CN111832138B - Regional pipe network topology optimization method - Google Patents
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Abstract
The invention discloses a regional pipe network topology optimization method, which is used for obtaining a better pipe network topology type and providing theoretical guidance for regional pipe network design optimization. The invention takes the total annual cost as an objective function, provides a new pipe network connection type (Steiner tree type), increases energy loss, namely operation cost, adopts different graph theory algorithms to respectively solve and compare and analyze different pipe network type algorithms so as to obtain a better pipe network topology type, and provides theoretical guidance for the pipe network design optimization of the regional system. Therefore, the method not only can minimize the annual total operation cost of pipe network projects, but also can achieve the purpose of energy conservation. The invention provides an effective method proposal for planning and optimizing the regional pipe network.
Description
Technical Field
The invention relates to a regional pipe network topology optimization method, which is used for obtaining a better pipe network topology type and providing theoretical guidance for regional pipe network design optimization.
Background
The renewable clean energy sources such as natural gas, biomass energy, solar energy, hydrogen energy and the like are taken as primary energy sources, and a small or miniature independent electric and thermal (cold) energy output system at a user side is used for realizing energy cascade utilization, and a support and supplement comprehensive energy production system is provided through a central energy supply system, wherein a transmission pipe network is an important component part in a distributed energy system, and the arrangement of pipes, pipe diameter optimization, selection of thickness of a heat preservation layer, determination of a transmission distance, hydraulic balance calculation and the like of the system have great influence on efficiency and economy of the system.
Aiming at pipe diameter optimization, heat preservation layer thickness selection, conveying distance determination and the like, students consider the changes of cold and heat supply loads and the operation adjustment of different time periods throughout the year, and adopt a genetic algorithm to solve the optimal combination of discrete diameters. Also, the learner can determine the pipe diameter by using integer coding genetic algorithm through improving genetic operators such as recombination and the like. Xia Bo an optimization model of the regional cooling area and the furthest conveying distance is established based on a life cycle cost analysis method, and an optimization model limiting condition and a solving method are provided. And the scholars also research the influence relationship of the base station action radius, the secondary pump position and the like on the system, construct the energy loss and investment function of the pipe network, and solve the problems by adopting an interior point algorithm. The method also has the advantages that a learner establishes a pipe network optimization model of the regional cooling system, and calculates and analyzes design parameters of the pipe network by applying an orthogonal optimization method.
And for the optimization of pipe network arrangement, a learner combines the load characteristics of the urban comprehensive cold and heat source system and the influence factors of the characteristics thereof to build a model for optimizing the pipeline of the urban comprehensive cold and heat source system, and adopts a genetic algorithm to solve the dendritic pipe network and the annular pipe network. Chen Juan and other scholars provide a decision-making and system-based Regional Distributed Energy System (RDES) double-layer optimization structure for the distributed energy system in the planning stage, and perform the pareto optimal solution of the multi-objective problem by adopting an NSGA-II multi-objective genetic algorithm for system optimization; for the layout and optimization of the station network, an energy distance concept of the annual value of the pipe network construction cost between supply and demand energy nodes is provided, a layout model for solving the bits in the RDES station network diagram P is constructed based on the energy distance concept, an RDES addressing network distribution algorithm based on the energy distance concept is adopted, and a determined optimal solution is finally obtained on the basis of traversing all feasible solutions in a solution set space. Feng Xiao the scholars of equal degree establish the overall optimization design model of the regional cooling system, select genetic algorithm to solve, put forward integer coding to genetic algorithm design and operation according to the research problem, adopt the optimal individual preservation strategy, the improved strategies such as the cross rate and the variation rate self-adaptation, use the heuristic back-pass method or the double-pass method to select loops at the same time so as to improve the pipe network resolving speed, apply the improved single-parent genetic algorithm to carry out the optimization arrangement of the dendritic pipe network, and design the corresponding fitness function, single-parent transposition operator and inversion operator. The Wang Chinese scholars combine the pipe network layout genetic optimization algorithm and the pipe diameter successive approximation optimization algorithm to construct a new algorithm to solve the problem of optimizing a huge amount of dimensional solution space in the overall optimization design of the complex dendritic pipe network, so that the pipe network optimization design efficiency is improved.
