# Power Factor’s Role in Active, Reactive and Apparent Power

## The diverse power terms in electrical generation systems include active, reactive, and apparent power, all of which lead to the introduction of ‘power factor’ effectiveness in an AC circuit.

Active, reactive, and apparent power are among the diverse power terms in electrical power systems, all leading to the introduction of ‘power factor’ effectiveness in AC circuits. AC circuits transfer energy to resistive and reactive loads. In the case of purely resistive loads, the energy is dissipated in the same way direct current dissipates energy in a resistor.

### What Is Power?

Electric power is the rate at which energy is transferred to or from a part of an electric circuit. In an electrical circuit, the power equals the voltage difference across the element times current \(V \times I\). The power is measured in watts \(1W=1J\)/\(s\)

$$Electric~Power = Voltage \times Current$$

$$P = V \times I$$

$$P = I^2 \times R$$

$$P = \frac{V^2}{R}$$

These equations are derived from Ohm’s law, which is \(V = I\times R\) where V = Voltage or potential difference in the circuit, I = current, and R = Resistance in the circuit.

*Figure 1. **Measuring AC is a major component of verifying power generation and dissipation in large loads. Image used courtesy of Canva*

*Figure 1.*

### Instantaneous Power

Instantaneous power means the power at any instant of time or the power at any given moment and can be written as:

$$P (t) = V (t) \times I (t)$$

In a DC circuit, the power required for a voltage V to force a current I through a circuit is equal to V times I. Similarly, if the alternating current is passed through the circuit, the power required at each instant is equal to the value of the voltage at that instant times the current at the same instant. In the practical world, loads combine resistive, inductive, and capacitive elements at the consumer end.

#### There are three types of loads.

1. **Resistive:** where V and I are in phase, and the power is always positive, like braking resistors, heaters, and light bulbs

2. **Inductive:** current lags by voltage like motors, fans, and transformers

3. **Capacitive:** current leads by voltage (few examples of pure capacitive loads)

The phase-angle difference between the current and voltage has an important effect on the power supplied, as the instantaneous voltage corresponding to any particular instantaneous current depends on the angle between them. Therefore, in alternating current circuits, power cannot usually be obtained simply by multiplying the effective voltages and effective amperes, as was done in the case of DC. The effect of the difference in phase angle between the current and voltage on the power must be considered.

### Types of Power

There are three main types of power.

#### 1. Active Power (kW, MW, GW)

#### 2. Reactive Power (kVAR, MVAR)

#### 3. Apparent Power (kVA, MVA)

Figure 2 describes the famous example used to understand the difference between the three power types. The glass filled with beer represents true power, the frothy foam on top is reactive power, and the sum of active and reactive power is apparent power in the system.

*Figure 2. **A famous analogy to describe active, reactive, and apparent power*

*Figure 2.*

### Active or Real Power

Active power is often called real, actual, true, or useful power. In DC circuits, power is simply the voltage across the load times the current flowing through it because, in DC circuits, there is no phase angle between the voltage and current; therefore, there is no power factor in DC circuits. In other words, the voltage and current are in phase with each other, meaning the voltage and current start at the same time, reach a peak, and then again touch zero at the same time.

$$P = V \times I~for~DC~circuits$$

AC circuits have a phase angle between voltage and current expressed with the added component of \(cos \theta\).

In a single-phase AC circuit, active power is:

$$P=V \times I\times cos\theta$$

In a 3-phase AC circuit:

$$P = \sqrt{3} \times V \times I\times cos\theta$$

In Figure 3, the current and voltage are in phase, making a +90-degree angle simultaneously. The positive voltage times positive current generates positive power. When both current and voltage are negative, the power is still positive; therefore, in both cases, the power is always positive, called active power. The power curve will lie entirely above the horizontal axis and reflect that all work done is positive.

*Figure 3. **Current and voltage are in phase with each other*

*Figure 3.*

The real power (also called useful power or watt-full power) does the real work in the circuit and always flows from source to load or is supplied to the load from the generator all of the time, as in Figure 4.

*Figure 4. **Active power flows from source to load*

*Figure 4.*

#### Features of Active Power

- Always positive and does not change its direction, always flows from source to load
- Denoted by P and measured in watts (kW, MW, GW)
- Measured using a wattmeter
- Produces heat, mechanical power, and light

### Reactive Power

Reactive power occurs in AC circuits when voltage and current are not in phase. Its unit is VAR (voltage ampere reactive). In the real world, loads are a combination of resistive, inductive, and capacitive elements, and it is impossible to determine the nature of the load (small/large, domestic/industrial inductive/capacitive).

There are two types of reactance:

- Capacitive (negative)
- Inductive (positive)

The power can be positive and negative. When the power flows from source to load, it’s positive, and the power flows from load to source, it’s called negative power. In general, reactive power is only defined for AC circuits and continuously bounces back and forth between source and load. It is symbolized by the letter Q in Figure 5.

