Understanding Active, Reactive, and Apparent power in an AC circuit

 When dealing with power in an AC circuit, you'll definitely come across these terms; Real(or active) power, Reactive power, and Apparent power. What is their difference? 

This post will explain all you need to know about power in an AC circuit, bit by bit.

What is electric power: Electric power refers to the rate in which electrical energy is transfered in an electric circuit. It is the rate per unit time at which work is done in a circuit.

In a linear AC circuit(circiuits that obeys ohms law hence, V=IR), we have basically two types of loads, which are:

1. Resistive loads: These are loads that just consume electrical power and dissipate them in form of heat while performing useful functions. For this kinds of load, current remains in phase with voltage i.e they draw current in the same proportion as the applied voltage. The type of power consumed by them is called the active power.

Examples of resistive loads include: Resistors, Electric heaters, incandescent bulbs etc.  

2. Reactive loads: These are loads that store power temporariy in the circuit and unlike resistive loads, energy consumed by reactive loads are not dissipated as heat but rather it is stored  for some time and again returned back to the circuit, making the net energy consumed by it to be zero. In reactive loads, There are two types of reactive loads.

* Capacitive loads and

* Inductive loads.

Examples of reactive loads include:  Inductors, transformers, line capacitors etc. The kind of power used by reactive loads are called reactive power. 

Note that reactive loads ideally do not consume power. But in practice, all reactive loads has some resistive component and leakages present, which causes power to be dissipated as heat and resulting in energy losses.

What is Active power

This is the actual amount of power that is being expended in the circuit to perform useful work  e.g creating heat, lighting a bulb etc. It is the power that is actually being dissipated by the circuit due to it resistive component. In other words, when your're using your household equipment, like Lightbulbs, Electric irons, TVs,  Washing machines etc power is being expended and the amount is reading on your meter. This kind of power which is being consumed by the circuit to do useful work is called active power. 

Active power can be alternatively called real, actual, useful or true power and it measured in Watt or kilowatt.

Formulas for calculating active power:

P = V I (In DC circuits)

P = VI Cosθ (in Single phase AC Circuits)

P = √3 VL IL Cosθ or (in Three Phase AC Circuits)

P = 3 VPh IPh Cosθ 

P = √ (S2 – Q2)or

P =√ (VA2 – VAR2) or 

Real or True power = √ (Apparent Power2– Reactive Power2) or

kW = √ (kVA2 – kVAR2)

What is Reactive power

The power that is not utilized to do any useful work but it continuously transfered from the load to source is called reactive power. 

In an AC circuit, Not all loads do consume power or dissipate them as heat. Taking a capacitor and an inductor for example. Inductors and capacitors ideally do not dissipate electric power but rather stores them in form of magnetic field and electrostatic field respectively. Power is needed to establish this respective fields. So the power needed for a capacitive load to build up an electrostatic field or for an inductive load to build up a magnetic field is called reactive power. It is called reactive power because the power consumed is not dissipated as heat or utilize to do any useful work. These fields will only build up in the positive half cycle of the AC waveform and will be given back to the circuit in the negative half cycle, making the net power consume by it to be zero.

Reactive power is measured in volt ampere reactive(VAR)

Formulas for calculating reactive power:

Q = V I Sinθ

Reactive Power=√ (Apparent Power2– True power2)

VAR =√ (VA2 – P2)

kVAR = √ (kVA2 – kW2)

If Active power is called useful power, does it mean that reactive power is useless?

No, not at all. Let use a ceiling fan as an example. Without the AC capacitor present inside the fan, the fan blades won't rotate. But power is thus needed to charge this capacitors and this power does not contribute in rotating the fan, but without the capacitor being charged, the coils making up the fan won't be energized and the fan won't rotate. So the energy used to charge the capacitor is not utilize to do any useful work as it just charging the capacitor. When the capacitor is fully charged, it will thus deliver this energy to the fan colis which will then utilize it to perform the useful work which is rotating the fan blade. 

What is Apparent power

Apparent power is the mathematical combination of active power and reactive power. It equals to the total power in an AC circuit, both dissipated and absorbed/returned. Thus in apparent power, the phase angle difference between the voltage nd the current is ignored.

Formulas for calculating Apparent power:

S = V I

Apparent Power = √ (True power2 + Reactive Power2)

kVA = √kW2 + kVAR2.

If you need further reasonning, you can consider the wheel barrow analogy below;

In order to make the wheel barrow move, it is obvious that we’ve to apply force at the handle.

But the force should be applied in the forward direction only after lifting the handle. Otherwise there would a hindrance for the motion due to the leg of the wheel-barrow.

Active Power is that which results in active work (propelling the wheel-barrow in forward direction). So active power is solely that work which is done on the wheels of the barrow for the procurement of real (useful) work. 

Reactive Power can be reckoned as that which helps to keep the barrow in the lifted position.

The total power which is the Apparent Power (Lifting + Pushing) is that which is applied at the handles.

Just imagine what would happen if the wheel barrow is thrust forward without lifting? The barrow moves forward, but not with much ease. There is much difficulty encountered to the person who is pushing it as well as on the wheel barrow. The same applies in the case of transmission system also. If reactive power support is not provided then there is much difficulty in transfer of power between buses. Moreover, in the case of a wheel barrow, one has to incur extra work in lifting the barrow so that it moves forward smoothly. Thus, reactive power is a necessary evil (it is not a part and parcel of useful work but it helps in useful work being done more easily).

Analogy extracted from quora.com

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