A method for generating virtual operation data of a heat exchange station in planning

Abstract

The application provides a kind of planning heat exchange station virtual operation data generation method, belongs to the virtual operation data generation technical field based on machine learning;Collect existing heat exchange station central heating system operation data and system hardware data;According to the different lag order between each heat exchange station in the heat exchange station network, the primary water temperature in the system operation data and the system hardware data are calculated;Build and train BTI-LNN model of different lag order, calculate the lag order of the primary water temperature of the nearest heat exchange station adjacent to the newly built heat exchange station, select the BTI-LNN model corresponding to the lag order, and predict the virtual operation data of the primary water temperature;Based on the virtual operation data of the primary water temperature, calculate other virtual operation data.The application breaks through the strong dependence on historical operation data, and realizes the high-precision generation of virtual data of new heat exchange station in full working condition without historical data.

Description

Technical Field

[0001] This invention belongs to the field of virtual operation data generation technology based on machine learning, and particularly relates to a method for generating virtual operation data of a heat exchange station in planning. Background Technology

[0002] Existing district heating systems are expanding rapidly, but because the planning process before expansion is based solely on engineering construction standards and expert experience, lacking historical data support, newly connected heat exchange stations can easily cause significant impacts on existing pipe networks and heat sources. This problem leads to an imbalance between planning and operation, increasing the uncertainty of actual operating parameters after construction, and consequently resulting in overheating and heat waste.

[0003] Traditional technologies primarily revolve around three core scenarios: predicting operating parameters for heat exchange stations, hydraulic optimization of heating networks, and planning and designing new heat exchange stations. Among these, the planning method based on engineering construction standards and expert experience is the most mainstream fundamental technology in the engineering field. It relies entirely on national and industry standards and engineering experience related to urban heating networks and building energy conservation. This method first determines the service area and building type of the new heat exchange station, then obtains the corresponding heat consumption per unit area from tables, calculates the design flow rate based on the temperature difference between the primary supply and return water temperatures recommended by standards, and estimates the primary supply and return water pressures by combining the average resistance of the network. Finally, it completes equipment selection and parameter presets. However, this method only provides a general parameter range for individual heat exchange stations and cannot adapt to the heterogeneity of network topology and the dynamic characteristics of operating conditions. It completely ignores the global hydraulic coupling effect of the new station on the existing network, and the parameter values ​​are conservative, easily leading to hydraulic imbalances, energy waste, or insufficient heating.

[0004] To compensate for the shortcomings of empirical methods, pure data-driven artificial intelligence prediction methods based on historical operational data have become one of the mainstream approaches in heating system data prediction. These methods use models such as BP / ANN, Long Short-Term Memory Neural Network / RNN, Transformer, and PCA combined with neural networks to learn the nonlinear mapping relationship between the input and output of historical SCADA data to achieve parameter prediction. The process covers data acquisition and preprocessing, model building and training, and result output. However, these methods heavily rely on historical data and are completely unsuitable for newly built heat exchange stations without historical data. Furthermore, they are pure black-box models with extremely poor physical interpretability, only considering the unidirectional influence of the pipeline network on the heat exchange station, making it difficult to capture the continuous dynamic characteristics and long-distance transmission lag effects of the heating system.

[0005] The gray-box modeling approach, which integrates physical models and data-driven methods, is currently the mainstream research path that balances prediction accuracy and physical interpretability. This method first establishes a simplified physical mechanism model of the heating system, then uses neural networks to fit nonlinear parameters that are difficult to calculate precisely, such as heat transfer coefficient and pipe wall friction coefficient, and combines physical equations to complete the prediction of operating parameters. However, its performance is highly dependent on the accuracy of the mechanistic model description and still requires sufficient full-condition measured data support. At the same time, it cannot characterize the global hydraulic coupling effect and inter-station spatiotemporal lag correlation of complex tree-like pipe networks.

[0006] Traditional generative artificial intelligence methods, represented by generative adversarial networks (GANs), learn the distribution of historical data through adversarial training between generators and discriminators, and then generate virtual operating data. However, they also heavily rely on historical data, the generated results lack physical constraints, may violate the laws of energy conservation and hydraulics, and do not consider the coupling effect between pipeline topology and stations, making it impossible to simulate the global operating condition changes after a new station is connected.

[0007] Traditional hydraulic optimization methods for addressing hydraulic imbalances in existing pipe networks rely on simplified network fluid dynamics models. They aim to minimize pump energy consumption or achieve hydraulic balance, using optimization algorithms to determine the optimal flow distribution scheme for each heat exchange station and issuing control commands. However, these methods oversimplify the network, neglecting the dynamic effects of topology and elevation differences, lacking research on dynamic expansion scenarios, and failing to predict network-wide disturbances from new station connections. This results in significant deviations between optimization results and actual operating conditions.

[0008] In summary, traditional technologies suffer from four common core pain points: First, except for the engineering standard method, all methods heavily rely on historical operating data of existing heat exchange stations, failing to address the fundamental problem of lack of data for newly built heat exchange stations; second, they generally ignore the global hydraulic coupling effect of tree-like pipe networks and the spatiotemporal lag correlation between stations, focusing only on individual heat exchange stations or local pipe networks; third, they lack sufficient physical constraints, and the generation and prediction results of purely data-driven methods may violate basic physical laws; and fourth, they have poor dynamic adaptability, failing to adapt to the dynamic expansion needs of heating systems and struggling to cope with complex on-site constraints and changes in operating conditions. Summary of the Invention

[0009] To address the above problems, this invention proposes a method for generating virtual operation data for planned heat exchange stations, comprising the following steps: S1 collects operational data and system hardware data of existing heat exchange station centralized heating systems; S2, based on the primary water supply temperature and system hardware data in the system operation data, use the Pearson correlation coefficient method to calculate the different hysteresis orders between each heat exchange station in the heat exchange station network; S3. Construct a BTI-LNN prediction model. The primary water supply temperature data of a heat exchange station in the existing system operation data is preprocessed and used as the input value. The primary water supply temperature data of the heat exchange station under different lag orders is used as the prediction value. The model adopts a unified framework that integrates physical information and liquid neural network (LNN) to train the BTI-LNN model and obtain BTI-LNN models with different lag orders. S4. Based on the pipe diameter and heat exchange station location in the hardware data of the new heat exchange station system, calculate the lag order between the new heat exchange station and the primary water supply temperature of the nearest adjacent heat exchange station. S5. Based on the lag order, select the BTI-LNN model with the corresponding lag order, input the primary water supply temperature of the adjacent heat exchange station into the BTI-LNN model, and obtain the virtual operating data of the primary water supply temperature of the new heat exchange station. S6 calculates virtual operating data for primary return water temperature, primary water flow rate, primary water supply pressure, and primary return water pressure based on virtual operating data of primary water supply temperature.

