This document discusses power system fundamentals and the per-unit system used for power system analysis. It begins with an introduction to power systems and covers topics like synchronous machines, transmission lines, power flow, and stability. It then describes the per-unit system for expressing voltages, currents, powers and impedances on a common base. Examples are provided for calculating per-unit values and transforming between bases. The per-unit equivalent circuits are developed for one-phase circuits and transformers.
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.
Per unit analysis is used to normalize variables in power systems to avoid difficulties in referring impedances across transformers. It involves choosing base values for voltage, power, impedance and current, then expressing all quantities as ratios of their actual to base values. This allows transformer impedances to be treated as single values regardless of which side they are referred to. It also keeps per unit quantities within a narrow range and clearly shows their relative values. The procedure is demonstrated through an example circuit solved first using single phase and then three phase per unit analysis with the same result.
Symmetrical Components
Symmetrical Component Analysis
Synthesis of Unsymmetrical Phases from Their Symmetrical Components
The Symmetrical Components of Unsymmetrical Phasors
Phase Shift of Symmetrical Components in or Transformer Banks
Power in Terms of Symmetrical Components
Representation of power system componentsPrasanna Rao
This document discusses the representation of power system components in circuit models for analysis. It introduces the key components of a power system, including generators, transmission lines, and distribution systems. It then covers circuit models for representing synchronous machines, transformers, transmission lines, and static and dynamic loads. The rest of the document discusses additional modeling techniques like one-line diagrams, impedance diagrams, per-unit systems, and calculating base values for analysis.
The document provides information on power system stability and transient stability studies. It introduces key concepts such as stability, transient stability studies, rotor dynamics, the swing equation, and the power-angle equation. The swing equation describes the acceleration of a generator's rotor and relates the mechanical input power to the electrical output power. The power-angle equation models the relationship between generator output power and the power angle during transient stability studies.
This document describes the method of fault analysis using a Z-bus matrix. It involves the following steps:
1) Drawing the pre-fault positive sequence network and obtaining the initial bus voltages
2) Forming the Z-bus matrix using the bus building algorithm
3) Calculating the fault current using Thevenin's theorem by inserting a voltage source in series with the fault impedance
4) Obtaining the post-fault bus voltages through superposition of the pre-fault voltages and voltage changes
5) Calculating the post-fault line currents based on the voltage differences and line impedances
Two examples applying this method on different systems are provided to illustrate the calculation of fault currents.
- A per-unit system expresses system quantities as fractions of a defined base unit quantity, allowing analysis of large interconnected power systems with various voltage levels and equipment capacities.
- To define a per-unit system requires specifying base values for voltage, current, apparent power, and impedance. Quantities can then be expressed as ratios of their actual to base values.
- Per-unit representation simplifies analysis by removing different voltage levels and reducing the system to simple impedances. It also allows easy comparison of equipment impedances irrespective of actual size.
This document provides an introduction to power system calculations using the per unit method. It discusses calculating fault levels using a four step process involving representing the system as a single line diagram, developing an equivalent circuit in per unit values, applying circuit reduction techniques, and calculating the fault level and current. It also briefly discusses performing load flow calculations to determine power flows and voltages in an interconnected system. The overall document provides instruction on basic power system analysis techniques.
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.
Per unit analysis is used to normalize variables in power systems to avoid difficulties in referring impedances across transformers. It involves choosing base values for voltage, power, impedance and current, then expressing all quantities as ratios of their actual to base values. This allows transformer impedances to be treated as single values regardless of which side they are referred to. It also keeps per unit quantities within a narrow range and clearly shows their relative values. The procedure is demonstrated through an example circuit solved first using single phase and then three phase per unit analysis with the same result.
Symmetrical Components
Symmetrical Component Analysis
Synthesis of Unsymmetrical Phases from Their Symmetrical Components
The Symmetrical Components of Unsymmetrical Phasors
Phase Shift of Symmetrical Components in or Transformer Banks
Power in Terms of Symmetrical Components
Representation of power system componentsPrasanna Rao
This document discusses the representation of power system components in circuit models for analysis. It introduces the key components of a power system, including generators, transmission lines, and distribution systems. It then covers circuit models for representing synchronous machines, transformers, transmission lines, and static and dynamic loads. The rest of the document discusses additional modeling techniques like one-line diagrams, impedance diagrams, per-unit systems, and calculating base values for analysis.
The document provides information on power system stability and transient stability studies. It introduces key concepts such as stability, transient stability studies, rotor dynamics, the swing equation, and the power-angle equation. The swing equation describes the acceleration of a generator's rotor and relates the mechanical input power to the electrical output power. The power-angle equation models the relationship between generator output power and the power angle during transient stability studies.
This document describes the method of fault analysis using a Z-bus matrix. It involves the following steps:
1) Drawing the pre-fault positive sequence network and obtaining the initial bus voltages
2) Forming the Z-bus matrix using the bus building algorithm
3) Calculating the fault current using Thevenin's theorem by inserting a voltage source in series with the fault impedance
4) Obtaining the post-fault bus voltages through superposition of the pre-fault voltages and voltage changes
5) Calculating the post-fault line currents based on the voltage differences and line impedances
Two examples applying this method on different systems are provided to illustrate the calculation of fault currents.
- A per-unit system expresses system quantities as fractions of a defined base unit quantity, allowing analysis of large interconnected power systems with various voltage levels and equipment capacities.
- To define a per-unit system requires specifying base values for voltage, current, apparent power, and impedance. Quantities can then be expressed as ratios of their actual to base values.
- Per-unit representation simplifies analysis by removing different voltage levels and reducing the system to simple impedances. It also allows easy comparison of equipment impedances irrespective of actual size.
This document provides an introduction to power system calculations using the per unit method. It discusses calculating fault levels using a four step process involving representing the system as a single line diagram, developing an equivalent circuit in per unit values, applying circuit reduction techniques, and calculating the fault level and current. It also briefly discusses performing load flow calculations to determine power flows and voltages in an interconnected system. The overall document provides instruction on basic power system analysis techniques.
This document provides an overview of two reaction theory, phasor diagrams, and slip tests for analyzing salient-pole generators. It explains that two reaction theory separates the armature mmf and flux into direct and quadrature axis components. A phasor diagram is also presented. Slip tests are described as a way to measure the direct axis and quadrature axis reactances (Xd and Xq) by taking voltage-to-current ratios at different points in the slip cycle when the armature mmf is aligned with either axis. Cautions for low slip are also noted when conducting these tests. References on electric machinery are listed at the end.
This document discusses per-unit analysis and impedance/reactance diagrams of power systems. It provides examples of calculating the per-unit values of components in a sample power system using given base values, and drawing the corresponding reactance diagram. It also works through another example of determining new per-unit values when changing the base values, and drawing the updated reactance diagram. The document is intended to teach per-phase and per-unit analysis techniques.
