Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Define power factor and its significance.
• Calculate real, apparent, and reactive power.
• Explain the causes and consequences of low power factor.
• Describe methods for power factor correction.
• Calculate the capacitance needed to improve power factor.

Lesson summary

This week, we delve into advanced AC theory and power factor correction, a critical area in Electrical Technology. Understanding these concepts is vital for any aspiring electrician or electrical engineer. Power factor correction is particularly important in South Africa, where efficient energy use is crucial to manage our electricity demand and reduce the strain on Eskom's infrastructure. Many industries and even households in South Africa can benefit from improving their power factor, leading to reduced electricity bills and a more stable power grid. Ignoring power factor leads to increased energy losses, higher electricity costs, and potential damage to electrical equipment.

Lesson notes

2.1 Power Factor (PF) Power factor is the ratio of real power (P) to apparent power (S) in an AC circuit. It's a dimensionless number between 0 and 1, or expressed as a percentage.

Real Power (P): The actual power consumed by the load, measured in Watts (W) or Kilowatts (kW). It's the power that does useful work (e.g., turning a motor, heating water).

Apparent Power (S): The product of the voltage and current in the circuit, measured in Volt-Amperes (VA) or Kilovolt-Amperes (kVA). It's the total power that the source appears to be supplying.

Reactive Power (Q): The power that oscillates between the source and the load due to inductive and capacitive elements, measured in Volt-Amperes Reactive (VAR) or Kilovolt-Amperes Reactive (kVAR). It does not perform useful work.

Formula: Power Factor (PF) = Real Power (P) / Apparent Power (S) = P / S = cos(θ) Where θ is the phase angle between the voltage and current waveforms.

Lagging Power Factor: Occurs when the current lags behind the voltage. This is typical in circuits with inductive loads (motors, transformers, etc.). These are VERY common in South African industry.

Leading Power Factor: Occurs when the current leads the voltage. This is typical in circuits with capacitive loads. While less common, they do appear. Unity Power Factor (PF = 1): Occurs when the voltage and current are in phase. This is the ideal situation where all the power supplied is used to do work. 2.2 The Power Triangle The power triangle is a visual representation of the relationship between real power (P), reactive power (Q), and apparent power (S).

It's a right-angled triangle where: The base represents Real Power (P) The height represents Reactive Power (Q) The hypotenuse represents Apparent Power (S)

Using Pythagoras' theorem: S² = P² + Q² And trigonometric relationships: cos(θ) = P / S (Power Factor) sin(θ) = Q / S tan(θ) = Q / P 2.3 Causes of Low Power Factor Low power factor is primarily caused by inductive loads. These loads require a magnetizing current to operate, which creates a phase difference between the voltage and current, resulting in reactive power.

Common inductive loads include: Induction motors (used extensively in South African industries and households) Transformers (used in power distribution networks) Ballasts in fluorescent lighting (becoming less common with LEDs) Welding machines 2.4 Consequences of Low Power Factor Increased Current: For a given amount of real power, a lower power factor means a higher current is required. This can overload cables and equipment, leading to overheating and potential damage.

Increased Losses: Higher current leads to increased I²R losses in conductors, transformers, and other equipment. These losses waste energy and increase operating costs.

Reduced System Capacity: Low power factor reduces the available capacity of the electrical system. Utilities may penalize customers with low power factor due to this strain on the grid.

Voltage Drops: High current can cause voltage drops, affecting the performance of sensitive equipment. Eskom can experience system-wide voltage drops during peak demand in areas with poor power factor. 2.5 Power Factor Correction (PFC) Power factor correction involves adding capacitive reactance to the circuit to offset the inductive reactance. This reduces the phase difference between the voltage and current, improving the power factor. The most common method is using capacitors connected in parallel with the inductive load. 2.6 Calculating Capacitance for Power Factor Correction To calculate the required capacitance (C) to improve the power factor from PF1 to PF2: Calculate the initial reactive power (Q1): Q1 = P * tan(θ1), where θ1 = arccos(PF1)

Calculate the desired reactive power (Q2): Q2 = P * tan(θ2), where θ2 = arccos(PF2) Calculate the required capacitive reactive power (Qc): Qc = Q1 - Q2 Calculate the capacitance (C): C = Qc / (ω * V²), where ω = 2πf (angular frequency) and V is the voltage. In South Africa, f = 50 Hz.