π Understanding Power Factor Correction with Phasor Diagrams
This lesson provides a visual explanation of power factor correction using phasor diagrams. We'll cover the basics, the need for correction, and how it's represented visually.
π― Learning Objectives
- π§ Define power factor and its implications.
- π Explain the concept of leading and lagging power factors.
- π‘ Illustrate power factor correction using phasor diagrams.
- π οΈ Describe the practical applications of power factor correction.
π§ͺ Materials
- π Ruler and protractor (for drawing phasor diagrams).
- π» Computer with internet access (for research and simulations).
- π Pen and paper (for notes and calculations).
π₯ Warm-up (5 mins)
Quick review of AC circuits. What are voltage, current, and impedance? How are they related?
π¨βπ« Main Instruction
Fundamentals of Power Factor
Power factor (PF) is the ratio of real power (kW) to apparent power (kVA). It indicates how effectively electrical power is being used.
$PF = \frac{Real Power (kW)}{Apparent Power (kVA)}$
- β‘ A power factor of 1 (unity) means that all the power supplied is being used effectively.
- π A power factor less than 1 indicates that some power is wasted due to reactive loads (inductive or capacitive).
Leading and Lagging Power Factors
- 𧱠Lagging Power Factor: Occurs when the current lags behind the voltage, typically due to inductive loads like motors and transformers.
- capacitor π‘ Leading Power Factor: Occurs when the current leads the voltage, typically due to capacitive loads like capacitor banks.
Phasor Diagram Representation
A phasor diagram is a graphical representation of the phase relationship between voltage and current in an AC circuit.
- π Voltage is usually taken as the reference phasor, drawn horizontally.
- β‘οΈ Current phasor is drawn at an angle relative to the voltage phasor. The angle represents the phase difference.
- β For a lagging power factor, the current phasor lags behind the voltage phasor (clockwise direction).
- β For a leading power factor, the current phasor leads the voltage phasor (counter-clockwise direction).
Power Factor Correction
Power factor correction involves adding capacitive or inductive reactance to offset the reactive component of the load, bringing the power factor closer to unity.
- π© For a lagging power factor (inductive load), capacitors are added in parallel to the load.
- β‘ The capacitor provides reactive power that cancels out some of the inductive reactive power.
- π In the phasor diagram, the capacitor current leads the voltage by 90 degrees, partially canceling the lagging inductive current.
- π‘ The net effect is a reduction in the total current drawn from the source and an improvement in the power factor.
Visual Example with Phasor Diagram
Consider an inductive load with a lagging power factor. The current ($I_L$) lags the voltage (V) by an angle $\theta$. To correct the power factor, a capacitor is added in parallel. The capacitor current ($I_C$) leads the voltage by 90 degrees.
The total current ($I_T$) is the vector sum of $I_L$ and $I_C$. By choosing an appropriate capacitor value, $I_T$ can be brought closer in phase with the voltage, improving the power factor.
Before Correction:
$\theta$ is large, indicating a poor power factor.
After Correction:
$\theta$ is smaller, indicating an improved power factor closer to 1.
π Assessment
Draw phasor diagrams to illustrate power factor correction for different load types (inductive, capacitive, and mixed). Explain how the addition of capacitors affects the overall current and power factor.
β
Practice Quiz
- β What is power factor, and why is it important?
- β Explain the difference between leading and lagging power factors.
- β How does adding a capacitor correct a lagging power factor?
- β Draw a phasor diagram showing a lagging power factor before and after correction.
- β What are the benefits of power factor correction in industrial applications?
- β How does the power factor affect the current drawn from the source?
- β Explain how to calculate the required capacitance for power factor correction.