For optimization of a distributed energy system pipe network, most of students aim at lowest cost, constraint conditions such as user demands, flow rates and pipe diameters are adopted, a layout optimization problem is generally converted into a minimum tree (MST) problem in graph theory, the pipe network is regarded as a dendritic pipe network by default, and a genetic algorithm or an improved genetic algorithm is used for solving. The invention provides a new pipe network connection type (Steiner tree type) based on the method, takes annual total cost as an objective function, increases and considers energy loss, namely operation cost, and adopts different graph theory algorithms to respectively solve and compare and analyze different pipe network type algorithms so as to obtain a better pipe network topology type, thereby providing theoretical guidance for pipe network design optimization of a regional pipe network system.
The Kruskal algorithm is a classical algorithm for solving a minimum spanning tree of a weighted connected graph, based on greedy thought, the calculation process of the Kruskal algorithm takes edges as a main factor, and the Prim algorithm is also corresponding to the Kruskal algorithm, and the calculation process of the Kruskal algorithm takes vertexes as a main factor. Since the former can avoid multiple ordering and is more efficient than the latter, the Kruskal algorithm is chosen for calculation here, and the flow is as follows:
(1) Knowing the weighted connectivity graph g= (V, E, W), where V, E and W are the set of vertices, edges and weights of edges in the connectivity graph, respectively, the edges in the initial minimum spanning tree are empty sets;
(2) Sequencing each edge in the connected graph according to the weight from small to large;
(3) Sequentially adding edges into the minimum spanning tree according to the sequence and judging whether the minimum spanning tree is looped, if yes, discarding the added edges and entering the step (4), otherwise, directly entering the step (4);
(4) Judging whether the number of edges in the minimum spanning tree is Np-1 (Np is the number of vertices of the connected graph), if so, outputting the result of the minimum spanning tree after the calculation is finished, otherwise, turning to the step (3) until the calculation is finished.
The geoSteiner algorithm is a relatively efficient method for accurately solving the Steiner tree at present. The generation of ESMT and RSMT involves two very important steps, namely the generation and concatenation of the Man Sitan nanotree. A preprocessing stage is performed before Man Sitan nanotree generation to reduce the complexity of the computation process. Then, the Mantanin tree is gradually generated by a recursion algorithm, and only the results after the distance test, the long-side test, the branch tree test and the Mantanin tree type test are passed are reserved in the final connection stage. The Man Sitan nanotree connection can be regarded as a problem of finding the minimum spanning tree in the hypergraph, the process can be solved through integer programming modeling, and also can be solved through dynamic programming.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a regional pipe network topology optimization method which comprehensively considers all limiting factors by using the pipe network connection type of the Steiner tree.
The invention solves the problems by adopting the following technical scheme: the regional pipe network topology optimization method is characterized by comprising the following steps of:
the objective function is shown in formula (1):
min C＝C pipe +C pressureloss +C heatloss (27)
wherein C (yuan-year) -1 ) Is the total annual cost of the device,
and->
The investment cost, the pressure loss cost and the heat loss cost of the annual steam pipe network are respectively, and n is the number of branch pipe sections in the pipe network system.
