Random Analysis Of Variables And Study On Optimal Design Considering Random Variables In Heat-Supply Network

Centralized heat-supply has already become the important infrastructure of modern city, and got rapid development and widespread application in the scope of world. As the important part of heat-supply system, the heat-supply network has the characteristic of large scale, complex structure and huge investment. Currently heat-supply network has been got a lot of research, but optimal design, reliability analysis, parameters identification and fault diagnosis of heat-supply network are still the weak links of research. In the current researches of heat-supply network, the variables of the network, such as flow-resistance characteristic coefficients of pipes and load of heat consuming installations, are regarded as certainty variables, but actually these variables are uncertain. The uncertainty of variables can affect results of design calculation and hydraulic regime analysis in heat-supply network. Research considering the uncertainty of variables has not been carried out in heat-supply network. This paper emphatically studies the uncertainty of other variables caused by randomness of flow-resistance characteristic coefficients of pipes, heating load of heat consuming installations, and optimal design method considering randomness of heating load, available heads of heat consuming installations and flow-resistance characteristic coefficients of pipes.Based on probability theory and graph theory of network, the first-order derivative matrixes of flow through pipes and pressure heads at nodes to flow-resistance characteristic coefficients of pipes are studied firstly, which is the basis of random analysis. Then, the random problem of flow through pipes and pressure heads at nodes caused by randomness of flow-resistance characteristic coefficients of pipes are discussed by the first-order Taylor expansion. Results show that flow through pipes and pressure heads at nodes are normal variables with first-order Taylor expansion. According to the matrixes solved, the mean, variance, the confidence intervals under some confidence level of flow through pipes and pressure heads at nodes are solved. The impacts of flow-resistance characteristic coefficients of pipes on flow through pipes and pressure heads are analyzed with an example.In order to improve the accuracy of random analysis in heat-supply network, the random problem of flow through pipes and pressure heads at nodes caused by randomness of flow-resistance characteristic coefficients of pipes is studied by the second-order Taylor expansion. Based on first-order derivative matrixes, the second-order derivative matrixes of flow through pipes and pressure heads at nodes to flow-resistance characteristic coefficients of pipes are deduced firstly. After that, random sampling method of flow through pipes and pressure heads at nodes by Monte Carlo method is proposed, and to test the distribution of sample, SPSS software and skewness-kurtosis method are used. The difference between first-order Taylor expansion and second-order Taylor expansion is discussed with the example.Except for the random effects of flow-resistance characteristic coefficients of pipes, the random impacts of heating load of heat consuming installations on flow through pipes and pressure heads at nodes are studied in this paper. The first-order derivative matrixes of flow through pipes and pressure heads at nodes to heating load of heat consuming installations are solved. Based on the matrixes, the random problem of flow through pipes and pressure heads at nodes caused by randomness of heating load of heat consuming installations is discussed. Results show that flow through pipes and pressure heads at nodes are normal variables with first-order Taylor expansion. The mean, variance, coupled with confidence intervals under some confidence level of flow through pipes and pressure heads at nodes are developed. The impacts of heating load of heat consuming installations on flow through pipes and pressure heads are analyzed with an example.A new improved genetic and simulated annealing algorithm is proposed, based on chaos algorithm and traditional genetic and simulated annealing algorithm, used for optimal design of heat-supply network. The analysis results combining with an example show that the running time of new algorithm greatly reduces compared with traditional algorithm, in the condition of guaranteeing the performance of the algorithm.The optimal design method of heat-supply network considering single random variable is studied. The method takes anneal annual converting cost of heat-supply network as objective function. The optimal models and solution methods considering randomness of heating load of heat consuming installations, available heads of heat consuming installations and flow-resistance characteristic coefficients of pipes, are respectively presented. The optimal confidence level of optimal design in heat-supply network is conformed by Fuzzy comprehensive evaluation method. With the optimal design method put forward, the heat-supply network as example is designed and the design results are compared with certain design results. Then the factors affecting the optimal design scheme are analyzed.Finally, the paper studies the optimal design method of heat-supply network, simultaneously considering the randomness of heating load of heat consuming installations, available heads of heat consuming installations and flow-resistance characteristic coefficients of pipes. The optimal design model and solution method are presented. With the heat-supply network as example, the difference among optimal design schemes simultaneously considering randomness of multi variables, optimal design scheme considering randomness of single variable and certain optimal design scheme in heat-supply network is discussed. Then, the effects of random variables to optimal design scheme of heat-supply work are analyzed.The paper studies the randomness effects of variable in heat-supply network and methods of random optimal design. It is a basis research, which can not only serve for hydraulic regime analysis and optimal design, but also proposes basis for identification in heat-supply network.