The wheel of misfortune of electric meters

All the old-fashioned electricity consumption meters, known as “electromechanics”, are gradually being replaced by “communicating” digital meters, the famous Linky. This is an opportunity to discover the working principle of these new meters, but also, before their complete disappearance, the old ones. And answer the disturbing question that many of us have asked ourselves: what makes the metal disk of these spinning and why does its spinning speed explain the power consumption?

In principle, nothing is simpler than determining the electrical power consumed by a device: it is the product at each instant of the value of the electrical voltage (U) at its terminals by the value of the electric current flowing through it (I). ). In practice, for example for a lamp, the voltage is determined simultaneously by a voltmeter placed in bypass and the current flowing through the device by introducing a series ammeter into the circuit. The power U x I is then calculated by hand or with a machine. This is exactly what modern electricity meters do.

© Bruno Vacaro

They are located between the arrival of the external power line and the domestic installation. Two analog / digital converters translate current and voltage into numbers that are then multiplied. In a Linky counter, this operation is performed thousands of times per second. The total energy consumed, expressed in kilowatt hours, is then the sum of all measured values ​​multiplied by the time between two successive measurements. Digitization greatly facilitates power measurement. But how did the electromechanical meters do the same thing, in a totally analog way, without an electronic chip?

Seen from the outside, the operation seems to depend on a thin toothed metal wheel whose edge we see and which rotates faster as the power consumption is high. To understand how this is possible, we open the device.

© Bruno Vacaro

A vertical shaft passes through the aluminum metal wheel. Operates the display mechanism by means of a pinion when the disc rotates. No electrical contact connects the disk to the circuit: on the other hand, we can see the presence of a horseshoe magnet whose poles frame the wheel, and electromagnets formed by coils of wire surrounding a soft iron core. Therefore, there is magnetism in the air.

According to what physical principle do the disk animate the magnetic fields created by these different magnets? Through induced electric currents: eddy currents. These currents appear as soon as an electrical conductor is in a magnetic field that varies over time. This corresponds to several situations: alternating current powered electromagnets, movement of a magnet near a conductor or, strictly speaking, movement of a conductor in a static magnetic field (independent of time) but not homogeneous (which varies in space). .

Induced currents and magnetic brakes

An experiment allows us to grasp the essence of this phenomenon. Consider a moving conductor relative to a magnet. For example, the counter-wheel, which when rotated sees a part of its periphery move in the air gap of the horseshoe magnet. If we move with the driver (the wheel), we find that, above him, moves the region where the magnetic field is. At the edge of this zone, the magnetic field changes rapidly. For example, in the region where the wheel exits the air gap of the magnet, the magnetic field decreases until it vanishes. This results in a conductor-induced current loop, the Foucault current, half of which is in the magnetic field of the magnet and the other half is outside.

current meter

© Bruno Vacaro

However, a magnetic field exerts a force on an electric current, the Laplace force, a force perpendicular to both the current and the magnetic field. Since only half of the current loop is in the magnetic field, the total force experienced is not zero. Given the geometry, this force opposes the speed of travel and therefore tends to slow down the driver. This result is in accordance with Lenz’s law, named after the German-Baltic physicist Heinrich Lenz, who states that the effect of induced current is to oppose variations in the magnetic field (here caused by the relative motion of the magnet and the conductor). The same goes for the area where the driver enters the air gap. Since the current is proportional to the rate of change of the magnetic field, which here is related to the speed of the conductor, this is also the case with the braking force. In doing so, here we have made a Foucault current brake like the ones found on trucks! The faster the driver goes, the harder the braking will be.

We can now analyze the effect of the coils present in the counter. How do they feed? As in the digital meter, the cables that power these coils are connected like the voltmeter and ammeter respectively. The lower device consists of two coils made with a very good electrical conductor and very little winding (and therefore also an insignificant electrical impedance) around a horseshoe-shaped soft iron core. They are connected in such a way that part of the current passes through them. This results in two areas of magnetic field proportional to the current and in opposite directions.

The upper coil consists of a very large number of turns and is connected to take the voltage. The voltage applied to the terminals of this coil is the source of an electric current. But when you connect a coil, the current does not appear instantly: it increases (or decreases) in proportion to the value of the voltage. The end result is, therefore, a zone of magnetic field located between the two zones created by the lower coils, and where the magnetic field is “out of phase” a quarter of a period with respect to the other two.

What happens when we operate an appliance in our apartment? Oscillating magnetic fields will be created in three contiguous areas that partially overlap. If we look at the geometry of this field and its evolution over time, we see that it seems to advance from one area to another and always in the same direction. In other words, it’s like moving a magnet on the surface of the conductor. Now, just as a fixed magnet slows down a moving conductor, a moving magnet sets a moving conductor. In detail, the mechanism is the same as that of braking: the current created by one of the magnetic field zones suffers a force from the magnetic field present in the adjacent zone. We are therefore convinced that the force is effectively proportional to the product of the fields created in the adjacent areas and, therefore, to the product of the current by the voltage, therefore. in short to power. The wheel is so light that this driving force is permanently compensated by the braking force due to the horseshoe magnet: the speed of the wheel (respectively the distance traveled or the number of revolutions it makes) is ultimately proportional to the driving force, that is. to power (respectively to energy consumed). We also find the proportionality constant clearly inscribed on the old counters. You have to hurry to look at them one last time, because more than 8 out of 10 French people are already equipped with the Linky counter!

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