The iron losses of a transformer includes two types of losses,
1. Hysteresis loss and 2. Eddy current loss
V = 4.44 f Φm N = 4.44 f Bm A N
Where A = area
... Bm α (V/f) .......... For constant A and N
Phα Bm1.6 f
The eddy current loss is given by,
Peα Bm2 f2
But Bmα (V/f)
... Phα (V/f)1.6 x f and Peα (V/f)2 x f2
... Ph1 /Ph2 = (V1 /V2)1.6 x (f2 /f1)1.6 x (f1/f2) and Pe1 /Pe2 = (V1 /V2)2 x (f2 /f1)2 x (f1/f2 )2
Now V2 = 2 V1 and f2 = 0.5 f1
... 750/Ph2 = (0.5)1.6 x (0.5)1.6 x 2 and 250/Pe2 = (0.5)2 x (0.5)2 x (2)2
... Ph2 = 3446.095 W and Pe2 = 1000 W
... Total new iron loss = Ph2 + Pe2 = 4446.095 W
For a given volume and thickness of laminations, these losses depend on the operating frequency, maximum flux density and the voltage.
It is known that for a transformer,
V = 4.44 f Φm N = 4.44 f Bm A N
Where A = area
... Bm α (V/f) .......... For constant A and N
Thus as voltage changes, the maximum flux density changes and both eddy current and hysteresis losses also changes. As voltage increases, the maximum flux density in the core increases and total iron loss increases.
As frequency increases, the flux density in the core decreases but as the iron loss is directly proportional to the frequency hence effect of increased frequency is to increase the iron losses.
Key Point : Thus iron loss increases as the voltage and frequency increases for the transformer.Example 1 : 1 kv/ 2 KV transformer has 750 W hysteresis losses and 250 W eddy current losses. When the applied voltage is doubled and frequency id halfed, find the new losses.
Solution : The hysteresis loss is given by,Phα Bm1.6 f
The eddy current loss is given by,
Peα Bm2 f2
But Bmα (V/f)
... Phα (V/f)1.6 x f and Peα (V/f)2 x f2
... Ph1 /Ph2 = (V1 /V2)1.6 x (f2 /f1)1.6 x (f1/f2) and Pe1 /Pe2 = (V1 /V2)2 x (f2 /f1)2 x (f1/f2 )2
Now V2 = 2 V1 and f2 = 0.5 f1
... 750/Ph2 = (0.5)1.6 x (0.5)1.6 x 2 and 250/Pe2 = (0.5)2 x (0.5)2 x (2)2
... Ph2 = 3446.095 W and Pe2 = 1000 W
... Total new iron loss = Ph2 + Pe2 = 4446.095 W
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thx,you really helped me
ReplyDeleteno sorry
Deletetransformers are rated in KVA not KW helped me in exam time thank you
ReplyDeleteReally helpful and understanable.. Thanks
ReplyDeleteThank u very much..it helps me to
ReplyDeleteunderstanding rating of T/F.
Thank you very much.. It was really helpful to me
ReplyDeleteVery clearly explained. Thank u very much!
ReplyDeleteIf frequency increased with constant voltage - hysteresis loss reduces and eddy current loss unaffected. Please correct
ReplyDeleteBut voltage is doubled here dude
Deleteiron losses depends on frequency is not correct to say , only hysteresis losses depends on frequency.
ReplyDeleteTq it is easy to under stand
ReplyDelete