In an AC system, the power factor is a very important parameter that defines how efficiently the electrical energy is used by the load. It is a rational number between -1 and 1, but has no unit. The power factor of a system depends on the type of load present, whether resistive, inductive or capacitive. The inductive and capacitive load has a negative effect on the p.f. out of. from the system. A bad p.f will lead to an increase in the current drawn by the load.

Table of contents

- Definition of power factor
- Active power (kW)
- Reactive power (kW)
- Apparent Power (kVA)
- unit power factor
- Leading power factor
- Lagging Power Factor

- Calculation of the power factor
- Why is power factor improvement important?
- Power factor correction techniques
- Calculation of the power factor correction
- Importance/ importance of the power factor.
- Causes of low p.f
- Disadvantages of poor power factor

## Definition of power factor

**Power factor can be defined as the ratio of real power (real power) to apparent power.**It can also be defined as the absolute value of the cosine of the phase shift between voltage and current in an AC circuit. It is characterized by the**Greek alphabet λ (lambda).**

**Power factor (λ)**= active power/apparent power

= VI.COS φ/ VI

= COS f

“V” are voltages in volts

"I" is current in amperes

"Φ" is the phase angle between voltage and current

### Active power (kW)

It is the**true power**transferred to the load for energy conversion. For example, a motor takes the true power from the circuit and converts it into mechanical power, while lamps, on the other hand, convert the same into light. It is represented by the letter P.

### Reactive power (kW)

Reactive power is the power needed to create the magnetic field in motors and transformers and directly affects the power factor. It is represented by the letter Q.

### Apparent Power (kVA)

**apparent power**is the product of voltage and current drawn by a load regardless of its phase angle. It is the combination of active and reactive power. It is represented by the letter S.

**Continue reading:**Active, reactive, complex and apparent power

### unit power factor

**unit power factor**is considered as a perfect scenario where apparent power and real power should be in phase. If the load is purely resistive, the current flow to the load is linear and therefore the phase shift between voltage and current is zero and cos Φ is one.

If the power factor cos φ=1, this means that there is no reactive power flow and the phase angle between voltage and current is zero.

### Leading power factor

The P.F is considered leading when the apparent power leads the real power (active power), (i.e.) the current leads the voltage. Capacitive loads cause the current to lead the voltage, i.e. the power factor.

### Lagging Power Factor

The PF is considered to be leading when the apparent power lags the real power (active power), (i.e.) the current lags the voltage. Inductive loads cause the current to lag the voltage, so the p.f.

## Calculation of the power factor

From the power triangle:**Power factor = real power/apparent power**

Also,

Also,

## Why is power factor improvement important?

**Improvement in power factor**aims at optimal use of electrical energy, reducing electricity bills and reducing energy loss.

- Power transformers are independent of P.F. When the power factor is close to unity, more load can be connected with the same transformer KVA rating. (Better the power factor will be lower the current flow).
- Penalties imposed by utility companies for non-compliance with the optimal p.f. can be avoided.
- Optimal sizing of power cables is possible when the power factor. Low power factor leads to higher copper losses (I
^{2}R) Loss should also drop more voltage across the cable.

## Power factor correction techniques

Most power loads are inductive, causing the current to lag the voltage. To overcome these few**Power Factor Correction Techniques**adjusted, which helps to neutralize this lagging current. The most common P.F. Correction technique is the use of static capacitors in parallel with the load. Static capacitors provide leading current to the system and reduce delay. Capacitor banks are connected in parallel with inductive loads. These capacitors are switched as needed via a contactor. Static VAR expansion joints are also used for p.f. used. Correction. These are power electronic versions of reactive power compensators and use thyristors to switch capacitors instead of contactors.

Other power factor correction techniques include connecting synchronous compensators in parallel with the load. They are synchronous motors that run with no load. When a synchronous motor is overexcited and idling, it acts as a capacitor and supplies reactive power to the grid.**synchronous compensators**are connected in parallel with the load.

## Calculation of the power factor correction

Suitable**Power Factor Corrective Action**must be taken to meet the required power factor of the system. Most often, capacitor bank engineers choose p.f. Correction. So the capacitor for p.f. needed. Correction is determined:

We can measure the supply voltage with a voltmeter and the load current draw with an ammeter. From this data we can calculate the actual power factor, apparent power and reactive power consumed by the load using the following formulas.

Apparent power = V x I (measured with ammeter and voltmeter)

Actual Power Factor = Load KW (Real Power) / Apparent Power

**From the power triangle:**

Blind power (kVAR) =**Sq.rt**((Apparent Power-kVA)^{2}– (Real Power-kW)^{2})

And,

From the above equation

Calculating the size of the capacitor used to achieve unity power factor can be calculated as follows:

Therewith,

Wo,

C is the capacitance value in farads

F is the supply frequency

Xc is the capacitive reactance.

## Importance/ importance of the power factor.

Active power (active power) is expressed as:

**P= VI.Cos Φ**

For a given load, P should always be constant and the voltage V supplied by the source should also be constant. The parameters I and Cos Φ are interdependent. For example, if the value of Cos Φ is one, then the current drained from the source by the load must be:

And if the p.f. Cos Φ is less than one, say "0.8" then the current drained from the source by the load must be:

From expressions 1 and 2 it follows that the current when transmitting the same power P at a lower p.f. has increased significantly.**Therefore, for a constant load at a constant voltage, the current drawn from the source is inversely proportional to the power factor.**

An increase in current directly affects the cost of generating electricity, and also increases transmission losses. The conductor used in devices is designed to pass a certain amount of current. If the power factor of the supply is poor, more current can flow to the device and either damage the device or shorten its life expectancy.

Utilities impose huge penalties on commercial consumers who have a p.f. below a certain level. Therefore, it is very important to keep p.f at a certain value for effective use of power.

## Causes of low p.f

The main cause of the low power factor is the highly inductive industrial load connected to the system. When we talk about inductive industrial load, induction motors make the biggest contribution. Most of these motors operate with a small lag p.f. When operating at light loads, it operates at a power factor of 0.1-0.4, rising to 0.8-0.9 at full load. Aside from induction motors, induction heating furnaces and arc lamps also have very poor p.f.

## Disadvantages of poor power factor

- Since kVA is inversely proportional to p.f. is, i.e. smaller the p.f. of the load, the kVA rating of the transformers, generators and switchgear used is higher.
- At a fixed kW, the cables carry more current when the p.f. is low. Therefore, this increases the size of the cables to be used.
- The higher the current flow, the higher the copper losses.
- Large currents at low p.f. Operation leads to poor voltage regulation in transformers, generators and transmission lines (due to internal copper losses).

#### references

- Ewald Fuchs; Mohammad A. S. Masoum (14. Juli 2015).
*Power quality in energy systems and electrical machines* *Calculation and correction of the power factor*, US