new = 50MVA
Base KV, KVb, new = 13.8KV
Reactance of the Generator G1:
;
; = 13.8
Reactance of the Transformer T1 :( Primary side)
;
; = 13.8
Reactance of the transmission line j 80Ω:
Actual reactance =80Ω
9. = 220 KV
Reactance of the transmission line j 100Ω:
Actual reactance =100Ω
= 220 KV
Reactance of the Transformer T2:( Primary side)
Connection; voltage rating: 220/18KV
;
; =220?
Reactance of the Generator G2:
10. ;
; = ?
= 18KV
Reactance of the Transformer T3 :( Secondary side)
;
; = 220
Reactance of the Generator G3:
;
; = ?
= 22KV
Reactance Diagram
j 0.5
j 0.2 j 0.0826 j 0.1033 j 0.1667
j 0.333j 0.1429
11. A simple power system is shown in fig. Redraw this system where the per unit impedance
of the components are represented on a common 5000 VA base and common system base
voltage of 250V.
Solution:
Base MVA, MVAb, new = 5000 VA = 5MVA
Base KV, KVb, new = 250V = 0.25KV
Impedance of the Generator G1:
;
; = 0.25
Impedance of the Generator G2:
Z=40 + j 150Ω
G1
T1 T2
G2
Load
1000VA
250V
Z = j0.2 p.u
2000VA
250V
Z = j0.3 p.u
4000VA
250/800V
Z = j0.2 p.u
8000VA
1000/500V
Z = j0.06 p.u
2500VA
400V
12. ;
; = 0.25
Impedance of the Transformer T1: (Primary side)
;
; = 0.25
Impedance of the transmission line Z= 40+ j 100Ω:
Actual impedance = (40+j150) Ω
= 800 V
Impedance of the Transformer T2: (Primary side)
;
; = 0.8
Impedance of the Load
Reactance Diagram
13. 2. The single line diagram of a three phase power system is shown in fig. Select a
common base of 100MVA and 13.8KV on the generator side. Draw per unit
impedance diagram
G: 90MVA, 13.8KV, X=18% ; T1 :50MVA, 13.8/220KV, X=10%
T2:50MVA, 220/11KV, X=10% ; T3 :50MVA, 13.8/132KV, X=10%
T4:50MVA, 132/11KV, X=10% ; M : 80MVA, 10.45KV, X=20%
LOAD : 57MVA, 0.8 p.f lagging at 10.45 KV ; Line 1 = j 50Ω ; Line 2 = j 70Ω
Solution:
Base MVA, MVAb, new = 100MVA
Base KV, KVb, new = 13.8KV
Reactance of the Generator G1:
;
; = 13.8
Reactance of the Transformer T1 :( Primary side)
j 0.75
j 0.25 0.3125 + j 1.17 j 0.0585 j0.5
j 1.0
Load
j 50Ω
T1 T2
2
j70Ω
G M
T3 T4
4
14. ;
; = 13.8
Reactance of the transmission line j 50Ω:
Actual reactance =50Ω
= 220 KV
Reactance of the Transformer T2 :( Primary side)
;
; = 220
Reactance of the Transformer T3 :( Primary side)
;
15. ; = 13.8
Reactance of the transmission line j 70Ω:
Actual reactance =70Ω
= 132KV
Reactance of the Transformer T4 :( Primary side)
;
; = 132
Reactance of the Motor M:
;
; = ?
= 11KV
16. The load is at 0.8 p.f lagging is given by
Load impedance is given by
Base impedance for the load is
Reactance Diagram
17. Part-A
1. What is Power system?
2. What is power system analysis?
3. What are the functions of power system analysis?
4. What are the components of power system?
5. What is modern power system?
6. Define per phase analysis.
7. Draw the per phase model or equivalent circuit model or representation
all components of power system? -
8. What is an infinite bus bar?.
9. What is single line diagram?
10. What is the purpose of using single line diagram?
11. What is impedance diagram? What are the approximations made in
impedance diagram?
12. What is reactance diagram? What are the approximations made in
reactance diagram?
Part-B
1. Explain the modeling of generator, load, transmission line and transformer for power
flow, short circuit and stability studies.
