Volt-Amperes Reactive (VAR) to Millivolt-Amperes Reactive (mVAR) conversion

What is volt-amperes reactive?

Understanding Volt-Amperes Reactive (VAR)

Volt-Amperes Reactive (VAR) is the unit of measurement for reactive power in an AC (alternating current) electrical system. Unlike real power, which performs actual work, reactive power supports the voltage levels needed for alternating current (AC) equipment to function. Without enough reactive power, voltage drops can occur, leading to inefficient operation and potential equipment damage.

The Formation of VAR

Reactive power arises from inductive and capacitive components in AC circuits.

• Inductors (like motors and transformers) store energy in a magnetic field, causing the current to lag behind the voltage.
• Capacitors store energy in an electric field, causing the current to lead the voltage.

This phase difference between voltage and current creates reactive power. The VAR value represents the amount of power that oscillates between the source and the load without doing any real work.

The relationship between real power (watts), reactive power (VAR), and apparent power (VA) can be visualized using the power triangle:

• Apparent Power (VA): The total power supplied by the source, which is the vector sum of real and reactive power.
• Real Power (W): The power that performs actual work (e.g., powering a motor or lighting a bulb).
• Reactive Power (VAR): The power that oscillates between the source and the load, providing the necessary voltage support.

Mathematically, this relationship is described by:

$S = P + jQ$

Where:

• $S$ is the apparent power in volt-amperes (VA)
• $P$ is the real power in watts (W)
• $Q$ is the reactive power in volt-amperes reactive (VAR)
• $j$ is the imaginary unit

Steinmetz and AC Circuit Analysis

Charles Proteus Steinmetz was a brilliant electrical engineer and mathematician who made significant contributions to the understanding and analysis of AC circuits. His work with complex numbers simplified the calculation of AC circuits involving reactive components. While VAR wasn't directly named after him, his work laid the foundation for understanding and quantifying reactive power.

Examples of VAR Values in Real-World Applications

• Large Induction Motors: Industrial motors can draw significant reactive power. A 100 HP induction motor might require 50-80 kVAR to operate efficiently.
• Transformers: Transformers also consume reactive power due to the magnetization of their cores. A large power transformer could require hundreds of kVAR.
• Long Transmission Lines: Transmission lines have inherent capacitance, which can generate reactive power. However, they also have inductance, which consumes reactive power. These lines might require compensation devices like shunt capacitors or reactors to balance reactive power.
• Power Factor Correction: Industries and power utilities use capacitor banks to supply reactive power and improve the power factor. For example, a manufacturing plant with a poor power factor (e.g., 0.7) might install capacitor banks to increase it to near unity (1.0), reducing reactive power demand.
• Wind Turbines: Many wind turbines utilize induction generators that require reactive power for magnetization. This reactive power can be supplied by the grid or by local compensation devices within the wind farm.

For further reading, refer to these resources:

• Reactive Power - an overview
• Reactive Power

What is Millivolt-Amperes Reactive (mVAR)?

Millivolt-Amperes Reactive (mVAR) is simply a smaller unit of reactive power, equal to one-thousandth of a VAR:

$1 \, \text{mVAR} = 0.001 \, \text{VAR}$

It's used when dealing with small reactive power values, which is common in low-power electronic circuits or when analyzing very small power losses.

How Reactive Power is Formed

Reactive power arises from the presence of inductors (coils) and capacitors in AC circuits.

• Inductors: Inductors store energy in a magnetic field when current flows through them. The current lags behind the voltage in an inductive circuit.
• Capacitors: Capacitors store energy in an electric field when a voltage is applied across them. The current leads the voltage in a capacitive circuit.

This leading or lagging relationship between voltage and current creates a phase difference. The greater the phase difference, the larger the reactive power.

The relationship between apparent power, active power and reactive power can be represented by the power triangle.

$S = \sqrt{P^2 + Q^2}$

Where:

• $S$ is the apparent power in Volt-Amperes (VA)
• $P$ is the real (active) power in Watts (W)
• $Q$ is the reactive power in Volt-Amperes Reactive (VAR)

The power factor, which is the ratio of the active power to the apparent power, indicates how effectively the electrical power is being used. A power factor of 1 means all the power is active power, and none is reactive. A lower power factor indicates a significant amount of reactive power.

$\text{Power Factor} = \frac{P}{S} = \cos{\phi}$

Where:

• $\phi$ is the phase angle between the voltage and the current.

Significance and Applications

While reactive power doesn't directly do work, it's essential for the operation of many electrical devices and systems.

• Motors and Transformers: Inductive loads like motors and transformers require reactive power to establish and maintain their magnetic fields. Without it, they cannot function correctly.
• Power Transmission: Reactive power plays a crucial role in maintaining voltage stability in power transmission systems.
• Power Factor Correction: Industries and large consumers often use power factor correction techniques (e.g., capacitor banks) to reduce reactive power consumption and improve efficiency.

Real-World Examples (Typical Values)

While it's uncommon to deal with large specific examples of mVAR alone (due to the small value), it's relevant in the context of measurements and losses in small electronic devices:

• Standby Power: A small electronic device in standby mode might draw a few mVAR of reactive power. This contributes to overall "phantom load."
• LED Lighting: Individual LED bulbs might have very small reactive power components, measurable in mVAR. The aggregate of many bulbs can become significant.
• Sensor Circuits: Precision sensor circuits may have tiny reactive power losses expressed in mVAR, which are important in the design and analysis of high-sensitivity applications.

Notable Figures and Related Laws

While there isn't a single "law" specifically for reactive power in the same vein as Ohm's Law, its behavior is governed by the fundamental laws of electromagnetism described by James Clerk Maxwell. These laws underpin the operation of inductors and capacitors and, therefore, the generation and effects of reactive power.