Valery Stennikov

Optimum load distribution between heat sources based on the Cournot model

One of the widespread models of the heat supply of consumers, which is represented in the “Single buyer” format, is considered. The methodological base proposed for its description and investigation presents the use of principles of the theory of games, basic propositions of microeconomics, and models and methods of the theory of hydraulic circuits. The original mathematical model of the heat supply system operating under conditions of the “Single buyer” organizational structure provides the derivation of a solution satisfying the market Nash equilibrium. The distinctive feature of the developed mathematical model is that, along with problems solved traditionally within the bounds of bilateral relations of heat energy sources-heat consumer, it considers a network component with its inherent physicotechnical properties of the heat network and business factors connected with costs of the production and transportation of heat energy. This approach gives the possibility to determine optimum levels of load of heat energy sources. These levels provide the given heat energy demand of consumers subject to the maximum profit earning of heat energy sources and the fulfillment of conditions for formation of minimum heat network costs for a specified time. The practical realization of the search of market equilibrium is considered by the example of a heat supply system with two heat energy sources operating on integrated heat networks. The mathematical approach to the solution search is represented in the graphical form and illustrates computations based on the stepwise iteration procedure for optimization of levels of loading of heat energy sources (groping procedure by Cournot) with the corresponding computation of the heat energy price for consumers.

Optimal Expansion and Reconstruction of Heat Supply Systems: Methodology and Practice

The paper addresses the issue of optimal expansion and reconstruction of heat supply systems, which includes a set of general and relatively specific problems. Therefore, a comprehensive approach to their solving is required to obtain a technically admissible and economically sound result. Solving the problem suggests search for effective directions in expansion of a system in terms of optimal allocation of new heat sources, their type, output, operating area; construction of new heat networks, their schemes and parameters; optimal detection of “bottlenecks†in the system and ways of their elimination (expansion, dismantling, replacement, strengthening of heat pipeline sections, construction of pumping stations and other components of heat supply networks). The authors present a mathematical statement of the problem, its decomposition into separate subproblems and an integrated technique to solve it. Consideration is given to a real problem solved for a real heat supply system. A set of arising problems is presented. The application of developed methodological and computational tools is shown.

New Results in Development of Methods for Optimization of Heat Supply System Parameters and Their Software Implementation

Modern practice of solving the problems of heat supply system design generates the need to solve the problem of choosing optimal parameters for a considerable set of equipment. The problem of choosing optimal parameters involves determining the diameters of new heat pipelines, searching for the methods to reconstruct existing network sections, and choosing the pressure heads of pumping stations and their sites. To solve this problem the authors suggest a dynamic programming method for optimization of branched networks and a multiloop optimization method for calculation of loop networks, both being developed in the theory of hydraulic circuits. The paper presents new versions of algorithms for the implementation of these methods and describes their capabilities. These algorithms are implemented in the software package SOSNA-M. This software was developed on the basis of a methodological approach created to develop algorithms and methods for optimization of heat supply system parameters, flexibly control the computational process, optimize heat supply system parameters on a feasible set of equipment and improve the types of reconstruction of the existing components.

Optimization of Developing Heat Supply System in Competitive Market Environment

The paper is aimed at working out the mathematical models and methods to solve the problems of operation of developing heat supply systems in a competitive market environment. The formation of new principles of functioning in this field is conditioned by the market mechanisms emerging due to the interaction between different owners of heat economy facilities within the single system. Today heat energy markets are represented by a great number of enterprises with different types of ownership that operate heat energy sources and heat networks. It is obvious that such a situation explicitly causes conflicts of interests among the heat energy market participants and unbalances the responsibility for production reliability, heat energy supply efficiency and its quality among the participants of centralized heat supply (heat sources – heat networks - consumers). A reasonable solution to this problem can make it possible to determine optimal conditions for operation of the developing heat energy market, and their implementation can increase technical, economic and energy efficiency of heat energy. These problems are solved by using the methods of hydraulic circuit theory, nonlinear dynamic programming and two level programming. The studies performed allowed the creation of mathematical models and methods for optimal construction of efficient heat supply systems, organization of their operation that ensure the realization of full energy saving potential in the field of heat supply to consumers, taking into account the interests of all participants of the heat energy market.

