Voltage Regulation of a Transformer

05/27/2025

Voltage Regulation Definition and Significance
Definition

Voltage regulation is defined as the change in magnitude between the sending-end and receiving-end voltages of a transformer. This parameter quantifies the transformer's capability to maintain steady output voltage under varying load conditions.

When a transformer operates with a constant supply voltage, its terminal voltage fluctuates in response to load variations and the load's power factor.

Mathematical Representation

Voltage regulation is mathematically expressed as:

Mathematical Notation

Where:

$E2$ : Secondary terminal voltage at no-load condition
$V2$ : Secondary terminal voltage at full-load condition

Voltage Regulation with Primary Voltage Consideration

When considering the primary terminal voltage, voltage regulation of the transformer is expressed as:

Voltage Regulation Illustration with Example

Consider the following scenario to understand voltage regulation:

No-Load Condition

When the transformer's secondary terminals are open-circuited (no load connected), only the no-load current flows through the primary winding. With zero current in the secondary, voltage drops across secondary resistive and reactive components are eliminated. The primary-side voltage drop is also negligible under this condition.

Full-Load Condition

When the transformer is fully loaded (load connected to the secondary terminals), voltage drops occur across both primary and secondary windings due to load current. For optimal transformer performance, the voltage regulation value should be minimized, as lower regulation indicates better voltage stability under varying loads.

Circuit Diagram Analysis and Conclusions

Based on the circuit diagram above, the following observations can be made:

The primary voltage of the transformer always exceeds the primary-induced EMF: $V1 > E1$ .
The no-load secondary terminal voltage is always higher than the full-load voltage: $E2 > V2$ .

Derived Equations from Circuit Diagram

The following equations are established by analyzing the circuit configuration:

The approximate expression for the no-load secondary voltage for the different types of the load is

1.For inductive load

2. For Capacitive load

In this way, we define the voltage regulation of the transformer.

Topics

Machines Transformer

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