2Autotransformer connected for step-down operation NHS = # of turns on the High SideNLS = # of turns “embraced by the Low Side
3Autotransformer Example Turns ratio = a = NHS / NLs = NA / NB = 80 / 20 = 4VLS = VHS / a = 120 V / 4 = 30 VILS = VLS / ZLOAD = 30/0.5 = 60A >> IHS = ILS / a = 60/4 = 15A
4Autotransformer Example continued How did the load current become 60A?15A provided directly to the load by VHS45A provided to the load by “transformer action”
5Example 3.1A 400-turn autotransformer, operating in the step-down mode with a 25% tap, supplies a 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.
6Example 3.1 part a a = NHS / NLS = 400/(0.25)(400) = 4 VLS = VHS / a = 2400 / 4 = 600 VILS = 4800 VA / 600 V = 8 A = ILOAD
7Example 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
8Two-Winding Transformer connected as an Autotransformer Reconnected as Autotransformer
10Example 3.2A 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.
11As a two-winding transformer Example 3.2 continuedAs a two-winding transformer
19Example 3.3The 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.
20Example 3.3 continuedThe required step-up voltage ratio is a’=VHS / VLS = 230/212 = 1.085Choose the best available voltage ratio from Table 3.1 as a’=1.100.Need a 240-V primary and 12-V secondariesConnect the 120-V primaries in seriesConnect the 12-v secondaries in series
21Example 3.3 (a)Output Voltage = a’VLS = (1.100)(212) = V
22Example 3.3 part (b)The required step-down voltage ratio is a’ = VHS / VLS = 246/230 = 1.070Choose a’ = from Table 3.1Need a 240-V primary and 16-V secondariesConnect the 120-V primaries in seriesConnect the 16-V secondaries in parallel
23Example 3.3 (b) Output voltage = VHS / a’ = 246/1.0667 = 230.6 V Check this connectionPage 102 of the text byHubertOutput voltage = VHS / a’ = 246/ = V