Investment cost of steam pipe network
Obtained by the following formula: />
Wherein t is year (year) is the period of use of the pipe network system, I is the annual interest rate, a k (yuan·m -1 ) Is the unit price of a steam pipeline, L k (m) is the length of each section of branch line;
a k (yuan·m -1 ) The inner diameter of the pipeline required in the calculation process of (1) is obtained by the formula (6):
in the method, in the process of the invention,
is the inner diameter of the steam pipeline, W k (kg·s -1 ) Is the mass flow rate ρ (kg.m) -3 ) For the steam density, u (m.s) -1 ) Is the flow rate; wherein each section of branch line W k Is different in the whole pipe network system; therefore, W is calculated by solving the following linear programming model k Is a value of (2);
constraint conditions:
w α,β,γ ≥0 (37)
w β,α,γ ≥0 (38)
wherein w is α,β,γ (kg·s -1 ) Is the mass flow rate in the branch line connecting the vertices α and β, b binary Is a binary variable, which represents whether two vertexes are connected by a pipeline or not, and is obtained according to a pipe network topology result by a formula (9); w (W) γ Is the mass flow rate of the apex γ; if the user produces steam, W γ Is a negative value, otherwise, it is a positive value; the steam flow in each branch line has two directions from alpha to beta and from beta to alpha (-1) in equation (8) r For controlling the flow direction of the steam;
for medium-low pressure steam, the steam is heated,
and Wt k Calculated from the following formula:
in the case of high-pressure steam,
and Wt k Calculated from the following formula:
the system steam belongs to medium-low pressure steam and is calculated according to formulas (13) - (14);
a k obtained from equation (17):
in the method, in the process of the invention,
is the outer diameter of the branch line, wt k (kg·m -1 ) Is the weight of the branch line per unit length, A 1 (yuan·kg -1 ) Representing the cost per unit weight of the pipeline, A 2 (yuan·m -0.48 ) Representing the installation cost, A 3 (yuan·m -1 ) Representing the road use cost A 4 (yuan·m -1 ) Representing the cost of maintaining the temperature.
The cost of the pressure loss is as follows:
the steam has pressure, so that the auxiliary conveying of a compressor is not needed, but certain pressure loss is caused in the conveying process, the steam enters the steam production device after being condensed and pressurized by a water pump, and therefore, the pressure loss cost of a pipe network is low
Calculating according to the power consumption of the water pump;
wherein a is E (yuan·kW -1 ·h -1 ) Is the electricity charge, t time (h) Is the number of years of operation of the device, N k (W) is the shaft power against resistance at the time of steam delivery, and is obtained by the following formula:
where η is the efficiency of the delivery device, ne k And (W) is the effective power, calculated by the following formula:
in zeta k Zeta is the local resistance coefficient when the section suddenly increases or decreases E Is the local resistance coefficient at the bend,
the sectional area of the branch line, σ is the coefficient of friction of the pipeline.
The heat loss costs are as follows:
wherein a (yuan. Kg) -1 ) And q (kJ.kg) -1 ) Steam unit price and latent heat of steam, Q k (kJ·m -1 ·s -1 ) Is heat loss;
in the presence of insulation, the heat loss of the pipe network is calculated by the following formula:
wherein T (DEG C) is the outer surface temperature of the pipe, T a The temperature (DEG C) is the ambient temperature,
and->
The outer diameter and the inner diameter of the heat insulation layer are respectively;
λ(W·m -1 ·k -1 ) Is the heat conductivity coefficient of the thermal insulation material product at the average temperature, epsilon (W.m) -2 ·k -1 ) Is the heat exchange coefficient between the outer surface of the heat-insulating layer and the atmosphere, and the inner diameter of the heat-insulating layer
Taking the steam pipe outside diameter, the insulation layer thickness is related to the pipe diameter and the temperature of the fluid to be delivered, the invention is selected according to table 1.
Table 1 table for selecting thickness of insulation layer
Compared with the prior art, the invention has the following advantages and effects: the annual total cost is used as an objective function, a new pipe network connection type (Steiner tree type) is provided, energy loss, namely operation cost, is increased, different pipe network type algorithms are respectively solved and compared and analyzed by adopting different graph theory algorithms, so that a better pipe network topology type is obtained, and theoretical guidance is provided for regional system pipe network design optimization. The invention can save energy and simultaneously minimize the annual total operation cost of pipe network projects.
