Relation between core diameter of transformer and the copper and iron losses
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In an electrical power transformer, there are primary, secondary and may be tertiary windings. The performance of a transformer mainly depends upon the flux linkages between these windings. For efficient flux linking between these windings, one low reluctance magnetic path common to all windings should be provided in the transformer. This low reluctance magnetic path in transformer is known as core of transformer.Influence of Diameter of Transformer CoreLet us consider, the diameter of transformer core be ′D′
Then, cross-sectional area of the core,Now, voltage per turn,Where, Bm is the maximum flux density of the core.E is proportional to D2.
Therefore voltage per turn is increased with increase in diameter of transformer core.
Again if voltage across the winding of transformer is V.
Then V = eN, where N is the number of turns in winding.
If V is constant, e is inversely proportional to N. And hence, D2 is inversely proportional to N. So, diameter of the core is increased, the number of turns in the transformer winding reduced. Reduction of number of turns, reduction in height of the core legs in-spite of reduction of core legs height increased in core diameter, results increase in overall diameter of magnetic core of transformer. This increased steel weight ultimately leads to increased core losses in transformer. Increased diameter of the core leads to increase in the main diameter on the winding. In – spite of increased diameter of the winding turns, reduced number of turns in the windings, leads to less copper loss in transformer.
So, we go on increasing diameter of the transformer core, losses in the transformer core will be increased but at the same time, load loss or copper loss in transformer is reduced. On the other hand, if diameter of the core is decreased, the weight of the steel in the core is reduced; which leads to less core loss of transformer, but in the same time, this leads to increase in number of turns in the winding, means increase in copper weight, which leads to extra copper loss in transformer. So, diameter of the core must be optimized during designing of transformer core, considering both the aspects.
Then, cross-sectional area of the core,Now, voltage per turn,Where, Bm is the maximum flux density of the core.E is proportional to D2.
Therefore voltage per turn is increased with increase in diameter of transformer core.
Again if voltage across the winding of transformer is V.
Then V = eN, where N is the number of turns in winding.
If V is constant, e is inversely proportional to N. And hence, D2 is inversely proportional to N. So, diameter of the core is increased, the number of turns in the transformer winding reduced. Reduction of number of turns, reduction in height of the core legs in-spite of reduction of core legs height increased in core diameter, results increase in overall diameter of magnetic core of transformer. This increased steel weight ultimately leads to increased core losses in transformer. Increased diameter of the core leads to increase in the main diameter on the winding. In – spite of increased diameter of the winding turns, reduced number of turns in the windings, leads to less copper loss in transformer.
So, we go on increasing diameter of the transformer core, losses in the transformer core will be increased but at the same time, load loss or copper loss in transformer is reduced. On the other hand, if diameter of the core is decreased, the weight of the steel in the core is reduced; which leads to less core loss of transformer, but in the same time, this leads to increase in number of turns in the winding, means increase in copper weight, which leads to extra copper loss in transformer. So, diameter of the core must be optimized during designing of transformer core, considering both the aspects.
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