3. Draw the per unit reactance diagram for the power systems shown below. Neglect
resistance and use a base of 100MVA, 220KV in 50 ohms line. The ratings of the
generator, motor and transformers are Draw the reactance diagram using a base of
50MVA and 13.8KV on generatorG1
G1 G3
G2
T1 T3
T2
Line 1 Line 2
j80Ω j100Ω
18. G1: 20MVA, 13.8KV, X’’=20% ; G2: 30MVA, 18.0KV, X’’=20%
G3: 30MVA, 20.0KV, X’’=20% ; T1: 25MVA, 220/13.8 KV, X =10%
T2:3Single phase unit each rated 10MVA, 127/18 KV, X =10%
T3: 35MVA, 220/22 KV, X =10%
4. A simple power system is shown in fig. Redraw this system where the per unit
impedance of the components are represented on a common 5000 VA base and
common system base voltage of 250V.
1. The single line diagram of a three phase power system is shown in fig. Select a
common base of 100MVA and 13.8KV on the generator side. Draw per unit
impedance diagram
G: 90MVA, 13.8KV, X=18% ; T1 :50MVA, 13.8/220KV, X=10%
T2:50MVA, 220/11KV, X=10% ; T3 :50MVA, 13.8/132KV, X=10%
T4:50MVA, 132/11KV, X=10% ; M : 80MVA, 10.45KV, X=20%
Z=40 + j 150Ω
G1
T1 T2
G2
Load
1000VA
250V
Z = j0.2 p.u
2000VA
250V
Z = j0.3 p.u
4000VA
250/800V
Z = j0.2 p.u
8000VA
1000/500V
Z = j0.06 p.u
2500VA
400V
j 50Ω
T1 T2
2
j70Ω
G M
T3 T4
4
19. LOAD : 57MVA, 0.8 p.f lagging at 10.45 KV ; Line 1 = j 50Ω ; Line 2 = j 70Ω
UNIT-II
POWER FLOW ANALYSIS
System model – The power flow equations (PFE) – System variables – PFE in real form –
Basic
problems, modified specification – Bus classification – Solution technique – Gauss-seidel
method
– Newton-raphson method – Fast-decoupled method – Comparison of solution techniques.
Bus
The meeting point of various components in a power system is called a bus.
The bus is a conductor made of copper or aluminium having negligible resistance .At
some of the buses power is being injected into the network, whereas at other buses it
is being tapped by the system loads.
Bus admittance matrix
The matrix consisting of the self and mutual admittance of the network of the
power system is called bus admittance matrix (Ybus).
Methods available for forming bus admittance matrix
Direct inspection method.
Singular transformation method.(Primitive network)
Power flow study or load flow study
The study of various methods of solution to power system network is referred
to as load flow study. The solution provides the voltages at various buses, power
flowing in various lines and line losses.
Information’s that are obtained from a load flow study
The information obtained from a load flow study is magnitude and phase angle
of voltages, real and reactive power flowing in each line and the line losses. The load
flow solution also gives the initial conditions of the system when the transient
behavior of the system is to be studied.
20. Need for load flow study
The load flow study of a power system is essential to decide the best operation
of existing system and for planning the future expansion of the system. It is also
essential foe designing a new power system.
Quantities associated with each bus in a system
Each bus in a power system is associated with four quantities and they are real
power (P), reactive power (Q), magnitude of voltage (V), and phase angle of
voltage (δ).
Different types of buses in a power system, buses are classified and its types
Types of bus Known or
specified
quantities
Unknown quantities or
quantities to be
determined.
Slack or Swing or Reference
bus
V, δ P,Q
Generator or Voltage control or
PV bus
P, V Q, δ
Load or PQ bus P, Q V, δ
Need for slack bus
The slack bus is needed to account for transmission line losses. In a power
system the total power generated will be equal to sum of power consumed by loads
and losses. In a power system only the generated power and load power are specified
for buses. The slack bus is assumed to generate the power required for losses. Since
the losses are unknown the real and reactive power are not specified for slack bus.
Iterative methods to solve load flow problems
The load flow equations are non linear algebraic equations and so explicit
solution as not possible. The solution of non linear equations can be obtained only by
iterative numerical techniques.
Mainly used for solution of load flow study
The Gauss seidal method, Newton Raphson method and Fast decouple
methods.
Flat voltage start
21. In iterative method of load flow solution, the initial voltages of all buses
except slack bus assumed as 1+j0 p.u. This is refereed to as flat voltage start
Effect of acceleration factor in load flow study
Acceleration factor is used in gauss seidal method of load flow solution to
increase the rate of convergence. Best value of A.F=1.6
Generator buses are treated as load bus
If the reactive power constraints of a generator bus violates the specified limits
then the generator is treated as load bus.
Advantages and disadvantages of Gauss serial method
Advantages: Calculations are simple and so the programming task is lessees.
