The nature of reactive power

Reactive power is a crucial aspect of alternating current (AC) electrical systems and is intimately linked with the behavior of inductive and capacitive elements within those systems.

1. Inductive Nature: Reactive power arises due to inductive elements in AC circuits, such as motors, transformers, and solenoids. When an alternating voltage is applied to an inductive load, such as a motor, it creates a magnetic field around the inductor. As the voltage changes, the magnetic field also changes, inducing a voltage in the opposite direction to the applied voltage, according to Faraday's law of electromagnetic induction. This induced voltage opposes the change in current, causing the current to lag behind the voltage in inductive circuits.

2. Capacitive Nature: Capacitive elements in AC circuits, such as capacitors, also contribute to reactive power. When an alternating voltage is applied to a capacitor, it charges and discharges according to the voltage waveform. The current leads the voltage in capacitive circuits because the capacitor initially draws current to charge up and then releases stored energy when the voltage decreases. This leading current creates a phase shift between voltage and current in capacitive circuits.

3. Energy Exchange: Reactive power represents the exchange of energy between the source and the reactive components (inductive or capacitive) in the circuit. Energy is alternately stored and released in the magnetic or electric fields associated with these components without performing useful work in the load.

4. Voltage and Current Relationship: In AC circuits, both real power (which performs useful work) and reactive power (which facilitates energy exchange) contribute to the total apparent power. The relationship between real power, reactive power, and apparent power is described by the power triangle or by the equation ${\text{Apparent Power}}^2={\text{Real Power}}^2+{\text{Reactive Power}}^2$.

5. Importance: Reactive power is essential for maintaining voltage stability and ensuring efficient power transmission and distribution. However, excessive reactive power can lead to voltage fluctuations, power losses, and decreased system efficiency. Therefore, managing reactive power is crucial for optimizing the performance of AC electrical systems.

Understanding the nature of reactive power is vital for designing, operating, and maintaining AC power systems effectively. Proper management of reactive power helps to improve power quality, reduce energy losses, and enhance the reliability of electrical networks.

Definition of reactive power

Reactive power is a component of electrical power that oscillates between the source and the load in an alternating current (AC) circuit without being consumed by the load to perform useful work. Unlike real power, which is responsible for doing useful work such as driving motors or lighting bulbs, reactive power facilitates the transfer of energy between the source and the load without actually being converted into useful work.

Reactive power arises primarily due to the presence of inductive or capacitive elements in the circuit. Inductive loads, such as electric motors and transformers, consume reactive power by storing energy in magnetic fields during one part of the AC cycle and returning it to the system during another part. Capacitive loads, on the other hand, supply reactive power by storing energy in electric fields.

Reactive power is measured in volt-amperes reactive (VAR) and is essential for maintaining the voltage levels and stability of AC power systems. While reactive power does not contribute to the real work performed by the load, it is necessary for maintaining the electromagnetic fields in motors and transformers and ensuring the efficient transmission of electrical energy.

Utilities and industries often need to manage reactive power to maintain the stability and efficiency of the power system. Power factor correction techniques, such as installing capacitors or inductors, are used to minimize reactive power and improve the overall efficiency of the system.

For most electrical loads like motors, the current I is lagging behind the voltage V by an angle φ.

If currents and voltages are perfectly sinusoidal signals, a vector diagram can be used for representation.

In this vector diagram, the current vector can be split into two components: one in phase with the voltage vector (component I_a), one in quadrature (lagging by 90 degrees) with the voltage vector (component I_r). See Fig. L1.

I_a is called the active component of the current.

I_r is called the reactive component of the current.

Fig. L1 : Current vector diagram

The previous diagram drawn up for currents also applies to powers, by multiplying each current by the common voltage V. See Fig. L2.

We thus define:

• Apparent power: S = V x I (kVA) 
• Active power: P = V x Ia (kW)
• Reactive power: Q = V x Ir (kvar)

Fig. L2 : Power vector diagram

In this diagram, we can see that:

• Power Factor: P/S = cos φ

This formula is applicable for sinusoidal voltage and current. This is why the Power Factor is then designated as "Displacement Power Factor".

• Q/S = sinφ
• Q/P = tanφ

A simple formula is obtained, linking apparent, active and reactive power:

• S² = P² + Q²

A power factor close to unity means that the apparent power S is minimal. This means that the electrical equipment rating is minimal for the transmission of a given active power P to the load. The reactive power is then small compared with the active power.

A low value of power factor indicates the opposite condition.

Useful formulae (for balanced and near-balanced loads on 4-wire systems):

• Active power P (in kW)

  -  Single phase (1 phase and neutral): P = V.I.cos φ
  -  Single phase (phase to phase): P = U.I.cos φ
  -  Three phase (3 wires or 3 wires + neutral): P = √3.U.I.cos φ

• Reactive power Q (in kvar)

  -  Single phase (1 phase and neutral): P = V.I.sin φ
  -  Single phase (phase to phase): Q = U.I.sin φ
  -  Three phase (3 wires or 3 wires + neutral): P = √3.U.I.sin φ

• Apparent power S (in kVA)

  -  Single phase (1 phase and neutral): S = V.I
  -  Single phase (phase to phase): S = U.I
  -  Three phase (3 wires or 3 wires + neutral): P = √3.U.I

where:
V= Voltage between phase and neutral
U = Voltage between phases
I = Line current
φ = Phase angle between vectors V and I.

