How to Calculate Transformer Losses?

Transformers are essential components in electrical power systems, serving to transfer electrical energy between circuits through electromagnetic induction. While they are highly efficient devices, they are not without losses. Understanding and calculating transformer losses is crucial for engineers and technicians to optimize performance, improve efficiency, and reduce operational costs. This blog will give a detailed overview of how to calculate transformer losses, which is one of the essential steps toward optimizing transformer design and operation.

Understanding Transformer Losses

Transformer losses can be broadly categorized into two main types: core losses (also known as iron losses) and copper losses (also known as winding losses). Each type of loss has distinct characteristics and causes, and understanding these is vital for accurate calculations.

1. Core Losses in Transformer

Core losses occur in the transformer’s magnetic core and are primarily due to two components: hysteresis loss and eddy current loss.

1.1 Hysteresis Loss

Hysteresis loss is caused by the magnetization and demagnetization of the core material as the alternating current (AC) flows through the transformer. Each cycle of magnetization results in energy loss due to the friction of magnetic domains within the material. The hysteresis loss can be calculated using the formula:

P_h = K_h⋅fⁿ⋅Bⁿ_max ⋅V

Where:

P_h = hysteresis loss (W)

K_h = Hysteresis loss constant (depends on the material)

f = frequency of the AC supply (Hz)

B_max = maximum flux density (Tesla)

( n ) and ( m ) = Material constants (typically ( n \approx 1.6 ) and ( m \approx 2 ))

The hysteresis loss is influenced by the frequency of the supply voltage and the maximum flux density. Higher frequencies and flux densities lead to increased hysteresis losses.

1.2 Eddy Current Loss

Eddy current loss is caused by circulating currents induced in the core material due to the changing magnetic field. These currents generate heat, leading to energy loss. Eddy current loss can be calculated using the formula:

P_e = K_e⋅B_max²⋅f²⋅t²⋅V

Where:

P_e = eddy current loss (W)

K_e = Eddy current loss constant (depends on the material)

t = thickness of the core laminations (m)

Eddy current losses can be minimized by using laminated cores, which reduce the thickness of the conductive material and thus limit the flow of eddy currents.

1.3 Total Core Loss

The total core loss in a transformer is the sum of hysteresis and eddy current losses:

P_core = P_h + P_e​

2. Copper Losses in Transformer

Copper losses occur due to the resistance of the windings when current flows through them. These losses are proportional to the square of the current and can be calculated using the formula:

P_c = I²⋅R

Where:

P_c = copper loss (W)

I = Load current (A)

R = Resistance of the winding (Ω)

Copper losses are significant, especially under heavy load conditions, and can account for a substantial portion of the total losses in a transformer.

2.1 Calculating Resistance

The resistance of the winding can be calculated using:

R = (ρ⋅L)/A

Where:

( \rho ) = Resistivity of the conductor material (Ω·m)

( L ) = Length of the conductor (m)

( A ) = Cross-sectional area of the conductor (m²)

How to Calculate Total Losses in Transformer?

The total losses in the transformer can be calculated by summing the core losses and copper losses:

P_total = P_core + P_c

Example Calculation: Step-by-Step Teaching Guidance

To illustrate the calculation of transformer losses, let’s consider a transformer with the following specifications:

Core material constants: ( k_h = 0.01 ), ( k_e = 0.002 )

Frequency ( f = 50 ) Hz

Maximum flux density ( B_max = 1.2 ) T

Volume of the core ( V = 0.1 ) m³

Load current ( I = 100 ) A

Resistance of the winding ( R = 0.5 ) Ω

Step 1: Calculate Hysteresis Loss

Using the hysteresis loss formula:

P_h =0.01⋅(50)^1.6⋅(1.2)²⋅0.1

Calculating each component:

( (50)^{1.6} \approx 112.2 )

( (1.2)^{2} = 1.44 )

Now substituting back:

Ph ≈ 0.01⋅112.2⋅1.44⋅0.1≈ 0.0162P h ≈ 0.01⋅112.2⋅1.44⋅0.1 ≈ 0.0162 W

Step 2: Calculate Eddy Current Loss

Using the eddy current loss formula:

P_e = 0.002⋅(50)²⋅(1.2)²⋅(0.01)²

Calculating each component:

( (50)^2 = 2500 )

( (1.2)^2 = 1.44 )

Now substituting back:

P_e ≈ 0.002⋅2500⋅1.44⋅0.0001 ≈ 0.00072 W

Step 3: Calculate Total Core Loss

Now, summing the core losses:

P_core = P_h + P_e ≈ 0.0162 + 0.00072 ≈ 0.01692 W

Step 4: Calculate Copper Loss

Using the copper loss formula:

P_c = I²⋅R = (100)²⋅0.5 = 10000⋅0.5 = 5000 W

Step 5: Calculate Total Losses

Finally, summing the total losses:

P_total  = P_core + P_c ≈ 0.01692 + 5000≈ 5000.01692 W

Conclusion

In a word, calculating transformer losses is a critical aspect of transformer design and operation. By understanding the types of losses — core losses and copper losses — engineers can make informed decisions to optimize transformer performance. Accurate calculations of hysteresis and eddy current losses, along with copper losses, allow for precise total losses in transformers,  leading to a better understanding of their efficiency running condition. Always ensure to use accurate material constants and measurements for precise calculations.