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qr code vb.net library Magnetic Coupling. Transformers in Visual Studio .NET
CHAPTER 10 Magnetic Coupling. Transformers Decode Code128 In .NET Framework Using Barcode Control SDK for VS .NET Control to generate, create, read, scan barcode image in VS .NET applications. USS Code 128 Maker In Visual Studio .NET Using Barcode creation for .NET Control to generate, create Code 128B image in Visual Studio .NET applications. The ThreePhase Power System. Introduction
Code 128 Code Set A Recognizer In VS .NET Using Barcode decoder for VS .NET Control to read, scan read, scan image in VS .NET applications. Create Bar Code In Visual Studio .NET Using Barcode drawer for Visual Studio .NET Control to generate, create bar code image in VS .NET applications. Let us begin with the ordinary singlegenerator, twowire, ac circuit of Fig. 245.
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Drawing Code 128 Code Set C In .NET Framework Using Barcode maker for ASP.NET Control to generate, create Code 128 Code Set A image in ASP.NET applications. Encode USS Code 128 In VB.NET Using Barcode drawer for VS .NET Control to generate, create Code 128 Code Set A image in .NET applications. We ll refer to this as a singlephase circuit, in which the basic equations for current and power are " " " I V =Z L and P VI cos Bar Code Generator In Visual Studio .NET Using Barcode drawer for Visual Studio .NET Control to generate, create barcode image in .NET applications. Draw Barcode In Visual Studio .NET Using Barcode drawer for .NET framework Control to generate, create barcode image in .NET applications. " " where V and I denote the magnitudes of the rms vector quantities V and I , and where is " and I vectors. " the phase angle between the V The singlephase circuit of Fig. 245 is, of course, very basic and much used in lowpower applications. It is, however, not wellsuited for the generation and transmission of large amounts of power, nor for the operation of large industrialtype ac motors. Thus, instead of the simple singlephase circuit of Fig. 245, almost all commercial electric power is generated and transmitted using what is called the threephase system.* There are important reasons for this. One is that the overall generation and transmission e ciency of threephase systems is considerably higher than that of singlephase systems. Another reason (as we ll show later on) is the fact that the INSTANTANEOUS POWER in a balanced threephase system is constant, which is completely unlike the pulsating form of power in a singlephase system. This is an important advantage in the operation of highhorsepower ac motors. Also, in regard to the muchused singlephase system of Fig. 245, there are three such singlephase circuits available in a threephase circuit. Threephase power is produced by a threephase generator, which can basically be described as follows. A threephase generator fundamentally consists of three separate but identical SINGLEPHASE GENERATORS rigidly attached to a common shaft. The three generators produce EQUAL MAGNITUDES OF RMS VOLTAGE of the same frequency, but the three sets of windings are positioned on the shaft so that there is a PHASE DISPLACEMENT OF 120 DEGREES between the three singlephase voltage waves. The three separate generators are then connected together to form ONE COMPLETE, SYMMETRICAL, SINUSOIDAL THREEPHASE GENERATOR. In regard to the last statement, let us note that the three component generators will be connected together to form either a Yconnected generator or Dconnected (deltaconnected) generator. These two basic generator connections are shown in Figs. 246 and Drawing Bar Code In .NET Framework Using Barcode drawer for VS .NET Control to generate, create barcode image in .NET framework applications. Generate UPCE In VS .NET Using Barcode creator for .NET framework Control to generate, create UPC  E1 image in .NET framework applications. * FREQUENCY is understood to be 60 cycles/second (60 Hz), ! 2f 377 rad/sec.
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Make Bar Code In Java Using Barcode encoder for Eclipse BIRT Control to generate, create barcode image in Eclipse BIRT applications. DataMatrix Printer In None Using Barcode maker for Office Excel Control to generate, create Data Matrix image in Microsoft Excel applications. " " " 247, in which Va , Vb , and Vc are the three singlephase voltages which, from now on, will be called the PHASE VOLTAGES. In the above, A, B, and C denote the OUTPUT TERMINALS of the threephase generators. These three terminals will be connected, by means of a threewire transmission line, to a threephase load. A threephase system is thus basically a threewire system, driven by three interconnected singlephase generators of the same frequency and same rms voltage but with phase di erences of 120 degrees. A threephase generator satisfying these conditions is said to be a BALANCED generator. YConnected Generator; Phase and Line Voltages
In all of our work we ll assume a Yconnected type of generator, since this is normally the connection used in threephase power generation, and we ll assume the generator to be completely balanced, unless speci cally stated otherwise. (The load impedance, however, can be of either the Ytype or the Dtype.) This is illustrated in Fig. 248, in which a balanced Yconnected generator is connected to a balanced threephase load. (The load is said to be balanced because all three Fig. 248
CHAPTER 10 Magnetic Coupling. Transformers
" impedances are given to have the same value of Z ohms.) In the gure we ve used, for the purpose of comparison, both the standard arrow notation and the doublesubscript notation to denote the positive direction of the rms voltage and current vectors relative to some particular reference vector. * In this section we wish to nd the relationships between the PHASE VOLTAGES and the LINE VOLTAGES, the line voltage being the voltage between any two output " " " lines (shown as VAB , VBC , and VCA in the gure). With this in mind, let us concentrate our attention on the generator end of the gure, paying special attention to the subscript notation, in which SMALL subscript letters denote PHASE voltages and LARGE subscript letters denote LINE voltages. Let us take the junction point n as the common reference point in the system. The three individual vector phase voltages are then given with respect to the point n. Thus, if " we take the phase voltage Vna to be the reference vector, then let us agree that, by de nition, we have " Vna Vna =08 where Vna Vnb Vnc Vp because it is given that the phase voltages all have EQUAL MAGNITUDES. Thus the relationships in eq. (421) can be written as " Vna Vp =08 " Vnb Vp = 1208 " Vnc Vp = 2408 422 " Vnb Vnb = 1208 " Vnc Vnc = 2408 421 where Vp is the MAGNITUDE of the phase voltages. Now, in the gure, imagine the junction point n to be the origin of the complex plane, and that Vna lies on the positive xaxis. Then the quantities in eq. (422) could be written in the complex rectangular form Vp cos j sin ; thus, using degrees, and remembering that cos cos and sin sin , " Vna Vp cos 0 j sin 0 Vp " Vnb Vp cos 120 j sin 120 Vp cos 120 j sin 120 0:5 j0:8660 Vp " Vnc Vp cos 240 j sin 240 Vp cos 240 j sin 240 0:5 j0:8660 Vp 425 424 423 Let us now look VERY CAREFULLY at Fig. 248, beginning with the two lines A and B, shown again in Fig. 249. " In Fig. 249, note that VAB is the voltage drop from line A to line B. If, now, we choose to start at A and trace around the loop in the cw sense (following the usual rule of setting the vector sum of the voltage drops equal to the vector sum of the generator voltages), we have that " " " VAB Vnb Vna Then, upon making use of eqs. (424) and (423), you should nd that " VAB 1:5 j0:8660 Vp

