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 power triangles.
• Explain the causes and consequences of low power factor.
• Describe how to correct power factor using capacitor banks.
• Calculate the required capacitor size for correction.

Lesson summary

This week, we delve deeper into Advanced AC Theory, with a specific focus on Power Factor Correction. In South Africa, efficient electricity usage is crucial due to increasing energy demands and the need for sustainable power generation. Understanding and correcting power factor helps reduce electricity costs, minimizes strain on Eskom's infrastructure, and contributes to a more stable and reliable electricity supply for all South Africans. Incorrect power factor can lead to penalties from municipalities for large industrial consumers. Also, improved power factor reduces transmission losses which benefits everyone by improving the overall efficiency of the electricity grid.

Lesson notes

2.1 Power Factor (PF): The Basics Power factor (PF) is the ratio of real power (kW) to apparent power (kVA) in an AC circuit. It is a dimensionless number between 0 and

1. It can also be defined as the cosine of the phase angle (θ) between the voltage and current waveforms: PF = cos(θ) = Real Power (kW) / Apparent Power (kVA)

Real Power (P): The power actually consumed by the load and converted into useful work (e.g., heat, light, mechanical energy). Measured in kilowatts (kW).

Reactive Power (Q): The power that oscillates between the source and the load, doing no useful work. It is associated with inductive and capacitive components in the circuit. Measured in kilovolt-amperes reactive (kVAR).

Apparent Power (S): The vector sum of real and reactive power. It represents the total power that the source must supply. Measured in kilovolt-amperes (kVA). A power factor of 1 indicates that the voltage and current are in phase, and all the power supplied is being used effectively. A power factor less than 1 indicates that some of the power is reactive power, and the circuit is not using the power efficiently. Power factors are generally classified as either leading (due to capacitive loads) or lagging (due to inductive loads). Most industrial loads are inductive (motors, transformers, etc.) leading to lagging power factors. 2.2 The Power Triangle The power triangle is a visual representation of the relationship between real, reactive, and apparent power.

It is a right-angled triangle with: The adjacent side representing real power (P). The opposite side representing reactive power (Q). The hypotenuse representing apparent power (S).

Using the Pythagorean theorem: S² = P² + Q² The angle between the real power (P) and apparent power (S) is the phase angle (θ), and cos(θ) is the power factor. 2.3 Causes of Low Power Factor Low power factor is typically caused by inductive loads such as: Induction Motors: Widely used in industries for various applications (pumps, compressors, fans, etc.)

Transformers: Used for voltage transformation in power distribution systems.

Ballasts in Fluorescent Lighting: Older types of lighting ballasts are inductive.

Arc Furnaces: Used in steel manufacturing. These inductive loads draw lagging current, which increases the reactive power and lowers the power factor. 2.4 Consequences of Low Power Factor Increased Current: For the same amount of real power, a lower power factor results in a higher current flow in the circuit (S = VI, therefore I = S/V, if S increases, I increases). This leads to increased I²R losses in cables and equipment.

Increased Voltage Drop: Higher current causes a larger voltage drop in the supply cables, potentially affecting the performance of equipment.

Reduced System Capacity: The higher current demand reduces the capacity of generators, transformers, and distribution lines.

Higher Electricity Bills: Many utilities, like Eskom, penalize industrial consumers for low power factors (typically below 0.9) because they must supply the extra reactive power.

Overheating: Higher currents lead to overheating of electrical equipment and reduces their lifespan. 2.5 Power Factor Correction Power factor correction aims to improve the power factor by reducing the reactive power in the circuit. This is typically achieved by adding capacitors in parallel with the inductive load. Capacitors generate leading reactive power, which cancels out some of the lagging reactive power drawn by the inductive load. This reduces the apparent power and improves the power factor. 2.6 Capacitor Bank Calculation To calculate the required capacitor size for power factor correction, we use the following formula: Qc = P * (tan θ₁ - tan θ₂)

Where: Qc = Reactive power of the capacitor bank (kVAR) P = Real power (kW) θ₁ = Original phase angle (before correction) θ₂ = Target phase angle (after correction) Since Qc = V² / Xc, where Xc = 1 / (2πfC) we can solve for C: C = Qc / (2πfV²)

Where: C = Capacitance (Farads) f = Frequency (Hz) V = Voltage (Volts)