Transformer On Load Condition

06/03/2025

Transformer Operation Under Load Conditions

When a transformer is under load, its secondary winding connects to a load, which can be resistive, inductive, or capacitive. A current

I 2

flows through the secondary winding, with its magnitude determined by the terminal voltage

V 2

and load impedance. The phase angle between the secondary current and voltage depends on the load characteristics.

Explanation of Transformer Load Operation

The operational behavior of a transformer under load is detailed as follows:

When the transformer secondary is open-circuited, it draws a no-load current from the main supply. This no-load current induces a magnetomotive force

N 0 I 0

, which establishes a flux Φ in the transformer core. The circuit configuration of the transformer under no-load conditions is illustrated in the diagram below:

Transformer Load Current Interaction

When a load connects to the transformer secondary, current

I 2

flows through the secondary winding, inducing a magnetomotive force (MMF)

N 2 I 2

. This MMF generates flux ϕ2 in the core, which opposes the original flux ϕ per Lenz's law.

Phase Difference and Power Factor in Transformer

The phase difference between

V1

and

I1

defines the power factor angle ϕ1 on the transformer's primary side. The secondary-side power factor depends on the load type connected to the transformer:

For an inductive load (as shown in the phasor diagram above), the power factor is lagging.
For a capacitive load, the power factor is leading.

The total primary current

I1

is the vector sum of the no-load current

I0

and the counter-balancing current

I'1

, i.e.,

Phasor Diagram of Transformer with Inductive Load

The phasor diagram of an actual transformer under inductive loading is illustrated below:

Steps to Construct the Phasor Diagram

Take flux Φ as the reference.
Induced emfs $E 1$ and $E 2$ lag the flux by 90°.
The primary applied voltage component balancing $E 1$ is denoted as $V' 1$ (i.e., $V'1 = -E1)$ .
No-load current $I0$ lags $V' 1$ by 90°.
For a lagging power factor load, current $I 2$ lags $E 2$ by angle ϕ₂.
Winding resistance and leakage reactance cause voltage drops, making the secondary terminal voltage: $V 2 = E 2 - (voltage drops)$
- $I 2 R$ ₂ is in phase with $I 2$ .
- $I 2 X 2$ is orthogonal to $I 2$ .

Primary current $I 1$ is the phasor sum of $I' 1$ and $I0$ , where $I' 1 = -I 2$ .
Primary applied voltage: $V1 = V'1 + (primary voltage drops)$
- $I 1 R 1$ is in phase with $I 1$ .
- $I 1 X 1$ is orthogonal to $I 1$ .
The phase difference between $V 1$ and $I 1$ defines the primary power factor angle ϕ1.
Secondary power factor:
- Lagging for inductive loads (as in the phasor diagram).
- Leading for capacitive loads.

Steps to Draw Phasor Diagram for Capacitive Load

Take flux Φ as the reference.
Induced emfs $E 1$ and $E 2$ lag the flux by 90°.
The primary applied voltage component balancing $E 1$ is denoted as $V' 1$ (i.e., $V' 1 = -E 1$ ).
No-load current $I 0$ lags $V' 1$ by 90°.
For a leading power factor load, current $I 2$ leads $E 2$ by angle ϕ_$2$.
Winding resistance and leakage reactance cause voltage drops, making the secondary terminal voltage: $V 2 = E 2 - (voltage drops)$
- $I 2 R 2$ is in phase with $I 2$ .
- $I 2 X 2$ is orthogonal to $I 2$ .
Counter-balancing current $I' 1 = -I 2$ (equal in magnitude, opposite in phase to $I 2$ ).
Primary current $I 1$ is the phasor sum of $I' 1$ and $I 0$ : $I^{1} = I^{1'} + I^{0}$
Primary applied voltage $V 1$ is the phasor sum of $V' 1$ and primary voltage drops: $V 1 = V' 1 +(primary voltage drops)$
- $I 1 R 1$ is in phase with $I 1$ .
- $I 1 X 1$ is orthogonal to $I 1$ .
Power factor angles:
- The phase difference between $V 1$ and $I 1$ defines the primary power factor angle ϕ_$1$.
- The secondary power factor (leading for capacitive loads) depends entirely on the connected load type.

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Wenzhou Rockwell Transformer Co., Ltd. It is a high - tech enterprise integrating R & D, production, sales, and service. It focuses on the manufacturing of power transformers and supporting equipment, and is committed to providing efficient, reliable, and energy - saving power transmission and distribution solutions for global customers. We can offer: •Distribution transformers and substations •Outdoor switchgears and breakers(recloser) •Switchgears and it’s components (GIS, RMU, VCB, SF6 CB) Market and Service: We always take customers as the orientation and provide customized services according to their requirements. Our products are exported to the Middle East, Africa, Northern Europe, South America, and many other countries and regions. Drive the future of electricity with technological innovation and become a leading global supplier of intelligent power equipment.