1) This lecture discusses power flow analysis and modeling voltage dependent loads. It introduces the Newton-Raphson power flow method and approximations like the decoupled power flow and fast decoupled power flow that reduce computation time.
2) The professor announces upcoming homework and exam details. Voltage dependent loads are modeled using their real and reactive power as functions of voltage magnitude and angle.
3) Examples are provided to demonstrate modeling a constant impedance load and solving a two bus system using the dishonest Newton-Raphson method where the Jacobian is only calculated on the first iteration.
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.
This document discusses the Newton-Raphson power flow method. It begins with announcements about homework assignments. It then provides an overview of the dishonest or shamanskii Newton-Raphson method, which calculates the Jacobian less frequently than the honest method to reduce computation time. An example is shown comparing the two methods. The document also discusses decoupled and fast decoupled power flow methods, which make additional approximations to further reduce computation time. It concludes with a brief discussion of power system control and indirect methods of controlling transmission line flows.
This document discusses power flow analysis in power systems. It begins with announcements about upcoming homework assignments and exams. It then provides background on transmission system planning and an example in ERCOT. The document covers the development of power flow equations using complex power definitions and the Newton-Raphson method for solving the nonlinear power flow equations. It includes the derivation of the power flow Jacobian matrix and provides a detailed two bus power flow example to demonstrate the Newton-Raphson method. The example is solved to determine the voltage magnitude and angle at the second bus.
This document discusses power flow analysis and the Newton-Raphson power flow method. It provides details on setting up the power flow problem, including defining the power balance equations in terms of real and reactive power. It also describes calculating the Jacobian matrix and differentiating the power flow equations to populate the matrix. An example power flow case is presented on a two bus system to illustrate applying the Newton-Raphson method through multiple iterations to solve for the voltage magnitude and angle.
1. The document describes the process of load flow analysis using the Newton-Raphson power flow method.
2. The Newton-Raphson power flow method uses Newton's method to solve the nonlinear power balance equations to determine the voltage magnitude and angle at each bus in the power system.
3. It derives the real and reactive power balance equations, defines the power flow variables, describes calculating the Jacobian matrix and its elements, and provides an example of applying the method to a two bus system to solve for the unknown voltage magnitude and angle at the second bus.
The document discusses the Newton-Raphson power flow method for solving power systems. Some key points:
- Newton-Raphson is commonly used for power flow analysis due to its fast convergence when initial guesses are close to the solution and large region of convergence. However, each iteration takes longer than Gauss-Seidel and it is more complicated to code.
- It uses Newton's method to determine the voltage magnitude and angle at each bus that satisfies the power balance equations. The power flow Jacobian matrix is calculated by differentiating the real and reactive power balance equations with respect to the voltage variables.
- A two-bus example demonstrates setting up and solving the power flow problem using Newton-Raphson
This document discusses transmission line models used in power system analysis. It begins with an overview of the distributed parameter model that represents an infinitesimal length of transmission line using series impedance and shunt admittance. It then derives the telegrapher's equations and uses them to develop a single second-order differential equation for the voltage along the line. The document presents solutions for this equation that allow determining the voltage and current at any point on the line given conditions at one end. It introduces transmission line parameters including characteristic impedance and propagation constant and shows how they relate the sending and receiving end quantities. Equivalent lumped-parameter π models are also derived in terms of the transmission line parameters. Finally, it discusses short
This document provides an overview of complex power in electrical systems. It defines phasor representation using complex exponentials to simplify analysis of constant frequency AC circuits. It describes how real and reactive power can be calculated from voltage and current phasors and discusses power factor. The document also discusses reactive compensation using capacitors to improve power factor by supplying reactive power locally. It provides an example of power factor correction and introduces balanced three-phase power systems with both wye and delta connections.
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.
This document discusses the Newton-Raphson power flow method. It begins with announcements about homework assignments. It then provides an overview of the dishonest or shamanskii Newton-Raphson method, which calculates the Jacobian less frequently than the honest method to reduce computation time. An example is shown comparing the two methods. The document also discusses decoupled and fast decoupled power flow methods, which make additional approximations to further reduce computation time. It concludes with a brief discussion of power system control and indirect methods of controlling transmission line flows.
This document discusses power flow analysis in power systems. It begins with announcements about upcoming homework assignments and exams. It then provides background on transmission system planning and an example in ERCOT. The document covers the development of power flow equations using complex power definitions and the Newton-Raphson method for solving the nonlinear power flow equations. It includes the derivation of the power flow Jacobian matrix and provides a detailed two bus power flow example to demonstrate the Newton-Raphson method. The example is solved to determine the voltage magnitude and angle at the second bus.
This document discusses power flow analysis and the Newton-Raphson power flow method. It provides details on setting up the power flow problem, including defining the power balance equations in terms of real and reactive power. It also describes calculating the Jacobian matrix and differentiating the power flow equations to populate the matrix. An example power flow case is presented on a two bus system to illustrate applying the Newton-Raphson method through multiple iterations to solve for the voltage magnitude and angle.
1. The document describes the process of load flow analysis using the Newton-Raphson power flow method.
2. The Newton-Raphson power flow method uses Newton's method to solve the nonlinear power balance equations to determine the voltage magnitude and angle at each bus in the power system.
3. It derives the real and reactive power balance equations, defines the power flow variables, describes calculating the Jacobian matrix and its elements, and provides an example of applying the method to a two bus system to solve for the unknown voltage magnitude and angle at the second bus.
The document discusses the Newton-Raphson power flow method for solving power systems. Some key points:
- Newton-Raphson is commonly used for power flow analysis due to its fast convergence when initial guesses are close to the solution and large region of convergence. However, each iteration takes longer than Gauss-Seidel and it is more complicated to code.
- It uses Newton's method to determine the voltage magnitude and angle at each bus that satisfies the power balance equations. The power flow Jacobian matrix is calculated by differentiating the real and reactive power balance equations with respect to the voltage variables.
