Glossary of Terms Used in NERC Reliability Standards Updated June 28, 2021
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Operating Reserves
TECHNICAL AND MARKET ISSUES FOR OPERATING RESERVES Eric Hirst and Brendan Kirby Consulting in Electric-Industry Restructuring Oak Ridge, Tennessee October 19, 1998 INTRODUCTION Ancillary services matter! That’s the key lesson to learn from the problems faced by the California Independent System Operator (ISO) during the summer of 1998. And California will not be alone. Unless ISO New England changes its market rules, it, too, will face serious problems in the acquisition, pricing, and costs of ancillary services. These problems arose (and will continue to occur) because the electricity industry as a whole does not yet recognize the technical and market importance of ancillary services. These services are, like transmission, essential for both reliability and commercial functions. Because most of these services are provided by the same pieces of equipment (generators) that produce energy, the energy and ancillary services markets are tightly coupled. Problems in one market will, unavoidably, cause problems in other markets. Poorly designed rules can amplify the problems from one market to the next. This paper uses operating reserves as an example to illustrate these issues, problems, and possible solutions. Electricity is the ultimate “real-time” product, with its production, transportation, and consumption occurring within a fraction of a second. Because electricity moves at nearly the speed of light and cannot be readily stored, bulk-power systems must maintain a continuous and near-instantaneous balance between production and consumption. Operating reserves are the ancillary services that maintain this balance when a major generator or transmission line unexpectedly fails. DEFINITION The utility industry understands well the technical requirements for operating reserves because the service has been an important part of operating power systems for decades (Hirst and Kirby 1997 and 1998). -
Completeness in Quasi-Pseudometric Spaces—A Survey
mathematics Article Completeness in Quasi-Pseudometric Spaces—A Survey ¸StefanCobzas Faculty of Mathematics and Computer Science, Babe¸s-BolyaiUniversity, 400 084 Cluj-Napoca, Romania; [email protected] Received:17 June 2020; Accepted: 24 July 2020; Published: 3 August 2020 Abstract: The aim of this paper is to discuss the relations between various notions of sequential completeness and the corresponding notions of completeness by nets or by filters in the setting of quasi-metric spaces. We propose a new definition of right K-Cauchy net in a quasi-metric space for which the corresponding completeness is equivalent to the sequential completeness. In this way we complete some results of R. A. Stoltenberg, Proc. London Math. Soc. 17 (1967), 226–240, and V. Gregori and J. Ferrer, Proc. Lond. Math. Soc., III Ser., 49 (1984), 36. A discussion on nets defined over ordered or pre-ordered directed sets is also included. Keywords: metric space; quasi-metric space; uniform space; quasi-uniform space; Cauchy sequence; Cauchy net; Cauchy filter; completeness MSC: 54E15; 54E25; 54E50; 46S99 1. Introduction It is well known that completeness is an essential tool in the study of metric spaces, particularly for fixed points results in such spaces. The study of completeness in quasi-metric spaces is considerably more involved, due to the lack of symmetry of the distance—there are several notions of completeness all agreing with the usual one in the metric case (see [1] or [2]). Again these notions are essential in proving fixed point results in quasi-metric spaces as it is shown by some papers on this topic as, for instance, [3–6] (see also the book [7]). -
Basic Properties of Filter Convergence Spaces
Basic Properties of Filter Convergence Spaces Barbel¨ M. R. Stadlery, Peter F. Stadlery;z;∗ yInstitut fur¨ Theoretische Chemie, Universit¨at Wien, W¨ahringerstraße 17, A-1090 Wien, Austria zThe Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA ∗Address for corresponce Abstract. This technical report summarized facts from the basic theory of filter convergence spaces and gives detailed proofs for them. Many of the results collected here are well known for various types of spaces. We have made no attempt to find the original proofs. 1. Introduction Mathematical notions such as convergence, continuity, and separation are, at textbook level, usually associated with topological spaces. It is possible, however, to introduce them in a much more abstract way, based on axioms for convergence instead of neighborhood. This approach was explored in seminal work by Choquet [4], Hausdorff [12], Katˇetov [14], Kent [16], and others. Here we give a brief introduction to this line of reasoning. While the material is well known to specialists it does not seem to be easily accessible to non-topologists. In some cases we include proofs of elementary facts for two reasons: (i) The most basic facts are quoted without proofs in research papers, and (ii) the proofs may serve as examples to see the rather abstract formalism at work. 2. Sets and Filters Let X be a set, P(X) its power set, and H ⊆ P(X). The we define H∗ = fA ⊆ Xj(X n A) 2= Hg (1) H# = fA ⊆ Xj8Q 2 H : A \ Q =6 ;g The set systems H∗ and H# are called the conjugate and the grill of H, respectively. -
