An industrial load is connected to a 60 Hz line and the load voltage is 480 ∠0^∘ V rms. The loa

step 1 In this problem I can write the value of theta old which is equal to Cos inverse 0 .75 which is

An industrial load is connected to a 60 Hz line and the...

An industrial load is connected to a $60 \mathrm{~Hz}$ line and the load voltage is $480 \angle 0^{\circ} \mathrm{V}$ rms. The load consumes $120 \mathrm{~kW}$ at $0.77 \mathrm{PF}$ lagging. $\mathrm{Sz}$ lect the capacitor value needed to raise th power factor to 0.9 lagging.

Key Concepts

Power Factor Correction

Power factor correction is the process used to improve the efficiency of an AC power system by reducing the phase difference between voltage and current waveforms. This is typically achieved by adding components, such as capacitors, that supply reactive power to counteract the effects of inductive loads, thereby minimizing energy losses and improving voltage regulation.

Real and Reactive Power

In AC circuits, real power (measured in watts) is the actual power consumed by loads to do useful work, while reactive power (measured in VARs) is the power exchanged between the source and reactive components like inductors and capacitors. The relationship between them is characterized by the power factor, which is defined as the cosine of the phase angle between the voltage and current waveforms. The reactive power can be calculated using the formula Q = P tan(acos(PF)), where PF is the power factor.

Capacitor Sizing for Power Factor Correction

Capacitor sizing for power factor correction involves determining the appropriate capacitive reactive power needed to offset the lagging reactive power of an inductive load so that the overall power factor is improved. This is done by calculating the difference in reactive power between the existing and the desired power factor levels, and then using the relationship Q_C = V^2 * ? * C to solve for the capacitance, where Q_C is the required capacitive reactive power, V is the line voltage, ? is the angular frequency, and C is the capacitance.

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