- A two-bus example demonstrates setting up and solving the power flow problem using Newton-Raphson
This document discusses transmission line models used in power system analysis. It begins with an overview of the distributed parameter model that represents an infinitesimal length of transmission line using series impedance and shunt admittance. It then derives the telegrapher's equations and uses them to develop a single second-order differential equation for the voltage along the line. The document presents solutions for this equation that allow determining the voltage and current at any point on the line given conditions at one end. It introduces transmission line parameters including characteristic impedance and propagation constant and shows how they relate the sending and receiving end quantities. Equivalent lumped-parameter π models are also derived in terms of the transmission line parameters. Finally, it discusses short
This document provides an overview of complex power in electrical systems. It defines phasor representation using complex exponentials to simplify analysis of constant frequency AC circuits. It describes how real and reactive power can be calculated from voltage and current phasors and discusses power factor. The document also discusses reactive compensation using capacitors to improve power factor by supplying reactive power locally. It provides an example of power factor correction and introduces balanced three-phase power systems with both wye and delta connections.
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 provides an overview of power flow analysis using the Gauss-Seidel and Newton-Raphson methods. It discusses key concepts such as different bus types, stopping criteria, and examples to illustrate the iterative process. The Gauss-Seidel method is introduced and examples are shown to demonstrate its use in solving power flows. Limitations of Gauss-Seidel are also outlined. The Newton-Raphson method is then presented as an alternative approach using sequential linear approximations to iteratively find the solution.
The document provides an overview of phasor analysis for power systems. It discusses:
1) Representing AC voltages and currents as phasors using Euler's identity, which allows simplifying the analysis of constant frequency AC systems.
2) The advantages of phasor analysis for representing impedances of components like resistors, inductors, and capacitors.
3) Examples of calculating real and reactive power in circuits using phasor representations and the power triangle.
4) Applications of reactive power compensation to reduce line losses and current.
This document provides an overview of load flow analysis and power flow solution techniques, specifically the Gauss-Seidel and Newton-Raphson methods. It begins with an example Gauss-Seidel power flow calculation for a two bus system. It then discusses the inclusion of PV generator buses in the Gauss-Seidel iteration and accelerated Gauss-Seidel convergence. The document concludes by introducing the Newton-Raphson power flow algorithm and comparing the advantages and disadvantages of Gauss-Seidel versus Newton-Raphson.
This lecture discusses power system protection and transient stability. It provides examples of how different types of relays like directional, impedance, and differential relays are used to protect transmission lines and other equipment. Sequence of events recording with GPS time synchronization is discussed for fault location. Models for generator electrical dynamics, mechanical dynamics, and the swing equation are presented. Transient stability analysis considers the pre-fault, faulted, and post-fault system states. Numerical integration and direct methods like the equal area criteria are presented for solving transient stability problems. An example of a single machine infinite bus system is analyzed.
(1) A symmetrical fault occurs on bus 3 of a 3-bus system.
(2) The Thevenin equivalent impedance is calculated to be j0.21 p.u.
(3) For a fault impedance of j0.19 p.u., the fault current is calculated to be -j2.5 p.u. and the post-fault bus voltages are determined.
(4) For a bolted fault with zero impedance, the fault current is -j4.76 p.u. and the post-fault bus voltages and line currents are found.
This document provides a summary of a lecture on power flow analysis. It begins with announcements about homework and reading assignments. It then discusses using the bus admittance matrix (Ybus) to solve for bus voltages and currents if one or the other is known. The remainder of the document discusses using the power balance equations and Newton-Raphson method to solve the power flow problem when bus real and reactive powers are known rather than voltages and currents. It provides examples of calculating the Jacobian matrix and using Newton-Raphson on a two bus system.
This document provides an overview of the Gauss-Seidel and Newton-Raphson power flow solution methods. It begins by describing the Gauss-Seidel iterative method for solving nonlinear power flow equations using a scalar example. It then discusses applying Gauss-Seidel to vector power flow problems and provides an example of solving a two bus system. The document next describes the Newton-Raphson method, extending it to multidimensional problems using Taylor series approximations and defining the Jacobian matrix. It concludes with brief discussions of advantages and disadvantages of each method.
A novel voltage reference without the operational amplifier and resistorsIJRES Journal
novel voltage reference has been proposed and simulated using a 0.18μm CMOS process in
this paper. A near-zero temperature coefficient voltage is achieved in virtue of the bias voltage subcirciut which
consists of two MOSFETs operating in the saturation region. The kind of bias voltage subcirciut is used to
adjust the output voltage and compensate the curvature. The output voltage is equal to the extrapolated
threshold voltage of a MOSFET at absolute zero temperature, which was about 591.5 mV for the MOSFETs we
used. The power supply rejection ratio (PSRR) is improved with three feedback loops. Although the output
voltage fluctuates with process variation, the circuit can monitor the process variation in MOSFET threshold
voltage. The simulation results show that the line regulation is 0.75 mV/V in a supply voltage range from 1.6 V
to 3.1 V and the temperature coefficient is around 10.8 ppm/℃ to 28.5 ppm/℃ at 9 different corners in a
temperature range from -20℃ to 120 ℃.
The PSRR is -70 dB at 100Hz with a supply voltage at 1.8 V, and the
layout size is 0.012mm2. The results of simulation and post layout simulation are almost the same.
This document is a 29-page report on power flow studies submitted by Akbar Pamungkas Sukasdi to Saxion University. It includes instructions for power flow calculations modeling loads as constant impedance, current, or power. It provides per unit calculations of line impedances and transformer admittances for a sample power system. The report then shows MATLAB code and results for calculating bus voltages and currents throughout the system. Cable currents and sending/receiving powers are also determined for cable 1. A comparison table shows calculations match values from the VISION software with no deviation.
The document contains 4 solved questions related to power systems.
1. It asks to draw the pu impedance diagram for a given power system and lists the ratings of generator, motor, and transformers. The solution provides step-by-step working to calculate the pu impedances.
2. It asks to calculate the terminal voltage of a synchronous machine in a given radial transmission system. The solution shows the calculations.
3. It provides ratings of a synchronous generator and asks to determine quantities based on given conditions. The solution includes a phasor diagram.
4. It asks to calculate the line current for a 3-phase star connected load with given impedances. The solution sets up equations based on the circuit
The document contains 4 solved questions related to power systems.