Long Term Evaluation of Operating Reserve with High Penetration of Renewable Energy Sources
1 Long Term Evaluation of Operating Reserve with High Penetration of Renewable Energy Sources Armando M. Leite da Silva, Fellow, IEEE, Mauro A. Rosa, Warlley S. Sales, and Manuel Matos, Member, IEEE Abstract − Due to the high penetration of renewable energy into quate to assess short-term risks for time intervals up to a few the energy matrix of today’s power networks, the design of gene- hours. In this case, the system risk obtained is conditioned to a rating systems based only on static reserve assessment does not short period, assuming that the operator knows a priori the seem to be enough to guarantee the security of power system op- generating units available to take up load. Conversely, in the eration. From the wind power integration perspective, this ener- medium- and long-term running, the operator does not know gy source imposes additional requirements, mainly due to the in- exactly the set of generating units that will be available for herent unpredictable characteristic of the wind. Besides the un- certainties in load and generating unit availabilities, the operat- each period of time and, therefore, the risk assessment must ing reserve needs also to deal with the fluctuation characteristic account for the chronological evaluation of the generating ca- of the wind power. Therefore, more flexibility of the conventional pacity system. generators (hydro and thermal) is required to provide system Due to the growing penetration of renewable energy into support services. This paper discusses a new methodology based the energy matrix of today’s power networks, the design of on chronological Monte Carlo simulation to evaluate the operat- generating system based only on static reserve assessment ing reserve requirements of generating systems with large does not seem to be enough to ensure the security of power amounts of renewable energy sources, in particular, wind power. -
ID #2013 005R, Operating Reserve
Information Document Operating Reserve ID #2013-005R Information Documents are not authoritative. Information Documents are for information purposes only and are intended to provide guidance. In the event of any discrepancy between an information document and any authoritative document1 in effect, the authoritative document governs. 1 Purpose This information document relates to the following authoritative documents: • Section 205.1 of the ISO rules, Offers for Operating Reserve; • Section 205.2 of the ISO rules, Issuing Dispatches for Operating Reserve; • Section 205.3 of the ISO rules, Restatements for Operating Reserve (“Section 205.3”); • Section 205.4 of the ISO rules, Regulating Reserve Technical Requirements and Performance Standards (“Section 205.4”); • Section 205.5 of the ISO rules, Spinning Reserve Technical Requirements and Performance Standards (“Section 205.5”); • Section 205.6 of the ISO rules, Supplemental Reserve Technical Requirements and Performance Standards (“Section 205.6”); and • Section 302.1 of the ISO rules, ISO Directives (“Section 302.1”). The purpose of this information document is to assist market participants in understanding the operating reserve market. This information document is likely of most interest to market participants who currently provide or may in the future provide operating reserve. 2 Operating Reserve Operating reserve acts as a safety net, making extra power available to help balance the supply of, and demand for, electricity in real time and stabilizing and protecting the interconnected electric system in the event of unforeseen problems. There are two types of operating reserve: regulating reserve and contingency reserve. Each type of operating reserve performs a unique function and has unique technical requirements. -
Topological Spaces and Neighborhood Filters
Topological spaces and neighborhood filters Jordan Bell [email protected] Department of Mathematics, University of Toronto April 3, 2014 If X is a set, a filter on X is a set F of subsets of X such that ; 62 F; if A; B 2 F then A \ B 2 F; if A ⊆ X and there is some B 2 F such that B ⊆ A, then A 2 F. For example, if x 2 X then the set of all subsets of X that include x is a filter on X.1 A basis for the filter F is a subset B ⊆ F such that if A 2 F then there is some B 2 B such that B ⊆ A. If X is a set, a topology on X is a set O of subsets of X such that: ;;X 2 O; S if Uα 2 O for all α 2 I, then Uα 2 O; if I is finite and Uα 2 O for all α 2 I, T α2I then α2I Uα 2 O. If N ⊆ X and x 2 X, we say that N is a neighborhood of x if there is some U 2 O such that x 2 U ⊆ N. In particular, an open set is a neighborhood of every element of itself. A basis for a topology O is a subset B of O such that if x 2 X then there is some B 2 B such that x 2 B, and such that if B1;B2 2 B and x 2 B1 \ B2, then there is some B3 2 B such that 2 x 2 B3 ⊆ B1 \ B2. -