The memory requirement is less. Useful for small systems; Disadvantages:
Requires large no. of iterations to reach converge .Not suitable for large systems.
Convergence time increases with size of the system
Advantages and disadvantages of N.R method
Advantages: Faster, more reliable and results are accurate, require less
number of iterations; Disadvantages: Program is more complex, memory is more
complex.
Compare the Gauss seidel and Newton raphson methods of load flow study
S.No G.S N.R FDLF
1 Require large number of
iterations to reach
convergence.
Require less number
of iterations to reach
convergence.
Require more number of
iterations than N.R method.
2 Computation time per
iteration is less
Computation time per
iteration is more
Computation time per iteration
is less
3 It has linear convergence
characteristics
It has quadratic
convergence
characteristics
------
4 The number of iterations
required for convergence
increases with size of the
system
The number of
iterations are
independent of the
size of the system
The number of iterations are
does not dependent of the size
of the system
5 Less memory
requirements.
More memory
requirements.
Less memory requirements
than N.R.method.
22. Y matrix of the sample power system as shown in fig. Data for this system is given in
table.
23. Find out the Y matrix of the sample power system network diagram as shown in fig.
24. Consider the system shown in fig. It shows a transmission network with impedance of
transmission lines all in p.u as shown. Compute Ybus matrix.
0.02+j0.04
0.0125+j0.0250.01+j0.03
1 2
3
26. The following is the system data for a load flow solution. Determine the voltages at
the end of first iteration using Gauss-Seidel method. Take α=1.6 .
The line admittances:
Bus code Admittance
1-2 2-j8.0
1-3 1-j4.0
2-3 0.666-j2.664
2-4 1-j4.0
27. 3-4 2-j8.0
The schedule of active and reactive powers:
Bus code P in p.u Q in p.u V in p.u Remarks
1 - - 1.06 Slack
2 0.5 0.2 1+j0.0 PQ
3 0.4 0.3 1+j0.0 PQ
4 0.3 0.1 1+j0.0 PQ
Solution
=
=
= 1.01187-j0.02888
V2
1
acc = (1.0+j0.0)+1.6(1.01187-j0.02888-1.0-j0.0) = 1.01899-j0.046208
V3
1
= 0.994119-j0.029248 ; V3
1
acc = 0.99059-j0.0467968
V4
1
= 0.9716032-j0.064684 ; V4
1
acc = 0.954565-j0.1034944
Fig shows that the one line diagram of a simple three bus system with generation at
bus 1.The magnitude of voltage at a bus 1 is adjusted to 1.05 p.u. The scheduled loads
at buses2 and 3 are as marked on the diagram. Line impedances are marked in n p.u
on a 100MVA base and the line charging susceptances are neglected.
a. Using the Gauss-Seidel method, determine the phasor values of the
voltages at the load buses 2 and 3(P-Q buses) accurate to decimal places.
b. Find the slack bus real and reactive power.
c. Determine the line flows and line losses. Construct a power flow diagram
showing the direction of line flow.
40. Part-A
1. What is a bus?
2. What is bus admittance matrix?
3. What are the methods available for forming bus admittance matrix?
41. 4. What is power flow study or load flow study?
.
5. What are the informations that are obtained from a load flow study?
6. What is the need for load flow study?
.
7. What are the quantities associated with each bus in a system?
8. What are the different types of buses in a power system? Or how the buses are
classified and what are its types?
9. What is the need for slack bus?
10. Why do we go for iterative methods to solve load flow problems?
11. What are the methods mainly used for solution of load flow study?
12. What do you mean by a flat voltage start?
13. Discuss the effect of acceleration factor in load flow study.
14. When the generator buses are treated as load bus.
Part-B
1. Find out the Y matrix of the sample power system as shown in fig. Data for this
system is given in table.
1. 2. Find out the Y matrix of the sample power system network diagram as shown in
fig.
42. 3. Consider the system shown in fig. It shows a transmission network with impedance
of transmission lines all in p.u as shown. Compute Ybus matrix.
0.02+j0.04
0.0125+j0.0250.01+j0.03
1 2
3
43. UNIT-III
SYMMETRICAL FAULT ANALYSIS
Internal voltages of loaded machines under fault conditions – Balanced three phase fault –
Fault
calculations using bus impedance matrix – Algorithm for formation of the impedance matrix
–
Selection of circuit breakers.
Fault
A fault in a circuit is any failure which interferes with the normal flow of
current. The faults are associated with abnormal change in current, voltage and
frequency of the power system.