[0010] Preferably, the system operation data includes primary water supply temperature, primary return water temperature, primary water supply pressure, primary return water pressure, primary water supply flow rate, indoor temperature, and outdoor temperature; the system hardware data includes heating area, building type, heat exchange station location, pipe diameter, and elevation.

[0011] Preferably, the specific process of S2 is as follows: Select the primary water supply temperature sequence of any two heat exchange stations and Calculate the sequence and The Pearson correlation coefficient; in turn, makes the sequence and This generates a phase difference of 1, 2... up to 30 sampling periods, corresponding to... k =1, 2, 3...30; calculate and record the Pearson correlation coefficient for each corresponding phase difference; select the sampling period phase difference corresponding to the maximum value of the Pearson correlation coefficient as the lag order. k ; Calculate the Pearson correlation coefficient for the primary water supply temperature series: ; In the formula, r(k) For lag k The Pearson correlation coefficient of order, Cov( X k , Y k ) is a sequence and covariance; For sequence and The product of the sample standard deviations.

[0012] Preferably, for the primary water supply temperature in the system operation data, the mean-variance normalization method is used: ; in, The original data, The sample mean. The standard deviation of the sample. This is the data after normalization.

[0013] Preferably, the BTI-LNN model includes a forward process physical information fusion module, a liquid neural network module, and a hybrid time constant regularization module. First, the primary water supply temperature is input into the forward process physical information fusion module of the BTI-LNN model. This module extracts the RC model of the heat exchange station from the features of data changes and calculates the physical constraint time constant based on the RC model. At the same time, the primary water supply temperature is input into the liquid neural network module, which calculates the data fitting time constant. Second, the data fitting time constant and the physical constraint time constant are input into the hybrid time constant regularization module. After regularization, the comprehensive time constant is output to control the response smoothness.

[0014] Preferably, the forward process physical information fusion module improves upon the unique liquid time constant in the LNN model by fusing data based on the characteristics of the RC model presented in the building data. It inputs the primary water supply temperature data of the heat exchange station, establishes a thermal balance differential equation based on the building's first-order linear thermal inertia RC model according to the attenuation trend of the water supply temperature, calculates and outputs the physical constraint time constant characterizing the building's thermal inertia. Represented as: ; and These are the indoor and outdoor temperatures, respectively, in degrees Celsius (°C). The initial temperature of the building, in °C; This refers to the duration of the building's free thermal decay process; the physical constraint time constant. It is a core parameter describing the thermal inertia of a building.

[0015] Preferably, in the liquid neural network module, the data fitting time constant is updated in the following way: ; In the formula, It is the lag quantity that is displayed in real time in the data, and is called the data fitting time constant; and These represent the minimum and maximum boundaries of the hysteresis, determined by the hydraulic characteristics of the heating network and the distribution characteristics of the heat exchange stations. This is the Sigmoid activation function, used to map the output to the [0,1] interval; and These are the weight matrix and bias vector of the hysteresis update network, respectively; x and h These are the input signal and the hidden state, respectively. It is the concatenated vector of the input signal and the hidden state.

[0016] Preferably, the mixed time constant regularization module specifically comprises: The combined time constant consists of the data fitting time constant, the physical constraint time constant, and the regularization factor. The inherent thermal inertia time constant calculated from the building thermophysical model. Dynamic lags mined from operational data It is obtained through weighted fusion; the expression is: ; Wherein, the regularization factor takes a range of values. The optimal value is determined by a grid search method.

[0017] Preferably, the specific process of S4 is as follows: Based on the location of the new heat exchange station, calculate the distance between the new heat exchange station and other heat exchange stations, and select the existing heat exchange station with the smallest straight-line distance as the adjacent benchmark heat exchange station; determine the actual laying length L of the primary water supply pipeline between the new heat exchange station and the adjacent benchmark heat exchange station; based on the pipe diameter D and engineering construction standards, determine the economic flow velocity v of hot water in the pipe of this diameter; and calculate the heat transfer lag time of the primary water supply from the adjacent benchmark heat exchange station to the new heat exchange station. The calculation formula is as follows: ; In the formula, L is the actual length of the primary water supply pipeline, in meters; v is the economic flow velocity of hot water in the pipeline, in meters per second. This refers to the heat transfer lag time, measured in seconds (s). Converted to system sampling period Lag order in units The calculation formula is as follows: ; In the formula, The sampling period for system operation data, in seconds; This is the rounding function; This represents the lag order of the primary water supply temperature of the new heat exchange station relative to the adjacent reference heat exchange station.

[0018] Preferably, in step S6, the calculation method for the primary return water temperature and the primary supply water flow rate is as follows: Based on the heat balance principle of the primary and secondary sides in a heat exchange station, and considering the heating area, building type, indoor temperature, and outdoor temperature of the building under the management of the heat exchange unit, the correlation between the primary side supply and return water temperature difference and the secondary side heat load is established: ; In the formula, The primary return water temperature is determined with reference to engineering construction standards. This is a virtual value of the water supply temperature at time t, in °C. Let t be the building heat load at time t, in kW, calculated from the heating area, building type and outdoor temperature; c is the specific heat capacity of water at constant pressure, taken as 4.2 kJ / (kg·℃); G s Let t be the single water supply flow rate at time t, expressed in kg / s. The rated heat exchange efficiency of the heat exchange unit is determined according to the technical manual of the plate heat exchanger in the heat exchange station. The calculation methods for primary water supply pressure and primary return water pressure are as follows: ; ; In the formula, This refers to either the primary water supply pressure or the primary return water pressure. This refers to the primary supply or return water pressure at adjacent heat exchange stations along the pipeline, expressed in Pa. The specific volume of the inlet working fluid reflects the volume per unit mass of working fluid, and the unit is m³. 3 , The specific volume of the working fluid at the outlet, in cubic meters. 3 , The inner diameter of the pipe represents its geometric dimensions, expressed in meters. The length of the pipeline represents the distance over which the friction resistance is applied, expressed in meters. Darcy friction coefficient is a function of Reynolds number Re, absolute roughness of pipe wall ks, and pipe diameter D, reflecting the friction resistance characteristics of the pipeline. The dynamic viscosity of the inlet working fluid. The dynamic viscosity of the working fluid at the outlet is expressed in Pa. s.