"Mathematics for Computer Science" (MCS)
“mcs” — 2016/9/28 — 23:07 — page i — #1 Mathematics for Computer Science revised Wednesday 28th September, 2016, 23:07 Eric Lehman Google Inc. F Thomson Leighton Department of Mathematics and the Computer Science and AI Laboratory, Massachussetts Institute of Technology; Akamai Technologies Albert R Meyer Department of Electrical Engineering and Computer Science and the Computer Science and AI Laboratory, Massachussetts Institute of Technology 2016, Eric Lehman, F Tom Leighton, Albert R Meyer. This work is available under the terms of the Creative Commons Attribution-ShareAlike 3.0 license. “mcs” — 2016/9/28 — 23:07 — page ii — #2 “mcs” — 2016/9/28 — 23:07 — page iii — #3 Contents I Proofs Introduction 3 0.1 References4 1 What is a Proof? 5 1.1 Propositions5 1.2 Predicates8 1.3 The Axiomatic Method8 1.4 Our Axioms9 1.5 Proving an Implication 11 1.6 Proving an “If and Only If” 13 1.7 Proof by Cases 15 1.8 Proof by Contradiction 16 1.9 Good Proofs in Practice 17 1.10 References 19 2 The Well Ordering Principle 29 2.1 Well Ordering Proofs 29 2.2 Template for Well Ordering Proofs 30 2.3 Factoring into Primes 32 2.4 Well Ordered Sets 33 3 Logical Formulas 47 3.1 Propositions from Propositions 48 3.2 Propositional Logic in Computer Programs 51 3.3 Equivalence and Validity 54 3.4 The Algebra of Propositions 56 3.5 The SAT Problem 61 3.6 Predicate Formulas 62 3.7 References 67 4 Mathematical Data Types 93 4.1 Sets 93 4.2 Sequences 98 4.3 Functions 99 4.4 Binary Relations 101 4.5 Finite Cardinality 105 “mcs” — 2016/9/28 — 23:07 — page iv — #4 Contentsiv 5 Induction 125 5.1 Ordinary Induction 125 5.2 Strong Induction 134 5.3 Strong Induction vs. -
MTH 304: General Topology Semester 2, 2017-2018
MTH 304: General Topology Semester 2, 2017-2018 Dr. Prahlad Vaidyanathan Contents I. Continuous Functions3 1. First Definitions................................3 2. Open Sets...................................4 3. Continuity by Open Sets...........................6 II. Topological Spaces8 1. Definition and Examples...........................8 2. Metric Spaces................................. 11 3. Basis for a topology.............................. 16 4. The Product Topology on X × Y ...................... 18 Q 5. The Product Topology on Xα ....................... 20 6. Closed Sets.................................. 22 7. Continuous Functions............................. 27 8. The Quotient Topology............................ 30 III.Properties of Topological Spaces 36 1. The Hausdorff property............................ 36 2. Connectedness................................. 37 3. Path Connectedness............................. 41 4. Local Connectedness............................. 44 5. Compactness................................. 46 6. Compact Subsets of Rn ............................ 50 7. Continuous Functions on Compact Sets................... 52 8. Compactness in Metric Spaces........................ 56 9. Local Compactness.............................. 59 IV.Separation Axioms 62 1. Regular Spaces................................ 62 2. Normal Spaces................................ 64 3. Tietze's extension Theorem......................... 67 4. Urysohn Metrization Theorem........................ 71 5. Imbedding of Manifolds.......................... -
History and Progress of Fractional–Order Element
296 A. KARTCI, N. HERENCSAR, J. T. MACHADO, L. BRANCIK, HISTORY AND PROGRESS OF FRACTIONAL–ORDER ELEMENT . History and Progress of Fractional–Order Element Passive Emulators: A Review Aslihan KARTCI 1;2, Norbert HERENCSAR 1, Jose Tenreiro MACHADO 3, Lubomir BRANCIK 4 1 Dept. of Telecommunications, Brno University of Technology, Technicka 3082/12, 616 00 Brno, Czech Republic 2 Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia 3 Institute of Engineering, Polytechnic of Porto, Dept. of Electrical Engineering, Porto, Portugal 4 Dept. of Radio Electronics, Brno University of Technology, Technicka 3082/12, 616 00 Brno, Czech Republic {kartci, herencsn, brancik}@feec.vutbr.cz, [email protected] Submitted April 5, 2020 / Accepted April 19, 2020 Abstract. This paper presents a state-of-the-art survey where Iαv¹tº denotes the "fractional-order time integral" [3] in the area of fractional-order element passive emulators with an order 0 < α < 1. Figure 1 shows these funda- adopted in circuits and systems. An overview of the different mental components in the frequency domain and possible approximations used to estimate the passive element values fractional-order elements (FOEs) in the four quadrants of by means of rational functions is also discussed. A short com- the complex plane [4]. Their impedance is described as parison table highlights the significance of recent methodolo- Z¹sº = Ksα, where ! is the angular frequency with s = j! gies and their potential for further research. Moreover, the and the phase is given in radians (φ = απ/2) or in degrees pros and cons in emulation of FOEs are analyzed. -