This document summarizes control of active and reactive power in a power system. It discusses that active power control is related to frequency control, while reactive power control is related to voltage control. It then discusses how active power and frequency are controlled through load-frequency control (LFC) to maintain a constant frequency for satisfactory power system operation. The document also discusses generator response to load changes and how speed governing works to reduce speed variations through a transfer function relationship between electrical and mechanical torques. It describes how system load responds to frequency deviations and provides an overall system block diagram.
This document discusses power system transients and overvoltages. It defines transients as occurring when a power system changes from one steady state to another, often due to switching actions. Travelling waves on transmission lines and their reflections are discussed. Circuit closing transients and recovery transients due to short circuit removal are examined. Overvoltages can be caused by switching or lightning, and their classification based on frequency content is explained. The document also analyzes symmetrical short circuits on alternators and the calculation of restriking voltage when circuit breakers open under fault conditions.
This presentation was presented to Dr. Chongru Liu in North China Electric Power University,Beijing,China by Mr. Aazim Rasool. This presentation will help to understand the control of HVDC system. Animations are not working like ppt. so I apologize on this.
Objectives: This course will provide a comprehensive overview of power system stability and control problems. This includes the basic concepts, physical aspects of the phenomena, methods of analysis, the integration of MATLAB and SINULINK in the analysis of power system .
Course Content: 1. Power System Stability: Introduction
2. Stability Analysis: Swing Equation
3. Models for Stability Studies
4. Steady State Stability
5. Transient Stability
6. Multimachine Transient Stability
7. Power System Control: Introduction
8. Load Frequency Control
9. Automatic generation Control
10. Reactive Power Control
DC-DC converters are circuits that convert a DC voltage to another DC voltage level. They use switching elements like transistors and power switches to efficiently step up or step down voltage. The buck converter is a common DC-DC converter topology that can step down voltage. It uses a switch, inductor, diode, and capacitor. By periodically opening and closing the switch, the inductor filters the output to produce a lower average voltage. The output voltage of an ideal buck converter is equal to the input voltage multiplied by the duty cycle of the switch. Real converters have non-ideal components that cause additional voltage ripple. Proper component selection and design considerations are needed to minimize ripple.
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.
This document provides a full module specification for a course on per unit quantities and related mathematics. It includes information such as the course name and code, academic year, instructors, credit hours, prerequisites, grading policy, teaching methodology, and method of evaluation. The document also provides several examples of calculating per unit quantities for systems including generators, transformers, and three phase systems. It defines per unit quantities, expresses the relationships between various voltage, current, power, and impedance quantities in per unit systems, and shows calculations for impedances referred to different bases within a system.
This document discusses power system stability and microgrids. It defines power system stability and classifies it into several types including rotor angle stability, voltage stability, and frequency stability. It also discusses microgrids, their interconnection to main grids for availability and economic benefits, and methods for connecting microgrids using switchgear or static switches. In conclusion, it states that power system stability is important for normal operation and can be improved through devices like capacitors and FACTS controllers, and that microgrids satisfy local loads while reducing transmission losses through local renewable generation.
This document discusses active and reactive power flow control using a Static Synchronous Series Compensator (SSSC). The SSSC injects a controllable voltage in series with a transmission line to regulate power flow. It can control both real and reactive power flow to improve transmission efficiency. The SSSC consists of a voltage source converter connected to the line via a transformer. It provides advantages like power factor correction, load balancing, and reducing harmonic distortion.
This chapter discusses per unit representation, which expresses values like current, voltage, impedance, and power as a ratio of an actual value to a reference or base value. This makes the quantities unitless and independent of physical size or ratings. The document provides examples of converting actual values to per unit values and explains the advantages, which include representing apparatus values consistently over a wide range, simplifying computations, and specifying machine impedances in per unit values according to manufacturers.
The document is a presentation on the Liluah 132/33/25 KV substation in West Bengal. It includes acknowledgments, a single line diagram of the substation, and sections covering various equipment found at the substation like electrical busbars, protective relay schemes, lightning protection, isolators, capacitor banks, powerline carrier communication, batteries, earth transformers, traction transformers, station service transformers, and power transformers. Technical specifications are provided for some of the major equipment.
Load flow studies analyze the steady state operation of a power system by determining voltage magnitudes and angles, as well as active and reactive power flows. The key purposes of load flow analysis include designing, planning, and optimizing the operation of a power system. The analysis models each bus in the system where generators, transmission lines, and loads connect. Buses are classified based on which two of four parameters - voltage magnitude, voltage angle, active power, and reactive power - are specified as inputs. Load flow equations are then solved to calculate the unknown parameters.
The document discusses various busbar arrangements used in power systems, including single busbar, single busbar with sectionalizer, main and transfer bus, double busbar, one and a half breaker, and ring/mesh arrangements. It provides details on each arrangement, including pros and cons as well as typical voltage applications. Simulation diagrams are also presented for single and double busbar schemes in Simulink. The key points are that busbar arrangements allow flexibility in distribution and maintenance while considering factors like cost, reliability, and complexity. Higher voltage systems typically use more sophisticated redundant arrangements to minimize outages.
three level diode clamp inverter. that converts any type of DC ( rectified, PV cell, battery etc.) to AC supply. we made by mosfet and ardiuno . in this ppt we present the Simulink model of a three-level inverter and the hardware presentation of the inverter.
Introduction to reactive power control in electrical powerDr.Raja R
Introduction to reactive power control in electrical power
Reactive power in transmission line :
Reactive power control
Reactive power and its importance
Apparent Power
Reactive Power
Apparent Power
Reactive Power Formula
The document discusses reactive power and voltage control in power systems. It defines voltage collapse as occurring when the system is unable to meet the reactive power demand, typically due to heavy loading, faults, or insufficient reactive power generation/compensation. Voltage collapse can be studied by examining the generation, transmission, and consumption of reactive power in the system. The nature of voltage collapse can be transient or long-term depending on the time scale of the disturbance and system components involved. Analytical methods for assessing voltage stability treat the system as a two-bus model and define a critical voltage and reactance value below which the system becomes unstable. Reactive power support measures are needed to maintain voltage stability.
- Power systems use transformers to transfer power between different voltage levels, ranging from 765 kV to 240/120 volts.
- An ideal transformer has no losses and perfect magnetic coupling between primary and secondary coils. Real transformers have losses and leakage flux.
- Transformer performance can be modeled using an equivalent circuit with resistances and inductances to represent winding losses, leakage effects, and core losses. The circuit parameters are determined from open and short circuit tests.
