Phasor Measurement Unit
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About the Phasor Pathways in Analogical Amplitude Modulations
About the Phasor Pathways in Analogical Amplitude Modulations H.M. de Oliveira1, F.D. Nunes1 ABSTRACT Phasor diagrams have long been used in Physics and Engineering. In telecommunications, this is particularly useful to clarify how the modulations work. This paper addresses rotating phasor pathways derived from different standard Amplitude Modulation Systems (e.g. A3E, H3E, J3E, C3F). A cornucopia of algebraic curves is then derived assuming a single tone or a double tone modulation signal. The ratio of the frequency of the tone modulator (fm) and carrier frequency (fc) is considered in two distinct cases, namely: fm/fc<1 and fm/fc 1. The geometric figures are some sort of Lissajours figures. Different shapes appear looking like epicycloids (including cardioids), rhodonea curves, Lemniscates, folium of Descartes or Lamé curves. The role played by the modulation index is elucidated in each case. Keyterms: Phasor diagram, AM, VSB, Circular harmonics, algebraic curves, geometric figures. 1. Introduction Classical analogical modulations are a nearly exhausted subject, a century after its introduction. The first approach to the subject typically relies on the case of transmission of a single tone (for the sake of simplicity) and establishes the corresponding phasor diagram. This furnishes a straightforward interpretation, which is quite valuable, especially with regard to illustrating the effects of the modulation index, overmodulation effects, and afterward, distinctions between AM and NBFM. Often this presentation is rather naïf. Nice applets do exist to help the understanding of the phasor diagram [1- 4]. However ... Without further target, unpretentiously, we start a deeper investigating the dynamic phasor diagram with the aim of building applets or animations that illustrates the temporal variation of the magnitude of the amplitude modulated phasor. -
Correspondence Between Phasor Transforms and Frequency Response Function in Rlc Circuits
CORRESPONDENCE BETWEEN PHASOR TRANSFORMS AND FREQUENCY RESPONSE FUNCTION IN RLC CIRCUITS Hassan Mohamed Abdelalim Abdalla Polytechnic Department of Engineering and Architecture, University of Studies of Udine, 33100 Udine, Italy. E-mail: [email protected] Abstract: The analysis of RLC circuits is usually made by considering phasor transforms of sinusoidal signals (characterized by constant amplitude, period and phase) that allow the calculation of the AC steady state of RLC circuits by solving simple algebraic equations. In this paper I try to show that phasor representation of RLC circuits is analogue to consider the frequency response function (commonly designated by FRF) of the total impedance of the circuit. In this way I derive accurate expressions for the resonance and anti-resonance frequencies and their corresponding values of impedances of the parallel and series RLC circuits respectively, notwithstanding the presence of damping effects. Keywords: Laplace transforms, phasors, Frequency response function, RLC circuits. 1. Introduction and mathematical background RLC circuits have many applications as oscillator circuits described by a second-order differential equation. The three circuit elements, resistor R, inductor L and capacitor C can be combined in different manners. All three elements in series or in parallel are the simplest and most straightforward to analyze. RLC circuits are analyzed mathematically in the phasor domain instead of solving differential equations in the time domain. Generally, a time-dependent sinusoidal function is expressed in the following way è [1]: () (1.1) where is the amplitude, is the angular frequency and is the initial phase of . () = sin ( + ) The medium value of is given by: () () (1.2) 1 2 = |()| = where is the period of the sinusoidal function . -
Complex Numbers and Phasor Technique
