Lecture 05 | Real Transformers| T/F | Electrical Machines

Introduction

This tutorial provides a comprehensive overview of the theory of operation of real single-phase transformers. It covers essential concepts such as voltage ratios, magnetization current, core-loss current, and how to convert a real transformer into an ideal transformer. Understanding these concepts is crucial for anyone studying electrical machines, as they form the foundation for more advanced topics in electrical engineering.

Step 1: Understand the Real Single-Phase Transformer

• A real single-phase transformer consists of two windings and a magnetic core.
• It operates on the principle of electromagnetic induction, converting electrical energy from one voltage level to another.
• Key parameters to consider include:
  • Primary winding: where the input voltage is applied.
  • Secondary winding: where the transformed voltage is obtained.

Step 2: Learn About Voltage Ratio

• The voltage ratio is a fundamental aspect of transformers and is defined as:

  [ \text{Voltage Ratio} = \frac{V_p}{V_s} = \frac{N_p}{N_s} ]

  where ( V_p ) and ( V_s ) are the primary and secondary voltages, respectively, and ( N_p ) and ( N_s ) are the number of turns in the primary and secondary windings.

• This relationship helps in determining how much the voltage is stepped up or stepped down.

Step 3: Explore Magnetization Current

• The magnetization current ( i_M ) is essential for producing the magnetic flux in the transformer core.
• It primarily overcomes the reluctance of the magnetic circuit.
• Characteristics of magnetization current:
  • It is typically a small fraction of the full load current.
  • It can be visualized using a magnetization curve, which plots the relationship between magnetization current and the magnetic flux density.

Step 4: Understand Core-Loss Current

• Core-loss current ( i_{h+e} ) compensates for hysteresis and eddy current losses in the transformer core.
• Hysteresis loss occurs due to the magnetic properties of the core material, while eddy currents are induced currents that generate heat.
• Together, these losses impact the efficiency of the transformer, making it crucial to minimize them through proper material selection and design.

Step 5: Calculate Total No Load (Excitation) Current

• The total no-load current in a transformer is the sum of the magnetization current and the core-loss current:

  [ I_0 = i_M + i_{h+e} ]

• This current is significant when the transformer is energized but not supplying load.

Step 6: Learn about Current Ratio and Dot Convention

• The current ratio in transformers is defined similarly to the voltage ratio, allowing for the analysis of load conditions.
• The dot convention helps in determining the phase relationship between primary and secondary currents.
• Ensure to place dots on the winding diagrams to signify polarity.

Step 7: Convert a Real Transformer into an Ideal Transformer

• For practical applications, certain assumptions may be made to simplify analysis:
  • Ignore winding resistance and leakage reactance.
  • Assume no core losses.
  • The ideal transformer operates without energy loss, which is useful for theoretical calculations.

Conclusion

In this tutorial, we explored the fundamental aspects of real single-phase transformers, including voltage ratios, magnetization and core-loss currents, and how to simplify a real transformer into an ideal one. Understanding these concepts is essential for further study in electrical machines and their applications in real-world scenarios. For next steps, consider diving deeper into transformer efficiency analysis or exploring three-phase transformer systems for more complex applications.