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 provides an overview of two reaction theory, phasor diagrams, and slip tests for analyzing salient-pole generators. It explains that two reaction theory separates the armature mmf and flux into direct and quadrature axis components. A phasor diagram is also presented. Slip tests are described as a way to measure the direct axis and quadrature axis reactances (Xd and Xq) by taking voltage-to-current ratios at different points in the slip cycle when the armature mmf is aligned with either axis. Cautions for low slip are also noted when conducting these tests. References on electric machinery are listed at the end.
This document discusses per-unit analysis and impedance/reactance diagrams of power systems. It provides examples of calculating the per-unit values of components in a sample power system using given base values, and drawing the corresponding reactance diagram. It also works through another example of determining new per-unit values when changing the base values, and drawing the updated reactance diagram. The document is intended to teach per-phase and per-unit analysis techniques.
This document summarizes control of active and reactive power in a power system. It discusses that active power control is related to frequency control, while reactive power control is related to voltage control. It then discusses how active power and frequency are controlled through load-frequency control (LFC) to maintain a constant frequency for satisfactory power system operation. The document also discusses generator response to load changes and how speed governing works to reduce speed variations through a transfer function relationship between electrical and mechanical torques. It describes how system load responds to frequency deviations and provides an overall system block diagram.
This document discusses power system transients and overvoltages. It defines transients as occurring when a power system changes from one steady state to another, often due to switching actions. Travelling waves on transmission lines and their reflections are discussed. Circuit closing transients and recovery transients due to short circuit removal are examined. Overvoltages can be caused by switching or lightning, and their classification based on frequency content is explained. The document also analyzes symmetrical short circuits on alternators and the calculation of restriking voltage when circuit breakers open under fault conditions.
This presentation was presented to Dr. Chongru Liu in North China Electric Power University,Beijing,China by Mr. Aazim Rasool. This presentation will help to understand the control of HVDC system. Animations are not working like ppt. so I apologize on this.
Objectives: This course will provide a comprehensive overview of power system stability and control problems. This includes the basic concepts, physical aspects of the phenomena, methods of analysis, the integration of MATLAB and SINULINK in the analysis of power system .
Course Content: 1. Power System Stability: Introduction
2. Stability Analysis: Swing Equation
3. Models for Stability Studies
4. Steady State Stability
5. Transient Stability
6. Multimachine Transient Stability
7. Power System Control: Introduction
8. Load Frequency Control
9. Automatic generation Control
10. Reactive Power Control
DC-DC converters are circuits that convert a DC voltage to another DC voltage level. They use switching elements like transistors and power switches to efficiently step up or step down voltage. The buck converter is a common DC-DC converter topology that can step down voltage. It uses a switch, inductor, diode, and capacitor. By periodically opening and closing the switch, the inductor filters the output to produce a lower average voltage. The output voltage of an ideal buck converter is equal to the input voltage multiplied by the duty cycle of the switch. Real converters have non-ideal components that cause additional voltage ripple. Proper component selection and design considerations are needed to minimize ripple.
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.
This document provides a full module specification for a course on per unit quantities and related mathematics. It includes information such as the course name and code, academic year, instructors, credit hours, prerequisites, grading policy, teaching methodology, and method of evaluation. The document also provides several examples of calculating per unit quantities for systems including generators, transformers, and three phase systems. It defines per unit quantities, expresses the relationships between various voltage, current, power, and impedance quantities in per unit systems, and shows calculations for impedances referred to different bases within a system.
This document discusses power system stability and microgrids. It defines power system stability and classifies it into several types including rotor angle stability, voltage stability, and frequency stability. It also discusses microgrids, their interconnection to main grids for availability and economic benefits, and methods for connecting microgrids using switchgear or static switches. In conclusion, it states that power system stability is important for normal operation and can be improved through devices like capacitors and FACTS controllers, and that microgrids satisfy local loads while reducing transmission losses through local renewable generation.
This document discusses active and reactive power flow control using a Static Synchronous Series Compensator (SSSC). The SSSC injects a controllable voltage in series with a transmission line to regulate power flow. It can control both real and reactive power flow to improve transmission efficiency. The SSSC consists of a voltage source converter connected to the line via a transformer. It provides advantages like power factor correction, load balancing, and reducing harmonic distortion.
This chapter discusses per unit representation, which expresses values like current, voltage, impedance, and power as a ratio of an actual value to a reference or base value. This makes the quantities unitless and independent of physical size or ratings. The document provides examples of converting actual values to per unit values and explains the advantages, which include representing apparatus values consistently over a wide range, simplifying computations, and specifying machine impedances in per unit values according to manufacturers.
The document is a presentation on the Liluah 132/33/25 KV substation in West Bengal. It includes acknowledgments, a single line diagram of the substation, and sections covering various equipment found at the substation like electrical busbars, protective relay schemes, lightning protection, isolators, capacitor banks, powerline carrier communication, batteries, earth transformers, traction transformers, station service transformers, and power transformers. Technical specifications are provided for some of the major equipment.
Load flow studies analyze the steady state operation of a power system by determining voltage magnitudes and angles, as well as active and reactive power flows. The key purposes of load flow analysis include designing, planning, and optimizing the operation of a power system. The analysis models each bus in the system where generators, transmission lines, and loads connect. Buses are classified based on which two of four parameters - voltage magnitude, voltage angle, active power, and reactive power - are specified as inputs. Load flow equations are then solved to calculate the unknown parameters.
The document discusses various busbar arrangements used in power systems, including single busbar, single busbar with sectionalizer, main and transfer bus, double busbar, one and a half breaker, and ring/mesh arrangements. It provides details on each arrangement, including pros and cons as well as typical voltage applications. Simulation diagrams are also presented for single and double busbar schemes in Simulink. The key points are that busbar arrangements allow flexibility in distribution and maintenance while considering factors like cost, reliability, and complexity. Higher voltage systems typically use more sophisticated redundant arrangements to minimize outages.
three level diode clamp inverter. that converts any type of DC ( rectified, PV cell, battery etc.) to AC supply. we made by mosfet and ardiuno . in this ppt we present the Simulink model of a three-level inverter and the hardware presentation of the inverter.
Introduction to reactive power control in electrical powerDr.Raja R
Introduction to reactive power control in electrical power
Reactive power in transmission line :
Reactive power control
Reactive power and its importance
Apparent Power
Reactive Power
Apparent Power
Reactive Power Formula
The document discusses reactive power and voltage control in power systems. It defines voltage collapse as occurring when the system is unable to meet the reactive power demand, typically due to heavy loading, faults, or insufficient reactive power generation/compensation. Voltage collapse can be studied by examining the generation, transmission, and consumption of reactive power in the system. The nature of voltage collapse can be transient or long-term depending on the time scale of the disturbance and system components involved. Analytical methods for assessing voltage stability treat the system as a two-bus model and define a critical voltage and reactance value below which the system becomes unstable. Reactive power support measures are needed to maintain voltage stability.
