# Reactive Power | Formula and Calculation of Reactive Power

In this article we will get the concept of Reactive Power and will also discuss about the necessity of Reactive Power. The term “Reactive Power” is generally used in alternating current (AC) system, and the unit is VAR which is an abbreviation of the word “Volt Ampere Reactive”. In modern days, the entire power system is changed totally and AC is used in almost all power grids. In India the operating frequency is 50 Hz, which means the voltage alternates along the sinusoidal curve 50 times per second, and the current changes its direction accordingly. But power means the rate of flow of electrical energy through a certain point or area. So we have to take an average value of the alternating voltage and alternating current for measuring the average power.

There are two types of electrical power, namely real power and reactive power, and the summation of them it called the apparent power. The reactive power or watt less power is that component of power which is fed from load to source and oscillating in between the source and load due to the presence of capacitive or inductive elements in a circuit. Although the amount of energy transferred in one direction is just equal to the amount of energy transferred in another direction. So it is easy to tell that the reactive power is neither generated by the source nor consumed by the load, which means it satisfies the conservation of energy laws. In some other words, the portion of power which is confined into the inductive or capacitive elements in the form of electric or magnetic field, and fed to the source, is called as reactive power. This is the simplest definition of the reactive power, and the details study and conceptual aspects are elaborated as follows.

## What is Reactive Power?

Suppose you have an alternating current source and a pure resistor. If you analyze the sinusoidal voltage current waveform (with respect to time) of the pure resistor, then you will found that there is no phase difference in between the alternating voltage and current. They moves equally along with the sinusoidal path, and for each and every cycle they complete both positive and negative half at the same time. We know that power is the product of voltage and current. In this case the product of voltage and current that is the power is positive at any instant of time. Because the voltage and current both will be either in positive half (+ + = +) or in negative half (- – = +) at any instant of time. Therefore in pure resistive circuits the power flow will be always positive, that means the energy will always flow from source to load and will consumed by the resistive load. This power is termed as the Real Power. In fact the electricity bills and tariffs are constructed on the basis of “how much real power you have consumed over a certain time period”.

But the scenario is changed slightly when dealing with the capacitors or inductors. When you will apply an AC source across a capacitor or inductor and study the voltage current waveform, then you will definitely found that there is a phase difference in voltage and current. Although they moves along with a definite sinusoidal curve to complete a cycle, but there will be a certain time interval in between them. In fact in a pure reactive network the phase difference is 90 °. Therefore the product of voltage and current will be positive for a half and negative for another half, which means that the transferred net energy through the area will be null. This product of voltage and current that is the power is termed as reactive power and it is transferred from source to load and returns from load to source. In this way it oscillates in between the source and load. The real power is utilized properly and this power acts like the active power which is mainly consumed by the loads.

## Reactive Power in Load Circuits

In practical world, all loads are not purely resistive; in fact they are a combination of resistive and reactive part. Consider a winding or coil of a power transformer, which is subjected to a three phase 50 Hz AC supply. As the winding is made up with copper wires so there will be a resistive part and as it forms a coil like structure so there will also an inductive part. Therefore it will draw a considerable amount of real power due to its resistive part, as well as also draw a little reactive power due to its reactive (here inductive) part. So the apparent power consumed by the coil is the summation of the real power and reactive power of the coil. The manufacturers are always aware about this fact and they design their products by considering the effect of reactive power. As the consumer loads are mostly inductive (or coil type) in nature, so there will sufficient reactive power generated by them which will be fed to the sources that is the transmission lines. So the summation of main power flow and reactive power flow will cause a huge current flow in power system network, which will create an adverse effect on the cables. That is why additional preventive measures like reactive power compensation techniques are applied in the generating stations and substations.

## Calculation of Reactive Power

The concept of reactive power is used for AC system analysis, because the phase angle difference arises in AC networks. In general for a single phase AC network, the reactive power will be VI sinθ. Suppose an inductive load Z consist a resistance part R and a reactance part x. And if this load is connected with a voltage source V then Current I will start flowing through the load.
∴ The Real Power = P = I2R
∴ The Reactive Power = Q = I2x
∴ The Apparent Power = S = I2Z

Consider a purely resistive circuit which consists of a resistance of 46 Ohm; which is fed from a 230 Volt AC source. Here only a pure resistance is connected with the voltage source. So the circuit current will be I = V / R = 230 / 46 = 5 Ampere. So the real power will be I2 R = 52 (46) = 1150 Watt and here no reactive power is developed because the load circuit is only resistive.

Now consider a practical load (like an inductor) which consists of a series resistance of 60 Ohm; and a reactance of 160 mH, both of them are connected with a 230 Volt AC source. The inductive reactance of the load will be 60.31 Ohm;. So the current flowing through the circuit will be 2.82 Ampere. Therefore the reactive power of the circuit will be I2x = 2.822 (60.31) = 479.6 VAR and the active or real power will be I2R = 2.822 (60) = 477.14 Watt. In this way, a practical load draws both real and reactive power.

## Reactive Power with Physical Analogy

Visualize the following diagram and this will help you to understand the concept of reactive power in easier way. Here the tank is situated at a certain height from ground, and the men have to bring water to the water tank by climbing the ladder. They goes in upward direction with full bucket of water, and after releasing the water into the tank, they returns with the empty bucket via the another ladder. The energy needed to climb with full bucket is greater than the energy needed when returning. Therefore there is some work done by the men. Now consider the following assumptions:

Height of the Tower = Real Power
Width of the Tower = Reactive Power
Length of the Ladder = Apparent Power
The climbing Ladder = Electricity line or cable
The number of men in Ladder = The Voltage
The amount of water each man carries = The Current
Amount of water added to tank per time interval = Frequency of system

So if the width of tank (that is reactive power) increases and the number of men in ladder (The Voltage) is constant then the water carrying capacity (The Current) must be increased to maintain the proper frequency. And if the height of tower (That is Real Power) is increased then the length of the ladder (The Apparent Power) must be increased to maintain the process. So the apparent power is depended up on the real power and reactive power both.

The reactive power should be minimized to improve the efficiency of the system. From the water tower model it is very easy to understand that it has an effect on the reliability of power system because it is also responsible to increase the voltage. Practically speaking, the real or active power is the original source of electrical energy which effectively utilized or consumed. And the reactive power is just a byproduct of AC power system so it must be controlled in some manner in order to increase the stability and reliability of system.

## Necessity of Reactive Power

The reactive power is present everywhere because all the real loads are either inductive or capacitive in nature. There are considerable portion of reactive power present in the transformers (in windings), synchronous generator, alternator, high voltage AC motor, transmission line. If the real power is the originally utilized as the source of energy so you might think that what is the necessity of reactive power? Let’s find the answer.

In case of transmission lines, maintaining the proper voltage throughout the entire span is very important. Because delivering the accurate amount of real power is necessary, as all the industrial and domestic loads are designed to operate in a certain range of voltage and frequency. High voltage causes several problems like heating of coils, damage in circuits as well as low voltage is also very harmful, because it leads the overheating of induction motor, and increases the noises, sometime electronic circuits are only operate after a certain voltage. There should be enough reactive power in the transmission line to boost the voltage and maintaining it to send enough real power for the loads. In transformers or other motor drives, the reactive power is the supporting hand of real power where it helps to convert the flow of charges into the works like magnetization and induction.