Fig. 257

Decode Code 128 Code Set C In VS .NETUsing Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in VS .NET applications.

Code128 Creation In VS .NETUsing Barcode printer for Visual Studio .NET Control to generate, create Code128 image in VS .NET applications.

" " " " Let IAB , IBC , and ICA denote the three phase currents. Also let VAB be the reference vector, and let be the phase angle between the phase voltages and phase currents, as shown in Fig. 258.

Recognize ANSI/AIM Code 128 In .NET FrameworkUsing Barcode reader for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications.

Create Barcode In VS .NETUsing Barcode maker for .NET Control to generate, create bar code image in Visual Studio .NET applications.

CHAPTER 10 Magnetic Coupling. Transformers

Bar Code Recognizer In .NETUsing Barcode reader for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications.

Draw Code128 In C#.NETUsing Barcode generation for .NET framework Control to generate, create Code 128B image in .NET framework applications.

Fig. 258

Code 128 Maker In .NET FrameworkUsing Barcode drawer for ASP.NET Control to generate, create Code128 image in ASP.NET applications.

Encoding Code-128 In VB.NETUsing Barcode generation for VS .NET Control to generate, create Code 128 image in .NET framework applications.

Now, in regard to Fig. 257, the power PER PHASE is equal to Pp Vp Ip cos hence, TOTAL POWER PT 3Vp Ip cos 441

Draw UPCA In VS .NETUsing Barcode drawer for .NET Control to generate, create UPC-A Supplement 2 image in VS .NET applications.

Bar Code Maker In .NETUsing Barcode encoder for .NET framework Control to generate, create barcode image in .NET framework applications.

as in eq. (439), where Vp and Ip are the magnitudes of the phase voltages and phase " currents and cos is the power factor of each of the three equal impedances Z . Inspection of Fig. 257 shows, however, that the line voltage is EQUAL to the phase voltage in a -connected load. Thus eq. (441) can be written as PT 3VL Ip cos 442

Drawing Barcode In .NET FrameworkUsing Barcode maker for .NET Control to generate, create barcode image in .NET framework applications.

Creating Code11 In .NETUsing Barcode maker for Visual Studio .NET Control to generate, create USD8 image in .NET framework applications.

where VL is the magnitude of line voltage. In the equation, however, we d like also to have the current expressed in terms of line current; this can be done as follows. Consider (for example) junction point A in Fig. 257; by Kirchho s current law, the current equation at A is equal to " " " IA ICA IAB 0 thus, " " " IA IAB ICA 443 " Now, for simplicity, let s consider IAB as the reference vector (this will have no e ect on " " the relative magnitudes of the phase and line currents). Then, since ICA lags IAB by 2408, and since the phase currents all have equal magnitudes, eq. (443) becomes (angles in degrees) " IA Ip =0 Ip = 240 Ip =0 Ip =120 cos 0 j sin 0 cos 120 j sin 120 Ip thus, " IA 1:5 j0:8660 Ip or since, from inspection of Fig. 257, jIA j jIL j

Code 128B Printer In Objective-CUsing Barcode maker for iPhone Control to generate, create Code 128C image in iPhone applications.

Code 128B Creation In .NET FrameworkUsing Barcode generator for ASP.NET Control to generate, create Code 128 Code Set C image in ASP.NET applications.

CHAPTER 10 Magnetic Coupling. Transformers

Barcode Reader In VS .NETUsing Barcode reader for .NET framework Control to read, scan read, scan image in VS .NET applications.

UPC A Creation In NoneUsing Barcode generation for Online Control to generate, create UPC Symbol image in Online applications.

the last equation becomes jIA j IL hence, in magnitudes, p 3I p

Code 128 Code Set B Recognizer In VS .NETUsing Barcode decoder for VS .NET Control to read, scan read, scan image in VS .NET applications.

Scanning Code 39 In C#Using Barcode reader for .NET Control to read, scan read, scan image in .NET applications.

p Ip IL = 3 p 3VL IL cos

Code-128 Generator In NoneUsing Barcode creation for Software Control to generate, create Code 128 image in Software applications.

Code 128 Code Set C Creator In JavaUsing Barcode creation for Android Control to generate, create Code 128 Code Set B image in Android applications.

thus eq. 442 becomes PT where

444

jIA j jIB j jIC j IL Thus, comparison of eqs. (440) and (444) shows that PT is calculated the same way for either a Y-connected or a -connected load. In the above, be reminded that VL and IL are the rms values of line voltage and line current, and thus PT is the total average power produced in a balanced three-phase load. In section 10.7 we mentioned that the total INSTANTANEOUS POWER in a balanced three-phase system is constant. This interesting and important fact can be proved as follows. In Fig. 257, let va , vb , and vc denote the instantaneous values of the three sinusoidal line voltages; then, letting V 0 denote the three equal peak voltages, the instantaneous values of the three voltage waves are va V 0 sin !t vb V 0 sin !t 1208 * vc V 0 sin !t 2408 V 0 sin !t 1208 Then, since the above voltages work into identical loads, the corresponding instantaneous currents would be, letting I 0 denote the three equal peak currents, ia I 0 sin !t ib I 0 sin !t 1208 ic I 0 sin !t 1208 where is the phase angle between the voltage and current waves. Then the total INSTANTANEOUS POWER p is equal to p va ia vb ib vc ic which, upon making the above substitutions, becomes p V 0 I 0 sin !t sin !t sin !t 1208 sin !t 1208 sin !t 1208 sin !t 1208 Note that the above result seemingly says that p is a function of time t, that is, that p varies from instant-to-instant, thus contradicting the statement we made that p remains

* Since it s always understood that !t 2ft radians, it s basically incorrect to write sin !t 1208); instead, since 1208 120 =180 2=3 rad., we should really write sin !t 2=3 . However, the particular operation above is such that there is no harm in writing 1208 instead of 2=3 radians if we wish to do so.