Topic 1: Basics of Power Systems

Size: px
Start display at page:

Download "Topic 1: Basics of Power Systems"

Transcription

1 Topic : asics of Power Systems ECE 52: Communications and Control for Smart Spring 202 A.H. Mohsenian Rad (U of T) Networing and Distributed Systems

2 Power Systems The Four Main Elements in Power Systems: Power Production / Generation Power Transmission Power Distribution Power Consumption / Load Of course, we also need monitoring and control systems. Communications and Control in Smart Grid Texas Tech University 2

3 Power Systems Power Production: Different Types: Traditional Renewable Capacity, Cost, Carbon Emission Step up Transformers Communications and Control in Smart Grid Texas Tech University

4 Power Systems Power Transmission: High Voltage (HV) Transmission Lines Several Hundred Miles Switching Stations Transformers Circuit reaers Communications and Control in Smart Grid Texas Tech University 4

5 Power Systems The Power Transmission Grid in the United States: Communications and Control in Smart Grid Texas Tech University 5

6 Power Systems Major Inter connections in the United States: Communications and Control in Smart Grid Texas Tech University 6

7 Power Systems Power Distribution: Medium Voltage (MV) Transmission Lines (< 50 V) Power Deliver to Load Locations Interface with Consumers / Metering Distribution Sub stations Step Down Transformers Distribution Transformers Communications and Control in Smart Grid Texas Tech University 7

8 Power Systems Power Consumption: Industrial Commercial Residential Demand Response Controllable Load Non Controllable Communications and Control in Smart Grid Texas Tech University 8

9 Power Systems Generation Transmission Distribution Load Communications and Control in Smart Grid Texas Tech University 9

10 Power Systems Power System Control: Data Collection: Sensors, PMUs, etc. Decision Maing: Controllers Actuators: Circuit reaers, etc. Communications and Control in Smart Grid Texas Tech University 0

11 Power Grid Graph Representation Nodes: uses Lins: Transmission Lines Generator Load Communications and Control in Smart Grid Texas Tech University

12 Power Grid Graph Representation Nodes: uses Lins: Transmission Lines uses (Voltage) Generator Load Communications and Control in Smart Grid Texas Tech University 2

13 Power Grid Graph Representation Nodes: uses Lins: Transmission Lines Generator Load Transmission Lines (Power Flow, Loss) Communications and Control in Smart Grid Texas Tech University

14 Power Grid Graph Representation Nodes: uses Lins: Transmission Lines Generator Load Consumers Communications and Control in Smart Grid Texas Tech University 4

15 Power Grid Graph Representation Nodes: uses Lins: Transmission Lines Generator 0 MW MW Load 7 MW Communications and Control in Smart Grid Texas Tech University 5

16 Transmission Line Admittance Admittance y is defined as the inverse of impedance z: z = r + j x y = g + j b (r: Resistance, x: Reactance) (g: Conductance, b: Susceptance) y = / z Parameter g is usually positive Parameter b: Positive: Capacitor Negative: Inductor Communications and Control in Smart Grid Texas Tech University 6

17 Transmission Line Admittance For the transmission line connecting bus ito bus : Addmitance: y i Example: y i = j 4 (per unit) Note that, y ii is denoted by y i and indicates: Susceptance for any shunt element (capacitor) to ground at bus i. Communications and Control in Smart Grid Texas Tech University 7

18 Y-us Matrix We define: Y bus = [ Y ij ] where Diagonal Elements: Y ii y i N y, i i Off diagonal Elements: Y ij y ij Note that Y bas matrix depends on the power grid topology and the admittance of all transmission lines. N is the number of busses in the grid. Communications and Control in Smart Grid Texas Tech University 8

19 Y-us Matrix Example: For a grid with 4 buses, we have: Y bus y y 2 y y y y 2 4 y 4 y 2 y 2 y y y 2 y y 24 y y y y y 2 y 4 2 y 4 y 4 y y y y y 42 y 4 After separating the real and imaginary parts: Y bus G j Communications and Control in Smart Grid Texas Tech University 9

20 us Voltage Let V i denote the voltage at bus i: Note that, V i is a phasor, with magnitude and angle. V i V i i In most operating scenarios we have: V i V j i j Communications and Control in Smart Grid Texas Tech University 20

21 Power Flow Equations Let S i denote the power injection at bus i: S i = P i + j Q i Active Power Reactive Power Generation us: P i > 0 Load us: P i < 0 (negative power injection) Communications and Control in Smart Grid Texas Tech University 2

22 Power Flow Equations Using Kirchhoff laws, AC Power Flow Equations become: P Q N j N j V V V V j j G G j j cos( sin( j ) ) j j j sin( cos( ) j ) j Do we now all notations here? If we now enough variables, we can obtain the rest of variables by solving a system of nonlinear equations. Communications and Control in Smart Grid Texas Tech University 22

23 Power Flow Equations The AC Power Flow Equations are complicated to solve. Next, we try to simplify the equations in three steps. Step : For most networs, G <<. Thus, we set G = 0: P Q N j N j V V V j V j j sin( ) j j cos( ) j Communications and Control in Smart Grid Texas Tech University 2

24 Power Flow Equations Texas Tech University Communications and Control in Smart Grid 24 Step 2: For most neighboring buses:. As a result, we have: to5 0 j i ) ( ) ( j j j Cos Sin N j j j N j j j j V V Q V V P ) (

25 Power Flow Equations Step : In per unit, V i is very close to.0 (0.95 to.05). As a result, we have: V i V j. P Q N j N N j j b j j ( ) j j, j P has a linear model and Q is almost fixed. Communications and Control in Smart Grid Texas Tech University 25

26 Power Flow Equations Step : In per unit, V i is very close to.0 (0.95 to.05). As a result, we have: V i V j. DC Power Flow Equations P Q N j N N j j b j j ( ) j j, j P has a linear model and Q is almost fixed. Communications and Control in Smart Grid Texas Tech University 26

27 Power Flow Equations Given the power injection values at all buses, we can use P j ( j ) j to obtain the voltage angles at all buses. N Let P ij denote the power flow from bus ito bus j, we have: P ij ij ( i j ) Communications and Control in Smart Grid Texas Tech University 27

28 Power Flow Equations Example: Obtain power flow values in the following grid: y4 j0 y j0 P g 2 pu P g 2 2 pu y2 j0 y4 j0 P l 2 pu P g 4 pu P l 4 pu y2 j0 Communications and Control in Smart Grid Texas Tech University 28

