NORME INTERNATIONALE CEI IEC INTERNATIONAL STANDARD 62271-100 Edition 1.1 2003-05 Appareillage à haute tension – Partie 100: Disjoncteurs à courant alternatif à haute tension High-voltage switchgear and controlgear – Part 100: High-voltage alternating-current circuit-breakers Numéro de référence Reference number CEI/IEC 62271-100:2001+A1:2002 Edition 1:2001 consolidée par l'amendement 1:2002 Edition 1:2001 consolidated with amendment 1:2002 Numérotation des publications Depuis le 1er janvier 1997, les publications de la CEI sont numérotées à partir de 60000. Ainsi, la CEI 34-1 devient la CEI 60034-1. Editions consolidées Les versions consolidées de certaines publications de la CEI incorporant les amendements sont disponibles. Par exemple, les numéros d’édition 1.0, 1.1 et 1.2 indiquent respectivement la publication de base, la publication de base incorporant l’amendement 1, et la publication de base incorporant les amendements 1 et 2. Informations supplémentaires sur les publications de la CEI Le contenu technique des publications de la CEI est constamment revu par la CEI afin qu'il reflète l'état actuel de la technique. Des renseignements relatifs à cette publication, y compris sa validité, sont dispo- nibles dans le Catalogue des publications de la CEI (voir ci-dessous) en plus des nouvelles éditions, amendements et corrigenda. Des informations sur les sujets à l’étude et l’avancement des travaux entrepris par le comité d’études qui a élaboré cette publication, ainsi que la liste des publications parues, sont également disponibles par l’intermédiaire de: • Site web de la CEI (www.iec.ch) • Catalogue des publications de la CEI Le catalogue en ligne sur le site web de la CEI (http://www.iec.ch/searchpub/cur_fut.htm) vous permet de faire des recherches en utilisant de nombreux critères, comprenant des recherches textuelles, par comité d’études ou date de publication. Des informations en ligne sont également disponibles sur les nouvelles publications, les publications rempla- cées ou retirées, ainsi que sur les corrigenda. • IEC Just Published Ce résumé des dernières publications parues (http://www.iec.ch/online_news/justpub/jp_entry.htm) est aussi disponible par courrier électronique. Veuillez prendre contact avec le Service client (voir ci-dessous) pour plus d’informations. • Service clients Si vous avez des questions au sujet de cette publication ou avez besoin de renseignements supplémentaires, prenez contact avec le Service clients: Email: custserv@iec.ch Tél: +41 22 919 02 11 Fax: +41 22 919 03 00 Publication numbering As from 1 January 1997 all IEC publications are issued with a designation in the 60000 series. For example, IEC 34-1 is now referred to as IEC 60034-1. Consolidated editions The IEC is now publishing consolidated versions of its publications. For example, edition numbers 1.0, 1.1 and 1.2 refer, respectively, to the base publication, the base publication incorporating amendment 1 and the base publication incorporating amendments 1 and 2. Further information on IEC publications The technical content of IEC publications is kept under constant review by the IEC, thus ensuring that the content reflects current technology. Information relating to this publication, including its validity, is available in the IEC Catalogue of publications (see below) in addition to new editions, amendments and corrigenda. Information on the subjects under consideration and work in progress undertaken by the technical committee which has prepared this publication, as well as the list of publications issued, is also available from the following: • IEC Web Site (www.iec.ch) • Catalogue of IEC publications The on-line catalogue on the IEC web site (http://www.iec.ch/searchpub/cur_fut.htm) enables you to search by a variety of criteria including text searches, technical Alternating Current versus Direct Current Alternating Current versus Direct Current Bởi: OpenStaxCollege Alternating