# Evgeniia Vladimirovna MarkovaMelentiev Energy Systems Institute, Russia, Irkutsk · Department of Applied Mathematics

Evgeniia Vladimirovna Markova

## About

22

Publications

520

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84

Citations

Introduction

**Skills and Expertise**

## Publications

Publications (22)

In this paper, we propose a new algorithm for constructing an integral model of a nonlinear dynamic system of the “input–output” type in the form of a quadratic segment of the Volterra integropower series (polynomial). We consider nonparametric identification of models using physically realizable piecewise linear test signals in the time domain. Th...

The paper focuses on the construction of information models for the technical energy systems' functioning. This is an urgent problem that arises in applications when describing the dynamics of systems of the "input-output" type. Constructive algorithms for solving typical inverse problems arising when evaluating the reliability of power systems are...

In this paper, we consider an approach to modeling strategies for the development of electric power systems. It is based on an integral model of developing systems. The model includes the non-classical Volterra equation of the first kind, which describes the balance between the desired level of electricity consumption and the input of generating ca...

The paper addresses the application of Volterra integral equations of the first kind for modeling dynamic power systems. We study the problem of forecasting the commissioning of capacities of the electric power system, taking into account various hypotheses about the dynamics of equipment aging, and the known prehistory. The numerical results of th...

This paper addresses an integral model of development a large electric power system using the example of the Unified Energy System of Russia. The model takes account of the age structure of the plants main equipment. Besides, generating equipment is divided into components depending on the types of energy resources used. The mathematical model is p...

The work discusses the technique for constructing an integral model of a nonlinear dynamic system with a vector input based on Volterra polynomials as applied to a section of the steam-water path of the power unit of the Nazarovo power station. The complexity of the applying the technique presented in the work is analyzed, and the number of initial...

This paper addresses an integral model of the developing system consisting of elements of n age groups. The model is described by means of the Volterra equation of the first kind with variable limits of integration. The case is considered when the moment of the system origin coincides with the beginning of the modeling, therefore there is no prehis...

The method for solution to the Volterra integral equations of the first kind
is proposed. Such equations appear in the theory of developing systems and they have kernels with discontinuities of the first kind. We construct the characteristic algebraic equation. Analytically and numerically we study the regular case when characteristic equation has...

In this study we consider an integral model of the large electric power system development. The model accounts for division of the generating equipment into certain age groups. Each of these groups is characterized by some efficiency coefficient. We consider a vector model with subdivision the equipment of the stations by fuel types. The model incl...

Our paper addresses an integral model of the large electric power system optimal development. The model takes into account the age structure of the main equipment, which is divided into several types regarding its technical characteristics. This mathematical model is a system of Volterra type integral equations with variable integration limits. The...

The paper addresses integral model of the developing system, in which the moment of its origin coincides with the beginning of the modeling, so there is no prehistory and for t = 0 all the age groups of the elements are empty.

The first part of the paper is devoted to the problem of optimal control in the area of electric power industry which is described on the basis of a one-sector variant of Glushkov integral model of developing systems. The authors consider the ways uncertain conditions of future electric power system development influence the optimal service life. T...

We develop an approach for constructing continuous solutions of integral Volterra equations of the first kind that arise in modeling developing dynamical systems. We give existence theorems for the solutions and study their asymptotic behavior. Theoretical results are illustrated with numerical computations on test examples.

The method for solution to the Volterra integral equations of the first kind is proposed. Such equations appear in the theory of developing systems and they have kernels with discontinuities of the first kind. We construct the characteristic algebraic equation. Analytically and numerically we study the regular case when characteristic equation has...

We consider integral models based on the mathematical model proposed by V.M. Glushkov. We describe a two-sector version of
the Glushkov model and consider the identification problem for model parameters. We propose a numerical identification method
and present results of test computations. We consider the problem of power grid field described with...

A problem is considered for the definition of long-term strategies of the placing in service and disassembly of electric powers
of an electric power system, which is described with the aid of nonclassical Volterra integral equations of the 1st kind.
A problem is stated of the search for optimal terms of service of generating powers that afford the...

The problem of determining long-term strategies for commissioning and decommissioning electrical capacities of a power system, described using Volterra system of integral equations of the first kind, is considered. A problem of searching for the optimum service lives of generating capacities ensuring the specified demand for electricity at minimum...

Consideration was given to the problem of determining the long-term strategies of commissioning and removing the power equipment of a power system. The problem was described in terms of the integral Volterra equations of the first kind. An algorithm to solve it by a special-purpose zero-order optimization method was proposed and realized, and reduc...

The problem of long-term strategies determination on introduction and disassembly of different parts of an electric power systems is considered. The problem is described with the help of the Volterra integral equations of the first kind. An algorithm is suggested and implemented for solving this problem with the help of the specialized optimization...

## Projects

Project (1)

The objective of this project is to get find the approximate solution of weakly regular Volterra integral equations of the first kind with jump discontinuous kernels with noisy input data (source function and kernel), also we plan to derive the optimal iterations number of method, the optimal approximation, optimal error and study the numerical instabilities. Such evolutionary integral equations enjoy non unique solutions and various applications of evolving dynamical systems, many inverse problems are formulated in terms of such equations.