1. It provides the step-by-step solution to draw the pu impedance diagram for a power system network including a generator, motor, and two transformers.
2. It calculates the terminal voltage of a synchronous machine in a radial transmission system with given component ratings and loads.
3. It determines the EMF and angle of a synchronous generator operating at a given power factor and current into an infinite bus.
4. It calculates the line current for a 3-phase, 3-wire star-connected unbalanced load using given impedance values connected to each phase.
This document discusses electromagnetic transmission lines and the Smith chart. It introduces equivalent electrical circuit models for coaxial cables, microstrip lines, and twin lead transmission lines using distributed inductors and capacitors. The telegrapher's equations are derived from Kirchhoff's laws. For sinusoidal waves on the transmission lines, phasor analysis is used. Key concepts covered include characteristic impedance, propagation velocity, wavelength, and modeling forward and backward traveling waves.
This document contains an unsolved past paper on electrical engineering from 2008. It consists of 35 multiple choice questions testing concepts related to electrical circuits, signals and systems, electronics, electromagnetic fields, and power systems. The questions cover topics such as circuit analysis, Thevenin's theorem, Fourier analysis, Laplace transforms, diodes, op-amps, transformers, transmission lines, motors, and more.
This document describes the Fast Decoupled Load Flow (FDLF) method for solving power system load flow problems. FDLF is based on the principle that real and reactive power are primarily governed by voltage angles and magnitudes, respectively. The method forms reduced Jacobian matrices J1 and J4 relating real/reactive power to angles/magnitudes. It then iteratively solves for voltage angle and magnitude corrections using these matrices until power mismatches converge to zero. The document provides an example applying FDLF to a 3-bus system in MATLAB, demonstrating the formation of the reduced Jacobian and iterative solution process.
This document provides an introduction to resonant circuits, discussing both series and parallel resonance. It defines resonance as occurring when the input voltage and current are in phase for a passive RLC circuit. For series resonance, the input impedance is completely real at resonance. Key equations for the resonant frequency, bandwidth, and quality factor Q are derived. Matlab programs are included to simulate the frequency response for different Q values. Duality between series and parallel circuits is also explained, where equations can be transformed between the two by substituting component values. Examples are worked through to calculate resonant components and bandwidth from given parameters.
This document provides an introduction to resonant circuits, discussing both series and parallel resonance. It defines resonance as occurring when the input voltage and current are in phase for a passive RLC circuit. For series resonance, the input impedance is completely real at resonance. Key equations for the resonant frequency, bandwidth, and quality factor Q are derived. Matlab programs are included to simulate the frequency response for different Q values. Duality between series and parallel circuits is also explained, where equations can be transformed between the two by substituting component values. Examples are worked through to calculate resonant components and bandwidth from given parameters.
This document summarizes Nathan Wendt's final project for EE321, which involved designing third-order passive frequency-selective circuits. Section I derives the general transfer function and analyzes low-pass behavior. Section II examines the low-pass frequency response and Butterworth design. Section III designs a high-pass Butterworth filter. MATLAB is used throughout to simulate and analyze the circuit designs.
The document describes modeling a power system network using an admittance matrix formulation. Key points:
1) Branches are modeled as admittances to relate voltage and current. The admittance matrix (Y-bus) is formed with diagonal elements equal to the sum of incident branch admittances and off-diagonals equal to the negative of branch admittances.
2) Kirchhoff's and Ohm's laws are used to write equations relating bus voltages and branch currents.
3) Simplifying assumptions are made to develop the "DC power flow" equations, including ignoring voltage magnitudes and angles and resistance. This leads to a linear relationship between bus voltage angles and real power injections
1) The passage provides a past paper for the Electrical Engineering GATE exam with 27 multiple choice questions covering topics like signals, circuits, transformers, machines, and more.
2) For each question, 4 possible answers are given labeled a, b, c, or d and the correct answer must be indicated in the answer book.
3) The questions cover topics testing knowledge of properties of signals, circuit analysis, transformer operation, machine operation, transmission lines, relays, power converters, sampling, diodes, state space representations, allpass systems, oscilloscopes, and more.
The document discusses power electronics and power semiconductor devices. It explains that power electronics involves using solid-state electronics like power devices and integrated circuits to control and convert electric power. Some key applications of power electronics mentioned include motor control, power supplies, vehicle propulsion systems, and HVDC transmission. The document also provides examples of different types of power converters like AC-DC converters, DC-DC converters, and DC-AC inverters. It describes the operating principles and voltage/current characteristics of these converters.
This document discusses various aspects of wind turbine power electronics and control systems. It begins with basics on how wind turbines convert kinetic wind energy into rotational energy. It then covers different types of generators that can be used, such as asynchronous and synchronous, and various ways to connect them to the electrical grid directly or via power converters. The document also discusses methods for controlling the turbine speed, such as pitch control and stall control, as well as optimizing the turbine's performance through control of the generator excitation or frequency. Finally, it provides two examples of control strategies - one for a fixed speed grid-connected system and one for a variable speed system with pitch control.
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 provides an overview of power flow analysis using the Gauss-Seidel and Newton-Raphson methods. It discusses key concepts such as different bus types, stopping criteria, and examples to illustrate the iterative process. The Gauss-Seidel method is introduced and examples are shown to demonstrate its use in solving power flows. Limitations of Gauss-Seidel are also outlined. The Newton-Raphson method is then presented as an alternative approach using sequential linear approximations to iteratively find the solution.
The document provides an overview of phasor analysis for power systems. It discusses:
1) Representing AC voltages and currents as phasors using Euler's identity, which allows simplifying the analysis of constant frequency AC systems.
2) The advantages of phasor analysis for representing impedances of components like resistors, inductors, and capacitors.
3) Examples of calculating real and reactive power in circuits using phasor representations and the power triangle.
4) Applications of reactive power compensation to reduce line losses and current.
