An analytical method for solving the problem of heat network load flow

Abstract

The author aimed to develop an analytical solution to the problem of the load flow of a six-, eleven- and twelve-circuit heat network, as well as to solve the problem of optimisation of a multi-circuit heat network, including the choice of the objective function and the determination of a number of variable technical parameters. For accelerating the optimisation process, the method of decomposition of the heat network graph was used. Decomposition involves is cutting the network graph at some nodes for the transition of a multi-circuit scheme to a branched scheme in the form of a tree. Optimisation of each branched circuit was carried out by the dynamic programming method, as a result of which new values of the variable parameters were obtained at the current iteration. Next, the author returned to the multi-circuit scheme to solve the load flow problem and calculate the value of the objective function. The iterative convergence of the decomposition method was not mathematically proven. The author proposed a method for splitting the graph, which eliminates the decomposition procedure when optimising a heat network. The following methods were applied: mathematical modelling of the hydraulic circuit, graph splitting method and the analytical method for solving the algebraic equation of the fourth degree. The following results were achieved: a scheme of the minimum element of a multi-circuit heat network was determined, the possibility of series and parallel circuits of minimum elements was shown, and analytical dependencies for the problem of load flow of a heat network of these schemes were obtained. The proposed analytical solution of the load flow problem for a multi-circuit heat network allows the problem of calculating a complex network to be reduced to the calculation of several minimum elements, which significantly reduces the amount of computational work when modelling a hydraulic circuit. The provided examples show that the calculation error does not exceed 3%.