A mathematical model for the virtual simulator of the power unit electrical part

The mathematical model is developed for a virtual training system (simulator) of the power unit electrical part operators of a thermal (nuclear) power plant. The model is used to simulating the main operating conditions of the power unit electrical part: generator idling, generator synchronization with the power system, excitation shifting from the main unit to the backup one and vice versa, switching in the power unit auxiliary system, and others. Furthermore, it has been implemented modelling some probable emergency conditions within a power plant: incomplete phase switching, damage to standard power unit equipment, synchronous oscillations, asynchronous mode, etc. The model of the power unit electrical part consists of two interacting software units: models of power equipment (turbine, generator with excitation systems, auxiliary system) and models of its control systems, automation, relay protection and signalling. The models are represented by the corresponding algebraic-differential equations that provide real-time mapping power unit processes at the operator’s request. The developed model uses optimal solving algebraic-differential equations to ensure the virtual process behaviour in real-time. In particular, the implicit Euler method is used to solve differential equations, which is stable when simulating processes in significant disturbances, such as accidental disconnection of the unit from the power system, tripping and energizing loads, generator excitation loss, etc.

On One Class of Algebraic Differential Equations

The article addresses second-order algebraic differential equations that have a separated linear part and admit a finite-order integer function as a solution. All possible integer solutions of such equations are described. It is shown that all solutions are the solutions of certain second-order linear differential equations the coefficients of which are represented by rational functions. It has been demonstrated that any such integer function y = f(z) is either a solution of the algebraic equation R(z, exp{Q(z)}, y) ≡ 0 (where R is a polynomial of three variables, and Q(z) is a polynomial of one variable), or a solution of a differential equation with separable variables y′ = a(z)y (for some rational function a(z)).

Characteristic sets verses generalised characteristic sets for ordinary differential polynomial sets

The concept of characteristic sets developed initially by Ritt and Wu has turned into a standard tool for the study of sets or systems of polynomial and algebraic differential equations. With the help of constructing characteristic sets, an arbitrary set or system of polynomials or differential polynomials can be triangularised. It means that it can be decomposed into a particular set or system of triangular forms. In this paper, a comparison of Ritt–Wu’s characteristic sets by Wang for the ordinary differential polynomial sets with the generalised characteristic sets of the ordinary differential polynomial sets by the authors has been presented. Keywords: Characteristic set, differential polynomial, pseudo-division, admissible reduction.