This document provides an overview of load flow analysis and power flow solution techniques, specifically the Gauss-Seidel and Newton-Raphson methods. It begins with an example Gauss-Seidel power flow calculation for a two bus system. It then discusses the inclusion of PV generator buses in the Gauss-Seidel iteration and accelerated Gauss-Seidel convergence. The document concludes by introducing the Newton-Raphson power flow algorithm and comparing the advantages and disadvantages of Gauss-Seidel versus Newton-Raphson.
This lecture discusses power system protection and transient stability. It provides examples of how different types of relays like directional, impedance, and differential relays are used to protect transmission lines and other equipment. Sequence of events recording with GPS time synchronization is discussed for fault location. Models for generator electrical dynamics, mechanical dynamics, and the swing equation are presented. Transient stability analysis considers the pre-fault, faulted, and post-fault system states. Numerical integration and direct methods like the equal area criteria are presented for solving transient stability problems. An example of a single machine infinite bus system is analyzed.
(1) A symmetrical fault occurs on bus 3 of a 3-bus system.
(2) The Thevenin equivalent impedance is calculated to be j0.21 p.u.
(3) For a fault impedance of j0.19 p.u., the fault current is calculated to be -j2.5 p.u. and the post-fault bus voltages are determined.
(4) For a bolted fault with zero impedance, the fault current is -j4.76 p.u. and the post-fault bus voltages and line currents are found.
This document provides a summary of a lecture on power flow analysis. It begins with announcements about homework and reading assignments. It then discusses using the bus admittance matrix (Ybus) to solve for bus voltages and currents if one or the other is known. The remainder of the document discusses using the power balance equations and Newton-Raphson method to solve the power flow problem when bus real and reactive powers are known rather than voltages and currents. It provides examples of calculating the Jacobian matrix and using Newton-Raphson on a two bus system.
This document provides an overview of the Gauss-Seidel and Newton-Raphson power flow solution methods. It begins by describing the Gauss-Seidel iterative method for solving nonlinear power flow equations using a scalar example. It then discusses applying Gauss-Seidel to vector power flow problems and provides an example of solving a two bus system. The document next describes the Newton-Raphson method, extending it to multidimensional problems using Taylor series approximations and defining the Jacobian matrix. It concludes with brief discussions of advantages and disadvantages of each method.
A novel voltage reference without the operational amplifier and resistorsIJRES Journal
novel voltage reference has been proposed and simulated using a 0.18μm CMOS process in
this paper. A near-zero temperature coefficient voltage is achieved in virtue of the bias voltage subcirciut which
consists of two MOSFETs operating in the saturation region. The kind of bias voltage subcirciut is used to
adjust the output voltage and compensate the curvature. The output voltage is equal to the extrapolated
threshold voltage of a MOSFET at absolute zero temperature, which was about 591.5 mV for the MOSFETs we
used. The power supply rejection ratio (PSRR) is improved with three feedback loops. Although the output
voltage fluctuates with process variation, the circuit can monitor the process variation in MOSFET threshold
voltage. The simulation results show that the line regulation is 0.75 mV/V in a supply voltage range from 1.6 V
to 3.1 V and the temperature coefficient is around 10.8 ppm/℃ to 28.5 ppm/℃ at 9 different corners in a
temperature range from -20℃ to 120 ℃.
The PSRR is -70 dB at 100Hz with a supply voltage at 1.8 V, and the
layout size is 0.012mm2. The results of simulation and post layout simulation are almost the same.
This document is a 29-page report on power flow studies submitted by Akbar Pamungkas Sukasdi to Saxion University. It includes instructions for power flow calculations modeling loads as constant impedance, current, or power. It provides per unit calculations of line impedances and transformer admittances for a sample power system. The report then shows MATLAB code and results for calculating bus voltages and currents throughout the system. Cable currents and sending/receiving powers are also determined for cable 1. A comparison table shows calculations match values from the VISION software with no deviation.
The document contains 4 solved questions related to power systems.
1. It asks to draw the pu impedance diagram for a given power system and lists the ratings of generator, motor, and transformers. The solution provides step-by-step working to calculate the pu impedances.
2. It asks to calculate the terminal voltage of a synchronous machine in a given radial transmission system. The solution shows the calculations.
3. It provides ratings of a synchronous generator and asks to determine quantities based on given conditions. The solution includes a phasor diagram.
4. It asks to calculate the line current for a 3-phase star connected load with given impedances. The solution sets up equations based on the circuit
The document contains 4 solved questions related to power systems.
1. It provides the step-by-step solution to draw the pu impedance diagram for a power system network including a generator, motor, and two transformers.
2. It calculates the terminal voltage of a synchronous machine in a radial transmission system with given component ratings and loads.
3. It determines the EMF and angle of a synchronous generator operating at a given power factor and current into an infinite bus.
4. It calculates the line current for a 3-phase, 3-wire star-connected unbalanced load using given impedance values connected to each phase.
This document discusses electromagnetic transmission lines and the Smith chart. It introduces equivalent electrical circuit models for coaxial cables, microstrip lines, and twin lead transmission lines using distributed inductors and capacitors. The telegrapher's equations are derived from Kirchhoff's laws. For sinusoidal waves on the transmission lines, phasor analysis is used. Key concepts covered include characteristic impedance, propagation velocity, wavelength, and modeling forward and backward traveling waves.
This document contains an unsolved past paper on electrical engineering from 2008. It consists of 35 multiple choice questions testing concepts related to electrical circuits, signals and systems, electronics, electromagnetic fields, and power systems. The questions cover topics such as circuit analysis, Thevenin's theorem, Fourier analysis, Laplace transforms, diodes, op-amps, transformers, transmission lines, motors, and more.
This document describes the Fast Decoupled Load Flow (FDLF) method for solving power system load flow problems. FDLF is based on the principle that real and reactive power are primarily governed by voltage angles and magnitudes, respectively. The method forms reduced Jacobian matrices J1 and J4 relating real/reactive power to angles/magnitudes. It then iteratively solves for voltage angle and magnitude corrections using these matrices until power mismatches converge to zero. The document provides an example applying FDLF to a 3-bus system in MATLAB, demonstrating the formation of the reduced Jacobian and iterative solution process.
