# [Equation Validity] - Current Characterization (AC) in Sockets

• HAgdn
In summary, the equation only contains sinusoidal waves and there is the possibility of multiple frequencies and phases. However, it is not a valid or correct use of the concept of Fourier in this scenario. The AC Mains voltage may have distortions and noise, and the current drawn by nonlinear loads may contain harmonic content. It may be more accurate to use a Fourier series for each load instead of one single frequency per load as written.
HAgdn
Homework Statement
I am trying mathematically characterize the current running a wire connected to the AC mains. This wire has a socket and can take n number of loads linear/non-linear load.

I assumed this:

Considering that the loads have different current draws and the possibility of non-linear load. And the current running through the wire is the sum of the draw current of the loads (is this valid to say?). Since the overall current running through the wire is the sum of all the draw current of the loads (which is periodic), then, Fourier's theorem can be applied by which the theorem states that a wave is composed of sinusoidal components having a proper amplitude and frequency. And such wave is the "REAL" current running through the wire when loads are connected.
Relevant Equations
Through my assumption, what I got is:

I = A_0 * sin(n_0wt + p) + A_1 * sin(n_1wt+p) + ... +A_n * sin(n_nwt+p)

Where:

I = current running through the wire connected to the AC mains whose socket whose socket has loads connected.

A_n = the draw current of an nth load

w = angular frequency

p = phase shift
I = A_0 * sin(n_0wt + p) + A_1 * sin(n_1wt + p) + ... +A_n * sin(n_nwt + p)

Looking at the equation, it only contains sinusoidal waves. Further, there is the possibility of waves having the same shift or no shift at all and even, having the same frequency. Is it really valid or correct to use the concept of Fourier in this scenario? I am trying to use the equation in a study of mine.

HAgdn said:
$$I = A_0 * sin(n_0\omega t + p) + A_1 * sin(n_1\omega t + p) + ... +A_n * sin(n_n\omega t + p)$$
Looking at the equation, it only contains sinusoidal waves. Further, there is the possibility of waves having the same shift or no shift at all and even, having the same frequency
When I look, I see
• Only a single ##p##, so all loads show the same phase lag ?
• multiple frequencies, which is strange: the mains only has one frequency
So: no, I don't think you are on the right path. Advice: read up on AC circuit analysis.

BvU said:
multiple frequencies, which is strange: the mains only has one frequency
The AC Mains voltage does have some low-order distortions and noise, but even assuming a perfect sinusoidal voltage, the current I(t) will depend on the load. If the load is non-linear, that can generate harmonic content in the I(t) waveform.

A good example is the current drawn by the common full-wave rectifier input stage for many power supplies:

https://www.researchgate.net/profile/Pablo_Lezana_Illesca/publication/3218408/figure/fig7/AS:668537572057093@1536403186524/Single-phase-rectifier-a-Circuit-b-Waveforms-of-the-input-voltage-and-current.png

BvU said:
multiple frequencies, which is strange: the mains only has one frequency
Since the loads are nonlinear the current will not be a pure sine wave. According to M. Fourier that means there will be harmonics.

The way it was written, OP postulated one single frequency per load. I agree a Fourier series per load makes more sense

berkeman

## 1. What is AC current characterization in sockets?

AC current characterization in sockets is the process of measuring and analyzing the electrical characteristics of a socket or plug, specifically during the transmission of alternating current (AC) power. This allows for the evaluation and validation of the socket's performance and safety.

## 2. How is AC current characterization performed?

AC current characterization is typically performed by connecting the socket to a power source and using specialized equipment to measure and record the electrical parameters, such as voltage, current, power, and frequency. This data is then analyzed to determine the socket's compliance with industry standards and specifications.

## 3. Why is AC current characterization important?

AC current characterization is important because it ensures the safety and reliability of electrical devices that use AC power. By accurately characterizing the current in sockets, potential hazards such as short circuits, overloading, and overheating can be identified and prevented.

## 4. What are the common parameters measured during AC current characterization?

The common parameters measured during AC current characterization include voltage, current, power, frequency, and power factor. Other parameters that may be measured include temperature, insulation resistance, and contact resistance.

## 5. What are the industry standards for AC current characterization in sockets?

There are several industry standards for AC current characterization in sockets, including IEC 60320, UL 60950, and CSA C22.2 No. 60950. These standards specify the requirements for the electrical and mechanical properties of sockets, as well as the testing methods for AC current characterization.

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