A method for optimizing topology of a heating system based on bionics principle

Abstract

This invention discloses a biomimetic method for optimizing the topology of a heating system. The method comprises the following steps: Step S1, acquiring the location and number of heat users, and performing cluster analysis based on their distribution; Step S2, based on biomimetic principles, considering the heat source, heating station, heat user buildings at all levels, and pipeline valve groups at all levels as nodes in the heating network, and constructing a topology model of the heating network using ArcGIS based on the network nodes and existing pipeline information; Step S3, constructing a heat dissipation and resistance model of the heating system based on the impedance model of the blood system; Step S4, using the minimum heat dissipation and resistance of the heating system as the objective function and solving for it, obtaining the optimized parameter values ​​for each node and pipeline structure. This invention achieves overall optimization of the heating system topology, providing a new approach for the analysis and evaluation of urban heating system topologies, and has reference value for the engineering design and renovation of actual heating systems.

Description

Technical Field

[0001] This invention belongs to the field of heating systems, specifically involving a method for optimizing the topology of a heating system based on biomimetic principles. Background Technology

[0002] Heating systems produce high-temperature hot water at heat source plants and drive the hot water to circulate within the primary side pipe network, supplying heat energy to various heating stations. Within the heating stations, heat exchange occurs between the primary and secondary sides, transferring heat from the primary to the secondary side, which then supplies heat to various users within its own secondary side pipe network. With the increasing complexity of heating pipe networks and the growing emphasis on energy conservation in heating systems, the suitability of existing heating pipe network design methods is gradually decreasing. Currently, the structural design of heating pipe network systems lacks an overall planning approach, and unreasonable pipe network topology leads to problems such as energy waste, low utilization efficiency, and difficulty in adjusting the hydraulic balance of the pipe network. Summary of the Invention

[0003] In view of the current lack of systematic evaluation methods for heating system network structures, this invention provides a method for optimizing the topology of heating systems based on biomimetic principles. First, a topology model is constructed using the actual distribution of heating systems to analyze and evaluate the advantages and disadvantages of its heating network structure. Then, based on the biomimetic principle of the blood system, the parameters of the network structure are further optimized.

[0004] This invention is achieved using the following technical solution:

[0005] This invention discloses a method for optimizing the topology of a heating system based on the biomimetic principle of the blood system, comprising the following steps:

[0006] Step S1: Obtain the location and number information of hot users, and perform cluster analysis based on the distribution of hot users;

[0007] Step S2: Based on the principle of bionics, the heat source, heating station, heat user buildings at all levels and pipeline valve groups at all levels of the heating system are taken as system network nodes. According to the system network nodes and existing pipeline information, the topological structure model of the heating network in the heating system is constructed using ArcGIS.

[0008] Step S3: Based on the impedance model of the blood system, construct the heat dissipation and heat resistance model of the heating system.

[0009] Step S4: Using the minimum heat dissipation and heat resistance of the heating system as the objective function, solve the objective function to obtain the optimized parameter values ​​of each node of the pipeline network and the pipeline structure, thereby obtaining the overall optimization result of the heating system topology.

[0010] In the above technical solution, further, in step S1, cluster analysis is performed based on the distribution of heat users. The specific method is as follows:

[0011] S11, First, the dispersed heat users in the heating system are grouped into a low-density data point set D = {X1, X2, X3, ..., X...} n}, where X1~X n Each corresponds to one of the hot users; assuming a neighborhood parameter (ε, MinPts), the specific value of which is selected based on the actual situation, is used to determine the ε-core neighborhood of the hot user and to select the core hot user object; for X j ∈D, its ε-neighborhood is: the ε-neighborhood contains all elements in dataset D that are the same as X. j Samples whose distance is not greater than ε; if hot user X j If the ε-core neighborhood contains at least MinPts samples, then X j As a core object; use the DBSCAN algorithm to find the ε-neighborhood of each data point in D and determine the core object set Ω;

[0012] S12, randomly select one core object from Ω, if X j Located in X i In the ε-neighborhood of X, and X i If it is the core object, then X j By X i Density direct reach; find all samples that are directly reachable by the density of the core object, forming a new cluster C1; then remove the core object contained in C1 from Ω to obtain the updated set Ω;

[0013] S13. Repeat step S12 until the set Ω is empty, then the clustering analysis results of the heat users are obtained.

