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What are electrical harmonics?

If you are interested in saving and energy efficiency, you have probably heard about reactive energy. You may have heard that it reduces the efficiency of installations, that it is bad for the electrical grid, and, above all, that if you consume reactive energy, you have a penalty on your electricity bill. But what exactly is reactive energy?

Explaining the concept of reactive energy is somewhat complicated. If you look it up in a book, you will be filled with equations of complex numbers, phasor algebra, and trigonometric relationships. The problem is that with so much math, there is a risk of forgetting the physical meaning. After all, what does it mean for a dipole to absorb complex power?

So, true to the subtitle of this blog, I am going to explain what reactive energy is without using a single equation. Furthermore, I will show it to you and let you play with it. At the end of this post, you have a complete application with which to experiment. But let’s not get ahead of ourselves, and let’s take it step by step.

A review of alternating current

As is known, the electrical grid we use is actually a source of alternating voltage. In Spain, this alternating voltage has nominal values of 230V between phase and neutral and 50 Hz. This means that the voltage in our plug alternates its direction (from positive to negative, and back to positive) 50 times every second, and it does work equivalent to that of a continuous voltage source of 230V. In this post, we will use these values, although the results and conclusions are valid for any other value of the grid.

Let’s graph this voltage with respect to time, measured in electrical degrees (360º electrical degrees will be 1/50Hz = 0.02s).

When we connect an electrical load to the alternating voltage, a certain amount of electrical current begins to pass 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 energy) the load also introduces a phase shift between current and voltage. This means that the current wave will lead or lag behind the voltage wave in time. This phase shift, which we will measure in electrical degrees, is what generates reactive energy.

But, what causes the voltage and current waves to be out of phase with each other? To explain this, we have 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, coils, and capacitors. Let’s look at the characteristics of each of them.

  • Resistors (resistive loads): Any element through which electricity flows offers a certain resistance to being crossed by the current. When crossed by the current, resistors dissipate energy. As an example of large resistances, we can cite the thermal resistors used to generate heat, but it should be noted that every connected load (electrical lines, lighting, motors, etc.) presents a resistance.
  • Coils (inductive loads): A coil is formed by an electrical conductor wound around a ferromagnetic core. When a current passes through it, it generates a magnetic field inside it. This magnetic field stores energy and opposes changes in the value of the electrical current. Coils are a fundamental part of multiple machines, for example in motors, transformers, and 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 it. This electric field stores energy and opposes changes in voltage. Unlike coils, large capacitors have little application in electricity. Their main use is in batteries to compensate for the reactive effects produced by the coils.

Resistors are passive elements that do not generate a phase shift in the current. However, coils and capacitors are reactive elements that generate, respectively, magnetic and electric fields. These fields have a certain “inertia” to be created or destroyed, and this “inertia” introduces phase shifts in the current. Both elements produce opposite effects on the current; coils introduce positive phase shifts, and capacitors negative phase shifts.

However, real loads are never “pure” but present an intermediate behavior between passive and reactive loads. To characterize real loads, we use the phase shift angle they introduce between voltage and current. A pure resistance is a load of 0º, a coil a resistance of 90º, and a capacitor -90º. Mixed behaviors present phase shift values intermediate between these limits.

In the following graphic, you can move the slider, modifying the behavior of the load, and observing 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 energy? To see the effect it has on the load, we will calculate the power consumed by a load, which we obtain simply by multiplying the voltage and the current at each instant of 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 with twice 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 is always fulfilled, for any type of connected load. The effective power value over time is the average of this power, which is shown with the line Smed.

Now, change the angle of the load and observe how the power wave S(t) starts to take negative values at certain times. Indeed, the load absorbs power during part of the time and returns it to the grid during another. Meanwhile, the average power Smed decreases. At the extreme values of -90º or 90º, corresponding to pure inductive or capacitive loads, the value Smed is zero. In these pure cases, the load absorbs energy during half a period and returns exactly the same energy during the next half period.

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 the power that the load actually absorbs.

  • The real power P(t) is the part of the power that pulses in phase with the voltage. This power, generated by the resistive elements of the load, is the one that actually does useful work.
  • The reactive power Q(t) is the power component that pulses at 90 or -90º. It is generated 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 depending on the angle.

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We have seen that the reactive elements of an electrical load introduce phase shifts between voltage and current. This phase shift is caused by 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 take on negative values, so the load gives up power for part of the time.

Reactive power is the power component that pulses at 90º with the voltage. The net work it does over time is zero. The energy absorbed in one half period is stored within the load in the form of a magnetic or electric field and is fully returned in the following half period. In contrast, active power is the component that pulses at 0º with the voltage and is the one that does effective work over time.

In a future post, we will see the negative effects of reactive power on an electrical grid and address certain myths and truths related to reactive energy in the field of energy efficiency.

To conclude, I leave you the complete graph with all the magnitudes seen in the post. You can turn on and off the functions you wish by clicking on their name in the legend.