Izvestiâ Akademii nauk SSSR. Ènergetika
ISSN (print): 0002-3310
Media registration certificate: ПИ № ФС 77 - 67158 от 16.09.2016
Founder: Russian Academy of Sciences
Editor-in-chief: Volkov E.P., academician RAS, Doctor of Sc., Full Professor
Frequency / Access: 6 issues per year / Subscription
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No 6 (2023)
Articles
Methods and Models for Optimal Managing of District Heating System Accounting Reliability Based on Lagrange Multiplier Method and Markov Random Process
Abstract
The main purpose of the study is to determine the optimal condition of the district heating system functioning while minimizing the operating costs for the production and distribution of thermal energy, accounting the expected economic damages from possible heating undersupplies in case of failures of system components. To identification the parameters corresponding to these conditions, a methodological approach is proposed, which consists in the comprehensive calculation of nodal prices for thermal energy and reliability indices for the studied system when different component failures. The determination of nodal prices for thermal energy is based on the Lagrange multiplier method, while the calculation is carried out accounting the different cost of production at heating sources and the distribution of thermal energy flows on the heating network. Within the framework of the studied methodological problem, heating undersupplies to consumers in emergency conditions of the system and the corresponding economic equivalents (damages) are used as reliability indices. Assessment of probabilities of emergency conditions (states) is carried out using models of the markov random process. The general methodological basis for modeling thermal-hydraulic conditions in the system, including emergency ones, are the models of the theory of hydraulic circuits. The developed methods and models, along with the main formulated problem of optimal managing, allow identifying “bottlenecks” in the studied system, corresponding to the maximum economic damages from heating undersupplies to consumers based on obtained reliability indices. A computational experiment was carried out using the proposed methodology. The results are analyzed, their graphical interpretations are presented, and directions for further research are formulated.
3-16
Method for Creating Mathematical Models of Heating Nuclear Power Units of Power Plants for Optimization Studies of Autonomous Electric Power Systems
Abstract
The authors present a two-stage method for creating mathematical models of cogeneration nuclear power units for optimization studies of autonomous electric power systems. The first stage of the methodology includes the development of a detailed model of a nuclear power unit, which provides a satisfactory accuracy of the description of physical and technological processes, as well as optimization calculations of operating modes. At the second stage, the energy dependencies are built based on the results of optimization calculations of the first stage. Energy dependencies define the boundaries of the region of feasible solutions in the form of polynomials. A simplified mathematical model of a nuclear power unit for optimization studies of autonomous EPS is created using polynomials. To solve the problem of finding a polynomial, a two-step approach is proposed. At the first step, the polynomial coefficients are selected such that the minimum of the maximum value of the modulus of the difference between the function determined using the polynomial and the function determined using the detailed model of the power unit is reached. At the second step, the deviation modules are limited to the value found at the first step, and the sum of the deviation modules is minimized at all points. The two-stage technique developed by the authors is demonstrated on the example of a cogeneration nuclear power unit, which is supposed to be operated in the climatic conditions of the Far North.
17-30
Energy-Mass and Thermoelectric Characteristics of the Current Convertor, Made on the Devices of Plasma Electric Power Industry
Abstract
In space power propulsion systems (SPPS) based on a low-voltage power source and high-voltage electric rocket thrusters, a current conversion system (CCS) is required. As one of the elements of promising high–temperature CCS, high-temperature plasma thermal emission valves (HPTV) of plasma electric power industry are considered – grid key elements (GKE) and high-voltage plasma thermal emission diodes (HVPTD). In the work, the modeling of the energy-mass characteristics of the CCS built on the GKE and HVPTD using heat pipes (HP) for cooling is carried out, the temperature conditions in which the minimum specific mass of the current converter is achieved are determined. The specific gravity values are determined. The results of the work can be used in the development of new high-temperature CCS space power propulsion systems for electrical power from tens to thousands of kilowatts.
31-43
New Analytical Solutions of Mathematical Models of Heat Shock of Local Non-Equilibrium Heat Transfer
Abstract
The article is devoted to practically new model representations of locally nonequilibrium heat transfer in terms of nonstationary heat conduction for hyperbolic type equations (wave equations), as well as dynamic models of heat shock based on wave equations. The results presented in the article practically open up an independent scientific direction in analytical thermal physics and in the theory of thermal shock, namely: the study of the thermal response of solids of a canonical form of finite sizes to intense heating and cooling under conditions of a locally nonequilibrium heat transfer process. This direction required the development of a special apparatus of operational calculus due to the appearance in analytical solutions of model problems in the image space according to Laplace of non-standard operational images, the originals of which are unknown and are not available in reference books on operational calculus. The presented images are typical for operational solutions of a wide class of generalized boundary value problems for equations of hyperbolic type in the theory of heat conduction, diffusion, hydrodynamics, vibrations, propagation of electricity, thermomechanics and other areas of science and technology. Illustrative examples of analytical solutions of specific model problems of locally nonequilibrium heat transfer and the theory of thermal shock for a finite region are given in both classical and generalized formulations (the latter taking into account the finite rate of heat propagation). The characteristic features of functional structures as analytical solutions of the considered mathematical models are revealed.
44-60
Vapor Bubble Growth in a Superheated Liquid (Pressure Blocking Effect)
Abstract
The vapor bubble growth problem in a superheated liquid is considered. The Stefan number in the metastable region us evaluated. The asymptotics of the “thermal explosion” is investigated in the framework of the energy thermal scheme. The “pressure blocking” effect is show to occur if the Stefan numbers exceeds 1. An analytical solution is obtained for the bubble growth law in a liquid with energy spinodal temperature. A numerical study of butane bubble growth in the near-spinodal region is performed. A comparison of the solution with the experimental results on the boiling of a butane drop is given.
61-78