Current Most of the examples dealt with so far, and particularly those utilizing batteries, have constant voltage sources Once the current is established, it is thus also a constant Direct current (DC) is the flow of electric charge in only one direction It is the steady state of a constant-voltage circuit Most well-known applications, however, use a time-varying voltage source Alternating current (AC) is the flow of electric charge that periodically reverses direction If the source varies periodically, particularly sinusoidally, the circuit is known as an alternating current circuit Examples include the commercial and residential power that serves so many of our needs [link] shows graphs of voltage and current versus time for typical DC and AC power The AC voltages and frequencies commonly used in homes and businesses vary around the world (a) DC voltage and current are constant in time, once the current is established (b) A graph of voltage and current versus time for 60-Hz AC power The voltage and current are sinusoidal and are in phase for a simple resistance circuit The frequencies and peak voltages of AC sources differ greatly 1/9 Alternating Current versus Direct Current The potential difference V between the terminals of an AC voltage source fluctuates as shown The mathematical expression for V is given by V = V0 sin 2πft [link] shows a schematic of a simple circuit with an AC voltage source The voltage between the terminals fluctuates as shown, with the AC voltage given by V = V0 sin 2πft, where V is the voltage at time t, V0 is the peak voltage, and f is the frequency in hertz For this simple resistance circuit, I = V/R, and so the AC current is I = I0 sin 2πft, where I is the current at time t, and I0 = V0/R is the peak current For this example, the voltage and current are said to be in phase, as seen in [link](b) Current in the resistor alternates back and forth just like the driving voltage, since I = V/R If the resistor is a fluorescent light bulb, for example, it brightens and dims 120 times per second as the current repeatedly goes through zero A 120-Hz flicker is too rapid for your eyes to detect, but if you wave your hand back and forth between your face and a fluorescent light, you will see a stroboscopic effect evidencing AC The fact that the light output fluctuates means that the power is fluctuating The power supplied is P = IV Using the expressions for I and V above, we see that the time dependence of power is P = I0V0 sin2 2πft, as shown in [link] Making Connections: Take-Home Experiment—AC/DC Lights Wave your hand back and forth between your face and a fluorescent light bulb Do you observe the same thing with the headlights on your car? Explain what you observe Warning: Do not look directly at very bright light 2/9 Alternating Current versus Direct Current AC power as a function of time Since the voltage and current are in phase here, their product is non-negative and fluctuates between zero and I0V0 Average power is (1 / 2)I0V0 We are most often concerned with average power rather than its fluctuations—that 60-W light bulb in your desk lamp has an average power consumption of 60 W, for example As illustrated in [link], the average power Pave is Pave = I0V0 This is evident from the graph, since the areas above and below the (1 / 2)I0V0 line are equal, but it can also be proven using trigonometric identities Similarly, we define an average or rms current Irms and average or rms voltage Vrms to be, respectively, Irms = I0 √2 and Vrms = V0 √2 where rms stands for root mean square, a particular kind of average In general, to obtain a root mean square, the particular quantity is squared, its mean (or average) is found, and the square root is taken This is useful for AC, since the average value is zero Now, Pave = IrmsVrms, which gives Pave = I0 √2 ⋅ V0 √2 = I0V0, as stated above It is standard practice to quote Irms, Vrms, and Pave rather than the peak values For