This document provides an introduction to resonant circuits, discussing both series and parallel resonance. It defines resonance as occurring when the input voltage and current are in phase for a passive RLC circuit. For series resonance, the input impedance is completely real at resonance. Key equations for the resonant frequency, bandwidth, and quality factor Q are derived. Matlab programs are included to simulate the frequency response for different Q values. Duality between series and parallel circuits is also explained, where equations can be transformed between the two by substituting component values. Examples are worked through to calculate resonant components and bandwidth from given parameters.
This document provides an introduction to resonant circuits, discussing both series and parallel resonance. It defines resonance as occurring when the input voltage and current are in phase for a passive RLC circuit. For series resonance, the input impedance is completely real at resonance. Key equations for the resonant frequency, bandwidth, and quality factor Q are derived. Matlab programs are included to simulate the frequency response for different Q values. Duality between series and parallel circuits is also explained, where equations can be transformed between the two by substituting component values. Examples are worked through to calculate resonant components and bandwidth from given parameters.
This document summarizes Nathan Wendt's final project for EE321, which involved designing third-order passive frequency-selective circuits. Section I derives the general transfer function and analyzes low-pass behavior. Section II examines the low-pass frequency response and Butterworth design. Section III designs a high-pass Butterworth filter. MATLAB is used throughout to simulate and analyze the circuit designs.
The document describes modeling a power system network using an admittance matrix formulation. Key points:
1) Branches are modeled as admittances to relate voltage and current. The admittance matrix (Y-bus) is formed with diagonal elements equal to the sum of incident branch admittances and off-diagonals equal to the negative of branch admittances.
2) Kirchhoff's and Ohm's laws are used to write equations relating bus voltages and branch currents.
3) Simplifying assumptions are made to develop the "DC power flow" equations, including ignoring voltage magnitudes and angles and resistance. This leads to a linear relationship between bus voltage angles and real power injections
1) The passage provides a past paper for the Electrical Engineering GATE exam with 27 multiple choice questions covering topics like signals, circuits, transformers, machines, and more.
2) For each question, 4 possible answers are given labeled a, b, c, or d and the correct answer must be indicated in the answer book.
3) The questions cover topics testing knowledge of properties of signals, circuit analysis, transformer operation, machine operation, transmission lines, relays, power converters, sampling, diodes, state space representations, allpass systems, oscilloscopes, and more.
The document discusses power electronics and power semiconductor devices. It explains that power electronics involves using solid-state electronics like power devices and integrated circuits to control and convert electric power. Some key applications of power electronics mentioned include motor control, power supplies, vehicle propulsion systems, and HVDC transmission. The document also provides examples of different types of power converters like AC-DC converters, DC-DC converters, and DC-AC inverters. It describes the operating principles and voltage/current characteristics of these converters.
This document discusses various aspects of wind turbine power electronics and control systems. It begins with basics on how wind turbines convert kinetic wind energy into rotational energy. It then covers different types of generators that can be used, such as asynchronous and synchronous, and various ways to connect them to the electrical grid directly or via power converters. The document also discusses methods for controlling the turbine speed, such as pitch control and stall control, as well as optimizing the turbine's performance through control of the generator excitation or frequency. Finally, it provides two examples of control strategies - one for a fixed speed grid-connected system and one for a variable speed system with pitch control.
This document discusses solving nonlinear systems of equations. It covers solving systems by substitution, elimination, and a combination of methods. The objectives are to solve nonlinear systems using substitution, elimination of two second-degree equations, and a mixed approach. Examples are provided to demonstrate each technique.
This document outlines Newton's method for solving nonlinear equations and systems of equations. It begins by introducing nonlinear problems and iterative methods for solving them. It then derives Newton's method, showing that it provides quadratic convergence near the solution. The document discusses applying Newton's method to multidimensional systems using the Jacobian matrix and iterative linearization. It also covers testing for convergence and techniques for improving convergence such as damping and continuation methods.
This document discusses various components involved in wind energy conversion systems including permanent magnet synchronous generators (PMSG), doubly fed induction generators (DFIG), squirrel cage induction generators (SCIG), and their connection to the grid through power converters. It describes the power flow from the wind turbine through a permanent magnet synchronous generator, rectifier, DC-link, inverter, and filter before connecting to the grid. It also mentions use of energy storage systems and flexible AC transmission systems to help integrate wind power onto the grid.
This document discusses the design of closed-loop control for region 2 operation of a wind turbine using a continuously variable transmission (CVT). It motivates using a CVT to reduce the cost of wind energy and improve capture. It outlines presenting the modeling of the rotor-drivetrain-generator system and developing closed-loop CVT control. The performance of the full modeled system is analyzed through simulations using 10 minutes of recorded wind data.
Uneven heating of the Earth's surface and its rotation cause global wind patterns and local wind variations. As air rises and falls on the planet, pressure differences drive global wind circulation. Additional localized patterns arise from terrain and other surface factors. Wind speed generally increases with height until turbulence decreases it again near the tropopause. The density of air decreases with increases in altitude and temperature. This document discusses how to calculate the power available in wind and energy production from wind resources using power curves and wind speed data. Key factors in the economics of wind energy projects are the levelized cost of energy and the capacity factor.
The document provides information about various power semiconductor devices. It begins with an overview of topics covered, which include semiconductor devices, controlled rectifiers, DC choppers, inverters, and AC choppers. It then discusses numerous power semiconductor devices in detail, including their structures, characteristics, and applications. Devices covered include power diodes, power transistors (BJTs, MOSFETs, IGBTs, SITs), thyristors (SCRs, triacs, GTOs, SITHs, MCTs), and provides comparisons of their performance and specifications. The document aims to educate about the operating principles and applications of important power electronics components.
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The document discusses various power semiconductor devices. It covers topics such as power diodes, power transistors including BJTs, MOSFETs, IGBTs, and SITs. For each device type, it discusses the basic structure, V-I characteristics, and applications. It also covers thyristors such as SCR, TRIAC, GTO, and their working principles including forward and reverse blocking modes, and triggering methods. The document contains detailed information on the structural features and operating characteristics of various important power semiconductor devices.
