10. Power Factor Correction

Principle: Power factor (PF) correction is the practice of reducing the reactive power in an AC system to improve the power factor toward unity (1.0). Loads with inductance—such as motors, transformers, and fluorescent lighting ballasts—draw current that lags the voltage, resulting in a PF less than 1. While the real power (kW) does useful work, reactive power (kVAR) causes additional current flow, increasing losses and loading generators and transformers. Correcting PF typically means adding capacitors (which supply leading reactive power), using synchronous condensers, or employing active filters so that the net reactive power drawn from the source is minimized. This not only reduces total current but also improves voltage stability.

Calculation of Required kVAR

To raise PF from an initial value cosφ₁ to a desired cosφ₂, you must supply the difference in reactive power. The fundamental relation is:

Qc = P (tanφ₁ − tanφ₂)

where Qc is the reactive power (in kVAR) of the capacitors needed, and P is the real power (in kW) of the load. (Recall that tanφ = Q/P.)

For example, consider a 100 kW load at 0.75 PF (lagging). Here, cosφ₁ = 0.75, so φ₁ = arccos(0.75) ≈ 41.4°. To correct to 0.95 PF (φ₂ ≈ 18.2°):

  • tanφ₁ = tan(41.4°) ≈ 0.88
  • tanφ₂ = tan(18.2°) ≈ 0.33
  • Thus, Qc = 100 × (0.88 − 0.33) = 55 kVAR.

Approximately 55 kVAR of capacitors would be installed across that load or on the distribution bus to ideally raise the PF to about 0.95.

Step-by-Step Example

A factory has a measured demand of 500 kW at 0.8 PF, and the utility imposes a penalty for PF below 0.9. How much capacitance is needed to achieve 0.9 PF?

  1. Given: P = 500 kW and cosφ₁ = 0.8 so that φ₁ = 36.87° and tanφ₁ ≈ 0.75.
  2. For a desired cosφ₂ = 0.90, φ₂ ≈ 25.84° and tanφ₂ ≈ 0.484.
  3. Calculate Qc = 500 × (0.75 − 0.484) = 500 × 0.266 = 133 kVAR.

Approximately 133 kVAR of capacitors are needed. If standard capacitor units are, say, 50 kVAR each, then installing 3 × 50 = 150 kVAR is common. This slight overshoot may raise the PF a bit above 0.9, which is acceptable (typically up to ~0.95–0.98 is beneficial, while one avoids exactly 1.0 to prevent a leading PF when loads drop).

Check: Originally, the reactive power is Q = 500 × tanφ₁ ≈ 500 × 0.75 = 375 kVAR. With 150 kVAR added, the new reactive power is 375 − 150 = 225 kVAR. The new PF becomes:

PF = 500 / √(500² + 225²) ≈ 0.91 (which is acceptable).

Niche and Less Common Applications

  • Over-correction (leading PF): If PF becomes leading (for instance, at light load with capacitors still connected), it can cause overvoltage or resonance with inductances. To prevent this, many systems use automatic capacitor banks that switch off steps when load reduces.
  • Harmonics and PF capacitors: When significant harmonics are present, capacitors in conjunction with system inductance may form resonant circuits. This is mitigated by adding series reactors (detuned filters) to the capacitors or by using active harmonic filters that also provide PF correction. In such cases, calculations include tuning frequency and ensuring that the capacitor does not resonate at a major harmonic (such as the 5th or 7th).
  • Synchronous condensers: In specialized applications, a synchronous motor operating with no load can be over-excited to provide reactive power. Although the calculation of its excitation and resulting kVAR is more complex, it essentially meets the Qc demand.
  • DC systems: Since PF is an AC concept, DC systems do not have PF; however, converters must be designed with good input PF (using power factor correction circuits).
  • High voltage transmission: PF correction in high voltage networks is achieved using shunt capacitors or reactors at substations. These devices are sized based on system studies that calculate MVAR needs to control voltage (adding capacitors raises local voltage; adding reactors lowers it).

Industry Relevance

Poor power factor results in higher currents for the same amount of useful power, which causes:

  • Increased losses (I²R losses in cables and transformers).
  • The need for larger capacity generators and UPS systems.
  • Voltage drop issues (since voltage drop = I × R).
  • Utility penalties: Many utilities impose additional fees if PF is below 0.9 or 0.95, or they may bill based on kVA demand instead of kW.

Companies invest in capacitor banks to mitigate these issues, and the return on investment can be calculated by comparing the cost of the capacitors with the annual savings on utility bills.

Standards

  • IEEE 141 (Red Book) and IEEE 1036: Provide guidance on the application of shunt capacitors, including connection methods and resonance avoidance.
  • IEC 60831 (Part 1 & 2): Covers low-voltage power capacitors for PF correction, specifying ratings, tolerances, and safety requirements.
  • BS 7671: Although it does not mandate PF correction, Appendix 5 mentions typical load PF values and Appendix 17 (18th Ed.) encourages PF improvement while ensuring capacitor banks do not cause overvoltage or resonance.
  • Grid Codes: Many utility regulations require customers to maintain a PF within a specified range at the point of common coupling (e.g., “PF between 0.95 lag and 0.98 lead for loads above 50 kW”), thereby necessitating PF correction.

Software Tools

  • Load flow analysis: Tools like ETAP or PowerFactory can calculate the baseline PF and automatically size capacitors by setting a target PF at the main bus.
  • Harmonic analysis software: Programs (such as ETAP or SKM) can simulate the effect of adding capacitors on harmonic distortion and suggest detuning reactor sizes if necessary.
  • Utility bill analyzers: Some software or Excel spreadsheets analyze interval data (e.g., 15-minute readings of kW and kVAR) to determine the required capacitor bank size based on peak kVA reduction.
  • Automatic capacitor bank controllers: These devices measure PF in real time and switch capacitor steps on or off to maintain the target PF dynamically.
  • Manual calculations and tables: Quick reference tables—such as “kVAR per 100 kW needed to raise PF from X to Y”—can be used in conjunction with the formula Qc = P (tanφ₁ − tanφ₂) (taking care with degree/radian conversion).

In summary, power factor correction calculations revolve around balancing reactive power. By supplying the required Qc locally through capacitors (or other devices), the system reduces the reactive demand on the source. This not only improves efficiency and voltage stability but also helps avoid unnecessary capacity burdens on the infrastructure.