[0019] Compared with the prior art, the present invention has the following beneficial effects: Breaking away from the strong reliance on historical operating data, this system achieves high-precision generation of virtual data for all operating conditions of newly built heat exchange stations in scenarios lacking historical data. Through a dual constraint system of engineering standards and physical equations, data can be generated by inputting only design parameters and existing pipeline network information. The generation errors for primary water supply temperature, primary water supply flow rate, primary water supply pressure, and primary return water pressure are less than 0.8℃, 1.4t / h, and 0.5bar, respectively. The determination coefficients under high and low load conditions are consistently above 0.960 and 0.953, respectively, solving the fundamental problem of data scarcity in the planning stage. It comprehensively depicts the global hydraulic coupling effect and the spatiotemporal lag correlation between stations. Using the Floyd algorithm to quantify the pipeline network topology and combining it with the Pearson coefficient to mine dynamic lag, the lag characteristic map calculated shows that the pipeline lag order error is mostly below 20%. After the new station is connected, the overall network flow margin stabilizes above 50m³ / h under low load, and after flow balancing adjustments under high load, the operating flow of all existing stations is higher than the allowable lower limit. A physically interpretable BTI-LNN model is constructed, transforming the black-box time constant into a thermal inertia mapping. The mean absolute error is reduced by 11.4% compared to the original liquid neural network module, significantly outperforming the Long Short-Term Memory (LSTM) neural network model and the Transformer. The generated data strictly adheres to the law of energy conservation. This invention possesses excellent engineering applicability; the generated data can be directly used for equipment selection and network-wide hydraulic balancing, adapting to existing engineering standards without large-scale hardware modifications. It can be widely applied to scenarios such as heating capacity expansion planning and source-grid-load coordinated scheduling. Attached Figure Description

[0020] To more clearly illustrate the technical solutions of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the following description is only one embodiment of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a schematic diagram of the method framework of the invention.

[0022] Figure 2 This is a diagram of the BTI-LNN model structure.

[0023] Figure 3 The diagram illustrates the relationship between primary water supply pressure, pipeline elevation, and pipeline length under high and low load conditions. (a) shows the relationship between pipeline elevation and primary water supply pressure under high load conditions; (b) shows the relationship between pipeline distance and primary water supply pressure under high load conditions; (c) shows the relationship between pipeline elevation and primary water supply pressure under low load conditions; and (d) shows the relationship between pipeline distance and primary water supply pressure under low load conditions.

[0024] Figure 4The diagram illustrates the relationship between primary return water pressure, pipeline elevation, and pipeline length under high and low load conditions. (a) shows the relationship between pipeline elevation and primary return water pressure under high load conditions; (b) shows the relationship between pipeline distance and primary return water pressure under high load conditions; (c) shows the relationship between pipeline elevation and primary return water pressure under low load conditions; and (d) shows the relationship between pipeline distance and primary return water pressure under low load conditions.

[0025] Figure 5 This is a schematic diagram showing the calculated and actual values ​​of the primary water supply flow rate of the heat exchange station under low load conditions.

[0026] Figure 6 This is a schematic diagram showing the calculated and actual values ​​of the primary water supply flow rate of a heat exchange station under high load conditions.

[0027] Figure 7 This diagram illustrates the error between the calculated lag order and the actual lag order. Detailed Implementation

[0028] The present invention will be further described below with reference to embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0029] This invention conducts research on the generation of virtual operation data for heat exchange stations in planning and the expansion and control of heating pipe networks. First, it constructs a graph theory-driven heating pipe network topology-hysteresis fusion modeling method. Second, it designs a BTI-LNN model that embeds the building thermophysical time constant. Finally, it forms a global hydraulic coupling virtual data generation process with dual constraints of engineering standards and physical equations.

[0030] The overall logic of this invention is as follows: Figure 1 As shown, the process unfolds according to the logic of data acquisition, preprocessing, building and training the BTI-LNN model, and virtual data generation.

[0031] The data acquisition stage is responsible for collecting operational data of the centralized heating system, including the primary supply water temperature, primary return water temperature, primary supply water pressure, primary return water pressure, primary supply water flow rate, indoor temperature, and outdoor temperature of the existing heat exchange stations; and collecting hardware data of the centralized heating system, including heating area, building type, location of heat exchange stations, pipe diameter, and elevation. The data processing stage integrates existing system operation data and system hardware data, uses Pearson correlation coefficient to complete the hysteresis detection between heat exchange stations, and calculates the dynamic hysteresis value of each pipe section.

[0032] The core of the method for constructing the BTI-LNN model is the BTI-LNN model that embeds the building thermophysical time constant.

[0033] Input preprocessed system operation data and system hardware data, and complete model training under the dual constraints of physical equations and engineering construction standards.

[0034] At the engineering application level, the BTI-LNN model can combine the system hardware data of the newly built heat exchange station with the system operation data of the adjacent heat exchange stations to calculate the system operation data of the newly built heat exchange station.

[0035] 1. Data Acquisition and Preprocessing The heat exchange station uses a PLC as the controller, employing a PID control method to regulate the opening of the primary water supply side electric valve based on the set temperature, thereby controlling the actual heat exchanger's capacity by controlling the flow rate. Specific component selections are shown in Table 1. Table 1. Models of Sensors and Control Valves for Heat Exchange Stations

[0036] The sensors are connected to an industrial communication network consisting of a PLC, gateway, configuration display screen, and switch. A network operator provides remote networking services, enabling cross-regional data transmission and aggregation. Within the communication network, the main control platform indirectly controls the primary flow rate by issuing secondary water supply setpoints to the PLC. This method ensures the stability of the heat exchange system.

[0037] The collected data is divided into heat exchanger system operating data, including primary supply water temperature, primary return water temperature, primary supply water pressure, primary return water pressure, indoor temperature, and outdoor temperature. The sampling period is set to 10 minutes to capture the dynamic changes in system operating parameters. The collected system hardware data is shown in Table 2. Table 2. Length of each heat exchange station from the heat source pipeline

[0038] 2. Preprocess the acquired data. For the date and time items in the data, considering their periodic fluctuations, a sinusoidal encoding method is used for processing, and the time data is normalized: ; In the formula, t s For normalized time data, t This is the original time data.