29 Power Flow Equations First, we obtain the Y bus matrix: Y bus b j b 2 b b b b 2 4 b 4 b 2 b b 2 b b b b 24 b b b b b b b 4 b 4 b b b b b 42 b 4 j j j Communications and Control in Smart Grid Texas Tech University 29

30 Power Flow Equations Next, we write the (active) power flow equations: P P P P This can be written as: P P2 P P Communications and Control in Smart Grid Texas Tech University 0

31 Power Flow Equations Texas Tech University Communications and Control in Smart Grid From the last two slides, we finally obtain: Therefore, the voltage angles are obtained as:

32 Power Flow Equations However, the last matrix in the previous slide is singular! Therefore, we cannot tae the inverse. The system of equations would have infinite solutions. The problem is that the four angles are not independent. What matters is the angular/phase difference. We choose one bus (e.g., bus ) as reference bus: 0. Communications and Control in Smart Grid Texas Tech University 2

33 Power Flow Equations Texas Tech University Communications and Control in Smart Grid We should also remove the corresponding rows/columns: The angular differences (with respect to ):

34 Power Flow Equations Finally, the power flow values are calculated as: P P P P P ( ) 0( ) 0.25 ( ) 0(0 0.5).5 ( ) 0( ) 0.25 ( ) 0( ).25 2 ( ) 0( ) P g 2 pu P g 2 2 pu P l 2 pu P g 4 pu P l 4 pu Communications and Control in Smart Grid Texas Tech University 4

35 Power Flow Equations What if the generator connected to bus is renewable? What if the capacity of transmission lin (,) is pu? What if we can apply demand response to load bus? What if one of the transmission lines fails? Communications and Control in Smart Grid Texas Tech University 5

36 Economic Dispatch Problem In the example we discussed earlier, we had: In particular, we had: Power Supply = Power Load g g g l l P P2 P4 P2 P g g g However, generation levels, P and P assumed given. P 2, 4 Q: What if the generators have different generation costs? Communications and Control in Smart Grid Texas Tech University 6

37 Economic Dispatch Problem For thermal power plants, generation cost is quadratic: Generation Cost = C(P) = a + a 2 x P + a x P 2 Example: a grid with three power plants: C (P ) = x P x (P ) 2 C 2 (P 2 ) = x P x (P 2 ) 2 C (P ) = x P x (P ) 2 50 MW P 600 MW 00 MW P MW 50 MW P 200 MW Each power plant has some min and max generation levels. Communications and Control in Smart Grid Texas Tech University 7

38 Economic Dispatch Problem For thermal power plants, generation cost is quadratic: Generation Cost = C(P) = a + a 2 x P + a x P 2 Example: a grid with three power plants: C (P ) = x P x (P ) 2 C 2 (P 2 ) = x P x (P 2 ) 2 C (P ) = x P x (P ) 2 50 MW P 600 MW 00 MW P MW 50 MW P 200 MW Each power plant has some min and max generation levels. Communications and Control in Smart Grid Texas Tech University 8

39 Economic Dispatch Problem For thermal power plants, generation cost is quadratic: Generation Cost = C(P) = a + a 2 x P + a x P 2 Example: a grid with three power plants: C (P ) = x P x (P ) 2 C 2 (P 2 ) = x P x (P 2 ) 2 C (P ) = x P x (P ) 2 50 MW P 600 MW 00 MW P MW 50 MW P 200 MW Each power plant has some min and max generation levels. Communications and Control in Smart Grid Texas Tech University 9

40 Economic Dispatch Problem For thermal power plants, generation cost is quadratic: Generation Cost = C(P) = a + a 2 x P + a x P 2 Example: a grid with three power plants: C (P ) = x P x (P ) 2 C 2 (P 2 ) = x P x (P 2 ) 2 C (P ) = x P x (P ) 2 50 MW P 600 MW 00 MW P MW 50 MW P 200 MW Each power plant has some min and max generation levels. Communications and Control in Smart Grid Texas Tech University 40

41 Economic Dispatch Problem For thermal power plants, generation cost is quadratic: Generation Cost = C(P) = a + a 2 x P + a x P 2 Example: a grid with three power plants: C (P ) = x P x (P ) 2 C 2 (P 2 ) = x P x (P 2 ) 2 C (P ) = x P x (P ) 2 50 MW P 600 MW 00 MW P MW 50 MW P 200 MW Each power plant has some min and max generation levels. Communications and Control in Smart Grid Texas Tech University 4

42 Economic Dispatch Problem We should select P, P 2, and P to: Meet total load P load = 850 MW Minimize the total cost of generation Economic Dispatch Problem: minimize P, P2, P subject to C P CP CP 50 P 00 P2 50 P P P P Communications and Control in Smart Grid Texas Tech University 42

43 Economic Dispatch Problem Is the formulated problem a convex program? Why? Convex programs can be solved efficiently. An useful software is CVX for Matlab ( The optimal economic dispatch solution: P = 9.2 MW P 2 = 4.6 MW Q: Do they satisfy all constraints? P = 22.2 MW Communications and Control in Smart Grid Texas Tech University 4

44 Economic Dispatch Problem Is the formulated problem a convex program? Why? Convex programs can be solved efficiently. An useful software is CVX for Matlab ( The optimal economic dispatch solution: P = 9.2 MW P 2 = 4.6 MW P = 22.2 MW Minimum Cost = = 894. Communications and Control in Smart Grid Texas Tech University 44

45 Economic Dispatch Problem What if we have to satisfy topology constraints? P P 2 P MW P 400 MW P P P ( ) Communications and Control in Smart Grid Texas Tech University 45

46 Economic Dispatch Problem The same optimal solutions are still valid: P 9.2 MW P MW MW 4.4 P MW 400 MW P 200 Communications and Control in Smart Grid Texas Tech University 46

47 Economic Dispatch Problem The same optimal solutions are still valid: P 9.2 MW P MW MW 4.4 What if P 70 P MW 400 MW P 200 Communications and Control in Smart Grid Texas Tech University 47

48 Economic Dispatch Problem Then the economic dispatch problem becomes: minimize P, P2, P,, 2, subject to C P CP CP 50 P 00 P2 50 P P P2 P P P Communications and Control in Smart Grid Texas Tech University 48

