If you are interested in savings and energy efficiency, you have certainly heard about reactive power. You’ve heard that it reduces the efficiency of installations, that it’s bad for the electrical grid, and, above all, that if you consume reactive power you get a penalty on your electricity bill. But what exactly is reactive power?
Explaining the concept of reactive power is somewhat complicated. If you look it up in a book, they will fill you with equations of complex numbers, phasor algebra, and trigonometric relationships. The problem is that with so much mathematics, there’s a risk of forgetting the physical meaning. Because after all, what the heck does it mean for a dipole to absorb complex power?
So, honoring the subtitle of this blog, I’m going to explain what reactive power is without using a single equation. In fact, I’m going to show it to you and let you play with it. At the end of this post, you have a complete application to experiment with. But let’s not get ahead of ourselves, and go step by step.
A Review of Alternating Current Electricity
As is known, the electrical grid we use is actually an alternating voltage source. In Spain, this alternating voltage has nominal values of 230V between phase and neutral and 50 Hz. This means that the voltage in our outlet alternates its direction (goes from positive to negative, and back to positive) 50 times every second, and it performs work equivalent to what a 230V DC voltage source would do. In this post, we will take these values, although the results and conclusions are valid for any other grid value.
Let’s graph this voltage over time, measured in electrical degrees (360 electrical degrees will be 1/50Hz = 0.02s),
When we connect an electrical load to alternating voltage, a certain amount of electrical current begins to flow through it. Logically, this current is also an alternating function. This means that the electricity changes the direction in which it passes through the load, from positive to negative and back to positive, 50 times per second.
The electrical current that flows is determined solely by the characteristics of the connected load. The amount of electricity, the amplitude of the current wave, is set by the impedance of the load. But (and here comes the interesting part for reactive power) the load also introduces a phase shift between current and voltage. This means that the current wave will lead or lag in time relative to the voltage wave. This phase shift, which we will measure in electrical degrees, is what causes reactive power.
But what causes the voltage and current waves to shift out of phase? To explain this, we need to briefly explain the types of loads that exist.
Types of Loads in Electricity
In electricity (not to be confused with electronics), there are three types of loads. Resistors, inductors, and capacitors. Let’s see the characteristics of each one.
- Resistors (resistive loads): Every element through which electricity flows offers some resistance to being traversed by current. When current flows through them, resistors dissipate energy. As examples of large resistors, we can cite thermal resistors used to generate heat, but it is noted that every connected load (power lines, lights, motors…) presents a resistance.
- Inductors (inductive loads): An inductor is formed by an electrical conductor wound around a ferromagnetic core. When current flows through it, it generates a magnetic field inside. This magnetic field stores energy and opposes changes in the value of the electrical current. Inductors are a fundamental part of many machines, for example in motors, transformers, fluorescent equipment.
- Capacitors (capacitive loads): A capacitor is formed by two conductors separated by an insulating material. When current flows through it, it generates an electric field inside. This electric field stores energy and opposes changes in the voltage value. Unlike inductors, large capacitors have little application in electricity. Their main use is in banks to compensate, precisely, the reactive effects produced by inductors.
Resistors are passive elements that do not generate a phase shift in the current. However, inductors and capacitors are reactive elements that generate magnetic and electric fields, respectively. These fields present a certain “inertia” to being created or destroyed, and it is this “inertia” that introduces phase shifts in the current. Both elements produce opposite effects on the current; inductors introduce negative phase shifts, and capacitors positive ones.
However, real loads are never “pure” but exhibit behavior intermediate between passive and reactive loads. To characterize real loads we use the phase shift angle they introduce between voltage and current. A pure resistor is a 0º load, an inductor 90º, and a capacitor -90º. Mixed behaviors present phase shift values between these limits.
In the following graph, you can move the slider, modifying the load’s behavior, and observe the phase shift introduced in the electrical current.
A Matter of Power
Why is this phase shift important and how can it be the cause of reactive power? To see the effect it produces on the load, let’s calculate the power consumed by a load, which we obtain simply by multiplying the voltage and current at each instant in time. The result, S(t), which we will call apparent power, is shown in the following graph.
It is observed that the apparent power is a wave at double the frequency of the voltage. That is, if we connect a lamp (a resistive element, angle 0º) it turns on and off 100 times per second. This fluctuating behavior in power always holds true, for any type of connected load. The effective power value over time is the average of this power, shown with the line Smed.
Now vary the load angle and observe how the power wave S(t) starts to have instants where it takes negative values. Indeed, the load absorbs power during part of the time and returns it to the grid in another part. Meanwhile, the average power Smed decreases. At the extreme values of 90º or -90º, corresponding to pure inductive or capacitive loads, the Smed value is zero. In these pure cases, the load absorbs energy during half a cycle and returns exactly the same energy during the next half cycle.
It only remains to use a small “mathematical trick” to decompose this apparent power S(t) into the sum of two purely active and reactive components. At all times, the sum of both components is the power S(t), which is what the load actually absorbs.
- The real power P(t) is the part of the power that pulsates in phase with the voltage. This power, originated by the resistive elements of the load, is what actually performs useful work.
- The reactive power Q(t) is the power component that pulsates at 90 or -90º. It is originated by the reactive elements of the load and does not generate useful work over time.
The amount of each component is marked by the phase shift between voltage and current. Specifically, the relationship between active power and apparent power is the cosine of the angle formed by voltage and current. This relationship is commonly called the power factor of the installation.
The following graph shows the distribution of power between the two components as a function of the angle.
Conclusion
We have seen that the reactive elements of an electrical load introduce phase shifts between voltage and current. This phase shift originates from the “inertia” of the load in the creation and destruction of magnetic and electric fields. The existence of this phase shift causes the power absorbed by the load, S(t), to acquire negative values, so the load delivers power during part of the time.
Reactive power is the component of power that pulsates at 90º to the voltage. The net work it performs over time is zero. The energy absorbed in one half-cycle is stored inside the load as a magnetic or electric field and is fully delivered in the next half-cycle. In opposition, active power is the component that pulsates at 0º to the voltage, and it is the one that performs effective work over time.
In a future post, we will see the negative effects of reactive power on an electrical grid, and we will address certain myths and truths related to reactive power in the field of energy efficiency.
To finish, I leave you the complete graph with all the magnitudes seen in the post. You can turn the functions on and off by clicking on their name in the legend.