[0039] For the water supply temperature in the dataset, the mean-variance normalization method is used: ; in, The original data, The sample mean. denoted as the standard deviation of the sample.

[0040] The following method is used to calculate pipeline pressure and flow rate based on the system hardware data and engineering construction standard constraints in the original data. The main components of the system are: heat source, feed water pump, feed water pipe, user-side load, and return water pipe. The working fluid circulation process is: heat source, feed water pump, feed water pipe, user heat exchanger with inlet flow regulated by control valves, return water pipe, and finally back to the heat source.

[0041] ; In the formula, The mass flow rate flowing into a heat exchanger or pipeline section per unit time, expressed in tons (t). The specific enthalpy of the working fluid reflects the energy state of a unit mass of working fluid, and its unit is J / kg. The specific enthalpy of the outflowing working fluid is expressed in J / kg. The thermal power output by the system represents the heat transferred per unit time, and the unit is J.

[0042] The pressure drop in the pipeline is approximated using the Darcy-Bach equation, and calculated based on the Darcy friction coefficient. The pipe wall roughness in the formula refers to the "Design Standard for Urban Heating Pipeline Networks CJJ / T34-2022". ; ; In the formula, For the pipeline inlet pressure, This refers to the outlet pressure of the pipeline, in Pa. The specific volume of the inlet working fluid reflects the volume per unit mass of working fluid, and the unit is m³. 3 , The specific volume of the working fluid at the outlet, in cubic meters. 3 , The inner diameter of the pipe represents its geometric dimensions, expressed in meters. The length of the pipeline represents the distance over which the friction resistance is applied, expressed in meters. Darcy's coefficient of friction (dimensionless) is denoted by and Reynolds number. Re Absolute roughness of pipe wall ks Pipe diameter D The function reflects the friction resistance characteristics of the pipeline. The dynamic viscosity of the inlet working fluid. The dynamic viscosity of the working fluid at the outlet is expressed in Pa. s.

[0043] For the water distribution problem involved in the simulation, the pressure drop is calculated using the formula for the Hassen-Williams equation: ; In the formula, This is the acceleration due to gravity. i The value is determined based on the quality of the incoming flow.

[0044] ; Based on the location of the new heat exchange station, calculate the distance between the new heat exchange station and other heat exchange stations, and select the existing heat exchange station with the smallest straight-line distance as the adjacent reference heat exchange station; determine the actual laying length of the primary water supply pipeline between the new heat exchange station and the adjacent reference heat exchange station. L Based on pipe diameter D The economic flow velocity of hot water in a pipe of this diameter is determined based on engineering construction standards. v ; and calculate the heat transfer lag time from the adjacent reference heat exchange station to the new heat exchange station for a single water supply. The calculation formula is as follows: ; In the formula, L The actual length of the primary water supply pipeline is expressed in meters. v The economic flow velocity of hot water in the pipe is expressed in m / s. This refers to the heat transfer lag time, measured in seconds (s). Converted to system sampling period Lag order in units The calculation formula is as follows: ; In the formula, The sampling period for system operation data, in seconds; This is the rounding function; This represents the lag order of the primary water supply temperature of the new heat exchange station relative to the adjacent reference heat exchange station.

[0045] For the processed runtime sequence data, the Pearson correlation coefficient is used to determine the lag order: ; In the formula, r(k) For lag k The Pearson correlation coefficient of order, Cov( X k , Y k ) is a sequence and The covariance. For sequence and The product of the sample standard deviations.

[0046] Based on the system hardware data, the maximum flow rate of the pipeline is calculated using the following method.

[0047] Given a directed graph Each of its edges has a capacity. This capacity represents the maximum capacity that this edge can pass through, for any edge. From arrive In the direction, there are at most A flow of units can pass through this directed graph. The source point indicates the first station on the heat source side. The sink point represents a heat exchange station.

[0048] For a single heat exchanger, based on the topological characteristics of the tree graph and the basic constraints of the flow network, there is one and only one simple path between any two nodes, and the maximum edge capacity is equal to the minimum edge capacity of the unique path from the source to the sink.

[0049] ; In the formula, The maximum edge capacity, in units of . , among them s Indicates the heat source. v 1, v 2…… v k This indicates each heat exchange station. This represents the set of maximum flow rates for each edge. In practical applications, it is selected based on the actual flow rate of the pipeline and the corresponding requirements in the "CJJ / T34-2022 Urban Heating Pipeline Design Standard".

[0050] Based on the law of conservation of mass, for any node in a pipeline network, the total flow rate into the node per unit time is... It equals the total flow rate at the outflow node, where the outflow node includes the flow rate passing through the heat exchanger and entering the return water system. and the flow into the next node The unit is ; ; For the flow rate at any edge of the pipe network, i.e., the flow rate of the pipe... The inflow per unit time is the sum of the downstream flows; ; In the formula, and These are the codes for the starting heat exchange station and the ending heat exchange station, respectively.

[0051] In scenarios involving dynamic load changes in the heating system or the addition of new heat exchange stations, a global redistribution of primary water supply flow is required. The core premise is that the output flow from the heat source must balance with the total demand flow at each collection point, while also meeting pipeline capacity constraints. Flow redistribution follows the optimization principle of reducing peak flows and filling heat gaps: for nodes where the actual flow exceeds the heat load demand, their transmission flow is reduced first; for nodes where the actual primary water supply flow is lower than the heat load demand, the demand gap is filled by adjusting the flow allocation of upstream shared pipelines. During the redistribution process, the maximum capacity constraints of the paths must be simultaneously verified to ensure that the flow in all pipelines does not exceed their design capacity, maintaining global hydraulic balance.

[0052] 3. Construct a prediction model The BTI-LNN model constructed in this invention includes a forward process physical information fusion module, a liquid neural network module, and a hybrid time constant regularization module. First, the primary water supply temperature is input into the forward process physical information fusion module of the BTI-LNN model. This module extracts the RC model of the heat exchange station from the features of data changes and calculates the physical constraint time constant based on the RC model. At the same time, the primary water supply temperature is input into the liquid neural network module, which calculates the data fitting time constant. Second, the data fitting time constant and the physical constraint time constant are input into the hybrid time constant regularization module. After regularization, the comprehensive time constant is output to control the response smoothness.

