Operation of Transformer on Load

Here is the operation of an electrical transformer operation under loaded condition:

• An electrical input supply voltage V₁ is connected across the primary winding. Due to the application of this voltage an electric current I₁ will starting flowing in the primary winding and sets up a magnetic flux in the core as shown in the above figure.
• This magnetic flux follows a path through the core and links to the secondary winding.
• An EMF E₂ is induced in the secondary winding that developers a voltage V₂ across its terminals.
• When a load is connected between the secondary winding terminals, a current will flow in the secondary winding and load circuit which is denoted by I₂.
• The secondary winding current also induces a counter magnetic flux that reduces the main flux in the core. But the main flux must be maintained at a constant value for operation of the transformer.
• Thus, an additional current is taken by the primary winding from the supply to cancel out the demagnetizing effect of secondary winding current. This is represented by I’₁ which is in-phase with the secondary winding current (I₂). Thus, the total current flowing in the primary winding under loaded condition of the transformer is I’₁.

Therefore, if N₁ and N₂ are the primary and secondary winding turns and I’₁ and I₂ are the primary and secondary currents, then the EMF balance equation of the transformer on load is given by,

[Tex]N_1 I’_1 = N_2 I_2 [/Tex]

Hence, the primary winding current will be,

[Tex]I’_1 = (\frac{N_2}{N_1})I_2 = kI_2 [/Tex]

Also, the total primary winding current (I₁) has two main components namely,

• No-load component – to set up main magnetic flux in the core and supply the losses.
• Counter balancing component – to overcome the effect of secondary winding current.

Thus, the total primary winding current of the transformer on load condition is given by,

[Tex]\bold{I_1 = I_0 + I’_1} [/Tex]

The bold facing letter denotes the phasor sum of current components.

In practice, the transformers mostly have inductive loads. So, let’s assume the load connected across the secondary of the transformer and draw the phasor diagram of it on load condition.

Phasor Diagram Explanation

The steps given below are to be followed to draw the phasor diagram of the transformer on load:

Step (1) : Taking main magnetic flux (ϕ) as the reference axis.

Step (2) : This magnetic flux induces EMFs E₁ and E₂ in primary and secondary windings. Hence, E₁ and E₂ lags the flux (ϕ) by an angle of 90°.

Step (3) : The applied voltage across the primary winding is utilized in three components namely, to induce emf E₁, voltage drop in primary winding resistance I₁R₁, and voltage drop in primary winding reactance I₁X₁. Hence, the primary winding voltage V₁ is the phasor sum of voltage component corresponding to E₁ and the voltage drops in primary winding.

Step (4) : If ϕ₁ is the power factor angle of the primary winding, then the current I₁ will lag the voltage V₁ by ϕ₁. It is the phasor sum of no-load current I₀ (lags the supply voltage by 90°) and counter balancing current I’₁ (in anti-phase with the secondary voltage V₂).

Step (5) : The secondary winding EMF E₂ is the phasor sum of voltage V₂ and the voltage drops in secondary winding resistance and reactance.

Step (6) : The magnitude and phase angle of the load current or secondary current I₂ depends on the load connected to the transformer. As in this case, we are assuming an inductive load, hence the load current I₂ will lag the voltage V₂. If the load is capacitive, the load current will lead the voltage V₂.

Thus, when we operate a transformer on load condition, it takes both no-load current and current required to handle the load connected across its secondary winding.

Let us now understand the theory of transformer on load with two other load conditions

• Transformer on load with purely resistive load
• Transformer on load with purely inductive load
• Transformer on load with purely capacitive load

Transformer on Load with Purely Resistive Load

When a purely resistive load is connected across the secondary winding of a transformer, it draws only active current from the transformer. The resistive load creates a phase difference of 0° between the load current and the secondary winding voltage.

The phasor diagram of the transformer on load with purely resistive load is shown in the following figure.

Transformer on Load with Purely Inductive Load

When a purely inductive load is connected across the secondary winding of the transformer. It cause a phase different of exactly 90° between the secondary voltage and load current.

