Autotransformer Autotransformer connected for stepdown operation NHS = # of turns on the High Side NLS = # of turns “embraced by the Low Side Autotransformer Example Turns ratio = a = NHS / NLs = NA / NB = 80 / 20 = 4 VLS = VHS / a = 120 V / 4 = 30 V ILS = VLS / ZLOAD = 30/0.5 = 60A >> IHS = ILS / a = 60/4 = 15A Autotransformer Example continued How did the load current become 60A? 15A provided directly to the load by VHS 45A provided to the load by “transformer action” Example 3.1 • A 400-turn autotransformer, operating in the step-down mode with a 25% tap, supplies a 4.8-kVA, 0.85 Fp lagging load. The input to the transformer is 2400-V, 60-Hz. Neglecting the small losses and leakage effects, determine – (a) the load current, – (b) the incoming line current, – (c) the transformed current, – (d) the apparent power conducted and the apparent power transformed. Example 3.1 part a a = NHS / NLS = 400/(0.25)(400) = 4 VLS = VHS / a = 2400 / 4 = 600 V ILS = 4800 VA / 600 V = 8 A = ILOAD Example 3.1 parts b, c, d • (b) ILINE = IHS = ILS / a = 8 A / 4 = 2 A • (c) ITR = ILS – IHS = (8 – 2) A = 6 A • (d) Scond = IHSVLS = (2 A)(600 V) = 1200 VA Strans = ITRVLS = (6 A)(600 V) = 3600 VA Two-Winding Transformer connected as an Autotransformer Two-Winding Transformer Reconnected as Autotransformer S (V V ) I at 1 S V I 2w 2 2 2 S (a 1) S at 2w 2 Example 3.2 • A 10-kVA, 60-Hz, 2400—240-V distribution transformer is reconnected for use as a step-up autotransformer with a 2640-V output and a 2400-V input. • Determine – (a) the rated primary and secondary currents when connected as an autotransformer; – (b) the apparent-power rating when connected as an autotransformer. Example 3.2 continued As a two-winding transformer 10kV A I 41.67A 240V 41.67A I 4.167A 10 LS HS Example 3.2 continued As an autotransformer 2400 S (a 1) S ( 1) 10 110kV A 240 at 2w Example 3.2 Simulation XWM1 T1 10 V I Iinput + 45.859 A AC 1e-009Ohm LOAD 63.35 Ohm V1 2400 V 60 Hz 0Deg + 4.357 + U1 2.640k V AC 1MOhm - Itransform ed A AC 1e-009Ohm + 41.672 - Iconducted A AC 1e-009Ohm Buck-Boost Transformer “Buck”>Subtract the low-voltage output from the line voltage “Boost” >>> Add the low-voltage output to the line voltage Buck-Boost Transformer voltages 120 X 240 V primary 12 X 24 V or 16 X 32 V secondary 120/240 V operation For 120 V operation, connect H1 to H3 and H2 to H4 For 240 V operation, connect H2 to H3 12/24 V or 16/32V operation For 12 V or 16 V operation, connect X1 to X3 and X2 to X4 For 24 or 32 V operation, connect X2 to X3 Available Buck-Boost Voltage Ratios Example 3.3 • The rated voltage of an induction motor driving an air conditioner is 230-V. The utilization voltage is 212-V. – (a) Select a buck-boost transformer and indicate the appropriate connections that will closely approximate the required voltage. – (b) Repeat (a), assuming the utilization voltage is 246-V. Example 3.3 continued • The required step-up voltage ratio is a’=VHS / VLS = 230/212 = 1.085 • Choose the best available voltage ratio from Table 3.1 as a’=1.100. • Need a 240-V primary and 12-V secondaries – Connect the 120-V primaries in series – Connect the 12-v secondaries in series Example 3.3 (a) Output Voltage = a’VLS = (1.100)(212) = 233.2 V Example 3.3 part (b) • The required step-down voltage ratio is a’ = VHS / VLS = 246/230 = 1.070 • Choose a’ = 1.0667 from Table 3.1 • Need a 240-V primary and 16-V secondaries – Connect the 120-V primaries in series – Connect the 16-V secondaries in parallel Example 3.3 (b) Check this connection Page 102 of the text by Hubert Output voltage = VHS / a’ = 246/1.0667 = 230.6 V