# An introduction to capacitor based PFC circuits

**Introduction**

Some of the AC power consumed by inductive loads is used to maintain magnetic reversals due to phase shift between current and voltage. This energy can be considered as wasted energy since it is not used in performing useful work. Power factor correction circuits are used to minimize reactive power and enhance the efficiency with which inductive loads consume AC power. Capacitors are essential components in power factor compensation circuits, and this article will explore some design considerations when using these components for power factor correction.

**Reactive power in inductive loads**

Inductive loads such as chokes, motors, inductive heating equipment, generators, transformers, and arc welding equipment produce an electrical lag that is commonly referred to as inductance. This inductance causes a phase difference between current and voltage. **Figure 1** shows current and voltage waveforms for a load with zero lag (purely resistive load).

As a result of phase shift due to inductance, there are times when current and voltage have different signs. During such times, negative energy is generated and fed back into the power supply network. When the two regain same sign, a similar amount of energy is required to generate the magnetic fields. The energy that is lost due to magnetic reversals in inductive loads is commonly referred to as reactive power.

Inductive AC loads are broadly classified into linear and non-linear devices. For linear loads, the current waveform and voltage waveform have matching sinusoidal profiles. **Figure 2** shows current and voltage waveforms for a typical linear load. On the other hand, since non-linear loads draw current at different frequencies, the current and voltage waveforms are different. For most non-linear loads, the current waveform is usually non-sinusoidal. **Figure 3** shows current and voltage waveforms for a non-linear load.

Some examples of linear electrical loads include heating equipment, motors, and incandescent lighting devices. Non-linear devices include variable frequency drives, DC drives, programmable controllers, arc-type lighting devices, induction furnaces, uninterruptible power supplies, and personal computers. Non-linear electrical loads are known to be a major cause of harmonic distortions in power distribution systems.

**Power factor**

The efficiency with which electrical devices or installations consume AC power varies. Some loads utilize power efficiently, while others waste a significant portion of the power that they consume. Power factor is used to describe the efficiency with which loads consume AC power. This dimensionless quantity ranges between 0 and 1.

As shown in **Figure 4** and **Figure 5**, the total AC power, also commonly known as apparent power, consumed by an electrical device or equipment depends on two components: useful power (active power) and reactive power. The useful power refers to the power that a device needs to accomplish a task. On the other hand, reactive power does not produce useful work. The useful power is usually measured in kW while the reactive power is measured in kVAR.

As shown in **Equation 1**, the power factor is equal to the ratio of active power (useful power) to total power (apparent power) drawn by an electrical device or equipment. It can be shown mathematically that the power factor is equal to the cosine of angle θ (**Equation 2**). The closer this ratio is to 1.0, the higher is the efficiency of the device or equipment.

For an ideal electrical load, the power factor is equal to 1.0 (unity power factor). This means that all the power drawn by a load is used to do useful work. However, it is difficult for an actual electrical load to achieve that. The impedance for the load represented by **Figure 5** is given by Equation 3, where XL is the inductive reactance and is given by **Equation 4**.

Why is it difficult for an electrical load to achieve unity power factor? Most electrical loads have inherent reactive properties that make it difficult for them to achieve the ideal power factor. To overcome this limitation, power factor correction circuits are added to a network to compensate for a load’s reactive characteristics.

**Power factor correction (compensation)**

Electrical loads that have a low power factor consume more power that it is needed to perform a task. This can result in a considerable power loss in a network and high transformer losses. Such increases in energy consumption increase the cost of running equipment or installations. Poor power factors also cause a power distribution network to have increased voltage drops. It is common for power suppliers to penalize industries whose power factor is below a specified value.

Electricity suppliers encourage industrial consumers to improve their power factor for various reasons. To start with, improving power factor can help to cut the electricity bill by a significant margin. Secondly, a high power factor helps to minimize efficiency losses in a consumer’s transformers. Thirdly, adding power factor correction system helps to boost the effective capacity of a consumer’s electricity network. Lastly, a high power factor helps to increase the service life of electrical equipment.

A power factor compensation network lessens the power demanded by a load thus improving the overall power factor. The compensation network enables electrical loads to achieve a good power factor, typically between 0.95 and 0.98. A power factor of 0.85 and below is usually considered by utility companies as a poor power factor.

**Capacitor-based power factor correction circuits**

There are various methods of improving the power factor of a load or an installation. One of the commonly used methods involves adding power factor correction capacitors to the network. **Figure 6** shows a simple circuit consisting of an AC source and an inductive load.

How does a capacitor help in improving the power factor? In an AC circuit, magnetic reversal due to phase difference between current and voltage occurs 50 or 60 times per second. A capacitor helps to improve the power factor by relieving the supply line of the reactive power. The capacitor achieves this by storing the magnetic reversal energy.

**Figure 7** shows an inductive load with a power factor correction capacitor. **Figure 8** above illustrates the improvement in power factor when the capacitor is added to the circuit. The impedance for a circuit with a power factor compensation capacitor is given by **Equation 5**, where XC is capacitive reactance and is given by **Equation 6**.

In most industries, a system of capacitors controlled by a power factor correction controller is installed for reactive power compensation. When designing a power factor correction system, it is important to avoid adding excess capacitance to the network. Adding excess capacitance to a circuit can lead to over-correction as illustrated in **Figure 9.**

Semiconductor devices are also widely used for power factor correction. Using semiconductor devices to a circuit to improve power factor is commonly referred to as active compensation. Overexcited synchronous machines are also commonly used to improve the power factor of a network.

**Conclusion**

Inductive loads such as transformers, generators, motors, chokes, and arc welding equipment produce an electrical lag that results in current and voltage having different signs. The energy required to maintain magnetic reversals in inductive loads is referred to as reactive power. Reducing reactive power by improving the power factor of an AC load helps to minimize the overall cost of running inductive loads. Capacitors are commonly used in industries to improve the power factor and minimize energy wastage.