Phase Academy · Power Factor Correction Simulator

Model Assumptions: This simulator assumes balanced sinusoidal loads and displacement power factor only. Nonlinear loads (VFDs, welders) have distortion power factor; capacitor correction for such loads requires harmonic analysis and may need detuned reactors or active filters.

⚠ Leading Power Factor Warning

⚡ Harmonics Caution

Adding capacitor banks to nonlinear loads (VFDs, welders) risks resonance. This simulator does not model harmonic resonance. Real installations require harmonic analysis and may need detuned reactors or active filters.

💡 Insight

Adjust the controls on the left to see how power factor correction affects your electrical system. Start by changing the capacitor bank slider.

⚡ Power Metrics

Real Power (P)

100.0

Reactive (Q) Before

+75.0

kVAR lagging

Apparent (S) Before

125.0

kVA

Reactive (Q) After

+75.0

kVAR lagging

Apparent (S) After

125.0

kVA

Cap kVAR Applied

0.0

kVAR

Before Correction

0.80 lag

Power Factor

150.4 A

Line Current

After Correction

0.80 lag

Power Factor

150.4 A

Line Current

📈 Current Change

Gauge arc spans 0–50%; the number always shows the true value.

💵 Illustrative Utility Penalty Model

Assumptions: 730 hrs/mo, $0.10/kWh base, penalty threshold PF = 0.90 (threshold applied to leading PF as well in this simplified model), formula: baseBill × (0.90/PF − 1). Actual utility tariffs vary.

Est. Penalty Before

per month

Est. Penalty After

per month

This is a simplified educational model. Actual utility penalty structures vary by region and tariff schedule. Do not use for billing estimates.

📋 System Summary

Three-Phase 480V | 100 kW motor load | PF 0.80 lag

📝 Event / Insight Log

Recent changes and simulator insights (newest first)

Educational Disclaimer: This simulator is for learning purposes only. Values are simplified approximations. Do not use for actual power system design, equipment sizing, or engineering decisions. Always consult a licensed professional engineer.

📐 Live Power Triangle — Before & After

⟶ Vector Phasor View

🔍 What Changed?

No correction applied yet. Move the capacitor bank slider to see changes.

⚠ Over-correction detected!

⚡ Harmonics risk

This load type contains nonlinear elements. Standard capacitor banks can amplify harmonic currents. This simulator does not model harmonic resonance. Real installations require harmonic analysis.

🧮 Step-by-Step Correction Analysis

Before

After

📊 Before vs After — Bar Comparison

🎯 Preset Scenarios

Click a scenario to load it into the simulator, then explore the Dashboard and Correction Lab tabs.

🏭 Factory Floor

480V 3-phase, 500 kW motor-heavy load, PF 0.72 lagging. High penalty risk.

🏢 Office Building

480V 3-phase, 200 kW mixed commercial, PF 0.88 lagging. Moderate improvement possible.

🔨 Welding Shop

240V single-phase, 80 kW welders, PF 0.60 lagging. Severe PF, harmonics concern.

🖥 Data Center

480V 3-phase, 1000 kW VFD-heavy, PF 0.92 lagging. Already decent; fine-tune correction.

⚠ Over-Correction Demo

See what happens when you add too many capacitors. 480V 3-phase, 150 kW, PF 0.75 lag + 200 kVAR cap.

↺ Leading Initial Load

480V 3-phase, 100 kW, PF 0.80 leading. Demonstrates auto-correct refusal for leading loads.

The Power Triangle

Every AC electrical load has three types of power:

Real Power (P) — measured in kW. This is the useful work: turning shafts, producing heat, running computers.
Reactive Power (Q) — measured in kVAR. This energy shuttles back and forth to sustain magnetic fields in motors, transformers, and ballasts. It does no useful work but is required by inductive loads.
Apparent Power (S) — measured in kVA. This is what the utility must deliver. It is the vector sum.

S = sqrt(P^2 + Q^2) PF = P / S = cos(theta) Q = P * tan(theta) Sign convention: +Q = lagging (inductive) -Q = leading (capacitive)

Power Factor

Power factor is the ratio of real power to apparent power. A PF of 1.0 means all supplied energy does useful work. A PF of 0.70 means the utility must deliver ~43% more current than needed for the real load, increasing losses and costs.

Lagging PF (most common) is caused by inductive loads — motors, transformers, solenoids. Leading PF can be caused by over-correction with capacitors or lightly loaded synchronous motors.

Power Factor Correction

Capacitors supply reactive power locally, reducing the reactive demand from the utility. The capacitor kVAR needed:

Q_cap = P * (tan(theta_1) - tan(theta_2)) Where: theta_1 = acos(PF_initial) theta_2 = acos(PF_target) Important: Capacitors correct lagging (inductive) PF only. Leading PF requires inductive compensation (reactors).

This reduces line current, transformer loading, and I²R losses. Many utilities charge penalties for PF below 0.90 or 0.85.

Worked Example

Given: 480V, 3-phase, 200 kW, PF = 0.75 lagging Target: PF = 0.95 Step 1: theta_1 = acos(0.75) = 41.41 deg Step 2: theta_2 = acos(0.95) = 18.19 deg Step 3: Q_cap = 200 * (tan(41.41) - tan(18.19)) = 200 * (0.8819 - 0.3287) = 200 * 0.5532 = 110.6 kVAR Before: S = 200/0.75 = 266.7 kVA, I = 266700/(sqrt(3)*480) = 320.8 A After: S = 200/0.95 = 210.5 kVA, I = 210500/(sqrt(3)*480) = 253.2 A Current reduction: 21.0%

Common Mistakes

Over-correcting to unity (PF = 1.0): Dangerous at light load. Target 0.95 to leave margin.
Ignoring harmonics: Capacitors + VFDs or welders can create resonance. Use detuned reactors.
Placing all capacitors at the main bus: Better to distribute near large motors.
Not accounting for load variation: Switched capacitor banks adapt; fixed banks can over-correct at light load.
Forgetting leading PF penalties: Some utilities penalize leading PF too.

Test Your Knowledge

See if you can answer these based on what you just learned.

Educational Disclaimer: This tool is for learning about power factor concepts. Actual power system design requires professional engineering analysis, detailed load studies, harmonic analysis, and compliance with NEC/IEEE/local codes.