[0014] Furthermore, step S2 specifically includes:

[0015] Step S21: First, obtain the specific location coordinates of the heat source, heating stations at all levels, heat user buildings at all levels, and valve groups at all levels in the pipeline network in the heating system; the pipeline length of the heating pipeline network; the specific location coordinates of the start and end points of the pipeline; and the fluid flow direction data in the pipeline.

[0016] Step S22: The heat source in the heating system is likened to the human heart, and the heat exchange station and valve groups at all levels are likened to the human regulatory organs; the pushing action of the pressurization pump in the heat source and heat exchange station at all levels on the heat medium is likened to the pushing action of the human heart on blood. The valve groups at all levels include shut-off valves, exhaust valves, and check valves, and the heat user buildings at all levels include terminal water tanks, pressure regulating towers, and radiators.

[0017] Step S23: Heat sources and heat exchangers and booster pumps of heat exchange stations at all levels are used as driving nodes of the heating system network model. The community heat exchange stations where heat user buildings are located are used as primary regulating nodes. Heat users’ radiators and valves are used as secondary regulating nodes. All regulating nodes and heating network pipelines are components of the heating system topology.

[0018] Step S24: Based on the component information of the topology structure in step S23, construct a topology model of the heating network using ArcGIS; thereby obtaining a three-dimensional visualization model of the heating system topology, which includes a three-dimensional model of the main and branch lines of the heating network and a terrain model of the overall heating area.

[0019] Furthermore, step S3 specifically includes:

[0020] Step S31: Based on the biomimetic principle of the blood system, the flow impedance model of the blood system is first obtained, expressed by the following formula:

[0021]

[0022] In the formula, R is the blood flow resistance; Q is the blood flow rate; P1 and P2 are the pressures at the beginning and end of the nodes in the blood network, respectively, in Pa.

[0023] Step S32: For a centralized heating system, first obtain the flow and temperature data of each node of the heating station, heating network and end-user radiator, and construct the corresponding heat loss and heat resistance models respectively.

[0024] The heat loss and heat resistance of the heat exchanger in the heating station can be expressed as:

[0025]

[0026] In the formula, m0 and m t These are the mass flow rates of hot water in the primary and secondary heating networks, respectively; c p Let K be the specific heat capacity at constant pressure of hot water, (KA). sub Thermal conductivity of heat exchangers in heating stations; m i Let be the mass flow rate of hot water in the i-th building, i = 1, 2, ..., n.

[0027] The heat loss and heat resistance of each node in a heating network can be expressed as:

[0028]

[0029] In the formula, The subscript ab indicates the b-th node of the a-th pipe, m ab Let be the mass flow rate of hot water in the pipe between nodes a and b; (KA)ab Indicates the thermal conductivity of the pipe;

[0030] The heat dissipation resistance of the heat sink of the end user can be expressed as:

[0031]

[0032] In the formula, the subscript rad represents the radiator, and the subscript ij (represents the radiator of the j-th terminal heat user in the i-th building, i = 1, 2, 3, ..., n, (KA)) ij For the heat sink of this user, the thermal conductivity is determined.

[0033] Furthermore, step S4 specifically includes:

[0034] Step S41, construct the optimization objective function with the goal of minimizing the heat loss and heat resistance of the heating system, which can be expressed as:

[0035]

[0036] In the formula, n is the total number of buildings, and N i Let be the total number of radiators for end-user heat in the i-th building.

[0037] Step S42: Determine the constraints for solving the objective function.

[0038] In a heating system, the total heat capacity of the secondary heating network is constant, i.e.

