Article Preview
TopIntroduction
The paper deals with the problem of modeling complex heat supply systems (HSSs) which includes a number of subproblems. The main of them are: the choice of an optimal structure, the determination of optimal parameters and the calculation of flow distribution in HSS.
Optimization problem of the multi-loop HSS development cannot be completely formalized and solved by one universal technique. Decomposition of a general problem into several subproblems makes it possible to separate their solving in time and adjust the process of solving, taking into account individual features of systems.
The following methods are applied to determine an optimal structure of heat supply system:
- 1.
Comparison of variants specified by an engineer (Shifrinson, 1940; Zanfirov, 1933);
- 2.
Search for an optimal configuration of the system (Courant & Robbins, 1941);
- 3.
Solving a transport problem (Ford & Fulkerson, 1966);
- 4.
Application of the technique of “redundant” design schemes (Merenkova, Sennova & Stennikov, 1982; Nekrasova & Khasilev, 1970).
This is the approach to be considered further.
The second and third methods do not take account of such features of HSSs as their distribution on the territory, obstacles to their construction, etc. They have limited practical application, whereas the method for comparison of variants and the technique of redundant design schemes are applied more widely to design heat supply systems.
Optimization problem of HSS parameters is described by a set of balance equations (flow rates and heads) and by technical and economic relationships. Optimization criterion is the minimum estimated (discounted) costs.
The parameters of branched HSS (without rings) are optimized by the dynamic programming (DP) method based on Bellman’s principle of optimality (Bellman, 1957).
Parametric optimization of multi-loop HSS is a multiextremal problem of nonlinear programming with discrete variables and complex constraints. A method of multi-loop optimization (MMO) (Sumarokov, 1976) was suggested to solve it. The method combines the techniques for calculation of flow distribution and optimization of branched heat network parameters. Methods similar to the MMO have not been found in publications.
Traditionally heat supply systems are reconstructed by determining pipeline diameters by the linear programming methods (Dantzig, 1963) or by the dynamic programming method for branched systems (Appleyard, 1978; Garbai & Molnar, 1974). However, for Russian large and multi-loop HSSs with a heat capacity above 4500 MW this leads to non-optimal solutions.
The flow distribution model includes a set of balance equations (analogues of Kirchhoff laws) (Cross, 1936; Kirchhoff, 1847; Maxwell, 1873) and closing relationships (Equations 11-14) that describe the relationship between pressure losses and flow rate in a heat network section.
The paper presents a new technique for solving the problem and results of its practical application in expansion and reconstruction of HSS in one of Russia’s cities.