Introduction #

This guide is for electrical engineers, facility managers, and energy consultants who need to accurately size capacitor banks for power factor correction in industrial and commercial facilities. It solves the problem of determining the correct capacitor size (kVAR) needed to improve power factor, eliminate utility penalties, and optimize electrical system performance. Use this knowledge when planning power factor correction projects, calculating ROI for capacitor installations, selecting between fixed and automatic capacitor banks, or troubleshooting existing power factor correction systems.

What is Capacitor Bank Sizing? #

Capacitor bank sizing is the process of determining the correct amount of reactive power (kVAR) that capacitors must supply to improve a facility's power factor from its current value to a target value (typically 0.95). Proper sizing ensures effective power factor correction without overcorrection (leading power factor) or undercorrection (insufficient improvement).

For a comprehensive overview of power factor concepts, why it matters, and how it affects electrical systems, see our Power Factor Guide.

Why Proper Capacitor Sizing Matters #

Accurate capacitor bank sizing is critical for several reasons:

Cost Optimization: Oversizing capacitors wastes capital investment and can cause leading power factor issues. Undersizing fails to eliminate penalties, resulting in continued costs. Proper sizing ensures optimal ROI.

System Performance: Correctly sized capacitors improve voltage regulation, reduce line losses, and free up system capacity. Incorrect sizing can cause voltage rise, harmonic resonance, or insufficient correction.

Equipment Protection: Properly sized capacitor banks protect against overvoltage conditions and harmonic distortion. Incorrect sizing can damage capacitors or other equipment.

Utility Compliance: Most utilities require power factor above 0.85-0.90 to avoid penalties. Proper sizing ensures compliance while avoiding overcorrection penalties.

Understanding the Capacitor Sizing Formula #

The fundamental formula for calculating required capacitor size is:

kVAR = kW × (tan θ₁ - tan θ₂)

Where:

  • kVAR = Required capacitor size in kilovolt-amperes reactive
  • kW = Real power (load) in kilowatts
  • θ₁ = Phase angle of current power factor (arccos of current PF)
  • θ₂ = Phase angle of target power factor (arccos of target PF)

Alternative Formula Using Power Factor Values #

If you know the current and target power factors directly, you can use:

kVAR = kW × [tan(arccos(PF₁)) - tan(arccos(PF₂))]

Or using the power triangle relationship:

kVAR = kW × [√((1/PF₁)² - 1) - √((1/PF₂)² - 1)]

Where:

  • PF₁ = Current power factor
  • PF₂ = Target power factor (typically 0.95)

Quick Reference: tan(arccos(PF)) Values #

For common power factor values, here are the tan(arccos(PF)) values:

Power Factor tan(arccos(PF))
0.70 1.020
0.75 0.882
0.80 0.750
0.85 0.620
0.90 0.484
0.95 0.329
0.98 0.203
1.00 0.000

Example: To improve from 0.80 to 0.95 PF on a 500 kW load:

kVAR = 500 × (0.750 - 0.329) = 500 × 0.421 = 210.5 kVAR

Step-by-Step Capacitor Sizing Process #

Step 1: Measure Current Power Factor #

Before sizing capacitors, you must accurately measure your current power factor. This can be done using:

Method 1: Power Quality Meter

  • Install at main service entrance
  • Measure kW, kVA, and PF over a representative period (1-4 weeks)
  • Record average and peak power factor values

Method 2: Utility Bill Analysis

  • Review utility bills for kW and kVA values
  • Calculate: PF = kW ÷ kVA
  • Note: This gives average PF, not peak PF

Method 3: Portable Power Analyzer

  • Temporary installation at key locations
  • Measure at main service and large motor feeders
  • Capture data during different operating conditions

For detailed measurement procedures, see our guide on How to Measure Power Factor in 3-Phase Systems.