[0039] In a centralized heating network, heat user buildings on the same branch are connected in parallel, meaning the hot water temperature delivered to heat users in building 1 and building i is equal. Therefore, the parallel constraint condition of the centralized heating network is expressed as:

[0040]

[0041] In the formula, T1 is the water temperature at the inlet of the radiator for the first user in each building, and Q... 11 For the heat load of the first heat user in the first building, R 11，rad The heat dissipation resistance of the radiator for the first terminal heat user in the first building; T i Let Q be the water temperature at the inlet of the radiator for the i-th user in each building. i1 R represents the heat load of the first heat user in the i-th building. i1，rad Let be the heat dissipation resistance of the radiator of the first terminal heat user in the i-th building;

[0042] Since the radiators of each heat user in the same building are connected in series, the series constraint conditions of the centralized heating network system, obtained by combining the energy conservation equation, can be expressed as:

[0043]

[0044] In the formula, T' and T" represent the water temperatures of the primary heating network before and after heat exchange at the heat exchange station, respectively, in K; Q t This is the sum of the heat loads of all heat users in the secondary heating network. Q ij Let Q be the heat load of the radiator of the j-th terminal heat user in the i-th building; let k be the heat load of the radiator of the k-th terminal heat user. ik Let be the heat load of the radiator for the kth terminal heat user in the i-th building.

[0045] Step S43: Construct the Lagrange function using the Lagrange multiplier method:

[0046]

[0047] In the formula, α and λ k , λ ij All are Lagrange multipliers, T k Let Q be the water temperature at the inlet of the radiator for the k-th user in each building. k1 R is the heat load of the first heat user in the k-th building. k1，rad m is the heat dissipation resistance of the radiator of the first terminal heat user in the k-th building; k Let be the mass flow rate of hot water in the k-th building;

[0048] Setting the partial derivatives of Π1 with respect to all variables to zero, we obtain the system of optimization equations:

[0049]

[0050] Solving the above set of optimization equations yields the optimal values ​​of heat dissipation and heat resistance at each node of the heating system. Further calculations are then performed to obtain the optimal values ​​of the heating system topology, pipe diameter, and pump / valve opening.

[0051] Step S44: Compare the existing heating system structural parameters and analyze and evaluate the heating system topology. For areas with significant differences in results, where it is difficult to achieve the network flow threshold and safety requirements by changing the pipeline diameter or regulating valve group equipment, add pipelines to the network to change the overall topology of the heating network. Then, use steps S41-43 to construct a new set of optimization equations for solving to obtain the optimal values ​​of the heating system topology, network diameter, and pump / valve opening.

[0052] The inventive concept of this invention is as follows:

[0053] The applicant, through biomimicry, discovered that the human circulatory system is similar to a heating system, with the heart analogous to a heat source, organs to heat exchange stations, and the arteriovenous network to a heating network. Furthermore, due to biological evolution, the human circulatory network possesses a high-performance topological structure to ensure blood transport and the overall function of the system. Therefore, this invention conducts in-depth research on the topological structure of the circulatory system and, based on this, optimizes the topological structure of the heating system.

[0054] The beneficial effects of this invention are as follows:

[0055] This invention provides a method for optimizing the topology of an existing heating system. Based on the principle of biomimicry and the blood system, it offers a new approach to the overall analysis and optimization of the heating system topology, achieving overall optimization of the heating network structure, improving the hydraulic and thermal imbalance and uneven heating of the system, and further enhancing the energy-saving effect of the system. Attached Figure Description

[0056] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0057] Figure 1 This is a flowchart of the method of the present invention.

[0058] Figure 2 This is a schematic diagram of the cluster analysis process in step 1 of the method of the present invention.

[0059] Figure 3 This is a schematic diagram of the topology optimization model of the heating system according to the method of the present invention. Detailed Implementation

[0060] The present invention provides a heating system topology optimization model and method based on the biomimetic principle of the blood system, comprising the following steps:

[0061] Step S1: Obtain the location and number information of hot users, and perform cluster analysis based on the distribution of hot users; the specific steps are as follows:

[0062] 1) First, obtain the specific location and number of heat user buildings in the heating system.

