Alternative course

See also: Alternative course (re-examined)

The alternative course (which can be shortened by CA , the unsuitable term AC , for Alternating Current in English, being however often used) is a Electric current which changes direction.

This alternative course is known as periodical if it changes regularly and periodically direction.

A periodic alternative course is characterized by its frequency, measured in Hertz (Hz). It is the number of “return tickets” which the electric current in one second carries out. A periodic alternative course of 50 Hz carries out 50 “return tickets” a second, i.e. it changes 100 times (50 outward journeys and 50 returns) of direction a second.

The most used form alternative course is current the sinusoidal, primarily for the commercial distribution of electrical energy.

The frequency of the electric current distributed by the networks to the private individuals is generally of 50 Hz in Europe and 60 Hz in North America.

One must distinguish:

• the purely alternating currents whose median value (component continues) is null, which can feed a transformer without danger.

• the alternative courses with component continues nonnull which cannot in no case to supply a transformer.

History

See History of electricity

With the the United States, Nikola Tesla in 1882 designs the alternator Triphasé. In parallel, in France, Lucien Gaulard invents the transformer. These two inventions make it possible to overcome the limitations imposed by the use of the D.C. current for the distribution of the electricity then recommended by Thomas Edison which had deposited many Brevet S in connection with this Technologie (and had distribution networks of D.C. current).

The advantages brought by the transport and the distribution of the electrical energy by alternative courses are undeniable. The industrial Westinghouse, holder of the patents, ends up imposing it on the United States.

Advantages

Contrary to the D.C. current, the purely alternating current can see its characteristics (tension/running) modified by a transformer with enroulements.
As soon as there exists a considerable continuous component, a transformer is unusable .

Thanks to the transformer:

• the current transported by distribution networks high voltage sudden of the losses by Joule effect much weaker. Into dividing simply by 10 the intensity of the transported current, one divides by 100 the losses due to the resistance of the electric cables, the power dissipated in a resistance being proportional to the square of the intensity of the current. ( P = IH)
• At constant power, one can strongly reduce the intensity of an alternative course by increasing its tension.
• One lowers then the tension in order to provide a food in low tension close to the place of distribution, in order to be able to use it with fine servants (the danger remaining however quite real, even in low tension).

Sinusoidal alternative courses

A sinusoidal alternative course is a sinusoidal Signal of homogeneous size to a running (expressed in amp S). In a strict way, its continuous component must be null to qualify it the alternate one, the sinusoid will thus have a median value equalizes to zero.

Explanation from a mathematical point of view

The current thus has an equation of the type: $i\; (T)\; =\; A.\; \backslash \; sin\; (\backslash \; frac\; \{2\; \backslash \; pi.\; T\}\; \{T\}\; +\; \backslash \; varphi)$ , or $i\; (T)\; =\; A.\; \backslash \; sin\; (2\; \backslash \; pi.\; F.\; T\; +\; \backslash \; varphi)$ , since $f\; =\; \backslash \; frac\; \{1\}\; \{T\}$, with $A\; \backslash ,$ the amplitude of the signal, $T\; \backslash ,$ the period of the signal expressed in seconds, and $\backslash \; varphi\; \backslash ,$ dephasing, or phase in the beginning, expressed in radians.

Generally one summarizes this equation with $s\; (T)\; =\; A.\; \backslash \; sin\; (\backslash \; omega.t\; +\; \backslash \; varphi)$, with $\backslash \; Omega\; \backslash ,$ the pulsation (expressed in rad/s) which thus corresponds to our $2.\; \backslash \; pi.f\; \backslash ,$ or $\backslash \; frac\; \{2.\; \backslash \; pi\}\; \{T\}$.

In a strict way, a sinusoidal alternative course is as much of time (T/2) positive that negative, which implies that its component continues is null. The sinusoid will thus oscillate in a way balanced around 0, implying a median value (mathematically) null, and a effective Valeur (electrically) of $\backslash \; frac\; \{has\}\; \{\backslash \; sqrt\; \{2\}\}$.

Here an example of sinusoidal signals.

One says these two signals which they are identical but out of phase of $\backslash \; pi$. Between their two equations, there is thus only the dephasing (or phase in the beginning) which differs.

Actually, the important thing is that the difference of the phases in the beginning is worth $\backslash \; varphi\_\; \{blue\}\; -\; \backslash \; varphi\_\; \{red\}\; =\; Z\; \backslash \; pi$ with $z\; \backslash ,$ an odd entirety, since such a dephasing ($\backslash \; pi$ radians corresponding to 180 degrees) corresponds to a shift of a half-turn on the trigonometrical circle. One thus associates with a signal, the opposite value of the other, because $\backslash \; sin\; (X\; +\; Z.\; \backslash \; pi)\; =\; -\; \backslash \; sin\; (X)$. When the blue signal is to the maximum, the red is at least, etc One thus notices that the two signals are opposite, i.e. symmetrical by the x-axis.

Single-phase current

The current Monophasé is used the most. It uses two cables: the phase and the neutral (generally connected to the ground with the last transformer, like the neutral of the three-phase current).

Three-phase current

Only the polyphase alternator S are likely to provide a high power. It is current the Triphasé which is used for the industrial production of electricity. The three-phase power supply uses four cables, for each one of the three phases, and a cable for the neutral. Each cable is traversed by a sinusoidal alternative course out of phase of 2$\backslash \; pi$/3 radians (120 degrees) compared to the two other cables. The neutral is generally connected to the ground at the beginning, it is thus not a cable of transport, on arrival it is simply recreated by a star coupling of secondary three-phase rollings up of the transformer of distribution low tension (230/400 volts). This neutral is again connected to an earth electrode at the places where that is necessary.

Other systems

The 19th century and the beginning of the 20th century were very prolix in the types of alternative courses. One can quote:

• two-phase System: single-phase current with a point medium
• quadriphasé System (4 or 5 wire): phases with 90 degrees
• diphasic System (3 wire): system resulting from quadriphasé with shift of the neutral.

The systems of frequencies were also varied. In France, one can quote the 25 Hz in South-west and the 42,5 Hz in the area of Nice.

Simple: Alternating current

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