49 Economic Dispatch Problem Then the economic dispatch problem becomes: minimize P, P2, P,, 2, subject to C P CP CP P P P 2 P P 2 P P P Still a Convex Program? Communications and Control in Smart Grid Texas Tech University 49

50 Economic Dispatch Problem The new optimal solutions are obtained as: P 280 MW P MW MW 60 P MW 400 MW The total generation cost becomes: $8,2.66 > $8,94. Here, we had to sacrifice cost for implementation. Communications and Control in Smart Grid Texas Tech University 50

51 Economic Dispatch Problem The new optimal solutions are obtained as: P 280 MW P MW MW 60 What if P 50 P MW 400 MW The total generation cost becomes: $8,2.66 > $8,94. Here, we had to sacrifice cost for implementation. Communications and Control in Smart Grid Texas Tech University 5

52 Unit Commitment Economic Dispatch is solved a few hours ahead of operation. On the other hand, we need to decide about the choice of power plants that we want to turn on for the next day. This is done by solving the Unit Commitment problem. We particularly decide on which slow starting power plants we should turn on during the next day given various constraints. The mathematical concepts are similar to the E D problem. Communications and Control in Smart Grid Texas Tech University 52

53 References W. J. Wood and. F. Wollenberg, Power Generation, Operation, and Control, John Wiley & Sons, 2 nd Ed., 996. J. McCalley and L. Tesfatsion, "Power Flow Equations", Lecture Notes, EE 458, Department of Electrical and Computer Engineering, Iowa State University, Spring 200. Communications and Control in Smart Grid Texas Tech University 5

Power System review W I L L I A M V. T O R R E A P R I L 1 0, 2 0 1 3

Power System review W I L L I A M V. T O R R E A P R I L 1 0, 2 0 1 3 Power System review W I L L I A M V. T O R R E A P R I L 1 0, 2 0 1 3 Basics of Power systems Network topology Transmission and Distribution Load and Resource Balance Economic Dispatch Steady State System

More information

A progressive method to solve large-scale AC Optimal Power Flow with discrete variables and control of the feasibility

A progressive method to solve large-scale AC Optimal Power Flow with discrete variables and control of the feasibility A progressive method to solve large-scale AC Optimal Power Flow with discrete variables and control of the feasibility Manuel Ruiz, Jean Maeght, Alexandre Marié, Patrick Panciatici and Arnaud Renaud manuel.ruiz@artelys.com

More information

SAMPLE OF THE STUDY MATERIAL PART OF CHAPTER 3. Symmetrical Components & Faults Calculations

SAMPLE OF THE STUDY MATERIAL PART OF CHAPTER 3. Symmetrical Components & Faults Calculations SAMPLE OF THE STUDY MATERIAL PART OF CHAPTER 3 3.0 Introduction Fortescue's work proves that an unbalanced system of 'n' related phasors can be resolved into 'n' systems of balanced phasors called the

More information

SYNCHRONOUS MACHINES

SYNCHRONOUS MACHINES SYNCHRONOUS MACHINES The geometry of a synchronous machine is quite similar to that of the induction machine. The stator core and windings of a three-phase synchronous machine are practically identical

More information

Understanding Power Factor and How it Affects Your Electric Bill. Presented by Scott Peele PE

Understanding Power Factor and How it Affects Your Electric Bill. Presented by Scott Peele PE Understanding Power Factor and How it Affects Your Electric Bill Presented by Scott Peele PE Understanding Power Factor Definitions kva, kvar, kw, Apparent Power vs. True Power Calculations Measurements

More information

Phasors. Phasors. by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department. ^ V cos (wt + θ) ^ V sin (wt + θ)

Phasors. Phasors. by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department. ^ V cos (wt + θ) ^ V sin (wt + θ) V cos (wt θ) V sin (wt θ) by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department EE 209 Fundamentals of Electrical and Electronics Engineering, Prof. Dr. O. SEVAİOĞLU, Page 1 Vector

More information

Topic 2: Introduction to Smart Grid

Topic 2: Introduction to Smart Grid Topic 2: Introduction to Smart Grid Department of Electrical & Computer Engineering Texas Tech University Spring 2012 A.H. Mohsenian Rad (U of T) Networking and Distributed Systems 1 Agenda Smart Grid:

More information

INTRODUCTION TO SYSTEM PROTECTION. Hands-On Relay School 2012

INTRODUCTION TO SYSTEM PROTECTION. Hands-On Relay School 2012 INTRODUCTION TO SYSTEM PROTECTION Hands-On Relay School 2012 CONGRATULATIONS On choosing the field of system protection. It is an exciting, challenging profession. System protection has changed considerably

More information

Weighted-Least-Square(WLS) State Estimation

Weighted-Least-Square(WLS) State Estimation Weighted-Least-Square(WLS) State Estimation Yousu Chen PNNL December 18, 2015 This document is a description of how to formulate the weighted-least squares (WLS) state estimation problem. Most of the formulation

More information

OPTIMAL DISPATCH OF POWER GENERATION SOFTWARE PACKAGE USING MATLAB

OPTIMAL DISPATCH OF POWER GENERATION SOFTWARE PACKAGE USING MATLAB OPTIMAL DISPATCH OF POWER GENERATION SOFTWARE PACKAGE USING MATLAB MUHAMAD FIRDAUS BIN RAMLI UNIVERSITI MALAYSIA PAHANG v ABSTRACT In the reality practical power system, power plants are not at the same

More information

AC Power. by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department

AC Power. by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department EE 209 Fundamentals of Electrical and Electronics Engineering, Prof. Dr. O. SEVAİOĞLU, Page 1 Voltage Waveform Consider the

More information

IMPROVED NETWORK PARAMETER ERROR IDENTIFICATION USING MULTIPLE MEASUREMENT SCANS

IMPROVED NETWORK PARAMETER ERROR IDENTIFICATION USING MULTIPLE MEASUREMENT SCANS IMPROVED NETWORK PARAMETER ERROR IDENTIFICATION USING MULTIPLE MEASUREMENT SCANS Liuxi Zhang and Ali Abur Department of Electrical and Computer Engineering Northeastern University Boston, MA, USA lzhang@ece.neu.edu

