Modified method of dynamic programming for optimization of hydraulic modes of distribution heating networks

Предложена оригинальная модификация метода динамического программирования, предназначенная для оптимизации гидравлических режимов распределительных тепловых сетей, опирающаяся на специальные свойства задачи. Продемонстрировано, что предложенная модификация метода динамического программирования обладает высокой вычислительной эффективностью по сравнению с возможными альтернативными методами дискретно-непрерывной оптимизации и гарантирует получение оптимального решения задачи. The paper discusses the problem of optimizing the hydraulic modes of the distribution of heat networks (RTS), which arises at the stage of preparing heating systems for the next heating season. The urgency of this task is due to the significant reserves of energy saving, improving the reliability and quality of heat supply to consumers, which can be realized through the optimal organization of RTS operation modes. Currently, there are no formally rigorous and simultaneously computationally efficient methods for solving this problem. A new effective method for optimizing RTS modes is presented, based on a dynamic programming scheme, which takes into account the specifics of the problem (specified flow distribution) and RTS topology (a tree in a single-line representation, multicontourness in a two-line representation, symmetry of supply and return pipelines). The proposed solution overcomes the main problem of applying the traditional dynamic programming scheme when optimizing multi-loop pipe networks associated with the need to comply with the second Kirchhoff law on contours when building conditionally optimal trajectories. The basic idea is to reduce the contours of the design scheme to parallel connections of branches (on the direct course of the algorithm) with simultaneous cutting of both non-optimal and inadmissible fragments of trajectories. And the latter here are easily cut off both in terms of the membership of the phase variables of the admissible region and in satisfying Kirchhoff’s second law. The reverse move is reduced to a simple procedure of unfolding the design scheme in the reverse sequence of reduction, in order to restore the optimal values of phase variables on it. Numerical examples illustrate the effectiveness of the proposed method, its suitability for solving problems with discrete and continuous optimality criteria, multi-criteria optimization, the possibility of solving several optimization problems simultaneously.