RaoApp-Av3.qxd 12/18/03 5:44 PM Page 779 APPENDIX A Complex Numbers and Phasor Technique In this appendix, we discuss a mathematical technique known as the phasor technique, pertinent to operations involving sinusoidally time-varying quanti- ties.The technique simplifies the solution of a differential equation in which the steady-state response for a sinusoidally time-varying excitation is to be deter- mined, by reducing the differential equation to an algebraic equation involving phasors. A phasor is a complex number or a complex variable. We first review complex numbers and associated operations. A complex number has two parts: a real part and an imaginary part. Imag- inary numbers are square roots of negative real numbers. To introduce the con- cept of an imaginary number, we define 2-1 = j (A.1a) or ;j 2 =-1 (A.1b) 1 2 Thus, j5 is the positive square root of -25, -j10 is the negative square root of -100, and so on.A complex number is written in the form a + jb, where a is the real part and b is the imaginary part. Examples are 3 + j4 -4 + j1 -2 - j2 2 - j3 A complex number is represented graphically in a complex plane by using Rectangular two orthogonal axes, corresponding to the real and imaginary parts, as shown in form Fig.A.1, in which are plotted the numbers just listed. Since the set of orthogonal axes resembles the rectangular coordinate axes, the representation a + jb is 1 2 known as the rectangular form. 779 RaoApp-Av3.qxd 12/18/03 5:44 PM Page 780 780 Appendix A Complex Numbers and Phasor Technique Imaginary (3 ϩ j4) 4 (Ϫ4 ϩ j1) 1 Ϫ2 2 Ϫ 4 0 3 Real Ϫ2 (Ϫ2 Ϫj2) Ϫ3 Ϫ FIGURE A.1 (2 j3) Graphical representation of complex numbers in rectangular form. -
Lesson 1: Representation of Ac Voltages and Currents1
1/22/2016 Lesson 1: Phasors and Complex Arithmetic ET 332b Ac Motors, Generators and Power Systems lesson1_et332b.pptx 1 Learning Objectives After this presentation you will be able to: Write time equations that represent sinusoidal voltages and currents found in power systems. Explain the difference between peak and RMS electrical quantities. Write phasor representations of sinusoidal time equations. Perform calculations using both polar and rectangular forms of complex numbers. lesson1_et332b.pptx 2 1 1/22/2016 Ac Analysis Techniques Time function representation of ac signals Time functions give representation of sign instantaneous values v(t) Vmax sin(t v ) Voltage drops e(t) Emax sin(t e ) Source voltages Currents i(t) Imax sin(t i ) Where Vmax = maximum ( peak) value of voltage Emax = maximum (peak) value of source voltage Imax = maximum (peak) value of current v, e, i = phase shift of voltage or current = frequency in rad/sec Note: =2pf lesson1_et332b.pptx 3 Ac Signal Representations Ac power system calculations use effective values of time waveforms (RMS values) Therefore: V E I V max E max I max RMS 2 RMS 2 RMS 2 1 Where 0.707 2 So RMS quantities can be expressed as: VRMS 0.707Vmax ERMS 0.707Emax IRMS 0.707Imax lesson1_et332b.pptx 4 2 1/22/2016 Ac Signal Representations Ac power systems calculations use phasors to represent time functions Phasor use complex numbers to represent the important information from the time functions (magnitude and phase angle) in vector form. Phasor Notation I I V VRMS RMS or or I I V VRMS RMS Where: VRMS, IRMS = RMS magnitude of voltages and currents = phase shift in degrees for voltages and currents lesson1_et332b.pptx 5 Ac Signal Representations Time to phasor conversion examples, Note all signal must be the same frequency Time function-voltage Find RMS magnitude v(t) 170sin(377t 30 ) VRMS 0.707170 120.2 V Phasor V 120.230 V Time function-current Find RMS magnitude i(t) 25sin(377t 20 ) IRMS 0.70725 17.7 A Phasor I 17.7 20 A Phase shift can be given in either radians or degrees. -
Waveguide Propagation
NTNU Institutt for elektronikk og telekommunikasjon Januar 2006 Waveguide propagation Helge Engan Contents 1 Introduction ........................................................................................................................ 2 2 Propagation in waveguides, general relations .................................................................... 2 2.1 TEM waves ................................................................................................................ 7 2.2 TE waves .................................................................................................................... 9 2.3 TM waves ................................................................................................................. 14 3 TE modes in metallic waveguides ................................................................................... 14 3.1 TE modes in a parallel-plate waveguide .................................................................. 14 3.1.1 Mathematical analysis ...................................................................................... 15 3.1.2 Physical interpretation ..................................................................................... 17 3.1.3 Velocities ......................................................................................................... 19 3.1.4 Fields ................................................................................................................ 21 3.2 TE modes in rectangular waveguides ..................................................................... -