Step 2: Determine Target Power Factor #

Recommended Target: 0.95

Most engineers target 0.95 power factor because:

  • Above most utility penalty thresholds (0.85-0.90)
  • Provides margin for load variations
  • Avoids overcorrection (leading PF)
  • Optimal balance between cost and benefit

Other Considerations:

  • 0.90: Minimum to avoid most penalties, lower capacitor cost
  • 0.98: Maximum practical target, higher cost, minimal additional benefit
  • Above 0.98: Risk of overcorrection and leading power factor

Step 3: Calculate Required kVAR #

Using the formula from Step 1:

Example Calculation:

  • Current Load: 500 kW
  • Current Power Factor: 0.80
  • Target Power Factor: 0.95
θ₁ = arccos(0.80) = 36.87°
θ₂ = arccos(0.95) = 18.19°
tan(36.87°) = 0.750
tan(18.19°) = 0.329

kVAR = 500 × (0.750 - 0.329) = 500 × 0.421 = 210.5 kVAR

Step 4: Select Standard Capacitor Size #

Capacitors are available in standard sizes. Select the next standard size above your calculated value.

Standard Capacitor Sizes (kVAR):

  • 5, 7.5, 10, 12.5, 15, 20, 25, 30, 40, 50, 60, 75, 100, 125, 150, 200, 250, 300, 400, 500

Selection Rule: Round up to the next standard size to ensure adequate correction.

Example: For calculated 210.5 kVAR, select 225 kVAR (combination of 200 kVAR + 25 kVAR, or single 225 kVAR unit if available).

Step 5: Verify Correction Result #

After selecting capacitor size, verify the resulting power factor:

Verification Formula:

New kVAR = Current kVAR - Capacitor kVAR
New kVA = √(kW² + New kVAR²)
New PF = kW ÷ New kVA

Example (continuing from above):

  • Current: 500 kW, 625 kVA, 0.80 PF, 375 kVAR
  • Capacitor: 225 kVAR
  • New kVAR = 375 - 225 = 150 kVAR
  • New kVA = √(500² + 150²) = 522.0 kVA
  • New PF = 500 ÷ 522.0 = 0.958 ✓ (exceeds 0.95 target)

Single-Phase vs Three-Phase Capacitor Sizing #

The capacitor sizing formula is the same for both single-phase and three-phase systems. The difference is in how you measure the initial kW and power factor values.

Single-Phase Systems #

Measurement:

  • Measure phase voltage (V)
  • Measure phase current (I)
  • Measure real power (kW)
  • Calculate: PF = kW ÷ (V × I)

Capacitor Sizing:

  • Use the same formula: kVAR = kW × (tan θ₁ - tan θ₂)
  • Capacitor voltage rating: Match system voltage (e.g., 120V, 240V)

Three-Phase Systems #

Measurement:

  • Measure line-to-line voltage (V_L)
  • Measure line current (I_L)
  • Measure real power (kW)
  • Calculate: PF = kW ÷ (V_L × I_L × √3)

Capacitor Sizing:

  • Use the same formula: kVAR = kW × (tan θ₁ - tan θ₂)
  • Capacitor voltage rating: Match line-to-line voltage (e.g., 480V, 600V)
  • Capacitor connection: Delta (Δ) or Wye (Y) depending on system

Important: The kVAR value calculated is the total three-phase kVAR, not per-phase. For delta-connected capacitors, each capacitor unit is rated at line voltage. For wye-connected capacitors, each unit is rated at phase voltage, but the total kVAR is the same.

Fixed vs Automatic Capacitor Banks #

Fixed Capacitor Banks #

Characteristics:

  • Constant kVAR output
  • No switching or controls
  • Lower initial cost
  • Simple installation

Best For:

  • Constant loads with stable power factor
  • Individual motor correction
  • Small facilities with minimal load variation

Limitations:

  • Cannot adjust to load changes
  • Risk of overcorrection during light loads
  • May cause leading power factor at low loads

Example Application:
A facility with constant 500 kW load at 0.80 PF, operating 24/7 with minimal variation. Fixed 225 kVAR capacitor bank is appropriate.

Automatic (Switched) Capacitor Banks #

Characteristics:

  • Multiple capacitor steps that switch in/out automatically
  • Power factor controller monitors PF and switches steps
  • Adjusts to load variations
  • Higher initial cost

Best For:

  • Variable loads with changing power factor
  • Facilities with significant load diversity
  • Large facilities where overcorrection risk is high

Operation:

  • Controller measures power factor continuously
  • Switches capacitor steps in when PF drops below setpoint
  • Switches steps out when PF rises above setpoint
  • Typically 4-12 steps (e.g., 25, 50, 75, 100 kVAR steps)

Example Application:
A manufacturing facility with 200-800 kW load variation throughout the day. Automatic bank with steps: 50, 50, 50, 75 kVAR (total 225 kVAR) provides optimal correction at all load levels.

