Lesson Note on Power in AC Circuits: Advantages, Disadvantages and Calculation of Power Factor for SS 2

Class: Senior Secondary School 2 (SS2 / SSS 2)
Term: 1st Term
Week: 7
Age: 16 years
Duration: 45 minutes
Subject: Basic Electronics
Curriculum Theme: Electricity and Magnetism
Previous Lesson: Power in AC Circuit: Power, Power Triangle, Power Factor and Correction.
Topic: POWER IN AC CIRCUITS
Subject Matter: Meaning of POWER IN AC CIRCUITS, advantages of power factor correction, disadvantages of power factor correction, power factor correction, calculation of power factor.

Specific Objectives

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

Cognitive Domain:

• Define power in AC circuits.
• State the advantages of power factor correction.
• Identify the disadvantages of power factor correction.
• Explain the purpose and methods of power factor correction.
• Recall the formula for calculating power factor.

Affective Domain:

• Appreciate the importance of power factor correction in electrical systems.
• Show interest in understanding and solving AC circuit problems.

Psychomotor Domain:

• Calculate power factor from given values of power or circuit parameters.
• Draw a simple power triangle.

Social Domain:

• Participate in discussions about the practical implications of power factor.
• Collaborate in solving power factor calculation problems.

Reference Materials

The following resources were used in planning this lesson:

• Senior Secondary Schools Education Curriculum
• State Unified Scheme of Work
• Basic Electronics for Senior Secondary Schools, Book 2

Instructional Materials

The teacher will teach this lesson with the aid of:

• Chart on power triangle and power factor
• Calculator

Rationale for the Lesson

This lesson helps pupils understand how power behaves in alternating current circuits and why managing power efficiency is important. It enables them to identify ways to improve electrical system performance and reduce energy waste, which is relevant in homes and industries.

Prerequisite/Previous Knowledge

Pupils should have prior knowledge of basic AC circuit concepts such as voltage, current, resistance, impedance, and phase angle.

Lesson Content/Board Summary

POWER IN AC CIRCUITS

Meaning of Power in AC Circuits

In AC circuits, power is categorized into three types:

• Real Power (P): Also known as active power or true power. This is the actual power consumed by the load and converted into useful work (e.g., heat, light, mechanical energy). It is measured in Watts (W).
• Reactive Power (Q): This is the power that oscillates between the source and the reactive components (inductors and capacitors) of the circuit. It does no useful work but is necessary to establish magnetic and electric fields. It is measured in Volt-Ampere Reactive (VAR).
• Apparent Power (S): This is the total power supplied by the source to the circuit. It is the vector sum of real power and reactive power. It is measured in Volt-Amperes (VA).

The relationship between these powers can be represented by the power triangle, where apparent power is the hypotenuse, real power is the adjacent side, and reactive power is the opposite side.

Power Factor (PF)

Power factor is a measure of how effectively electrical power is being converted into useful work. It is defined as the ratio of real power to apparent power in an AC circuit. It is also the cosine of the phase angle (φ) between the voltage and current waveforms.

Formula:

Power Factor (PF) = Real Power (P) / Apparent Power (S)

OR

PF = cos(φ)

Where φ is the phase angle between voltage and current.

A power factor of 1 (or unity) indicates maximum efficiency, while a power factor less than 1 indicates that a portion of the apparent power is reactive power, not doing useful work.

Power Factor Correction

Power factor correction is the process of improving the power factor of an AC electrical power system by compensating for the reactive power. This is typically achieved by adding capacitors to inductive loads, which supply reactive power to the circuit, thereby reducing the total reactive power drawn from the supply.

Purpose: To reduce the phase difference between voltage and current, making the power factor closer to unity (1).

Methods: The most common method involves connecting capacitors in parallel with the inductive load. Other methods include using synchronous condensers.

Advantages of Power Factor Correction

The following are advantages of power factor correction:

• Reduced Energy Bills: Utilities often charge penalties for low power factors, so improving it reduces costs.
• Improved Voltage Regulation: A higher power factor leads to a smaller voltage drop in the supply lines, resulting in more stable voltage at the load.
• Increased System Capacity: For a given apparent power, a higher power factor means more real power can be delivered, increasing the system’s ability to handle useful loads.
• Reduced Losses: Lower current flow for the same real power reduces resistive (I²R) losses in cables and transformers.
• Reduced Equipment Size: Transformers, generators, and distribution equipment can be smaller and more efficient.

Disadvantages of Power Factor Correction

The following are disadvantages of power factor correction:

• Installation Cost: The initial cost of purchasing and installing power factor correction equipment (e.g., capacitors) can be significant.
• Maintenance: Power factor correction equipment requires regular maintenance, which adds to operational costs.
• Overcorrection Issues: If too much capacitance is added, the power factor can become leading, which can also lead to inefficiencies and voltage instability.
• Harmonic Resonance: In systems with significant harmonic distortion, adding capacitors can sometimes create resonance conditions that amplify harmonics, potentially damaging equipment.