example, most household electricity is 120 V AC, which means that Vrms is 120 V The common 10-A circuit breaker will interrupt a sustained Irms greater than 10 A Your 1.0-kW microwave oven consumes Pave = 1.0 kW, and so on You can think of these rms and average values as the equivalent DC values for a simple resistive circuit 3/9 Alternating Current versus Direct Current To summarize, when dealing with AC, Ohm’s law and the equations for power are completely analogous to those for DC, but rms and average values are used for AC Thus, for AC, Ohm’s law is written Irms = Vrms R The various expressions for AC power Pave are Pave = IrmsVrms, Pave = V2rms R , and Pave = I2rmsR Peak Voltage and Power for AC (a) What is the value of the peak voltage for 120-V AC power? (b) What is the peak power consumption rate of a 60.0-W AC light bulb? Strategy V We are told that Vrms is 120 V and Pave is 60.0 W We can use Vrms = √20 ...692 ALTERNATING-CURRENT WAVE-FORM. [Sept. 28 DISCUSSION ON " THE EFFECT OF IRON IN DISTORTING ALTER- NATING-CURRENT WAVE-FORM" AT NEW YORK, SEPTEMBER 28, 1906. Charles Proteus Steinmetz: This paper deals with the wave-shape distortion produced in alternating-current cir- cuits by the introduction of iron. It is a theoretical paper, and while of scientific interest appears at first of rather little practical value to the electrical engineer. There is, however, to-day only a very short step between pure scientific investiga- tion and engineering practice; and I hope to show youi that the phenomena dealt with in this paper, and similar phenomena, are of very great practical importance in alternating-current dis- __.LjL_ _ 8 z_ _ m~~~~~F 1 t<_r_ }f FIG I tribution; that is, wave-shape distortion may lead to effects not only very marked and pronounced but occasionally disastrous. In general, in investigating the effect of iron in alternating- current circuits, the curve of exciting current is calculated from the hysteresis cycle of the iron. Dr. Bedell proceeds inversely by superposing different harmonics of current. From these complex currents he produces a hysteresis loop, noting whether this hysteresis loop is a reasonable one or not, and deriving there- from relations regarding the relative intensity and phase of the triple harmonic in the wave of exciting current. As far as the investigation goes, it extends only to the fundamental and triple harmonics; the investigation of higher harmonics is left to a future occasion. ÆTHERFORCE 19(6] DISCUSSION AT NEW YORK. 693 These higher harmonics obviouslv modify to a certain extent the conclusions arrived at by assuming merely the fundamental and triple harmonic as present. For instance, by superposing a triple harmonic upon the fundamental wave, one gets a wave of the shape shown in Fig. 1., with a hump on the rising side and a hollow on the decreasing side. Introducing a triple harmonic of higher amplitude causes the hump to develop into a double peak as in Fig. 2. It is obvious that a double peak cannot exist, because whatever relation may exist between the magnetism and the magnetizing current, the c urrent nmust rise as long as the magnet- ism rises; an(d therefore the maximum possible value of the triple harmonic is that value which (does not yet give a A = ~~~~~~~FIG 2 downwarcl bend, buit merely flattens the current wave on the rising side. This maximum amplitude of the third harmonic can, however, be exceeded if higher harmonics are present. Assume for instance a fifth harrnonic which has such a phase relation as to be neo,ative at A Fig. 2, and positive at B, and then superpose this fifth harmonic on the double- peaked wave; it wvill be seen that it cuts ofif the peak and fills up the hollow, and gives a wavTe which represents a possible hy- steresis cvcle, as seen in Fig. 3. The eiffect of the fifth harmonic, then, is to permit the existence of a triple harmonic, larger than could exist in the absence of the fifth lharmonic. It is quite prob- able that not ilifrequently in the exciting current there occur triple-harmonlic culrrenlts higher than the rnaximum value cal- ÆTHERFORCE 694 ALTERNATING-CURRENT WAV-FORM. [Sept. 28 culated in Dr. Bedell's paper, and the double peak is cut off by the fifth harmonic. 