Selection Guidelines #

Load Characteristic Recommended Type
Constant load (±10% variation) Fixed
Variable load (>20% variation) Automatic
Multiple shifts with different loads Automatic
Single large motor Fixed (at motor)
Facility-wide correction Automatic
Load < 100 kW Fixed
Load > 500 kW with variation Automatic

Capacitor Installation Location Strategies #

The location of capacitor banks significantly affects system performance and correction effectiveness.

Strategy 1: Centralized (Main Service) #

Installation: Single capacitor bank at main service entrance or main distribution panel.

Advantages:

  • Simple installation and maintenance
  • Lower cost (single location)
  • Easy to monitor and control
  • Effective for facility-wide correction

Disadvantages:

  • Doesn't reduce feeder currents
  • Less efficient for distributed loads
  • All correction at one point

Best For:

  • Small to medium facilities (< 1000 kW)
  • Concentrated loads
  • Simple power factor correction needs

Strategy 2: Distributed (Load Centers) #

Installation: Multiple smaller capacitor banks at load centers or distribution panels throughout the facility.

Advantages:

  • Reduces feeder currents (lower I²R losses)
  • Better voltage regulation at loads
  • More efficient correction
  • Reduces transformer loading

Disadvantages:

  • Higher installation cost
  • More maintenance points
  • More complex control coordination

Best For:

  • Large facilities (> 1000 kW)
  • Distributed loads across multiple buildings/areas
  • Facilities with long feeder runs
  • When voltage regulation is critical

Strategy 3: Load-Specific (At Motors) #

Installation: Individual capacitors at large motors (typically > 50 HP).

Advantages:

  • Most efficient (correction at source)
  • Reduces motor feeder current
  • Improves motor voltage
  • Reduces transformer and cable loading

Disadvantages:

  • Higher total cost (multiple installations)
  • More maintenance points
  • Requires coordination with motor controls

Best For:

  • Facilities with few large motors
  • When individual motor correction is needed
  • When reducing feeder currents is critical

Selection Guidelines #

Facility Size Load Distribution Recommended Strategy
< 500 kW Concentrated Centralized
< 500 kW Distributed Centralized or Distributed
500-2000 kW Concentrated Centralized
500-2000 kW Distributed Distributed
> 2000 kW Any Distributed or Load-Specific
Multiple buildings Any Distributed

Real-World Sizing Examples #

Example 1: Small Manufacturing Plant #

Scenario:

  • Facility: Small manufacturing plant
  • Load: 200 kW (constant)
  • Current PF: 0.75
  • Target PF: 0.95
  • Load variation: Minimal (±5%)

Step 1: Calculate Required kVAR

tan(arccos(0.75)) = 0.882
tan(arccos(0.95)) = 0.329
kVAR = 200 × (0.882 - 0.329) = 200 × 0.553 = 110.6 kVAR

Step 2: Select Standard Size

  • Calculated: 110.6 kVAR
  • Standard size: 125 kVAR (next standard above)

Step 3: Select Type

  • Load is constant → Fixed capacitor bank

Step 4: Select Location

  • Small facility, concentrated load → Main service entrance

Result: Install 125 kVAR fixed capacitor bank at main service.

Example 2: Medium Food Processing Facility #

Scenario:

  • Facility: Food processing plant
  • Load: 500-800 kW (varies by shift)
  • Current PF: 0.82 (average)
  • Target PF: 0.95
  • Load variation: Significant (60% to 100% of peak)

Step 1: Calculate Required kVAR (at average load)

Average load: 650 kW
tan(arccos(0.82)) = 0.698
tan(arccos(0.95)) = 0.329
kVAR = 650 × (0.698 - 0.329) = 650 × 0.369 = 239.9 kVAR

