Transformer Losses and Cooling Methods for SS 3

Class: SS 3
Term: First Term
Week: 3
Age: 16 years
Duration: 45 minutes
Subject: Basic Electricity
Previous Lesson: Trans
Topic: TRANSFORMER LOSSES AND COOLING METHODS
Subject Matter: Sources of transformer losses: Types of transformer losses and Effects of transformer losses

Specific Objectives

By the end of the lesson, pupils/students should be able to:

Cognitive Domain

• Identify the sources of transformer losses.
• Describe the different types of transformer losses.
• Explain the effects of transformer losses on efficiency.
• State the formulas for calculating transformer losses.
• List various methods used for cooling transformers.

Affective Domain

• Appreciate the importance of minimizing losses in transformers.
• Recognize the need for efficient cooling systems in electrical equipment.

Psychomotor Domain

• Calculate simple transformer losses given relevant parameters.
• Illustrate different transformer cooling methods with diagrams.

Reference Materials

The following resources were used in planning this lesson:

• 2025 Revised 9 Years Basic Education Curriculum
• Relevant State Unified Scheme of Work
• A suitable Basic Electricity textbook for SS 3
• The HeadTeacher Scheme of work

Instructional Materials

The teacher will teach this lesson with the aid of:

• Charts showing different types of transformers and their cooling systems.
• Diagrams illustrating eddy currents and hysteresis loops.
• Whiteboard and markers.
• Calculator.

Rationale for the Lesson

Understanding transformer losses and cooling methods is essential for SS 3 students as it provides insight into the efficiency and operational limits of transformers. This knowledge is crucial for designing, maintaining, and troubleshooting electrical power systems, ensuring reliable and sustainable electricity supply.

Prerequisite/Previous Knowledge

Students should have prior knowledge of the basic working principle of a transformer, including mutual induction, primary and secondary windings, and the concept of ideal transformers.

Lesson Content/Board Summary

TRANSFORMER LOSSES AND COOLING METHODS

Sources of Transformer Losses

Transformer losses are primarily due to the resistance of the windings and the magnetic properties of the core material. These losses result in the dissipation of energy as heat, reducing the efficiency of the transformer.

Types of Transformer Losses

Transformer losses are generally categorized into two main types:

1. Copper Losses (I²R Losses): These losses occur in the primary and secondary windings of the transformer due to the resistance of the copper conductors. When current flows through the windings, heat is generated.
2. Iron Losses (Core Losses): These losses occur in the transformer core due to the alternating magnetic flux. Iron losses are further divided into:
   1. Eddy Current Loss: This loss is caused by circulating currents induced in the transformer core itself, due to the changing magnetic flux. These currents flow in closed loops within the core, generating heat.
   2. Hysteresis Loss: This loss occurs due to the repeated magnetization and demagnetization of the transformer core material as the alternating current reverses its direction. Energy is expended to realign the magnetic domains within the core.

Effects of Transformer Losses

Transformer losses have several significant effects:

1. Reduced Efficiency: Losses mean that the output power is less than the input power, leading to lower efficiency.
2. Heat Generation: All losses are dissipated as heat, which increases the operating temperature of the transformer.
3. Reduced Lifespan: Excessive heat can degrade the insulation materials of the windings, shortening the transformer’s operational lifespan.
4. Energy Waste: Losses represent wasted energy, leading to higher operational costs and environmental impact.

Calculation of Transformer Losses

The total transformer loss is the sum of copper losses and iron losses.

Formula for Copper Loss

( P_{cu} = I_1^2 R_1 + I_2^2 R_2 )

Where:

1. ( P_{cu} ) = Total copper loss
2. ( I_1 ) = Primary current
3. ( R_1 ) = Primary winding resistance
4. ( I_2 ) = Secondary current
5. ( R_2 ) = Secondary winding resistance

Formula for Iron Loss

( P_{i} = P_{e} + P_{h} )

Where:

1. ( P_{i} ) = Total iron loss
2. ( P_{e} ) = Eddy current loss
3. ( P_{h} ) = Hysteresis loss

Iron losses are often considered constant at a given frequency and voltage.

