An autotransformer utilizes a single continuous winding. On the other hand, a two-winding transformer consists of two separate windings, one for the primary and the other for the secondary. In an autotransformer, the secondary is tapped from a specific turn of its winding. It saves some copper. Obviously, copper means money. So this optimizes the cost of the transformer.
Theory of Autotransformers
Here, AB is the total winding. C is the tap point from which we take out the secondary terminal. The primary voltage V1 is applied across AB. The load is connected across BC. Say the load voltage is V2. Now, let the primary current be I1, and the secondary current be I2.
Now, we shall apply Kirchhoff’s current law in this circuit. We will see that at point C, current I1 enters from the upper side (meaning from point A). The current I2 leaves from point C towards the load. So, how much current flows through the middle common portion of the winding, i.e., through CB? Obviously, the current flowing through this portion is (I2 − I1) from B to C.
Now we know that the quantity of copper required to construct a winding depends on two factors:
- The cross-sectional area of the conductor of the winding
- The number of turns used in the winding
Again, the cross-sectional area of the conductor depends on the rated amount of current that will flow through it. So, we can say that the quantity of copper required for a winding depends on the product of these two factors: the number of turns in that winding and the current passing through it.
Weight of Copper
Accordingly, we can say that the weight of copper of the AC portion of the winding is directly proportional to (N1 − N2) × I1. Here, N1 is the number of turns of the entire winding. N2 is the number of turns for the common portion of the winding. In other words, we can say that N1 is the number of primary turns and N2 is the number of secondary turns.
Now, moving to the BC portion. Here, the weight of copper is proportional to the number of turns in the BC portion, which is N2, and the current through that portion, i.e., (I2 − I1).
Now, consider the weight of copper required for the entire winding is WA. Therefore, we can write: \[W_A\propto(N_1-N_2)I_1+N_2(I_2-I_1)\]
Now consider a two-winding transformer of the same rating. That means:
- The primary has voltage V1, full-load current I1, and number of turns N1.
- The secondary has voltage V2, current I2, and number of turns N2.
Obviously, the weight of copper of the primary winding will be proportional to N1I1. Additionally the weight of copper of the secondary winding will be proportional to N2I2. So, the total weight of copper of the windings will be proportional to (N1I1+N2I2). Therefore, we can write: \[W_T\propto(N_1I_1+N_2I_2)\]. Where WT is the total weight of two windings together.
Therefore, the ratio of the weight of copper of an autotransformer to the weight of copper of a two-winding transformer will be:\[\frac{W_A}{W_T} = \frac{(N_1-N_2)I_1+N_2(I_2−I_1)}{N_1I_1+N_2I_2}\]\[=\frac{1-\frac{2N_2}{N1}}{1+\frac{N_2I_2}{N_1I_1}}\]\[=\frac{1-\frac{2}{K}}{2}=1-\frac{1}{K}\]Where K is the transformation ratio of the transformer (same for both the autotransformer and the two-winding transformer).
Copper Saving
From the previous result\[\frac{W_T}{W_A}=1−\frac{1}{K}\]\[W_A = W_T\left(1 − \frac{1}{K}\right)\]\[W_A=W_T – \frac{W_T}{K}\]Therefore, the saving of copper is\[W_T−W_A = \frac{W_T}{K}\] That means, the saving is equal to the weight of copper of an ordinary two-winding transformer divided by the transformation ratio (K).
Now, suppose the transformation ratio is small, meaning it is nearer to unity. In that case, the copper saving becomes high. If the transformation ratio is higher (more than 2), the copper saving will not be very significant. Even though we can achieve some savings. We always have to provide an additional winding in autotransformers. We call it the tertiary winding. It requires extra copper expenditure for this delta-connected winding.
Now, if we compare the cost of the tertiary winding with the saving of copper, we find that copper saving in an autotransformer is justified only when the transformation ratio is less than 2. As soon as the transformation ratio becomes more than 2, the amount of copper saved by using an autotransformer becomes less than the copper spent on arranging the tertiary winding.
In an autotransformer, a tertiary winding is a must. On the other hand, does not require tertiary wind. Because in a two-winding transformer, at least one side always has a delta winding. Then there is no need for an additional tertiary winding. So, in that case, the extra expenditure for the tertiary winding does not arise. Therefore, only when the transformation ratio is less than 2, an autotransformer is economically justified. Otherwise, an autotransformer is not very economical.