Faults occur in a power system
The faults occur in a power system due to
Insulation failure of equipment
Flashover of lines initiated by a lighting stroke
Due to permanent damage to conductors and towers or due to
accidental faulty operations.
various types of faults
(i) Series fault or open circuit fault
One open conductor fault
44. Two open conductor fault
(ii) Shunt fault or short circuit fault.
Symmetrical fault or balanced fault
Three phase fault
Unsymmetrical fault or unbalanced fault
Line to ground (L-G) fault
Line to Line (L-L) fault
Double line to ground (L-L-G) fault
Relative frequency of occurrence of various types of fault
Types of fault Relative frequency of
occurrence of faults
Three phase fault 5%
Double line to ground fault 10%
Line to Line fault 15%
Line to ground fault 70%
.
Symmetrical fault or balanced three phase fault
This type of fault is defined as the simultaneous short circuit across all the
three phases. It occurs infrequently, but it is the most severe type of fault encountered.
Because the network is balanced, it is solved by per phase basis using Thevenins
theorem or bus impedance matrix or KVL, KCL laws.
Need for short circuit studies or fault analysis
Short circuit studies are essential in order to design or develop the protective
schemes for various parts of the system .To estimate the magnitude of fault current for
the proper choice of circuit breaker and protective relays.
Bolted fault or solid fault
45. A Fault represents a structural network change equivalent with that caused by
the addition of impedance at the place of a fault. If the fault impedance is zero, the
fault is referred as bolted fault or solid fault.
Reason for transients during short circuits
The faults or short circuits are associated with sudden change in currents.
Most of the components of the power system have inductive property which opposes
any sudden change in currents, so the faults are associated with transients.
Doubling effect
If a symmetrical fault occurs when the voltage wave is going through zero
then the maximum momentary short circuit current will be double the value of
maximum symmetrical short circuit current. This effect is called doubling effect.
DC off set current
The unidirectional transient component of short circuit current is called DC off
set current.
Synchronous reactance or steady state condition reactance
The synchronous reactance is the ratio of induced emf and the steady state rms
current. It is the sum of leakage reactance (Xl) and the armature reactance (Xa).
Sub transient reactance
Fault
46. The synchronous reactance is the ratio of induced emf on no load and the sub
transient symmetrical rms current.
Transient reactance
The synchronous reactance is the ratio of induced emf on no load and the transient
symmetrical rms current.
short circuit capacity of power system or fault level.
Short circuit capacity (SCC) or Short circuit MVA or fault level at a bus is defined
as the product of the magnitude of the prefault bus voltage and the post fault current.
SCC or Short circuit MVA =
Or
SCC =
fault current in fig., if the prefault voltage at the fault point is 0.97 p.u.
Fault
Fault
j0.15j0.15
j0.2 F
47. j0.2 and j 0.15 are in series. j0.2+ j 0.15 = j 0.35
J0.35 is in parallel with j 0.15
=
Bus impedance matrix
Bus impedance matrix is the inverse of the bus admittance matrix.
The matrix consisting of driving point impedance and transfer impedances of
the network is called as bus impedance matrix. Bus impedance matrix is symmetrical.
Methods available for forming bus impedance matrix
Form bus admittance matrix and take the inverse to get bus impedance matrix.
Using bus building algorithm.
Using L-U factorization of Y-bus matrix.
A synchronous generator and a synchronous motor each rated 20MVA, 12.66KV
having 15% reactance are connected through transformers and a line as shown in fig.
the transformers are rated 20MVA,12.66/66KV and 66/12.66KV with leakage
reactance of 10% each. The line has a reactance of 8% on base of 20MVA, 66 KV.
The motor is drawing 10MW at 0.8 leading power factors and a terminal voltage
11KV when symmetrical three phase fault occurs at the motors terminals. Determine
the generator and motor currents. Also determine the fault current.
Solution
49. Three 11.2 KV generators are interconnected as shown in figure by a tie -bar through current
limiting reactors. A three phase feeder is supplied from the bus bar of generator A at line
voltage 11.2 KV. Impedance of the feeder is (0.12+j0.24) ohm per phase. Compute the
maximum MVA that can be fed into a symmetrical short circuit at the far end of the feeder.
50. Assume a zero pre-fault current (no load pre-fault condition).Circuit model for the
fault calculation is given
51. A 4 bus sample power system is shown in fig. Perform the short circuit analysis for a three
phase solid fault on bus 4.data are given below
G1: 11.2KV, 100MVA, X=0.08 p.u
G1: 11.2KV, 100MVA, X=0.08 p.u
T1: 11/110KV, 100MVA, X=0.06 p.u
T2: 11/110KV, 100MVA, X=0.06 p.u
Assume prefault voltages 1.0 p.u and prefault currents to be zero.
