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qr code vb.net library Magnetic Coupling. Transformers in .NET framework
CHAPTER 10 Magnetic Coupling. Transformers Code 128 Code Set B Scanner In .NET Framework Using Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in .NET applications. Making Code 128 Code Set B In VS .NET Using Barcode printer for Visual Studio .NET Control to generate, create Code 128 Code Set A image in .NET framework applications. constant, independent of time. If, however, you have the patience to carefully apply the following trigonometrical identities sin x sin y 1 cos x y cos x y 2 and cos x y cos x cos y sin x sin y note 6 in Appendix note 25 in Appendix Recognizing Code 128A In Visual Studio .NET Using Barcode reader for .NET Control to read, scan read, scan image in .NET framework applications. Paint Barcode In .NET Using Barcode encoder for VS .NET Control to generate, create bar code image in Visual Studio .NET applications. to the foregoing equation for p, you ll nd that the expression actually reduces to p 1:5V 0 I 0 cos 445 Reading Barcode In Visual Studio .NET Using Barcode decoder for Visual Studio .NET Control to read, scan read, scan image in .NET applications. Encoding Code128 In Visual C# Using Barcode drawer for .NET framework Control to generate, create Code 128C image in Visual Studio .NET applications. which, since V 0 , I 0 , and are all constants in any given case, shows that p is also constant in any given case in any balanced threephase system. Problem 206 Show that p, in eq. (445), is EQUAL to PT in eqs. (440) and (444). Encode Code 128 Code Set B In Visual Studio .NET Using Barcode printer for ASP.NET Control to generate, create Code 128A image in ASP.NET applications. Make Code 128 Code Set B In Visual Basic .NET Using Barcode encoder for .NET framework Control to generate, create Code 128A image in Visual Studio .NET applications. The Unbalanced Case; Symmetrical Components
Creating Barcode In .NET Using Barcode generation for Visual Studio .NET Control to generate, create barcode image in VS .NET applications. Barcode Creation In .NET Using Barcode maker for VS .NET Control to generate, create bar code image in Visual Studio .NET applications. Let us begin by observing that a SINGLE plane vector is de ned in terms of two independent variables, its MAGNITUDE and its ANGULAR POSITION relative to an agreedupon reference axis. The independent variables are also referred to as degrees of freedom ; thus, a single " plane vector is said to have two degrees of freedom. Such a vector, A A=h, is illustrated in Fig. 259, where A and h are the two degrees of freedom. (As always, positive angles are measured in the ccw direction from the reference axis.) Drawing EAN13 Supplement 5 In .NET Using Barcode drawer for .NET Control to generate, create European Article Number 13 image in Visual Studio .NET applications. Code 2 Of 5 Generation In .NET Framework Using Barcode encoder for Visual Studio .NET Control to generate, create 2/5 Industrial image in VS .NET applications. Fig. 259
Code 39 Generator In Java Using Barcode encoder for Eclipse BIRT Control to generate, create Code39 image in BIRT applications. EAN13 Supplement 5 Encoder In ObjectiveC Using Barcode printer for iPad Control to generate, create EAN 13 image in iPad applications. Next consider a balanced set of three plane vectors. As we know, this is any set of three vectors having EQUAL MAGNITUDES and EQUAL PHASE DISPLACEMENTS. " " " Now let A1 , B1 , and C1 be such a balanced set, in which the equal phase displacement is "1 as the reference vector, displaced an angle h from the reference 1208, and let us take A " " " axis, as illustrated in Fig. 260, where jA1 j jB1 j jC1 j A1 B1 C1 : We are already familiar with the fact that the vector sum of such a balanced set of vectors is equal to zero. In this regard, note that a balanced set of plane vectors has just TWO degrees of freedom, these being the common magnitudes of the vectors and the angular displacement h of the reference vector from the reference axis. Thus the common magnitude, A1 B1 C1 , and the reference angle h are the two degrees of freedom in Fig. 260. Printing Data Matrix In ObjectiveC Using Barcode creation for iPhone Control to generate, create Data Matrix image in iPhone applications. Make USS128 In Java Using Barcode generator for Android Control to generate, create UCC.EAN  128 image in Android applications. CHAPTER 10 Magnetic Coupling. Transformers
Drawing UPCA Supplement 5 In C#.NET Using Barcode creator for VS .NET Control to generate, create Universal Product Code version A image in .NET framework applications. Drawing ECC200 In Visual Studio .NET Using Barcode generation for ASP.NET Control to generate, create DataMatrix image in ASP.NET applications. Fig. 260
Painting GS1128 In C#.NET Using Barcode encoder for VS .NET Control to generate, create EAN128 image in Visual Studio .NET applications. Encode USS Code 39 In Java Using Barcode creator for Java Control to generate, create Code 39 Extended image in Java applications. Next, in Fig. 260, assuming the diagram to be drawn on the complex plane, note that* " " B1 A1 j120 and " " C1 A1 j240 where 120 and 240 are understood to be angles in degrees{ (1208 and 2408), and thus that general form of the algebraic equation for the balanced case of Fig. 260 can be written as " " " A1 A1 j120 A1 j240 0 446 the righthand side re ecting the fact that the vector sum of such a balanced set of vectors is zero. " " " Now consider an unbalanced set of three plane vectors A, B, and C, such as is illustrated in Fig. 261, in which let " " " " S A B C 447 Fig. 261
" " * Let V V ja be a vector quantity on the complex plane. Now multiply V by jb , thus " V jb V ja jb V j a b " " " showing that multiplying a vector V by rotates V through the angle b but does not change the magnitude of V . { See footnote in connection with eq. (159) in Chap. 6.
CHAPTER 10 Magnetic Coupling. Transformers
" " where S is the vector sum of the three vectors, in which S MAY or MAY NOT be equal to zero, depending upon the particular circumstances. It follows that such an unbalanced set of three vectors will, in general, have SIX degrees of freedom (two for each of the individual vectors). As you would expect, unbalanced conditions sometimes do occur in practical threephase work. Fortunately, the solution of such problems can be expedited by means of what is called symmetrical components. This is an algebraic procedure based upon the fact an UNBALANCED set of three vectors can be expressed as the sum of THREE BALANCED SETS of three vectors each. The procedure is important because it allows the solution of a more di cult unbalanced problem in terms of the superposition of three easier balanced problems. In this regard, let us remark that the procedure is not only of great practical value but is also an interesting example of the application of the algebra of the complex plane to electric circuit problems. Let us begin our explanations as follows. First, we ve seen that a balanced set of plane vectors possesses just two degrees of freedom, while an unbalanced set of three plane vectors possesses, in general, six degrees of freedom. Now, in regard to physical systems, it is a fundamental fact that the number of degrees of freedom must remain the same in any valid equivalent description of a system. It thus follows that it will, in general, require the sum of three balanced sets to replace one unbalanced set. OUR PROBLEM, therefore, is to nd three balanced sets that are vectorially equivalent to A GIVEN UNBALANCED SET of three vectors. In the method of symmetrical components the problem is solved by resolving the given unbalanced set into three balanced sets called the positive sequence set, the negative sequence set, and the zero sequence set. Let us rst consider the positive sequence and negative sequence sets, which we ll de ne in connection with Figs. 262 and 263.