Formula for Total Loss

( P_{total} = P_{cu} + P_{i} )

Example 1

Question: A transformer has a primary winding resistance of 0.5 Ω and a secondary winding resistance of 0.2 Ω. If the primary current is 5 A and the secondary current is 10 A, calculate the total copper loss.

Solution:

Step 1: Write the formula for copper loss.

( P_{cu} = I_1^2 R_1 + I_2^2 R_2 )

Step 2: Substitute the values.

( P_{cu} = (5^2 times 0.5) + (10^2 times 0.2) )

( P_{cu} = (25 times 0.5) + (100 times 0.2) )

( P_{cu} = 12.5 + 20 )

Step 3: Simplify and write the answer.

( P_{cu} = 32.5 , W )

Answer: ( 32.5 , W )

Transformer Cooling Methods

To dissipate the heat generated by losses and prevent damage, transformers employ various cooling methods:

1. Air Natural (AN): Small transformers are often cooled by natural convection of surrounding air.
2. Air Blast (AB): Fans are used to force air over the transformer windings and core, increasing the rate of heat dissipation.
3. Oil Natural Air Natural (ONAN): The transformer core and windings are immersed in insulating oil, which circulates naturally by convection, transferring heat to the tank walls. The tank walls then dissipate heat to the surrounding air by natural convection.
4. Oil Natural Air Forced (ONAF): Similar to ONAN, but fans are used to force air over the radiator fins or tank surface, enhancing heat dissipation.
5. Oil Forced Air Forced (OFAF): Oil is circulated by pumps through external radiators, where it is cooled by forced air from fans before returning to the transformer tank.
6. Oil Forced Water Forced (OFWF): Oil is circulated by pumps through heat exchangers, where it is cooled by forced water circulation. This method is used for very large transformers.

Teaching Methods/Instructional Techniques

Discussion, Demonstration, Guided Practice, Question and Answer, Explanation, Problem Solving, Individual Practice

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Review/Engage

Teacher’s Activity: The teacher asks students to recall the basic principle of a transformer and its components. The teacher then introduces the concept that no electrical machine is 100% efficient due to energy losses, leading to today’s topic.

Pupils’ Activity: Students respond to questions about transformers and listen attentively to the introduction.

Learning Point: Introduction to transformer losses

Step 2: Sources of Transformer Losses

Time: 7 minutes

Teaching Skill: Explanation/Illustration

Teacher’s Activity: The teacher explains that transformer losses originate from the resistance of the windings (copper) and the magnetic properties of the core (iron). The teacher uses a diagram of a transformer to point out these areas.

Pupils’ Activity: Students observe the diagrams and listen to the explanation, asking questions for clarity.

Learning Point: Origins of energy loss

Step 3: Types of Transformer Losses (Copper Losses)

Time: 7 minutes

Teaching Skill: Explanation/Definition

Teacher’s Activity: The teacher explains copper losses, emphasizing that they are due to the resistance of the windings and vary with the square of the current (I²R losses). The teacher writes the formula for copper loss on the board.

Pupils’ Activity: Students listen, take notes, and copy the formula for copper loss.

Learning Point: Understanding copper losses

Step 4: Types of Transformer Losses (Iron Losses)

Time: 7 minutes

Teaching Skill: Explanation/Comparison

Teacher’s Activity: The teacher explains iron losses, differentiating between eddy current loss and hysteresis loss. The teacher uses simple analogies or diagrams to illustrate how these losses occur in the core.

Pupils’ Activity: Students listen, observe diagrams, and differentiate between eddy current and hysteresis losses.