1 TRẮC NGHIỆM ĐIỆN XOAY CHIỀU(AC:ALTERNATING CURRENT)(CB) I.Tính toán các đại lượng đặc trưng của dòng điện xoay chiều 1. chọn phát biểu đúng cho dòng điện xoay chiều: A. dòng điện xoay chiều hình cos có pha biến thiên tuần hoàn. B. có cường độ biến thiên điều hòa theo thời gian C. có chiều dòng điện biến thiên điều hoà theo thời gian D. có cườngđộ biến thiên tuần hoàn theo thời gian. 2. dòng điện xoay chiều dạng cos có tínhchất nào kể sau đây? A. cường độ biến thiên tuần hoàn theo thời gian B. chiều dòng điện thay đổi tuần hoàn theo thời gian C. cường độ biến thiên, điều hoà theo thời gian. D. cả 3 tính chất trên. 3. dòng điện xoay chiều có tần số f = 50Hz. hỏi trong mỗi giây dòng điện đổi chiều mấy lần? A. 50 lần B. 25 lần C. 100 lần D. một đáp số khác. 4. Giá trị hiệu dụng của dòng điện xoay chiều có biểu thức i = 2 3 cos100t (A) bằng bao nhiêu? A. 2A B. 3 2 A C. 3 A D. 6 A 5. tìm giá trị hiệu dụng của hiệu điện thế xoay chiều có biểu thức u = 220 5 cos 120t (v). A. 200v B. 110 10 v C. 110 5 v D. 110 2 5 v 7.Cho một đoạn mạch gồm 2 phần tử R và C nối tiếp: R=50 ; C =(200/)F. Đặt vào hai đầu đoạn mạch một hiệu điện thế xoay chiều: u AB = 100 2 cos(100t - / 4  ) (V).Cường độ hiệu dụng qua đoạn mạch bằng: A.2 2 A B. 2 A 2 /2A D.2A 9.Cho một đoạn mạch gồm 2 phần tử R và L nối tiếp:L =( 3 /)H . Đặt vào hai đầu đoạn mạch một hiệu điện thế xoay chiều: u = 100cos(100t - / 4  ) (V).Cường độ dòng điện lệch pha /3 so với hiệu điện thế 2 đầu đoạn mạch .Giá trị của điện trở R bằng: A.R =100 B. R=100 3  C. R=(100/ 3 ) D. R= 300 10. đoạn mạch có điện trở R nối tiếp cuộn dây có điện trở thuần r và độ tự cảm L. tổng trở đoạn mạch này được tính theo công thức nào? A. z = 222 )( LrR   B. z = 22 )( LrR   C. z = 22 )()( LrR   D. z = R + 22 )( Lr   11.Cho một đoạn mạch gồm 2 phần tử R và C nối tiếp: R=50 . Đặt vào hai đầu đoạn mạch một hiệu điện thế xoay chiều: u = 50 2 cos(100t )(V).Hiệu điện thế 2 đầu đoạn mạch lệch pha /6 so với cường độ dòng điện trong mạch.Giá trị của điện dung C trong mạch bằng: A.(100 3 /)F B .(100/2)F C .(200 3 /)F D. (1000/)F 12. đặt vào hai đầu một cuộn dây thuần cảm L = 0,8H một hiệu điện thế xoay chiều 220V, 50Hz. tính cảm kháng và cường độ dòng đi qua mạch. A. 150 và 0,66A B. 215 và 0,50A C. 251 và 0,88A D. 151 và 0,88A 13.một đoạn mạch R,L,C nối tiếp gồm có R = 140, L = 1H và C = 25F. dòng điện xoay chiều đi qua mạch có cường độ I = 0,5A và tần số f = 50Hz. tìm tổng trở của đoạn mạch và hiệu điện thế hai đầu đoạn mạch. A. 332 và 110v B. 232 và 220v C. 233 và 117v D. 323 và 117v 14 một đoạn mạch gồm một điện trở R nối tiếp với tụ C. một vôn kế điện trở rất lớn đo hai đầu đoạn mạch thấy chỉ 100v, đo hai đầu điện trở thấy chỉ 60v. tìm số chỉ vôn kế khi đo giữa hai bản tụ C. A. 40v B. 120v C. 80v D. 160v 15. Biểu thức của cường độ dòng điện trong một đoạn mạch AC là : i = 5 2 cos(100t + /6  ) (A) Ở thời điểm t = 300 1 s cường độ trong mạch đạt giá trị: A. Cực đại B. Cực tiểu C. Bằng không D. Một giá trị khác Intersecting families in the alternating group and direct product of symmetric groups Cheng Yeaw Ku Department of Mathematics, California Institute of Technology Pasadena, CA 91125, USA cyk@caltech.edu. Tony W. H. Wong Department of Mathematics, The Chinese University of Hong Kong, Hong Kong tonywhwong@yahoo.com.hk. Submitted: Oct 27, 2006; Accepted: Mar 6, 2007; Published: Mar 15, 2007 Mathematics Subject Classification: 05D99 Abstract Let S n denote the symmetric group on [n] = {1, . . . , n}. A family I ⊆ S n is intersecting if any two elements of I have at least one common entry. It is known that the only intersecting families of maximal size in S n are the cosets of point stabilizers. We show that, under mild restrictions, analogous results hold for the alternating group and the direct product of symmetric groups. 