Step 2: Verify at Peak Load

Peak load: 800 kW
Required kVAR at peak = 800 × 0.369 = 295.2 kVAR

Step 3: Select Standard Size

  • Need to correct at peak: 295.2 kVAR
  • Standard size: 300 kVAR (or 250 + 50 kVAR combination)

Step 4: Select Type

  • Variable load → Automatic capacitor bank

Step 5: Select Steps

  • Recommended steps: 50, 50, 50, 50, 50, 50 kVAR (6 steps, total 300 kVAR)
  • Or: 75, 75, 75, 75 kVAR (4 steps, total 300 kVAR)

Step 6: Select Location

  • Medium facility, some distribution → Main service (centralized)

Result: Install 300 kVAR automatic capacitor bank (6 steps of 50 kVAR each) at main service.

Example 3: Large Data Center #

Scenario:

  • Facility: Large data center
  • Load: 2000 kW (relatively constant, ±10%)
  • Current PF: 0.88
  • Target PF: 0.95
  • Multiple UPS systems and cooling equipment

Step 1: Calculate Required kVAR

tan(arccos(0.88)) = 0.540
tan(arccos(0.95)) = 0.329
kVAR = 2000 × (0.540 - 0.329) = 2000 × 0.211 = 422 kVAR

Step 2: Select Standard Size

  • Calculated: 422 kVAR
  • Standard size: 400 kVAR (or 500 kVAR if margin desired)
  • Select: 400 kVAR (adequate, avoids overcorrection)

Step 3: Select Type

  • Relatively constant load → Fixed capacitor bank (or automatic with few steps)

Step 4: Select Location

  • Large facility, multiple load centers → Distributed (at main service and key load centers)
  • Option: 200 kVAR at main service, 100 kVAR at each of two load centers

Result: Install 400 kVAR fixed capacitor bank, distributed: 200 kVAR at main service, 100 kVAR at each of two primary load centers.

Example 4: Facility with Large Motors #

Scenario:

  • Facility: Manufacturing plant
  • Total load: 1000 kW
  • Large motors: 3 × 100 HP motors (75 kW each = 225 kW total)
  • Motor PF: 0.75 (when loaded)
  • Facility PF: 0.80 (including other loads)
  • Target PF: 0.95

Strategy: Load-Specific Correction

Step 1: Calculate Motor Correction

Per motor: 75 kW at 0.75 PF
tan(arccos(0.75)) = 0.882
tan(arccos(0.95)) = 0.329
kVAR per motor = 75 × (0.882 - 0.329) = 41.5 kVAR
Select: 40 kVAR per motor (standard size)

Step 2: Calculate Remaining Load Correction

Remaining load: 1000 - 225 = 775 kW
Assume remaining load PF improves to 0.85 after motor correction
Facility-wide still needs improvement
Calculate total facility correction needed

Step 3: Combined Strategy

  • Install 40 kVAR fixed capacitor at each of 3 motors (120 kVAR total)
  • Install 150 kVAR automatic bank at main service for remaining correction
  • Total: 270 kVAR

Result: Install 40 kVAR fixed capacitor at each large motor, plus 150 kVAR automatic bank at main service.

Harmonic Considerations #

When sizing capacitors, you must consider harmonic distortion in the electrical system. Harmonics can cause capacitor resonance, leading to equipment damage and power quality issues.

Detuned Capacitor Banks #

When to Use:

  • Total Harmonic Distortion (THD) > 5%
  • Significant VFDs, variable speed drives, or electronic loads
  • Measured harmonic content at 5th, 7th, 11th, 13th harmonics

How They Work:

  • Series reactor (inductor) with capacitor forms a tuned filter
  • Tuned to avoid resonance at common harmonic frequencies
  • Typically detuned to 189 Hz or 210 Hz (avoiding 5th and 7th harmonics at 250 Hz and 350 Hz)

Sizing Consideration:

  • Detuned capacitors have slightly different kVAR ratings
  • Specify detuning frequency when ordering
  • Cost is 20-30% higher than standard capacitors

Standard Capacitor Banks #

When to Use:

  • THD < 5%
  • Primarily linear loads (motors, heaters, lighting)
  • Minimal electronic loads

Standard capacitors are sufficient for most industrial applications with primarily motor loads.