52.
53. Two generators G1 and G2 are rated 15MVA, 11KV and 10MVA, 11KV
respectively. The generators are connected to a transformer as shown in fig. Calculate
the subtaransient current in each generator when a three phase fault occurs on the high
voltage side of the transformer.
54. A radial power system network is shown in fig. a three phase balanced fault occurs at
F. Determine the fault current and the line voltage at 11.8 KV bus under fault
condition.
55.
56. A 100MVA,11KV generator with X’’=0.20 p.u is connected through a transformer
and line to a bus bar that supplies three identical motor as shown in fig. and each
motor has X’’=0.20 p.u and X’=0.25 p.u on a base of 20MVA,33KV.the bus voltage
at the motors is 33KV when a three phase balanced fault occurs at the point F.
Calculate
(a) subtransient current in the fault
(b) subtransient current in the circuit breaker B
(c) Momentary current in the circuit breaker B
(d) The current to be interrupted by CB B in (i) 2 cycles (ii) 3 cycles (iii) 5
cycles (iv) 8 cycles
60. Obtain impedance matrix ZBUS for shown in figure.
Obtain impedance matrix ZBUS for shown in figure
61.
62. Part-A
1.What is meant by a fault?
2.How the faults are classified?
3.List the symmetrical and unsymmetrical faults.
4.Write the relative frequency of occurrence of various types of faults.
5.What is the need for short circuit studies or fault analysis?
6.What is meant by doubling effect?
7.What are the main factors to be considered to select a circuit breaker?
8.Define short circuit interrupting of a circuit breaker.
9.Write equation for subtransient internal voltage and transient internal voltage of motor and
generator.
10.Find the momentary current through the circuit breaker if the initial symmetrical short
circuit current through it is 5270.9A.
Part-B
1). A synchronous generator and motor are rated for 30,000KVA,13.2KV and both have
subtransient reactance of 20%.The line connecting them has a reactance of 10% on the base
of machine ratings. The motor is drawing 20,000KW at 0.8 pf leading.The terminal voltage
of the motor is 12.8KV.When a symmetrical three-phase fault occurs at motor terminals,find
the subtransient current in generator,motor and at the fault point. (16)
2. Explain in detail about transients due to a short circuit in 3-Phase alternator and in
transmission line.
3.) A 3-phase ,5MVA,6.6KV alternator with a reactance of 8% is connected to a feeder of
series impedance of ).12+j0.48ohms/phase per km.The transformer is rated at
3MVA,6.6KV/33KV and has a reactance of 5%.Determine the fault current supplied by the
generator operating under no-load with a voltage of 6.9 kv, when a 3-phase symmetrical fault
occurs at a point 15km along the feeder. (16)
(
(a)Explain in detail about bus impedance matrix in fault calculations (8).
(b).Explain in detail about selection of circuit breakers. (8)
4) Explain about the symmetrical fault current estimation using kirchoff’s laws and using a
Thevenin’s theorem.
(7)
63. 5. ) The bus impedance matrix of four bus system with values in p.u. is given by
If a 3-phase fault occurs at bus-1when there is no-load,find the subtransient current in
the fault and voltages at all buses.Also find the subtrasient current supplied by the generator
connected to bus-2 by taking the subtransient reactance of generator as j0.2 p.u.
UNIT- IV
SYMMETRICAL COMPONENTS AND UNBALANCED FAULT
ANALYSIS
64. Symmetrical component analysis of unsymmetrical faults – LG – LL – LLG faults – Open
conductor faults – Unbalanced fault analysis using bus impedance matrix.
Symmetrical components of a 3 phase system
In a 3 phase system, the unbalanced vectors (either currents or voltage) can be
resolved into three balanced system of vectors.
They are Positive sequence components
Negative sequence components
Zero sequence components
Unsymmetrical fault analysis can be done by using symmetrical components.
Positive sequence components
It consists of three components of equal magnitude, displaced each other by
120˚ in phase and having the phase sequence abc .
Negative sequence components
It consists of three components of equal magnitude, displaced each other by
120˚ in phase and having the phase sequence acb .
120˚
120˚
120˚ Ia1
Ib1
Ic1
65. Zero sequence components
It consists of three phasors equal in magnitude and with zero phase
displacement from each other.