[0053] The liquid neural network module structure is shown in Figure 2. Its core advantages lie in its inherent continuous-time dynamics, strong robustness, and parameter efficiency. Unlike traditional static neural networks where weights are fixed after training, the connection weights of the liquid neural network module are not constant values ​​but evolve dynamically over time, determined by both the current input signal and the network's hidden state. This characteristic gives it typical dynamic system properties, enabling a smooth and continuous response to the input time-series signal. The smoothness of the liquid neural network module's response to the input signal is controlled by the network's built-in time constant. This parameter directly determines the network's memory of historical input signals and is the core hyperparameter for regulating its dynamic response characteristics. Compared to traditional discrete-time neural networks, it is more suitable for time-series prediction tasks of continuous dynamic processes in heating systems. The general continuous dynamic equation for the neuron state of the liquid neural network module can be expressed as: ; in, For the network at all times t The hidden state vector. For a moment t The input signal vector, These are all the learnable parameters of the network.

[0054] A liquid neural network module is a time-continuous recurrent neural network that processes data sequentially, retains memory of past inputs, adjusts its behavior based on new inputs, and can handle variable-length inputs to enhance the neural network's task understanding. This allows it to process time-series data more efficiently than traditional neural networks. A continuous-time neural network has the following characteristics: ; In the formula, This represents the dynamic weight matrix between hidden layer neurons. To control the rate of state change, a synthesis time constant is introduced, with a fixed weight matrix from the input layer to the hidden layer. This parameter combines the combined effects of the data fitting time constant and the physical constraint time constant. It is a non-linear activation function. b This is a bias term.

[0055] In centralized heating systems, different heat exchange stations are affected by factors such as equipment parameters, operating conditions, building envelope characteristics, and outdoor environment, resulting in significant individual heterogeneity in heat transfer lag and building thermal inertia. The time constant in traditional liquid neural network modules is a purely data-driven free parameter without clear physical meaning, belonging to black-box adaptive optimization. It cannot effectively correlate with the physical characteristics of the heating system, easily leading to insufficient model generalization ability and poor physical interpretability. To address these limitations, this invention proposes a liquid neural network module embedding building thermodynamic features. The core of this module is to embed the physical constraint time constant of the building into the network's time constant calculation, transforming the originally meaningless black-box parameter into a thermal inertia mapping with clear physical meaning, achieving a deep integration of data-driven and physical prior knowledge.

[0056] In the BTI-LNN model, the overall time constant is... Instead of freely optimized parameters, they are physical constraint time constants calculated by the building thermophysical model. Fitting the time constant of the data mined from the running data The expression obtained through weighted fusion is: ; Wherein, the regularization factor takes a range of values. The optimal value is determined by a grid search method. The physical constraint time constant is calculated based on the analytical properties of the building's thermophysical characteristics and is determined by the inherent properties of the building served by the heat exchange station. To fit the time constant of data extracted in real time from system operation data, it can adapt to the changes in hysteresis characteristics caused by fluctuations in operating conditions.

[0057] Among them, the physical constraint time constant of the building Based on the derivation and calculation of the first-order linear thermal inertia RC model of a building, this model can accurately describe the dynamic change law of indoor temperature in a building. Its thermal balance differential equation is: ; In the formula, The heat capacity of a building, kJ / K. ν represents the rate of change of room temperature, in K / h. , and These represent the primary water supply temperature, indoor temperature, and outdoor temperature, respectively, in degrees Celsius (°C). and These represent the thermal resistances of the water supply pipes dissipating heat into the room and the heat resistances of the room dissipating heat to the outside, respectively, in K / W. Setting the input heat to zero, we solve the above equation. Based on this, we solve the differential equation to obtain the temperature exponential decay model, expressed as: ; Physical constraint time constant Represented as: ; In the formula, The initial temperature of the building is expressed in °C. The duration of the building's free thermal decay process. The physical constraint time constant of the building. It is a core parameter describing the thermal inertia of a building, reflecting the building envelope's ability to resist temperature changes. Its physical definition is based on the lumped parameter method, i.e., the building RC model, and is expressed as: ; It is the data fitting time constant, and its update method is shown below.

[0058] ; In the formula, and These represent the minimum and maximum boundaries of the hysteresis, determined by the hydraulic characteristics of the heating network and the distribution characteristics of the heat exchange stations. This is the Sigmoid activation function, used to map the output to the [0,1] interval. and These are the weight matrix and bias vector of the hysteresis update network, respectively; It is the concatenated vector of the input signal and the hidden state.

[0059] After embedding the physical information of the time constant, the BTI-LNN model retains the dynamic weight evolution mechanism of the liquid neural network module, and the dynamic weight matrix... By regulating network G Real-time generation, its equation is: ; Adjusting the network G It is typically implemented using a simple neural network, with the input including the current hidden state. Input signal and learnable parameters .

[0060] The static weights of traditional neural networks cannot adapt to dynamic inputs. Liquid neural network modules, through... make Adjust network parameters in real time according to the input signal. Training via gradient descent, The evolution aligns with task requirements. To prevent excessive oscillations in dynamic weights, a trainable gating vector is introduced. Control weight adjustment range ; In the formula, is a trainable gated vector. ⊙ represents the Hadamard product. To adjust the initial weights of the network, This is the updated weight.

[0061] The core of model training is minimizing the loss function. L To obtain the minimum loss Loss The loss is due at the end of the time window. T e Predicted output y p Compared with the true value y true The error is determined by: ; The forward propagation process of the model involves the numerical solution of ordinary differential equations, and the loss function during training... Loss For parameters θ The gradient cannot be directly calculated using the traditional backpropagation algorithm; therefore, the adjoint method is used to achieve efficient gradient calculation. From the end point of time... T e Begin reverse calculation, with the initial value of the accompanying state. For loss Loss For the final hidden state gradient: ; In the formula, The terminal condition, representing the model's predicted output at the final time step, is derived from the mapping relationship between the loss function and the readout layer. This adjoint state satisfies the following inverse differential equation: ; In the formula, Accompanying state rate of change over time Accompanying state The transpose of . Nonlinear mapping function f Consistent with the neuron dynamics equations: ; The adjoint method uses inverse integration for solution, and its core terminal boundary condition is the end point of the prediction time window. T e The associated state value at point is given. The final gradient can be expressed as: ; In the formula, This represents all trainable network parameters.