[0063] 2) Based on the distribution of heat users, a dynamic clustering method is used for cluster analysis. The specific steps are as follows:

[0064] 21) First, the dispersed heat users in the heating system are organized into a low-density data point set D = {X1, X2, X3, ..., X...} n}, where X1~X nEach corresponds to one of the hot users; assuming a neighborhood parameter (ε, MinPts), the specific value of which is selected based on the actual situation, is used to determine the ε-core neighborhood of the hot user and to select the core hot user object; for X j ∈D, its ε-neighborhood is: the ε-neighborhood contains all elements in dataset D that are the same as X. j Samples whose distance is not greater than ε; if hot user X j If the ε-core neighborhood contains at least MinPts samples, then X j As a core object; use the DBSCAN algorithm to find the ε-neighborhood of each data point in D and determine the core object set Ω;

[0065] 22), randomly select one core object from Ω, if X j Located in X i In the ε-neighborhood of X, and X i If it is the core object, then X j By X i Density direct reach; find all samples that are directly reachable by the density of the core object, forming a new cluster C1; then remove the core object contained in C1 from Ω to obtain the updated set Ω;

[0066] 23), repeat step 22) until the set Ω is empty, then the clustering analysis results of the hot users are obtained.

[0067] Step S2, based on biomimetic principles, takes the heat source, heating station, buildings of various levels of heat users, and valve groups of various levels of pipelines in the heating system as system network nodes. Based on these network nodes and existing pipeline information, a topological model of the heating network in the heating system is constructed using ArcGIS. The specific steps are as follows:

[0068] 1) First, obtain the specific location coordinates of the heat source, heating stations at all levels, heat user buildings at all levels, and valve groups at all levels in the pipeline network in the heating system; the pipeline length of the heating pipeline network and the specific location coordinates of the start and end points of the pipeline and the fluid flow direction data in the pipeline.

[0069] 2) The heat source in the heating system is likened to the heart of the human body, and the heat exchange station and valve groups at all levels are likened to the regulatory organs of the human body; the pushing action of the pressurizing pump in the heat source and heat exchange station at all levels on the heat medium is likened to the pushing action of the human heart on the blood; the valve groups at all levels include shut-off valves, exhaust valves, and check valves; and the heat user buildings at all levels include terminal water tanks, pressure regulating towers, and radiators.

[0070] 3) Heat sources and heat exchangers and booster pumps of heat exchange stations at all levels are used as driving nodes of the heating system network model. The heat exchange stations of the communities where the heat user buildings are located are used as primary regulating nodes. The radiators and valves of the heat users are used as secondary regulating nodes. All regulating nodes and heating network pipelines are the constituent units of the heating system topology.

[0071] 4) Based on the component information of the topology in step 3), construct a topology model of the heating network using ArcGIS; thereby obtain a three-dimensional visualization model of the heating system topology, which includes a three-dimensional model of the main and branch lines of the heating network and a terrain model of the overall heating area.

[0072] Step S3: Based on the impedance model of the blood system, construct the heat dissipation and resistance model of the heating system; the specific steps are as follows:

[0073] 1) Based on the biomimetic principle of the blood system, the flow resistance model of the blood system is first obtained, expressed by the following formula:

[0074]

[0075] In the formula, R is the blood flow resistance; Q is the blood flow rate; P1 and P2 are the pressures at the beginning and end of the nodes in the blood network, respectively, in Pa.

[0076] 2) For centralized heating systems, first obtain the flow and temperature data of each node of the heating station, heating network and end-user radiator, and then construct the corresponding heat loss and heat resistance models respectively.

[0077] The heat loss and heat resistance of the heat exchanger in the heating station can be expressed as:

[0078]

[0079] In the formula, m0 and m t These are the mass flow rates of hot water in the primary and secondary heating networks, respectively; c p Let K be the specific heat capacity at constant pressure of hot water, (KA). sub Thermal conductivity of heat exchangers in heating stations; m i Let be the mass flow rate of hot water in the i-th building, i = 1, 2, ..., n.

