Vol 90, No 4 (2019)

Using multilevel topologies for a stand-alone inverter, which is a part of induction or synchronous ac drives, makes it possible to achieve their operation under some fault conditions related to, for example, the failure of any element in a power circuit or short-term blackout in operation of distribution line of centralized power supply system. In the last case, due to switching the speed loop into the mode of voltage control of capacitor filters, it turns out during short-term interval to maintain at the set level the magnetic condition and mechanical coordinates of electrical machine without direct disconnection of converter by corresponding signal feeding from a security unit. The work considers the design formulas for synthesis of special algorithms of vector control by an ac actuating motor under the absence of power supply based on the set distribution of the roots of characteristic polynomial on the complex plane. As well as the reduction of logarithmic amplitude–phase–frequency characteristic of the loop in open condition to the normalized form is presented in the work. Within the framework of these formulas, the regeneration of electric energy in the stand-alone inverter with series-connected H-bridges is carried out to stabilizing the voltage of capacitor bank in each power module owing to when workability recovery of three-phase network, the ac drive returns to normal operation without significant degradation of quality of processes by rotor rotational speed.

Simulation of the eddy-current fields in the ferromagnetic materials is impossible without information on the dependence of the magnetic field induction on its intensity—the magnetic curve. Experimental determination of the magnetization curves encounters technical problems and the reference data contain, as a rule, a small number of values and they are unsuitable for direct application. For this reason, the transition from original magnetization curve to its approximation is relevant. Three very popular approximation methods of the magnetization curves in the calculation practice are considered in this article: the Frelich approximation, the Melgui approximation, and the universal Pentegov approximation. The average deviation from the original magnetization curve, difference in the average density and the calculation error of the active power are accepted as the approximation effectiveness. The experimental data about magnetization of materials with different properties were used for comparative analysis of approximations. It is shown that the minimum error in calculation of eddy-current fields is provided by the universal approximation. Replacement of the magnetization curve by other approximations may lead to calculation errors of active power exceeding 15%. The obtained results may be used for the nonlinear finite element analysis of the eddy-current field in ferromagnetic materials.

Methods for solving linear and nonlinear equations for steady-state operation modes are important for the development and operation of electrical networks. Linear equations are solved analytically or with the use of iterative methods, while nonlinear equations are solved only with use of iterative methods, usually the Newton–Raphson method. Iterative methods have two significant drawbacks. First, the iterative process can diverge, with the divergence being dependent on both the form of the nonlinear equation and the choice of the initial approximation. Second, in the case of convergence, the iterative method allows finding only one solution for each initial approximation, whereas a nonlinear equation can have several solutions corresponding to different operation modes of the electric network. Development of methods that are free of these drawbacks is an important problem. This paper proposes a noniterative method for solving nonlinear equations describing the steady-state operation modes of electric networks; the equations are written in the complex form. The method uses the resultant to transform set of nonlinear equations to a set of polynomials. The polynomials are composed in such a way that their zeros determine one of the coordinates of the solution vector of the nonlinear equation system. Thus, the problem of solving of the nonlinear equations system is reduced to the well-studied problem of finding the zeros of one-variable polynomials. There are numerous methods of solving this problem that do not require specifying the initial approximation and allow finding all zeros. The effectiveness of the method is illustrated by solving the equations of node network voltages in the form of power balance. The equations were solved by the traditional iterative method and the proposed method using the MathCAD-15 program. The drawbacks of the iterative method are illustrated by its divergence at certain values of the initial approximation and by the failure of finding all the solutions. In contrast, the use of the proposed noniterative method allows one to find two solutions and to establish that there is no other solutions. Further development of this method will be connected with taking into account the sparseness of the matrix of conductivities that would allow reducing the degree used polynomials, as well as with the extension of this method to the domain of real values in which the equations can be written down in the algebraic and trigonometric form.