Reliability Of District Heating System Based On Graph Theory

District heating system, as society's"Lifeline Engineering", has great relationship with people's work and life, and also is an important part of the national economy. It can lead to bad heating of living quarters and public buildings, and people's daily life and working environment are deteriorated when the heating system with high temperature and high capacity breaks down. Thence, it must cause incalculable social consequences. In order to make sure reliable operation of heating system, Russian scholars raised strict requirements on design of heating system, like the spare structure, the spare transmission capacity, repair time and quota heating. They also put forward reliability index of function and quality, and then proposed a set of reliability design and final assessment methods. However, the lack of reliability evaluation methods during design of heating system still exists, such as design of network topology and pipe capacity. In addition, design and operation management of heating system in different districts has great difference because of the difference of regional economic and technological development. In view of present problems of heating system design and operation in China, this paper mainly researches on reliability evaluation methods of heating system when design network topology and pipe capacity, and reliability index which is used to evaluate existent heating system with different design and operation level.For the problem of reliability evaluation in each step of heating system design, firstly, according to heat users, heat source and system, connectedness model of heating system is built based on connectedness theory of network system. The connectedness reliability is expressed by min-path matrix. The improved traversal algorithm of min-path set and the matrix partitioning algorithm for solving Boolean sum have been put forward. In addition, the connectedness importance degree of pipe is built to reflect the influence of each pipe on reliability of heating system. Thus, a fairly method to evaluate the spare structure based on connectedness reliability is formed. The effect of network topology, location and the number of heat source on connectedness is analyzed by practical examples.Secondly, the planar heating network is transformed into edge weighted communication net based on the maximum flow and min-cut theory. The reliability design method of pipe capacity is raised considering quota heating under failure condition. Then, reliability indices for evaluating the spare transmission capacity of heating system are established, including maximal flow reliability, quota heating flow reliability and part-load flow reliability.Combined with the integrated reliability evaluation of heating system, the increase of structure and transport capacity spare can effectively improve the integrated reliability of heating system through analysis of reconstruction of a district heating system with single heat source. It can illustrate that reliability design of network topology and pipe capacity based on connectedness reliability and flow reliability is an effective method in design process of heating system.Integrated reliability evaluation of district heating system should follow the steps of failure isolation, reconstruction of failure network, and hydraulic simulation of failure network and reliability calculation. First, planar network is transformed into the valve net based on matrix traversal algorithm by constructing a hybrid correlation matrix which contains information of valves. Scheme of shutting valves and shutting area when component fails can be calculated by correlation matrix of the valve net. Reconstruction of failure planar network and spatial network is finished by searching all connected sub-graph of planar pipe network when failure component is isolated. In addition, the invalid valve and parallel valves in network are analyzed based on the model of valve net, and their determinant rules and related characteristics are given.Assuming completely controllable and uncontrollable performance as the upper and lower bounds of controllable degree of heating system, based on the primary hydraulic model and failure spatial network, the simulation models of completely controllable and uncontrollable system are established according to their regulating characteristics under failure conditions. Hydraulic characteristics of the uncontrollable and completely controllable heating system are analyzed by a practical example. The completely controllable system is the means to realize reliability design, which is an applicable control measures for structure spare and transport capacity spare.Finally, according to the state space method and the reliability evaluation index of functional and quality, and considering the disadvantages of the designed heat load reliability, in this paper the quota heating reliability is established to evaluate heating system synthetically. The integrated reliability evaluation of heating system is finished by calculation of valve net, hydraulic model of failure network and quota heating reliability.The effects of circulating pumps, controllability, and multi-pipe installation on the reliability of heating systems are analyzed based on quota heating reliability. This paper presents the minimal length requirement of main line from heat source when multi-pipe installation is used, and indicates that circulating pumps with steep performance curve can improve system reliability. The ultimate quota heating reliability based on the first kind of problem is presented, which illustrates that system reliability can achieve maximum when network topology, heat load distribution, diameter and valve settings stay in the same conditions. Optimal scheme of additional valve setting in a heating system with multi-source and multi-loop is analyzed based on the ultimate quota heating reliability.