Apparent Power: Definition, Formula and Examples

Apparent Power Explained in Brief

The total power in an alternating current system consists of active power and reactive power. It is expressed in volt-amperes (VA) and is relevant when dimensioning inverters, cables and other electrical components.

Key Points

Apparent power consists of active power and reactive power.
Its unit is the volt-ampere (VA).
Its magnitude is calculated using the formula S = √(P² + Q²).
It is relevant when dimensioning electrical systems and inverters.

What Is Apparent Power?

In an alternating current system, apparent power is the total electrical power resulting from active power and reactive power. Its unit is the volt-ampere (VA). This quantity is particularly relevant when dimensioning and analysing alternating current systems. Mathematically, its magnitude is calculated as the square root of the sum of the squares of active power and reactive power.

Official definition: According to the IEEE - Institute of Electrical and Electronics Engineers, apparent power is defined as “the vectorial sum of active power and reactive power”. Source: IEEE Standard 100, “The Authoritative Dictionary of IEEE Standards Terms”.

What Is Complex Apparent Power?

Complex apparent power is a representation of apparent power in complex-number form. Active power forms the real part, while reactive power forms the imaginary part. Complex apparent power can therefore be written as S = P + jQ, where S is the complex apparent power, P is the active power and Q is the reactive power. This representation is particularly useful when analysing AC circuits.

There is no separate official definition of complex apparent power. In electrical engineering, however, it is used as the mathematical representation of total power in complex-number form.

What Is the Difference Between Apparent Power, Active Power and Reactive Power?

To understand the difference between apparent power, active power and reactive power, they can be considered as different components of electrical power. Imagine the total power as a glass of beer that represents the different types of power.

Type of Power	Symbol	Unit	Meaning
Apparent power	S	VA	Resultant quantity comprising active power and reactive power
Active power	P	W	Power used to perform actual work
Reactive power	Q	var	Power component that oscillates between the source and the load

Overview of the different types of electrical power.

Apparent power (S):
Apparent power is the combination of active power and reactive power. In the beer-glass comparison, it corresponds to the total volume of the drink.

Active power (P):
Active power is the part of electrical power that provides an actual benefit and is measured in kilowatts (kW). In the beer glass, active power corresponds to the beer that can actually be consumed. It is the portion that is genuinely used.

Reactive power (Q):
Reactive power is the power in a system that is not converted into useful work and is measured in kilovolt-amperes reactive (kvar). In the beer-glass comparison, reactive power corresponds to the foam. It adds volume to the glass but provides no direct benefit.

The beer glass illustrates the relationship between the three types of electrical power.

In summary, apparent power corresponds to the entire contents of the glass, active power to the usable beer and reactive power to the foam.

Relationship between apparent power, active power and reactive power illustrated using a beer glass — Figure 1: Relationship between apparent power, active power and reactive power.

What Is Apparent Power in Relation to Inverters?

For inverters and electrical systems, understanding these terms is essential when optimising the efficiency and performance of photovoltaic systems. In photovoltaic systems, inverters convert the direct current generated by the solar cells into alternating current suitable for domestic use. Apparent power plays an important role because it describes the total load that the inverter must handle.

Understanding active power and reactive power helps ensure that the system is dimensioned appropriately and operated efficiently. Knowledge of these quantities is therefore important not only for technicians and engineers, but also for operators of photovoltaic systems seeking to maximise the performance and efficiency of their installations.

How Is Apparent Power Calculated?

The Formula

Illustration of a smart electricity grid for classifying electrical power quantities

The following formula is used to calculate apparent power:

Where:

S is the apparent power in volt-amperes (VA),
P is the active power in watts (W),
Q is the reactive power in volt-amperes reactive (var).

This formula calculates the total power in alternating current systems. The unit of apparent power is VA - volt-amperes.

For three-phase systems, the electrical power formula can be extended by the factor √3:

Here, U is the voltage and I is the current in the three-phase system.

The following formula is used to convert apparent power into active power:

Here, cos ϕ is the power factor, which indicates the ratio of active power to apparent power. The unit of active power P is watts (W).

Apparent power can be determined from active power using the rearranged formula:

For complex apparent power, the sum of active power P and reactive power Q applies:

Here, j is the imaginary unit. This allows electrical power to be represented in complex-number form.

Apparent Power: Practical Examples

Photovoltaic system: In a photovoltaic system, apparent power is relevant when dimensioning the inverter. It comprises active power and reactive power. The inverter must be capable of handling this total power so that the system can reliably feed energy into the grid.

Three-phase systems: In three-phase systems, which are commonly used in industrial installations and larger buildings, determining the total power is important. Devices with inductive or capacitive loads, such as motors, transformers or capacitors, generate reactive power. Apparent power indicates the total electrical power that the system must provide.

Star-connected inverters: In applications involving inverters, particularly in a star connection, apparent power is a relevant parameter. It describes the total load that the inverter must handle.

Relevance of apparent power: Determining this quantity is particularly relevant when inductive and capacitive loads are present. Inductive loads, such as motors, generate reactive power, while capacitive loads, such as capacitors, can absorb reactive power. Apparent power supports the appropriate dimensioning of components and efficient energy transmission.

FAQ - Frequently Asked Questions About Apparent Power

What is apparent power in simple terms?

Apparent power is the total electrical power in an alternating current system. It consists of active power and reactive power and is expressed in volt-amperes (VA).

How is apparent power calculated?

Its magnitude is calculated using the formula S = √(P² + Q²). Here, P represents active power and Q represents reactive power.

What is the unit of apparent power?

The unit of apparent power is the volt-ampere, abbreviated as VA. Larger values are commonly expressed in kilovolt-amperes (kVA).

Why is apparent power important for inverters?

Apparent power describes the total power that an inverter must provide or process. It is therefore relevant when dimensioning the inverter correctly.

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