Linear power networks - Definitions, principles, methods

The aim of the first part of this article is to define the various elements that make up an electrical network, and the models that represent them. Each model involves the current i(t) flowing through the element under consideration and the voltage v(t) (or potential difference) across its terminals, both functions of an independent variable: time t. Even though each model must remain independent of the actual size of the physical component, it must be borne in mind that the quantities v(t) and i(t) are always assumed to be below their limit values, depending in particular on the component manufacturing method, the material used and the intended field of application. A resistor, for example, can be designed to dissipate a power of a quarter of a watt or several tens of kilowatts; in both cases, the model is the same and its use assumes that the network in which it is used imposes a current below the limit value it is capable of withstanding. Furthermore, the behavior of the various electrical elements of a network cannot be reduced to the relationship between currents and voltages. The notion of electrical power is also fundamental. Under this general term are hidden notions as different as active, reactive, fluctuating or apparent power, which must be precisely defined and, above all, physically interpreted.

Models involving time functions are simple in themselves, but not always easy to apply. The Laplace transformation leads to a form that is easier to exploit, where the variable is no longer directly time. This transformation also leads to the notion of transfer function, which is particularly rich in applications. This is the subject of the second part.