- Power systems use transformers to transfer power between different voltage levels, ranging from 765 kV to 240/120 volts.
- An ideal transformer has no losses and perfect magnetic coupling between primary and secondary coils. Real transformers have losses and leakage flux.
- Transformer performance can be modeled using an equivalent circuit with resistances and inductances to represent winding losses, leakage effects, and core losses. The circuit parameters are determined from open and short circuit tests.
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 provides an overview of transformers and per unit analysis in power systems. Key points include:
1) Transformers are used to transfer power between different voltage levels in power systems. An ideal transformer model and a more accurate model accounting for losses and leakage flux are described.
2) Per unit analysis is introduced as a method to normalize variables across different voltage bases. All values are expressed relative to selected system base values.
3) Examples of per unit analysis are provided for both single phase and three phase systems, showing how quantities can be converted between per unit and actual values.
The document discusses the per-unit system used in power systems analysis. It begins by explaining that per-unit values allow comparison of different sized elements by expressing their values relative to a common base. It then provides the equations to convert actual values to per-unit values using a defined base power and voltage. Several examples are given of applying per-unit analysis to a sample power system network diagram by selecting appropriate voltage and power bases and calculating the per-unit impedances.
This document provides a summary of key topics covered in Lecture 10 of ECE 476 Power System Analysis including:
1) Per unit calculations and the procedure for converting values to per unit.
2) Examples of per unit calculations for single phase and three phase systems.
3) Different transformer connections including Y-Y, D-D, D-Y, and Y-D and their per unit models.
4) Announcements about homework assignments, exams, and scholarships.
BEF 23803 - Lecture 14 - Per Unit Analysis of Three Phase System.pptLiewChiaPing
This document provides an overview of per-unit analysis of a three-phase power system. It explains how to calculate per-unit values for system components using a common base value. An example is provided to demonstrate calculating per-unit impedances for a generator, transformers, transmission line, and load using a base MVA of 100 MVA and base voltages of 66kV, 132kV and 275kV. The transmission line current is then calculated from the per-unit impedance diagram.
This document provides instructions for experiments on power semiconductor switches and switch-mode power converters to be carried out by students. The experiments involve testing an SCR using a multimeter, studying the turn-on and turn-off states of an SCR, and effects of gate current. Students will also study the switching parameters of a BJT and build a buck converter circuit. Performance in the experiments, teamwork, and learning attitude will contribute towards marks. Students are advised to read the instructions fully before conducting the experiments.
This document contains 54 questions related to electromechanical energy conversion, DC machines, transformers, and parallel operation of transformers. The questions cover topics such as magnetic field energy, armature reaction, commutation, DC generator characteristics, transformer tests, efficiency calculations, and load sharing between parallel transformers.
This document describes a new mode of operation for pentode or tetrode power tubes in audio power amplifiers. It involves using back-to-back connected diodes to alternately connect the screen grids of the power tubes to different taps on the output transformer plate winding. This causes the power tubes to operate under different characteristics depending on the polarity of the grid signal voltage. This allows the power tubes to avoid operating in cutoff regions, preventing notch distortion while maintaining high efficiency. The design provides advantages over conventional amplifier designs like higher power output with lower distortion and components costs.
This document discusses flyback converter design considerations for multi-kilowatt power conversion applications. It outlines flyback converter advantages and disadvantages, and solutions to overcome the disadvantages. Specifically, it focuses on single-stage power factor correction (PFC) applications using a flyback topology. The document discusses adapting the flyback converter for PFC, selecting an appropriate PFC control IC, modifying the control IC for high power applications, and transformer design considerations. It provides block diagrams and partial schematics as examples.
The document describes tests conducted on a single-phase transformer to determine its efficiency and regulation. An open circuit test was conducted to measure no-load losses. A short circuit test was used to determine copper losses and develop an equivalent circuit model. Efficiency was calculated at various load levels and power factors based on losses from the two tests. Regulation was also calculated using the short circuit test results. Plots of efficiency versus load and tables of efficiency and regulation values are presented.
Design, Simulation and Implementation of Flyback based, True Single Stage, Is...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Engineering Research and DevelopmentIJERD Editor
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Lab 7 diode with operational amplifiers by kehali b. haileselassie and koukehali Haileselassie
This document describes an electronics experiment involving diodes and operational amplifiers. The experiment consisted of two parts: 1) using diodes in a circuit to multiply DC voltage output, and 2) using a diode and op-amp circuit as a logarithmic converter. Key results showed the DC output voltage increasing as the load resistance decreased in part 1. Part 2 results demonstrated the output voltage varying logarithmically with the input voltage as expected based on diode characteristics. The conclusion discusses applications of diode multipliers and logarithmic converters in electrical and electronics circuits.
The document discusses various concepts related to electric circuits including:
- Ideal and non-ideal voltage and current sources and their characteristics
- Converting between voltage and current sources using Ohm's law
- Thevenin's and Norton's theorems for simplifying two-terminal circuits
- Superposition theorem for analyzing circuits with multiple sources
- Maximum power transfer occurring when load resistance equals source resistance
International Journal of Engineering Research and DevelopmentIJERD Editor
This document summarizes a research paper that proposes a single-phase multilevel inverter topology fed by a photovoltaic panel. The inverter uses a multicarrier phase disposition sinusoidal pulse width modulation scheme to generate gate signals for power switches. It can produce 3, 5, 7, or 9 output voltage levels by controlling the modulation index. The proposed inverter configuration was tested supplying power to an R-L load. Simulation results in MATLAB/Simulink analyzed the performance of the topology and THD values for output current and voltage.
1) The document discusses the history and operation of transformers, including their use in power distribution systems to step up voltage for transmission and step down voltage for distribution to loads.
2) A transformer consists of coils wrapped around a common core and works by electromagnetic induction to convert AC voltages from one level to another while maintaining the same frequency.
3) An ideal transformer is analyzed, and equations are provided showing how it transforms voltages and currents while maintaining power, reactive power, and power factor between windings. Impedance transformation is also discussed.
Stability with analysis and psa and load flow.pptZahid Yousaf
The document summarizes a lecture on Newton-Raphson power flow analysis. It provides a two bus example to demonstrate the Newton-Raphson method. The example calculates the voltage magnitude and angle at the second bus iteratively until convergence is reached. There are two possible solutions for this system, a high voltage and low voltage solution, depending on the starting guess values. The document also briefly describes a three bus PV case example.
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
Low power architecture of logic gates using adiabatic techniquesnooriasukmaningtyas
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Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
13. 1. Basic Concepts
2. Synchronous Machines and
Transformer Modelling
3. Transmission Line Modelling
4. Power Flow Analysis
5. Fault Analysis
6. Power System Stability
7. Economic Operation of Power
System,
27. 27
Per-Unit System
In the per-unit system, the voltages, currents, powers,
impedances, and other electrical quantities are expressed on a per-
unit basis by the equation:
Quantity per unit =
Actual value
Base value of quantity
It is customary to select two base quantities to define a given per-
unit system. The ones usually selected are voltage and power.