More information

Optimal Branch Exchange for Feeder Reconfiguration in Distribution Networks

Optimal Branch Exchange for Feeder Reconfiguration in Distribution Networks Optimal Branch Exchange for Feeder Reconfiguration in Distribution Networks Qiuyu Peng and Steven H. Low Engr. & App. Sci., Caltech, CA Abstract The feeder reconfiguration problem chooses the on/off status

More information

Steady-State Power System Security Analysis with PowerWorld Simulator

Steady-State Power System Security Analysis with PowerWorld Simulator Steady-State Power System Security Analysis with PowerWorld Simulator S: Power System Modeling Methods and Equations 00 South First Street Champaign, Illinois 680 + (7) 384.6330 support@powerworld.com

More information

LAB1 INTRODUCTION TO PSS/E EE 461 Power Systems Colorado State University

LAB1 INTRODUCTION TO PSS/E EE 461 Power Systems Colorado State University LAB1 INTRODUCTION TO PSS/E EE 461 Power Systems Colorado State University PURPOSE: The purpose of this lab is to introduce PSS/E. This lab will introduce the following aspects of PSS/E: Introduction to

More information

Basic Laws Circuit Theorems Methods of Network Analysis Non-Linear Devices and Simulation Models

Basic Laws Circuit Theorems Methods of Network Analysis Non-Linear Devices and Simulation Models EE Modul 1: Electric Circuits Theory Basic Laws Circuit Theorems Methods of Network Analysis Non-Linear Devices and Simulation Models EE Modul 1: Electric Circuits Theory Current, Voltage, Impedance Ohm

More information

Fault Analysis I13-1. 2008 PowerWorld Corporation

Fault Analysis I13-1. 2008 PowerWorld Corporation Fault Analysis Analysis of power system parameters resulting from a ground or line to line fault somewhere in the system Simulator contains a tool for analyzing faults in an automatic fashion Can perform

More information

INTRODUCTION TO HARMONIC ASSESSMENT IN POWER SYSTEMS

INTRODUCTION TO HARMONIC ASSESSMENT IN POWER SYSTEMS INTRODUCTION TO HARMONIC ASSESSMENT IN POWER SYSTEMS LIST OF CONTENT 1. INTRODUCTION... 1 2. HARMONIC VOLTAGE ASSESSMENT REQUIREMENT IN THE UK... 2 3. THE ASSESSMENT... 2 3.1. SYSTEM MODELLING...3 3.2.

More information

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4 - ALTERNATING CURRENT

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4 - ALTERNATING CURRENT EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4 - ALTERNATING CURRENT 4 Understand single-phase alternating current (ac) theory Single phase AC

More information

A Direct Numerical Method for Observability Analysis

A Direct Numerical Method for Observability Analysis IEEE TRANSACTIONS ON POWER SYSTEMS, VOL 15, NO 2, MAY 2000 625 A Direct Numerical Method for Observability Analysis Bei Gou and Ali Abur, Senior Member, IEEE Abstract This paper presents an algebraic method

More information

Chapter 3 AUTOMATIC VOLTAGE CONTROL

Chapter 3 AUTOMATIC VOLTAGE CONTROL Chapter 3 AUTOMATIC VOLTAGE CONTROL . INTRODUCTION TO EXCITATION SYSTEM The basic function of an excitation system is to provide necessary direct current to the field winding of the synchronous generator.

More information

Trigonometry for AC circuits

Trigonometry for AC circuits Trigonometry for AC circuits This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,

More information

Sophomore Physics Laboratory (PH005/105)

Sophomore Physics Laboratory (PH005/105) CALIFORNIA INSTITUTE OF TECHNOLOGY PHYSICS MATHEMATICS AND ASTRONOMY DIVISION Sophomore Physics Laboratory (PH5/15) Analog Electronics Active Filters Copyright c Virgínio de Oliveira Sannibale, 23 (Revision

More information

Load Flow Analysis on IEEE 30 bus System

Load Flow Analysis on IEEE 30 bus System International Journal of Scientific and Research Publications, Volume 2, Issue 11, November 2012 1 Load Flow Analysis on IEEE 30 bus System Dharamjit *, D.K.Tanti ** * Department of Electrical Engineering,

More information

Inductors in AC Circuits

Inductors in AC Circuits Inductors in AC Circuits Name Section Resistors, inductors, and capacitors all have the effect of modifying the size of the current in an AC circuit and the time at which the current reaches its maximum

More information

Circuits with inductors and alternating currents. Chapter 20 #45, 46, 47, 49

Circuits with inductors and alternating currents. Chapter 20 #45, 46, 47, 49 Circuits with inductors and alternating currents Chapter 20 #45, 46, 47, 49 RL circuits Ch. 20 (last section) Symbol for inductor looks like a spring. An inductor is a circuit element that has a large

More information

Transmission Lines. Smith Chart

Transmission Lines. Smith Chart Smith Chart The Smith chart is one of the most useful graphical tools for high frequency circuit applications. The chart provides a clever way to visualize complex functions and it continues to endure

More information

RLC Resonant Circuits

RLC Resonant Circuits C esonant Circuits Andrew McHutchon April 20, 203 Capacitors and Inductors There is a lot of inconsistency when it comes to dealing with reactances of complex components. The format followed in this document

More information

Introduction to PowerWorld Simulator: Interface and Common Tools

Introduction to PowerWorld Simulator: Interface and Common Tools Introduction to PowerWorld Simulator: Interface and Common Tools 2001 South First Street Champaign, Illinois 61820 +1 (217) 384.6330 support@powerworld.com http://www.powerworld.com Fault Analysis Analysis

More information

Equipment: Power Supply, DAI, Variable resistance (8311), Variable inductance (8321)

Equipment: Power Supply, DAI, Variable resistance (8311), Variable inductance (8321) Lab 4: 3-phase circuits. Objective: to study voltage-current relationships in 3-phase circuits; to learn to make delta and Y connections; to calculate and measure real, apparent, and reactive powers. Equipment:

More information

Experiment #11: LRC Circuit (Power Amplifier, Voltage Sensor)

Experiment #11: LRC Circuit (Power Amplifier, Voltage Sensor) Experiment #11: LRC Circuit (Power Amplifier, Voltage Sensor) Concept: circuits Time: 30 m SW Interface: 750 Windows file: RLC.SWS EQUIPMENT NEEDED Science Workshop Interface Power Amplifier (2) Voltage

