As far as we know, until the end of the nineteenth century there were neither relayers nor relay protection as such. But electric power and electrical engineering already existed at that time. And short circuits obviously happened periodically. What then protected the electrical equipment from electrical damage?

## The essence of the Fourier transform

The content of this note reveals the questions of how and why the Fourier transform known to all power engineers works. Here we tried to refrain from using a complex conceptual apparatus, all the calculations used should be clear to anyone who has somehow mastered the initial level of the university course in higher mathematics. For all others, it is possible that the material presented is intuitive.

## Phase Coordinates Method: An Example of Compiling a Network Model

Consider an example of compiling a power transmission model using the phase coordinate method. In fig. 1 shows the power transmission, a mathematical model of which must be compiled. It is necessary to determine the currents in the short circuit mode at the beginning of the line.

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## Phase Coordinates Method: Short Circuit with Break Model

Some complex types of damage can occur in power lines, for example, a short circuit with a wire break. This mode can occur when a wire of any phase falls to the ground (Fig. 1).

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## Phase Coordinates Method: Break Model

During operation of electric power systems, not only short-circuit modes can occur, but also breaks. The phase coordinate method allows you to simulate wire breakage.