29. 29
Per-Unit System
And the per-unit system is:
b
actual
u
p
V
V
V
.
.
b
actual
u
p
I
I
I
.
.
b
actual
u
p
S
S
S
.
.
b
actual
u
p
Z
Z
Z
.
.
%
100
% .
.
u
p
Z
Z
Percent of base Z
rated
b V
V
rated
b S
S
b
b
b
V
S
I
b
b
b
b
b
S
V
I
V
Z
2
30. 30
Example 1
An electrical lamp is rated 120 volts, 500 watts. Compute the per-
unit and percent impedance of the lamp. Give the p.u. equivalent
circuit.
Solution:
(1) Compute lamp resistance
(2) Select base quantities
(3) Compute base impedance
(4) Find the per-unit impedance
120 volts
500 watts
31. 31
Example 1
An electrical lamp is rated 120 volts, 500 watts. Compute the per-
unit and percent impedance of the lamp. Give the p.u. equivalent
circuit.
Solution:
(1) Compute lamp resistance
power factor = 1.0
8
.
28
500
)
120
( 2
2
2
P
V
R
R
V
P
0
8
.
28
Z
120 volts
500 watts
32. 32
Example 1
(2) Select base quantities
(3) Compute base impedance
(4) The per-unit impedance is:
VA
Sb 500
V
Vb 120
8
.
28
500
)
120
( 2
2
b
b
b
S
V
Z
.
.
0
1
8
.
28
0
8
.
28
.
. u
p
Z
Z
Z
b
u
p
33. 33
Example 1
(5) Percent impedance:
(6) Per-unit equivalent circuit:
%
100
%
Z
.
.
0
1 u
p
Z
.
.
0
1 u
p
VS
34. 34
Example 2
An electrical lamp is rated 120 volts, 500 watts. If the voltage
applied across the lamp is twice the rated value, compute the
current that flows through the lamp. Use the per-unit method.
Solution:
(1) Compute lamp resistance
(2) Select base quantities
(3) Compute base impedance
(4) Find the per-unit impedance
120 V
500 W
2 X 120 V
240 V
35. 35
Example 2
An electrical lamp is rated 120 volts, 500 watts. If the voltage
applied across the lamp is twice the rated value, compute the
current that flows through the lamp. Use the per-unit method.
Solution:
V
Vb 120
.
.
0
2
120
240
.
. u
p
V
V
V
b
u
p
.
.
0
1
.
. u
p
Z u
p
36. 36
Example 2
The per-unit equivalent circuit is as follows:
.
.
0
1 u
p
Z
.
.
0
2 u
p
VS
.
.
0
2
0
1
0
2
.
.
.
.
.
. u
p
Z
V
I
u
p
u
p
u
p
A
V
S
I
b
b
b 167
.
4
120
500
A
I
I
I b
u
p
actual 0
334
.
8
167
.
4
0
2
.
.
37. 37
Per-unit System for 1- Circuits
One-phase circuits
LV
bLV V
V
I
V
S
Sb
1
where
neutral
to
line
V
V
current
line
I
I
HV
bHV V
V
bLV
b
bLV
V
S
I
bHV
b
bHV
V
S
I
Transformer
38. 38
Per-unit System for 1- Circuits
b
bLV
bLV
bLV
bLV
S
V
I
V
Z
2
)
(
b
bHV
bHV
bHV
bHV
S
V
I
V
Z
2
)
(
*
pu
pu
b
pu I
V
S
S
S
cos
pu
pu
b
pu I
V
S
P
P
sin
pu
pu
b
pu I
V
S
Q
Q
39. 39
Transformation Between Bases
Selection 1
A
b V
V
1
A
b S
S
1
Then
1
1
b
L
pu
Z
Z
Z
1
2
1
1
b
b
b
S
V
Z
Selection 2
B
b V
V
2
B
b S
S
2
Then
2
2
b
L
pu
Z
Z
Z
2
2
2
2
b
b
b
S
V
Z
41. 41
Transformation Between Bases
Generally per-unit values given to another base can be converted
to new base by by the equations:
2
1
1
_
_
_
2
_
_
_ )
,
,
(
)
,
,
(
base
base
base
on
pu
base
on
pu
S
S
S
Q
P
S
Q
P
2
1
1
_
_
_
2
_
_
_
base
base
base
on
pu
base
on
pu
V
V
V
V
1
2
2
2
2
1
1
_
_
_
2
_
_
_
)
(
)
(
)
,
,
(
)
,
,
(
base
base
base
base
base
on
pu
base
on
pu
S
V
S
V
Z
X
R
Z
X
R
When performing calculations in a power system, every per-unit value
must be converted to the same base.
42. 42
Per-unit System for 1- Transformer
Consider the equivalent circuit of transformer referred to LV side and
HV side shown below:
LV
V HV
V LV
V HV
V
S
S jX
R
1
N 2
N
2
2
a
X
j
a
R S
S
(1) Referred to LV side (2) Referred to HV side
Define 1
2
1
N
N
V
V
a
HV
LV
S
43. 43
Per-unit System for 1- Transformer
Choose:
rated
LV
b V
V ,
1
rated
b S
S
Compute:
1
1
2
1
b
b
LV
HV
b V
a
V
V
V
V
b
b
b
S
V
Z
2
1
1
b
b
b
S
V
Z
2
2
2
2
2
1
2
1
2
2
2
1
2
1
)
1
(
a
V
a
V
V
V
Z
Z
b
b
b
b
b
b
Normally choose rated
values as base values
44. 44
Per-unit System for 1- Transformer
Per-unit impedances are:
1
1
.
.
b
S
S
u
p
Z
jX
R
Z
1
2
1
2
2
2
2
2
2
.
.
b
S
S
b
S
S
b
S
S
u
p
Z
jX
R
a
Z
a
jX
a
R
Z
a
jX
a
R
Z
So:
2
.
.
1
.
. u
p
u
p Z
Z
Per-unit equivalent
circuits of transformer
referred to LV side and
HV side are identical !!