*Figure 5. **Reactive power flows from source to load and back to the source*

*Figure 5.*

Reactive Power (Q)

$$Q = V \times I \times sin\theta$$

#### Features of Reactive Power

- It changes its direction periodically, and it is positive and as well as negative
- Donated by letter “Q” and measured in VAR, kVAR, MVAR
- Measured using a VAR meter
- Transformers and induction motors use reactive power to produce a magnetic field

Transformers also need reactive power to generate a magnetic field in the primary coil and induce a voltage in the secondary coil. Therefore, if the reactive power supply is inadequate, the transformer will not transform voltages, and the motor will not rotate. The synchronous alternators also generate or absorb reactive power depending upon DC excitation to its field winding. When the generator is over-excited, it generates reactive power and absorbs reactive power when the generator is under-excited.

### Apparent Power

Apparent power combines active and reactive power and is expressed in volt-ampere or kilovolt-amperes (kVA). Most of the loads in daily life (electric fan, electric iron, induction motor) are a combination of resistive and inductive loads. The resistive load consumes active power, the inductive load consumes reactive power, and the total power delivered by the source is the combination of active and reactive power (apparent power).

Apparent Power (S):

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

Where S = Apparent Power measured in kVA, Q = Reactive Power in kVAR and P = Active Power in kW

#### Features of Apparent Power

- Sum of active and reactive power
- Denoted by letter “S”
- Measured in VA, kVA, and MVA

### Power Triangle

The relationship between powers can be represented in vectors called the “Power Triangle.” The active power is represented as horizontal, whereas reactive power is shown as a vertical vector. The apparent power connects the active and reactive vectors. If the angle “θ” between active and apparent power increases, reactive power increases.

*Figure 6. **The power triangle describes the relationship between active, reactive, and apparent power.*

*Figure 6.*

### Power Factor

Power factor is an important concept in an electrical system. A good power factor determines the design quality and effective supply use in the electrical system. It shows the relation of the real power to the apparent power and is simply the ratio of active (real) power in watts to apparent power in volt-amperes.

$$Power~Factor = \frac{Active~Power}{Apparent~Power}$$

A power factor of 1.0 is called a “unity power factor” or 100 percent power factor, which means the current and voltage are “in phase.” However, a 100% power factor is impossible to obtain at all power system parts. In transmission lines, high power factor is necessary to reduce transmission losses and is also better for an inductive load-like motor to run efficiently and avoid overheating.

The question is: What does the power factor indicate? Suppose the power factor is 0.8. This means that, out of 100%, the system is consuming 80% active power and 20% reactive power. This is the significance of the power factor, indicating the total amount of active power in the system. The power factor is an important term in an AC power system if the voltage and power of the system are constant then the power factor is inversely proportional.

$$Line~Current \propto \frac{1}{Power~Factor}$$

The expression of three-phase power is written as:

$$P = \sqrt{3} \times V \times I \times cos\theta$$

Therefore,

$$I = \frac{P}{\sqrt{3} \times V \times cos\theta}$$

Here the factors \(P\), \(\sqrt{3}\), and \(V\) are constants, therefore current is inversely proportional to \(cos \theta\) i.e. \(I \propto 1\) / \(cos \theta\). If the system’s power factor is low, the system’s current becomes large.

### Disadvantages of Low Power Factor

- The system’s current is large if the system power factor is lower.
- Large KVA rating of the equipment: alternators, transformers, and switchgear are rated in KVA as we know that \(KVA=KW\)/\(cos \theta\), so if you need power in KW from the machine, the KVA of the machine needs to be higher. Therefore, to increase the machine’s current carrying capacity, the machine’s cross-section conducting parts must be made larger, making the machine larger, heavier, and more expensive.
- Greater conductor size: At a low power factor, transmitting the same quantity of power requires a larger cross-section of the conductor. This is because more current is required to fulfill the consumer’s useful power demand at low power factor conditions.
- Large copper losses: As we already know, that current is inversely proportional to the power factor; therefore, if the power factor of the power system is low, the current will increase. \(I \propto 1\)/\(PF\). The line losses increased by \(I^2 \times R\), resulting in lower system efficiency.
- Low lagging power factor causes a high voltage drop in alternators and transformers.

### Lagging vs. Leading Power Factor

In the power network system, reactive power can be increased and decreased using system excitation. If excitation increases, flux increases, and reactive power will increase. When reactive power increases, power factor lags (decreases). The lagging load consumes reactive power, and the generator supplies reactive power.

*Figure 7. **Visualization of ‘leading’ power factor.*

*Figure 7.*

When the voltage decreases, excitation decreases, which means flux decreases. Consequently, reactive power decreases, and power factor leads (increases). The generator consumes reactive power from the load. This reactive power is used to build the magnetic field required by the generator to work properly. So, over-excited synchronized machines act as capacitors, and under-excited synchronized machines act as inductors. The power factor is lagging when the current lags the supply voltage and leading when the current leads the supply voltage.

### Power Factor Effect on a System

Active power is useful power that does some real work in an AC circuit, whereas reactive power is non-useful power that flows back and forth (in both directions from source to load) but produces electric or magnetic flux. Apparent power is total power in the system and is a combination of active and reactive power measured in kVAR. Large industrial types of equipment like transformers are mentioned in KVA. The lower the power factor, the larger the size of the source to generate that power, resulting in an increasing cost to generate and transmit electrical energy.

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