Fall 2017 Commencement Program
TE TA UN S E ST TH AT I F E V A O O E L F A DITAT DEUS N A E R R S I O Z T S O A N Z E I A R I T G R Y A 1912 1885 ARIZONA STATE UNIVERSITY COMMENCEMENT AND CONVOCATION PROGRAM Fall 2017 December 11-13, 2017 THE NATIONAL ANTHEM THE STAR-SPANGLED BANNER O say can you see, by the dawn’s early light, What so proudly we hailed at the twilight’s last gleaming? Whose broad stripes and bright stars through the perilous fight O’er the ramparts we watched, were so gallantly streaming? And the rockets’ red glare, the bombs bursting in air Gave proof through the night that our flag was still there. O say does that Star-Spangled Banner yet wave O’er the land of the free and the home of the brave? ALMA MATER ARIZONA STATE UNIVERSITY Where the bold saguaros Raise their arms on high, Praying strength for brave tomorrows From the western sky; Where eternal mountains Kneel at sunset’s gate, Here we hail thee, Alma Mater, Arizona State. —Hopkins-Dresskell MAROON AND GOLD Fight, Devils down the field Fight with your might and don’t ever yield Long may our colors outshine all others Echo from the buttes, Give em’ hell Devils! Cheer, cheer for A-S-U! Fight for the old Maroon For it’s Hail! Hail! The gang’s all here And it’s onward to victory! Students whose names appear in this program have completed degree requirements. -
Chapter 16 Waves I
Chapter 16 Waves I In this chapter we will start the discussion on wave phenomena. We will study the following topics: Types of waves Amplitude, phase, frequency, period, propagation speed of a wave Mechanical waves propagating along a stretched string Wave equation Principle of superposition of waves Wave interference Standing waves, resonance (16 – 1) A wave is defined as a disturbance that is self-sustained and propagates in space with a constant speed Waves can be classified in the following three categories: 1. Mechanical waves. These involve motions that are governed by Newton’s laws and can exist only within a material medium such as air, water, rock, etc. Common examples are: sound waves, seismic waves, etc. 2. Electromagnetic waves. These waves involve propagating disturbances in the electric and magnetic field governed by Maxwell’s equations. They do not require a material medium in which to propagate but they travel through vacuum. Common examples are: radio waves of all types, visible, infra-red, and ultra- violet light, x-rays, gamma rays. All electromagnetic waves propagate in vacuum with the same speed c = 300,000 km/s 3. Matter waves. All microscopic particles such as electrons, protons, neutrons, atoms etc have a wave associated with them governed by Schroedinger’s equation. (16 – 2) Transverse and Longitudinal waves (16 – 3) Waves can be divided into the following two categories depending on the orientation of the disturbance with r respect to the wave propagation velocity v. If the disturbance associated with a particular wave is perpendicular to the wave propagation velocity, this wave is called "transverse ". -
Coordination of Wind and Hydro Power Plant by Using Optimization Technique