Sequence operator
In unbalanced problem, to find the relationship between phase voltages and
phase currents, we use sequence operator ‘a’.
a = 1∠120˚ = = - 0.5+j0.866
Unbalanced currents from symmetrical currents
Let, Ia, Ib, Ic be the unbalanced phase currents
Let, Ia0, Ia1, Ia2 be the symmetrical components of phase a
120˚
120˚
120˚ Ia2
Ic2
Ib2
Ia0
Ib0
Ic0 Ia0 = Ib0 = Ic0
66. Determination of symmetrical currents from unbalanced currents.
Let, Ia, Ib, Ic be the unbalanced phase currents
Let, Ia0, Ia1, Ia2 be the symmetrical components of phase a
Sequence impedance and sequence network
The sequence impedances are the impedances offered by the power system
components or elements to +ve, -ve and zero sequence current.
The single phase equivalent circuit of power system consisting of impedances
to current of any one sequence only is called sequence network.
The phase voltage across a certain load are given as
67. Compute positive, negative and zero sequence component of voltage
Solution:
A balanced delta connected load is connected to a three phase system and supplied to
it is a current of 15 amps. If the fuse is one of the lines melts, compute the
symmetrical components of line currents.
Draw zero sequence network of the power system as shown in fig.
68. Draw zero sequence network of the power system as shown in fig.
Draw zero sequence network of the power system as shown in fig. Data are given below.
69. A 50MVA, 11KV, synchronous generator has a sub transient reactance of 20%.The
generator supplies two motors over a transmission line with transformers at both ends
as shown in fig. The motors have rated inputs of 30 and 15 MVA, both 10KV, with
25% sub transient reactance. The three phase transformers are both rated 60MVA,
10.8/121KV, with leakage reactance of 10% each. Assume zero sequence reactance
for the generator and motors of 6% each. Current limiting reactors of 2.5 ohms each
are connected in the neutral of the generator and motor number 2. The zero sequence
reactance of the transmission line is 300 ohms. The series reactance of the line is 100
ohms. Draw the positive, negative and zero sequence networks.
70.
71. A 30 MVA, 13.2KV synchronous generator has a solidly grounded neutral. Its
positive, negative and zero sequence impedances are 0.30, 0.40 and 0.05 p.u
respectively. Determine the following:
a) What value of reactance must be placed in the generator neutral so that
the fault current for a line to ground fault of zero fault impedance shall
not exceed the rated line current?
b) What value of resistance in the neutral will serve the same purpose?
c) What value of reactance must be placed in the neutral of the generator
to restrict the fault current to ground to rated line current for a double
line to ground fault?
d) What will be the magnitudes of the line currents when the ground
current is restricted as above?
e) As the reactance in the neutral is indefinitely increased, what are the
limiting values of the line currents?
72. 2. Two alternators are operating in parallel and supplying a synchronous motor which
is receiving 60MW power at 0.8 power factor lagging at 6.0 KV. Single line
diagram for this system is given in fig. Data are given below. Compute the fault
current when a single line to ground fault occurs at the middle of the line through a
fault resistance of 4.033 ohm.
73.
74.
75.
76.
77. Part-A
1.What are the symmetrical components of a 3 phase system?
2.What are the positive sequence components?
3.What are the negative sequence components?
4.What is sequence operator?
5.Write down the equations to convert symmetrical components into
unbalanced phase currents. (Or) Determination of unbalanced currents from
symmetrical currents.
6.Write down the equations to convert unbalanced phase currents into
symmetrical components. (Or) Determination of symmetrical currents from
unbalanced currents.
.7What are sequence impedance and sequence network?
.8.Draw the positive, negative and zero sequence network of all power system
components.
--
9.Write the equation to determine fault current for L-G, L-L and L-L-G fault
with impedance.
78. 10.Draw the equivalent sequence network diagram for L-G, L-L and L-L-G
fault .
Part-B
1.A balanced delta connected load is connected to a three phase system and supplied to it is a
current of 15 amps. If the fuse is one of the lines melts, compute the symmetrical components
of line currents
2.Draw zero sequence network of the power system as shown in fig.
3.A 50MVA, 11KV, synchronous generator has a sub transient reactance of 20%.The
generator supplies two motors over a transmission line with transformers at both ends as
shown in fig. The motors have rated inputs of 30 and 15 MVA, both 10KV, with 25%
sub transient reactance. The three phase transformers are both rated 60MVA,
10.8/121KV, with leakage reactance of 10% each. Assume zero sequence reactance for
the generator and motors of 6% each. Current limiting reactors of 2.5 ohms each are
connected in the neutral of the generator and motor number 2. The zero sequence
reactance of the transmission line is 300 ohms. The series reactance of the line is 100
ohms. Draw the positive, negative and zero sequence networks.
