Analysis of the main trends in the innovative transformation of the mathematical model of flow distribution in gas supply systems and new properties they acquire

The purpose of the paper is to consider the proposals for the possible account of new properties of gas supply system in a mathematical model of the generalized problem of flow distribution as compared to the traditional formulation; to introduce an arc coefficient considering gas flow value alteration when passing through the arc, increment vector of arc flow rate and lower limits on gas flows in the arcs; to analyze new management conditions (optimization criteria of load flows and establishment of fictitious gas consumption prices allowing to take into account a high priority supply of a certain group of consumers). Network analysis methods are widely used in solving the problems of long-term planning and development of gas supply systems for mathematical modeling of optimal gas flows. The account of new trends of innovative transformation in mathematical models is caused by the modern development of gas supply systems, their renovation and modernization. To solve the problems of gas load flow in gas supply systems the network analysis methods based on the graph theory are used when dealing with the problems of gas supply system operation in various conditions. Based on the traditional problem of flow modeling a generalized solution of load flow is formulated taking into account the new properties of gas supply system. A mathematical formulation is given, its implementation is successively executed in the computational program. The gas flow calculation for the aggregate Unified gas supply system in 2030 is given as an example of the proposed approaches. This calculation takes into account the capacity increments of gas transmission system arcs and the coefficients showing a decrease in the volumes of gas supply for own needs and leakages. To solve the problems of load flows in the optimization of gas supply system development the following innovative improvements have been proposed: arc coefficients taking into account gas flow value alteration when passing through the arc are introduced; increment vectors of arc capacities and gas flow lower limits in the arcs are given, new economic conditions (flow load optimization criteria and fictitious prices on gas consumption) allowing to consider a high priority supply of a certain group of consumers are taken into account.

gas supply system, mathematical model, load flow, arc coefficient, arc increment, lower arc limits