Paul Hertz Astrophysics Subcommittee
Paul Hertz Astrophysics Subcommittee February 23, 2012 Agenda • Science Highlights • Organizational Changes • Program Update • President’s FY13 Budget Request • Addressing Decadal Survey Priorities 2 Chandra Finds Milky Way’s Black Hole Grazing on Asteroids • The giant black hole at the center of the Milky Way may be vaporizing and devouring asteroids, which could explain the frequent flares observed, according to astronomers using data from NASA's Chandra X-ray Observatory. For several years Chandra has detected X-ray flares about once a day from the supermassive black hole known as Sagittarius A*, or "Sgr A*" for short. The flares last a few hours with brightness ranging from a few times to nearly one hundred times that of the black hole's regular output. The flares also have been seen in infrared data from ESO's Very Large Telescope in Chile. • Scientists suggest there is a cloud around Sgr A* containing trillions of asteroids and comets, stripped from their parent stars. Asteroids passing within about 100 million miles of the black hole, roughly the distance between the Earth and the sun, would be torn into pieces by the tidal forces from the black hole. • These fragments then would be vaporized by friction as they pass through the hot, thin gas flowing onto Sgr A*, similar to a meteor heating up and glowing as it falls through Earth's atmosphere. A flare is produced and the remains of the asteroid are eventually swallowed by the black hole. • The authors estimate that it would take asteroids larger than about six miles in radius to generate the flares observed by Chandra. -
Guide for the Use of the International System of Units (SI)
Guide for the Use of the International System of Units (SI) m kg s cd SI mol K A NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (Supersedes NIST Special Publication 811, 1995 Edition, April 1995) March 2008 U.S. Department of Commerce Carlos M. Gutierrez, Secretary National Institute of Standards and Technology James M. Turner, Acting Director National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 2008; 2nd printing November 2008) CODEN: NSPUE3 Note on 2nd printing: This 2nd printing dated November 2008 of NIST SP811 corrects a number of minor typographical errors present in the 1st printing dated March 2008. Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is becoming the dominant measurement system used in international commerce. The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418] changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the added task of helping U.S. -
An Experiment in High-Frequency Sediment Acoustics: SAX99
An Experiment in High-Frequency Sediment Acoustics: SAX99 Eric I. Thorsos1, Kevin L. Williams1, Darrell R. Jackson1, Michael D. Richardson2, Kevin B. Briggs2, and Dajun Tang1 1 Applied Physics Laboratory, University of Washington, 1013 NE 40th St, Seattle, WA 98105, USA [email protected], [email protected], [email protected], [email protected] 2 Marine Geosciences Division, Naval Research Laboratory, Stennis Space Center, MS 39529, USA [email protected], [email protected] Abstract A major high-frequency sediment acoustics experiment was conducted in shallow waters of the northeastern Gulf of Mexico. The experiment addressed high-frequency acoustic backscattering from the seafloor, acoustic penetration into the seafloor, and acoustic propagation within the seafloor. Extensive in situ measurements were made of the sediment geophysical properties and of the biological and hydrodynamic processes affecting the environment. An overview is given of the measurement program. Initial results from APL-UW acoustic measurements and modelling are then described. 1. Introduction “SAX99” (for sediment acoustics experiment - 1999) was conducted in the fall of 1999 at a site 2 km offshore of the Florida Panhandle and involved investigators from many institutions [1,2]. SAX99 was focused on measurements and modelling of high-frequency sediment acoustics and therefore required detailed environmental characterisation. Acoustic measurements included backscattering from the seafloor, penetration into the seafloor, and propagation within the seafloor at frequencies chiefly in the 10-300 kHz range [1]. Acoustic backscattering and penetration measurements were made both above and below the critical grazing angle, about 30° for the sand seafloor at the SAX99 site.