[0062] 4. Training process The hyperparameter combination was optimized using a grid search method. The types of hyperparameters and their optimal value ranges are shown in Table 3.

[0063] Table 3 Hyperparameter Settings

[0064] 5. Output prediction results Primary supply and return water pressures are core operating parameters of heat exchange stations. Their steady-state characteristics are strongly coupled with heat load, primary supply water flow rate, and the hydraulic characteristics of the pipe network, determining the efficiency of heat transfer and the stability of end-point heat dissipation. Under steady-state operating conditions, the primary supply water pressure of the heat exchange station is based on the rated design pressure. Significant differences exist in the steady-state pressure levels of different stations, determined by the hydraulic resistance characteristics of the pipe network, such as pipe length, pipe diameter, and pipe wall roughness. Stations with higher network resistance coefficients typically have higher baseline primary supply water pressures to ensure effective heat transfer overcoming resistance. Due to the incompressibility of water, the primary supply and return water pressures of the heat exchange station do not exhibit lag; the operating conditions of the main circulation pump on the heat source side can be reflected in real-time at the end of the pipe network.

[0065] The most significant factor affecting pipeline pressure is altitude. Theoretically, a water depth of 10 meters can generate 1 bar of pressure. Based on the engineering model of the pipeline heating system and actual field operation data, the relationship between pressure, pipe diameter, and elevation is as follows: Figure 3 and Figure 4 As shown.

[0066] from Figure 3 and Figure 4It can be seen that the fitting relationship between the pressure difference of the heat exchange station and the altitude difference and pipeline distance difference under both high and low load conditions shows a very strong positive linear correlation between the pressure difference and the altitude difference, regardless of whether the load is low or high. The corresponding fitting determination coefficient is high. Both values ​​are close to 0.93, and the difference in fitting strength between the two load conditions is extremely small, indicating that load changes have no significant impact on the linear correlation between "altitude difference and pressure difference"; while the pressure difference and pipeline distance difference also show a positive linear correlation, the coefficient of determination is much smaller. The correlation coefficient (0.73) is significantly lower than the fitting level for altitude difference, and the data points are more dispersed relative to the fitted line, indicating that the fitting ability of pipeline distance difference for pressure difference is weaker than that for altitude difference. Therefore, in a primary water supply system, altitude difference is the dominant factor affecting pressure difference.

[0067] The quantitative characteristics of the fitting results show that the prediction of primary supply and return water pressures using linear fitting relationships is truly effective. Under both high and low load conditions, the linear trends and fitting strengths of the two types of fitting relationships did not fluctuate significantly, indicating that the linear relationship between altitude and distance differences and pressure differences is an inherent characteristic of the system, conforming to physical constraints, and not a random correlation under specific operating conditions. Predicting pressure differences corresponding to different altitude and pipeline distance differences using linear fitting relationships and physical constraints can well reflect the pressure change patterns of actual water supply systems. It can provide reliable prediction basis in engineering scenarios such as system pressure regulation and parameter preset, and its fitting results have real application effectiveness.

[0068] Figure 5 This chart presents a multi-site time-series comparison of primary water supply flow rates at 16 heating stations under low-load conditions, spanning a 24-hour timescale. The variables include simulated flow curves corresponding to three indoor temperature settings: 26℃, 22℃, and 18℃, represented by solid red, dashed green, and solid blue lines, respectively. The solid green line represents the actual operating primary water supply flow rate, with each sub-chart corresponding to a different heating station. Theoretically, within the same station, higher indoor temperature settings generally correspond to higher primary water supply flow rates, a characteristic consistent with the driving mechanism of building heat load. The time-series fluctuation characteristics of primary water supply flow rates at different stations exhibit significant heterogeneity. Some stations show relatively small fluctuations in primary water supply flow rates within the daily cycle, indicating relatively stable heating control modes; however, some stations exhibit hydraulic imbalances, with primary water supply flow parameters showing drastic short-term fluctuations. This phenomenon is typically related to factors such as dynamic changes in heat load within the station's coverage area and the response characteristics of real-time control strategies. This feature can serve as a validation basis for the correlation model between room temperature and primary water supply flow rate. The quantitative analysis of its matching degree can provide empirical data support for the coordinated optimization of thermal comfort requirements and energy consumption levels of heating systems.

[0069] like Figure 6 As shown, high heating load conditions correspond to scenarios with low outdoor temperatures and large temperature differences between indoor and outdoor environments. Under these conditions, building heat demand is in a high range, and the predicted primary water supply flow curve can fit the dynamic characteristics of the actual primary water supply flow well. Compared to Figure 5 Under low-load conditions, the fluctuation of primary water supply flow rate at the SSCY and JXYS heat exchange stations was significantly reduced. This is because, under constant primary water supply pressure, the flow control valves configured at the heat exchange stations have a specific flow regulation range, with the lower limit of this range greater than 0. When the actual flow demand is within the range of 0 to the lower limit of the regulation range, constrained by the controller logic, the flow control valve frequently switches between fully closed and minimum open states, achieving flow control through duty cycle adjustment. This process is reflected in significant numerical oscillations in the sampled primary water supply flow rate data. Under high heating load conditions, the actual primary water supply flow demand increases significantly and falls within the effective regulation range of the flow control valve. At this time, the valve can achieve continuous and stable flow regulation, thus greatly reducing flow fluctuation. The THJ12 heat exchange station serves an area of ​​180,000 square meters, with a population density significantly higher than the average level of conventional residential communities. Furthermore, the heat exchange station is relatively new, and the supporting building envelope has excellent thermal insulation performance. These factors collectively contribute to its high thermal energy utilization efficiency. Analysis results based on the measured dataset show that, in actual operation, the heat exchange station only needs to maintain about 70% of the theoretically calculated flow rate to meet the regional design heating standards.

[0070] This part of the work can establish a linear relationship between primary water supply temperature, primary water supply flow rate, and primary return water temperature, providing support for the generation of heat exchange station data.

[0071] Table 4 shows the error values ​​between the actual primary water supply flow rate and the theoretical optimal primary water supply flow rate at a room temperature of 22℃.

[0072] Table 4 is... Figure 5 and Figure 6 Although the calculated primary water supply flow rate differs from the actual primary water supply flow rate from the quantitative error table, except for a few special heat exchange stations, the actual operating load of other heat exchange stations is above the minimum load of the heating standard. The heating network has the flow margin requirement to connect to the new heat exchange station.

