Power Factor

Power factor is a key electrical term that measures how efficiently electrical power is used in a system. It is the ratio of real power (used to do work) to apparent power (total power supplied). A high power factor indicates efficient energy usage, while a low power factor means wasted energy. Improving the power factor reduces electricity costs, enhances equipment performance, and minimizes power losses—making it crucial for both industrial and commercial energy management.

1.0Definition of Power Factor

• The power factor is defined as the cosine of the phase angle between voltage and current in an AC circuit.
• In an alternating current (AC) circuit, there is usually a phase difference, denoted by ϕ, between the voltage and current. The expression cos ϕ represents the power factor of the circuit. In inductive circuits, the current lags behind the voltage, which affects the value of the power factor accordingly.
• In inductive circuits, current lags behind voltage; in capacitive circuits, current leads the voltage.
• The power factor (p.f.) is the cosine of the phase angle (ϕ) between voltage (V) and current (I):

$\text{Power factor}=\cos \varphi$

Phasor Representation

Current (I)is resolved into two components:

• $I\cos \varphi –inphasewithvoltage(activeorrealcomponent)$
• $I\sin \varphi –90^{\circ }outofphasewithvoltage(reactiveorwattlesscomponent)$

Note:

• A small reactive component (I sin ϕ)⇒ smaller angle ϕ⇒ higher power factor
• A large reactive component ⇒ lower power factor
• Power factor cannot exceed 1.
• When current lags voltage, it’s called a lagging power factor.
• When current leads voltage, it’s called a leading power factor.

2.0Power Triangle                

By multiplying each side of the current triangle OAB  by voltage V , the power triangle OAB is formed.

Components of Power Triangle

OA = VI cos ϕ represents the active power(in watts or kW)

AB = VI sin ϕ represents reactive power(in VAR or kVAR)

OB = VI represents apparent power (in VA or kVA)

Apparent Power has two components-Active Power and Reactive Power which are perpendicular.

$O{B}^2=O{A}^2+A{B}^2$

$(\text{apparent power}{)}^2=(\text{active power}{)}^2+(\text{reactive power}{)}^2$

${\text{kVA}}^2={\text{kW}}^2+{\text{kVAR}}^2$

Power Factor cos ϕ is the ratio of active power to apparent power

$\cos \varphi =\frac{OA}{OB}=\frac{\text{active power}}{\text{apparent power}}=\frac{\text{kW}}{\text{kVA}}$

• Lagging reactive power causes low power factor.
• From the power triangle ,smaller reactive power means higher power factor.
• Relationship between reactive power and power factor

$\text{kVAR}=\text{kVA}\sin \varphi =\text{kW}\frac{\sin \varphi }{\cos \varphi }$

$\text{kVAR}=\text{kW}\tan \varphi$

• If current lags voltage, reactive power is lagging reactive power.
• If current leads voltage, reactive power is leading reactive power.

3.0Limitation of Low Power Factor

The power consumed in an AC circuit depends on the power factor.

For Single Phase Supply

$P=V_L{I}_L\cos \varphi$

$I_L=\frac{P}{V_L\cos \varphi }$

For Three Phase Supply

$P=\sqrt{3}{V}_L{I}_L\cos \varphi$

$I_L=\frac{P}{\sqrt{3}{V}_L\cos \varphi }$

Note: For a fixed power and voltage, load current increases as power factor decreases, and decreases as power factor increases.
Here’s a modified, shortened, and rephrased version of the content in point form for clarity and quick understanding:

4.0Effects of Low Power Factor

1.Higher Equipment Rating (kVA): Low power factor increases the kVA rating of machines like transformers and alternators, making them larger and more expensive.

2.Bigger Conductor Size: More current is needed at low power factor, requiring thicker cables and increasing installation costs.

3.Increased Copper Losses: Higher current leads to greater $I^{2}R$ losses, reducing system efficiency and generating excess heat.

4.Poor Voltage Regulation:Greater current causes voltage drops across the network, affecting equipment performance and requiring voltage correction devices.

5.Lower System Capacity: Reactive power takes up part of the system’s capacity, limiting the amount of usable real power and reducing overall system efficiency.

5.0Key Contributors to Low Power Factor

1. Induction Motors
   Most AC motors (single-phase and three-phase) are induction type, which operate at low power factor—especially under light load (0.2-0.3), improving only slightly at full load (0.8-0.9).
2. Discharge-Type Loads
   Devices like arc lamps, electric discharge lamps, and industrial furnaces draw lagging reactive power, resulting in low power factor.
3. Fluctuating Load on Power System
   During low demand periods (like midday or late night), voltage rises, increasing magnetizing current in transformers and motors—this lowers the overall power factor.

6.0Power Factor Optimization

• Most electrical loads are inductive in nature (like motors), which draw lagging current, leading to a low power factor.
• To improve power factor, a device that draws leading current should be connected in parallel with the load.
•  Capacitors are commonly used for power factor correction as they supply leading reactive power.
• The capacitor offsets or neutralizes the lagging reactive power from the load, thereby improving the overall power factor.

7.0Techniques of Power Factor Optimization

• In large generating stations, the power factor usually ranges between 0.8 to 0.9.
• Sometimes, the power factor may drop further and needs to be improved.
• Improving the power factor helps in reducing losses and improving system efficiency.

The following equipment is commonly used for power factor Optimization

1. Static Capacitors:Provide leading reactive power to offset lagging currents.
2. Synchronous Condensers:Overexcited synchronous motors running without load, used to supply reactive power.
3. Phase Advancers:Used with induction motors to improve their power factor by supplying excitation current.