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Power factor measures how effectively electrical power is converted into useful work output. It is the ratio of real power in kilowatts that does the work to the apparent power in kilovolt-amperes supplied to the circuit. A power factor closer to unity indicates more efficient power usage and less wasted reactive power in the system.

A low lagging power factor occurs when inductive electrical loads absorb more reactive power. This causes large voltage drops across the load and thermal losses in the transmission system. These losses increase electricity costs and reduce overall system efficiency, making power factor correction necessary for cost-effective operation.

Shunt capacitors are connected parallel to the load and provide a leading current that offsets the lagging reactive current caused by inductive loads. By counteracting the inductive effects, shunt capacitors reduce the amount of reactive power drawn from the supply, bringing the overall power factor closer to unity and making the system more efficient.

The power triangle graphically represents the relationship between real power, reactive power, and apparent power. By examining the power triangle of the original circuit, engineers can determine real and reactive power values. Adding a capacitive load decreases the power factor angle without changing real power, allowing calculation of the corrected reactive power needed.

Series capacitors are used in long transmission lines and counteract the inductive nature of the line by providing a leading current that neutralizes some lagging reactive power. Shunt capacitors, the most widely used method, connect parallel to the load. Both approaches improve power factor, but series capacitors target transmission line inductance while shunt capacitors address load-side reactive power.

When a compensating capacitor is added parallel to the load, the real power remains unchanged. The capacitor only reduces the reactive power component and decreases the power factor angle. This selective reduction in reactive power results from the shunt capacitance, allowing the system to maintain useful work output while improving efficiency.

The shunt capacitor value is determined by revisiting the expressions of reactive power and analyzing the power triangle. By calculating the difference between original and corrected reactive power values from the power triangle, engineers can determine the exact capacitance needed to bring the power factor as close to unity as possible for optimal system performance.