This document provides a 5-step guide to conducting a literature review. It explains that a literature review surveys scholarly sources on a topic, provides an overview of current knowledge, and identifies gaps. The 5 steps are: 1) searching for relevant literature using keywords and databases; 2) evaluating and selecting sources; 3) identifying themes, debates and gaps; 4) outlining the structure; and 5) writing the literature review, which typically includes an introduction, body and conclusion. The document emphasizes finding trends over time, engaging with debates, and discussing implications and suggestions for future research.
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This document provides an overview of load modeling and induction motor modeling. It discusses how load modeling is important for transient stability simulations but challenging due to the diverse and changing nature of loads. Static load models like the ZIP model are commonly used to represent aggregate load behavior. Induction motors make up a large portion of load and can be modeled statically or dynamically, with the dynamic model typically being a third-order model that neglects stator transients. The document provides details on modeling considerations and differences between modeling induction motors versus synchronous machines.
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1) This lecture discusses power flow analysis and modeling voltage dependent loads. It introduces the Newton-Raphson power flow method and approximations like the decoupled power flow and fast decoupled power flow that reduce computation time.
2) The professor announces upcoming homework and exam details. Voltage dependent loads are modeled using their real and reactive power as functions of voltage magnitude and angle.
3) Examples are provided to demonstrate modeling a constant impedance load and solving a two bus system using the dishonest Newton-Raphson method where the Jacobian is only calculated on the first iteration.
1) This lecture discusses power flow analysis and modeling voltage dependent loads. It introduces the Newton-Raphson power flow method and approximations like the decoupled power flow and fast decoupled power flow that reduce computation time.
2) The professor announces upcoming homework and exam details. Voltage dependent loads are modeled using their real and reactive power as functions of voltage magnitude and angle.
3) Examples are provided to demonstrate modeling a constant impedance load and solving a two bus system using the dishonest Newton-Raphson method where the Jacobian is only calculated on the first iteration.
Power flow studies analyze the steady state operation of power systems by calculating the voltage magnitude and angle at each bus. They use numerical methods like Gauss-Seidel and Newton-Raphson to solve the nonlinear power flow equations iteratively. Power flow studies classify buses as load buses with specified real and reactive power, generator/voltage controlled buses that control voltage magnitude, and a reference slack bus that balances the system.
The document discusses various topics related to electrical engineering concepts like insulation, breakdown mechanisms, testing methods, and tariff structures. Some key points:
1) It discusses different theories of insulation breakdown like formative time lag, statistical time lag, Paschen's law, bubble theory, and stressed oil volume theory.
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3) It explains different tariff structures used for electricity billing like two-part tariff, three-part tariff, block rate tariff and their advantages or disadvantages.
International Conference on NLP, Artificial Intelligence, Machine Learning an...gerogepatton
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CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Low power architecture of logic gates using adiabatic techniquesnooriasukmaningtyas
The growing significance of portable systems to limit power consumption in ultra-large-scale-integration chips of very high density, has recently led to rapid and inventive progresses in low-power design. The most effective technique is adiabatic logic circuit design in energy-efficient hardware. This paper presents two adiabatic approaches for the design of low power circuits, modified positive feedback adiabatic logic (modified PFAL) and the other is direct current diode based positive feedback adiabatic logic (DC-DB PFAL). Logic gates are the preliminary components in any digital circuit design. By improving the performance of basic gates, one can improvise the whole system performance. In this paper proposed circuit design of the low power architecture of OR/NOR, AND/NAND, and XOR/XNOR gates are presented using the said approaches and their results are analyzed for powerdissipation, delay, power-delay-product and rise time and compared with the other adiabatic techniques along with the conventional complementary metal oxide semiconductor (CMOS) designs reported in the literature. It has been found that the designs with DC-DB PFAL technique outperform with the percentage improvement of 65% for NOR gate and 7% for NAND gate and 34% for XNOR gate over the modified PFAL techniques at 10 MHz respectively.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
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.
A review on techniques and modelling methodologies used for checking electrom...nooriasukmaningtyas
The proper function of the integrated circuit (IC) in an inhibiting electromagnetic environment has always been a serious concern throughout the decades of revolution in the world of electronics, from disjunct devices to today’s integrated circuit technology, where billions of transistors are combined on a single chip. The automotive industry and smart vehicles in particular, are confronting design issues such as being prone to electromagnetic interference (EMI). Electronic control devices calculate incorrect outputs because of EMI and sensors give misleading values which can prove fatal in case of automotives. In this paper, the authors have non exhaustively tried to review research work concerned with the investigation of EMI in ICs and prediction of this EMI using various modelling methodologies and measurement setups.
Presentation of IEEE Slovenia CIS (Computational Intelligence Society) Chapte...University of Maribor
Slides from talk presenting:
Aleš Zamuda: Presentation of IEEE Slovenia CIS (Computational Intelligence Society) Chapter and Networking.
Presentation at IcETRAN 2024 session:
"Inter-Society Networking Panel GRSS/MTT-S/CIS
Panel Session: Promoting Connection and Cooperation"
IEEE Slovenia GRSS
IEEE Serbia and Montenegro MTT-S
IEEE Slovenia CIS
11TH INTERNATIONAL CONFERENCE ON ELECTRICAL, ELECTRONIC AND COMPUTING ENGINEERING
3-6 June 2024, Niš, Serbia
2. 1
Announcements
Be reading Chapter 6, also Chapter 2.4 (Network Equations).
HW 5 is 2.38, 6.9, 6.18, 6.30, 6.34, 6.38; do by October 6
but does not need to be turned in.
