What Is Apparent Power? Definition And Formula

What Is Apparent Power? Definition And Formula
Apparent Power

What Is Apparent Power?

Apparent power is the total power generated by a power plant or a generator. It’s product of root-mean-square voltage and the root-mean-square (RMS) current.

Different types of power dissipate in AC power systems i.e. Active, Reactive, Apparent, and complex powers.

The measure of alternating current (AC) power is obtained from the multiplication of the root-mean-square voltage and the root-mean-square (RMS) current.

We can denote apparent power using (S) and the formula is given below,

S = ErmsIrms

Where

S is the apparent power in Volt Ampere.

Electric Motor Service Factor Expla...
Electric Motor Service Factor Explained

Erms is the root-mean-square (rms) voltage in volts.

Irms is the rms current in amperes.

Formula and unit

The basic formula for the calculation of apparent power for any circuit is given below.

  • S = VI  for single phase loads
  • S = √3VI  for three phase loads

The Unit is Volt Ampere (VA). We normally use it in terms of “KVA”.

If the power (Apparent) in the electric circuit is supplied from a power supplier to the grid. It includes both real & reactive power consumption in the loads.

By the help of the power factor triangle, which shows the relationship between apparent, active, reactive power and power factor we cane find another apparent power formula as follows.

Power factor triangle
Power factor triangle

From the triangle above we find S = √ (Active Power2 + Reactive Power2)

Or

S = √(Q2 + P2)

where

Q is reactive power consumption in load (VAR)

P is active power consumption in load (W)

apparent power calculation Example

Assume we have a three phase 10 KW load working on a 400 Volt power source. This Load has 0.85 power factor.

We need to calculate the apparent power of this load.

Solution

In this example, we have the load active power which is 10 KW, And the power factor of the load is 0.85 we calculate current first as follows

P = √3 V * I * PF   ⇒  I = P / (√3 *V * PF ) = 10,000/(1.73*400*0.85)

I = 17 A

Then, S =√3 V * I

S = 1.73*400*17 = 11.7 KVA

Note that, the active power is greater than the apparent one. This means that this load draws reactive power.

This is clear as the PF is 0.85 (the lower the power factor, the smaller the active power), For more information about pf, read my article here.

Could S(KVA) be less than P(KW)? S, is either less than or equal to P. In case of unity PF the two powers are equals.

Why Is Apparent Power Important?

The importance of apparent power shows up when making electrical calculations. To calculate the actual load current you need to know the apparent power.

Apparent power is the combination of both active and reactive power. Real or the active power is actually the result of the circuit having only resistive components.

On the other hand, reactive power is the result of a circuit having capacitive or inductive or both components.

Usually all the AC circuits have resistive, capacitive, and inductive components.

Because the reactive power is that power which takes away from the real power, so it is a must ensuring point in an electrical system. This ensures that the supplied apparent power is sufficient enough to supply the given load.

Usually it is considered that only real power is important and it is actually that power which does useful work. But, apparent power is also important as we have to consider the apparent power for the purpose of sizing the source.

Power generation stations produce a combination of both active and reactive power; we call this combination apparent power.

However, electrical loads don’t use all this power, loads only use active power to do whatever it suppose to do, we can’t consider only the true power when choosing the power generator capacity.

We, instead, do calculations taking apparent power, active and reactive, of the loads to get a generator suitable for the load.

As I just mentioned above, apparent power is the one to be considered when making calculations to get the load current. You may ask why we should take a useless power, i.e. reactive power, in our calculations.

It’s simply because both active and reactive power draw current from the source, this current still current no matter what it does for the load.

If you don’t consider apparent power in your calculations your system will fail. That’s why apparent power is so important in power system.

What Are The Applications of Apparent Power?

Apparent power has many applications in the electrical power systems. It is used in the sizing of different electrical equipment including alternators and the transformers.

As I told you above, the use of apparent power in electrical calculations is required to know the real current a load will draw from the source, no matter what this current will do after that. You know that the reactive power draw current however it’s useless.

We should take it into consideration when making calculations. If we don’t the circuit sizing will be wrong, i.e. circuit breakers, cable sizing and generators will be underestimated.

Underestimating loads, circuit breakers and cables is the last thing we need to do.

Apparent power depends on the current and voltage values rather than load power factor. If the value of load current is not changed then no matter what the value of load power factor is, the alternator and transformer KVA/MVA rating will be remain constant.

