## Transformer Losses

Table of Contents

Primary copper loss and Secondary copper loss, Transformer Losses, Iron loss, Dielectric loss, Stray load loss

**Transformer Losses**

Transformer losses are caused by the magnetic field alternating in the core and the electrical current flowing in the coils. The losses produced in the core are known as no-load losses, whereas the losses connected to the coils are known as load losses.

1. Primary copper loss

2. Secondary copper loss

3. Iron loss

4. Dielectric loss

5. Stray load loss

These are explained below.

#### Primary copper loss and Secondary copper loss

Primary and Secondary copper losses take place in the Respective winding resistances due to the flow of the current in them. The primary and secondary resistances differ from their d.c. values due to skin effect and the temperature rise of the Windings. While the average temperature rise can be Approximately used, the skin effect is harder to get Analytically. The short circuit test gives the value of Re taking into account the skin effect.

#### Iron loss

The iron losses contain two components – Hysteresis loss and Eddy current loss.

The Hysteresis loss is a function of the material used for the core. **Ph = KhB1.6f ** For constant voltage and constant Frequency operation this can be taken to be constant. The eddy current loss in the core arises because of the induced emf in the steel lamination sheets and the eddies of current formed due to it. This again produces a power loss Pe in the lamination. where is the thickness of the steel lamination used. As the lamination thickness is much smaller than the depth of Penetration of the field, the eddy current loss can be reduced by reducing the thickness of the lamination. Present day laminations are of 0.25 mm thickness and are capable of operation at 2 Tesla.

As a result, the core’s eddy current losses are Decreased. Due to constant voltage and frequency of operation, this loss also stays constant. The open circuit test can be used to calculate the total of eddy current and hysteresis losses.

#### Dielectric loss

Due to the high electric stress, there are dielectric losses in the Transformer’s insulation. For low voltage Transformers, this can be disregarded. This can be taken for granted as a constant in constant voltage operation.

#### Stray load loss

The transformer’s leakage fluxes are what cause the stray load losses. Eddy current losses are created in these metallic structural components, such as the tank and leakage fluxes that connect them. As a result, they occur “all around” the transformer rather than in a specific location, hence the name “stray.” Additionally, in contrast to the mutual flux, which is proportional to the applied voltage, the leakage flux is directly proportional to the load current. Therefore, this loss is known as a “stray load” loss. Additionally, this can be calculated experimentally.

Another resistance in the equivalent circuit’s series branch can be used to model it. Due to the absence of the metallic tank, stray load losses in air-cored transformers are extremely low. Therefore, there are two categories of losses. Constant losses and variable losses, which are primarily voltage dependent (current dependant). Losses and Pvar, the variable losses at full load, can be used to express the efficiency of a transformer operating at a load power factor of 2 and a fractional load of x of its rated load. Thus, an expression for in terms of the variable x is obtained for a given power factor. The condition for maximum efficiency is discovered by differentiating with respect to x and equating the result to zero.

##### maximum effectiveness It is simple to infer that this maximum value increases with power factor and is zero when the load’s power factor is zero. Choosing the operating load point to be at the maximum efficiency point may be regarded as a good practice. Therefore, if a transformer is operating at full load for the majority of the time, the maximum load can be achieved by carefully choosing both constant and variable losses. However, the iron losses in contemporary transformers are so low that it is virtually impossible to bring the copper losses at full load down to that level. A design like that wastes a lot of copper. An example is used below to illustrate this point.

Two 100 kVA transformers And B are taken. Both transformers have total full load losses to be 2 kW. The break up of this loss is chosen to be different for the two transformers. Transformer A: iron loss 1 kW, and copper loss is 1 kW. The maximum efficiency of 98.04%occurs at full load at unity power factor. Transformer B: Iron loss =0.3 kW and full load copper loss =1.7 kW. This also has a full load of 98.04%. Its maximum occurs at a fractional load of q0.31.7 = 0.42. The maximum efficiency at unity power factor being at the corresponding point the transformer A has an efficiency of Transformer A uses iron of more loss per kg at a given flux density, but transformer B uses lesser quantity of copper and works at higher current density.

When the primary of a transformer is connected to the source of an ac supply and the secondary is open circuited, the transformer is said to be on no load. Which will create alternating flux. No-load current, also known as excitation or exciting current has two components the magnetizing component Im and the energy component Ie.

##### Im is used to create the flux in the core, and Ie is used to overcome hysteresis and eddy current losses as well as small copper losses that only occur in the primary by using Ie (no copper loss occurs in the secondary, because it carries no current, being open circuited.) It is clear from the vector diagram above that

1. Induced emfs in primary and secondary windings and lag the main flux by and are in phase with each other.

2. Applied voltage to primary and leads the main flux by and is in phase opposition to

3. Secondary voltage is in phase and equal to since there is no voltage drop in secondary.

4. In phase with and so lags

5. In phase with the applied voltage .

6. Input power on no load = cosq

**Transformer on Load**

When the secondary circuit of the transformer is finished by a load or impedance, it is said to be loaded. When the load is non-inductive, inductive, or capacitive, the magnitude and phase of the secondary current—i.e., the current flowing through the secondary—with respect to the secondary terminals will be in phase, lag behind, and lead the terminal voltage, respectively. Regardless of the load conditions, the net flux through the core is nearly constant from no load to full load, and as a result, core losses are nearly constant as well.

secondary windings Resistance and Leakage Reaction In actual usage, both the primary and secondary have some ohmic resistance, resulting in voltage drops and copper losses in the windings. In reality, the total flux generated is split into three parts: the main or mutual flux, which links the primary and secondary windings, the primary leakage flux, which links with the primary winding only, and the secondary leakage flux, which links with the secondary winding only.

The primary leakage flux is produced by primary ampere-turns and is proportional to primary current, number of primary turns being fixed. The primary leakage flux is in phase with and produces self inducedemf is in phase with and produces self inducedemf E given as 2f in the primary winding. The self inducedemf divided by the primary current gives the reactance of primary and is denoted by .

i.e. **E = 2fπ**