POWER FACTOR CORRECTION – GATE LEVEL NOTES

 

1. POWER FACTOR (PF) – BASIC DEFINITION

Power factor is the cosine of angle between voltage and current.

$$\text{Power Factor} = \cos \phi$$

Where
$\phi$ = angle between V and I

Range:

$$0 \le PF \le 1$$

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2. POWER TRIANGLE (VERY IMPORTANT)

Relationship:

$$S^2 = P^2 + Q^2$$

Where:

• $P$ = Active Power (kW)
• $Q$ = Reactive Power (kVAR)
• $S$ = Apparent Power (kVA)

$$PF = \frac{P}{S} = \cos \phi$$ $$\tan \phi = \frac{Q}{P}$$

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3. NEED FOR POWER FACTOR CORRECTION

Most loads are inductive:

• Induction motors
• Transformers
• Fans
• Pumps

These consume reactive power → PF becomes low.

Typical PF without correction:

$$0.7 \text{ to } 0.85$$

Desired PF:

$$0.95 \text{ to } 1$$

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4. DISADVANTAGES OF LOW POWER FACTOR

1. Higher current

$$I = \frac{P}{V \cos \phi}$$

Low PF → High current

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2. Higher copper losses

$$Loss = I^2 R$$

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3. Larger conductor size required

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4. Poor voltage regulation

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5. Increased electricity bill (penalty)

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5. POWER FACTOR CORRECTION METHODS

1. Shunt Capacitor (MOST IMPORTANT)

Capacitor supplies leading reactive power.

Cancels inductive reactive power.

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2. Synchronous Condenser

Over-excited synchronous motor.

Supplies reactive power.

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3. Phase Advancer

Used with induction motors.

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6. PRINCIPLE OF POWER FACTOR CORRECTION

Inductive load consumes lagging reactive power.

Capacitor supplies leading reactive power.

Net reactive power reduces → PF improves.

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7. POWER FACTOR CORRECTION FORMULA (VERY IMPORTANT FOR GATE)

Required capacitor reactive power:

$$Q_c = P (\tan \phi_1 - \tan \phi_2)$$

Where:

$Q_c$ = capacitor kVAR
$P$ = active power (kW)
$\phi_1$ = initial angle
$\phi_2$ = final angle

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8. CAPACITOR VALUE CALCULATION

Reactive power supplied by capacitor:

Single phase:

$$Q_c = \frac{V^2}{X_c}$$

Where:

$$X_c = \frac{1}{\omega C}$$

Therefore:

$$Q_c = V^2 \omega C$$

So,

$$C = \frac{Q_c}{\omega V^2}$$

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9. THREE-PHASE SYSTEM FORMULA

Total capacitor kVAR:

$$Q_c = \sqrt{3} V_L I_c$$

OR

$$Q_c = P (\tan \phi_1 - \tan \phi_2)$$

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10. EFFECT OF POWER FACTOR CORRECTION

Before correction:

Current:

$$I_1 = \frac{P}{V \cos \phi_1}$$

After correction:

$$I_2 = \frac{P}{V \cos \phi_2}$$

Since:

$$\cos \phi_2 > \cos \phi_1$$

Therefore:

$$I_2 < I_1$$

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11. ADVANTAGES OF POWER FACTOR CORRECTION

1. Reduced current

2. Reduced losses

3. Improved voltage regulation

4. Increased system capacity

5. Reduced electricity bill

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12. POWER FACTOR IMPROVEMENT GRAPH (CONCEPT)

Before correction:

Large reactive power triangle

After correction:

Smaller reactive power triangle

Active power remains same.

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13. ECONOMIC POWER FACTOR (IMPORTANT THEORY)

Economic PF is when total cost is minimum.

Cost includes:

• Capacitor cost
• Energy loss cost

Typical value:

$$0.95$$

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14. GATE EXAM IMPORTANT FORMULAS (VERY IMPORTANT)

Most important formula:

$$Q_c = P (\tan \phi_1 - \tan \phi_2)$$

Power factor:

$$PF = \frac{P}{S}$$

Reactive power:

$$Q = P \tan \phi$$

Capacitor:

$$Q_c = V^2 \omega C$$

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15. GATE EXAM CONCEPT QUESTIONS

Power factor improvement reduces:

✔ Line current
✔ Losses
✔ Voltage drop

Does NOT change:

✔ Active power

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16. ONE-PAGE REVISION SHEET

Power factor:

$$PF = \cos \phi$$

Correction formula:

$$Q_c = P (\tan \phi_1 - \tan \phi_2)$$

Capacitor supplies leading reactive power.

PF correction reduces:

Current, losses, voltage drop

Does NOT change:

Active power