More information

Voltage Stability Improvement using Static Var Compensator in Power Systems

Voltage Stability Improvement using Static Var Compensator in Power Systems Leonardo Journal of Sciences ISSN 1583-0233 Issue 14, January-June 2009 p. 167-172 Voltage Stability Improvement using Static Var Compensator in Power Systems Department of Electrical/Computer Engineering,

More information

Introduction to Complex Numbers in Physics/Engineering

Introduction to Complex Numbers in Physics/Engineering Introduction to Complex Numbers in Physics/Engineering ference: Mary L. Boas, Mathematical Methods in the Physical Sciences Chapter 2 & 14 George Arfken, Mathematical Methods for Physicists Chapter 6 The

More information

1 Introduction. 2 Power Flow. J.L. Kirtley Jr.

1 Introduction. 2 Power Flow. J.L. Kirtley Jr. Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.061 Introduction to Power Systems Class Notes Chapter 5 Introduction To Load Flow J.L. Kirtley Jr. 1 Introduction

More information

Application Guide. Power Factor Correction (PFC) Basics

Application Guide. Power Factor Correction (PFC) Basics Power Factor Correction (PFC) Basics Introduction Power Factor, in simple terms, is a number between zero and one that represents the ratio of the real power to apparent power. Real power (P), measured

More information

Synchronized real time data: a new foundation for the Electric Power Grid.

Synchronized real time data: a new foundation for the Electric Power Grid. Synchronized real time data: a new foundation for the Electric Power Grid. Pat Kennedy and Chuck Wells Conjecture: Synchronized GPS based data time stamping, high data sampling rates, phasor measurements

More information

Dynamic Security Assessment in the Future Grid. Vijay Vittal Ira A. Fulton Chair Professor Arizona State University

Dynamic Security Assessment in the Future Grid. Vijay Vittal Ira A. Fulton Chair Professor Arizona State University 1 Dynamic Security Assessment in the Future Grid Vijay Vittal Ira A. Fulton Chair Professor Arizona State University 2 Key requirements for DSA Need to perform DSA as close to real time as possible Need

More information

Figure 1. Diode circuit model

Figure 1. Diode circuit model Semiconductor Devices Non-linear Devices Diodes Introduction. The diode is two terminal non linear device whose I-V characteristic besides exhibiting non-linear behavior is also polarity dependent. The

More information

ε: Voltage output of Signal Generator (also called the Source voltage or Applied

ε: Voltage output of Signal Generator (also called the Source voltage or Applied Experiment #10: LR & RC Circuits Frequency Response EQUIPMENT NEEDED Science Workshop Interface Power Amplifier (2) Voltage Sensor graph paper (optional) (3) Patch Cords Decade resistor, capacitor, and

More information

Lecture Notes ELE A6

Lecture Notes ELE A6 ecture Notes EE A6 Ramadan El-Shatshat Three Phase circuits 9/12/2006 EE A6 Three-phase Circuits 1 Three-phase Circuits 9/12/2006 EE A6 Three-phase Circuits 2 Advantages of Three-phase Circuits Smooth

More information

Critical thin-film processes such as deposition and etching take place in a vacuum

Critical thin-film processes such as deposition and etching take place in a vacuum WHITEPAPER INTRODUCING POWER SUPPLIES AND PLASMA Critical thin-film processes such as deposition and etching take place in a vacuum SYSTEMS chamber in the presence of a plasma. A plasma is an electrically

More information

Ver 3537 E1.1 Analysis of Circuits (2014) E1.1 Circuit Analysis. Problem Sheet 1 (Lectures 1 & 2)

Ver 3537 E1.1 Analysis of Circuits (2014) E1.1 Circuit Analysis. Problem Sheet 1 (Lectures 1 & 2) Ver 3537 E. Analysis of Circuits () Key: [A]= easy... [E]=hard E. Circuit Analysis Problem Sheet (Lectures & ). [A] One of the following circuits is a series circuit and the other is a parallel circuit.

More information

PHASOR DIAGRAMS HANDS-ON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER - BPA

PHASOR DIAGRAMS HANDS-ON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER - BPA PHASOR DIAGRAMS HANDS-ON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER - BPA What are phasors??? In normal practice, the phasor represents the rms maximum value of the positive half cycle of the sinusoid

More information

ACADEMIC INTERGRITY POLICY

ACADEMIC INTERGRITY POLICY Western Michigan University, Electrical and Computer Engineering Department ECE 4300/5300 Electric Power Systems (3-0), Spring 2016 Course Information and Policies CRN: 11647-100/14042-100 9:30-10:20 a.m.

More information

Impedance Matching. Using transformers Using matching networks

Impedance Matching. Using transformers Using matching networks Impedance Matching The plasma industry uses process power over a wide range of frequencies: from DC to several gigahertz. A variety of methods are used to couple the process power into the plasma load,

More information

13 ELECTRIC MOTORS. 13.1 Basic Relations

13 ELECTRIC MOTORS. 13.1 Basic Relations 13 ELECTRIC MOTORS Modern underwater vehicles and surface vessels are making increased use of electrical actuators, for all range of tasks including weaponry, control surfaces, and main propulsion. This

More information

Static Analysis of Power Systems. Lennart Söder and Mehrdad Ghandhari

Static Analysis of Power Systems. Lennart Söder and Mehrdad Ghandhari Static Analysis of Power Systems Lennart Söder and Mehrdad Ghandhari Electric Power Systems Royal Institute of Technology August 200 ii Contents Introduction 2 Power system design 3 2. The development

More information

Lecture Notes: ECS 203 Basic Electrical Engineering Semester 1/2010. Dr.Prapun Suksompong 1 June 16, 2010

Lecture Notes: ECS 203 Basic Electrical Engineering Semester 1/2010. Dr.Prapun Suksompong 1 June 16, 2010 Sirindhorn International Institute of Technology Thammasat University School of Information, Computer and Communication Technology Lecture Notes: ECS 203 Basic Electrical Engineering Semester 1/2010 Dr.Prapun

More information

Background: State Estimation

Background: State Estimation State Estimation Cyber Security of the Smart Grid Dr. Deepa Kundur Background: State Estimation University of Toronto Dr. Deepa Kundur (University of Toronto) Cyber Security of the Smart Grid 1 / 81 Dr.