Apparent power is very useful for the sizing purpose of wiring, circuit breaker and all the electrical system.

Differences Between Apparent Power and Real Power

Apparent Power

Real Power

Apparent power is the combination of both real and the reactive power. Total Power in a circuit dissipated and returned power.

The actual amount of dissipated or used power  in the circuit is usually called real power

Apparent power is symbolized by the capital S

Real Power is symbolized by the capital P

The unit of Apparent power is Volt Ampere(VA)

The unit of Real Power is Watt

Apparent power in a circuit is actually the function of circuit’s total impedance

Real power in a circuit is actually the function of circuit’s dissipative elements and usually it is Resistance

Apparent power is the product of the root mean square(rms) values of the current and voltage

Real power is the product of the instantaneous values of the current and voltage in the circuit

In the AC Circuits, total flow of the electric power is apparent power whether useful or not useful.

The portion of the total power(apparent power) which does the useful work in the system is real or active power

Apparent power formula is S = V * I

Real or active power formula is  P = V I cos ø

Which Is Greater, Apparent Or Real Power?

Apparent power is greater than real power. When the impedance of the circuit is purely resistive, then apparent power equals the real power.

But, when there is any reactance in the circuit, apparent power is greater than the real power, as apparent power is the combination of both active and reactive.

Apparent Power Cannot Be Less Than The Real Power. It can be equal to the real power.

When Power factor is equal to one, then apparent power equals the real power. This shows that there is no reactive component in the circuit, this case is happened when the load is purely resistive.

PF = Kw / kVA = P / S

Above mentioned equation shows that there is not inductive or capacitive component in the circuit, it is very uncommon, and thus apparent powers is equal to the real power.

If PF = 1 then above equation becomes P = S

I have written a detailed article about Power Factor Correction, you can check it for more information.

Why Is Apparent Power Always Positive?

Apparent power cannot be negative, it’s always a positive value.

Let’s find out why? Apparent power is represented by the below equation:

S = √ (P2+Q2)

Here, P shows the real power, Q is reactive power, and S is apparent power.

Real or the active power can only be positive value as power flow is always from the source to the load.

Reactive power can be positive as well negative because power flows from source to load and load to source.

Above equation shows that even if reactive power value is negative, apparent power will be positive in this case too because, it is equal to the combination of squared values of real and reactive powers.

From the apparent power equation, it’s clear that the apparent power is always positive value no matter what value the active or reactive power is.

Do You Pay Electricity Bill For Real Power Or Apparent Power?

Usually residential bills are charged only for real or the active power. The unit in which residential customers’ utility bills are charged is Watt hours.

Power factor does not affects the cost of the electricity bill directly as far as residential consumers are concerned.

Some utilities in some countries charge the industrial consumers for the poor power factor. It means that these industrial consumers are being charged for real and the reactive powers.

In some areas of USA, power authorities charge the industrial consumers having less than 0.9 power factor.

So, it clearly depends upon the electricity bill charging responsible authority’s policy in a specific area. Poor power factor usually happens in the large inductive loads.

But, in some countries of the globe, bill charging responsible authority does not charge for the apparent power even if the power factor is a bit poor.

Industrial and commercial customers apply power factor correction for the loads, this helps in reducing the consumption of the reactive power.

Several years ago, I worked for a plastic pipes factory. Back then, we installed a large capacitor bank in parallel with the incoming power source, the transformer of the factory, to reduce the power factor and ,of course, the electricity bill.

This wasn’t an option, it was a mandatory action required by the authority, if we didn’t, there could be consequences.

The capacitor bank worked automatically, it measured the power factor, and controls the number of units of capacitors to connect to the loads. It worked as it should.

What Is The Derivation Of Apparent Power Formula?

Power factor triangle
Power triangle

The real power is represented by capital letter P, reactive power is represented by capital letter Q, and apparent power is represented with capital letter S.

P=V *I* cosø     Q=V*I*sinø

OA = Active current     OC = Reactive Current      OB = Circuit Current

The power triangle is obtained from the above phasor diagram.

OB2= OA2 + OC2

Above diagram represents the vector diagram of current.

