Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Define power factor and its significance.
• Calculate power factor using the power triangle.
• Explain the causes and consequences of low power factor.
• Describe how capacitors are used for correction.
• Calculate the required capacitor size for correction.

Lesson summary

This week delves into advanced AC theory and power factor correction, a critical area in electrical technology, particularly relevant to South Africa's industrial and residential power usage. Power factor correction directly impacts the efficiency of our electricity grid, reducing energy waste and lowering electricity costs for homes and businesses. South Africa, facing energy security challenges, needs skilled technicians who understand and can implement power factor correction techniques to optimize our existing infrastructure.

Lesson notes

2.1 Power Factor (PF) Explained Power factor (PF) is a dimensionless number between 0 and 1 that represents the ratio of real power (kW) to apparent power (kVA) in an AC circuit. It indicates how effectively electrical power is being used.

Real Power (P): The actual power consumed by the load and dissipated as heat or used to do work (measured in kW or Watts). This is what you're billed for by Eskom.

Reactive Power (Q): The power that oscillates between the source and the load due to reactive components like inductors and capacitors (measured in kVAR – kilo Volt-Ampere Reactive). Reactive power does no useful work but loads the system, causing increased current flow and losses.

Apparent Power (S): The vector sum of real and reactive power (measured in kVA – kilo Volt-Amperes). It's the product of voltage and current. The relationship is represented by the power triangle: S² = P² + Q². And PF = P / S = cos(θ), where θ is the phase angle between voltage and current. A power factor of 1 (unity) means that all the power supplied is being used to do useful work. A power factor less than 1 indicates that some of the power is being used to support reactive loads. 2.2 Causes of Low Power Factor The primary cause of low power factor in most AC systems is inductive loads.

These are common in: Motors: Induction motors, used extensively in industries for pumps, compressors, conveyors, etc., consume reactive power to establish magnetic fields.

Transformers: Transformers also require reactive power for magnetization. South Africa's grid is full of transformers.

Arc Welders: Welding machines utilize inductive circuits. Fluorescent and LED Lighting (with ballasts): Older fluorescent lights and some LED lighting circuits with electromagnetic ballasts contribute to low power factor. Inductive loads cause the current to lag behind the voltage, resulting in a lagging power factor. A capacitive load, conversely, causes the current to lead the voltage, resulting in a leading power factor. 2.3 Consequences of Low Power Factor Increased Current: For the same amount of real power delivered, a lower power factor means a higher current must flow through the system.

Higher current leads to: Increased I²R Losses: The power lost as heat in cables and equipment is proportional to the square of the current. This wasted energy increases operating costs for the consumer and reduces the overall efficiency of the power grid, impacting Eskom's ability to deliver power effectively.

Voltage Drops: Higher current causes larger voltage drops along the distribution lines, potentially affecting the performance of equipment.

Overloaded Equipment: Existing cables, transformers, and switchgear may become overloaded, leading to premature failure and increased maintenance costs.

Reduced System Capacity: A low power factor reduces the amount of real power that can be delivered through the existing infrastructure. This can limit the ability to add new loads or expand operations.

Penalties from Eskom: Many industrial consumers in South Africa are penalized by Eskom for operating with a low power factor. These penalties are designed to incentivize companies to improve their power factor and reduce the strain on the grid. 2.4 Power Factor Correction using Capacitors Power factor correction involves adding capacitors to the AC circuit to counteract the inductive reactance. Capacitors supply reactive power, which reduces the amount of reactive power that must be supplied by the utility (Eskom). This improves the power factor, reduces current flow, and minimizes losses.

How it works: Capacitors store electrical energy and release it back into the circuit. When connected in parallel with an inductive load, the capacitor provides the reactive power required by the load, reducing the overall reactive power demand from the grid. This effectively "cancels out" some of the inductive reactance.

Capacitor Placement: Capacitors can be installed at various locations: Individual Equipment: Correcting the power factor at the source of the inductive load (e.g., at each motor). This is the most effective method but can be more expensive.

Group Correction: Correcting the power factor for a group of loads at a distribution board.

Central Correction: Correcting the power factor for the entire facility at the main service entrance. This is the least expensive but may not be as effective as individual or group correction. 2.5 Calculating Capacitor Size for Power Factor Correction The required capacitor kVAR (Qc) can be calculated using the following formula: Qc = P * (tan θ₁ - tan θ₂)

Where: Qc = Required capacitor reactive power (kVAR) P = Real power (kW) θ₁ = Original phase angle (before correction) θ₂ = Desired phase angle (after correction) To find the phase angles, use: θ = arccos(PF)