Question

A single-phase two-winding transformer is rated at 15 kVA, 1100/220 V. It is reconnected as an autotransformer with a voltage rating of 1320/1100 V. Find the kVA rating of the autotransformer.

Hint:

When a two-winding transformer is reconfigured as an autotransformer, its kVA rating increases by a factor of \((k+1)\), where \(k\) is the turns ratio of the original high-voltage winding to the low-voltage winding. This is a quick way to find the new rating.

Answer 1

Step 1: Understanding the Question:
We are given a standard two-winding transformer's specifications. It is then reconnected to function as an autotransformer. The goal is to calculate the new, higher kVA rating in the autotransformer configuration. The connection is from 1100 V to 1320 V, which is an additive polarity step-up connection (1100 V + 220 V = 1320 V).
Step 2: Key Formula or Approach:
The kVA rating of an autotransformer formed by reconnecting a two-winding transformer can be found using the following relation: \[ (kVA)_{auto} = \left( \frac{V_{High}}{V_{High} - V_{Low}} \right) \times (kVA)_{two-winding} \] Alternatively, using the transformation ratio (\(k\)) of the original two-winding transformer: \[ (kVA)_{auto} = (k+1) \times (kVA)_{two-winding} \quad \text{(for additive polarity)} \] where \(k = \frac{V_{HV}}{V_{LV}}\) of the two-winding transformer.
Step 3: Detailed Explanation:
Method 1: Using Voltages of the Autotransformer

• Autotransformer High Voltage, \(V_{High} = 1320\) V.
• Autotransformer Low Voltage, \(V_{Low} = 1100\) V.
• Two-winding transformer kVA rating, \((kVA)_{two-winding} = 15\) kVA.

Substituting these values into the formula: \[ (kVA)_{auto} = \left( \frac{1320}{1320 - 1100} \right) \times 15 \] \[ (kVA)_{auto} = \left( \frac{1320}{220} \right) \times 15 \] \[ (kVA)_{auto} = 6 \times 15 = 90 \text{ kVA} \] Method 2: Using Transformation Ratio of the Two-winding Transformer

• High Voltage winding, \(V_{HV} = 1100\) V.
• Low Voltage winding, \(V_{LV} = 220\) V.
• Transformation ratio, \(k = \frac{1100}{220} = 5\).

Using the formula for additive polarity: \[ (kVA)_{auto} = (k+1) \times (kVA)_{two-winding} \] \[ (kVA)_{auto} = (5+1) \times 15 = 6 \times 15 = 90 \text{ kVA} \] Step 4: Final Answer:
Both methods yield the same result. The kVA rating of the autotransformer is 90 kVA. This significant increase in power handling capacity is a key advantage of using an autotransformer when the voltage ratio is close to unity.