If we talk about the vector diagram of power as shown in the diagram then the equations will be:

S2 = P2 + Q2

S = (P2 + Q2)

Power factor is defined as the angle between the real and the apparent power

As, we know that

Cosø = Base/Hypotenuse = active or Real power / Apparent Power = P / S = kW / kVA

Calculate Current From The Apparent Power?

Apparent power is the product of the rms values of the current and the voltage. If voltage and apparent power values are given then current can be calculated.

Apparent Power – Single Phase Formula:

S = V * I

(Current) I = (Apparent Power) S / (Voltage) V

I = S / V = (P2 + Q2)/ V

Apparent Power – Three Phase Formula:

S = √ 3 *V * I

I = S / √ 3 V

Note: S is the apparent Power in VA

This equation shows that if value of the real or active power, reactive power, and the voltage is known then current value can be calculated.

Calculating Current From The Apparent Power Example:

One of the most common examples of this calculation I face in my work is Transformer Current calculations. You know, transformers power is given in KVA, i.e in apparent power, In this case we use the formula:

I = S / V

Calculate current of a three phase transformer of 100KVA Power and 400V voltage.

Transformer Current (I) = Apparent Power (S)/Voltage (V)

I = (100*1000) / (√ 3 * 400) = 144.34 A

Calculate Current From Apparent Power

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Can you measure Apparent Power?

Yes, apparent power can be measured. Apparent power is that energy which you actually measure during the operation of an electrical system.

In simple words, Apparent power is actually the rated voltage times the rated current. We measure voltage and current by a multi-meter, voltage is measured in parallel and current in series, multiply them gives you the apparent power.

Apparent power is actually that power which a power source supplies to a load like a motor, However, the load only uses the real power, its the result of multiply voltage and current of the load.

Apparent power is measured in Volt Ampere (VA)and it is denoted by the capital letter S.

Why the apparent power is used in sizing generators?

Electrical generator produces active and reactive power, the value of each power depends on the load power factor, which varies from one load to another. The load of a generator depends on the application it will be used to feed, this is why its much accurate to use apparent power for generator sizing.

As apparent power is the product of output voltage and current of the generator, so it is the most accurate rating the generator , regardless how much active power the load need.

The generator manufacturer does not know what load will be connected to the generator, so maker of the generator want to provide the maximum possible exact load the generator will provide.

Apparent power is also used in the sizing because, it gives the maximum magnitude of the current and obviously rating of the electrical equipment is directly related to the determining the maximum value of current because, this maximum current magnitude will determine the maximum rated temperature.

In a 100% efficient electrical system,real power equals the apparent power, i.e zero reactive power. But, usually electrical systems are not 100% efficient, reactive power should be taken into account when sizing the generator, i.e using apparent power.

Does generator produce apparent power?

Yes, generator produces the apparent power. The current drawn from a generator depends on its apparent power produced by the generator, i.e both active and reactive power.

Generators produce apparent power which is the vector sum of the real or active power and the reactive power, the load consumes active and reactive power depending on its power factor.

What do you mean by power triangle?

Power factor triangle
Power triangle

The power triangle is a triangle used to show the relation between apparent power, active power and reactive power in power system.

I, personally, draw the power triangle to memorize the relationship between these power types.

Base of this triangle shows the real or true or active power of the circuit. Perpendicular of the triangle shows the reactive power. Hypotenuse of the triangle shows the apparent power.

The power triangle is actually, the phasor representation of the inductive or capacitive load connected to the source.

  • S is the apparent power
  • P is the real or active power
  • Q is the reactive power.
  • φ is the angle between the apparent power and the real power.

When the circuit overall current is multiplied with the voltage, it is called the apparent power and shown in the hypotenuse of the triangle with the symbol of capital S.

As shown in the power triangle above, power factor can be obtained by taking the ratio between the active or real power and apparent power.

Power Factor (PF) = Active Power (KW) / Apparent Power (KVA) = P / S

For more information about Power Factor read my article Power Factor Correction, 8 Important Answers.

Is the rated power input same as the apparent power?

No, the rated power input of a load is not same as the apparent power in inductive loads.

Rated power is actually the active power, it’s the amount of energy in the unit of kilowatt (kW).

Load rated power is that energy which a device actually will consumes at its peak design operational state.

While the apparent power is the total power provided by the power source to a load, it’s the real and reactive power, depending on the load power factor.

Apparent power equals the rated power in resistive loads because, the power factor is unity.

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