For resonance theory, THD thresholds, and when to choose detuned vs standard capacitors, see Harmonics in Power Factor Correction.

Common Sizing Errors and How to Avoid Them #

Error 1: Using Average Load Instead of Peak Load #

The Mistake: Calculating capacitor size based on average load, then finding insufficient correction at peak demand.

Example:

  • Average load: 400 kW at 0.80 PF → Calculates 168 kVAR needed
  • Peak load: 600 kW at 0.80 PF → Actually needs 252 kVAR
  • Result: Undercorrection at peak, penalties still apply

The Correct Approach: Always size capacitors based on peak demand load, not average load. This ensures adequate correction at all times.

Error 2: Ignoring Load Variation #

The Mistake: Installing fixed capacitors for highly variable loads, causing overcorrection during light loads.

Example:

  • Peak load: 800 kW → Installs 300 kVAR fixed capacitors
  • Light load: 200 kW → Capacitors cause leading PF (overcorrection)
  • Result: Voltage rise, potential utility penalties for leading PF

The Correct Approach: For loads with >20% variation, use automatic capacitor banks that adjust to load changes.

Error 3: Forgetting the √3 Factor in Measurements #

The Mistake: Using single-phase power factor measurement formulas for three-phase systems, leading to incorrect initial PF values.

The Correct Approach: Always use three-phase formulas: PF = kW ÷ (V × I × √3) for three-phase systems.

Error 4: Not Accounting for Future Load Growth #

The Mistake: Sizing capacitors for current load only, then needing to add more capacitors when facility expands.

The Correct Approach: Consider planned load growth (typically 10-20% margin) or design for easy expansion (automatic banks with room for additional steps).

Error 5: Incorrect Installation Location #

The Mistake: Installing all capacitors at main service for a large facility with distributed loads, missing opportunity to reduce feeder losses.

The Correct Approach: For large facilities (>1000 kW) with distributed loads, consider distributed capacitor banks at load centers to reduce feeder currents and losses.

For more detailed information on common power factor correction mistakes, see our guide on Power Factor Correction: Common Mistakes.

Verification and Testing #

After capacitor installation, verify that correction is working correctly:

Measurement Verification #

Procedure:

  1. Measure power factor before and after installation
  2. Verify PF is at or above target (typically 0.95)
  3. Check for overcorrection (leading PF) at light loads
  4. Measure voltage to ensure no excessive voltage rise

Acceptable Results:

  • Power factor: 0.95-0.98 (lagging)
  • Voltage rise: < 3% of nominal voltage
  • No leading power factor at any load condition

Ongoing Monitoring #

Recommended:

  • Monthly review of utility bills for power factor penalties
  • Quarterly power factor measurements
  • Annual comprehensive power quality audit
  • Monitor capacitor bank operation (automatic banks)

Frequently Asked Questions #

Q1: Can I install more capacitors than calculated to be safe? #

A: Generally, no. Oversizing capacitors can cause:

  • Leading power factor (overcorrection)
  • Voltage rise (can damage equipment)
  • Utility penalties for leading PF
  • Wasted capital investment

Size capacitors accurately based on calculations. If you want margin, target 0.96-0.97 PF instead of 0.95, but don't significantly oversize.

Q2: How do I size capacitors for multiple loads with different power factors? #

A: Calculate correction for the total facility load using weighted average power factor, not individual loads. Alternatively, install capacitors at individual loads if load-specific correction is desired.

Q3: What's the difference between delta and wye-connected capacitors? #

A:

  • Delta (Δ): Capacitors rated at line voltage, typically used for 3-phase, 3-wire systems
  • Wye (Y): Capacitors rated at phase voltage, used for 3-phase, 4-wire systems with neutral

The total kVAR is the same for both connections when properly sized.

Q4: Can I add capacitors to an existing installation? #

A: Yes, but consider:

  • Total correction (avoid overcorrection)
  • Coordination with existing capacitor bank controls
  • Available space and installation location
  • For automatic banks, ensure controller can handle additional steps

Q5: What happens if I install capacitors but don't need them? #

A: You'll have leading power factor (overcorrection), which can:

  • Cause voltage rise
  • Result in utility penalties (some utilities penalize leading PF)
  • Waste capital investment
  • Potentially damage equipment

Always measure and calculate before installing capacitors.

