QUESTION 3: THREE-PHASE TRANSFORMERS 3.1 State TWO functions of the oil used in oil-filled transformers - NSC Electrical Technology Power Systems - Question 3 - 2016 - Paper 1

1. Copper Losses: These losses occur due to the resistance in the windings of the transformer, leading to heat generation when current flows.
2. Iron Losses: Also known as core losses, these arise due to the magnetization and demagnetization of the transformer core as the alternating current flows through.

1. Higher Efficiency: Three-phase transformers are generally more efficient and can transfer more power with less loss compared to single-phase transformers.
2. Reduced Size: They are more compact for the same power rating, which leads to savings in materials and space requirements.

A transformer operates on the principle of conservation of energy. The output power cannot exceed the input power, as losses due to heat and other factors must be taken into account. Therefore, while the voltage can be increased (step-up transformer), the power (the product of voltage and current) remains constant, meaning that increasing voltage would result in a decrease in current.

If the load on a step-down transformer is increased, the transformer will draw more power from the supply to deliver the increased load. Assuming the voltage remains constant, the primary current will increase to meet the demand of the load.

To calculate the primary line current ($I_{PL}$), we use the formula:

$I_{PL} = \frac{S}{\sqrt{3} V_{LP}}$

Where:

• $S = 20000$ VA (20 kVA)
• $V_{LP} = 6600$ V (primary line voltage)

Substituting in the values:

$I_{PL} = \frac{20000}{\sqrt{3} \times 6600} \approx 1.75 A$.

To find the secondary phase voltage ($V_{PH}$), we use:

$V_{PH} = \frac{V_{LS}}{\sqrt{3}}$

Where the secondary line voltage ($V_{LS}$) is 380 V:

$V_{PH} = \frac{380}{\sqrt{3}} \approx 219.39 V$.

The transformer ratio ($TR$) can be calculated using:

$TR = \frac{V_{PH (primary)}}{V_{PH (secondary)}}$

Thus,

• $V_{PH (primary)} = 6600 / \sqrt{3}$
• $V_{PH (secondary)} = 219.39$

Therefore:

$TR = \frac{\frac{6600}{\sqrt{3}}}{219.39} \approx 30:1$.