T/F: under-loaded distribution transformer losses

FALSE.

Justification:

A transformer has two kinds of loss:

• No-load (core) loss $P_i$: constant whenever the transformer is energised, regardless of load.
• Load (copper) loss: $P_{cu} = x^2 P_{cu,FL}$, where $x$ is the fraction of rated load.

Efficiency is maximum when copper loss equals core loss, i.e. at load fraction

$$x_{\eta,max} = \sqrt{\frac{P_i}{P_{cu,FL}}}$$

which is typically 40–60% of rating for distribution transformers.

When the transformer is significantly under-loaded:

• Copper loss becomes very small, but the core loss continues for all 8760 hours.
• The energy delivered is small, so the percentage energy loss rises.

Example: 100 kVA unit, $P_i = 200$ W, $P_{cu,FL} = 1100$ W, LLF taken as 0.3 for illustration.

The 20 kVA case carries one-third of the load but has two-thirds of the losses, so loss per kWh delivered is about twice as high.

Therefore gross under-loading (oversized transformers) wastes energy through core loss, as well as capital. Moderate under-loading near the maximum-efficiency point is beneficial; very light loading is not. This is why transformers should be sized for the realistic design-year demand and why low-loss cores are used where load factor is low.