More information

Introduction to the Smith Chart for the MSA Sam Wetterlin 10/12/09 Z +

Introduction to the Smith Chart for the MSA Sam Wetterlin 10/12/09 Z + Introduction to the Smith Chart for the MSA Sam Wetterlin 10/12/09 Quick Review of Reflection Coefficient The Smith chart is a method of graphing reflection coefficients and impedance, and is often useful

More information

UTILITY RATE STRUCTURE

UTILITY RATE STRUCTURE UTILITY RATE STRUCTURE Electricity and Natural Gas Service Residential Commercial Industrial Examples Electricity Use Characteristics Variety of customers with differing use patterns: residential- lighting,

More information

Application of GA for Optimal Location of FACTS Devices for Steady State Voltage Stability Enhancement of Power System

Application of GA for Optimal Location of FACTS Devices for Steady State Voltage Stability Enhancement of Power System I.J. Intelligent Systems and Applications, 2014, 03, 69-75 Published Online February 2014 in MECS (http://www.mecs-press.org/) DOI: 10.5815/ijisa.2014.03.07 Application of GA for Optimal Location of Devices

More information

Chapter 35 Alternating Current Circuits

Chapter 35 Alternating Current Circuits hapter 35 Alternating urrent ircuits ac-ircuits Phasor Diagrams Resistors, apacitors and nductors in ac-ircuits R ac-ircuits ac-ircuit power. Resonance Transformers ac ircuits Alternating currents and

More information

Coupled Inductors. Introducing Coupled Inductors

Coupled Inductors. Introducing Coupled Inductors Coupled Inductors From power distribution across large distances to radio transmissions, coupled inductors are used extensively in electrical applications. Their properties allow for increasing or decreasing

More information

Three phase circuits

Three phase circuits Three phase circuits THREE PHASE CIRCUITS THREE-PHASE ADVANTAGES 1. The horsepower rating of three-phase motors and the kva rating of three-phase transformers are 150% greater than single-phase motors

More information

Control Development and Modeling for Flexible DC Grids in Modelica

Control Development and Modeling for Flexible DC Grids in Modelica Control Development and Modeling for Flexible DC Grids in Modelica Andreas Olenmark 1 Jens Sloth 2 Anna Johnsson 3 Carl Wilhelmsson 3 Jörgen Svensson 4 1 One Nordic AB, Sweden, andreas.olenmark@one-nordic.se.

More information

SIMULATING HYBRID ENERGY GRIDS IN SMART CITIES FOCUS ON ELECTRIC ENERGY SYSTEMS

SIMULATING HYBRID ENERGY GRIDS IN SMART CITIES FOCUS ON ELECTRIC ENERGY SYSTEMS Sawsan Henein AIT Austrian Institute of Technology Electric Energy Systems Research Group SIMULATING HYBRID ENERGY GRIDS IN SMART CITIES FOCUS ON ELECTRIC ENERGY SYSTEMS Sustainable Places 2015 Savona,

More information

Chapter 12: Three Phase Circuits

Chapter 12: Three Phase Circuits Chapter 12: Three Phase Circuits 12.1 What Is a Three Phase Circuit? 12.2 Balance Three Phase Voltages 12.3 Balance Three Phase Y to Y Connection 12.4 Other Balance Three Phase Connections 12.5 Power in

More information

EMC STANDARDS STANDARDS AND STANDARD MAKING BODIES. International. International Electrotechnical Commission (IEC) http://www.iec.

EMC STANDARDS STANDARDS AND STANDARD MAKING BODIES. International. International Electrotechnical Commission (IEC) http://www.iec. EMC STANDARDS The EMC standards that a particular electronic product must meet depend on the product application (commercial or military) and the country in which the product is to be used. These EMC regulatory

More information

EEL303: Power Engineering I - Tutorial 4

EEL303: Power Engineering I - Tutorial 4 1. Determine the voltage at the generating station and the efficiency of the following system (Figure 1): Both transformers have ratio of 2kV/11kV. The resistance on LV side of both Figure 1: transformers

More information

MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS. + + x 2. x n. a 11 a 12 a 1n b 1 a 21 a 22 a 2n b 2 a 31 a 32 a 3n b 3. a m1 a m2 a mn b m

MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS. + + x 2. x n. a 11 a 12 a 1n b 1 a 21 a 22 a 2n b 2 a 31 a 32 a 3n b 3. a m1 a m2 a mn b m MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS 1. SYSTEMS OF EQUATIONS AND MATRICES 1.1. Representation of a linear system. The general system of m equations in n unknowns can be written a 11 x 1 + a 12 x 2 +

More information

Lab 14: 3-phase alternator.

Lab 14: 3-phase alternator. Lab 14: 3-phase alternator. Objective: to obtain the no-load saturation curve of the alternator; to determine the voltage regulation characteristic of the alternator with resistive, capacitive, and inductive

More information

Power Technology Issue 106. Modeling of Three-Winding Voltage Regulating Transformers for Positive Sequence Load Flow Analysis in PSS E

Power Technology Issue 106. Modeling of Three-Winding Voltage Regulating Transformers for Positive Sequence Load Flow Analysis in PSS E SIEMENS Siemens Energy, Inc. Power Technology Issue 106 Modeling of Three-Winding Voltage Regulating Transformers for Positive Sequence Load Flow Analysis in PSS E Carlos Grande-Moran, Ph.D. Principal

More information

Estimation of electrical losses in Network Rail Electrification Systems

Estimation of electrical losses in Network Rail Electrification Systems Estimation of electrical losses in Network Rail Electrification Systems Page 1 of 16 Contents 1. BACKGROUND...3 2. PURPOSE...3 3. SCOPE...3 4. DEFINITIONS & ABBREVIATIONS...4 5. NETWORK RAIL INFRASTRUCTURE

More information

Modeling of Transmission Lines

Modeling of Transmission Lines Modeling of Transmission Lines Electric Power Transmission The electric energy produced at generating stations is transported over high-voltage transmission lines to utilization points. The trend toward

More information

THE PER-UNIT SYSTEM. (2) The per-unit values for various components lie within a narrow range regardless of the equipment rating.

