Determination of optimal current in the non-ideal one-phase system with unsteady parameters

Some of parameters in electrical systems cannot be considered as constants. In particular, some electrical loads should be described as unsteady because of physical reasons, e.g. arc and arc-resistance furnaces. One of the method to describe parameters of such loads is description by fuzzy numbers. Moreover, this description enables to determine optimal current of the system with unsteady parameters by an application of the optimisation technique called as fuzzy mathematical programming. The optimisation problem has been presented for one-phase system with sinusoidal waveforms. The obtained solution (optimal current) can be determined as crisp one (real numbers) in frequency domain in the numerical way. The determined optimal current has minimal RMS value in this case when the power constraints do not have to be fulfilled strictly because of changes of system parameters. It means simultaneously the minimisation of power losses in the system. This solution generalizes the classical optimisation solution obtained for the systems with constant parameters. In order to illustrate the problem the appropriate example has been presented.