First exam is October 11 during class. Closed book, closed
notes, one note sheet and calculators allowed. Exam covers
thru the end of lecture 13 (today)
An example previous exam (2008) is posted. Note this is
exam was given earlier in the semester in 2008 so it did not
include power flow, but the 2011 exam will (at least
partially)
3. 2
Modeling Voltage Dependent Load
So far we've assumed that the load is independent of
the bus voltage (i.e., constant power). However, the
power flow can be easily extended to include voltage
depedence with both the real and reactive l
Di Di
1
1
oad. This
is done by making P and Q a function of :
( cos sin ) ( ) 0
( sin cos ) ( ) 0
i
n
i k ik ik ik ik Gi Di i
k
n
i k ik ik ik ik Gi Di i
k
V
V V G B P P V
V V G B Q Q V
4. 3
Voltage Dependent Load Example
2
2 2 2 2
2 2
2 2 2 2 2
2 2 2 2
In previous two bus example now assume the load is
constant impedance, so
P ( ) (10sin ) 2.0 0
( ) ( 10cos ) (10) 1.0 0
Now calculate the power flow Jacobian
10 cos 10sin 4.0
( )
10
V V
Q V V V
V V
J
x
x
x
2 2 2 2 2
sin 10cos 20 2.0
V V V
6. 5
Voltage Dependent Load, cont'd
Line Z = 0.1j
One Two
1.000 pu
0.894 pu
160 MW
80 MVR
160.0 MW
120.0 MVR
-10.304 Deg
160.0 MW
120.0 MVR
-160.0 MW
-80.0 MVR
With constant impedance load the MW/Mvar load at
bus 2 varies with the square of the bus 2 voltage
magnitude. This if the voltage level is less than 1.0,
the load is lower than 200/100 MW/Mvar
7. 6
Dishonest Newton-Raphson
Since most of the time in the Newton-Raphson
iteration is spend calculating the inverse of the
Jacobian, one way to speed up the iterations is to
only calculate/inverse the Jacobian occasionally
– known as the “Dishonest” Newton-Raphson
– an extreme example is to only calculate the Jacobian for
the first iteration
( 1) ( ) ( ) -1 ( )
( 1) ( ) (0) -1 ( )
( )
Honest: - ( ) ( )
Dishonest: - ( ) ( )
Both require ( ) for a solution
v v v v
v v v
v
x x J x f x
x x J x f x
f x
8. 7
Dishonest Newton-Raphson Example
2
1
(0)
( ) ( )
( ) ( ) 2
(0)
( 1) ( ) ( ) 2
(0)
Use the Dishonest Newton-Raphson to solve
( ) - 2 0
( )
( )
1
(( ) - 2)
2
1
(( ) - 2)
2
v v
v v
v v v
f x x
df x
x f x
dx
x x
x
x x x
x
9. 8
Dishonest N-R Example, cont’d
( 1) ( ) ( ) 2
(0)
(0)
( ) ( )
1
(( ) - 2)
2
Guess x 1. Iteratively solving we get
v (honest) (dishonest)
0 1 1
1 1.5 1.5
2 1.41667 1.375
3 1.41422 1.429
4 1.41422 1.408
v v v
v v
x x x
x
x x
We pay a price
in increased
iterations, but
with decreased
computation
per iteration
10. 9
Two Bus Dishonest ROC
Slide shows the region of convergence for different initial
guesses for the 2 bus case using the Dishonest N-R
Red region
converges
to the high
voltage
solution,
while the
yellow region
converges
to the low
voltage
solution
12. 11
Decoupled Power Flow
The completely Dishonest Newton-Raphson is not
used for power flow analysis. However several
approximations of the Jacobian matrix are used.
One common method is the decoupled power flow.
In this approach approximations are used to
decouple the real and reactive power equations.
13. 12
Decoupled Power Flow Formulation
( ) ( )
( ) ( )
( )
( )
( ) ( ) ( )
( )
2 2 2
( )
( )
General form of the power flow problem
( )
( )
( )
where
( )
( )
( )
v v
v v
v
v
v v v
v
D G
v
v
n Dn Gn
P P P
P P P
P P
θ
θ V P x
f x
Q x
V
Q Q
θ V
x
P x
x
14. 13
Decoupling Approximation
( ) ( )
( )
( ) ( )
( )
( ) ( ) ( )
Usually the off-diagonal matrices, and
are small. Therefore we approximate them as zero:
( )
( )
( )
Then the problem
v v
v
v v
v
v v v
P Q
V θ
P
0
θ P x
θ
f x
Q Q x
V
0
V
1 1
( ) ( )
( )
( ) ( ) ( )
can be decoupled
( ) ( )
v v
v
v v v
P Q
θ P x V Q x
θ V
15. 14
Off-diagonal Jacobian Terms
Justification for Jacobian approximations:
1. Usually r x, therefore
2. Usually is small so sin 0
Therefore
cos sin 0
cos sin 0
ij ij
ij ij
i
i ij ij ij ij
j
i
i j ij ij ij ij
j
G B
V G B
V V G B
P
V
Q
θ
17. 16
Fast Decoupled Power Flow
By continuing with our Jacobian approximations we
can actually obtain a reasonable approximation that
is independent of the voltage magnitudes/angles.
This means the Jacobian need only be built/inverted
once.
This approach is known as the fast decoupled power
flow (FDPF)
FDPF uses the same mismatch equations as
standard power flow so it should have same solution
The FDPF is widely used, particularly when we
only need an approximate solution
18. 17
FDPF Approximations
ij
( ) ( )
( )
( ) 1 1
( ) ( )
bus
The FDPF makes the following approximations:
1. G 0
2. 1
3. sin 0 cos 1
Then
( ) ( )
Where is just the imaginary part of the ,
except the slack bus row/co
i
ij ij
v v
v
v
v v
V
j
P x Q x
θ B V B
V V
B Y G B
lumn are omitted
19. 18
FDPF Three Bus Example
Line Z = j0.07
Line Z = j0.05 Line Z = j0.1
One Two
200 MW
100 MVR
Three 1.000 pu
200 MW
100 MVR
Use the FDPF to solve the following three bus system
34.3 14.3 20
14.3 24.3 10
20 10 30
bus j
Y
23. 22
“DC” Power Flow
The “DC” power flow makes the most severe
approximations:
– completely ignore reactive power, assume all the voltages
are always 1.0 per unit, ignore line conductance
This makes the power flow a linear set of equations,
which can be solved directly
1
θ B P
24. 23
Power System Control
A major problem with power system operation is
the limited capacity of the transmission system
– lines/transformers have limits (usually thermal)
– no direct way of controlling flow down a transmission
line (e.g., there are no valves to close to limit flow)
– open transmission system access associated with industry
restructuring is stressing the system in new ways
We need to indirectly control transmission line flow
by changing the generator outputs
27. 26
DC Power Flow 5 Bus Example
slack
One
Two
Three
Four
Five
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1.000 pu 1.000 pu
1.000 pu
1.000 pu
1.000 pu
0.000 Deg -4.125 Deg
-18.695 Deg
-1.997 Deg
0.524 Deg
360 MW
0 Mvar
520 MW
0 Mvar
800 MW
0 Mvar
80 MW
0 Mvar
Notice with the dc power flow all of the voltage magnitudes are
1 per unit.
