Losses in Transformer - Hysteresis Loss & Eddy Current Loss (Core or Iron Loss), Copper Loss, Stray Load Loss and Dielectric Loss

 In any machine the difference between input power and output power is defined as the 'loss' of that machine.

In a Transformer, different types of losses are occurred during running condition, like - 

1. Copper Loss or I²R Loss
2. Iron Loss or Core Loss
3. Stray Load Loss
4. Dielectric Loss

 

As a transformer is a static device that's why there is no mechanical loss, means no friction loss and no windage loss is present.

 Copper Loss in Transformer 

Basically in a machine Copper loss or Cu loss or I²R Loss is concerned with the windings, due to winding resistances. In transformer Copper losses is occurred with primary winding and secondary winding. 

Copper Loss Formula : Total Copper Loss Pcu = I₁²R₁ + I₂²R₂ = I₁²R₀₁ = I₂²R₀₂

Where  R₀₁ = Equivalent resistance referred to primary winding = R₁ + R₂՛ = R₁ + (R₂/K²)

     and R₀₂ = Equivalent resistance referred to secondary winding = R₂ + R₁՛ = R₂ + (K²R₁)

             K = Turns Ratio = N₂/N₁

                                                      ∴ Pcu ∝ I²

Full Load Copper Loss Formula : Pcufl = (Ifl)₁²R₀₁ = (Ifl)₂²R₀₂

But usually a transformer may not work at full load. Usually the distribution transformer (located near your house) does not work on full load because the load varies. Generally in day light we may not switch on the tube light and in night time we may switch on the tube lights. Hence a transformer does not operate at full load but a variable load. 

       x % of full load means IL = (x/100) Ifl

That means here the loading is defined by the current. 10% of full load means the current that is flowing 10% of full load current. 

               ∴ Copper loss at x% of full load, Pcu =  (x/100)²Pcufl = {(x/100) Ifl,₁}²R₀₁ 

                                                               ∴ Pcu ∝  x²

In pu full load cu loss = ( I₁²R₀₁/VArating) = (I₁²R₀₁/ E₁I₁) = (I₁R₀₁/E₁) x (I₁/I₁) = pu resistance drop

                           ∴ In pu system %full load Cu loss = % resistance drop 

If x is in terms of fraction then ,        Pcu = x²Pcufl

Where Pcu  = copper loss occurs in the winding of the transformer at any value of current

and Pcufl = cu loss occurs in the winding of the transformer at full load current or rated value of the current. 

Core Loss or Iron Loss

The core loss is occurred in the core of the transformer due to alternating flux set up by the primary winding. 

As the core is made of silicon(Si) steel and steel is made of iron that's why this loss is known as Iron loss also.

Core loss has two components - 1. Hysteresis Loss and 2. Eddy Current Loss.

Hysteresis Loss 

All the magnetic material which we used for construction of transformer are ferromagnetic in nature. In ferromagnetic material spontaneous magnetization is present, that means the magnetization that is present even the absence of magnetic field. Magnetic dipoles retain their magnetization even after absence or removal of magnetic field. In ferromagnetic material, there is some residual flux density (Br).

Brief Description :  

Since the developed flux or magnetic field in the transformer core is alternating in nature, then the dipoles are oriented in one direction for positive cycle and for negative cycle the dipoles are oriented in reversal direction, means the magnetization of dipoles reverse periodically. So we have to apply some energy to dipoles to orient them or reverse them (180⁰) in their orientation. And this energy comes from supply of primary winding. Such energy loss is called as hysteresis loss. 

The hysteresis curve for a magnetic material  looks like - 

Br = Residual flux density. 

The red line curve in the figure represent the freshly prepare sample of magnetic material. When a newly prepared magnetic ferromagnetic material is taken. It is known as virginal curve.

There are two different values of magnetic flux density for same value of magnetic field intensity depending upon whether magnetic field intensity is decreasing or increasing. 

The area under hysteresis loop provides hysteresis loss per cycle.

            ∴ Area of the curve = Hysteresis loss/cycle.  

Total hysteresis loss (for frequency f) = Area of hysteresis curve ✖️ Cycle

                                                            = Area of hysteresis curve ✖️f

Steinmentz Formula :     Phys = ηBₘˣfv 

Where η = Steinmentz constant, x = Steinmentz exponent, f = frequency , v = volume of the core

x depends on properties of material. 

x = 1.6 for Si-steel (CRGO steel). 

We know   Bmax ∝ V/F

Case I : If V/f = constant ⇒ Bmax  = constant ; then  Phys ∝ f.