ISSN (Online) : 2319 - 8753 ISSN (Print) : 2347 - 6710 International Journal of Innovative Research in Science, Engineering and Technology An ISO 3297: 2007 Certified Organization Volume 6, Special Issue 14, August 2017 Two Days National Conference on Modernization in Engineering Science (NCMES 2K17) 23rd-24th March 2017 Organized by Dept. of EEE, Sri Krishna College of Engineering & Technology, Coimbatore 641 008, Tamil Nadu, India Coordination of Wind and Hydro Power Plant by Using Optimization Technique P.Ranjithkumar1, Saravana Prabaakar1 , M.Suganya2, Niranjana B2 UG Scholar, Department of EEE, SKCET, Coimbatore-641008, Tamil Nadu, India1 Assistant Professor, Department of EEE, SKCET, Coimbatore-641008, Tamil Nadu, India2 ABSTRACT: Wind power production experiences new challenges in operation of a power system due to its variability and uncertainty of the wind. The challenges can be met when we introduce a new storage facility which was already available in the existing power system. Existing hydro power plants with larger reservoirs or pumped storage hydro power plants can be used for compensation of this drawback. It is known that wind power is an uncertain energy source compared to hydroelectric generation which is easily scheduled. In this abstract, the method for coordinating wind power plant and hydroelectric power plant is carried out by using Fourier transform technique to measure and control the state of wind and hydro power plants. Hydroelectric generation is employed as a method of energy reserve and compensation for wind power fluctuation in order to provide efficient power supply to benefit wind providers. The Fourier technique, which is generally used for relation of periodic functions like sine and cosine waves, is used here for the purpose of co-ordination. -
5 Application of Phasor Measurement Unit in Smart Grid.Pdf
PRATIBHA: INTERNATIONAL JOURNAL OF SCIENCE, SPIRITUALITY, BUSINESS AND TECHNOLOGY (IJSSBT), Vol. 1, No.2, FEBRUARY 2013 ISSN (Print) 2277—7261 APPLICATION OF PHASOR MEASUREMENT UNIT IN SMART GRID 1Chandarani Sutar, 2Dr. K. S. Verma 1RRSIMT Amethi (U.P.), 2KNIT Sultapur (U.P.) Email: [email protected], 2 [email protected] , Abstract-A smart Grid uses two way digital for intelligent linkages between the elements of the communication with advanced sensors to collect grid while participating in the decision making that and analyze data for transforming the existing delivers value to the utility and supply and demand electric grid into intelligent, dynamic self- entities connected to it. healing, self optimizing transmission and distribution grid . As critical grid events often II. ADVANTAGES OF SMART GRID require real-time recognition and real time i) Enables active participation by of consumers by response .A smart grid uses IP-based ,open providing choices and incentives to modify standard, intelligent communication to electricity purchasing patterns and behavior. measure real-time events such as congestion ii) Autonomous control actions to enhance ,system stability ,equipment performance, reliability by increasing resiliency against outages and demand response events . component failures and natural disasters actions. Synchrophasor measurement technology is iii) Efficiency enhancement by maximizing asset accurate and real-time monitoring with high utilization. resolution of actual system conditions in wide iv) Resiliency against malicious attacks by virtue area . of better physical and IT security protocols. The proposed methods has been verified, v) Integration of renewable resources including compared and studied using PSAT Software solar, wind, and various types of energy storage. -
PMU)-Like Metering for Behind-The-Meter (BTM) Solar Systems Using Blockchain- Assisted Smart Inverters Preprint Abdullah A
Secure and Cost-Effective Micro Phasor Measurement Unit (PMU)-Like Metering for Behind-the-Meter (BTM) Solar Systems Using Blockchain- Assisted Smart Inverters Preprint Abdullah A. Hadi,1 Gomanth Bere,1 Taesic Kim,1 Justin J. Ochoa,1 Jianwu Zeng,2 and Gab-Su Seo3 1 Texas A&M University-Kingsville 2 Minnesota State University 3 National Renewable Energy Laboratory Presented at the 2020 IEEE Applied Power Electronics Conference and Exposition (IEEE APEC) New Orleans, Louisiana March 15–19, 2020 NREL is a national laboratory of the U.S. Department of Energy Conference Paper Office of Energy Efficiency & Renewable Energy NREL/CP-5D00-75447 Operated by the Alliance for Sustainable Energy, LLC March 2020 This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. Contract No. DE-AC36-08GO28308 Secure and Cost-Effective Micro Phasor Measurement Unit (PMU)-Like Metering for Behind-the-Meter (BTM) Solar Systems Using Blockchain- Assisted Smart Inverters Preprint Abdullah A. Hadi,1 Gomanth Bere,1 Taesic Kim,1 Justin J. Ochoa,1 Jianwu Zeng,2 and Gab-Su Seo3 1 Texas A&M University-Kingsville 2 Minnesota State University 3 National Renewable Energy Laboratory Suggested Citation Hadi, Abdullah A., Gomanth Bere, Taesic Kim, Justin J. Ochoa, Jianwu Zeng, and Gab-Su Seo. 2020. Secure and Cost-Effective Micro Phasor Measurement Unit (PMU)-Like Metering for Behind-the-Meter (BTM) Solar Systems Using Blockchain-Assisted Smart Inverters: Preprint. Golden, CO: National Renewable Energy Laboratory. NREL/CP-5D00- 75447. https://www.nrel.gov/docs/fy20osti/75447.pdf. © 2020 IEEE. -
