This paper presents an electrical circuit connected to a non-sinusoidal power
source. In real consumers of electrical energy, due to the presence of parametric elements,
the shape of the voltage and current curves distort the shapes of these function curves at the
receivers, resulting in additional energy losses and a reduction in their efficiency. Graphical,
graph-analytical and analytical methods are used to calculate such schemes. A polynomial
approximation method for numerical integration of the function is applied as an
analytical solution, since any continuous function can be approximated with any
precision within any closed interval by a polynomial of sufficiently high degree. We
describe the classical Wee strass theorem for approximation. Graphical
representations of the geometrical interpretation of the multistep method and a
general view of the multistep formula for numerical integration of order "k" are
shown. The term numerical integration is introduced because methods of this type
are similar to those used for numerical integration of functions. The order of a
numerical integration method refers to the maximum degree of polynomial solution
in which the formula gives the exact value for x(t n+i) in the absence of rounding
error.
This paper presents an electrical circuit connected to a non-sinusoidal power
source. In real consumers of electrical energy, due to the presence of parametric elements,
the shape of the voltage and current curves distort the shapes of these function curves at the
receivers, resulting in additional energy losses and a reduction in their efficiency. Graphical,
graph-analytical and analytical methods are used to calculate such schemes. A polynomial
approximation method for numerical integration of the function is applied as an
analytical solution, since any continuous function can be approximated with any
precision within any closed interval by a polynomial of sufficiently high degree. We
describe the classical Wee strass theorem for approximation. Graphical
representations of the geometrical interpretation of the multistep method and a
general view of the multistep formula for numerical integration of order "k" are
shown. The term numerical integration is introduced because methods of this type
are similar to those used for numerical integration of functions. The order of a
numerical integration method refers to the maximum degree of polynomial solution
in which the formula gives the exact value for x(t n+i) in the absence of rounding
error.
| № | Author name | position | Name of organisation |
|---|---|---|---|
| 1 | Abidov K.G. | teacher | TSTU |
| 2 | Rakhmatullayev A.I. | teacher | TSTU |
| № | Name of reference |
|---|---|
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| 15 | K.G. Abidov., A.I. Rakhmatullaev. “Investigation of an electromagnetic vibrationexcitation device with a series-connected capacitor in an electric circuit”, 2018. 58 |
| 16 | K.G. Abidov., A.I. Rakhmatullaev. “Possibility of application of a reciprocity principle at conversions of currents and voltages on the nonlinear four-poles”, 2019. 80 |