Power Triangle Calculator (kW, kVA, kVAR)

Commercial-grade tool for analyzing AC power relationships. Calculate missing variables in the Power Triangle and size Capacitor Banks for Power Factor Correction. Features step-by-step vector math and interactive diagrams.

Engineering Guide: Power Triangle & Factor Correction

1. The Physics of AC Power

In Alternating Current (AC) circuits, power is not as simple as $Volts \times Amps$. Because voltage and current waveforms can shift out of phase (due to inductance or capacitance), we deal with three distinct types of power:

  • Real Power (P) - kW: The power that performs actual work (turns the motor shaft, lights the bulb, heats the element). It is the horizontal component of the triangle.
  • Reactive Power (Q) - kVAR: The power that oscillates back and forth between source and load to sustain magnetic fields in motors and transformers. It does no useful work but occupies current capacity. It is the vertical component.
  • Apparent Power (S) - kVA: The vector sum of P and Q. This is what the utility generates and transmits. Cables and transformers are sized based on kVA (heat limit), not kW.

2. The Power Triangle Geometry

The relationship follows the Pythagorean theorem:

$$ S = \sqrt{P^2 + Q^2} $$ $$ P = S \times \cos(\theta) $$ $$ Q = S \times \sin(\theta) $$

The Power Factor (PF) is simply the ratio of Real Power to Apparent Power ($P/S$), which equals the cosine of the phase angle ($\theta$). A PF of 1.0 means 100% efficiency (Current in phase with Voltage). A PF of 0.8 means only 80% of the supplied kVA is doing real work.

3. Power Factor Correction

Industrial loads (motors) are inductive, causing current to "lag" voltage. This draws significant kVAR. To fix this, we add Capacitors which draw leading current (capacitive kVAR). This cancels out the inductive kVAR locally.

Benefits of Correction:

  • Eliminates utility penalties (often charged if PF < 0.95).
  • Releases system capacity (transformers can carry more kW).
  • Reduces voltage drop and $I^2R$ losses in cables.

The formula to size the capacitor bank ($Q_c$) required to improve PF from $\theta_{old}$ to $\theta_{new}$ is:

$$ Q_c = P [ \tan(\arccos(PF_{old})) - \tan(\arccos(PF_{new})) ] $$

4. Frequently Asked Questions (FAQ)

1. What is the difference between kW and kVA?
kW (Kilowatts) is Real Power, the power that actually does useful work (heat, light, motion). kVA (Kilovolt-Amperes) is Apparent Power, the total vector sum of Real Power and Reactive Power (kVAR). kVA is always equal to or greater than kW.
2. Why do I need to correct Power Factor?
Low power factor draws higher current for the same amount of useful work, leading to higher line losses, voltage drops, and utility penalties (kVA demand charges). Correcting PF reduces your electricity bill and frees up system capacity.
3. What is kVAR?
kVAR (Kilovolt-Amperes Reactive) represents Reactive Power. It is the power required to magnetize motors and transformers. It bounces back and forth between the source and load, doing no 'real' work but occupying wire capacity.
4. How does a Capacitor Bank improve PF?
Inductive loads (motors) consume reactive power (lagging current). Capacitors supply reactive power (leading current). By placing capacitors near the load, they supply the kVAR locally, reducing the kVAR drawn from the utility grid.
5. Can Power Factor be negative?
Yes, in four-quadrant metering. A negative power factor usually indicates power is being exported (like from Solar PV) or the load is extremely capacitive (leading), though mathematically it is often treated as the direction of power flow.
6. What is the formula for Power Factor?
Power Factor (PF) = Real Power (kW) / Apparent Power (kVA). It is also the cosine of the phase angle (θ) between voltage and current waveforms.
7. What causes low Power Factor?
The main culprits are inductive loads such as induction motors, transformers, welding machines, arc furnaces, and fluorescent lighting ballasts. Lightly loaded motors have a significantly worse power factor than fully loaded ones.
8. What is a "Penalty" Power Factor?
Most utilities charge a penalty if your facility's PF drops below a certain threshold, commonly 0.85 or 0.90 or 0.95. This is because they must size their infrastructure to carry your 'wasted' reactive current.
9. How do I calculate required Capacitor kVAR?
kVAR Required = P(kW) × [tan(acos(PF_old)) - tan(acos(PF_new))]. This tool performs this calculation automatically in the "Correction" module.
10. Does this tool work for Single and Three Phase?
Yes. Power Triangle relationships (S² = P² + Q²) hold true for both. However, when calculating current (Amps) from kVA, you must apply the √3 factor for 3-phase systems.