R FIGURE 64.3 A practical equivalent circuit. X1 X1 FIGURE 64.4 Transformer polarity terminology:(a)subtractive;(b)additive The circuit of Fig 64.3 is a refinement on that of Fig. 64. 2(c). The values R,, R2, R,, X,, X2, X, are all small (less than 0.05 per-unit)and R, Xm large(greater than 10 per-unit). The circuit of Fig 64.3 requires that all values be in per-unit Circuit data are available from the manufacturer or obtained from conventional tests. It must be noted that although the circuit of Fig 64.3 is commonly used, it is not rigorously correct because it does not properly account for the mutual couplings between windings. The terms primary and secondary refer to source and load sides, respectively (i.e, energy flows from primary to secondary). However, in many applications energy can flow either way, in which case the distinction is meaningless. Also, the presence of a third winding (tertiary) confuses the issue. The terms step up and step down refer to what the transformer does to the voltage from source to load. ANSI standards require that for a two-winding transformer the high-voltage and low-voltage terminals be marked as H1-H2 and X1-X2, respec- ively, with HI and XI markings having the same significance as dots for polarity markings. [Refer to ANSI 57 for comprehensive information. Additive and subtractive transformer polarity refer to the physical posi- tioning of high-voltage, low-voltage dotted terminals as shown in Fig. 64.4. If the dotted terminals are adjacent, then the transformer is said to be subtractive, because if these adjacent terminals(H1-X1)are connected togethe the voltage between H2 and X2 is the difference between primary and secondary. Similarly, if adjacent terminal XI and H2 are connected, the voltage(H1-X2)is the sum of primary and secondary values. The Two-Winding Transformer The device can be simplified to two windings. Common two-winding transformer circuit models are shown z=21+22 64.17) c 1999 by CRC Press LLC© 1999 by CRC Press LLC The circuit of Fig. 64.3 is a refinement on that of Fig. 64.2(c). The values R1, R2, R3, X1, X2, X3 are all small (less than 0.05 per-unit) and Rc, Xm, large (greater than 10 per-unit). The circuit of Fig. 64.3 requires that all values be in per-unit. Circuit data are available from the manufacturer or obtained from conventional tests. It must be noted that although the circuit of Fig. 64.3 is commonly used, it is not rigorously correct because it does not properly account for the mutual couplings between windings. The terms primary and secondary refer to source and load sides,respectively (i.e., energy flows from primary to secondary). However, in many applications energy can flow either way, in which case the distinction is meaningless. Also, the presence of a third winding (tertiary) confuses the issue. The terms step up and step down refer to what the transformer does to the voltage from source to load. ANSI standards require that for a two-winding transformer the high-voltage and low-voltage terminals be marked as H1-H2 and X1-X2, respec￾tively, with H1 and X1 markings having the same significance as dots for polarity markings. [Refer to ANSI C57 for comprehensive information.] Additive and subtractive transformer polarity refer to the physical posi￾tioning of high-voltage, low-voltage dotted terminals as shown in Fig. 64.4. If the dotted terminals are adjacent, then the transformer is said to be subtractive, because if these adjacent terminals (H1-X1) are connected together, the voltage between H2 and X2 is the difference between primary and secondary. Similarly, if adjacent terminals X1 and H2 are connected, the voltage (H1-X2) is the sum of primary and secondary values. The Two-Winding Transformer The device can be simplified to two windings. Common two-winding transformer circuit models are shown in Fig. 64.5. (64.17) FIGURE 64.3 A practical equivalent circuit. FIGURE 64.4 Transformer polarity terminology: (a) subtractive; (b) additive. Ze = + Z1 2 Z