Learning Point: Core loss mechanisms

Step 5: Effects of Transformer Losses

Time: 5 minutes

Teaching Skill: Discussion/Analysis

Teacher’s Activity: The teacher leads a discussion on the practical effects of these losses, such as reduced efficiency, heat generation, and potential damage to the transformer. The teacher asks students to suggest ways to mitigate these effects.

Pupils’ Activity: Students participate in the discussion, identifying effects and suggesting mitigation strategies.

Learning Point: Impact of losses

Step 6: Transformer Cooling Methods and Calculation of Losses

Time: 7 minutes

Teaching Skill: Demonstration/Problem Solving

Teacher’s Activity: The teacher explains various cooling methods (AN, ONAN, ONAF, OFWF) using charts or diagrams. The teacher then works through an example of calculating total copper loss on the board, using the formula previously introduced.

Pupils’ Activity: Students observe the cooling diagrams, follow the calculation example, and ask questions.

Learning Point: Cooling methods and calculation

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. Mention two sources of transformer losses.
2. Differentiate between copper loss and iron loss.
3. State two effects of transformer losses.
4. List three methods used for cooling transformers.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Assessment of understanding

Step 8: Note-Taking

Time: 4 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides pupils/students to copy the essential Board Summary notes on transformer losses, their types, effects, calculation, and cooling methods into their notebooks.

Pupils’ Activity: Pupils/students copy the notes carefully into their notebooks.

Learning Point: Recording key concepts

Step 9: Conclusion

Time: 3 minutes

Teaching Skill: Summarizing/Reinforcement

Teacher’s Activity: The teacher briefly summarizes the key points of the lesson, reiterating the importance of understanding transformer losses and effective cooling for efficient operation. The teacher encourages students to continue exploring related topics.

Pupils’ Activity: Students listen and ask any final questions.

Learning Point: Consolidation of learning

Continuous Assessment/Further Study

Type: Homework

Instruction: Answer the following questions in your notebook:

1. Explain why transformer losses are undesirable.
2. A transformer has copper losses of 200 W and iron losses of 150 W. Calculate the total losses of the transformer.
3. Describe one method of transformer cooling and explain how it works.
4. Suggest two ways to reduce eddy current losses in a transformer core.

Lesson Keywords

• Copper Loss – Energy loss in transformer windings due to resistance.
• Iron Loss – Energy loss in the transformer core, comprising eddy current and hysteresis losses.
• Eddy Current Loss – Circulating currents induced in the core, causing heat.
• Hysteresis Loss – Energy loss due to repeated magnetization and demagnetization of the core.
• Cooling Methods – Techniques used to dissipate heat from transformers, e.g., Air Natural, Oil Natural Air Natural.
• Efficiency – The ratio of output power to input power, affected by losses.

Differentiation

For slower learners, the teacher can provide simplified diagrams of cooling methods and focus on identifying the main types of losses. For faster learners, the teacher can challenge them to research how transformer efficiency is calculated and the factors affecting it, or to explore more advanced cooling techniques.

Suggested Lesson Videos

For further understanding, search on YouTube for:

• “Transformer losses and efficiency SS3”
• “Transformer cooling methods explained”
• “Copper and iron losses in transformers”

Teacher Guide for Using This Lesson Plan

Before the lesson, ensure you have prepared clear diagrams or charts illustrating the internal structure of a transformer, the concept of eddy currents, hysteresis, and various cooling methods. Begin by reviewing the basic transformer principles to ensure students have a solid foundation. During the lesson, explain each type of loss clearly, using practical examples where possible. When discussing cooling methods, emphasize why each method is suitable for different transformer sizes and applications. Guide students through the calculation of transformer losses step-by-step, allowing them to practice. Ensure students copy the Board Summary notes accurately during the note-taking stage. Encourage questions and address any misconceptions promptly. Provide additional support to weaker learners by simplifying explanations and offering more guided practice, while challenging faster learners with extended research or problem-solving tasks.