Complex power polynomials for solving the problem of identifying linear circuit parameters

The identification of parameters of linear electrical circuits refers to the problems of analysis and inverse problems of electrical engineering. Modern research in this field mainly boils down to determining the impulse response and/or the transfer function of an electrical circuit. The tasks of identifying the parameters of linear electrical circuits are usually limited to identifying two or three linear components connected in series and/or in parallel, or as T- and U-shaped fourpoles. In this case, the parameters are identified by examining the circuit in short-circuit and idle modes. There are also several particular solutions to the problem of identification at a given frequency. In this paper, we propose a solution to the problem of identifying the parameters of linear electrical circuits using polynomials expressing complex power and additional equations. To solve the problem of identifying the parameters of a passive linear bipolar, a method has been developed for synthesizing basic equations using the difference in complex power, calculated analytically and calculated as a result of instrument measurements and represented by an interpolation polynomial. A method for synthesizing additional equations based on the frequency derivatives of complex resistance and complex conductivity has been developed. The upper bound of the number of independent equations is estimated as the power of the set of degrees at a circular frequency, which is part of the polynomial under study. Estimating the largest number of independent equations will allow us to conclude that the problem is solvable using the basic equations, as well as the need to form additional equations. The solutions to the problem of identifying the parameters of linear passive electrical circuits are implemented numerically using computer algebra. The practical application of the developed methods is shown by the numeric example. As an example of the application of the proposed methods, the solution of the problem of determining the parameters of all elements of an electrical circuit is shown. The simulation is implemented in the Wolfram Mathematica software environment. The proposed solution, unlike the known approaches, allows us to determine the parameters of the components of linear passive electrical circuits (bipolar). For the first time, a method for synthesizing equations based on differences in complex power obtained as a result of analytical calculations and instrument measurements is proposed. The method of synthesizing additional equations by differentiating complex resistances and conductivities by frequency makes it possible to obtain relatively simple forms of equations. Such equations can be synthesized in advance for the most common typical schemes.