Control of Power Grid Development: Numerical Solutions

Иванов, Д. В.; Karaulova, I. V.; Markova, E. V.; Trufanov, V.V.; Khamisov, Oleg V.

doi:10.1023/b:aurc.0000019380.88379.d9

Cited by 12 publications

(8 citation statements)

References 1 publication

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“…The solution ϕ for N(s 0 , s 0 − s 1 ) ∈ ∆ 2 is denoted by ϕ (2) . The continuity of ϕ on Ω 1 ∪ Ω 2 implies conditions ( 27)-( 29), (32). Repeating this process N times, we obtain ( 27)-( 29), (32) on the entire domain Ω, since Ω = ∪ N+1 k=1 Ω k .…”

Section: And πmentioning

confidence: 88%

“…In following works [32][33][34][35][36], mathematical models of the development of generating capacities of EPS were considered with different degrees of aggregation by power plant types. There are estimated models (analysis of the consequences of a given strategy for renewing capacities), optimization ones (optimization of the capacities lifetime), and models that describe the processes of extending the lifetime of generating equipment (modernization).…”

Section: Integral Models Based On Volterra Equations Of the First Kindmentioning

confidence: 99%

“…1 gives ( 27) and (32), and the continuity of ϕ (0) on Ω 0 additionally implies (28) and (29). We denote ϕ for N(s 0 , s 0 − s 1 ) ∈ ∆ 1 by ϕ (1) .…”

Section: And πmentioning

confidence: 99%

See 2 more Smart Citations

Integral Models Based on Volterra Equations with Prehistory and Their Applications in Energy

2021

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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 the application of two models to the problem of the development of a large electric power system using the example of the Unified Energy System of Russia are presented. Theoretical results were formulated for a two-dimensional Volterra integral equation of the first kind with variable limits of integration. This class of equations arises when solving the actual problem of identifying variable characteristics of a nonlinear dynamic system of the “input-output” type.

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Section: And πmentioning

confidence: 88%

Section: Integral Models Based On Volterra Equations Of the First Kindmentioning

confidence: 99%

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Integral Models Based on Volterra Equations with Prehistory and Their Applications in Energy

2021

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“…Mathematical models of generating capacities development of electric power system are considered in the works [3,16,17,21,22]: models with different degrees of aggregation by types of power plants, estimation models (analysis of the consequences of the specified capacity upgrading strategy) and optimization ones (optimization of the capacities lifetime), models with describing the processes of prolonging the lifetime of the generating equipment (modernization) or without it.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of the age structure optimization problem for basic types of power plants

Markova

Sidler

2019

Yugosl J Oper Rres

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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 system describes the balance between the given demand for electricity, the commissioning of new equipment and the dismantling of obsolete equipment, as well as the shares of different types of power plants in the total composition of the electric power system equipment. Based on the developed model, we got numerical solution to the problem of finding the optimal strategy for replacing equipment with a minimum of the cost functional. The case study is the Unified Electric Power System of Russia. Calculations of the forecast for development of the electric power system of Russia until 2050 were made using real-life data.

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“…In particular, a one-sector version of the Glushkov's model applied to the power engineering problems was considered in [10][11][12]. In the recent years the researchers have got attracted by the equation (see [13] and references therein) that in a general case has the following form:…”

Section: Introductionmentioning

confidence: 99%