45. 45
Per-unit Eq. Circuit for 1- Transformer
LV
V HV
V
S
S jX
R
1
N 2
N
Fig 1. Eq Ckt referred to LV side
1
2
1
N
N
V
V
a
HV
LV
S
1
b
Z
1
b
V 2
b
V
Fig 2. Per-unit Eq Ckt referred to LV side Fig 3.
pu
S
Z ,
1
:
1
1
b
V 2
b
V
pu
S
Z ,
1
b
V 2
b
V
b
S
46. 46
Per-unit Eq. Circuit for 1- Transformer
LV
V HV
V
1
N 2
N
Fig 4. Eq Ckt referred to HV side
1
2
1
N
N
V
V
a
HV
LV
S
2
b
Z
2
b
V
Fig 5. Per-unit Eq Ckt referred to HV side Fig 6.
pu
S
Z ,
1
:
1
1
b
V 2
b
V
pu
S
Z ,
1
b
V 2
b
V
1
b
V
2
2
a
X
j
a
R S
S
b
S
47. 47
Voltage Regulation
%
100
load
full
load
full
load
no
V
V
V
VR
Voltage regulation is defined as:
%
100
,
,
,
load
full
pu
load
full
pu
load
no
pu
V
V
V
VR
In per-unit system:
Vfull-load: Desired load voltage at full load. It may be equal
to, above, or below rated voltage
Vno-load: The no load voltage when the primary voltage is
the desired voltage in order the secondary voltage
be at its desired value at full load
48. 48
Voltage Regulation Example
A single-phase transformer rated 200-kVA, 200/400-V, and 10% short circuit
reactance. Compute the VR when the transformer is fully loaded at unity PF
and rated voltage 400-V.
Solution:
Fig 7. Per-unit equivalent circuit
P
V S
V
1
.
0
j
load
S
V
Vb 400
2
kVA
Sb 200
pu
S pu
load 0
1
,
pu
j
X pu
S 1
.
0
,
S
X
49. 49
Voltage Regulation Example
Rated voltage:
pu
V pu
S 0
0
.
1
,
pu
j
j
X
I
V
V
o
pu
S
pu
pu
S
pu
P
7
.
5
001
.
1
1
.
0
1
1
.
0
0
0
.
1
0
0
.
1
,
,
,
pu
V
S
I
pu
S
pu
load
pu
load 0
0
.
1
0
0
.
1
0
0
.
1
*
*
,
,
,
50. 50
Voltage Regulation Example
pu
V
V o
pu
P
load
no
pu 7
.
5
001
.
1
,
,
pu
V
V pu
S
load
full
pu 0
0
.
1
,
,
Secondary side:
Voltage regulation:
%
1
.
0
%
100
0
.
1
0
.
1
001
.
1
%
100
,
,
,
load
full
pu
load
full
pu
load
no
pu
V
V
V
VR
51. 51
Problem 1
Select Vbase in generator circuit and Sb=100MVA,
compute p.u. equivalent circuit.
G
100
j
20 kV 22kV/220kV
80MVA
14%
220kV/20kV
50MVA
10%
50MVA
0.8 PF
lagging
52. 52
Per-unit System for 3- Circuits
Three-phase circuits
LV
L
bLV V
V ,
I
V
S
S
Sb 3
3 1
3
where
3
/
)
(line
L
neutral
to
line V
V
V
L
current
line I
I
I
HV
L
bHV V
V ,
L
L
b I
V
S 3
bHV
bHV
bLV
bLV
b I
V
I
V
S 3
3
53. 53
Per-unit System for 3- Circuits
b
bLV
b
bLV
bLV
LV
LV
bLV
S
V
S
V
V
I
V
Z
2
)
(
3
3
b
bHV
bHV
S
V
Z
2
)
(
*
*
3
3
3
pu
pu
b
b
L
L
b
pu I
V
I
V
I
V
S
S
S
bLV
b
bLV
V
S
I
3
bHV
b
bHV
V
S
I
3
54. 54
Per-unit System for 3- Transformer
Three 25-kVA, 34500/277-V transformers connected in -Y. Short-
circuit test on high voltage side:
Determine the per-unit equivalent circuit of the transformer.
V
V SC
Line 2010
,
A
I SC
Line 26
.
1
,
W
P SC 912
,
3
55. 55
Per-unit System for 3- Transformer
(a) Using Y-equivalent
3
34500
277
S
S jX
R
VA
Sb 25000
3
2010
SC
V
26
.
1
SC
I
00
.
921
26
.
1
47
.
1160
SC
Z
V
VSC 47
.
1160
3
2010
56. 56
Per-unit System for 3- Transformer
So
86
.
900
48
.
191
921 2
2
2
2
S
SC
S R
Z
X
W
P 304
3
912
48
.
191
26
.
1
304
2
2
SC
S
I
P
R
86
.
900
48
.
191 j
ZSC
VA
Sb 25000
V
V HV
b 58
.
19918
3
34500
,
99
.
15869
25000
58
.
19918 2
,HV
b
Z
pu
j
j
Z Y
pu
SC 0568
.
0
012
.
0
99
.
15869
86
.
900
48
.
191
,
,
57. 57
Per-unit System for 3- Transformer
(b) Using -equivalent
34500 277
,
SC
Z
VA
Sb 25000
2010
SC
V
3
26
.
1
SC
I
79
.
2764
727
.
0
2010
,
SC
Z
V
VSC 2010
A
ISC 727
.
0
3
26
.
1
58. 58
Per-unit System for 3- Transformer
So
30
.
2704
18
.
575
79
.
2764 2
2
2
,
2
,
, S
SC
S R
Z
X
W
P 304
3
912
18
.
575
727
.
0
304
2
2
,
SC
S
I
P
R
86
.
900
48
.
191 j
ZSC
VA
Sb 25000
V
V HV
b 34500
,
47610
25000
34500 2
,HV
b
Z
pu
j
j
Z pu
SC 0568
.
0
012
.
0
47610
30
.
1704
18
.
575
,
,
59. 59
In power systems there are so many different elements such as Motors, Generators and Transformers with very
different sizes and nominal values.
To be able to compare the performances of a big and a small element, per unit system is used
Physical Components in the system are represented by a mathematical model.
Mathematical models of components are connected in exactly the same way as the physical components to
obtain the system representation.
Various physical components have different ratings or basis.
It is convenient to obtain the representation with respect to a common basis.
60. 60
The numerical per unit value of any quantity is its ratio to the chosen base quantity of the same dimensions.
Thus a per unit quantity is a normalized quantity with respect to a chosen base value.
Percent is the per unit quantity multiplied by a 100
In the per-unit system of representation, device parameters tend to fall in a relatively fixed range, making
erroneous values prominent.
Ideal transformers are eliminated as circuit elements. This results in a large saving in component representation
and reduces computational burden.
The voltage magnitude throughout a given power system is relatively close to unity in the per-unit system for a
power system operating normally. This characteristic provides a useful check on the calculations.
61. 61
The numerical per unit value of any quantity is its ratio to the chosen base quantity of the same dimensions.
In power system calculations the nominal voltage of lines and equipment is almost always known, so the voltage
is a convenient base value to choose.
The apparent power (volt-ampere) is usually chosen as a second base. In equipment this quantity is usually
known and makes a convenient base.