An example of power calculations (see Fig. L3)

Type of circuit		Apparent power S (kVA)	Active power P (kW)	Reactive power Q (kvar)
Single-phase (phase and neutral)		S = VI	P = VI cos φ	Q = VI sin φ
Single-phase (phase to phase)		S = UI	P = UI cos φ	Q = UI sin φ
Example	5 kW of load	10 kVA	5 kW	8.7 kvar
	cos φ = 0.5
Three phase 3-wires or 3-wires + neutral		S =  UI	P =  UI cos φ	Q =  UI sin φ
Example	Motor Pn = 51 kW	65 kVA	56 kW	33 kvar
	cos φ= 0.86
	ρ= 0.91 (motor efficiency)

Fig. L3 : Example in the calculation of active and reactive power

The calculations for the three-phase example above are as follows:

Pn = delivered shaft power = 51 kW
P = active power consumed

S = apparent power

So that, on referring to diagram Figure L3 or using a pocket calculator, the value of tan φ corresponding to a cos φ of 0.86 is found to be 0.59

Q = P tan φ = 56 x 0.59 = 33 kvar (see Figure L15).

Alternatively:

Fig. L2b : Calculation power diagram

Definition of Power Factor

Power factor is a measure of the efficiency with which electrical power is consumed in an alternating current (AC) circuit. It represents the ratio of real power (also known as active power) to apparent power in the circuit.

Real power is the actual power that performs useful work, such as lighting bulbs or driving electric motors. It is measured in watts (W). Apparent power, on the other hand, is the product of voltage and current in the circuit, measured in volt-amperes (VA).

The formula for power factor is:

$\text{Power Factor}=\frac{\text{Real Power}}{\text{Apparent Power}}$

A power factor of 1.0 indicates a purely resistive load where real power and apparent power are equal, meaning all the electrical power is being used to do useful work. However, in many practical AC circuits, especially those involving inductive or capacitive elements, the power factor is less than 1.0 due to the presence of reactive power.

Inductive loads, such as electric motors and transformers, cause the current to lag behind the voltage, leading to a lagging power factor (usually denoted as "PF"). Capacitive loads, on the other hand, cause the current to lead the voltage, resulting in a leading power factor.

Utilities and industries often aim to improve power factor to reduce energy losses, improve system efficiency, and avoid penalties imposed by utilities for poor power factor. This is typically achieved by installing power factor correction capacitors or other devices to offset the effects of inductive loads and bring the power factor closer to unity (1.0).

Parallel operation of transformers

• Parallel operation of transformers involves connecting two or more transformers to a common electrical system so that they share the load. This arrangement offers several benefits, including increased system reliability, load flexibility, and efficiency. Here's how parallel operation of transformers works:

  1. Similar Characteristics: Before connecting transformers in parallel, it's crucial to ensure that they have similar voltage ratios, phase shifts, impedance values, and other characteristics. Transformers with significantly different characteristics can cause circulating currents and uneven distribution of the load.

  2. Parallel Connection: Transformers are connected in parallel by connecting their primary windings to a common supply source and their secondary windings to a common load. The connections must be made so that the polarities of the windings are aligned correctly.

  3. Load Sharing: Once connected in parallel, the transformers share the total load in proportion to their respective ratings and impedance characteristics. Transformers with lower impedance or higher ratings will carry a larger portion of the load.

  4. Load Distribution: In ideal conditions, the load is distributed evenly among the parallel transformers. However, slight differences in transformer characteristics or unequal loading can lead to unequal load distribution. Transformers with higher impedance may experience higher voltage drops and carry less load.

  5. Circulating Currents: If transformers connected in parallel have slightly different voltage ratios or phase shifts, circulating currents may flow between them. These circulating currents can lead to increased losses, reduced efficiency, and overheating of the transformers. To mitigate circulating currents, transformers can be equipped with phase-shifting devices or parallel reactors.

  6. Control and Protection: Parallel operation of transformers requires proper control and protection measures to ensure safe and reliable operation. This includes synchronizing the transformers' voltages and frequencies, monitoring load sharing, and implementing protective devices such as fuses, circuit breakers, and relays.

  7. Maintenance: Regular maintenance and inspection of parallel transformers are essential to identify and address any issues that may arise, such as imbalances in load sharing, insulation degradation, or mechanical failures.

  Overall, parallel operation of transformers offers advantages such as increased system reliability, load flexibility, and efficiency. However, it requires careful planning, installation, and maintenance to ensure safe and reliable operation. Proper control, protection, and monitoring are essential to prevent issues such as circulating currents, unequal load distribution, and transformer overheating.