Use of multilevel modeling for determining optimal parameters of heat supply systems

The problem of finding optimal parameters of a heat-supply system (HSS) is in ensuring the required throughput capacity of a heat network by determining pipeline diameters and characteristics and location of pumping stations. Effective methods for solving this problem, i.e., the method of stepwise optimization based on the concept of dynamic programming and the method of multicircuit optimization, were proposed in the context of the hydraulic circuit theory developed at Melentiev Energy Systems Institute (Siberian Branch, Russian Academy of Sciences). These methods enable us to determine optimal parameters of various types of piping systems due to flexible adaptability of the calculation procedure to intricate nonlinear mathematical models describing features of used equipment items and methods of their construction and operation. The new and most significant results achieved in developing methodological support and software for finding optimal parameters of complex heat supply systems are presented: a new procedure for solving the problem based on multilevel decomposition of a heat network model that makes it possible to proceed from the initial problem to a set of interrelated, less cumbersome subproblems with reduced dimensionality; a new algorithm implementing the method of multicircuit optimization and focused on the calculation of a hierarchical model of a heat supply system; the SOSNA software system for determining optimum parameters of intricate heat-supply systems and implementing the developed methodological foundation. The proposed procedure and algorithm enable us to solve engineering problems of finding the optimal parameters of multicircuit heat supply systems having large (real) dimensionality, and are applied in solving urgent problems related to the optimal development and reconstruction of these systems. The developed methodological foundation and software can be used for designing heat supply systems in the Central and the Admiralty regions in St. Petersburg, the city of Bratsk, and the Magistral’nyi settlement.

Integrated energy systems: Challenges, trends, philosophy

The creation of an energy metasystem that combines electrical, heat, cooling, and gas supply systems on an intellectual framework is a manifestation of a new energy paradigm. Integrated intelligent power supply systems combine complexity, intelligence, efficiency, reliability, controllability, flexibility of energy conversion, transmission, storage technologies and assume an active consumer.

Methods for Comprehensive Analysis of Heat Supply Reliability

The paper deals with the problem of comprehensive analysis of heat supply reliability for consumers. It implies a quantitative assessment of the impact of all stages of heat energy production and distribution on heat supply reliability for each consumer of the heat supply system. A short review of existing methods for the analysis of fuel and heat supply reliability is presented that substantiates the key approaches to solving the problem of comprehensive analysis of heat supply reliability. A methodological approach is suggested, in which mathematical models and methods for nodal evaluation of heat supply reliability for consumers are developed and the studies on the impact of different elements of fuel and heat supply systems on its level are described. Mathematical modeling is based on the Markov random processes, models of flow distribution in a heat network, deterministic dependences of thermal processes of heat energy consumption and some other models.

Mathematical Modeling of the Heat Energy Market on a Single Heat Supplier Basis

Organizational models of the heat energy market on a Single Heat Supplier basis (SHS) operating in free (liberalized) and regulated tariff environments are considered. An equilibrium mathematical model is proposed for the liberalized tariff setting conditions based on a microeconomic monopolistic market model. This mathematical model allows for taking into account energy production and transportation costs as part of a single economic criterion and to determine the supply-and-demand equilibrium for heat energy. A regulated heat energy market model on the SHS basis considers an option of a tariff setting for consumers of the housing and utility sector at the level of average total costs and on the demand basis for industrial consumers. Hydraulic circuit theory models and methods, as well as basic microeconomic provisions, are adopted as a scientific and methodological basis describing the proposed mathematical models. To solve the energy supply and demand equilibrium problem, an algorithm is developed for both energy tariff options based on univariate relaxation using redundant design schemes and simple iteration. The developed mathematical models fully reflect the current “rules of the game” between heat energy producers and consumers and allow a maximum consideration for the interests of all participants of the heat supply process under physical and engineering constraints on heat energy sources and heat networks. By means of the developed mathematical models, practical studies are carried out on the effect of the adopted heat energy price calculation method on both the market supply-and-demand equilibrium and on the main technical and economic characteristics of the real heat supply system of the city of Angarsk. Technical and economic assessments performed according to the indicated tariffs make it possible to conclude that the lack of regulation will lead to an uncontrolled rise in prices for heat energy for consumers and gaining of abnormal profits by energy suppliers.

Optimization of joint operation of district and distributed heat sources for effective and reliable heat supply to consumers

The problem of optimal load distribution between district and distributed heat sources (heat sources of prosumers) in the district heating systems are considered. The methodical approach and mathematical model for solving this problem are proposed. They are based on methods of the theory of system energy researches, theory of industrial organization, theory of hydraulic circuits, and basic laws of cogeneration. The case study results obtained by using the developed methodology are presented. The potential economic effect of the prosumer adoption under specified conditions is demonstrated. The conclusions and directions for further research are formulated.

Interior Point and Newton Methods in Solving High Dimensional Flow Distribution Problems for Pipe Networks

In this paper optimal flow distribution problem in pipe network is considered. The investigated problem is a convex sparse optimization problem with linear equality and inequality constrains. Newton method is used for problem with equality constrains only and obtains an approximate solution, which may not satisfy inequality constraints. Then Dikin Interior Point Method starts from the approximate solution and finds an optimal one. For problems of high dimension sparse matrix methods, namely Conjugate Gradient and Cholesky method with nested dissection, are applied. Since Dikin Interior Point Method works much slower then Newton Method on the matrices of big size, such approach allows us to obtain good starting point for this method by using comparatively fast Newton Method. Results of numerical experiments are presented.