[0080] The heat loss and heat resistance of each node in a heating network can be expressed as:

[0081]

[0082] In the formula, The subscript ab indicates the b-th node of the a-th pipe, m ab Let be the mass flow rate of hot water in the pipe between nodes a and b; (KA)ab Indicates the thermal conductivity of the pipe;

[0083] The heat dissipation resistance of the heat sink of the end user can be expressed as:

[0084]

[0085] In the formula, the subscript rad represents the radiator, and the subscript ij represents the radiator of the j-th terminal heat user in the i-th building (i = 1, 2, 3, ..., n), (KA). ij For the heat sink of this user, the thermal conductivity is determined.

[0086] Step S4: Using the minimum heat loss and thermal resistance of the heating system as the objective function, solve the objective function to obtain the optimized parameter values ​​of each node and pipeline structure in the pipeline network, thereby obtaining the overall optimization result of the heating system topology; the specific steps are as follows:

[0087] 1) The objective function for optimizing the heating system is to minimize heat loss and thermal resistance, which can be expressed as:

[0088]

[0089] In the formula, n is the total number of buildings, and N i Let be the total number of radiators for end-user heat in the i-th building.

[0090] 2) Determine the constraints for solving the objective function.

[0091] In a heating system, the total heat capacity of the secondary heating network is constant, i.e.

[0092] In a centralized heating network, heat user buildings on the same branch are connected in parallel, meaning the hot water temperature delivered to heat users in building 1 and building i is equal. Therefore, the parallel constraint condition of the centralized heating network is expressed as:

[0093]

[0094] In the formula, T1 is the water temperature at the inlet of the radiator for the first user in each building, and Q... 11 For the heat load of the first heat user in the first building, R 11，rad The heat dissipation resistance of the radiator for the first terminal heat user in the first building; T i Let Q be the water temperature at the inlet of the radiator for the i-th user in each building. i1 R represents the heat load of the first heat user in the i-th building. i1，rad Let be the heat dissipation resistance of the radiator of the first terminal heat user in the i-th building;

[0095] Since the radiators of each heat user in the same building are connected in series, the series constraint conditions of the centralized heating network system, obtained by combining the energy conservation equation, can be expressed as:

[0096]

[0097] In the formula, T' and T" represent the water temperatures of the primary heating network before and after heat exchange at the heat exchange station, respectively, in K; Q t This is the sum of the heat loads of all heat users in the secondary heating network. Q ij Let Q be the heat load of the radiator of the j-th terminal heat user in the i-th building; let k be the heat load of the radiator of the k-th terminal heat user. ik Let be the heat load of the radiator for the kth terminal heat user in the i-th building.

[0098] 3) Construct the Lagrange function using the Lagrange multiplier method:

[0099]

[0100] In the formula, α and λ k , λ ij All are Lagrange multipliers, T k Let Q be the water temperature at the inlet of the radiator for the k-th user in each building. k1 R is the heat load of the first heat user in the k-th building. k1，rad m is the heat dissipation resistance of the radiator of the first terminal heat user in the k-th building; k Let be the mass flow rate of hot water in the k-th building;

[0101] Setting the partial derivatives of Π1 with respect to all variables to zero, we obtain the system of optimization equations:

[0102]

[0103] Solving the above set of optimization equations yields the optimal values ​​of heat dissipation and heat resistance at each node of the heating system. Further calculations are then performed to obtain the optimal values ​​of the heating system topology, pipe diameter, and pump / valve opening.

[0104] 4) Compare the existing heating system structural parameters and analyze and evaluate the heating system topology. For areas with significant differences in results, where it is difficult to achieve the network flow threshold and safety requirements by changing the pipeline diameter or regulating valve group equipment, add pipelines to the network to change the overall topology of the heating network. Then, use steps S41-43 to construct a new set of optimization equations for solving to obtain the optimal values ​​of the heating system topology, network diameter, and pump valve opening.