[0073] The lag correlation of time-series data from upstream and downstream stations was analyzed using Pearson correlation coefficients. The specific operational procedure is as follows: First, time-series data of upstream and downstream heat exchange stations in the target pipe segment of the heating network were collected, ensuring that the time granularity of all data remained consistent. Then, for each pair of upstream and downstream stations, the Pearson correlation coefficient under different lag values ​​was calculated. By performing Pearson correlation coefficient analysis on the time-series data of each heat exchanger, the quantitative characteristics of the lag values ​​were obtained. In this dataset, due to the lack of an effective group control strategy, the regulation of each heat exchange station was too conservative, and the flow difference of the entire network under high and low load conditions was small, which did not reflect changes in the lag order. Based on the lag value patterns of the dataset, a mathematical model of lag correlation was constructed and applied to feature analysis. Based on the existing pipe length, flow rate, and pipe diameter data, the lag order can be verified by inversion.

[0074] The lag order can be calculated based on the flow rate, pipe diameter, and pipe length in each pipeline, such as... Figure 7 As shown in the diagram, the horizontal axis marks the start and end points of each pipe section in the heating network, corresponding to specific pipe sections in the heating network physical structure described earlier. The left vertical axis represents the lag order, with the blue bars representing the lag order derived based on pipe length, diameter, and flow rate, and the orange bars representing the actual lag order presented in the dataset. The right vertical axis displays the percentage of absolute error between the calculated and actual values, reflecting the accuracy of the inversion method. In terms of trend matching, the calculated and actual lag orders show a high degree of consistency, verifying that the heating network physical structure determines the lag effect. Regarding error distribution, the absolute error percentage for most pipe sections is below 20%, with only a few sections showing slightly higher deviations due to flow rate fluctuations during actual operation; the overall error remains within a controllable range. The method of inverting the lag order using physical parameters demonstrates high reliability.

[0075] Urban centralized heating networks are characterized by large-scale spatial distribution, resulting in significant time lag effects in their thermal response. The hydraulic transport delay of hot water from the heat source to the end of the network can be as long as 3 hours. During the transport of hot water along the network, the primary water supply temperature is affected by multiple nonlinear factors, such as pipe wall thermal inertia and friction loss, leading to complex dynamic changes that are difficult to predict accurately. For units exhibiting differentiated lag characteristics in existing operational data, the BTI-LNN model is used to predict the real-time dynamic changes of the primary water supply temperature. This model can provide highly reliable trends in the evolution of the primary water supply temperature and, based on this theoretical and data foundation, provide quantitative guidance for the regulation of the primary water supply flow.

[0076] Table 5 Loss of Prediction Effect for Primary Water Supply Temperature

[0077] The comparative experimental results in Table 5 show that, under high-load conditions, the average MSE of the BTI-LNN model is 0.250, lower than that of the liquid neural network module (average 0.261), the long short-term memory neural network model (average 0.452), and the Transformer (average 2.519); the corresponding average RMSE is 0.495, lower than that of the liquid neural network module (average 0.508), the long short-term memory neural network model (average 0.672), and the Transformer (average 1.525); the average MAE is 0.341, lower than that of the liquid neural network module (average 0.359), the long short-term memory neural network model (average 0.468), and the Transformer (average 1.244). This indicates that the BTI-LNN model has better fitting accuracy and stability under high-load, nonlinear, and drastic fluctuation scenarios.

[0078] Under low load conditions, the average MSE of the BTI-LNN model is 0.207, lower than that of the Liquid Neural Network module (average 0.299), the Long Short-Term Memory Neural Network model (average 0.416), and the Transformer (average 1.570); the average RMSE is 0.452, lower than that of the Liquid Neural Network module (average 0.543), the Long Short-Term Memory Neural Network model (average 0.635), and the Transformer (average 1.233); the average MAE is 0.357, lower than that of the Liquid Neural Network module (average 0.430), the Long Short-Term Memory Neural Network model (average 0.502), and the Transformer (average 0.991). This indicates that the BTI-LNN model can maintain high-precision fitting even under low-load, stable, and gradually changing scenarios.

[0079] Compared to long short-term memory neural network models and Transformer, BTI-LNN achieves more stable and accurate virtual data generation under all operating conditions, including high and low loads, providing a more reliable theoretical and engineering solution to the data scarcity problem in the planning stage of heating systems.

[0080] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0081] While the specific embodiments of the present invention have been described above, they are not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for generating virtual operation data of a planned heat exchange station, characterized in that, The process includes the following: S1 collects operational data and system hardware data of existing heat exchange station centralized heating systems; S2, based on the primary water supply temperature and system hardware data in the system operation data, use the Pearson correlation coefficient method to calculate the different hysteresis orders between each heat exchange station in the heat exchange station network; S3. Construct a BTI-LNN prediction model. The primary water supply temperature data of a heat exchange station in the existing system operation data is preprocessed and used as the input value. The primary water supply temperature data of the heat exchange station under different lag orders is used as the prediction value. The model adopts a unified framework that integrates physical information and liquid neural network (LNN) to train the BTI-LNN model and obtain BTI-LNN models with different lag orders. S4. Based on the pipe diameter and heat exchange station location in the hardware data of the new heat exchange station system, calculate the lag order between the new heat exchange station and the primary water supply temperature of the nearest adjacent heat exchange station. S5. Based on the lag order, select the BTI-LNN model with the corresponding lag order, input the primary water supply temperature of the adjacent heat exchange station into the BTI-LNN model, and obtain the virtual operating data of the primary water supply temperature of the new heat exchange station. S6 calculates virtual operating data for primary return water temperature, primary water flow rate, primary water supply pressure, and primary return water pressure based on virtual operating data of primary water supply temperature.

2. The method for generating virtual operation data of a heat exchange station in planning as described in claim 1, characterized in that: The system operation data includes primary water supply temperature, primary return water temperature, primary water supply pressure, primary return water pressure, primary water supply flow rate, indoor temperature, and outdoor temperature; the system hardware data includes heating area, building type, heat exchange station location, pipe diameter, and elevation.