79. 4.A 30 MVA, 13.2KV synchronous generator has a solidly grounded neutral. Its
positive, negative and zero sequence impedances are 0.30, 0.40 and 0.05 p.u
respectively. Determine the following:
f) What value of reactance must be placed in the generator neutral so that
the fault current for a line to ground fault of zero fault impedance shall
not exceed the rated line current?
g) What value of resistance in the neutral will serve the same purpose?
h) What value of reactance must be placed in the neutral of the generator
to restrict the fault current to ground to rated line current for a double
line to ground fault?
i) What will be the magnitudes of the line currents when the ground
current is restricted as above?
j) As the reactance in the neutral is indefinitely increased, what are the
limiting values of the line currents?
80. UNIT- V
POWER SYSTEM STABILITY
Rotor dynamics and swing equation – Stability classification – Small signal stability – Large
signal
stability – Equal area criterion and solution of SMIB system problems – Solution of swing
equation – Point-by-point method, R-K method and modified euler method – Techniques for
stability improvement.
power system stability
The stability of an interconnected power system means is the ability of the
power system is to return or regain to normal or stable operating condition after
having been subjected to some form of disturbance.
Power system stability is classified
Rotor angle stability
Rotor angle stability is the ability of interconnected synchronous machines of
a power system to remain in synchronism.
81. steady state stability
Steady state stability is defined as the ability of the power system to bring it to
a stable condition or remain in synchronism after a small disturbance.
Steady state stability limit
The steady sate stability limit is the maximum power that can be transferred
by a machine to receiving system without loss of synchronism
Transient stability
Transient stability is defined as the ability of the power system to bring it to a
stable condition or remain in synchronism after a large disturbance.
transient stability limit
The transient stability limit is the maximum power that can be transferred by a
machine to a fault or a receiving system during a transient state without loss of
synchronism.
Transient stability limit is always less than steady state stability limit
Dynamic stability
It is the ability of a power system to remain in synchronism after the initial
swing (transient stability period) until the system has settled down to the new steady
state equilibrium condition
Voltage stability
It is the ability of a power system to maintain steady acceptable voltages at all
buses in the system under normal operating conditions and after being subjected to a
disturbance.
82. Causes of voltage instability
A system enters a state of voltage instability when a disturbance, increase in
load demand, or change in system condition causes a progressive and uncontrollable
drop in voltage
The main factor causing instability is the inability of the power system to meet
the demand for reactive power.
Power angle equation and draw the power angle curve
Where, P – Real Power in watts
Vs – Sending end voltage; Vr- Receiving end voltage
XT - Total reactance between sending end receiving end
- Rotor angle.
Maximum power transfer.
Swing equation for a SMIB (Single machine connected to an infinite bus bar)
system.
M
Where H = inertia constant in MW/MVA
83. f = frequency in Hz
M = inertia constant in p.u
Swing curve
The swing curve is the plot or graph between the power angle δ and time t.
From the nature of variations of δ the stability of a system for any disturbance can be
determined.
3 machine system having ratings G1, G2 and G3 and inertia constants M1, M2 and
M3.What is the inertia constants M and H of the equivalent system.
Where G1, G2, G3 – MVA rating of machines 1, 2, and 3
Gb = Base MVA or system MVA
Assumptions made in stability studies.
Machines represents by classical model
The losses in the system are neglected (all resistance are neglected)
The voltage behind transient reactance is assumed to remain constant.
Controllers are not considered ( Shunt and series capacitor )
Effect of damper winding is neglected.
Equal Area Criterion
The equal area criterion for stability states that the system is stable if the area
under P – δ curve reduces to zero at some value of δ.
84. This is possible if the positive (accelerating) area under P – δ curve is equal to
the negative (decelerating) area under P – δ curve for a finite change in δ. hence
stability criterion is called equal area criterion.
Critical clearing angle.
The critical clearing angle , is the maximum allowable change in the power
angle δ before clearing the fault, without loss of synchronism.
The time corresponding to this angle is called critical clearing time, .It can
be defined as the maximum time delay that can be allowed to clear a fault without loss
of synchronism.
Methods of improving the transient stability limit of a power system.
