Question

A company plans to purchase a transformer that will be used 12 hours at full load and 12 hours with no load but still connected to the power supply at all times. The transformer has copper losses of 5 kW and core losses of 3.5 kW. Electricity costs $0.07/kW-hr. What is the total cost of transformer losses over a period of 1 year?

Answer 1

When the transformer is at full load both copper loss and core loss occur. But core loss is negligible compared to the copper loss as there will be a huge surge of current passing through it as it is in short circuit Thus total power is 5 = 8.5kW.

When the transformer is not connected to the load but is still connected to the power supply it experiences core loss mainly as the primary current loading is very small and we neglect it.Thus total power is 3.5kW.

(For reason scroll further below)

That means on a day total power loss is (12*5) + (12*3.5) = 102kW-hr/day.

It costs 0.07*102 = $7.14/day.

For a year it would cost 7.14*365 = $2606.1

Copper loss occurs when current passes through the conductor of the transformer winding and energy is dissipated as heat. It is also known as I²R loss.It is the same loss that occurs when we connect a battery to a resistor and current flows through it. The energy of the battery is dissipated as heat in the resistor. Another familiar example I can provide is the case of a light bulb, which converts the electrical energy into light and heat.

Core loss occurs due to the changing magnetic field which is dissipated in the core of the transformer.

It is categorized into three categories:

1. Hysteresis loss: To understand this best, look into the B field vs H field graph of a magnetic material which forms a close loop. The process is irreversible and there is energy loss. This occurs when the magnetic field through the core changes, the magnetization of the core material changes by expansion and contraction of the tiny magnetic domains it is composed of, due to movement of the domain walls. This process causes losses because the domain walls get snagged on defects in the crystal structure and then snap past them, dissipating energy as heat.

2. Eddy current: The changing magnetic field induces circulating currents in the core which is proportional to the area of the core. This is due to electromagnetic induction. The circular loop flows perpendicular to the magnetic field and the energy is dissipated as heat. This is the reason why we see cores made thin with insulating coatings.

3. Anamalous loss: It includes any loss other than the above two

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