THE PER-UNIT SYSTEM. (2) The per-unit values for various components lie within a narrow range regardless of the equipment rating. THE PER-UNIT SYSTEM An interconnected power system typically consists of many different voltage levels given a system containing several transformers and/or rotating machines. The per-unit system simplifies

More information

Typical Data Requirements Data Required for Power System Evaluation

Typical Data Requirements Data Required for Power System Evaluation Summary 66 Carey Road Queensbury, NY 12804 Ph: (518) 792-4776 Fax: (518) 792-5767 www.nepsi.com sales@nepsi.com Harmonic Filter & Power Capacitor Bank Application Studies This document describes NEPSI

More information

Lecture - 4 Diode Rectifier Circuits

Lecture - 4 Diode Rectifier Circuits Basic Electronics (Module 1 Semiconductor Diodes) Dr. Chitralekha Mahanta Department of Electronics and Communication Engineering Indian Institute of Technology, Guwahati Lecture - 4 Diode Rectifier Circuits

More information

ADMS(Advanced Distribution Management System ) in Smart Grid

ADMS(Advanced Distribution Management System ) in Smart Grid ADMS(Advanced Distribution Management System ) in Smart Grid 柯 佾 寬 博 士 Yi-Kuan Ke, Ph.D. 2014/03/28 Smart Grid Solution Smart Grid Solution Overview Smart Grid Solutions Smart Network Operation - Distribution

More information

MAC 1114. Learning Objectives. Module 10. Polar Form of Complex Numbers. There are two major topics in this module:

MAC 1114. Learning Objectives. Module 10. Polar Form of Complex Numbers. There are two major topics in this module: MAC 1114 Module 10 Polar Form of Complex Numbers Learning Objectives Upon completing this module, you should be able to: 1. Identify and simplify imaginary and complex numbers. 2. Add and subtract complex

More information

Power Technology Issue 104. Modeling of Two-Winding Voltage Regulating Transformers for Positive Sequence Load Flow Analysis in PSS E

Power Technology Issue 104. Modeling of Two-Winding Voltage Regulating Transformers for Positive Sequence Load Flow Analysis in PSS E SIEMENS Siemens Energy, Inc. Power Technology Issue 104 Modeling of TwoWinding Voltage Regulating Transformers for Positive Sequence Load Flow Analysis in PSS E Carlos GrandeMoran, Ph.D. Principal Consultant

More information

CHAPTER 3 SECURITY CONSTRAINED OPTIMAL SHORT-TERM HYDROTHERMAL SCHEDULING

CHAPTER 3 SECURITY CONSTRAINED OPTIMAL SHORT-TERM HYDROTHERMAL SCHEDULING 60 CHAPTER 3 SECURITY CONSTRAINED OPTIMAL SHORT-TERM HYDROTHERMAL SCHEDULING 3.1 INTRODUCTION Optimal short-term hydrothermal scheduling of power systems aims at determining optimal hydro and thermal generations

More information

Series and Parallel Circuits

Series and Parallel Circuits Direct Current (DC) Direct current (DC) is the unidirectional flow of electric charge. The term DC is used to refer to power systems that use refer to the constant (not changing with time), mean (average)

More information

Linear Programming Notes V Problem Transformations

Linear Programming Notes V Problem Transformations Linear Programming Notes V Problem Transformations 1 Introduction Any linear programming problem can be rewritten in either of two standard forms. In the first form, the objective is to maximize, the material

More information

MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS

MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS Systems of Equations and Matrices Representation of a linear system The general system of m equations in n unknowns can be written a x + a 2 x 2 + + a n x n b a

More information

CIRCUITS LABORATORY EXPERIMENT 3. AC Circuit Analysis

CIRCUITS LABORATORY EXPERIMENT 3. AC Circuit Analysis CIRCUITS LABORATORY EXPERIMENT 3 AC Circuit Analysis 3.1 Introduction The steady-state behavior of circuits energized by sinusoidal sources is an important area of study for several reasons. First, the

More information

Chapter 29 Alternating-Current Circuits

Chapter 29 Alternating-Current Circuits hapter 9 Alternating-urrent ircuits onceptual Problems A coil in an ac generator rotates at 6 Hz. How much time elapses between successive emf values of the coil? Determine the oncept Successive s are

More information

Frequency response: Resonance, Bandwidth, Q factor

Frequency response: Resonance, Bandwidth, Q factor Frequency response: esonance, Bandwidth, Q factor esonance. Let s continue the exploration of the frequency response of circuits by investigating the series circuit shown on Figure. C + V - Figure The

More information

Lecture 7 Circuit analysis via Laplace transform

Lecture 7 Circuit analysis via Laplace transform S. Boyd EE12 Lecture 7 Circuit analysis via Laplace transform analysis of general LRC circuits impedance and admittance descriptions natural and forced response circuit analysis with impedances natural

More information

Advanced Protection of Distribution Networks with Distributed Generators

Advanced Protection of Distribution Networks with Distributed Generators Date:- 8 10 March 2011 Venue: University of Manchester EES-UETP Course title Advanced Protection of Distribution Networks with Distributed Generators Peter Crossley Director of the Joule Centre School

More information

Motor Efficiency and Power Factor ME 416/516

Motor Efficiency and Power Factor ME 416/516 Motor Efficiency and Power Factor Motivation More than half of all electric energy generated goes to power electric motors. Electric motor converts electric power into shaft power. In thermodynamics terms,

More information

System Protection Schemes in Eastern Denmark

System Protection Schemes in Eastern Denmark System Protection Schemes in Eastern Denmark Joana Rasmussen COWI A/S, Energy Department System Protection Schemes in Eastern Denmark 1.Advanced system protection schemes are investigated and perspectives

More information

Lecture 3. Linear Programming. 3B1B Optimization Michaelmas 2015 A. Zisserman. Extreme solutions. Simplex method. Interior point method

Lecture 3. Linear Programming. 3B1B Optimization Michaelmas 2015 A. Zisserman. Extreme solutions. Simplex method. Interior point method Lecture 3 3B1B Optimization Michaelmas 2015 A. Zisserman Linear Programming Extreme solutions Simplex method Interior point method Integer programming and relaxation The Optimization Tree Linear Programming

More information

DOKUZ EYLUL UNIVERSITY FACULTY OF ENGINEERING OFFICE OF THE DEAN COURSE / MODULE / BLOCK DETAILS ACADEMIC YEAR / SEMESTER. Course Code: EEE 2073

DOKUZ EYLUL UNIVERSITY FACULTY OF ENGINEERING OFFICE OF THE DEAN COURSE / MODULE / BLOCK DETAILS ACADEMIC YEAR / SEMESTER. Course Code: EEE 2073 Offered by: Elektrik-Elektronik Mühendisliği Course Title: FUNDAMENTALS OF ELECTRIC AND ELECTRONICS Course Org. Title: FUNDAMENTALS OF ELECTRIC AND ELECTRONICS Course Level: Lisans Course Code: EEE 07