Calculation of Power Factor

Power factor (PF) can be calculated using various parameters of the AC circuit.

Formulae:

• PF = P / S (Real Power / Apparent Power)
• PF = R / Z (Resistance / Impedance)
• PF = cos(φ) (Cosine of the phase angle)

Example 1:

An AC circuit has a real power consumption of 12 kW and an apparent power of 15 kVA. Calculate the power factor.

Step 1: Identify the given values.

P = 12 kW

S = 15 kVA

Step 2: Use the formula PF = P / S.

PF = 12 kW / 15 kVA

Step 3: Perform the calculation.

PF = 0.8

The power factor is 0.8 (lagging, as it’s typically an inductive load).

Example 2:

A series RLC circuit has a resistance (R) of 60 Ω and an impedance (Z) of 100 Ω. Calculate the power factor of the circuit.

Step 1: Identify the given values.

R = 60 Ω

Z = 100 Ω

Step 2: Use the formula PF = R / Z.

PF = 60 Ω / 100 Ω

Step 3: Perform the calculation.

PF = 0.6

The power factor is 0.6.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Set Induction

Teacher’s Activity: The teacher greets the pupils and asks them to recall what they understand by power in DC circuits and introduces the concept of power in AC circuits, highlighting that it’s more complex than DC power.

Pupils’ Activity: Pupils respond to the teacher’s questions about DC power and listen attentively to the introduction of AC power.

Learning Point: Pupils are introduced to the topic and connect it to their previous knowledge.

Step 2: Meaning of Power in AC Circuits

Time: 5 minutes

Teaching Skill: Explanation

Teacher’s Activity: The teacher explains the three types of power in AC circuits (real, reactive, and apparent power) and their units, making reference to the power triangle chart.

Pupils’ Activity: Pupils listen, observe the chart, and ask questions for clarification.

Learning Point: Pupils understand the different components of power in AC circuits.

Step 3: Explanation of Power Factor

Time: 7 minutes

Teaching Skill: Explanation/Definition

Teacher’s Activity: The teacher defines power factor, explains its significance in terms of efficiency, and introduces the basic formulas relating power factor to real and apparent power, and to the phase angle.

Pupils’ Activity: Pupils define power factor and note down the formulas.

Learning Point: Pupils grasp the concept and importance of power factor.

Step 4: Power Factor Correction

Time: 8 minutes

Teaching Skill: Explanation/Illustration

Teacher’s Activity: The teacher explains the purpose of power factor correction and describes the common methods, particularly the use of capacitors, illustrating with diagrams where necessary.

Pupils’ Activity: Pupils listen and understand why and how power factor is corrected.

Learning Point: Pupils learn about the methods and objectives of power factor correction.

Step 5: Advantages and Disadvantages of Power Factor Correction

Time: 7 minutes

Teaching Skill: Listing/Discussion

Teacher’s Activity: The teacher lists and explains the advantages and disadvantages of implementing power factor correction, providing practical examples.

Pupils’ Activity: Pupils state the advantages and disadvantages and discuss their implications.

Learning Point: Pupils understand the benefits and limitations of power factor correction.

Step 6: Calculation of Power Factor

Time: 8 minutes

Teaching Skill: Demonstration/Problem-solving

Teacher’s Activity: The teacher demonstrates how to calculate power factor using the provided formulas and worked examples on the board, guiding pupils through each step.

Pupils’ Activity: Pupils pay attention, copy the examples, and attempt to solve similar problems.

Learning Point: Pupils learn to apply the power factor formulas to solve problems.

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. Define Real Power, Reactive Power, and Apparent Power.
2. What is power factor?
3. State two advantages of power factor correction.
4. Mention two disadvantages of power factor correction.
5. If an AC circuit has a real power of 20 kW and an apparent power of 25 kVA, calculate the power factor.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 1 minute

Teaching Skill: Summarization

Teacher’s Activity: The teacher summarizes the key points of the lesson and assigns homework for further practice.

Pupils’ Activity: Pupils listen to the summary and note down the homework.

Learning Point: Pupils consolidate their learning and prepare for independent practice.

Lesson Keywords

• Real Power – The actual power consumed by the load and converted to useful work.
• Reactive Power – Power that oscillates between source and reactive components, doing no useful work.
• Apparent Power – The total power supplied by the source.
• Power Factor – The ratio of real power to apparent power, or the cosine of the phase angle.
• Power Factor Correction – The process of improving the power factor, typically by adding capacitors.

Differentiation

The teacher will provide additional simpler examples for struggling learners and more complex problems for advanced learners. Group work will be encouraged to foster peer learning and discussion. Visual aids like charts and diagrams will support visual learners.

Note for teachers using this lesson plan

Ensure pupils understand the difference between real, reactive, and apparent power before moving to power factor. Emphasize the practical implications of low power factor in industries. Encourage pupils to use calculators for the numerical problems. Review basic trigonometry if pupils struggle with the concept of cosine of the phase angle.