Synchrophasor Based Islanding & Open Phase Fault Protection In
Western University Scholarship@Western Electronic Thesis and Dissertation Repository 2-24-2020 11:00 AM Synchrophasor Based Islanding & Open phase fault Protection in Distribution Systems Mansour Jalali The University of Western Ontario Supervisor Tarlochan Sidhu The University of Western Ontario Graduate Program in Electrical and Computer Engineering A thesis submitted in partial fulfillment of the equirr ements for the degree in Doctor of Philosophy © Mansour Jalali 2020 Follow this and additional works at: https://ir.lib.uwo.ca/etd Part of the Power and Energy Commons, and the Systems and Communications Commons Recommended Citation Jalali, Mansour, "Synchrophasor Based Islanding & Open phase fault Protection in Distribution Systems" (2020). Electronic Thesis and Dissertation Repository. 6947. https://ir.lib.uwo.ca/etd/6947 This Dissertation/Thesis is brought to you for free and open access by Scholarship@Western. It has been accepted for inclusion in Electronic Thesis and Dissertation Repository by an authorized administrator of Scholarship@Western. For more information, please contact [email protected]. Abstract With the rapid growth of renewable energy resources, energy efficiency initiatives, electric vehicles, energy storage, etc., distribution systems are becoming more complex such that conventional protection, control, and measurement infrastructure – typically concentrated at the main substation, with little to no access to information along the feeder – cannot maintain the reliability of the system without some sort of additional protection, control and measurement functionalities. As an example, a dedicated communication channel for carrying the transfer trip signal from the substation to the Point of Common Coupling (PCC) to prevent islanding operation of alternative resources, has been a requirement for many utilities. -
A Comparative Study on Phasor and Frequency Measurement Techniques in Power Systems
A Comparative Study on Phasor and Frequency Measurement Techniques in Power Systems Aravinth Sridharan Vaskar Sarkar Department of Electrical Engineering Department of Electrical Engineering Indian Institute of Technology Hyderabad Indian Institute of Technology Hyderabad E-mail: [email protected] E-mail: [email protected] Abstract—The objective of this paper is to make a comparative to slow function like expansion planning. Hence, the real- study on different phasor and frequency measurement algorithms time measurement of power system quantities is helpful in available for power systems. The dynamic nature of the power improving the reliability of the power system network. With system signals has made the estimation of frequency and phasors difficult. Over the years, many digital algorithms have been an increase in the usage of power electronic devices and other developed to overcome these difficulties and to provide accurate nonlinear components, there is an increase in the harmonic real-time frequency and phasor measurements. In this paper, four contamination in power systems. It is, therefore, essential for different algorithms for frequency estimation and three different utilities to seek and depend on reliable models for accurate algorithms for phasor estimation are studied and compared. A estimation of phasor and frequency. Supervisory Control and case study is performed by considering a three-phase voltage signal with time-varying amplitude and frequency to verify the Data Acquisition (SCADA) is an existing real-time monitoring effectiveness of these estimation algorithms. and control system that is available for power systems. Due Index Terms—Amplitude, complex valued least squares, dis- to high latency in data flow and slower estimation techniques crete fourier transform, frequency, phase angle, phase locked used, the real-time dynamic variations in power system quan- loop, phasor, polynomial fitting, prony, smart discrete fourier tities are not observed by SCADA.