The phasor diagram of a transformer on load with purely inductive load is shown in the following figure. It can be observed that the load current I₂ lags the secondary voltage V₂ by an angle of 90°.

Transformer on Load with Purely Capacitive Load

When a purely capacitive load is attached to the secondary winding of the transformer, it draws a leading current from the secondary winding. This causes a phase difference of 90° between the load current and the secondary voltage. Where, the load current I₂ leads the secondary voltage V₂ by an angle of 90° as shown in the following phasor diagram.

Till this section of the article, we have discussed about the operation of a practical transformer on no-load and on-load (with resistive load, inductive load, and capacitive load).

Also, we have analyzed a practical transformer on load with winding resistances and leakage reactances. However, there can be three other possible cases, they are:

• Transformer on Load with No Winding Resistances and Leakage Reactances
• Transformer on Load with Winding Resistances but No Leakage Reactances
• Transformer on Load with Leakage Reactances but No Winding Resistances

Let us understand these three cases of transformer operation on load in detail.

Transformer on Load with No Winding Resistances and Leakage Reactances

When we consider a transformer on load with no winding resistances and leakage reactances, then its electrical circuit will look like as shown in the following figure.

In this case, there are no voltage drops due to resistances and leakage reactances of the windings. Thus, the terminal voltages and induced emfs are equal i.e.,

E₁ = V₁ and E₂ = V₂

If we consider a practical inductive load connected across the secondary winding, then the load current I₂ will lags behind the secondary winding voltage V₂ by an angle of ϕ₂. Where, ϕ₂ is the power factor angle of the load.

In this condition, the primary winding current I₁ will supply the following two things:

• It supplies the no-load current I₀ to establish magnetic flux in the core and iron losses.
• It cancel out the demagnetising effect of the secondary winding current.

Therefore, the primary winding current is given by,

[Tex]\bold{I_1 = I_0 + I_1′} [/Tex]

Here, the component I’₁ is the counter balance current of the secondary winding current.

If we draw the phasor diagram for this case of the transformer on load, then it will look like as shown below.

In this phasor diagram, the secondary winding voltage V₂ is equal to the secondary winding emf E₂ and they are in-phase. While, the primary winding voltage V₁ is equal to the primary winding emf E₁ but they are out of phase with each other. The primary winding current is the phasor sum of I₀ and I’₁.

Transformer on Load with Winding Resistances but No Leakage Reactances

The circuit diagram of a transformer on load having winding resistances but no leakage reactances is shown below.

In this circuit diagram, the resistors R₁ and R₂ represent the primary and secondary winding resistances. A practical inductive load is connected across the secondary winding terminals.

When the input voltage V₁ is connected to the primary winding, there will be a voltage drop in the primary winding resistance R₁ and the secondary winding resistance R₂.

Therefore, we get the following equations of the voltages,

[Tex]V_1 = E_1 + I_1 R_1 [/Tex]

And

[Tex]E_2 = V_2 + I_2 R_2 [/Tex]

The phasor diagram for this case of transformer on load is depicted in the following figure.

Transformer on Load with Leakage Reactances but No Winding Resistances

The circuit diagram of a transformer on load having leakage reactances only and not having the winding resistances is shown in the figure.

Here, X₁ and X₂ represents the leakage reactances of the primary and secondary windings respectively.

The voltage equations are given by,

[Tex]V_1 = E_1 + I_1 X_1 [/Tex]

And

[Tex]E_2 = V_2 + I_2 X_2 [/Tex]

The phasor diagram for this case of transformer on load is depicted below. Where, we have considered a practical inductive load.

In this article, we will study the theory of transformer on load and no load operation. A transformer is a static electrical machine used to increase or decrease the value of voltage and current in an electrical circuit. The transformer operates on the principle of electromagnetic induction and mutual inductance. A transformer typically consists of two copper winding and a magnetic core. The windings are named as primary winding and secondary winding. The input supply is connected to the primary winding and the output electrical supply is taken from the secondary winding. Hence, the secondary winding is one to which the electrical load is connected.

Let us understand the operation of a transformer on load and no-load conditions.