Interactive kW / kVAR / kVA power triangle · Capacitor bank staging · Demand savings
This simulator lets engineers stage capacitor banks interactively on an animated power triangle to see how reactive power compensation improves power factor and reduces apparent power (kVA). It is used when designing capacitor bank switching schemes for facilities with variable load profiles and utility power factor penalty clauses.
Power factor correction uses capacitors to supply reactive power (kVAR) locally rather than drawing it from the utility. The power triangle shows the relationship: kVA² = kW² + kVAR². When capacitors are switched on, their leading kVAR cancels lagging kVAR from inductive loads, shrinking the kVAR component and rotating the kVA vector toward the horizontal (unity PF) axis.
The required kVAR to achieve a target PF is: Q_C = P × (tan θ_old − tan θ_new). Staging multiple banks allows the capacitor kVAR to be matched to the load kVAR as it varies throughout the day. A facility might have a 500 kW load with 350 kVAR demand at full production but only 100 kVAR at night — a single fixed 350 kVAR bank would over-correct at night, causing leading PF and potential ferroresonance.
The simulator calculates demand savings based on kVA reduction: the utility's demand charge ($/kVA/month) multiplied by the kVA reduction gives the monthly savings. Typical demand charges range from $10–$20/kVA/month, making PF correction one of the highest-return electrical investments for facilities with significant inductive loads.
NEC Article 460 governs capacitor installation: disconnecting means (NEC 460.8), overcurrent protection sized at 135% of capacitor rated current (NEC 460.8(B)(1)), and discharge resistors to reduce voltage to 50V or less within 1 minute (NEC 460.6). IEEE 1036 is the guide for application of shunt power capacitors and covers bank sizing, switching transients, harmonic resonance, and overvoltage protection. IEEE 18 defines the standard for shunt power capacitors used in ac systems. NEMA CP-1 covers utility-type shunt capacitors.
Automatic power factor correction (APFC) controllers monitor the system PF continuously and switch capacitor banks on and off to maintain the target PF. The switching sequence should avoid hunting (rapid on/off cycling) by implementing a deadband (e.g., only switch if PF deviates by more than 0.02 from target for 30 seconds). Transient switching surges can damage capacitors — use pre-insertion inductors or zero-voltage switching controllers to limit inrush.
Harmonic resonance is the most common cause of capacitor bank failures. The parallel resonant frequency between the capacitor bank and source inductance is: f_r = 60 × √(MVA_sc / MVAR_cap). If this frequency coincides with a dominant harmonic from VFDs or rectifiers (5th = 300 Hz, 7th = 420 Hz), harmonic current amplification can destroy capacitors within hours. A detuning reactor (typically 5th harmonic, 6% impedance) in series with the capacitor prevents this.
Set the facility true power (kW), existing power factor, and target power factor. The simulator shows the required kVAR and estimates the annual demand savings. Use the Auto-Select button to automatically switch on the minimum combination of banks needed to reach the target PF, or toggle individual banks manually to explore staging strategies. The power triangle updates in real time, and the PF gauge shows before and after correction values. Compare the corrected kVA and kVAR values against your utility bill kVA demand measurement.
Most utilities stop penalizing at PF ≥ 0.95. Correcting beyond 0.95 yields diminishing demand charge savings while increasing the risk of over-correction. Unity PF (1.00) is never the design target for capacitor banks — leading PF causes voltage rise, ferroresonance, and can actually increase utility bills if the utility charges for leading kVAR export. Target PF 0.95–0.97 lagging.
A 500 kW industrial facility with PF 0.72 draws 694 kVA. Correcting to PF 0.95 reduces demand to 526 kVA — 168 kVA reduction. At $15/kVA/month, savings are $2,520/month or $30,240/year. A properly sized capacitor bank typically pays for itself in 1–3 years. The savings are higher in facilities with heavy motor loads and high demand charges.
Fixed banks are always on, regardless of load. They are suitable for loads that are consistently inductive and do not vary much — for example, a compressor running continuously at full load. Automatic banks use a PF controller with current transformers to sense the actual PF and switch banks in/out to maintain the target. Use automatic banks for facilities with variable loads, multiple production shifts, or weekend shutdowns.
Yes, and this is the most effective placement for capacitor compensation. Capacitors at motor terminals eliminate reactive current on all conductors between the motor and the utility — reducing losses in feeders, transformers, and service entrance equipment. NEC 460.7 requires that the capacitor rating not exceed the no-load magnetizing current of the motor, to prevent self-excitation and overvoltage when the motor disconnects.
VFDs generate significant harmonic current at the 5th (300 Hz), 7th (420 Hz), 11th, and 13th harmonics. Capacitors have low impedance at high frequencies, so these harmonic currents preferentially flow into the capacitor bank, causing thermal overload, dielectric stress, and fuse operation. The solution is a detuned harmonic filter: a series reactor with the capacitor tuned to just below the dominant harmonic, which presents high impedance to harmonic currents while still providing reactive compensation at 60 Hz.
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