Drawings
FIG. 1 is a diagram of Star-type pipe network in an embodiment of the present invention.
FIG. 2 is a diagram of an MST-type pipe network in accordance with an embodiment of the present invention.
FIG. 3 is a diagram of an RMST-type pipe network in an embodiment of the invention.
FIG. 4 is a diagram of an EMST-type pipe network according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail by way of examples with reference to the accompanying drawings, which are illustrative of the present invention and not limited to the following examples.
Examples
In this embodiment, a topology optimization method for a regional pipe network specifically includes:
the objective function is shown in formula (1):
min C＝C pipe +C pressureloss +C heatloss (53)
wherein C (yuan-year) -1 ) Is the total annual cost of the device,
and->
The investment cost, the pressure loss cost and the heat loss cost of the annual steam pipe network are respectively, and n is the number of branch pipe sections in the pipe network system.
Investment cost of steam pipe network
Obtained by the following formula:
wherein t is year (year) is the period of use of the pipe network system, I is the annual interest rate, a k (yuan·m -1 ) Is the unit price of a steam pipeline, L k (m) is the length of each section of branch line;
a k (yuan·m -1 ) The inner diameter of the pipeline required in the calculation process of (1) is obtained by the formula (6):
in the method, in the process of the invention,
is the inner diameter of the steam pipeline, W k (kg·s -1 ) Is the mass flow rate ρ (kg.m) -3 ) For the steam density, u (m.s) -1 ) Is the flow rate; wherein each section of branch line W k Is different in the whole pipe network system; therefore, W is calculated by solving the following linear programming model k Is a value of (2);
constraint conditions:
w α,β,γ ≥0 (63)
w β,α,γ ≥0 (64)
wherein w is α,β,γ (kg·s -1 ) Is the mass flow rate in the branch line connecting the vertices α and β, b binary Is a binary variable representing two verticesWhether pipelines are connected or not is obtained according to a pipe network topology result by a formula (9); w (W) γ Is the mass flow rate of the apex γ; if the user produces steam, W γ Is a negative value, otherwise, it is a positive value; the steam flow in each branch line has two directions from alpha to beta and from beta to alpha (-1) in equation (8) r For controlling the flow direction of the steam;
for medium-low pressure steam, the steam is heated,
and Wt k Calculated from the following formula:
in the case of high-pressure steam,
and Wt k Calculated from the following formula:
the system steam belongs to medium-low pressure steam and is calculated according to formulas (13) - (14);
a k obtained from equation (17):
in the method, in the process of the invention,
is the outer diameter of the branch line, wt k (kg·m -1 ) Is the weight of the branch line per unit length, A 1 (yuan·kg -1 ) Representing the cost per unit weight of the pipeline, A 2 (yuan·m -0.48 ) Representing the installation cost, A 3 (yuan·m -1 ) Representing the road use cost A 4 (yuan·m -1 ) Representing the cost of maintaining the temperature.
The cost of the pressure loss is as follows:
the steam has pressure, so that the auxiliary conveying of a compressor is not needed, but certain pressure loss is caused in the conveying process, the steam enters the steam production device after being condensed and pressurized by a water pump, and therefore, the pressure loss cost of a pipe network is low
Calculating according to the power consumption of the water pump;
wherein a is E (yuan·kW -1 ·h -1 ) Is the electricity charge, t time (h) Is the number of years of operation of the device, N k (W) is the shaft power against resistance at the time of steam delivery, and is obtained by the following formula:
where η is the efficiency of the delivery device, ne k And (W) is the effective power, calculated by the following formula:
in zeta k Zeta is the local resistance coefficient when the section suddenly increases or decreases E Is the local resistance coefficient at the bend,
the sectional area of the branch line, σ is the coefficient of friction of the pipeline.
