Interpretation of the Relationship Between Rated Voltage and Voltage Ratio in Single-phase Transformers

I. Introduction

In power systems, single-phase transformers are fundamental devices for energy transmission and voltage transformation. Understanding the relationship between the rated voltage and the voltage ratio (turns ratio) is essential for the proper selection, operation, and maintenance of transformers.

II. Key Concepts

1. Rated Voltage

The rated voltage refers to the designed operating voltage of a transformer under normal working conditions. It typically includes two parameters:

• Primary rated voltage
• Secondary rated voltage

For example:

• Primary rated voltage: 220V
• Secondary rated voltage: 110V

This indicates that the transformer converts an input AC voltage of 220V to an output of 110V.

2. Voltage Ratio (Turns Ratio)

The voltage ratio is the ratio of the number of turns in the primary winding to the number of turns in the secondary winding, and can also be expressed as the ratio of primary voltage to secondary voltage:

Where:

• $N_1$: Number of turns in the primary winding
• $N_2$: Number of turns in the secondary winding
• $V_1$: Primary voltage
• $V_2$: Secondary voltage

III. Relationship Between Rated Voltage and Voltage Ratio

The rated voltage directly determines the voltage ratio of the transformer. Based on the above formula:

• The voltage ratio can be calculated if the primary and secondary voltages are known.
• If the voltage ratio and one side's voltage are known, the other side’s voltage can be determined.
• The voltage ratio indicates whether the transformer is a step-up (ratio < 1) or step-down (ratio > 1) type.

Example:
A single-phase transformer with a rated voltage of 220V/110V has a voltage ratio of:

indicating it is a step-down transformer.

IV. Practical Considerations

1. Input Voltage Must Match the Primary Rated Voltage

Applying a voltage higher or lower than the rated value may cause core saturation, reduce efficiency, or even damage the transformer.

2. Output Voltage Varies Slightly Under Load

Although the voltage ratio is fixed, the output voltage may vary slightly between no-load and full-load conditions due to internal resistance and leakage reactance.

3. Voltage Ratio Affects Current and Power Relationships

According to the principle of power conservation (ignoring losses):

Therefore:

V. Conclusion

There is a close relationship between the rated voltage and the voltage ratio in single-phase transformers. By selecting appropriate rated voltages and calculating the correct voltage ratio, transformers can operate safely and efficiently. Understanding these basic relationships is crucial for electrical engineers, equipment selection personnel, and designers of automation control systems.