The choice of these two base quantities will automatically fix the base of current, impedance, and admittance.
In a system study, the volt-ampere base can be selected to be any convenient value such as 100 MVA, 200 MVA,
etc
The same volt-ampere base is used in all parts of the system. One base voltage in a certain part of the system is
selected arbitrarily. All other base voltages must be related to the arbitrarily selected one by the turns ratio of
the connecting transformers.
62. 62
Power system quantities such as voltage, current and impedance are often expressed in per unit or percent of
specified values.
Per unit quantities are calculated as:
Quantity per unit =
Actual value
Base value of quantity
64. 64
Per-Unit System
And the per-unit system is:
b
actual
u
p
V
V
V
.
.
b
actual
u
p
I
I
I
.
.
b
actual
u
p
S
S
S
.
.
b
actual
u
p
Z
Z
Z
.
.
%
100
% .
.
u
p
Z
Z
Percent of base Z
65. 65
Per-unit System for 1- Circuits
One-phase circuits
LV
bLV V
V
I
V
S
Sb
1
where
neutral
to
line
V
V
current
line
I
I
HV
bHV V
V
bLV
b
bLV
V
S
I
bHV
b
bHV
V
S
I
66. 66
Per-unit System for 1- Circuits
b
bLV
bLV
bLV
bLV
S
V
I
V
Z
2
)
(
b
bHV
bHV
bHV
bHV
S
V
I
V
Z
2
)
(
*
pu
pu
b
pu I
V
S
S
S
cos
pu
pu
b
pu I
V
S
P
P
sin
pu
pu
b
pu I
V
S
Q
Q
67. 67
Transformation Between Bases
Selection 1
A
b V
V
1
A
b S
S
1
Then
1
1
b
L
pu
Z
Z
Z
1
2
1
1
b
b
b
S
V
Z
Selection 2
B
b V
V
2
B
b S
S
2
Then
2
2
b
L
pu
Z
Z
Z
2
2
2
2
b
b
b
S
V
Z
69. 69
Transformation Between Bases
Generally per-unit values given to another base can be converted
to new base by by the equations:
2
1
1
_
_
_
2
_
_
_ )
,
,
(
)
,
,
(
base
base
base
on
pu
base
on
pu
S
S
S
Q
P
S
Q
P
2
1
1
_
_
_
2
_
_
_
base
base
base
on
pu
base
on
pu
V
V
V
V
1
2
2
2
2
1
1
_
_
_
2
_
_
_
)
(
)
(
)
,
,
(
)
,
,
(
base
base
base
base
base
on
pu
base
on
pu
S
V
S
V
Z
X
R
Z
X
R
When performing calculations in a power system, every per-unit value
must be converted to the same base.
74. 74
RP + JXP
RC JXM
VP VS
NS
NP
+
+
-
-
RS + JXS
Schematic of a Real Transformer
75. 75
s
s
p
s
N
V
N
V
'
s
s
p
s I
N
N
I
'
s
p
N
N
a
2
2
)
(
s
p
N
N
a s
s
p
s V
N
N
V )
(
'
S
S aV
V
'
S
P
s
S I
N
N
I
'
a
I
I
s
s
'
Referring to primary side
JXM
RC
RP + JXP a2RS + Ja2XS
V’s
+
-
+
-
VP
VS
+
-
NS
NP
Is’ Is
76. 76
Referring to secondary side
p
p aI
I
'
p
p
s
p V
N
N
V
'
s
p
p
p
N
V
N
V '
p
s
p
p I
N
N
I '
a
V
V p
p
'
IP
VP
+
-
I’P RP/a2 + JXP/a2 RS + JXS
+
-
VS
JXM/a2
RC/a2
IS
NS
NP
VP’
77. 77
Approximate Equivalent circuit
Place the magnetizing branch at the primary side
VP VS
+ +
- -
JXM
RC
IE
RP+JXP RS+JXS
JXM
RC
VP
-
+
+
VS
-
NP NS
NP NS
REQP=RP+a2RS
XEQP=XP+a2XS
REQ+JXEQ
Original
Circuit
Looking
From
primary
78. 78
a
V
V
p
p
' s
p
EQS R
a
R
R
2
p
p aI
I
' s
P
EQS X
a
X
X
2
Place the magnetizing branch at the primary side
VP VS
+ +
- -
JXM/a2
RC/a2
REQ+JXEQ
V’P
+
-
IE
NP NS
I’P
IP
Looking
From
Secondary
84. 84
Per-unit System for 1- Transformer
Consider the equivalent circuit of transformer referred to LV side and
HV side shown below:
LV
V HV
V LV
V HV
V
S
S jX
R
1
N 2
N
2
2
a
X
j
a
R S
S
(1) Referred to LV side (2) Referred to HV side
Define 1
2
1
N
N
V
V
a
HV
LV
S
85. 85
Per-unit System for 1- Transformer
Choose:
rated
LV
b V
V ,
1
rated
b S
S
Compute:
1
1
2
1
b
b
LV
HV
b V
a
V
V
V
V
b
b
b
S
V
Z
2
1
1
b
b
b
S
V
Z
2
2
2
2
2
1
2
1
2
2
2
1
2
1
)
1
(
a
V
a
V
V
V
Z
Z
b
b
b
b
b
b
Normally choose rated
values as base values
86. 86
Per-unit System for 1- Transformer
Per-unit impedances are:
1
1
.
.
b
S
S
u
p
Z
jX
R
Z
1
2
1
2
2
2
2
2
2
.
.
b
S
S
b
S
S
b
S
S
u
p
Z
jX
R
a
Z
a
jX
a
R
Z
a
jX
a
R
Z
So:
2
.
.
1
.
. u
p
u
p Z
Z
Per-unit equivalent
circuits of transformer
referred to LV side and
HV side are identical !!