1 Introduction Let S n (or Sym([n])) denote the symmetric group on the symbol-set [n] = {1, . . . , n}. Throughout, the product (or composition) of two permutations g, h ∈ S n , denoted by gh, will always mean ‘do h first followed by g’. We say that a family I ⊆ S n of permutations is intersecting if {x : g(x) = h(x)} = ∅ for every g, h ∈ I, i.e. the Hamming distance d H (g, h) = |{x : g(x) = h(x)}| ≤ n − 1 for every g, h ∈ I. In a setting of coding theory, Deza and Frankl [5] studied extremal problems for permutations with given maximal or minimal Hamming distance. Among other results, they proved that if I is an intersecting family in S n then |I| ≤ (n − 1)!. Recently, Cameron and Ku [4] showed that equality holds if and only if I = {g ∈ S n : g(x) = y} for some x, y ∈ [n], i.e. I is a coset of a point stabilizer. This can also be deduced from a more general theorem of Larose and Malvenuto [8] about Kneser-type graphs. the electronic journal of combinatorics 14 (2007), #R25 1 Theorem 1.1 ([5], [4], [8]) Let n ≥ 2 and I be an intersecting family in S n . Then |I| ≤ (n − 1)!. Moreover, equality holds if and only if I = {g ∈ S n : g(x) = y} for some x, y ∈ [n]. Here we extend the study of intersecting families of S n to that of the alternating group A n and the direct product of symmetric groups S n 1 ×· · ·×S n q . We say that a family I ⊆ A n (or respectively I ⊆ S n 1 ×· · ·×S n q ) is intersecting if {x : g(x) = h(x)} = ∅ for any g, h ∈ I (or respectively if, for every (g 1 , . . . , g q ), (h 1 , . . . , h q ) ∈ I, we have {x : g i (x) = h i (x)} = ∅ for some i). Our main results characterize intersecting families of maximal size in these groups. Theorem 1.2 Let n ≥ 2 and I be an intersecting family in A n . Then |I| ≤ (n − 1)!/2. Moreover, if n = 4, then equality holds if and only if I = {g ∈ A n : g(x) = y} for some x, y ∈ [n]. The following example shows that the condition n = 4 in Theorem 1.2 is necessary for the case of equality: {(1, 2, 3, 4), (1, 3, 4, 2), (2, 3, 1, 4)} (we use the notation (a 1 , . . . , a n ) to denote the permutation that maps i to a i ). Theorem 1.3 Let 2 ≤ m ≤ n and I be an intersecting family in Sym(Ω 1 ) × Sym(Ω 2 ), Ω 1 = [m], Ω 2 = [n]. Then |I| ≤ (m−1)!n!. Moreover, for m < n such that (m, n) = (2, 3), equality holds if and only if I = {(g, h) : g(x) = y} for some x, y ∈ Ω 1 , while for m = n such that (m, n) = (3, 3), equality holds if and only if I = {(g, h) : g(x) = y} for some x, y ∈ Ω 1 or I = {(g, h) : h(x) = y} for some x, y ∈ Ω 2 . The following examples show that the conditions (m, n) = (2, 3), (3, 3) in Theorem 1.3 are necessary for the case of equality: • J 23 = {((1, 2), (2, 3, 1)), ((1, 2), (1, 2, 3)), ((1, 2), (3, 1, 2)), ((2, 1), (2, 1, 3)), ((2, 1), (3, 2, 1)), ((2, 1), (1, 3, 2))}. • J 33 = {((1, 3, 2), (1, 2, 3)), ((2, 1, 3), (1, 2, 3)), ((2, 1, 3), (1, 3, 2)), ((2, 1, 3), (2, 1, 3)), ((2, 1, 3), (3, 2, 1)), ((2, 3, 1), (1, 2, 3)), ((2, 3, 1), (2, 3, 1)), ((2, 3, 1), (3, 1, 2)), ((3, 1, 2), (1, 3, 2)), ((3, 1, 2), (2, 1, 3)), ((3, 1, 2), (3, 2, 1)), ((3, 2, 1), (1, 2, 3))}. For the direct product of finitely many symmetric groups, we prove Theorem AJIT KUMAR CHATTOPADHYAY © PHOTODISC W ith the rapid developments of high-power semiconductors and microprocessor/digital signal processor (DSP)-based control and estimation technologies, high-power, high-performance ac drives using either induction motors (IMs) or synchronous motors (SMs) with cycloconverters or inverters have replaced the earlier dc drives for applications in the steel industry during the last 30 years In this article, a review of the state-of-the-art high-power devices, such as siliconcontrolled rectifiers (SCRs), gate turn-off thyristors (GTOs), insulated-gate bipolar transistors (IGBTs), integrated Digital Object