2 N, 3 FIGURE 64.2 Ideal three-winding transformer(a)Ideal three-winding transformer;(b)schematic symbol;(c)per-unit rival 0=N1i1+N2i2+N3l3 Transform Eq (64.8)into phasor notation N11+N22+N33=0 quations(64.6)and(64.)are basic to understanding transformer operation. Consider Eq. (64.6). Also note that-Vp-V2, and-V3 must be in phase, with dotted terminals defined positive. Now consider the total input complex power -S (64.10) Hence, ideal transformers can absorb neither real nor reactive power It is customary to scale system quantities(V, S, 2) into dimensionless quantities called per-unit values. The basic per-unit scaling equation is Per-unit values actual value The base value always carries the same units as the actual value, forcing the per-unit value to be dimensionless Base values normally selected arbitrarily are Vbase and Sase. It follows that© 1999 by CRC Press LLC 0 = N1i1 + N2i2 + N3i3 (64.8) Transform Eq. (64.8) into phasor notation: (64.9) Equations (64.6) and (64.9) are basic to understanding transformer operation. Consider Eq. (64.6). Also note that –V1, –V2, and –V3 must be in phase, with dotted terminals defined positive. Now consider the total input complex power –S. (64.10) Hence, ideal transformers can absorb neither real nor reactive power. It is customary to scale system quantities (V, I, S, Z) into dimensionless quantities called per-unit values. The basic per-unit scaling equation is The base value always carries the same units as the actual value, forcing the per-unit value to be dimensionless. Base values normally selected arbitrarily are Vbase and Sbase. It follows that: FIGURE 64.2 Ideal three-winding transformer. (a) Ideal three-winding transformer; (b) schematic symbol; (c) per-unit equivalent circuit. NI N I NI 11 2 2 3 3 ++= 0 S VI V I VI =++ = 11 2 2 3 3 *** 0 Per-unit value = actual value base value I S V Z V I V S base base base base base base base base = = = 2