True Power, Reactive Power, and Apparent Power

In electrical engineering, we often come across terms like ‘True Power,’ ‘Reactive Power,’ and ‘Apparent Power.’ While these terms may seem intimidating, they are fundamental concepts that engineers and technicians must understand when dealing with alternating current (AC) circuits. This article will demystify these terms, show you how they’re calculated, and tie them to everyday utilities.

What is True Power?

Also known as ‘Real Power,’ True Power (P) is the power consumed by the AC circuit’s load. It is expressed in watts (W) and is the power that does useful work, like lighting up a bulb or running an electric motor.

The True Power is calculated by the product of the circuit current (I), circuit voltage (V), and the cosine of the phase angle (cos φ). The phase angle is the angle between the current and voltage waveforms. In mathematical terms:

P = V * I * cos φ

What is Reactive Power?

Reactive Power (Q), measured in volt-amps reactive (VAR), is the power absorbed and then returned by reactive elements like inductors and capacitors in an AC circuit.

While Reactive Power does no real work, it’s essential for functioning devices with magnetic fields, like motors and transformers. Reactive Power is calculated as the product of the circuit current (I), circuit voltage (V), and the sine of the phase angle (sin φ):

Q = V * I * sin φ

What is Apparent Power?

Apparent Power (S), measured in volt-amps (VA), is the vector sum of True Power and Reactive Power. It represents the total power in an AC circuit, both the power consumed and the power absorbed/returned. Apparent Power can be calculated as the product of the circuit voltage (V) and circuit current (I):

S = V * I

You can visualize this relationship between True, Reactive, and Apparent Power as a right triangle. Apparent Power is the hypotenuse, True Power is the adjacent side (base), and Reactive Power is the opposite side (height). This is commonly referred to as the Power Triangle.

From the Pythagorean theorem, we can calculate Apparent Power using True Power and Reactive Power:

S = sqrt(P^2 + Q^2)

Practical Examples: Inductors and Capacitors

Let’s dive into some practical examples of how True Power, Reactive Power and Apparent Power play out in circuits with inductors and capacitors.

Example 1: Purely Inductive Load

An inductor is a reactive component that stores energy in its magnetic field. Suppose we have an AC circuit with an inductor. When voltage is applied to the inductor, the current lags 90 degrees.

In this case, the power factor (cos φ) is 0, and as a result, the True Power (P) is also 0 (From Eq.1). However, the Reactive Power (Q) is at a maximum as sin φ = 1 (From Eq.2).

Example 2: Purely Capacitive Load

On the other hand, a capacitor stores energy in an electric field. In an AC circuit with a capacitor, the current leads the voltage by 90 degrees.

Here too, the power factor is 0, meaning the True Power (P) is 0, but the Reactive Power (Q) is at a maximum.

While Reactive Power does no real work in these components, it’s essential for their functioning. It also has a significant impact on the power system’s efficiency and reliability.

Power Meters and Home Utilities

Power meters, commonly used by utility companies, measure the True Power consumed by the appliances in your house. They’re interested in the actual work done, so they bill you based on the kilowatt-hours (kWh), a unit of True Power.

However, it’s important to note that while customers are typically billed based on True Power, utilities must still supply the Apparent Power (S) from the power distribution network, which includes Reactive Power. This is also influences the wire used to accommodate the ampacity requirements. This means that a home with a lot of inductive or capacitive loads can significantly affect the power factor and overall power efficiency. This is one reason why power factor correction devices are used in some industrial and commercial settings.

In conclusion, understanding the concepts of True Power, Reactive Power, and Apparent Power is crucial in electrical engineering, especially in designing and operating efficient power systems. So, the next time you switch on a light or run a motor, you’ll appreciate the complex interplay of powers that makes our everyday electrical conveniences possible.

Before you go, check out this writeup on heavy duty 2/0 wire, as well as wire strippers I like to use for smaller gauge wire in the home.

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