3. The method for generating virtual operation data of a heat exchange station in planning as described in claim 1, characterized in that: The specific process of S2 is as follows: Select the primary water supply temperature sequence of any two heat exchange stations and Calculate the sequence and The Pearson correlation coefficient; in turn, makes the sequence and This generates a phase difference of 1, 2... up to 30 sampling periods, corresponding to... k =1, 2, 3...30; calculate and record the Pearson correlation coefficient for each corresponding phase difference; The phase difference of the sampling period corresponding to the maximum value of the Pearson correlation coefficient is selected as the lag order. k ; Calculate the Pearson correlation coefficient for the primary water supply temperature series: ； In the formula, r(k) For lag k The Pearson correlation coefficient of order, Cov( X k , Y k ) is a sequence and covariance; For sequence and The product of the sample standard deviations.

4. The method for generating virtual operation data of a heat exchange station in planning as described in claim 1, characterized in that: For the primary water supply temperature in the system operation data, the mean-variance normalization method is used: ； in, The original data, The sample mean. The standard deviation of the sample. This is the data after normalization.

5. The method for generating virtual operation data of a heat exchange station in planning as described in claim 1, characterized in that: The BTI-LNN model includes a forward process physical information fusion module, a liquid neural network module, and a hybrid time constant regularization module. First, the primary water supply temperature is input into the forward process physical information fusion module of the BTI-LNN model. This module extracts the RC model of the heat exchange station from the features of data changes and calculates the physical constraint time constant based on the RC model. At the same time, the primary water supply temperature is input into the liquid neural network module, which calculates the data fitting time constant. Second, the data fitting time constant and the physical constraint time constant are input into the hybrid time constant regularization module. After regularization, the comprehensive time constant is output to control the smoothness of the response.

6. The method for generating virtual operation data of a heat exchange station in planning as described in claim 5, characterized in that: The forward process physical information fusion module improves upon the unique liquid time constant in the LNN model by fusing data based on the characteristics of the RC model presented in the building data. It inputs the primary water supply temperature data of the heat exchange station, and based on the attenuation trend of the water supply temperature, establishes a thermal balance differential equation based on the building's first-order linear thermal inertia RC model. It then calculates and outputs the physical constraint time constant, which characterizes the building's thermal inertia. Represented as: ； and These are the indoor and outdoor temperatures, respectively, in degrees Celsius (°C). The initial temperature of the building, in °C; This refers to the duration of the building's free heat decay process; Physical constraint time constant It is a core parameter describing the thermal inertia of a building.

7. The method for generating virtual operation data of a heat exchange station in planning as described in claim 5, characterized in that: In the liquid neural network module, the data fitting time constant is updated in the following way: ； In the formula, It is the lag quantity that is displayed in real time in the data, and is called the data fitting time constant; and These represent the minimum and maximum boundaries of the hysteresis, determined by the hydraulic characteristics of the heating network and the distribution characteristics of the heat exchange stations. This is the Sigmoid activation function, used to map the output to the [0,1] interval; and These are the weight matrix and bias vector of the network that update the hysteresis, respectively; x and h These are the input signal and the hidden state, respectively. It is the concatenated vector of the input signal and the hidden state.

8. The method for generating virtual operation data of a heat exchange station in planning as described in claim 5, characterized in that: The hybrid time constant regularization module is specifically as follows: The combined time constant consists of the data fitting time constant, the physical constraint time constant, and the regularization factor. The inherent thermal inertia time constant calculated from the building thermophysical model. Dynamic lags mined from operational data It is obtained through weighted fusion; the expression is: ； Wherein, the regularization factor takes a range of values. The optimal value is determined by a grid search method.

9. The method for generating virtual operation data of a heat exchange station in planning as described in claim 1, characterized in that: The specific process of S4 is as follows: Based on the location of the new heat exchange station, calculate the distance between the new heat exchange station and other heat exchange stations, and select the existing heat exchange station with the smallest straight-line distance as the adjacent benchmark heat exchange station; determine the actual laying length L of the primary water supply pipeline between the new heat exchange station and the adjacent benchmark heat exchange station; based on the pipe diameter D and engineering construction standards, determine the economic flow velocity v of hot water in the pipe of this diameter; and calculate the heat transfer lag time of the primary water supply from the adjacent benchmark heat exchange station to the new heat exchange station. The calculation formula is as follows: ； In the formula, L is the actual length of the primary water supply pipeline, in meters; v is the economic flow velocity of hot water in the pipeline, in meters per second. This is the heat transfer lag time, measured in seconds (s). Heat transfer hysteresis Converted to system sampling period Lag order in units The calculation formula is as follows: ； In the formula, The sampling period for system operation data, in seconds; This is the rounding function; This represents the lag order of the primary water supply temperature of the new heat exchange station relative to the adjacent reference heat exchange station.

10. The method for generating virtual operation data of a heat exchange station in planning as described in claim 1, characterized in that: In step S6, the primary return water temperature and primary supply water flow rate are calculated as follows: Based on the heat balance principle of the primary and secondary sides in a heat exchange station, and considering the heating area, building type, indoor temperature, and outdoor temperature of the building under the management of the heat exchange unit, the correlation between the primary side supply and return water temperature difference and the secondary side heat load is established: ； In the formula, The primary return water temperature is determined with reference to engineering construction standards. This is a virtual value of the water supply temperature at time t, in °C. Let t be the building heat load at time t, in kW, calculated from the heating area, building type and outdoor temperature; c is the specific heat capacity of water at constant pressure, taken as 4.2 kJ / (kg·℃); G s Let t be the single water supply flow rate at time t, in kg / s; The rated heat exchange efficiency of the heat exchange unit is determined according to the technical manual of the plate heat exchanger in the heat exchange station. The calculation methods for primary water supply pressure and primary return water pressure are as follows: ； ； In the formula, This refers to either the primary water supply pressure or the primary return water pressure. This refers to the primary supply or return water pressure at adjacent heat exchange stations along the pipeline, expressed in Pa. The specific volume of the inlet working fluid reflects the volume per unit mass of working fluid, and the unit is m³. 3 , The specific volume of the working fluid at the outlet, in cubic meters. 3 , The inner diameter of the pipe represents its geometric dimensions, expressed in meters. The length of the pipeline represents the distance over which the friction resistance is applied, expressed in meters. Darcy friction coefficient is a function of Reynolds number Re, absolute roughness of pipe wall ks, and pipe diameter D, reflecting the friction resistance characteristics of the pipeline. The dynamic viscosity of the inlet working fluid. The dynamic viscosity of the working fluid at the outlet is expressed in Pa. s.

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