The heat loss costs are as follows:
wherein a (yuan. Kg) -1 ) And q (kJ.kg) -1 ) Steam unit price and latent heat of steam, Q k (kJ·m -1 ·s -1 ) Is heat loss;
in the presence of insulation, the heat loss of the pipe network is calculated by the following formula:
wherein T (DEG C) is the outer surface temperature of the pipe, T a The temperature (DEG C) is the ambient temperature,
and->
The outer diameter and the inner diameter of the heat insulation layer are respectively;
λ(W·m -1 ·k -1 ) Is the heat conductivity coefficient of the thermal insulation material product at the average temperature, epsilon (W.m) -2 ·k -1 ) Is the heat exchange coefficient between the outer surface of the heat-insulating layer and the atmosphere, and the inner diameter of the heat-insulating layer
Taking the steam pipe outside diameter, the insulation layer thickness is related to the pipe diameter and the temperature of the fluid to be delivered, the invention is selected according to table 1.
Table 1 table for selecting thickness of insulation layer
In this embodiment, there are four types of pipe network connections between the heat source and each user, namely Star, MST, RSMT and ESMT. Wherein MST is solved by Kruskal algorithm, RSMT and ESMT are solved by GeoSteiner algorithm, and the whole optimization process is realized by C++ programming.
The case data is from a heat supply pipe network project, and the geodetic coordinates (longitude and latitude are converted into geodetic coordinates if longitude and latitude are adopted) and the heat load of the heat source and each user are extracted. The heat load of the user is specified to be positive and the heat load of the heat source point is specified to be negative. The data are summarized in table 2.
Table 2 heat source raw data
The required parameters in the model are shown in table 3 below.
TABLE 3 parameter Table
The case calculations are summarized below. FIGS. 1-4 are respectively topology schemes of four pipe network types, in which the diameter of the branch line varies with the thickness of the line segment.
Table 4 calculation results
As shown in Table 4, in this example, the EMST-type pipe network has the lowest total cost, while the RMST-type pipe network has the highest annual total cost. Star and MST type networks are more similar in cost, but still 13.6% and 10.1% higher than EMST type networks, respectively. The star-shaped pipe network connection mode is the simplest as can be seen from the pipe network topology scheme, but the layout is the least reasonable in engineering practice, and especially when a heat source is out of a user area, the pipeline length can be greatly increased, so that the pipe network conveying efficiency is reduced. In contrast, the schemes of MST, RSMT and EMST are reasonable. The MST pipe network is relatively simple in connection mode, but the length of the pipeline can be increased to a certain extent, so that energy conservation and consumption reduction are not facilitated. The RSMT pipeline has regular path, is beneficial to the maintenance and management of a pipe network to a certain extent, but has the highest total cost. In the comprehensive view, the EMST type pipe network has the shortest length and the lowest cost, and is the optimal pipe network topology type.
What is not described in detail in this specification is all that is known to those skilled in the art.
Although the present invention has been described with reference to the above embodiments, it should be understood that the invention is not limited to the embodiments described above, but is capable of modification and variation without departing from the spirit and scope of the present invention.