Reduction in system transfer reactance
Increase of system voltage and use AVR
Use of high speed excitation systems
Use of high speed reclosing breakers
Numerical integration methods of power system stability
i. Point by point method or step by step method
ii. Euler method
iii. Modified Euler method
iv. Runge-Kutta method(R-K method)
86. A 400 MVA synchronous machine has H1=4.6 MJ/MVA and a 1200 MVA machines
H2=3.0 MJ/MVA. Two machines operate in parallel in a power plant. Find out Heq
relative to a 100MVA base.
87. A 100 MVA, two pole, 50Hz generator has moment of inertia 40 x 103
kg-m2
.what is
the energy stored in the rotor at the rated speed? What is the corresponding angular
momentum? Determine the inertia constant h.
The sending end and receiving end voltages of a three phase transmission line at a
200MW load are equal at 230KV.The per phase line impedance is j14 ohm. Calculate
the maximum steady state power that can be transmitted over the line.
89. A single line diagram of a system is shown in fig. All the values are in per unit on a common
base. The power delivered into bus 2 is 1.0 p.u at 0.80 power factor lagging. Obtain the
power angle equation and the swing equation for the system. Neglect all losses.
94. A 50Hz synchronous generator capable of supplying 400MW of power is connected to a
larger power system and is delivering 80MW when a three phase fault occurs at its terminals,
determine (a) the time in which the fault must be cleared if the maximum power angle is to be
-85˚ assume H=7MJ/MVA on a 100MVA base (b) the critical clearing angle.
95. A 2220 MVA, 24KV and 60 Hz synchronous machine is connected to an infinite bus
through transformer and double circuit transmission line, as shown in fig. The infinite
bus voltage V=1.0 p.u .The direct axis transient reactance of the machine is 0.30 p.u,
the transformer reactance is 0.20 p.u, and the reactance of each the transmission line
is 0.3 p.u,all to a base of the rating of the synchronous machine. Initially, the machine
is delivering 0.8 p.u real power and reactive power is 0.074 p.u with a terminal
voltage of 1.0 p.u. The inertia constant H=5MJ/MVA. All resistances are neglected. A
three phase fault occurs at the sending end of one of the lines, the fault is cleared, and
the faulted line is isolated. Determine the critical clearing angle and the critical fault
clearing time.
The current flowing into the infinite bus is
The transfer reactance between internal voltage and the infinite bus before
fault is
X = Xg +XT +Xtr.line
X = 0.3 + 0.2 +0.3/2 = 0.65
The transient internal voltage is
96. E = V +j X I = 1.0+ (j0.65) (0.8- j0.074)
= 1.17
Since both lines are intact when the fault is cleared, the power angle equation
before and after the fault is
The initial operating angle is given by = 0.8
δ0 = 26.388 = 0.46055 rad
δmax =180º - δ0 = 153.612 =2.681rad
Critical clearing angle
δc =
Critical clearing time tc = = = 0.26 second
A synchronous generator is connected to a large power system and supplying 0.45 pu
MW of its maximum power capacity. A three phase fault occurs and the effective
terminal voltage of the generator becomes 25% of its value before the fault. When the
fault is cleared, generator is delivering 70% of the original maximum value.
Determine the critical clearing angle.
97. Find the critical clearing angle of the power system shown in fig. for a three phase
fault at the point F. Generator is supplying 1.0 p.u MW power under pre-fault
condition.
98.
99.
100. Factors influencing transient stability
Numerical integration methods of power system stability? Explain any one methods.
v. Point by point method or step by step method
vi. Euler method
vii. Modified Euler method
viii. Runge-Kutta method(R-K method)
104. Part-A
1What is power system stability?
2.How power system stability is classified?
3.What is rotor angle stability?
4.What is steady state stability?
5.What is steady state stability limit?
6.What is transient stability?
7.What is transient stability limit?
8.What is dynamic stability?
9.What is voltage stability?
10.State the causes of voltage instability.
.
11.Write the power angle equation and draw the power angle curve.
Part-B
1.Derive swing equation for a single machine connected to infinite bus system
1. A 400 MVA synchronous machine has H1=4.6 MJ/MVA and a 1200 MVA
machines H2=3.0 MJ/MVA. Two machines operate in parallel in a power plant.
Find out Heq relative to a 100MVA base.
2.
A 100 MVA, two pole, 50Hz generator has moment of inertia 40 x 103
kg-
m2
.what is the energy stored in the rotor at the rated speed? What is the
corresponding angular momentum? Determine the inertia constant h
3. The sending end and receiving end voltages of a three phase transmission line at
a 200MW load are equal at 230KV.The per phase line impedance is j14 ohm.
Calculate the maximum steady state power that can be transmitted over the
line.