Case II : If V/f ≠ constant ⇒ Bmax  ≠ constant ; then  Phys ∝ Vˣ f¹⁻ˣ 

                                             

By keeping applied voltage as  constant and by increasing the frequency, hysteresis loss will decrease. 

Eddy Current Loss

The flux is alternating in nature that is set up in the core by primary winding. Then an emf will be induced in the core which causes the swirling current in the core. This current will flow in circular loop like eddy in the sea, that's why this current is called as Eddy Current. And the losses due to this eddy current or circular current is known as Eddy Current Loss.

So, Eddy Current, Iₑ ∝ δ          where δ  = Conductivity

                        ⇒ Rₑ ∝ 1/δ             Rₑ = Resistance of the core.

  Eddy Current Loss Pₑ = IₑRₑ²

                                Pₑ ∝ δ² (1/δ) Pₑ 

                                ∴ Pₑ ∝ δ

If the core is taken as conducting material, we will have more eddy current losses. That's why we add silicon with steel to increase resistivity which will help to reduce the eddy current losses. But we can not add Si more than 4% otherwise core will be brittle. 

Eddy Current Loss Formula : Eddy Current loss, Pₑ = (kBₘ²f²t²)/ρ      

Where Bₘ = Maximum flux density, t= Thickness of the lamination, ρ = Resistivity of the core.

                                              ∴ Pₑ = kₑBₘ²f²t²          

                                               ∴  Pₑ ∝ t²

So thinner the lamination, eddy current loss will be decrease. 

High frequency transformer should have thinner laminations to reduce eddy current losses, Pₑ.  

 

Case I : If V/f = constant ⇒ Bmax  = constant ; then  Pₑ ∝ f².

Case II : If V/f  ≠  constant ⇒ Bmax  ≠ constant ; then  Pₑ ∝ Bₘ²f²

                                                                                 ∴ Pₑ ∝ (V/f)f²

                                                                                 ∴ P ₑ∝ (V/f)²  

                                                                                 ∴ Pₑ ∝ Ⅴ²  

So Eddy current loss is constant if voltage is constant.              

So, if the voltage is kept constant and the frequency is reduced then no change in eddy current loss but Hysteresis loss increases.

 N.B. : How can we separate hysteresis loss and eddy current loss from iron loss ?

  Ans - From open circuit test we can determine iron losses of a transformer.

If V/f  ≠  constant but V  ≠ constant and also f ≠ constant, that means V and f is varying in same proportion to maintain V/f as constant. then we know,

Hysteresis loss, P hys∝ f  and Eddy current loss, Pₑ ∝ f²

Total iron losses, P = P + Pₑihys

                                  = Kₕf +Kₑf²

                            ∴ P / f = Kₕ + Kₑf i  Phys

Kₕ and Kₑ can be determined from the graph by slope and the intercept.

Stray Load Loss

A transformer has iron structure it is not only about core and winding but it will have some outer shield, base, stand. All those things are made of iron. Stray loss occur in those iron parts of the transformer. Hence this loss doesn't occur at a definite place. That means stray load loss no fixed location. Stray load loss depend on load current. 

• Why is it called stray ?

Because this loss occurs in the iron parts of te transformer which are not linked  to the core or to the windings.

             ∴ Variable Loss = Stray load loss, Cu loss

Due to I₂ (load current), leakage flux (φₗ) will be produced, and that leakage flux links with iron part as well as secondary winding, due to which an emf will be induced and for this emf the eddy current will be also induced which will lead to loss.

The Stray load loss has two components.

1. Iron stray load loss
2. Copper stray load loss

In transformer, magnetic leakage flux generates some additional iron losses that are counted against losses of iron stray load. More or less eddy current loss depend on load. 

Copper Stray Load Losses occur in primary and secondary transformer winding conductors and can be minimized by using Stranded Conductors instead of Solid Conductors.

Practically, Stray load loss = 0.5% of output power.

That's why stray load loss is mostly neglected. 

Dielectric Loss

Normally this loss occurs in the in the transformer such as the inter winding insulation, transformer oil. insulating material

No insulator is perfect None of the insulator can guaranty that there will be zero current through it. Though in an insulator the resistivity is very high, still there will be a leakage current through insulator. This leakage current value is very small, . Due to this leakage current dielectric losses occur in the transformer. So we can say these losses occur  due to finite resistivity of the insulating material and it allow a leakage current through it.Reason of dielectric loss :in the form of mA and μA

                     Dielectric loss = 0.25% of output power.

Dielectric losses are depended on the applied voltage instead of the current, carrying by the load.

                ∴ Dielectric loss = constant loss.