Autotransformer connected for step- down operation N HS = # of turns on the High Side N LS = # of turns embraced by the Low Side
Autotransformer Example Turns ratio = a = N HS / N Ls = N A / N B = 80 / 20 = 4 V LS = V HS / a = 120 V / 4 = 30 V I LS = V LS / Z LOAD = 30/0.5 = 60A >> I HS = I LS / a = 60/4 = 15A
Autotransformer Example continued How did the load current become 60A? 15A provided directly to the load by V HS 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 F p 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 = N HS / N LS = 400/(0.25)(400) = 4 V LS = V HS / a = 2400 / 4 = 600 V I LS = 4800 VA / 600 V = 8 A = I LOAD
Example 3.1 parts b, c, d (b)I LINE = I HS = I LS / a = 8 A / 4 = 2 A (c)I TR = I LS – I HS = (8 – 2) A = 6 A (d)S cond = I HS V LS = (2 A)(600 V) = 1200 VA S trans = I TR V LS = (6 A)(600 V) = 3600 VA
Two-Winding Transformer connected as an Autotransformer Two-Winding TransformerReconnected as Autotransformer
Example 3.2 A 10-kVA, 60-Hz, 2400240-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
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=V HS / V LS = 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 = aV LS = (1.100)(212) = 233.2 V
Example 3.3 part (b) The required step-down voltage ratio is a = V HS / V LS = 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 = V HS / a = 246/1.0667 = 230.6 V