When per-unit scaling is applied to transformers vase is usually taken as Rated as in each winding. Sb common to all windings; for the two- winding case Sus is Srated, since Srated is common to both windings Per-unit scaling simplifies transformer circuit models. Select two primary base values, VIbus and S,hase Base alues for windings 2 and 3 are V (64.11) By definition 1、=513 (6413) It follows that (6414) Thus, Eqs. (64.3)and(64.)scaled into per-unit become: 64.15) +1、+ (64.16) The basic per-unit equivalent circuit is shown in Fig. 64.2(c). The extension to the n-winding ing case is clear. A Practical Three-Winding Transformer Equivalent Circuit The circuit of Fig. 64.2(c)is reasonable for some power system applications, since the core and windings of actual transformers are constructed of materials of high u and o, respectively, though of course not infinite However, for other studies, discrepancies between the performance of actual and ideal transformers are too great to be overlooked. The circuit of Fig. 64. 2(c)may be modified into that of Fig 64.3 to account for the most important discrepancies. Note RR2 R, Since the winding conductors cannot be made of material of infinite conductivity, the windings must have X,,X2 X, Since the core permeability is not infinite, not all of the flux created by a given winding current will be confined to the core. The part that escapes the core and seeks out parallel paths in surroundir structures and air is referred to as leakage flux. ReAm Also, since the core permeability is not infinite, the magnetic field intensity inside the core is not zero. Therefore, some current flow is necessary to provide this small H. The path provided in the circuit for this"magnetizing "current is through Xm. The core has internal power losses, referred to as core loss, due to hystereses and eddy current phenomena. The effect is accounted for in the resistance R. Sometimes R, and Xm are negle c 1999 by CRC Press LLC© 1999 by CRC Press LLC When per-unit scaling is applied to transformers Vbase is usually taken as Vrated as in each winding. Sbase is common to all windings; for the two- winding case Sbase is Srated, since Srated is common to both windings. Per-unit scaling simplifies transformer circuit models. Select two primary base values, V1base and S1base. Base values for windings 2 and 3 are: (64.11) and (64.12) By definition: (64.13) It follows that (64.14) Thus, Eqs. (64.3) and (64.6) scaled into per-unit become: (64.15) (64.16) The basic per-unit equivalent circuit is shown in Fig. 64.2(c). The extension to the n-winding case is clear. A Practical Three-Winding Transformer Equivalent Circuit The circuit of Fig. 64.2(c) is reasonable for some power system applications, since the core and windings of actual transformers are constructed of materials of high m and s, respectively, though of course not infinite. However, for other studies, discrepancies between the performance of actual and ideal transformers are too great to be overlooked. The circuit of Fig. 64.2(c) may be modified into that of Fig. 64.3 to account for the most important discrepancies. Note: R1,R2,R3 Since the winding conductors cannot be made of material of infinite conductivity, the windings must have some resistance. X1,X2,X3 Since the core permeability is not infinite, not all of the flux created by a given winding current will be confined to the core. The part that escapes the core and seeks out parallel paths in surrounding structures and air is referred to as leakage flux. Rc,Xm Also, since the core permeability is not infinite, the magnetic field intensity inside the core is not zero. Therefore, some current flow is necessary to provide this small H. The path provided in the circuit for this “magnetizing” current is through Xm. The core has internal power losses, referred to as core loss, due to hystereses and eddy current phenomena. The effect is accounted for in the resistance Rc. Sometimes Rc and Xm are neglected. V N N V V N N 2 V 2 1 1 3 3 1 1 base base base base = = S S S S 1 2 3 base = base = base = base I S V I S V I S V 1 1 2 2 3 3 base base base base base base base base base = = = I N N I I N N I 2 1 2 1 3 1 3 1 base base base base = = V1 V2 V3 pu pu pu = = I I I 1 2 3 0 pu pu pu + + =