Identifier 10.1109/MIE.2010.938719 30 IEEE INDUSTRIAL ELECTRONICS MAGAZINE n DECEMBER 2010 Advancements in the Last 30 Years gate-commutated thyristors (IGCTs), and injectionenhanced gate transistors (IEGTs), converters, such as cycloconverters and three-level inverters, and control technologies adopted for such drives, such as the vector control (VC) and the direct torque control (DTC), is presented with brief features of the industrial ac drives developed for the steel industry by the leading drive manufacturers worldwide The steel industry continues to play an indispensable role in supporting the abundance of human life by providing the basic material for construction and economic development of a country The process of manufacturing the steel products from iron ore involves raw material handling, primary steel making (coke oven, blast furnace, and steel melting), refining, casting, hot and cold rolling, 1932-4529/10/$26.00&2010IEEE Coal from Mines Iron Ore from Mines Coke Oven Sinter Plant The steel industry continues to play an indispensable role in supporting the abundance of human life by providing the basic material for construction and economic development of a country Blast Furnace Basic Oxygen Furnace Continuous Casting Roughing Mill Finishing Mill Finished Product Cold Rolling Mill Finished Product FIGURE – Material flow in an integrated steel plant and finishing as shown in the material flow diagram (Figure 1) and a pictorial manufacturing process diagram (Figure 2) [1] of an integrated steel plant As shown in Figure 2, after the Iron Making Pellet blast furnace and basic oxygen furnace process, the molten steel is cast by continuous casting machine to produce slabs, blooms, and billets These castings are rolled to the required dimensions by the rolling mills to produce the steel products The steel shapes, bars, and wire rods are processed on section and bar mills and wire-rod mills, plates are worked on reversing mills, and hotrolled steel sheets are worked on hotstrip mills After pickling to remove scale from the surface, the hot-rolled steel sheets are transformed to coldrolled steel sheets on reversing mills or tandem rolling mills, and then they are tinned or galvanized to produce finished steel products Steel Making Continuous Casting Coke Since the early 1960s, the integrated steel plants around the world having large capacity motors have progressively introduced new technologies in drive control through power electronics for the processing of steel Although motors used in the primary area of steel making, such as the coke oven, blast furnace, and steel melting shop, not need very accurate speed or torque regulation, the motors used in roughing mills, finishing mills, plate mills, tube mills, run-out tables, coilers/uncoilers, and pinch roles need speed and torque regulation of higher accuracy [2] In most of the early steel mill applications, dc motors driven by four-quadrant converters (thyristor Leonard drives) Rolling Section Mill Rail Sheet Pile Shape Bar Wire Rod Iron Ore Sintered Limestone Ore Wire Rod Mill Billet Hot Metal Basic Oxygen Furnace (BOF) Hot Direct Rolling (HDR) Plate Plate Mill Hot Rolled Coil and Sheet Hot-Strip Mill Bloom Cold Rolling Tandem Mill Slab Blast Furnace (BF) Welded Pipe Mill Scrap Main Products Electric Arc Furnace (EAF) Cold-Rolled Coil and ... you observe Warning: Do not look directly at very bright light 2/9 Alternating Current versus Direct Current AC power as a function of time Since the voltage and current are in phase here, their... voltage is a constant 120 V Solution for (b) Peak power is peak current times peak voltage Thus, 4/9 Alternating Current versus Direct Current (1 ) P0 = I0V0 = 2 I0V0 = 2Pave We know the average... Strategy 5/9 Alternating Current versus Direct Current We are given Pave = 100 MW, Vrms = 200 kV, and the resistance of the lines is R = 1.00 Ω Using these givens, we can find the current flowing