The Power Triangle
Electrical power has three components: real power P (watts, which performs useful work), reactive power Q (vars, which sustains magnetic fields in motors and transformers), and apparent power S (volt-amperes, which the generator and transmission system must deliver). These form a right triangle where S² = P² + Q², and the power factor is the cosine of the angle between P and S. The visualization shows this triangle dynamically as you adjust parameters.
The Cost of Poor Power Factor
A power factor of 0.75 means the grid must deliver 33% more current than necessary to supply the same real power. Since line losses are proportional to I² (current squared), losses increase by 78%. Transformers, cables, and switchgear must all be oversized to handle this excess current. For a 200 kW load at PF 0.75, the apparent power is 267 kVA — requiring infrastructure rated for 267 kVA even though only 200 kW does useful work.
Capacitor Bank Sizing
The required capacitive reactive power Q_c equals the difference between the reactive power at the old and new power factors: Q_c = P × (tan(arccos(PF_old)) − tan(arccos(PF_new))). Standard capacitor bank sizes come in discrete steps, so engineers round up to the nearest available unit. The simulation accounts for this and shows the actual achieved power factor after installing a standard-sized bank.
Practical Considerations
Real installations use automatic power factor correction (APFC) controllers that switch capacitor banks in and out based on measured power factor. This prevents overcorrection during light load periods and avoids resonance with system harmonics. Modern installations increasingly use static VAR compensators (SVCs) or STATCOMs for faster, smoother, and more precise reactive power control — especially important near renewable energy sources with variable output.