Engineer's Practical Insight #

From 13+ years of power systems design and power factor correction experience: The most common mistake I see is engineers sizing capacitors based on average load instead of peak demand. I've reviewed dozens of projects where someone calculated capacitor size for 400 kW average load, but the facility peaks at 800 kW. The result is undercorrection at peak hours—exactly when penalties are calculated—so the facility still pays penalties despite having capacitors installed. Always size for peak demand, not average. I use the highest 15-minute demand from the utility bill or power quality meter data, not the monthly average.

Critical field observation: Load variation is often ignored in capacitor sizing. A facility might have 500 kW peak load but only 200 kW during nights and weekends. Installing 200 kVAR fixed capacitors sized for peak load will cause severe overcorrection (leading PF) during light loads. I've seen facilities with 0.98 leading power factor during off-hours, causing voltage rise and potential equipment damage. For any facility with >20% load variation, I always recommend automatic capacitor banks, even if the initial cost is higher. The long-term benefits far outweigh the cost difference.

Practical sizing strategy: I never use the exact calculated kVAR value. Instead, I round up to the next standard size, but then verify the resulting power factor. If rounding up gives me 0.97-0.98 PF, that's perfect—a small margin without overcorrection risk. If it gives me >0.98, I might go with the lower standard size or split the difference. For example, if calculation gives 210 kVAR, standard sizes are 200 kVAR or 225 kVAR. I'll verify both: 200 kVAR might give 0.94 PF (acceptable) or 225 kVAR might give 0.96 PF (ideal). I choose based on the verification, not just the calculation.

Installation location reality: Most engineers default to installing capacitors at the main service because it's simpler, but for large facilities (>1000 kW) with distributed loads, this misses a huge opportunity. I once redesigned a capacitor installation from centralized (main service) to distributed (3 load centers). The facility saved an additional $3,000/year in reduced feeder losses, on top of the penalty savings. The distributed installation cost 15% more initially, but paid back in 8 months from the additional savings. Always evaluate installation location based on facility size and load distribution, not just convenience.

Harmonic consideration reality: Many engineers ignore harmonics until there's a problem. I've seen facilities install standard capacitors in systems with 8-10% THD from VFDs, only to have capacitor failures within 2 years due to harmonic resonance. The cost of replacing failed capacitors plus the downtime far exceeds the 20-30% premium for detuned capacitors. I always measure harmonics before specifying capacitors. If THD > 5% or there are significant VFDs, I specify detuned capacitors from the start. It's cheaper than fixing problems later.

ROI calculation accuracy: When presenting capacitor projects to management, I always include a detailed ROI calculation with multiple scenarios. Base case uses current penalty rates, but I also calculate with 3% and 5% annual rate increases over 10 years. A $20,000 capacitor installation might have a 2-year payback at current rates, but with rate increases, the 10-year savings can exceed $150,000, making it an obvious investment. I also include "soft" benefits like increased system capacity and reduced transformer loading, which can defer expensive equipment upgrades.

If you need to calculate or verify capacitor kVAR for power factor correction, use our PF & kW/kVA Converter.

Industry Resources #

Conclusion #

Properly sizing capacitor banks for power factor correction requires accurate measurement of current power factor, understanding of load characteristics, and selection of appropriate capacitor type and installation location. By following the step-by-step sizing process outlined in this guide—calculating required kVAR, selecting standard sizes, choosing between fixed and automatic banks, and determining optimal installation locations—you can effectively improve power factor, eliminate utility penalties, and optimize electrical system performance. Remember to size based on peak demand (not average), consider load variation when selecting capacitor type, account for harmonics in systems with significant electronic loads, and verify correction after installation. Accurate capacitor sizing ensures optimal ROI and long-term system reliability.

About the Author: Sarah Martinez, P.E. is a licensed electrical engineer with 13+ years of experience in power systems design and energy management. Former utility engineer specializing in power quality, power factor correction, and industrial energy optimization. Has designed power factor correction systems for manufacturing facilities, data centers, and commercial buildings. All content in this guide has been reviewed and validated by licensed engineers.