A small plant has a bank of induction motons that consume 64 kW at a PF of 0.68 lagging. The 60

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A small plant has a bank of induction motons that consume 64...

A small plant has a bank of induction motons that consume $64 \mathrm{~kW}$ at a PF of 0.68 lagging. The $60 \mathrm{~Hz}$ line voltage across the motors is $220 \angle 0^{\circ} \mathrm{V}$ rms. The local power company has told the plant to raise the PF to 0.92 lagging. What value of capacitance is required?

Key Concepts

Power Factor Improvement

Power factor improvement is the process of increasing the power factor of a system to reduce the phase difference between voltage and current. By using methods such as capacitive compensation, the reactive power demand is minimized, thereby enhancing the efficiency of power delivery and reducing the load on the electrical infrastructure.

AC Circuit Analysis and Capacitor Sizing

In AC circuit analysis, determining the correct capacitor size involves calculating the amount of reactive power that needs to be compensated. This is done by comparing the initial and desired reactive power levels, and then applying the relationship Q = V^2?C to solve for the required capacitance, where V is the RMS voltage and ? is the angular frequency.

Capacitive Compensation

Capacitive compensation involves adding capacitors to a system to supply locally produced reactive power. This helps to offset the reactive power drawn by inductive loads and improves the overall power factor, leading to more efficient energy usage and reduced losses.

Reactive Power

Reactive power is the component of power that oscillates between the source and reactive elements (like inductors and capacitors) in an AC circuit. It does not perform any real work but is essential for establishing the magnetic fields needed by inductive devices such as motors.

Power Factor

Power factor is a measure of how effectively electrical power is being used, defined as the cosine of the phase angle between voltage and current. It indicates the proportion of total power that is used to do useful work, with a lagging power factor (common in inductive loads) signifying that the current lags behind voltage.

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