[0105] like Figure 3As shown, by adding a pipeline to the original heating system, the hydraulic and thermal balance of the entire system is achieved, which improves the safety of the heating system and makes the solution of the subsequent optimization equations more accurate.

Claims

1. A method for optimizing the topology of a heating system based on biomimetic principles, characterized in that, Includes the following steps: Step S1: Obtain the location and number information of hot users, and perform cluster analysis based on the distribution of hot users; Step S2: Based on the principle of bionics, the heat source, heating station, heat user buildings at all levels and pipeline valve groups at all levels of the heating system are taken as system network nodes. According to the system network nodes and existing pipeline information, the topological structure model of the heating network in the heating system is constructed using ArcGIS. Step S3: Based on the impedance model of the blood system, construct the heat dissipation and heat resistance model of the heating system. Step S4: Taking the minimum heat loss and heat resistance of the heating system as the objective function, solve the objective function to obtain the parameter optimization values ​​of each node of the pipeline network and the pipeline structure, thereby obtaining the overall optimization result of the heating system topology. The specific steps of step S3 are as follows: Step S31, based on the biomimetic principle of the blood system, first obtain the flow impedance model of the blood network, expressed by the following formula: In the formula, R is the blood flow resistance; Q is the blood flow rate; P1 and P2 are the pressures at the beginning and end of the node in the blood network, respectively, in Pa. Step S32: For a centralized heating system, first obtain the flow and temperature data of each node of the heating station, heating network and end-user radiator, and construct the corresponding heat loss and heat resistance models respectively. The heat loss and heat resistance of the heat exchanger in the heating station can be expressed as: In the formula, ; and These are the mass flow rates of hot water in the primary and secondary heating networks, respectively. The specific heat capacity at constant pressure of hot water, Thermal conductivity of heat exchangers in heating stations; m i Let be the mass flow rate of hot water in the i-th building, i=1,2,…,n; The heat loss and heat resistance of each node in a heating network can be expressed as: In the formula, The subscript ab indicates the b-th node of the a-th pipe. The mass flow rate of hot water in the pipe between nodes a and b; Indicates the thermal conductivity of the pipe; The heat dissipation resistance of the heat sink of the end user can be expressed as: In the formula, the subscript rad represents the radiator, and the subscript ij represents the radiator of the j-th terminal heat user in the i-th building. For the heat sink of this user.

2. The method for optimizing the topology of a heating system based on biomimetic principles according to claim 1, characterized in that, In step S1, cluster analysis is performed based on the distribution of heat users. The specific method is as follows: S11, firstly, group the dispersed heat users in the heating system into a low-density data point set. Where X1~X n Each corresponds to one of the hot users; assuming a neighborhood parameter (ε, MinPts), the specific value of which is selected based on the actual situation, it is used to determine the ε-core neighborhood of the hot user and to select the core hot user object; for X j ∈D, its ε-neighborhood is: the ε-neighborhood contains all elements in dataset D that are the same as X. j Samples whose distance is not greater than ε; if hot user X j If the ε-core neighborhood contains at least MinPts samples, then X j As a core object; use the DBSCAN algorithm to find the ε-neighborhood of each data point in D and determine the core object set Ω; S12, randomly select one core object from Ω, if X j Located in X i In the ε-neighborhood of X, and i If it is the core object, then X j By X i Density direct reach; find all samples that are directly reachable by the density of the core object, forming a new cluster C1; then remove the core object contained in C1 from Ω to obtain the updated set Ω; S13. Repeat step S12 until the set Ω is empty, then the clustering analysis results of the heat users are obtained.

