Iron and copper losses in transformers

Losses occur in any kind of electrical equipment over a long period of time, and power transformers are no exception. In the power transformer loss
In the power transformer loss, mainly divided into copper loss and iron loss two parts.

Copper loss
Definition and principle
Copper in the transformer plays an important role in the transformer winding will usually use copper wire, which transformer ‘copper loss’ is the copper wire loss.
The ‘copper loss’ in a transformer is the loss produced by the copper conductor. The ‘copper loss’ of a transformer is also called the load loss. The so-called load loss is a variable loss, which changes.
When the transformer is operated under load, the current through the wire will have resistance, resulting in resistance loss. According to Joule’s law, this resistance
flow through the current will produce Joule heat, and the higher the current, the greater the power loss. Thus, the resistance loss is proportional to the square of the current and
It is independent of the voltage. It is because it changes with the size of the current changes, so the copper loss (load loss) is variable loss, it is also the
The main loss in the operation of the transformer.

Influencing factors
Current size: as mentioned above, the copper loss is proportional to the square of the current, so the current size is the key factor affecting the copper loss.
Winding resistance: the size of the winding resistance directly affects the copper loss. The higher the resistance, the higher the copper loss.
Coil layers: the more layers of coil, the longer the path of current flow in the winding, the resistance will increase accordingly, resulting in increased copper losses.
Switching frequency: The effect of switching frequency on transformer copper loss is directly related to the distribution parameters of the transformer and the load characteristics. In the load
characteristics and distribution parameters together with the inductive characteristics, copper losses with the increase in switching frequency and reduce; together with the capacitive characteristics, copper losses with the increase in switching frequency and increase.
When the load characteristics and distribution parameters are inductive together, the copper loss decreases with the increase of switching frequency.
Temperature effect: load loss is also affected by the transformer temperature, while the leakage flux caused by the load current will generate eddy current loss inside the winding and eddy current loss outside the winding.
loss in the winding, and in the metal part of the winding outside the stray loss.

There are two calculation formulas
1. Formula based on rated current and resistance:
Copper loss (unit: kW) = I² × Rc × Δt
Where I is the rated current of the transformer, Rc is the resistance of the copper wire, Δt is the operating time of the transformer.
2. Formula based on rated current and total copper resistance:
Copper loss = I² × R
Where I denotes the rated current of the transformer and R denotes the total copper resistance of the transformer.
The total copper resistance R of the transformer can be calculated by the following formula:

R = (R1 + R2) / 2
Where, R1 denotes the primary side copper resistance of the transformer and R2 denotes the secondary side copper resistance of the transformer.

Methods of reducing copper losses
Improve the winding cross-sectional area of the transformer: reduce the conductor resistance, thus effectively reducing the transformer copper loss.
Adopt high quality conductor material: such as copper foil or aluminium foil to reduce the winding resistance.
Reduce the light-load operation time of the transformer: limit the proportion of time for light-load operation of the transformer, which is conducive to reducing the copper loss of the transformer.

Iron loss
Definition and principle
Different from copper loss, iron loss of transformer has nothing to do with the winding, current size and other factors, as the name suggests, iron loss is related to iron, which is produced by iron
It is produced by the iron core. Transformer iron loss is also known as ‘no-load loss’, because it exists in the transformer full load, zero load state, is a fixed loss of the transformer.
It is a fixed loss of the transformer. However, under load, the power loss decreases as the electric field strength decreases.

Transformer iron loss is divided into hysteresis loss and eddy current loss.
Hysteresis losses
The working principle of transformer is precisely based on the principle of electromagnetic induction to achieve the lift voltage and current change, and the magnetic flux inside the transformer is flowing on the iron core.
The magnetic flux inside the transformer is flowing on the iron core, and the iron core has magnetic resistance to the magnetic flux, just like a conductor has resistance to the current, which also generates heat, and this kind of loss is called ‘hysteresis loss’.
This loss is called ‘hysteresis loss’.
Eddy current loss
When the primary winding of the transformer is energised, the magnetic flux generated by the coil flows in the iron core, because the core itself is a conductor, perpendicular to the plane of the magnetic lines of force.
Magnetic line of the plane will be induced potential, this potential in the section of the iron core to form a closed loop and produce current, like a vortex, so it is called ‘eddy current loss’.
This potential forms a closed loop in the section of the core and produces a current, like a vortex, so it is called ‘eddy current’. The loss generated by this eddy current is called ‘eddy current loss’. It is precisely because the core generates eddy currents that the core is made thin.
It is also because the core generates eddy currents that it is made into a thin piece, because the thinner it is, the higher the resistance and the lower the current.
Influencing factors
Operating voltage and frequency: iron loss and transformer operating voltage and frequency, because these factors will affect the core of the magnetic field strength and hysteresis phenomenon.
and hysteresis.

Iron core material: the hysteresis nature of the core material will affect the size of the iron loss. If the core material is not well chosen, the hysteresis loss will increase.

Manufacturing process: the manufacturing process of the transformer also has a certain impact on the iron loss. For example, the core of the stacked piece way, insulation treatment will affect the
The size of the iron loss.

Calculation method
1. Based on the rated current and hysteresis, resistance loss formula:
Iron loss (unit: kVA) = I² × (Rm + Ra)
Where I is the rated current of the transformer, Rm is the hysteresis loss of the core, Ra is the resistance loss of the core.

2. Equation based on constant, flux density and operating frequency:
P iron = Kf × (Bm)^2 × f
Where PFe is the iron loss, Kf is the constant, Bm is the magnetic flux density, and f is the transformer operating frequency.

Reduction method
Selection of high-quality core materials: selection of hysteresis loss of small core materials, can reduce the iron loss of the transformer.
Optimise the manufacturing process: by improving the iron core stacking method, insulation treatment and other manufacturing processes, reduce iron loss.

Reasonable design: in the design stage of the transformer, through the optimisation of structural design and parameter selection, reduce iron loss.