Claims (1)
1. The regional pipe network topology optimization method is characterized by comprising the following steps of:
the objective function is shown in formula (1):
min C＝C pipe +C pressureloss +C heatloss (1)
wherein C is the annual total cost in units of yuan-year -1 ；
And->
The investment cost, the pressure loss cost and the heat loss cost of the annual steam pipe network are respectively expressed in the units of yuan-year -1 The method comprises the steps of carrying out a first treatment on the surface of the n is the number of branch pipe sections in the pipe network system;
investment cost of steam pipe network
Obtained by the following formula:
wherein t is year The service cycle of the pipe network system is given by year; i is annual interest rate; a, a k Is the unit price of the steam pipeline, and the unit is yuan.m -1 ；L k Is the length of each section of branch line, and the unit is m;
a k the inner diameter of the pipeline is required in the calculation process of (a) and is expressed in terms of yuan.m -1 Obtained by the formula (6):
in the method, in the process of the invention,
is the inner diameter of the steam pipeline, and the unit is m; w (W) k The mass flow rate is in kg.s -1 The method comprises the steps of carrying out a first treatment on the surface of the ρ is the steam density in kg.m -3 The method comprises the steps of carrying out a first treatment on the surface of the u is the flow rate in m.s -1 The method comprises the steps of carrying out a first treatment on the surface of the Wherein each section of branch line W k Is different in the whole pipe network system; therefore, W is calculated by solving the following linear programming model k Is a value of (2);
constraint conditions:
w α,β,γ ≥0 (11)
w β,α,γ ≥0 (12)
wherein w is α,β,γ Is the mass flow rate in kg.s in the branch line connecting the vertices α and β -1 ；b binary Is a binary variable, which represents whether two vertexes are connected by a pipeline or not, and is obtained according to a pipe network topology result by a formula (9); w (W) γ Is the mass flow rate of the apex γ; if the user produces steam, W γ Is a negative value, otherwise, it is a positive value; the steam flow in each branch line has two directions from alpha to beta and from beta to alpha (-1) in equation (8) r For controlling the flow direction of the steam;
for medium-low pressure steam, the steam is heated,
and Wt k Calculated from the following formula:
in the case of high-pressure steam,
and Wt k Calculated from the following formula:
the system steam belongs to medium-low pressure steam and is calculated according to formulas (13) - (14);
a k obtained from equation (17):
in the method, in the process of the invention,
is the outer diameter of the branch line in m; wt (Wt) k Is the weight of the branch line per unit length, and the unit is kg.m -1 ：A 1 Represents the cost per unit weight of pipeline in terms of yuan kg -1 ；A 2 Representing the installation cost in units of yuan.m -0.48 ；A 3 Represents road use cost, and the unit is yuan.m -1 ；A 4 Represents the heat-preserving cost, and the unit is yuan.m -1 ；
The cost of the pressure loss is as follows:
the steam has pressure, so that the auxiliary conveying of a compressor is not needed, but certain pressure loss is caused in the conveying process, the steam enters the steam production device after being condensed and pressurized by a water pump, and therefore, the pressure loss cost of a pipe network is low
Calculating according to the power consumption of the water pump;
wherein a is E The unit is yuan kW for electricity charge -1 ·h -1 ；t time The unit is h, which is the number of annual operation hours of the device; n (N) k Is the shaft power which overcomes the resistance in the steam delivery, and the unit is W; the method is obtained by the following formula:
where η is the efficiency of the delivery device, ne k Is effective power, the unit is W, calculated by the following formula:
in zeta k A local resistance coefficient when the section suddenly increases or decreases; zeta type E Is the local resistance coefficient at the elbow;
the unit of the cross-sectional area of the branch line is m 2 The method comprises the steps of carrying out a first treatment on the surface of the Sigma is the friction coefficient of the pipeline;
the heat loss costs are as follows:
wherein a is a steam unit price and the unit is yuan.kg -1 The method comprises the steps of carrying out a first treatment on the surface of the q is the latent heat of steam in kJ.kg -1 ；Q k Is the heat loss in kJ.m -1 ·s -1 ；
In the presence of insulation, the heat loss of the pipe network is calculated by the following formula:
wherein T is the temperature of the outer surface of the pipeline and the unit is the temperature; t (T) a Is ambient temperature in degrees celsius;
and->
The outside diameter and the inside diameter of the heat insulation layer are respectively m; lambda is the coefficient of thermal conductivity of the thermal insulation material product at average temperature, and the unit is W.m -1 ·k -1 The method comprises the steps of carrying out a first treatment on the surface of the Epsilon is the heat exchange coefficient between the outer surface of the heat-insulating layer and the atmosphere, and the unit is W.m -2 ·k -1 The method comprises the steps of carrying out a first treatment on the surface of the Inner diameter of heat insulation layer>
Taking the outer diameter of the steam pipeline, the thickness of the heat preservation layer is related to the diameter of the pipeline and the temperature of the conveyed fluid. />
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