# Active, Reactive, Apparent Power and Power Triangle

Contents

There are three types of power: active, reactive, apparent power. These three form a Power Triangle which is showing the relationship between them.

If you have not learned about AC circuits then maybe you only know about one kind of power, that is active power. Since a DC circuit only uses DC source then there are no reactive elements such as inductor and capacitor that are able to produce reactive power.

## Electrical Power Definition

For a common definition,

Power is the ability to do something or act in a particular way.

For a science definition,

Power is the rate of doing work or the rate of transfer of energy.

But for electrical term,

Power is the supply (a device) with electrical energy.

For proper electrical term,

Power is the rate of electrical energy absorbed and converted into another form of energy (light, mechanical, heat, and many more).

Electrical power is exclusive for us electrical engineering.

We can define electrical energy simply by using an equivalent mathematical term as what we have learned before,

Power is the product of voltage drop across an element with the electrical current flowing through it.

## Types of Electrical Power

If you have known the difference between AC circuit and DC circuit, you might have known about AC power and DC power. These two are the only types of electrical power.

1. DC Power

DC Power is a power absorbed by a DC circuit which is supplied by DC voltage or current. The common example is battery cells. Since there is no reactive element, DC power is only about active power or real power. Where:

P = power, measured in watt (W)
V = voltage, measured in volts (V)
I = current, measured in ampere (A)

2. AC Power

Unlike DC power where we can calculate its power without any hard variable, AC power is a Complex Power. This complex power consists of three forms of power:

• Active power (P)
• Reactive power (Q)
• Apparent Power (S)

## What is Active Power?

The definition of active power or true power or real power,

Active power is the power that is fully consumed or utilized in a circuit. Active power is measured in watt and represented by the letter P.

Active power (P) is measured in watt (W) and commonly used higher digit such as:

• Kilowatt (kW)
• Megawatt (MW)

We can get this power easily in a DC circuit or a circuit where its impedance is purely resistive. Active power is easily calculated by an equation below: Where:

P = active power, measured in watt (W)
V = voltage, measured in volts (V)
I = current, measured in ampere (A)
ɸ = phase angle between voltage and current (degree)

When the circuit is purely resistive, there is no phase shift between voltage and current, thus ɸ = 0.

Since Simplify the equation above becomes As same as power calculation for a DC circuit.

## What is Reactive Power?

Reactive power only exists where reactive elements exist in the circuit. Reactive power is caused by the use of an inductor and/or capacitor in the circuit.this power flows back and forth into the source from the inductor and/or capacitor. Reactive power can affect the Power Factor negatively.

While reactive power exists, it does not deliver any useful energy, but is a burden for our consumed electricity bill. Summary, reactive power is useless and brings harm rather than benefit, a wattless energy.

Power factor where we use it to measure our efficiency is getting worse because of the reactive power in the circuit.

Remember when we read about active power that exists when the circuit is purely resistive?

Reactive power exists when the circuit is not purely resistive or there is some phase shift between voltage and current.

Guess what, inductance and capacitance are the culprit behind this phase shift.

Unlike resistor (resistance), inductor (inductance) and capacitor (capacitance) do not consume power generated by the source, but delivering it back to the source a bit later depends on the value of the reactance.

This is why there will be phase shift between voltage and current, unless the inductance and capacitance balance each other (we will not talk about this here).

This flow of power in the circuit between the source and reactive element(s) is known as Reactive Power (Q) measured in VAR (Volt-Ampere-Reactance).

This ‘exclusive’ type of power for AC circuit is measured by Where:

Q = reactive power, measured in VAR
V = voltage, measured in volts (V)
I = current, measured in ampere (A)
ɸ = phase angle between voltage and current (degree)

When the circuit is purely resistive, then there is no phase shift between voltage and current, thus ɸ = 0.

Since Thus, there is no reactive power generated in the circuit, only active power, where we read above.

• Inductor causes the current lags the voltage
• Capacitor causes the current leads the voltage

If these two have values that balance each other, there will be no phase shift.

## What is Apparent Power?

Apparent power is the combination of active power and reactive power. Since both active power and reactive power exist in an AC circuit, the apparent power is the total power in the circuit.

Like what we have talked about, the power found in an AC circuit is a complex power. It means the power consists of real value and imaginary value. Thus: We can easily measure apparent power (S) with root mean square (RMS) of the product of active power (P) and reactive power (Q). Apparent power is measured in volt-ampere (VA). Where:

S = apparent power, measured in volt-ampere (VA)

Vrms = RMS value of the voltage

Irms = RMS value of the voltage

Thus, ## What is Active, Reactive, Apparent Power and Power Triangle?

Power triangle represents the relationship between active power (P), reactive power (Q), and apparent power (S) found in a circuit. Remember what equation we have to measure apparent power? Yes it is a RMS or root mean square of the product of active power and reactive power.

Do you know where we have seen this form of equation before?

Exactly, it is a pythagoras equation originally: Thus, using this triangle to represents active power, reactive power, and apparent power become Where:   For another illustration of a relationship between active power, reactive power, and apparent power can be shown below: 