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Active, Reactive, and Apparent Power calculation

What are the different kinds of power of a motor and how to calculate them

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Section summary
1. Introduction
2. Active Power (Real Power)
3. Reactive Power
4. Apparent Power
5. Differences between Active, Reactive, and Apparent Power

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1. Introduction

In electrical engineering, the concepts of active power, reactive power, and apparent power are indispensable to understand the behavior of alternating current (AC) circuits. These parameters play key roles in ensuring efficient energy transmission and consumption. In this page, those different kinds of power are explained, along with methods on how to calculate them.

2. Active Power (Real Power)

Active power, often referred to as real power, is a fundamental electrical parameter measured in watts (W). It represents the actual power consumed or produced by an electrical device, which is responsible for performing useful work. Active power is what powers lights, turns motors, and runs electronic devices.

3.1 Active power calculation for single phase current

Active power can be calculated using the following formula for single phase current motors :

\[ P = U \cdot I \cdot \text{PF} \]

(\(\text{PF} = \cos \varphi\))

\[ P = U \cdot I \cdot \cos \varphi \]

Where:
P = Active power (W)
U = voltage in volts (V).
I = current in amperes (A).
φ = phase angle difference between voltage and current
PF = Power Factor

3.2 Active power calculation for three phase current

Active power can be calculated using the following formula for 3-phase current motors :

\[ P = \sqrt{3} \cdot U \cdot I \cdot \text{PF} \]

(\(\text{PF} = \cos \varphi\))

\[ P = \sqrt{3} \cdot U \cdot I \cdot \cos \varphi \]

Where:
P = Active power (W)
U = voltage in volts (V).
I = current in amperes (A).
φ = phase angle difference between voltage and current
PF = Power Factor

3.3 Active power measurement

Measuring active power is typically accomplished using a device called a wattmeter, which directly reads the active power in a circuit.

3. Reactive Power

Reactive power, denoted as Q, is a vital component of AC power systems. It is measured in volt-amperes reactive (VAR). Reactive power does not perform any useful work but is essential for maintaining voltage levels and supporting the operation of inductive loads like motors and transformers, as well as capacitive loads like capacitors.

3.1 Reactive power calculation for single phase current

Reactive power can be calculated using the following formula for single phase current motors :

\[ Q = U \cdot I \cdot \sin \varphi \]

Where:
Q = reactive power (VAR)
U = voltage in volts (V).
I = current in amperes (A).
φ = phase angle difference between voltage and current

3.2 Reactive power calculation for three phase current

Reactive power can be calculated using the following formula for 3-phase current motors :

\[ Q = \sqrt{3} \cdot U \cdot I \cdot \sin \varphi \]

Where:
Q = reactive power (VAR)
U = voltage in volts (V).
I = current in amperes (A).
φ = phase angle difference between voltage and current

The calculation of reactive power involves trigonometric relationships within the power triangle, formed by active power, reactive power, and apparent power.

4. Apparent Power

Apparent power, symbolized as S and measured in volt-amperes (VA), is the vector sum of active power and reactive power. It represents the total power flow in an AC circuit, encompassing both the power that performs work (active) and the power that oscillates back and forth (reactive).

4.1 Apparent power general formula

The apparent power, often noted as S, can be calculated when knowing the real power and the reactive power of a motor :

\[ S = \sqrt{P^2 + Q^2} \]

With

S = apparent power (VA)
Q = Reactive power consumption (VAR)
P = Active power consumption (W)

Apparent power is analogous to the hypotenuse in the power triangle, and its magnitude is the square root of the sum of the squares of active and reactive power. Understanding apparent power is crucial in three-phase power systems, where balancing active and reactive power is very important.

5. Differences between Active, Reactive, and Apparent Power

To differentiate these types of power, consider the following:

• Purpose : Active power performs useful work (e.g., lighting a bulb), reactive power maintains voltage (e.g., inductive loads), and apparent power represents the total power flow.

• Units : Active power is measured in watts (W), reactive power in volt-amperes reactive (VAR), and apparent power in volt-amperes (VA).

• Calculation : Active power is directly measured using wattmeters, while reactive power and apparent power are calculated using relevant formulas (see above).

• Effect on Systems : Active power consumption directly affects utility bills, while reactive power affects system voltage stability. Apparent power reflects the capacity required from power sources.

In summary, active power is the tangible effect of electrical systems, reactive power stabilizes voltage, and apparent power encapsulates the complete power picture.

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