28. 27
Indirect Transmission Line Control
What we would like to determine is how a change in
generation at bus k affects the power flow on a line
from bus i to bus j.
The assumption is
that the change
in generation is
absorbed by the
slack bus
29. 28
Power Flow Simulation - Before
One way to determine the impact of a generator change
is to compare a before/after power flow.
For example below is a three bus case with an overload
Z for all lines = j0.1
One Two
200 MW
100 MVR
200.0 MW
71.0 MVR
Three 1.000 pu
0 MW
64 MVR
131.9 MW
68.1 MW 68.1 MW
124%
30. 29
Power Flow Simulation - After
Z for all lines = j0.1
Limit for all lines = 150 MVA
One Two
200 MW
100 MVR
105.0 MW
64.3 MVR
Three
1.000 pu
95 MW
64 MVR
101.6 MW
3.4 MW 98.4 MW
92%
100%
Increasing the generation at bus 3 by 95 MW (and hence
decreasing it at bus 1 by a corresponding amount), results
in a 31.3 drop in the MW flow on the line from bus 1 to 2.
31. 30
Analytic Calculation of Sensitivities
Calculating control sensitivities by repeat power
flow solutions is tedious and would require many
power flow solutions. An alternative approach is to
analytically calculate these values
The power flow from bus i to bus j is
sin( )
So We just need to get
i j i j
ij i j
ij ij
i j ij
ij
ij Gk
V V
P
X X
P
X P
32. 31
Analytic Sensitivities
1
From the fast decoupled power flow we know
( )
So to get the change in due to a change of
generation at bus k, just set ( ) equal to
all zeros except a minus one at position k.
0
1
0
θ B P x
θ
P x
P Bus k
33. 32
Three Bus Sensitivity Example
line
bus
1
2
3
For the previous three bus case with Z 0.1
20 10 10
20 10
10 20 10
10 20
10 10 20
Hence for a change of generation at bus 3
20 10 0 0.0333
10 20 1 0.0667
j
j
Y B
3 to 1
3 to 2 2 to 1
0.0667 0
Then P 0.667 pu
0.1
P 0.333 pu P 0.333 pu
34. 33
Balancing Authority Areas
An balancing authority area (use to be called
operating areas) has traditionally represented
the portion of the interconnected electric grid
operated by a single utility
Transmission lines that join two areas are
known as tie-lines.
The net power out of an area is the sum of the
flow on its tie-lines.
The flow out of an area is equal to
35. 34
Area Control Error (ACE)
The area control error (ace) is the difference
between the actual flow out of an area and
the scheduled flow, plus a frequency
component
Ideally the ACE should always be zero.
Because the load is constantly changing, each
utility must constantly change its generation
to “chase” the ACE.
int sched
ace 10
P P f
36. 35
Automatic Generation Control
Most utilities use automatic generation
control (AGC) to automatically change their
generation to keep their ACE close to zero.
Usually the utility control center calculates
ACE based upon tie-line flows; then the
AGC module sends control signals out to the
generators every couple seconds.
37. 36
Power Transactions
Power transactions are contracts between
generators and loads to do power
transactions.
Contracts can be for any amount of time at
any price for any amount of power.
Scheduled power transactions are
implemented by modifying the value of Psched
used in the ACE calculation
38. 37
PTDFs
Power transfer distribution factors (PTDFs) show
the linear impact of a transfer of power.
PTDFs calculated using the fast decoupled power
flow B matrix
1
( )
Once we know we can derive the change in
the transmission line flows
Except now we modify several elements in ( ),
in portion to how the specified generators would
participate in the pow
θ B P x
θ
P x
er transfer
39. 38
Nine Bus PTDF Example
10%
60%
55%
64%
57%
11%
74%
24%
32%
A
G
B
C
D
E
I
F
H
300.0 MW
400.0 MW 300.0 MW
250.0 MW
250.0 MW
200.0 MW
250.0 MW
150.0 MW
150.0 MW
44%
71%
0.00 deg
71.1 MW
92%
Figure shows initial flows for a nine bus power system
40. 39
Nine Bus PTDF Example, cont'd
43%
57%
13%
35%
20%
10%
2%
34%
34%
32%
A
G
B
C
D
E
I
F
H
300.0 MW
400.0 MW 300.0 MW
250.0 MW
250.0 MW
200.0 MW
250.0 MW
150.0 MW
150.0 MW
34%
30%
0.00 deg
71.1 MW
Figure now shows percentage PTDF flows from A to I
41. 40
Nine Bus PTDF Example, cont'd
6%
6%
12%
61%
12%
6%
19%
21%
21%
A
G
B
C
D
E
I
F
H
300.0 MW
400.0 MW 300.0 MW
250.0 MW
250.0 MW
200.0 MW
250.0 MW
150.0 MW
150.0 MW
20%
18%
0.00 deg
71.1 MW
Figure now shows percentage PTDF flows from G to F
43. 42
Line Outage Distribution Factors (LODFS)
LODFs are used to approximate the change in the
flow on one line caused by the outage of a second
line
– typically they are only used to determine the change in
the MW flow
– LODFs are used extensively in real-time operations
– LODFs are state-independent but do dependent on the
assumed network topology
,
l l k k
P LODF P
44. 43
Flowgates
The real-time loading of the power grid is accessed
via “flowgates”
A flowgate “flow” is the real power flow on one or
more transmission element for either base case
conditions or a single contingency
– contingent flows are determined using LODFs
Flowgates are used as proxies for other types of
limits, such as voltage or stability limits
Flowgates are calculated using a spreadsheet