87. 87
Per-unit Eq. Circuit for 1- Transformer
LV
V HV
V
S
S jX
R
1
N 2
N
Fig 1. Eq Ckt referred to LV side
1
2
1
N
N
V
V
a
HV
LV
S
1
b
Z
1
b
V 2
b
V
Fig 2. Per-unit Eq Ckt referred to LV side Fig 3.
pu
S
Z ,
1
:
1
1
b
V 2
b
V
pu
S
Z ,
1
b
V 2
b
V
b
S
88. 88
Per-unit Eq. Circuit for 1- Transformer
LV
V HV
V
1
N 2
N
Fig 4. Eq Ckt referred to HV side
1
2
1
N
N
V
V
a
HV
LV
S
2
b
Z
2
b
V
Fig 5. Per-unit Eq Ckt referred to HV side Fig 6.
pu
S
Z ,
1
:
1
1
b
V 2
b
V
pu
S
Z ,
1
b
V 2
b
V
1
b
V
2
2
a
X
j
a
R S
S
b
S
89. 89
Voltage Regulation
%
100
load
full
load
full
load
no
V
V
V
VR
Voltage regulation is defined as:
%
100
,
,
,
load
full
pu
load
full
pu
load
no
pu
V
V
V
VR
In per-unit system:
Vfull-load: Desired load voltage at full load. It may be equal
to, above, or below rated voltage
Vno-load: The no load voltage when the primary voltage is
the desired voltage in order the secondary voltage
be at its desired value at full load
90. 90
Voltage Regulation
%
100
load
full
load
full
load
no
V
V
V
VR
Voltage regulation is defined as:
%
100
,
,
,
load
full
pu
load
full
pu
load
no
pu
V
V
V
VR
In per-unit system:
Vfull-load: Desired load voltage at full load. It may be equal
to, above, or below rated voltage
Vno-load: The no load voltage when the primary voltage is
the desired voltage in order the secondary voltage
be at its desired value at full load
91. 91
Voltage Regulation Example
A single-phase transformer rated 200-kVA, 200/400-V, and
10% short circuit reactance. Compute the VR when the
transformer is fully loaded at unity PF and rated voltage
400-V.
Solution:
Fig 7. Per-unit equivalent circuit
P
V S
V
1
.
0
j
load
S
V
Vb 400
2
kVA
Sb 200
pu
S pu
load 0
1
,
pu
j
X pu
S 1
.
0
,
S
X
92. 92
Voltage Regulation Example
Rated voltage:
pu
V pu
S 0
0
.
1
,
pu
j
j
X
I
V
V
o
pu
S
pu
pu
S
pu
P
7
.
5
001
.
1
1
.
0
1
1
.
0
0
0
.
1
0
0
.
1
,
,
,
pu
V
S
I
pu
S
pu
load
pu
load 0
0
.
1
0
0
.
1
0
0
.
1
*
*
,
,
,
93. 93
Voltage Regulation Example
pu
V
V o
pu
P
load
no
pu 7
.
5
001
.
1
,
,
pu
V
V pu
S
load
full
pu 0
0
.
1
,
,
Secondary side:
Voltage regulation:
%
1
.
0
%
100
0
.
1
0
.
1
001
.
1
%
100
,
,
,
load
full
pu
load
full
pu
load
no
pu
V
V
V
VR
94. 94
Select Vbase in generator circuit and Sb=100MVA,
compute p.u. equivalent circuit.
Problem 1
G
100
j
20 kV 22kV/220kV
80MVA
14%
220kV/20kV
50MVA
10%
50MVA
0.8 PF
lagging
95. 95
Per-unit System for 3- Circuits
Three-phase circuits
LV
L
bLV V
V ,
I
V
S
S
Sb 3
3 1
3
where
3
/
)
(line
L
neutral
to
line V
V
V
L
current
line I
I
I
HV
L
bHV V
V ,
L
L
b I
V
S 3
bHV
bHV
bLV
bLV
b I
V
I
V
S 3
3
96. 96
Per-unit System for 3- Circuits
b
bLV
b
bLV
bLV
LV
LV
bLV
S
V
S
V
V
I
V
Z
2
)
(
3
3
b
bHV
bHV
S
V
Z
2
)
(
*
*
3
3
3
pu
pu
b
b
L
L
b
pu I
V
I
V
I
V
S
S
S
bLV
b
bLV
V
S
I
3
bHV
b
bHV
V
S
I
3
97. 97
Three 25-kVA, 34500/277-V transformers
connected in -Y. Short-circuit test on high voltage
side:
Determine the per-unit equivalent circuit of the
transformer.
Per-unit System for 3- Transformer
V
V SC
Line 2010
,
A
I SC
Line 26
.
1
,
W
P SC 912
,
3
98. 98
(a) Using Y-equivalent
Per-unit System for 3- Transformer
3
34500
277
S
S jX
R
VA
Sb 25000
3
2010
SC
V
26
.
1
SC
I
00
.
921
26
.
1
47
.
1160
SC
Z
V
VSC 47
.
1160
3
2010
99. 99
So
Per-unit System for 3- Transformer
86
.
900
48
.
191
921 2
2
2
2
S
SC
S R
Z
X
W
P 304
3
912
48
.
191
26
.
1
304
2
2
SC
S
I
P
R
86
.
900
48
.
191 j
ZSC
VA
Sb 25000
V
V HV
b 58
.
19918
3
34500
,
99
.
15869
25000
58
.
19918 2
,HV
b
Z
pu
j
j
Z Y
pu
SC 0568
.
0
012
.
0
99
.
15869
86
.
900
48
.
191
,
,
100. 100
(b) Using -equivalent
Per-unit System for 3- Transformer
34500 277
,
SC
Z
VA
Sb 25000
2010
SC
V
3
26
.
1
SC
I
79
.
2764
727
.
0
2010
,
SC
Z
V
VSC 2010
A
ISC 727
.
0
3
26
.
1
101. 101
So
Per-unit System for 3- Transformer
30
.
2704
18
.
575
79
.
2764 2
2
2
,
2
,
, S
SC
S R
Z
X
W
P 304
3
912
18
.
575
727
.
0
304
2
2
,
SC
S
I
P
R
86
.
900
48
.
191 j
ZSC
VA
Sb 25000
V
V HV
b 34500
,
47610
25000
34500 2
,HV
b
Z
pu
j
j
Z pu
SC 0568
.
0
012
.
0
47610
30
.
1704
18
.
575
,
,
102. 102
Related Materials in Textbook
(1) Section 2.6 and 2.7, page 83~90, Chapman
book
(2) Section 2.10, page 113~116, Chapman book
103. 103
•More meaningful when comparing different voltage levels
•The per unit equivalent impedance of the transformer remains the same when referred to either the primary or the
secondary side
•The per unit impedance of a transformer in a three-phase system is the same, regardless the winding connection
•The per unit method is independent of voltage changes and phase shifts through transformers
•Manufacturers usually specify the impedance of the equipment in per unit or percent on the base of its nameplate
ratings
•The per unit impedance values of various ratings of equipment lie in a narrow range
Transformer equivalent circuit can be simplified by properly specifying base quantities.
Give a clear idea of relative magnitudes of various quantities such as voltage, current, power and impedance.
Avoid possibility of making serious calculation error when referring quantities from one side of transformer to
the other
Per-unit impedances of electrical equipment of similar type usually lie within a narrow numerical range when the
equipment ratings are used as base values.
Manufacturers usually specify the impedances of machines and transformers in per-unit or percent in
nameplate rating
The circuit laws are valid in per unit systems, and the power and voltage equation are simplified since the factor
√3 and 3 are eliminated in the per-unit systems.
Ideal for the computerized analysis and simulation of complex power system problems.