Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Define and relate true, reactive, and apparent power.
• Calculate power factor in AC circuits.
• Explain the causes and effects of low power factor.
• Describe how to correct power factor using capacitors.
• Calculate the capacitance needed for correction.

Lesson summary

This week, we delve into the intricacies of Advanced AC Theory and Power Factor Correction, a crucial aspect of electrical engineering that has significant implications for efficient energy distribution and cost savings. In South Africa, with our challenges in electricity supply and the rising cost of energy, understanding and implementing power factor correction is more important than ever. Industries and even households can significantly reduce their energy bills and improve the stability of the electrical grid by addressing power factor issues.

Lesson notes

2.1 Power Factor (PF): Power factor is defined as the ratio of real power (P) flowing to the load to the apparent power (S) in the circuit. It is a dimensionless number between 0 and

1. Real Power (P): Also known as active power or true power, measured in Watts (W) or Kilowatts (kW). This is the power actually consumed by the load to perform useful work (e.g., turning a motor, heating an element).

Apparent Power (S): The product of the RMS voltage and RMS current in the circuit, measured in Volt-Amperes (VA) or Kilovolt-Amperes (kVA). It's the total power that appears to be flowing, even if some of it isn't being used productively.

Reactive Power (Q): Power that oscillates between the source and the load without doing any real work. It is associated with inductive and capacitive components in the circuit, measured in Volt-Amperes Reactive (VAR) or Kilovolt-Amperes Reactive (kVAR).

Formula: `Power Factor (PF) = P / S` Power Triangle: The relationship between P, Q, and S can be visually represented using the power triangle, where: S is the hypotenuse. P is the adjacent side. Q is the opposite side. The angle between S and P is φ (phi), the power factor angle. `PF = cos(φ)` 2.2 Inductive and Capacitive Loads: Inductive Loads: Examples include motors, transformers, and fluorescent lighting ballasts. Inductive loads cause the current to lag behind the voltage, resulting in a lagging power factor (PF < 1). This means the current waveform reaches its peak after the voltage waveform.

Capacitive Loads: Examples include capacitors, and some electronic power supplies. Capacitive loads cause the current to lead the voltage, resulting in a leading power factor (PF < 1). This means the current waveform reaches its peak before the voltage waveform. Most industrial and commercial loads are inductive. 2.3 Consequences of Low Power Factor: Increased Current: For a given amount of real power required, a low power factor results in higher current flowing through the conductors. This is because `S = V I`, and `PF = P/S`. If PF is low, then S must be high to deliver the same P, meaning I must be high. Increased I²R Losses: Higher current leads to increased losses in the conductors due to the resistance of the wires (I²R losses), wasting energy and potentially overheating conductors.

Voltage Drop: High current flow can cause excessive voltage drop along the distribution lines, affecting the performance of equipment connected to the system.

Reduced System Capacity: Low power factor reduces the available capacity of the electrical system, as more current is being used to deliver the same amount of real power. This can necessitate expensive upgrades to transformers and cables.

Increased Electricity Bills: Utility companies often charge customers with low power factors a penalty because they are placing a greater strain on the grid. 2.4 Power Factor Correction using Capacitors: Power factor correction typically involves adding capacitors in parallel with the inductive load. Capacitors generate reactive power that is opposite in phase to the reactive power consumed by the inductive load. This effectively cancels out some of the inductive reactive power, reducing the overall apparent power and improving the power factor. 2.5 Calculating Capacitance for Power Factor Correction: Determine the existing power factor (PF1) and the desired power factor (PF2). Calculate the angle φ1 corresponding to PF1 (φ1 = arccos(PF1)) and the angle φ2 corresponding to PF2 (φ2 = arccos(PF2)). Calculate the reactive power before correction (Q1 = P * tan(φ1)). Calculate the reactive power after correction (Q2 = P * tan(φ2)). Calculate the reactive power to be supplied by the capacitor (Qc = Q1 - Q2). Calculate the required capacitance (C = Qc / (ω * V²)), where ω = 2πf (angular frequency) and V is the voltage.