12.4 Power in AC circuits and power factor

AC circuits aren't just about voltage and current. Power plays a crucial role too. In this part, we'll look at different types of power: real, reactive, and apparent. We'll see how they relate to each other and why they matter.

We'll also dive into power factor and phase angle. These concepts help us understand how efficiently power is used in AC circuits. By the end, you'll get why power factor correction is a big deal in real-world electrical systems.

Power Types in AC Circuits

Real Power (Active Power)

• Real power ($P$) represents the actual power consumed by the load that performs useful work
• Measured in watts (W)
• Calculated using the formula: $P = VI \cos \phi$, where $V$ is the voltage, $I$ is the current, and $\phi$ is the phase angle between voltage and current
• In a purely resistive circuit, all the power is real power (e.g., a heating element or an incandescent light bulb)

Reactive Power

• Reactive power ($Q$) represents the power that is stored and released by reactive components (inductors and capacitors) in an AC circuit
• Measured in volt-ampere reactive (VAR)
• Calculated using the formula: $Q = VI \sin \phi$
• Reactive power does not perform useful work but is necessary for maintaining the magnetic and electric fields in inductors and capacitors
• In a purely reactive circuit (e.g., an ideal inductor or capacitor), all the power is reactive power

Apparent Power

• Apparent power ($S$) is the vector sum of real power and reactive power
• Represents the total power supplied by the source to the circuit
• Measured in volt-amperes (VA)
• Calculated using the formula: $S = \sqrt{P^2 + Q^2} = VI$
• In a circuit with both resistive and reactive components, apparent power is always greater than or equal to real power

Power Factor and Phase Angle

Power Factor

• Power factor ($\cos \phi$) is the ratio of real power to apparent power
• Represents the efficiency of power utilization in an AC circuit
• Calculated using the formula: $\cos \phi = \frac{P}{S}$
• A power factor of 1 indicates that all the power supplied is consumed by the load (purely resistive circuit), while a power factor of 0 indicates that no power is consumed (purely reactive circuit)

Phase Angle

• Phase angle ($\phi$) is the angle between the voltage and current waveforms in an AC circuit
• Determines the nature of the circuit: resistive ($\phi = 0^\circ$), inductive ($\phi > 0^\circ$), or capacitive ($\phi < 0^\circ$)
• Affects the power factor and the efficiency of power transmission
• Can be calculated using the formula: $\phi = \tan^{-1} \frac{Q}{P}$

Power Triangle

• The power triangle is a graphical representation of the relationship between real power, reactive power, and apparent power
• Real power forms the adjacent side, reactive power forms the opposite side, and apparent power forms the hypotenuse of the right-angled triangle
• The angle between real power and apparent power is the phase angle ($\phi$)
• Helps visualize the power factor and the relative magnitudes of real, reactive, and apparent power in an AC circuit

Improving Power Efficiency

Power Factor Correction

• Power factor correction is the process of improving the power factor of an AC circuit to maximize power efficiency and reduce power losses
• Involves adding compensating devices (e.g., capacitor banks) in parallel with the load to counteract the reactive power consumed by inductive loads
• Capacitor banks provide leading reactive power to cancel the lagging reactive power consumed by inductive loads, bringing the power factor closer to 1
• Benefits of power factor correction include reduced power losses in transmission lines, improved voltage regulation, and increased capacity of electrical systems
• Power utility companies often charge penalties for low power factor, making power factor correction economically beneficial for industries with large inductive loads (e.g., motors, transformers)