3. The method for optimizing the topology of a heating system based on biomimetic principles according to claim 2, characterized in that, The specific steps of step S2 are as follows: Step S21: First, obtain the specific location coordinates of the heat source, heating stations at all levels, heat user buildings at all levels, and valve groups at all levels in the heating system, as well as the pipeline length, the specific location coordinates of the starting and ending points of the pipeline, and the fluid flow direction data in the pipeline. Step S22: The heat source in the heating system is likened to the human heart, and the heat exchange station and valve groups at all levels are likened to the human regulatory organs; the pushing action of the pressurization pump in the heat source and heat exchange station at all levels on the heat medium is likened to the pushing action of the human heart on blood. The valve groups at all levels include shut-off valves, exhaust valves, and check valves, and the heat user buildings at all levels include terminal water tanks, pressure regulating towers, and radiators. Step S23: Heat sources and heat exchangers and booster pumps of heat exchange stations at all levels are used as driving nodes of the heating system network model. The community heat exchange stations where heat user buildings are located are used as primary regulating nodes. Heat users’ radiators and valves are used as secondary regulating nodes. All regulating nodes and heating network pipelines are components of the heating system topology. Step S24: Based on the component information of the topology structure in step S23, construct a topology model of the heating network using ArcGIS; thereby obtaining a three-dimensional visualization model of the heating system topology, which includes a three-dimensional model of the main and branch lines of the heating network and a terrain model of the overall heating area.

4. The method for optimizing the topology of a heating system based on biomimetic principles according to claim 1, characterized in that, The specific steps of S4 are as follows: Step S41, construct the optimization objective function with the goal of minimizing the heat loss and heat resistance of the heating system, which can be expressed as: In the formula, n is the total number of buildings, and N i Let be the total number of radiators for end-user heat in the i-th building; Step S42: Determine the constraints for solving the objective function; In a heating system, the total heat capacity of the secondary heating network is constant, i.e. ; In a centralized heating network, heat user buildings on the same branch are connected in parallel, meaning the hot water temperature delivered to heat users in building 1 and building i is equal. Therefore, the parallel constraint condition of the centralized heating network is expressed as: In the formula, T1 is the water temperature at the inlet of the radiator for the first user in each building, and Q... 11 For the heat load of the first heat user in the first building, R 11，rad The heat dissipation resistance of the radiator for the first terminal heat user in the first building; T i Let Q be the water temperature at the inlet of the radiator for the i-th user in each building. i1 R represents the heat load of the first heat user in the i-th building. i1，rad Let be the heat dissipation resistance of the radiator of the first terminal heat user in the i-th building; Since the radiators of each heat user in the same building are connected in series, the series constraint conditions of the centralized heating network system can be obtained by combining the energy conservation equation, which can be expressed as: In the formula, T ’ and T ’’ These are the water temperatures (K) of the hot water in the primary heating network before and after heat exchange at the heat exchange station; Q represents the water temperature of the hot water in the primary heating network before and after heat exchange. t This is the sum of the heat loads of all heat users in the secondary heating network. Q ij Let Q be the heat load of the radiator of the j-th terminal heat user in the i-th building; let k be the heat load of the radiator of the k-th terminal heat user. ik Let be the heat load of the radiator of the kth terminal heat user in the i-th building; Step S43: Construct the Lagrange function using the Lagrange multiplier method: In the formula, All are Lagrange multipliers, T k Let Q be the water temperature at the inlet of the radiator for the k-th user in each building. k1 R is the heat load of the first heat user in the k-th building. k1，rad m is the heat dissipation resistance of the radiator of the first terminal heat user in the k-th building; k Let be the mass flow rate of hot water in the k-th building; make The partial derivatives with respect to all variables are equal to zero, resulting in the system of optimization equations: Solving the optimization equations yields the optimal values ​​of heat dissipation and heat resistance at each node of the heating system. Further calculations are then performed to obtain the optimal values ​​of the heating system topology, pipe diameter, and pump / valve opening. Step S44: Compare the existing heating system structural parameters and analyze and evaluate the heating system topology. For areas with significant differences in results, where it is difficult to achieve the network flow threshold and safety requirements by changing the pipeline diameter or regulating valve group equipment, add pipelines to the network to change the overall topology of the heating network. Then, use steps S41-43 to construct a new set of optimization equations for solving to obtain the optimal values ​​of the heating system topology, network diameter, and pump / valve opening.

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