More information

NETWORK RECONFIGURATION FOR LOSS REDUCTION IN THREE-PHASE POWER DISTRIBUTION SYSTEMS

NETWORK RECONFIGURATION FOR LOSS REDUCTION IN THREE-PHASE POWER DISTRIBUTION SYSTEMS NETWORK RECONFIGURATION FOR LOSS REDUCTION IN THREE-PHASE POWER DISTRIBUTION SYSTEMS A Thesis Presented to the Faculty of the Graduate School of Cornell University in Partial Fulfillment of the Requirements

More information

Chapter 24. Three-Phase Voltage Generation

Chapter 24. Three-Phase Voltage Generation Chapter 24 Three-Phase Systems Three-Phase Voltage Generation Three-phase generators Three sets of windings and produce three ac voltages Windings are placed 120 apart Voltages are three identical sinusoidal

More information

AN ULTRA-CHEAP GRID CONNECTED INVERTER FOR SMALL SCALE GRID CONNECTION

AN ULTRA-CHEAP GRID CONNECTED INVERTER FOR SMALL SCALE GRID CONNECTION AN ULTRA-CHEAP GRID CONNECTED INVERTER FOR SMALL SCALE GRID CONNECTION Pramod Ghimire 1, Dr. Alan R. Wood 2 1 ME Candidate Email: pgh56@student.canterbury.ac.nz 2 Senior Lecturer: Canterbury University

More information

Alternating Current and Direct Current

Alternating Current and Direct Current K Hinds 2012 1 Alternating Current and Direct Current Direct Current This is a Current or Voltage which has a constant polarity. That is, either a positive or negative value. K Hinds 2012 2 Alternating

More information

DHANALAKSHMI COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING EE2302 - ELECTRICAL MACHINES II UNIT-I SYNCHRONOUS GENERATOR

DHANALAKSHMI COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING EE2302 - ELECTRICAL MACHINES II UNIT-I SYNCHRONOUS GENERATOR 1 DHANALAKSHMI COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING Constructional details Types of rotors EE2302 - ELECTRICAL MACHINES II UNIT-I SYNCHRONOUS GENERATOR PART A 1.

More information

Supplement Reading on Diode Circuits. http://www.inst.eecs.berkeley.edu/ edu/~ee40/fa09/handouts/ee40_mos_circuit.pdf

Supplement Reading on Diode Circuits. http://www.inst.eecs.berkeley.edu/ edu/~ee40/fa09/handouts/ee40_mos_circuit.pdf EE40 Lec 18 Diode Circuits Reading: Chap. 10 of Hambley Supplement Reading on Diode Circuits http://www.inst.eecs.berkeley.edu/ edu/~ee40/fa09/handouts/ee40_mos_circuit.pdf Slide 1 Diodes Circuits Load

More information

Email: mod_modaber@yahoo.com. 2Azerbaijan Shahid Madani University. This paper is extracted from the M.Sc. Thesis

Email: mod_modaber@yahoo.com. 2Azerbaijan Shahid Madani University. This paper is extracted from the M.Sc. Thesis Introduce an Optimal Pricing Strategy Using the Parameter of "Contingency Analysis" Neplan Software in the Power Market Case Study (Azerbaijan Electricity Network) ABSTRACT Jalil Modabe 1, Navid Taghizadegan

More information

Full representation of the real transformer

Full representation of the real transformer TRASFORMERS EQVALET CRCT OF TWO-WDG TRASFORMER TR- Dots show the points of higher potential. There are applied following conventions of arrow directions: -for primary circuit -the passive sign convention

More information

ANALYTICAL METHODS FOR ENGINEERS

ANALYTICAL METHODS FOR ENGINEERS UNIT 1: Unit code: QCF Level: 4 Credit value: 15 ANALYTICAL METHODS FOR ENGINEERS A/601/1401 OUTCOME - TRIGONOMETRIC METHODS TUTORIAL 1 SINUSOIDAL FUNCTION Be able to analyse and model engineering situations

More information

Sensitivity Analysis of Waveform Distortion Assessment for Wind Plants

Sensitivity Analysis of Waveform Distortion Assessment for Wind Plants Sensitivity Analysis of Waveform Distortion Assessment for Wind Plants Mariana B. Pereira 1, Einar V. Larsen 2, Sebastian A. Achilles 3 Energy Consulting General Electric 1 Av. Magalhães de Castro 4800,

More information

Impedance Matching and Matching Networks. Valentin Todorow, December, 2009

Impedance Matching and Matching Networks. Valentin Todorow, December, 2009 Impedance Matching and Matching Networks Valentin Todorow, December, 2009 RF for Plasma Processing - Definition of RF What is RF? The IEEE Standard Dictionary of Electrical and Electronics Terms defines

More information

Fast analytical techniques for electrical and electronic circuits. Jet Propulsion Laboratory California Institute of Technology

Fast analytical techniques for electrical and electronic circuits. Jet Propulsion Laboratory California Institute of Technology Fast analytical techniques for electrical and electronic circuits Vatché Vorpérian Jet Propulsion Laboratory California Institute of Technology PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE

More information

ASEN 3112 - Structures. MDOF Dynamic Systems. ASEN 3112 Lecture 1 Slide 1

ASEN 3112 - Structures. MDOF Dynamic Systems. ASEN 3112 Lecture 1 Slide 1 19 MDOF Dynamic Systems ASEN 3112 Lecture 1 Slide 1 A Two-DOF Mass-Spring-Dashpot Dynamic System Consider the lumped-parameter, mass-spring-dashpot dynamic system shown in the Figure. It has two point

More information

Slide 1 / 26. Inductance. 2011 by Bryan Pflueger

Slide 1 / 26. Inductance. 2011 by Bryan Pflueger Slide 1 / 26 Inductance 2011 by Bryan Pflueger Slide 2 / 26 Mutual Inductance If two coils of wire are placed near each other and have a current passing through them, they will each induce an emf on one

More information

Lab 7: Operational Amplifiers Part I

Lab 7: Operational Amplifiers Part I Lab 7: Operational Amplifiers Part I Objectives The objective of this lab is to study operational amplifier (op amp) and its applications. We will be simulating and building some basic op amp circuits,

More information